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=pn0+pno(exp(U,/U,)
- 1 ) exp(-X/Lp)
(4.3.18)
For the diffusion flow density of holes
Ip = - q o dP pdx we need the first differentiation. If we substitute this, we find that
(4.3.19)
Crystalline Silicon Solar Cells
64
Similarly, for the electron current density we find that qDn ' n o In = -(exp(UA/UT)- 1 ) exp(-x/Ln) Ln
(4.3.21)
We have determined this current density at the limits of the space charge region. To find the total current density we must determine the current at the point x = 0. We assume for this purpose that within the space charge region the injected currents are constant at the first approximation, and there is no change in the current. We can then equate the current densities at the edges of the space charge region to the current density at the point x = 0 and thus find the total current density as the sum of the two. 'total
= p'
+In
(4.3.22)
and thus
This equation is known as the diode equation, and the first expression in parentheses is the saturation current density I,. If we now introduce for P n o and n p o p,, =ni'lND
resp.
npo = n i2 INA
(4.3.24)
we find that for I, (4.3.25)
The current density at a p-n junction - in a diode - is thus found to be
I = I , (expUA/UT - 1 )
(4.3.26)
The p-n Junction References [l]
Schottky W., Zeitschriyt fur Physik 118, 1942, p. 23
[2]
Shockley W., Bell Syst. Techn. 28, 1949, p. 435
65
5 The Physics of Solar Cells
5.1
THE ILLUMINATED INFINITE p-n JUNCTION
For a simple theoretical treatment, we once again consider a crystal with a p-n junction, in which the two doped regions are infinitely extended. (In practice a crystal thickness which is very large compared to the diffusion length of the charge carrier is sufficient). We once again start from Figure 4.1. We now illuminate the entire crystal equally, in such a way that there is a homogeneous generation of charge carrier pairs in the crystal. This can be achieved in practice if the silicon crystal is exposed to infrared light near to the band edge. Then the absorption coefficient of the light is very small, or in other words the absorption is weak and thus almost equal throughout the crystal. Using the continuity equation under these assumptions, we find a similar differential equation to (4.3.12). However, in this case we must also take generation into account. For holes as the minority carriers on the n-side, it holds that (5.1.1)
and also (5.1.2)
68
Crystalline Silicon Solar Cells
Since generation is assumed to be constant and L, is also a constant, a similar solution applies here as for (4.3.12), i.e. A p = G T +~ A exp(x/Lp) + B exp(-xILp)
(5.1.3)
With the boundary conditions of an infinite p-n junction we find that for the hole current density
Zp
= -(exp(U/U,)Dp P n o
1 ) exp( - x/Lp) -qGLpexp( -xILp)
(5.1.4)
LP
and similarly for the electron current density in the p region
I,
= -(exp(U/U,) q’n npo
- l)exp( - x/L,) -qGLnexp( -xILn)
(5.1.5)
Ln If we again disregard recombination in the space charge region and add the two above current densities (at the point where x = 0) to the current density from the space charge region, where
IR = q G W
(5.1.6)
then the current density in the solar cell is
I =Z,(exp[U/U,]
-
1) -qG(Ln +Lp + W )
(5.1.7)
If we designate q x G x (Ln+Lp+W) with ZL (the current density generated by the light), we find that
I =Zo(exp[U/U,] -I)-IL
(5.1.8)
We note that only those charge carriers generated either in the space charge region or at a distance of one diffusion length from the p-n junction contribute to current. Only this region of a solar cell is ‘active’. The corresponding charge carrier distribution is shown in Figure 5.1 and the current-voltage characteristic is shown in Figure 5.2.
69
The Physics ofsolar Cells
A
*I Figure 5.1
5.1.1
xr
X
Charge carrier distribution in an illuminated infinite solar cell
The Current-Voltage Characteristic of an Infinite Solar Cell
We see that the I-V characteristic of an illuminated solar cell lies in the fourth quadrant (electro-technical standardisation). For the purpose of comparison with this I-V characteristic, the current-voltage characteristic of an unilluminated solar cell is also drawn in Figure 5.2. The voltages are the same in both cases, whereas the current in the illuminated solar cell is negative, i.e. the solar current flows against the conventional direction of a forward biased diode. We now describe the most important parameters of a solar cell. 5. I.1.I
Short Circuit Current
As its name suggests, this current is obtained if the solar cell is short circuited, i.e. there is no voltage at the cell. This current is designated Z,, (from short circuit current). From equation (5.1.8) we find that ZBc=-ZL, i.e. the short circuit current is equal to the absolute light-current amount. We note here that the
Crystalline Silicon Solar Cells
70
Figure 5.2
Voltage-current characteristic of an infinite solar cell
magnitude of the current, disregarding all losses in the cell, with AM1.5 radiation, can reach a peak of 44 mA/cmZ. 5. I . I .2
Open Circuit Voltage
The open circuit voltage V , is obtained when no current is drawn from the solar cell. From (5.1.8) this is found to be V,, = U, In (1,/Io + 1 )
(5.1.9)
Since even at very low current densities we can disregard the value 1 compared with ZL/Ioand IL= I,, , we find that for V,, Voc
= UT In ( L110)
(5.1.10)
i.e. the open circuit voltage is proportional to the logarithm of the ratio of short circuit current to dark current. Since in good solar cells the short circuit current very quickly nears a saturation value, the increase in the
71
The Physics of Solar Cells
open circuit voltage and thus efficiency is basically a question of reducing the saturation current. From equation (4.3.25), following (5.2.13) we find that for small dark current values the following three conditions must be fulfilled: diffusion length of minority charge carriers as high as possible, doping concentration NA,No high, and crystal volume as low as possible (thin wafer). The first two parameters are linked to each other to some degree. Considerations about optimal parameter combinations are dealt with in Chapter 6. 5.1.1.3
Fill Factor
As always in electrical engineering, optimal power output requires a suitable load resistor I?,, which corresponds to the ratio V,/I, (Figure 5.2). V, and I, are, by definition, the voltage and current at the optimal operating point and P , is the maximum achievable power output. We now form the ratio of peak output (V, I,) to the variable (VocIsc) and call this ratio the fill factor FF of a solar cell:
FF = V , I , I VocIsc
(5.1.1 1)
The fill factor is so named because when graphically represented it indicates how much area underneath the I-V characteristic is filled by the rectangle V , I, in relation to the rectangle VocIsc. The fill factor normally lies in the range 0.75 to 0.85. 5.1.1.4
Efficiency
The efficiency of a solar cell is defined as the ratio of the photovoltaically generated electric output of the cell to the luminous power falling on it: (5.1.12)
The current record for efficiency is held by a solar cell made of monocrystalline silicon using very complex technology at approximately 23-24% (area 2x2 cm', radiation AM1 3.Commercially produced cells currently have an efficiency of between 14% and 16%. In individual special cases large area cells (and modules) have been produced with 17%
72
Crystalline Silicon Solar Cells
-19%. The significance of high efficiency for reducing the cost of a complete solar array will be described in Chapter 6. In general, the efficiency of photovoltaic energy conversion is very limited for physical reasons. Around 24% of solar radiation has such a long wavelength that it is not absorbed. A further 33% is lost as heat, as the excess photon energy (in the short wavelength region) is converted into heat. Further losses of approximately 15-20% occur because the cell voltage only reaches around 70% of the value which corresponds to the energy gap. 5.2
REAL SOLAR CELLS
The following investigations are based upon the structure of a modem solar cell. The cross-section of such a cell is shown in Figure 5.3. The base, the starting material for a solar cell, is almost always p-doped. Emitter SC region -,a r 7
x=o
x:
J
L.1 - 7
Base
x;+w J
I4
H'
N
Figure 5.3
Cross-section of a real silicon solar cell
b
*
73
The Physics of Solar Cells
The n-doped region is called the emitter, a designation which has been adopted from transistor physics. It is more highly doped than the base by some orders of magnitude. The p-n junction is therefore unsymmetrically doped. The space charge region, with width W therefore extends mainly into the p region. The point xj marks the penetration depth of the p-n junction. In practice it amounts to only a few tenth pm, so that for a crystal thickness H of approximately 200 pm, the thickness of the base H’ is roughly equal to H. 5.2.1
Photocurrents in a Real Solar Cell
To calculate photocurrents we assume that the light enters on the emitter side. The calculation is first made for monochromatic light. In the case of the illumination by a spectrum we must integrate over all wavelength regions of this spectrum. The integration limits for this are kin, the smallest occurring wavelength, and ,,A the wavelength corresponding to the energy of the semiconductor band gap, as longer wavelengths are not absorbed. For sunlight h,, is around 0.3 pm, as at shorter wavelengths there is almost no radiation, and in the case of silicon h,, z 1.11 pm. We now need to calculate the current densities in the three regions, emitter [El,space charge region [SCR],and base [B], so that (5.2.1) and the total current density is
(5.2.2)
5.2.I . I
Photocurrent from the Base
Because in general the base is homogeneously doped, and a low level of injection is present with normal solar radiation, a precise solution can be found for the photocurrent in the base (in the short circuit case). The applicable differential equation for the electrons is thus d 2(An)
Dn-T=-G After some manipulation this yields
+R
(5.2.3)
74
Crystalline Silicon Solar Cells -dZ(An) =-
dxz
An - G
~,2
(5.2.4)
Dn
In the case of monochromatic radiation this generation of charge carrier pairs at distance x is G(x) = a F ( l - R r ) e x p ( - a x )
(5.2.5)
where a is known to be the absorption coefficient of light in the semiconductor, R , is the reflection coefficient and F is the photon flux (the radiation power) supplied to the surface of the solar cell. These three variables are all dependent upon wavelength. We thus find for equation
(5.2.3)
7
- -An = O
Dn d ’(An) + a F ( l - R , ) e x p ( - a x )
(5.2.6)
‘n
The general solution for this is An(x) =Acosh(x/L,) + Bsinh(x/L,)
a F ( l -R,)rn
(5.2.7)
a’L,2 - 1 where (5.2.8)
To determine the constants we apply the following two boundary conditions, i.e. we take into account that recombination takes place at the surface. The surface recombination velocity, measured in cm/s, is designated S,. SnAn = -Dn- d(An) at x=H (5.2.9)
dx An = O
at x qj+W
75
The Physics of Solar Cells After some manipulation we find that
+ aLn exp(X
aLn -
/
Lsinh DnLn
\
-
/
aH‘)
\
[ y,]
+cosh -
(5.2.10)
The bracketed expression is called the geometry factor (see also [l]). 5.2.1.2
Photocurrent from the Emitter
If the emitter is homogeneously doped, then the solution for the photoelectric current from the emitter is found to be the same as for the base:
sPLP + a L p -exp(-axj) X
DP
However, homogeneous doping hardly ever occurs in practice. For a diffused emitter, high dopant effects such as band gap narrowing and the
Crystalline Silicon Solar Cells
76
dead layer’ must be taken into account. The dopant profile also has the consequence that lifetime and the diffusion constant depend upon doping. This is described in further detail in Chapter 6. 5.2.1.3
Photocurrent from the Space Charge Region
This photocurrent is very easily determined, since the charge carriers generated in this region are drawn out of this area very quickly due to the electric field. They virtually cannot recombine and therefore contribute entirely to the current. This is found to be I,,,(k) = q F ( l - R f ) e x p ( - a x , ) ( 1 - e x p ( - a W ) )
(5.2.12)
Saturation Currents in a Real Solar Cell
5.2.2
To calculate the saturation current density of a real cell we must once again take into account the recombination effect at the surface. 5.2.2.1
Saturation Current from the Base
From a similar calculation to that for the photocurrent we find the following relationship: (5.2.13)
where G, is a geometry factor which reads
G, =
cosh(H’lL,)
+ (SJS,) sinh(H’lL,)
(5.2.14)
(S,/S,) cosh(H’lL,) + sinh(H’/L,)
where S, = D,/Ln, the recombination velocity in the crystal.
’ A dead layer is a highly doped region near the surface with such a short lifetime that photons absorbed in it cannot contribute to the photoelectric current.
77
The Physics of Solar Cells
The geometry factor is determined by the two variables S,/S,, and H’IL, i.e. by the ratio of inner to outer recombination and the ratio of base thickness H’ to diffusion length L . Figure 5.4 [ 2 ] shows this relationship. If the diffusion length is around half the cell thickness, then the surface recombination no longer has any effect on the dark current. The geometry factor is 1.
10’2
100
10-1 HlLn
Figure 5.4
Geometry factor as a function of the base thicknessldiffusion length relationship
If, however, the diffusion length is greater than cell thickness, then we can differentiate between three cases:
where S,, > S, then G, > 1. In this case the dark current increases, thus decreasing the efficiency of the solar cell. where S,, = S, then G, = 1. The cell behaves like an ‘infinite’ cell. where S, < S, then G, < 1. The dark current decreases with the decreasing value of S,,. The dark current decreases, circuit voltage increases and the efficiency of the solar cell is improved. This behaviour opens the potential for increasing open circuit voltage and
Crystalline Silicon Solar Cells
78
thus efficiency in thin solar cells made of silicon [3],[4]. 5.2.2.2
Saturation Current from the Emitter
The saturation current from the emitter is much more complex to determine than that from the base. Since in reality the emitter always has a doping profile, it follows that: internal fields are present, the diffusion length and the mobility of charge carriers are not constants due to their dependence upon dopant concentration, band gap narrowing takes place due to the high level of doping.
10.5
9.o 7.5 6 .O
4.5
3.0 1.5
1.0 L 1018
1019 NS
Figure 5.5
1020 Icm -31
Saturation current of an emitter as a function of surface concentration, with S, being parameter
A solution to this problem is given in the literature [ 5 ] using multiple integration. We can demonstrate the influence of surface concentration and the
The Physics of Solar Cells
79
surface recombination rate on the saturation current of the emitter by looking at Figure 5 . 5 . The n’-doped emitter has a Gaussian type dopant profile, its penetration depth is 1 pm. We find from this, that for low saturation current - and thus high open circuit voltages - two requirements must be fulfilled: a surface recombination velocity less than lo3 cm/s, and a surface concentration less than 2 ~ 1 0cm”. ’~ At high recombination rates (1 0’-l O6 cm/s) the surface concentration should be approximately lozo ~ m - Detailed ~. investigations are made in Chapter 6. 5.2.3
Ohmic Resistance in Real Solar Cells
Ohmic resistances also influence the efficiency of solar cells. We divide these resistances into shunt resistance and series resistance.
5.2.3.1
Shunt Resistance (RJ
The magnitude of this resistance is determined by leaking currents along the edges of the solar cell. Point defects in the p-n junction can also lead to low parallel resistance. Such defects can be interruptions of the p-n junction, which originate during the diffusion of the n emitter, impurity particles have hindered diffusion at certain points. The base material can also be in electrical contact with the finger system at some points, thus creating a short circuit (if only a small one).
5.2.3.2
Series Resistance (R&
This resistance has the following components: a contact resistance metal-semiconductor, ohmic resistance in the metal contacts, ohmic resistance in the semiconductor material. Further considerations follow in Chapter 6. 5.2.4
The Two Diode Model
The simple exponential relationship between voltage and current density as given by (4.3.26) is almost never observed at low voltages in the forward direction [0.1-0.5 V] in real solar cell p-n junctions. For conventional
Crystalline Silicon Solar Cells
80
diodes this is of very little significance, but for solar cells the functional dependency in this voltage range is very important. As we will discover later, the fill factor and thus efficiency are considerably influenced by this. Therefore, we want to investigate this in detail. For this purpose, we need to investigate recombination in the space charge region more closely. The SRH recombination formula (3.4.5) after some manipulation, reads (5.2.15)
We make the simplifying assumption that the following apply: The impurity level lies exactly at the intrinsic Fermi level, i.e. roughly in the mid-band region and it is distributed completely uniformly in the space charge region. At both sides of the p-n junction dopant level, lifetime and mobility are of equal magnitude. Then n , and p , are equal to n, [equations (3.4.6) and (3.4.7)]. If we first consider the case where we apply a reverse voltage, then it becomes clear that both types of charge carrier are very quickly ‘washed out’ due to the high electric field in the space charge region, so that their densities become small compared with n,. The equation (5.2.15) is then reduced to a generation rate of
- R =ni/2r,
(5.2.16)
where we also define T~,= T~,= T,. However, if a voltage is applied in the forward direction, then the recombination is slightly different. In the middle of the space charge region the concentration of n and p must be equal. Since n p = niz exp(U,/U,)
(5.2.17)
we find that n = p = n , exp(UA/2UT)
(5.2.18)
The recombination rate at the limits of the space charge region is therefore
81
The Physics of Solar Cells
R
=
n.
(5.2.19)
IexpUA/2U, 2=0
and the recombination rate decreases - without giving further explanation - (more detail in [ 6 ] ) exponentially on either side of the space charge barrier, with a characteristic length of kT
(5.2.20)
9Ema.x
where Em, is the electric field at the p-n junction. We then find that for the recombination current 2kTqni
I*
=
4 =,Emax
exp
[../ y]
(5.2.21)
Precise calculations show that a multiplication by xl2 is required, giving (5.2.22)
The factor before the exp function is designated IOz and now the diode equation can be expanded to (5.2.23)
I = I,, exp U,lU, + Io2 exp UA/2U ,
5.2.4.1
Equivalent Circuit of a R e d Solar Cell
If we also take into account the resistances in the following equation for the current-voltage characteristic line, then we find that
1[
V -IRS V -IRs I( V ) i , , exp --1 +Io2 exp --1 +- ' - I R ~
[
nlvT
n2VT
]
(5.2.24)
Rp
The corresponding equivalent circuit diagram is shown in Figure 5 . 6 . Theoretically, we should find that n , = l and n2=2. In practice, however, considerable deviations have been determined.
Crystalline Silicon Solar Cells
82
Figure 5.6
Equivalent circuit diagram for the two diode model of a real solar cell
After some manipulation [6],[7], we can expand formula (5.2.22) to the very complex equation
where y.',
0,and
mP
W
is the built-in voltage, is the potential of the quasi Fermi level, is the space charge region width.
As well as precise knowledge of the dependency of the space charge region W on the applied voltage and the applicable corrected built-in voltage [7], it is mainly the factor f(b) that is decisive for the current distribution in this starting region. The most decisive factors inf(b) are the and T,,,, but above all their ratio to one another. Choo [S] expande on the theory of Sah et a1 [9]. He found that the dependency of the valueffi) at room temperature is dependent upon the applied voltage as shown in Figure 5.7, where E,-E,, is a measure for the energetic distance of the recombination centre from the intrinsic energy level Ei and the ratio TpO/rnO is a parameter. The bend of the curve is larger, the greater is the difference between T,, and T,,. Consequently, the increase in initial current is no longer
2
83
The Physics of Solar Cells
I
0.0
Figure 5.7
0.1
OL
I
I
1
I
03
OW4
05
0'6
f(b) as a function of voltage, parameter T,,,, /
T , ~[7]
proportional to exp(V/2VT), but increases less sharply, which itself has the consequence that the diode characteristic has a negative curvature in the starting region. The typical shape of a characteristic is shown in Figure 5 . 8 . This can have consequences for efficiency, mainly if the charge carrier generation rate is low [sun < AM1.51, [10],[11]. Particularly solar cells with a p-n junction lying very close to the surface may have severe space charge defects, i.e. significantly differing values for T~~ and T~~ may occur. Such cells are therefore bound to have a curved characteristic. Other new investigations show that different conditions of surface recombination lead to similar characteristics [ 121.
5.2.4.2
The Influence of Ohmic Resistances
The influence of ohmic resistances on solar cell parameters are shown in Figure 5.9 and Figure 5.10. Figure 5.9 shows the influence of shunt or parallel resistance. With decreasing resistance the fill factor FF decreases in the first approximation and only at very small values (below 100 ncm2 ) does the open circuit voltage also decrease. Short circuit current is not influenced by parallel
Crystalline Silicon Solar Cells
84
ooo omo oooo 0 0
0
-
8 0 0
1
10-9
0.0
O
I
0.1
I
0.2
I
0.3
I
lJ Figure 5.8
I
0.4
0.5
I
0.6
PI
I
0.7
.a
The dark current characteristic of a Si solar cell
resistance. As the shunt resistance in monocrystalline cells is greater than 1000 SZcm', we barely need to consider its influence. In polycrystalline cells, on the other hand, due to internal shunt resistance at the grain boundaries we should expect the parallel resistance to have an effect. Figure 5.10 shows the influence of series resistance. Here too it is primarily the fill factor that is influenced by increasing resistance. Only at high (normally not possible) values does the short circuit current fall off. To obtain the highest efficiency possible it is imperative that series resistance is kept as low as possible (I 0.5 Clcm*).
85
The Physics of Solar Cells
-u 0.1
0.2
0.4
0.5
[Volt] 0.6
0.7
- -20 -
Figure 5.9
The influence of shunt resistance on solar cell parameters
0.0
0,3
0,s
u [Volt] 0,6
-10 N E U -15 h E -20 -5
n
-
-35
-
-40 L
Figure 5.10
The influence of series resistance on solar cell parameters
0,7
Crystalline Silicon Solar Cells
86
References Sze S. M. Physics of Semiconductor Devices, 2nd Edn, 1981, p. 802 Aberle A,, Thesis, Univ. Freiburg, 1991 Knobloch J., Von B. and Goetzberger A., Proc. of th 6th PVSEC, London, 1985, p. 285 Goetzberger A,, Knobloch J. and Von B., Proc. of the 1st PVSEC, Kobe, Japan, 1984, p. 517 Park S. S, Neugroschel A. and Lindholm F. A,, IEEE-TED 33, 1986, p 240 Sah Ch. T., Noyce R. N. and Shockley W., Proc. of the IRE 45, 1957, 1228 Chawla B. R. and Gummel H. K., ZEEE
- TED 18, 1971, p. 178
Choo S. C., Solid State Electron. 11, 1968, p. 1069 Sah Ch.T., Noyce R. N. and Shockley W., Proc. of the IRE 45, 1957, p. 1228 Baier J., Thesis, Univ. Freiburg, 1992 Beier J. and Von B., Proc. of the 23th IEEE-PVSC, Louisville, Kentucky, 1993, p. 321 Robinson S. J., Wenham S. R. et al., J. Appl. Phys. 78, 1995, p. 4746
High Efficiency Solar Cells
THE SIGNIFICANCE OF HIGH EFFICIENCY
6.1
At this point we wish to briefly explain the degree to which the total costs of a photovoltaic array can be reduced by high efficiency solar cells.
Figure 6.1
The cost breakdown of a solar array
The manufacturing costs of a solar array - power related costs such as inverters and accumulators are not considered here - made up of crystalline solar cells can be divided into four main categories. These are costs for
silicon wafers, process technology, module manufacturing, and
88
Crystalline Silicon Solar Cells
land, land preparation, electrical connections, etc. The percentage cost breakdown shown in Figure 6.1 applies approximately for large solar arrays. All costs in the first approximation are proportional to area, and thus for a solar array roughly inversely proportional to efficiency. Many writers have dealt with this subject in detail [1]-[5]. High efficiency solar cells require high grade silicon and costly technology. Cost estimates show, however, that despite the increased cell cost, an increase in efficiency of approximately 40% (relative) will reduce the cost of a large area solar array by approximately 20% [6]-[8]. Looking at the matter from another point of view, we can calculate the permissible module costs at different efficiencies for the desired cost of electricity (planning target). This relationship is shown in Figure 6.2 [9]. 150
Module efficiency 1
-
N
E
I
100
-
-tit L
8
8
-
Q)
3
I
50
0
Figure 6.2
1
Permissible module costs as a function of given electricity costs, calculated for different efficiencies [ 91
According to this, given a desired cost of 6 centskWh, an increase of efficiency from 10% to 15% makes a module three times as expensive permissible. Since the 1980s, therefore, the majority of all research and development work in the photovoltaic sector has concentrated on driving the efficiency level as high as possible.
High Eflciency Solar Cells
89
The basis for achieving high efficiency is the reduction of the total amount of loss. We investigate this area intensively in this chapter. The following considerations and calculations are based exclusively on solar cells made of crystalline silicon. Many results will however - at least partially - be applicable to other solar cell configurations. Figure 6.3 gives an overview and classification of the different mechanisms for loss. These can be divided principally into two areas.
I electrical
ohmic
1
recombination
I
- Emitter region -
Figure 6.3
Emitter Contact material Finger Collection bus Junction
-
-
SC material Surface Base region SC material Surface Space charge region
Loss mechanisms in a solar cell
Optical losses reduce the level of solar radiation by reflection and shadowing of the light as well as inadequate absorption of long wavelength radiation, whereas electrical losses have a detrimental effect on both the current and, above all, the voltage of a solar cell.
Crystalline Silicon Solar Cells
90
The final type of loss is based on semiconductor physics and technology. Minimising this is therefore at the centre of work into achieving high efficiency solar cells. We begin by investigating electrical losses, and specifically the influences related to semiconductor physics, i.e. losses by recombination, and we investigate ohmic losses in the second section. We conclude by considering optical losses and procedures for their reduction. 6.2
ELECTRICAL LOSSES
6.2.1
Recombination Losses
For this analysis we use the formulae for photocurrents and saturation currents in real solar cells, and investigate the influences of diffusion length of the charge carrier, dopant concentration and dopant profile, and surface recombination velocity. These sensitivity analyses are based on the most common solar cell structure - emitter n+- and p-doped [10’6cm”] base. The penetration depth of the emitter varies within the range 0.2-1 pm. The emitter surface concentration varies within the range 5x10” to 1x1OZo~ m ’ ~ We. have selected a crystal thickness of 200 pm, if not otherwise specified. 6.2.1.1
Recombination Losses in the Base
The photocurrent and saturation current from the base area are described by the formulae (5.2.10) and (5.2.13). In order to better demonstrate the function of the base area we assume that the emitter has no influence (ideal emitter), and there are no shadowing and reflection or unabsorbed radiation. Figure 6.4 shows short circuit current I C as a function of diffusion length L , in the base with Surface Recombination Velocity [SRV] S, on the back surface of the solar cell being a parameter. This representation yields the following results: If the diffusion length L , of the charge carrier is more than twice the crystal thickness, then the short circuit current will reach a saturation value.
91
High Efficiency Solar Cells LL
1
I
I
I
I
I
1,lO
I
-
42
-
100
LO
-
38
-
1000 104
E 36
-
-8 34
-
-
32
-
-
“E
u
105,106
\
4
I
Sn=cmls
-
For very high photocurrents the surface recombination rate S, must be less than 100 cm/s. If the diffusion length L , falls below the value of the crystal thickness, then the photocurrent will drop sharply. If, however, the diffusion length L , is less than half the crystal thickness, then the short circuit current I,,, although reduced, will be almost independent of the surface recombination velocity S, . Figure 6.5 shows the dependency of open circuit voltage V,, on diffusion length L,, again with S, being a parameter. This representation yields the following information: For high values of S,, (10’-106 cm/s) diffusion lengths higher than the crystal thickness are of no advantage, V,, achieves a saturation value. For high open circuit voltages, S, must be 660 E u 640
>O
620 600
580
0
200 Loo
600 800 loo0 1200 1400 1600 Ln [ p m l
Figure 6.5
V, of a base dominated n'p solar cell as a function of diffusion length in the base with recombination velocity at the reverse side being the parameter
The result of this calculation is that for very high efficiencies the diffusion length in the base represents a cardinal parameter. At diffusion lengths greater than the crystal thickness, the reduction of surface recombination on the back surface is decisive for the achievement of high levels of efficiency. 6.2.1.1.1 The Back Surface Field The reduction of reverse side recombination is, however, hindered by various constraints. Since the back of a normal solar cell is completely metal coated, it goes without saying that there is a high surface recombination velocity (Ohmic metal-semiconductor contacts require high recombination velocities). One familiar technical measure to improve this situation is the creation of a highly doped p'-zone on the back surface of the solar cell base. This p+-p junction (high-low-junction) is also known as a 'back surface field' (BSF). Owing to the electric field which is created, less of the minority
High Efficiency Solar Cells
93
charge camers created in the base can recombine on the back surface. The BSF functions like an electrical mirror, 'throwing back' the charge carriers into the inside of the cell. Its behaviour depends upon several parameters: the surface concentration of p+ doping as well as its concentration profile and penetration depth, recombination in the p'-layer itself, and charge carrier density at the junction, i.e. the relationship between diffusion length and crystal thickness. There is a whole range of methods for calculating this behaviour precisely. We now give the results from [lo], which were calculated with the help of the PC-ID programme Ell]. 720
I
I
I
I
I
I
I
I
I
I
I
710
700 c
>
-
690
E
>8
680 670
660
-
d
Gauss profile S, = 1xlO6 cmls I
I
I
I
I
I
1
I
I
Figure 6.6 shows the influence of the BSF layer penetration depth and surface concentration on V,, where S,, is lo6 cm/s (full metal coating). A more technologically practicable value for penetration depth of approximately 1 pm still does not yield a sufficient reduction in the effective recombination rate to achieve very high efficiency. An improvement on this structure was suggested by van Overstraaten and Nijs in 1969 [12]. Like a graded base transistor, this was based on a graduated p-doping throughout the entire base, increasing from the p-n
Crystalline Silicon Solar Cells
94
junction to the back surface. Their calculations showed that in comparison with a homogeneously doped base, it was possible to reduce the saturation current by a factor of 20. Technological realisation is however extremely costly, and to our knowledge has never occurred. Recently, other ways have been found to reduce S,. The solution is to coat a significant section of the back surface with a thermally generated SiO, film, thus electrically passivating it. For the bonding of the cell, this layer contains a number of holes of fixed distance and diameter, whose total area is only approximately 1%-4% of the total area. Metal
Si02 2
1
1
'
n+ emitter
Base
Si 02 Metal Figure 6.7
Schematic structure of a high efficiency solar cell with a local
B SF
Figure 6.7shows schematically the cross-section of this type of cell. For a good ohmic contact we also require high doping p+ under the contact point, which also functions as a local BSF. We now have an effective surface recombination rate which is composed of the recombination of charge carriers at the Si-SiO, barrier and the - small percentage contribution of the metal area. SiO, layers are of course also used for the passivation of the emitter. Therefore, we now therefore examine some of their main characteristics. 6.2.1.1.2 SiO, Layer The SiO, layer has played a decisive role in almost all silicon semiconductor devices right from the start. Its relatively simple manufacturing process by high temperature treatment under oxygen, but predominantly the masking behaviour of the SiO, toward dopants and its passivating effect, contributed decisively to making silicon the basic material for most semiconductor devices. There are countless investigations, mostly for use in IC or MOS structures. A comprehensive overview is
High Efficiency Solar Cells
95
provided by Nicollian and Brews [13]. Fundamental work on this theme has also been carried out by Goetzberger [14],[15]. The effect of the SiO, layer can be described as follows. The abrupt ending of the crystal at the surface leads to a density of defects of approximately 10’’ cm-’, which are traps in the forbidden band, thus giving rise to a high recombination rate. These traps are largely saturated by the SiO, layer and thus become ineffective. By additional annealing, e.g. in forming gas, the trap density can be reduced to values between 10’’ and 10” ern-', thus achieving surface recombination rates of 10-100 cm/s. There are currently, for solar cell production, no better alternatives to this passivating method. For further information, see Sze [16]. 6.2.1.2
Photocurrent and Saturation Current from the Emitter
We can make the following statements about the photocurrent in the emitter of a high efficiency solar cell, As the emitter is very thin, with a penetration depth of a few tenths pm, and as the surface concentration of the dopant concentration in high effrciency cells is only some 10’’ cm”, the diffusion length of the minority carriers (holes) created here is several times greater than the thickness of the emitter. They do not recombine in the emitter, either recombining at the surface or travelling to the p-n junction as photocurrent. This combined effect is enhanced at the p-n junction by the electric field, which is caused by the doping concentration gradient. This type of emitter is called transparenf. When considering the photocurrent we can therefore restrict ourselves to the influence of the surface recombination rate Spat the emitter surface.’ For an emitter with a surface concentration of 1x 10’’ cm-3- required for low saturation current, as shown in Figure 5 . 5 - and a penetration depth of x=OS pm, Figure 6.8 shows the influence of Sp on photocurrent. To ihustrate this effect we have selected the term ‘Spectral Response’ (see Chapter 9). The photocurrent is determined for radiation with light of different wavelengths. Since the short wavelength light is predominantly absorbed in the emitter, the current that is created in this region can show very clearly the influence of Sp.This shows that a value Sp of around lo3 cm/s is sufficiently low for an optimal photocurrent. The saturation current density of an emitter depends on many p armeters :
An emitter with the above penetration depth absorbs approximately 10%
of AM1.5 radiation.
Crystalline Silicon Solar Cells
96 110 100 $?
v
8
-
1
I
I
I
I
1
1
30 20 NS = 1 x1019 ~ r n - x~ ,= 0,Spm
10
0 300 Figure 6.8
the the the the
’
50
+i
-
1
90 80
h
C
1
100,1000
400 500 600 700 800 900 1000 1100 1200 Wavelength (nm)
Internal spectral response of a solar cell (emitter with a Gaussian profile, N,=10’9cmS3,xj=0.5 pm)
dopant profile, surface doping concentration, penetration depth of the emitter, and surface recombination velocity.
The calculations for this were carried out by Aberle [lo] and Ruckteschler [ 171, based upon the model of serial development of multiple integrals suggested by Park [18]. The calculation has been carried out for a Gaussian doping profile, since current diffusion technology gives high efficiency solar cells this profile (see Chapter 7). This calculation takes into account the band gap narrowing (reduction of the band gap at high doping) and the dopant dependent mobility of charge carriers. For a real solar cell we must also take into account the recombination under the metal coated finger. Figure 6.9 shows this relation~hip.~ From this representation we see that: For all values where Sp>103cm/s the dark current density is at a minimum. Figure 6.9 is identical to Figure 5.5 as we wish to explain this in more detail here.
97
High Eflciency Solar Cells
12.0 I
I
I
I I Ilrlr
I
I
I I I1111
x j =lpm
NS Figure 6.9
Saturation current of an emitter as a function of surface
concentration N , where Spis a parameter For all values where Sp>103cm/s the dark current density is at a minimum. S, values lozo cm-' and a penetration depth of 2-3 pm. The SiO, passivation has a thickness of approximately 100 nm to achieve a high antireflection effect on the emitter side (light entry). The back surface contact has reflective characteristics and consists, for example, of vapour-deposited aluminium. For a cell of dimensions 2x2 cmz the gridJingers have a width of approximately 15 pm and a thickness of around 8 pm (tapering away from the busbar). The busbar has a width of approximately 150 pm, and the contact connection is located in the middle of the busbar. As well as these constructive measures it must be ensured technologically that the diffusion length in the base remains high throughout all the process stages (see Chapter 7). By implementing these measures it is possible to increase the efficiency of monocrystalline solar cells in the laboratory under AM 1.5 to 23%-24%, very close to the theoretical efficiency [33]-[35]. A further increase in efficiency can be achieved in crystalline silicon by using thinner cells of approximately 10-30 pm. However, this requires excellent passivation of the crystal surface and very good 'optical confinement'.
6.5.
MANUFACTURING PROCESS FOR HIGH EFFICIENCY SILICON SOLAR CELLS
In order to fulfil the requirements for these types of solar cells described in the previous section, highly complex technologies are necessary which call for a large number of technological steps. However, in the sequence of these many steps of high temperature, photolithography and chemical processes, the crucial point is the compatibility of the process steps that follow one another. These must be selected and coordinated, so that they
124
Crystalline Silicon Solar Cells
do not interfere with each other. The design of such process chains is one of the most important developmental tasks for all semiconductor devices. We now describe two process sequences for high efficiency Si solar cells, which have been developed in our institute. They naturally rely on many known technologies. The first manufacturing process achieves an efficiency of 23%. This is naturally also the more complex procedure. However, since its high cost overcompensates for the cost reducing potential brought by high efficiency, a simpler, more economical process has been developed, whereby attention is focused on keeping the sacrifice of efficiency as low as possible. All the process stages described in the following section are described and explained in more detail in Chapter 7. References are made at certain points. 6.5.1
Process Sequence for the Highest Efficiency
In Figure 6.33 the entire process sequence is divided into eight process blocks, with each individual block containing several individual steps. The process is explained based on this illustration. The starting point is - as already mentioned - Fz-Si (float zone pulled Si material, see Chapter 7, Section 7.15) with a resistivity between 0.5 and 1.5 R, a wafer thickness of approximately 250 pm and a crystal orientation of (100) at right angles to the surface of the Si wafer. The surfaces are etched or polished on both sides. The wafer diameter is 3 in. or 4 in.
Texturizing: The silicon wafer is given an approximately 80 nm thick film of SiO, by means of a high temperature process (see Chapter 7, Section 7.2.2.). A window structure is then created on one side of the Si wafer (to be the front side, the side turned towards the light) using photolithography and an etching process in buffered hydrofluoric acid, creating a multitude of oxide-free square windows with dimensions 20 x 20 pm'. Deep etching then takes place in these windows in a hot alkaline solution. Inverted pyramids are created by this anisotropic etching with (1 11) orientation (see Chapter 7, Section 7.2.5.2). The remaining SiO, ridgetops, not affected by the alkaline solution, are then removed in an HF solution. Boron-BSF Dvfision: By a further oxidation process, an SiO, film is created with a thickness of 200 nm. On the other side - to be the back of the cell - some windows are opened using a photoresist processes. Boron is diffused into these windows in a high temperature process to create a local pt back surface field. The remainding oxide is later removed by etching.
High EfJiciency Solar Cells
Figure 6.33 Process sequence for the manufacture of a LBSF (Local Back Surface Field procedure) solar cell with very high efficiency
I25
Crystalline Silicon Solar Cells
I26
n++Diffusion: Another oxidation process follows with an oxide thickness of 200 nm. Windows are opened along long ridges on the front (again using photoresist and etching processes). An n++diffusion takes place in a high temperature process using phosphorus (see Chapter 7, Section 7.2.1.2). The remaining oxide is again removed and is followed by n+ diffusion.
n+ Drfusion: This stage begins with a further protective oxidation with an oxide thickness of 200 nm. In this high temperature process the phosphorus, which was previously only diffused into the surface, is diffused to a depth of approximately 1-2 pm. When the oxide film on the front is opened, an n+ diffusion takes place.6 Oxide Passivation: In a further high temperature process a 105 nm thick SiO, film is created which, as mentioned, firstly serves as a single layer antireflection coating on the front surface, and secondly, it also provides the required surface passivation on both sides, keeping the surface recombination velocity of charge carriers as low as possible. This completes the semiconductor specific processes. Metalising (back): of the cell. Again using photoresist, holes are opened in the SiO, on the back of the cell for contact points, exactly at the points where boron has been diffused. On top of this a continuous aluminium layer with a thickness of 2 pm is vacuum evaporated. This aluminium also serves as a mirror for the photons that have not yet been absorbed. Metalising front): of the solar cell. Oxide windows are also opened on the ridges and on the busbar, and using the ‘Lift Off Technique’ (see Chapter 7, Section 7.2.4.1) a sequence of layers of Ti-Pd-Ag is vacuum evaporated with a total thickness of approximately 0.1 pm. Contact Reinforcement, Annealing: Because the galvanic resistance in the grid contact is a critical variable for total serial resistance, the metal of the fingers and the busbar is reinforced by electroplating to approximately 10 pm. Since the fingers should if possible not be wider than they are high, great efforts are required to achieve narrow, but high fingers. This galvanic film, to improve contact with the evaporated silver, then undergoes tempering at approximately 400°C in forming gas (6% hydrogen), This also has the advantage of significantly improving the quality of the oxide. The multitude of processes can be seen in Table 1. The highest level of efficiency achieved using this method is over 23% (cell area 4 cm2) [3 61,[371.
n+ means high surface concentration.
High Efficiency Solar Cells
127
Figure 6.34 Reduced process sequence for the LBSF (Local Back Surface Field) procedure for the manufacture of a high efficiency Si solar cell
128
Crystalline Silicon Solar Cells
6.5.2
The Simplified Manufacturing Process
The aim was to reduce the processing cost compared with the process described above. The process described below uses significantly fewer process stages (see Figure 6.34 and Table 1 right). The resulting solar cell structure is called a RP-PERC structure.’
LBSF Process
RP-PERC Process
5 High temperature oxidations
2 High temperature oxidations
3 Dopant diffusions
1 Dopant diffusion
6 Photolithography processes
3 Photolithography processes
Texturizing: The surface of the Si-wafer (the same starting material as described in Section 6.5.1), is etched in a hot alkali-alcohol mixture after an oxidation process and the uncovering of what will become the front side. This creates statistically distributed vertical pyramids (‘random texture’). Then, without any intermediate step (only rinsing and cleaning), n+ diffusion takes place. n+ Diffusion: Diffusion of phosphorus onto the texturised side, creating a phosphorus glass layer on both sides (see Section 7.2.1.2.1). Oxide Passivation: After the etching of this phosphorus glass film, the 105 nm thick passivating and antireflection SiO, film is created in a second high temperature process. Metallising (Jront contact): Using photoresist processes and the ‘Lift-off technique, contact points on the front and back are opened and the Ti-Pd-Ag contact system is vacuum evaporated onto the front. Metallising (back surface): Contact windows are opened on the back surface and aluminium is vacuum evaporated over the entire area. Finally, the galvanic reinforcement of the contact grid takes place and it is annealed under the forming gas.
’ Random Pyramids - Passivated Emitter Rear Cell
High Eflciency Solar Cells
129
Material
Fz-Si
Fz-Si
Cz-Si
Cell area [cm’]
4
21
4
n (in YO)
21.6
20.9
19.7
The efficiency levels achieved are shown in Table 2. With Fz-Si and an area of 4 cmz an efficiency of 21.6% can be achieved instead of > 23% with the more complicated procedure. It is worth noting that even with CzSi (Czochralski material, crucible pulled) a very economic Si material, with efficiencies of almost 20 %, can be achieved. Altering the process, as an experiment, an additional p+ back surface field is added by the diffusion of boron. Efficiency increases, due to the lower level of recombination on the back surface, so that for example, with Fz-Si and an area of 4 cm’, 22.6% efficiency is achieved. It is thus documented that even with greatly simplified processes, very high efficiencies can be achieved. Table 1 shows the number of process stages for the LBSF process and for the RP-PERC process. Table 2 shows the efficiencies achieved by the RP-PERC process. References Wolf M., Proc. 3rd EC PV Solar Energy ConJ, Cannes, France, 1980, p. 204 Goldmann H., Proc. 14th IEEE PVSpec. Conf San Diego, California, 1980, p. 923
Redfield S., Proc. 13th IEEE P V S p e c . ConJ, Washington, DC, USA, 1978, p. 911 Ross jr. R. G., Proc 13th IEEE PV Spec. C o n f , Washington, DC, USA, 1 9 7 8 , ~ 1067 . Grenon L. A. and Coleman M. G., Proc. 13th IEEE PV Spec. Conf., Washington, DC, USA, 1978, p. 246
Vofl B., Statusreport Photovoltaik, 1987, p. 73 Knobloch J., Aberle A. and Vofl B., Proc. 9th EC PV Solar Energy ConJ, Freiburg, Germany, 1989, p. 777 Von B. and Knobloch J., Internationales Sonnenforum, 1988, p. 468
130 [91
Crystalline Silicon Solar Cells DOE-Studie zitiert von Fan J.C.C. in Proc. 5th PVSEC, Kyoto, Japan, 1990, p. 607 Aberle A., Thesis Univ. Freiburg, 1992 Basore P. A. Proc. 22nd IEEE PV Spec. Con$, Las Vegas, Nevada, USA, 1991, p. 299 van Overstraaten R. and Nijs J. JEEE TED 16, 1969, p. 632 Nicollian E. H. and Brews J. R., MOS Physics and Technology, Wiley & Sons, New York, 1982 Goetzberger A., Bell Syst. Techn. 45, 1966, p. 1097 Goetzberger A. et al., Appl. Phys. Lett. 12, 1968, p. 95 Sze S. M., Physics Of Semiconductor Devices, 2nd Edn, Wiley & Sons, New York, 1981 Ruckteschler R., Thesis, Univ. Freiburg, Germany, 1986 Park J. S., Neugroschel A. and Lindholm F. A., IEEE TED 33, 1986, p. 240 Schottky W., ZeitschriftJ Physik 113, 1939, p. 367 Shockley W., Bell System Techn. 28, 1949, p. 435 Schroder D.K. and Meier D.L., IEEE TED 31, 1984, p. 637 Chang C. Y. and Sze S. M., Solid State Electron. 13, 1970, p. 727 Padovani F. A. and Stratton R., Solid State Electron. 9 , 1966, p. 695 Yu A. Y. C., Solid State Electron. 13, 1970, p. 239 Chang C. Y. et al., Solid State Electron. 14, 1971, p. 541 Meier D. L. and Schroder D. K., IEEE TED 31, 1984, p. 647 Hower P. L., Hooper W. W., et al. in Semiconductors and Semimetals, Willsrdson R. K. and Beer A. C., eds. Academic Press, New York, 1971, pp. 178-183 Murman H. and Widmann D., IEEE TED, ED 16, 1969, p. 1022 Goetzberger A,, Proc. JSth IEEE PVSpec. Con$, Kissimmee, Florida, USA, 1981, p. 867 Campbell P., Wenham S. R. and Green M. A., IEEE TED. 37,1990, p. 331 Campbell P., Wenham S. R. and Green M. A., IEEE TED 35, 1988, p. 713 Uematsu T., Ida M., Hane K.,Kokunai S. and Saitoh T., IEEE TED 37, 1990, p. 344
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131
[33] Green M. A,, Proc. 10th EC PV Solar Energy Con$, Lissabon, Portugal, 1991, p. 250 [34] Sterck S., Knobloch J. and Wettling W., Progress in Photovoltaics, 2, 1994, p. 19 [35] Knobloch, J., GlUnz S. W., Biro D., Warta W., Schaffer E. and Wettling W., Proc. 25th IEEE P V S p e c . ConJ, Washington, DC, USA, 1996, p. 405
[ 3 6 ] Zhao J., Wang A., Altermatt P. P., Wenham S. R. and Green M. A,, First World Conference on Photovoltaic Energy Conversion, Hawaii, USA, 1994, p. 1477 [37] Glum S. W., Knobloch J., Biro D. and Wettling W., Proc. 24rh EC PV Solar Energy Con/, Barcelona, Spain, 1997, in press
7 Si Solar Cell Technology
TECHNOLOGY FOR THE MANUFACTURE OF SILICON
7.1
In this chapter we first of all wish to describe in detail the process for the production of highly pure crystalline silicon. We then want to explain the technological processes which are applied to the manufacture of solar cells from this material. 7.1.1
Basic Material
Apart from oxygen, silicon is the most commonly occurring element on the earth. It mainly occurs as silicon dioxide (SiO,) in quartz and sand. Its synthesis has been familiar for many decades. It is extracted from (mainly) quartzite reduction with carbon in an arc furnace process. Figure 7.1 gives an overview of the manufacturing process [l].' The pulverised quartz and carbon are put in a graphite crucible. An arc causes them to melt at approximately 1800°C. Then the reduction process takes place according to the formula SiO,
+ 2C
-+
Si
+ 2CO
(7.1.1)
The liquid silicon collected at the bottom of the crucible (melting point 1415°C)can then be drawn off. Its purity is approximately 98%. This is called metallurgic-grade silicon (MG-Si) and a large quantity is used in the iron and aluminium industries. More than 500,000 tonnes are manufactured per year worldwide .
'
The first six illustrations are direct copies of the originals, as listed in [ 11 and [2]
I34
Figure 7.1
Crystalline Silicon Solar Cells
A smelting furnace for the production of metallurgic silicon [ 11
As the energy consumed by this process is very high at 14 kWhkg, production takes place in areas of the world where excess hydroelectric power is available (e.g. Noway, Canada). However, for silicon to be used in the semiconductor industry, the impurities must be removed almost completely by further processes. The remaining impurities in electronic grade silicon may only be some lo-''%. For such a high purity grade, multistage processes must be implemented.
Si Solar Cell Technology
7.1.2
I35
Refractioning Processes
The processes described here and in the following Section 7.1.3 are based on developments by Siemens in the 1950s. They are now the standard processes for the production of electronic grade silicon. In the first stage pulverised metallurgic silicon is exposed to hydrochloric gas in a fluidized-bed reactor. Trichlorosilane and hydrogen are produced by the chemical reaction Si + 3 HCl + SiHCI, + H, (exothermic reaction). Since trichlorosilane is a liquid at temperatures below 30°C it can easily be separated from hydrogen. The chlorides of the impurities from the process must now be separated from the trichlorosilane. In a second stage the trichlorosilane is freed from these impurities in fractional distillation columns. The other silicon chlorides are also removed. Trichlorosilane distilled in this way fulfils the requirements for electronic grade silicon. The impurity level is less than
1O-'O%. 7.1.3
The Manufacture of Polycrystalline Si Material
The manufacture of high purity silicon takes place according to the principle demonstrated in Figure 7.2 [2]. Polycrystalline silicon is deposited in a reactor vessel following the CVD principle (Chemical Vapor Deposition). The process is as follows: a thin silicon rod (in this case u-shaped) is electrically heated to a temperature of approximately 1350°C. A mixture of hydrogen (which must also be high-purity) and trichlorosilane is introduced into the reactor vessel. Trichlorosilane is reduced to silicon on the hot surface of the silicon, which deposits itself on the rod surface. The process takes place according to the following formula: 4 SiHC1,
+ 2 H,
+3
Si + SiC1,
+ 8
HCI
(7.1.2)
Thus, high-purity polycrystalline silicon is produced in a continuous process to rod diameters up to 30 cm and rod lengths up to approximately 2 m. More recently another process has been developed, based upon similar chemical principles. In a type of fluidized-bed reactor, silicon is deposited on the surface of fine silicon balls using silane created in situ. The silicon powder manufactured in this manner with a particle size of some tenths of a millimetre can be used either in the CZ pulling process described below (Section 7.1.4.1) or for the direct manufacture of silicon foil (Sections 7.1.7.1 and 7.1.7.2).
Crystalline Silicon Solar Cells
I36
Figure 7.2
7.1.4
Equipment for the industrial precipitation of polysilicon [2]
Crystal Pulling Process
For the manufacture of semiconductor devices, as well as having high purity levels, the silicon should be in single crystal form and free of defects. Two processes have become established, the crucible pulling process, also known as the Czochralski Process [3], and the float zone pulling process. 7. I. 4. I
The Czochralsh (CZ) Process
Figure 7.3 [4] shows the principle of the CZ process. Polycrystalline material in the form of fragments obtained from polysilicon as described in Section 7.1.3, is placed in a quartz crucible, which is itself located in a graphite crucible, and melted by induction heating under inert gases. The pulling process begins with the immersion of the single crystal silicon seed. The vertical pulling movement and the rotary movement silicon to grow in monocrystalline form on the seed crystal. Extremely precise balancing and
Si Solar Cell Technology
137
control of both movements, and precise control of the temperature of the silicon melt allows the diameter of the crystal to be precisely adjusted. Adding highly doped silicon fragments permits the simultaneous adjustment of the desired doping, dependent upon level and type of conductivity.
Figure 7.3
Single crystal pulling by the Czochralski process [3]
It is unavoidable that a certain amount of oxygen, originating from the quartz crucible, is incorporated in the crystal during this process. For most semiconductor applications this is of minor importance, and in some cases is even used to good effect to achieve gettering. For high efficiency solar cells, however, it is a disadvantage as oxygen forms precipitates, which act as recombination centres to reduce the lifetime of charge carriers. Our institute, however, has managed to achieve an efficiency of 22% using this material and suitable technologies.
Crystalline Silicon Solar Cells
I38 7.1.4.2
Float Zone Pulling
In float zone pulling the starting point is a polycrystalline rod, produced by the CV‘D process described in Section 7.1.3 (but a straight rod of the desired diameter). The principle is explained in more detail based on Figure 7.4 [ 5 ] .
Figure 7.4
Single crystal pulling by the float zone pulling method [ 5 ]
The puller is located within an enclosure flushed with inert gas. At the lower end a single crystal seed is again melted onto the polycrystalline rod by induction heating. After melting, a region of liquid silicon is propelled
Si Solar Cell Technology
139
upwards by the vertical movement of the induction coil whilst being rotated. When the silicon cools, it solidifies in single crystal form. The desired doping is achieved by the addition of a suitable dopant in gaseous form (e.g. phosphine PH, or diborane B,H,) to the inert gas. One advantage of this process is the additional cleaning of the crystal. Impurities (in particular metallic impurities) possess a very low segregation coefficient ), i.e. their solubility in liquid silicon is some orders of to magnitude higher than in solids. Thus these substances are largely carried with the fluid zone and transported to the upper end of the crystal. This process makes it possible - particularly with repeated pulling - to achieve very perfect crystals of high purity and thus - if desired - high resistivity. 7.1.5
The Manufacture of Silicon Wafers
Most semiconductor devices, including solar cells, require thin wafers with a thickness of approximately 0.2 to 0.5 mm. The standard process for wafers used the so-called inner diameter saw (ID), where diamond particles are imbedded around a hole in the saw blade. The process is very cost intensive and has the disadvantage that up to 50% of the material is wasted. A new process has been established in the form of the so-called multiwire saw, in which a wire of several kilometres in length is moved across the crystal rod in several coils within an abrasive suspension, whilst being wound from one coil to another (Figure 7.5) [ 6 ] . The advantage of this is that thinner wafers can be produced and the sawing losses are reduced by approximately 30% in comparison with the ID saw process. Also crystal defects on the surface of the silicon slice are significantly lower, reducing the manufacturing cost and increasing the efficiency of the solar cells. 7.1.6
Polycrystalline Silicon Material
As the cost of silicon is a significant proportion of the cost of a photovoltaic array [Chapter 61, great efforts have been made to reduce these costs since the beginning of worldwide photovoltaic activities in 1973. One principle which has emerged from these efforts is so-called block casting, which does not involve the costly crystal pulling process. This is shown in Figure 7.6 [7]. Silicon melted in a quartz crucible 1 is poured into a square graphite crucible 8. Controlled cooling produces a polycrystalline silicon block with a large grain structure. Precise control of the cooling mechanism ensures that the grain boundaries are columnar, i.e. aligned vertically to the surface. The grain size is some mm to cm. The
Crystalline Silicon Solar Cells
I40
U Figure 7.5
Sawing Si slices by the "wire cutting technique" [6]
silicon blocks, with dimensions of up to 30 x 30 cm2 are initially sawn into blocks with surfaces of 20 x 20 cm' or 10 x 10 cm'. Then, the above sawing processes are used to produce square Si wafers of 10 x 10 cm2 and 0.3-0.4 mm thickness (very recently dimensions of 15 x 15 cm2 have also been produced). Thus this starting material for solar cells is called polycrystalline silicon. This material is widely used and currently covers about 30% of all silicon requirements for terrestrial energy photovoltaics. New research and development work has made great progress both in relation to homogeneous crystal growth and, more importantly, in reducing the number of crystal defects in the individual grains [8]. We will go into more details about solar cells made of this material in Chapter 8. One important point is that unlike CZ material, this material contains non-critical quantities of oxygen as it is crystallised in a graphite crucible, but on the other hand does contain residual impurities from the crucible walls. Improvements have been achieved here too by appropriate surface coating of the crucible.
141
Si Solar Cell Technology
%Y Figure 7.6
7.1.7
Cross-section of a block casting equipment [7]
Sheet Materials
To avoid sawing processes in the manufacture of silicon wafers, activities have for years been concentrated on the production of so-called sheet material. In past decades a multitude of processes have been developed and tested worldwide. With a few exceptions almost none of these got past the laboratory testing stage. There are two reasons for this. For one thing in many cases the required level of purity could not be achieved, as too many impurities were introduced by the apparatus used at the high process temperatures. Secondly, many defects and faults are created in the crystal during the recrystallisation process, due to the high cooling speed which is sometimes required. We will restrict ourselves to the reproduction of two selected processes here.
I42 7. I. 7. I
Crystalline Silicon Solar Cells
The EFG Process
The EFG process (Edge defined Film Growth), based on the principle shown in Figure 7.7 [9], consists of an octagonal tube being drawn from a silicon melt using suitable graphite templates. The edge length of the octagonal segments is a little above 100 mm, giving a total tube diameter of approximately 30 cm. The thickness of the tube wall and thus the thickness of the slices produced of a few tenths mm is set by the shape of the graphite capillary as well as the prevailing temperature and pulling speed (some cm/min). Tubes with a length of 4-5 m can be pulled using this technique. Crystal Growth of Silicon Ribbons
LI
level in crucible
Figure 7.7
The principle of an EFG plant [9]
The separation of individual wafers - dimensions lOOx 100 mm2 - is by laser cutting. The material itself is polycrystalline, as in block cast silicon. Solar cells in pilot production have achieved efficiencies of 13% to 15%. This corresponds to the efficiency of solar cells made of polycrystalline block cast Si material as well as monocrystalline CZ material in industrial production.
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7. I . 7.2
143
The SSP Process
The SSP process (silicon sheet from powder) as shown in Figure 7.8 [lo] consists of silicon powder being placed in a quartz form (e.g. the above mentioned spherical silicon powder can be used). In the first stage the powder is sintered together. In the second stage the now self-supporting foil undergoes a zone melting process. A polycrystalline material with very large grains (millimetres to centimetres) is created. The melting process is brought about by focused, incoherent light. Silicon sheets with a thickness of approximately 400 pm can be produced in this manner. Solar cells have been produced on a laboratory scale with an efficiency of approximately 13%.
Figure 7.8
Silicon foil production by the SSP process [ 101
To conclude Section 7.1 we should mention the work which was aimed at replacing expensive gas phase refractioning processes for the manufacture of high-purity starting silicon by metallurgic preparation methods (leaching, gas blowing, etc.). Despite great efforts, the necessary purity has never been achieved using these methods. The efficiencies of solar cells made of this material are too low. This work was stopped a few years ago.
7.2
Si SOLAR CELL TECHNOLOGY
In this section we want to demonstrate the technologies for producing solar cells from crystalline silicon. We can divide this field into four areas, i.e. Technologies Technologies Technologies Technologies
for the production of p-n junctions. for the growing of SiO, layers. for the production of electrical contacts. for the reduction of reflection on the silicon surface,
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Crystalline Silicon Solar Cells
We also briefly describe the necessary auxiliary technologies such as etching and cleaning techniques and photolithography. 7.2.1
Technologies for the p-n Junction
In semiconductor technology two basic procedures are known for the production of p n junctions. These are diffusion and ion implantation techniques. The latter however only plays a minor role in the production of solar cells due to the high costs associated with it. It is only used in the manufacture of specialised solar cells for satellite technology. The third process, the alloying technique, was the dominant technology in early semiconductors at the beginning of the 1950s. However, it is rarely used today due to the wide dispersion of electrical parameters and high costs. We will therefore only describe diffusion technologies. 7.2.I . I
Difflusion Technologies and the Theory of D ffusion
The diffusion of solid substances in the Si solid obeys Fick's second law, which in one-dimensional form reads: (7.2.1)
where
N(x, t) D
is the concentration of diffusing substances at point x and time t ; is the diffusion coefficient specific to each material, which depends very strongly on temperature.
We will consider two solutions to this partial differential equation here. 7.2.I.1.1 The Complementary Error Function Distribution The dopant source is inexhaustible. The concentration on the surface (N,) is thus constant throughout the entire diffusion process. The concentration within the silicon is only dependent upon diffusion time and diffusion temperature (Figure 7.9). The boundary conditions for the mathematical solution are: N , = constant where 0 < t < 00 and N(x) = 0 where t = 0 and 0 < x < 00 where N , is the surface concentration.
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Si Solar Cell Technology
Figure 7.9
Concentration distribution of dopant for an inexhaustible dopant source
The solution for the differential equation (7.2.1) is thus X
(7.2.2)
The expression in parentheses is called the complementary error function distribution, and is represented by the letters erfc, thus X
N ( x , t ) = N, erfc 2 fi7
(7.2.3)
Figure 7.10 shows the relationship between the ratio of concentrations (NJN,) and the argument x i (Dt)"'. To calculate the penetration depth xj of a p-n junction, we first find the ratio of background concentration in the base silicon to surface
Crystalline Silicon Solar Cells
146
Figure 7.10 Concentration distribution according to the complementary error
function distribution concentration. If this value is that
for example, we find from Figure 7.10,
X
- = 5.4
$7
(7.2.4)
and thus x. = 5.4 I
$7
(7.2.5)
choosing diffusion constant, temperature and time leads to the penetration depth.
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147
7.2. I. I.2 Gaussian Distribution In this diffusion process there is an exhaustible dopant source on the surface with a concentration Q (cm-*). The solution of the partial differential equation (7.2.1) for this reads:
N(x,t)
=
-( x / ~ J D ; ) Z
Q exp
&Dt
(7.2.6)
where the surface concentration N s is found to be N s =-
Q
S,Ei
(7.2.7)
and is thus dependent upon the diffusion parameters. Figure 7.11 shows this relationship. As is clear, the desired surface concentration (high or low) can be adjusted - as discussed in Chapter 6.
1
f
T x-------+ Figure 7.1 1 Concentration profiles of dopants with an inexhaustible diffusion source
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148
7.2.1.1.3 Diffusion CoeSficient The diffusion process takes place in semiconductors according to two main principles. The diffusing substances can move across interstitials or diffuse via vacancies. The speed of migration is very variable, but in both cases is strongly dependent upon temperature. The quantative relationship is given by the formula (7.2.8):
D = D o exp(-AlkT)
(7.2.8)
where for a given substance Do and A are constant over wide temperature and concentration ranges. The variable A is also called the activation energy. The functional dependency of coefficients on temperature can be represented in the form of a so-called Arrhenius curve (log D + l/T). Figure 7.12 shows the diffusion coefficients for many elements in relation to temperature [ll]. Most of these values were determined in the early 1950s [12]. We see from Figure 7.12 that metals (e.g. Ti, Ag, Au) have higher diffusion coefficients than dopants (e.g. Ph, B, As) by several orders of magnitude, and therefore diffuse significantly quicker in silicon (substances such as Cu and Fe not shown in this representation diffuse even quicker). Therefore semiconductor technology requires extreme cleaness of laboratory and process equipment. We also see that due to the exponential temperature dependency of diffusion coefficients, the process temperature must be very strictly adhered to. Diffusion time, on the other hand, is much less critical, because the penetration depth according to the formula (7.2.5) is proportional to dt. 7.2.1.2
Diffusion Technologies
In the diffusion process and the subsequent oxidation process, an electrically heated tube furnace with a quartz tube is usually used. In solar cell technology diffusion temperatures vary between 800°C and 1200°C. The silicon slices to be treated are put into the constant temperature zone of the furnace in quartz trays. Temperature consistency across the zone length and over the diffusion times is better than 1"C, achieved using modem diffusion equipment. Figure 7.13 shows the principle of the standard diffusion process. Both gaseous and liquid diffusion sources are used. Nitrogen, argon and oxygen are used as carrier gases in the so-called open tube process. The quantity and mix ratios must be adjusted according to the application, but require very precise control.
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Si Solar Cell Technology
l/T
-
Figure 7.12 Temperature dependency of the diffusion coefficients of different elements in silicon (according to Landolt-Barnstein)
The diffusion process requires, in addition to precise control of time and temperature, certain heating and cooling phases. Slow cooling can be used to produce a getter effect [13]-[14]. In this case impurities, mainly metals, wander to the surface due to the drastic reduction of their solubility in silicon with the sinking temperature, and their still high diffusion rate at low tempzratures. They are absorbed there and are therefore harmless as recombination centres. The diffusion processes used in solar cell manufacture are described in detail below.
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150
Wafers on carrier
Wafers on carrier
# bh -Valvesand flow meter I!@,
IflrkDopant liquid
Figure 7.13 Principle of the diffusion process (open tube process)
7.2.1.2.1 Emitter Diffusion Processes Since the starting wafers for solar cells are almost always doped with boron and are thus p-conductive (concentrations from 10” to l O ” ~ m - ~an ) , ndoped emitter is created using phosphorus. Gas diffusion processes are used almost exclusively, whereby phosphorus is introduced into the diffusion furnace either in the form of phosphine (PH) or gaseous phosphorus oxychloride (POCI,). The latter is introduced using nitrogen as a carrier gas. At the high temperatures of approximately 800°C the dopant gases react with the surface of the silicon when oxygen is added. In accordance with Si + 0, => SiO, silicon dioxide is produced on the surface and secondly, phosphine is converted according to 2 P H + 3 0 , -+P,O,
+H,O
(7.2.9)
phosphorus pentoxide. The P,O, created combines with the silicon dioxide growing on the silicon surface to form liquid phosphorus silicate glass. This glass then becomes the diffusion source. The process using POC1, is similar. P,O, is also created in this process. In addition, chlorine is released. Its significance for the cleaning of silicon surfaces is well known in semiconductor technology as chlorine creates volatile metal compounds [15]. In practice, however, phosphorus diffusion shows deviating behaviour from the simple theory for the case of low penetration depth. In the case of an inexhaustible source, the diffusion profiles obtained do not match the above diffusion theory. Concentration profiles are obtained which are more like those shown in Figure 7.14. to
Si Solar Cell Technology
Figure 7.14 Phosphorus profiles at diffusion temperatures of 950°C in relation to diffusion time [ 161
This anomalous behaviour has been explained by various authors [ 161-[ 191, by the fact that the diffusion coefficient rises sharply with high
concentrations and only at a certain low concentration does it behave according to the familiar diffusion coefficients. This effect has the disadvantage for solar cells that a dead layer is created, as already mentioned. A dead layer of, for example, 0.3 pm depth will reduce efficiency to approximately 10% (relatively). A dead layer can be impeded using the following diffusion process for reducing the surface concentration of the emitter. In a double diffusion process [20],[21] the first diffusion step is a predisposition coat - a low level diffusion of phosphorus at a temperature of approximately 800°C. Then the phosphorus-silicate glass layer is removed by chemical means. In a second diffusion step - this time at a temperature of 1000-1 100 "C - the desired penetration depth of the phosphorus is achieved. A diffusion profile
152
Crystalline Silicon Solar Cells
is obtained which follows the Gauss distribution. Both diffusion steps are coordinated with each other in temperature and time, such that instead of the saturation concentration of approximately 10” cm”, surface concentrations of approximately 10’’ cm-, can be produced. 7.2.1.2.2 The Diffusion Process for the Back Surface Field As we have already mentioned, a so-called back surface field (BSF) is necessary for high efficiency solar cells. The required pi doping is achieved by the diffusion of boron. BBr, can serve as the boron source for this purpose, which can be handled in a very similar manner to POCI,. In industrial practice, aluminium is used for the creation of a BSF. The technological doping process is that aluminium is introduced onto the surface using vacuum evaporation or in the form of an ink by screen printing, and alloyed at approximately 800°C (eutectic point 577°C). At this temperature the aluminium partially diffuses and creates a p+ doping. The recrystallised layers also act as good getter sinks. 1.2.2
Oxidation Technologies
The thermal oxidation process (dry, i.e. without the addition of water vapour) is, as mentioned above, according to the following formula: Si + 0, +SiO,
(7.2.10)
Oxygen diffuses through the SiO, layer which is forming. With this process there is therefore no saturation thickness although the rate of growth slows with the increasing thickness. At the outset the layer thickness grows in proportion to time, at greater layer thicknesses (>1 pin) approximately in proportion to the square root of time. An SiO, layer requires a silicon layer of approximately 45% of its own thickness. Wet oxidation (with water vapour) takes place according to the formula 2Si +O, + 2 H , O +2SiO,
+2H,
(7.2.11)
The rate of growth in this case is significantly higher than for dry oxidation, since the reaction process is clearly stimulated by the hydrogen. Figure 7.15 shows the influence on the SiO, layer thickness of dry or wet oxidation as a function of the reaction time and the oxidation temperature P21. Other influences can also alter the growth rate of SiO,. The oxidation of highly doped silicon (>lozocm-’) is around 20% faster. Likewise the oxide grows approximately 30% faster on the (111) orientated surfaces than on
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t i hl 10
1
10
1 xO
[PI 10-1
10-2 10
102
103
t I min 1 Figure 7.15 The oside layer thickness with dry and wet oxidation
the (100) surfaces. The addition of chlorine ions during the oxidation process is also beneficial [23],[24]. As well as the removal of traces of metal by volatile metal chloride, alkali atoms such as sodium are also removed and the passivating characteristics of the SiO, layer thus improved. Chlorine can be added to the process, e.g. by the addition of trichloroethane (TCA); (formula C,H,CI,). The reaction for this oxidation process is C,H,Cl, + 2 0 , +3HC1 + 2 C O ,
(7.2.12)
and 4HC1 + O , +2H,O
+2C1,
(7.2.13)
When TCA is added the supply of oxygen must be ensured, as otherwise the highly poisonous phosgene may be formed because TCA is
154
Crystalline Silicon Solar Cells
now replaced by trans-LCD (also contains chlorine) for environmental protection. The results are very similar. New research - including that in our institute - into the use of SiO, as a passivation layer in solar cells has yielded the following sumniarised results:
Dry oxidation under high oxidation temperatures yields the lowest values for the interface trap density and thus very low surface recombination rates. The density can be reduced even further by an annealing process at approximately 45OOC (preferably in forming gas). The lowest densities are achieved with (100) surfaces. The masking effect of an SiO, layer in the diffusion process relies upon the fact that the rate of diffusion of many diffusants in silicon dioxide is lower by orders of magnitude than in silicon itself. The required SiO, layer thickness for different diffusion temperatures and times is shown in Figure 7.16 for the two diffusants boron and phosphorus [25]-[26]. It is evident that boron is masked by significantly thinner SiO, layers than is phosphorus. Fkherniore, SiO? is used for masking in alkaline etching processes as well as for surface texturing. We will return to this subject in Section 7.2.5.2.
1
xO
[ pml 10-1
10 -2
Figure 7.16 Necessary oxide layer thickness for complete masking against boron and phosphorus [ 251,[ 261
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155
Auxiliary Technologies
7.2.3
Before examining in inore detail the technologies of solar cell surface treatments, such as metal coating, antireflection coating and texturing, we wish to comment upon the auxiliary teclinologies such as etching, cleaning and photolithography. 7.2.3.I
Etching and Cleaning Techniques
Various different etching and cleaning techniques are necessary for the manufacture of semiconductor devices. The surfaces of the silicon wafers must be free of contaminants as far as is possible. These contaminants may be of molecular, ionic, or atomic nature. Residues of the lapping, polishing and photoresist processes are, for example, of molecular nature. Contamination by ions usually occurs by the absorption of ions from the etching solution, whilst heavy metals such as silver, copper and gold have an atomic character. The most widely used procedure for surface cleaning is currently the socalled RCA cleaning 1271.' This process is based upon the use of hydrogen peroxide (H202)firstly as an addition to a weak solution of ammonium hydroxide (NH,OH), and secondly hydrochloric acid (HCI). The cleaning process is as follows: After preliminary cleaning in hot dilute nitric acid (HNO,) and etching in buffered hydrofluoric acid (HF) the silicon wafers are exposed to the peroxide solution at 80°C. Due to the severe oxidising effect the organic residues are oxidised and simultaneously a large part of the metallic traces complexed. In the subsequent cleaning stages - in the hydrochloric acid again at 80°C - the remaining traces of metals are converted into volatile metal chlorides and thus removed. Etching the silicon dioxide layers occurs mainly in a weak solution of hydrofluoric acid. Depending upon the desired etching rate the HF-solution can be buffered with ammonium fluoride (NH,F). Isotropic ,etching of silicon occurs in a solution of nitric acid and hydrofluoric acid. The nitric acid oxidises the silicon to SiO,, which is then dissolved by the hydrofluoric acid. The mix ratio determines the etching rate and the surface structure created. To obtain, for example, a very smooth, almost mirror finished surface, or a very low dissolve rate, the etching mixture can be buffered with acetic acid (CH,COOH) and phosphoric acid (H,PO,). Comprehensive information can be found in [28].
This cleaning process is named after the company RCA.
Crystalline Silicon Solar Cells
156
Following all cleaning processes rinsing with deionised water must take place as the final stage. The current state of the art is a specific resistance of 17-1 8 MRcm (near the theoretical value due to natural dissociation). A separate branch of the chemical industry developed decades ago concerned with the preparation of the necessary chemicals in extremely pure form. As well as pure chemicals a multitude of compounds with different mix ratios are available. All processes are performed in ‘clean room s * . 7.2.3.2
Photolithography
Photolithography is used to structure the silicon dioxide used in the various masking processes as described above. A thin film of photoresist is spun in a yellow area - due to the light sensitivity of the photosensitive resist - on the silicon wafer. Depending upon viscosity and revolution speed (some thousands of revolutions per minute) a homogeneous film is created with a thickness of 0.5-2 pm. After the film has been dried, it is passed through suitable masks and illuminated with short wavelength light (approximately 0.4 pm). This process occurs in mask aligners, which permit structural precision of about 1pm. In the case of a positive resist, the long molecule chains are cracked at the illuminated points and thus prepared for dissolving in alkaline solutions. After successful etching of the SiO, layer the remaining resist is removed using acetone. In the case of a negative resist the illuminated points remain. It is used if silicon is to be etched locally (positive resist is not resistant to this). The resist is dissolved in hot chemicals. 1.2.4
The Metallising of Solar Cells
Of the many contact technologies which are used for semiconductors, we only wish to describe those which are used in solar cell technology. We first examine the structuring of the finger grid. 7.2.4.1
The Structuring of the Finger Grid
Three methods are used for the structuring of the contact finger. In the first a vacuum evaporation template with a perforated strip pattern is used, which has the disadvantage that the smallest finger width is approximately 100 pm - or at best 50 pm. If narrower contact fingers are required to reduce shadowing, the photoresist technique must be used.
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Photoresist
Solvent Metal
I
P
P+ !----/- -. I Mask illumination Photoresist development
Evaporation of c.g. Ti, Pd, Ag
after dissolution of photoresist
Figure 7.17 The principle of the ‘lift-off process
As shown in Figure 7.17, the required sequence of layers is vacuum evaporated as a complete layer upon a structured photoresist. The crucial point is that the photoresist layer has to be thicker than the vacuum evaporated metal layer, so that the edges can be accessed during the dissolution of the photoresist. The simultaneous use of ultrasound is helpful during dissolving. In this way it is possible to produce structures which are only some pm wide. The third method, screen printing, in which metal paste is used, dominates in a wide range of production techniques as it is particularly cost effective, but the maximum finger width is about 100 pm. 7.2,4.2
High Vacuum Evaporation Technologies
The most up to date method for contacting is the vacuum evaporation of metal layers, in many cases in several layers [2S]. The contact material to the semiconductor is selected from the point of view of the required banier height. Since, as described in Chapter 6 , the surface concentration of dopant must be low ( -10”9 crns3)in a high efficiency solar cell to reduce the surface recombination velocity, almost only titanium, with a barrier height of approximately 0.5 eV can be considered. Owing to its low vapour pressure and the necessary high temperature almost exclusively electron beam evaporation is used. Experiments involving theniial evaporation from a tungsten boat have been carried out to determine how high the negative influence of the electron beam evaporation is on the SiO, passivating layer. The sharp
Crystalline Silicon Solar Cells
I58
increase in the surface recombination velocity which occurs can, however, be completely eliminated by subsequent annealing under forming gas [29]. As well as its low barrier height, titanium also has the advantage that it belongs to the easily oxidizable metals and thus can reduce thin SiO, layers whilst retaining good adhesion to the silicon. The normal layer thickness is 30 to 50 nm. Titanium must, however, be protected from external oxidation by another metal. Metals can be considered which themselves barely corrode and which are compatible with the contact material, i.e. do not diffuse too highly with the bonding agent and the subsequent covering material. Nickel and palladium are suitable partners, these are deposited in approximately the same thickness as titanium (m50 nm). For the external contacting a third metal layer with good conductivity and very low corrosion must be evaporated. Silver is preferred in many cases. The silver layer is evaporated with a thickness of approximately 0.1 pm. The subsequent sintering at a temperature of approximately 400°C under forming gas ensures a good adhesion between the contact layers. For the necessary reduction of the electrical resistance of the contact finger it is reinforced by the electroplating of Ag. Approximately 8 pm Ag is grown onto the approximately 15 pm wide fingers of high efficiency solar cells. In the case of a high emitter surface concentration (approximately lozo~ m ' ~Cr-Ni ) contacts also give very good results. The back surface contact on high efficiency cells consists of vacuum evaporated aluminium, which produces a very good ohmic contact to the p-base material due to its p-doping effect. In the case of solar cells with a local BSF, the silicon dioxide on 98% of the surface is coated with aluminium. This functions as a very effective optical reflector. 7.2.4.3
Thick Film Technology
The advantage of thick film metal coating using the screen printing process, which is, as mentioned, widespread in industrial solar cell manufacturing [30]-[32], lies on the one hand in the low investment cost and on the other hand in the scope for automating the process. The metallic pastes used have, in addition to an organic binder which determines viscosity, a flux, also known as sintered glass. Typically, such pastes contain, in addition to 70% Ag in the form of platelets a few pm thick and approximately 5 to 15 pm wide for the front contact, approximately 2% sintered glass. The sintered glass is composed of lead oxide, lead-boron-silicate or zinc-boron-silicate, the rest is binder. After depositing, the layer is sintered at temperatures of approximately 600°C. The sintered glass components melt and dissolve a small layer of silicon. At the same time, this melt is enriched by silver. Upon cooling a
Si Solar Cell Technology
1.59
recrystallised Si layer is created as with normal alloying, which contains a high proportion of Ag and thus creates a good ohmic contact. This process only gives sufficiently low contact resistances at surface concentrations on the n+ emitter of approximately 10'' cm-3 . Only aluminium (in the form of a paste) is used for the manufacture of back surface contacts. Aluminium has two advantages. It forms alloys at 577°C (eutectic point) and has a relatively good solubility with concentrations of approximately 10'' cm" in silicon. Thus in the recrystallised layer formed upon cooling a p+ doping is achieved and thus a BSF created. Normally sintering takes place at temperatures around 800°C since the best results are achieved thus. The significant increase in open circuit voltage observed in practice at high sintering temperatures can be explained by the above mentioned gettering effect. Since A1 is not directly solderable, a silver-palladium paste is also sintered onto this layer [331. 1.2.5
Antireflection Technologies
7.2.5.1
Applying an Antireflection Coating
High vacuum evaporation technologies and thick film techniques are also used for the manufacture of antireflection coatings. For a single layer antireflection coating, titanium dioxide (TiO,) is used almost exclusively. Its refraction index can be adjusted within a specific range during the evaporation process by the selection of evaporation rate and the addition of small quantities of oxygen. We thus obtain values of n=1.9 to n=2.3 with very good transparency. The latter is a very important prerequisite for high efficiency. Thick film technologies are also used in mass production for costs reasons. A paste containing titanium dioxide compounds is deposited onto the surface of the silicon, either by spinning on or by the screen printing technique. Finally, sintering takes place at temperatures of 600-800°C. These antireflection processes can be linked to the above metal coating by screen printing. The TiO, paste previously dried at temperatures around 200°C has silver paste added to it for the grid structure. Both are then simultaneously sintered. As the thickness variance of the antireflection layer only influences total reflection behaviour slightly (AM 13), then this gives good antireflection characteristics.
160
7.2.5.2
Crystalline Silicon Solar Cells The Manufacture of Textured Silicon Surfaces
To produce such structures the chemical-physical effect is used, that the etching rate of silicon in an alkaline solution is dependent upon the crystal direction [34],[35].For example, the dissolution rate of silicon in the (111) crystal orientation is one or two orders of magnitude smaller than in the (100) direction. The reason for this is that in the (111) plane for the cubic face centred diamond lattice of silicon there is only one free valence to the surface per atom, whereas for the (100) direction two valences are available. It is therefore plausible that a considerably higher energy expenditure is required to dissolve an atom from the ( 111) direction as for the (100) direction. Therefore in high efficiency solar cells the (100) crystal orientation, vertically to the surface, is selected. The etching process takes place in an alkaline solution at approximately 70°C.Weak solutions of KOH or NAOH with a concentration of 10%-30%
Figure 7.18 Electron microscopic picture of silicon wafers with random pyramids
Si Solar Cell Technology
161
are normal. To achieve the desired pyramid structures, the silicon surface must be first fitted with a corresponding SiO, stripe structure, which, as mentioned, will not be attacked by the alkaline solution. As the etch depth and of course also the undercut is dependent upon the distance between the individual SiO, strips and their width, these parameters must be carefully matched to each other. Etching continues until the two neighbouring sides underneath make contact. Inverted pyramid structures have become dominant. As mentioned, a reduction in reflection is achieved if the deposited SiO, passivating layer has a thickness of 100 nm, so that with a refraction index n=l.46 the h/4 condition is fulfilled. References [ 11
Diet1 J., Helmreich D. and Sirtal E., Crystals: Growth, Properties and Applications, Vol. 5 , Springer-Verlag, 1981, p.57
[2]
Zulehner W. and Huber D., Crystals: Growth, Properties and Applications, Vol. 8, Springer-Verlag, 1982, p. 92
[3]
Czochralski J., Z. Phys. Chernie 92, 1977, p. 219
[41
see P I , p.4
PI
see P I , P. 6
[6]
see [l], p. 73
[7]
see [l], p. 67
[8]
Schtitzel P., Zollner Th., Schindler R. and Eyer A., Proc 23rd IEEE PV Spec. Con$, Louisville, Kentucky, 1993, p. 78
[9]
Wald F. V., Crystals: Growth, Properties and Applications, Vol. 5 , Springer-Verlag, 198 1, p. 157
[ 10) Eyer A., Schillinger N., Reis I. and Rtiuber A., Cryst. Growth, 104, 1990, p.
119 [ 111 Landolt-Bornstein Vol. 17 Part C Springer-Verlag, 1984, p. 494 [ 121 Fuller C. S. and Ditzenberger J. A., J. Appl. Phys., 27, 1956, p. 544
[13] Goetzberger A. and Schockley W.,J. Appl. Phys., 31, 1960, p. 1821 [ 141 Clays C. L., Proc. 2nd Brazillian Workshop on Microelectronics, Sao Paulo,
1980 [ 151 Rouen R. S. and Robinson P. H., J . Electrochem. Soc., 119, 1972, p. 747
162
Crystalline Silicon Solar Cells Tsai S. C., Proc. IEEE, 57, 1969, p. 1499 Fair R. B. and Tsai S. C., J . Electrochem. Soc., 127, 1977, p. 1107 Jeppson K. 0. and Anderson D. J., J . Electrochem. SOC.,136, 1986, p. 397 Hu S.M. et al., J. Appl. Phys., 54, 1983, p. 6912 Knobloch J., Aberle A. and Vofl B., Proc. 9th EC PV Solar Energy C o n j , Freiburg, Germany, 1989, p. 777 Blakers A. W., et al., Proc. 9th EC PV Solar Energy C o n j , Freiburg, Germany, 1989, p. 328 Wolf H. F., Silicon Semiconductor Data, Pergamon Press, 1976
Convell E. M., Proc. IRE, 46, 1958, p . 1281 Cosway R. G. and Wu C. F., J . Electrochem. Soc., 132, 1985, p. 15 1 Sah C. T. et al., J. Phys. Chem. Solids, 11, 1959, p. 288 Morinche S. and Yamaguchi S., Jpn. Appl. Phys., 1, 1962, p. 3 14 Kern W. and Puotinen D. A,, RCA-Review, 1970, p. 187 Bogenschutz A. L., Atzpraxis f i r Halbleiter, Hanser Verlag, 1967 Kopp J., Knobloch J. and Wettling W., Proc. 11th EC PV Solar Energy ConJ:, Montreux, 1992, p. 49 1301 Cheek C., et al., IEEE TED, 31, 1984, p. 602 [3 11 Mertens R., et. al., Pmc. 14th EC PVSolar Energy C o n j , San Diego, 1980, p. 1347 [32] Dubey G. C., Solar Cells, 15, 1985, p. 1 [33] Ralph E. L., Proc. 11th IEEE PVSpec. C o n j , 1975, p. 315 [34] Heuberger A., Mikromechanik, Springer-Verlag, 1989 [35] Price J. B., Semiconductor Silicon, Princeton, NJ, 1983, p. 339
Selected Solar Cell Types
In the first part of this Chapter we will describe four specific solar cell configurations made of crystalline silicon. These are: Cells for concentrator applications. Cells manufactured according to MIS technology [Metal Insulator Semiconductor]. Cells made of polycrystalline silicon. Cells with thin base layers [20-50 pm].
In the second part of this Chapter we will concentrate on some thin film solar cells made of other semiconductor materials, i.e. Cells made of amorphous silicon (a-Si). Cells made of semiconducting compounds e.g. gallium-arsenide (GaAs). and cadmium-telluride (Cd-Te). Cells made of copper-indium-diselenide, known by the abbreviation CIS. We will conclude with some consideration of tandem cells and dye sensitized solar cells.
8.1 8.1.1
CRYSTALLINE SILICON SOLAR CELLS Crystalline Silicon Concentrator Cells
The concentration of sunlight brings two advantages for solar cells. Firstly, the required area can be reduced according to concentration, so the cell can be based on good monocrystalline silicon and use costly technologies. As concentration rises, cell cost becomes less of a factor for the solar array. Furthermore, open circuit voltage increases with the higher short circuit current of the cell, which in the first approximation is proportional to
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Crystalline Silicon Solar Cells
radiation power. This effect is intensified because due to the high injection of charge carriers, their diffusion lengths are greater than in the case of low injection (one sun). Thus the saturation current is reduced and therefore open circuit voltage increased. At 100-fold concentration an increase in efficiency of 20% (relatively) is achieved. For even higher radiation, however, the influence of Auger recombination becomes so noticeable due to the high carrier density that the increase in efficiency flattens out considerably. Sinton et al. [ l ] redefined the Auger coefficient from the dependence of open circuit voltage as a function of radiation, obtaining a value approximately four times larger than was previously realised. First generation concentrator cells were a development of conventional solar cells with a finger structure on the surface facing the light. The main problem was the minimising of serial resistance, which is primarily determined by the layer resistance of the emitter and the resistance of the contact finger. The distance between fingers therefore had to be very low and to minimise shadowing, the fingers had to be very narrow.
Figure 8.1
The structure of an IBIC cell for concentrated light [ 5 ]
A word on the history of the solar cell. In 1977 Burgess et al. [2] introduced a cell with what was at the time a high efficiency of 15% at 50fold solar radiation. In 1980 Khemthong et al. [3] increased this value to over 20% (at 40 suns). A decisive improvement was achieved by Sinton et al. [4] and Swanson et al. [ 5 ] when they implemented and improved the
Selected Solar Cell Types
I65
structure suggested by Lammert et al. [6] in 1974, the IBC [Interdigitated Back Contact]. As the name suggests, both n+ and p+ diffusion structures (Figure 8.1) and therefore also both connection contacts lie on the back of the cell. This structure has the following advantages: There is no shadowing of light by the finger structure. The metal contacts can be broad and take up almost the entire back surface. They are therefore of very low impedance, thus achieving a very low series resistance. The penetration depth of n+- and p+- layers are non-critical. There are no losses due to a dead layer. A disadvantage is that the diffusion length in the base of the cell must be very high (if possible five times greater than the cell thickness), and the surface recombination on the side facing the light must be extremely low. Short wavelength light also increased the surface recombination velocity on the front surface and caused degradation in the first cells. The problem was solved, however, [7] by applying a very thin (a few tenths pm thick) p+ zone with a surface concentration in the region of approximately 10" cm-3 to the side facing the light. A disadvantage of this cell is that the nt- and p'-connections must be insulated from each other at the points of contact in a module. Efficiencies of approximately 27% are achieved with this type of solar cell at 100 suns. For lower concentrations around 50 suns, a cell has recently been developed in which the p+ layer is again applied to the side facing the light. Efficiencies of 26% have been achieved with these cells
PI.
The application of concentrator cells is limited to use in sun rich areas. The problems of cost effective light concentration and sun tracking must be solved. This cell, in a slightly modified form, has proved that it can be used under normal sunlight conditions. In the World Solar Challenge, the race for solar powered automobiles over 3000 km in Australia from Darwin to Adelaide in 1993, the company Sun Power Corporation, California, in cooperation with Honda, Japan, manufactured 7000 solar cells of this type [9]. The cells had dimensions of 7.3 x 2.4 cmz. They were manufactured from Fz-Si with a resistivity of approximately 50 Rcm to achieve a very high carrier lifetime of up to 2 ms. The cell thickness was 160 pm, reduced using etching techniques. The contact layout was altered from the original design. It consisted of many interlinked contact fingers with two longitudinal collecting contacts. For the electrical insulation of the contacts, as in many power semiconductors, the plastic polyimide is used. In the manufacture of the 7000 cells a yield of ~ 9 0 %was achieved referred to a cell efficiency of >20%. The average cell efficiency was
Crystalline Silicon Solar Cells
166
21.1%. This is an exceptionally good result. The solar powered car fitted with with these cells won the race.
8.1.2
Biracial Solar Cells
If, instead of the very wide interdigitated fingers, an interdigitated finger grid is deposited with a similar layout, but narrow like the high efficiency solar cells, as shown in Figure 8.1, then this cell can be illuminated from both sides. Various laboratories have worked on this type of cell [lo]-[13]. Such a cell, for example, is capable of collecting diffused light from the back surface, thus increasing total efficiency. One variant of this cell consists of a cell with an n+ layer on its back surface. This gives a structure similar to a transistor. Cells built in our Institute according to this principle have achieved efficiencies of 21.4% when illuminated on the nonmetallised side (under AM13 global) and 20.2% when illuminated on the grid side (somewhat lower due to shadowing). This is the first bifacial solar cell with efficiency on both sides >20%. These high, and very consistent, values show both that the two sided surface passivation is very effective, and that the carrier lifetime in the base material must be very high. Both indicate a high standard of technology.
8.1.3
Buried Contact Solar Cells
Another type of high efficiency solar cell is the Buried Contact Si solar cell shown in Figure 8.2. This structure was first suggested in 1985 [14], and is patented in many countries. The significant difference in this cell is the buried contact. Using laser technology, grooves of approximately 20 pm wide and up to 100 pm deep are cut in Si wafers texturised according to the principle of random pyramids to hold the grid fingers. The etching process which follows removes the silicon destroyed by this process. These grooves provide two advantages. Firstly, shadowing is reduced significantly when compared with the normal grid structure of commercial solar cells. Values of only 3% surface shadowing are obtained. Secondly, the grooves can be filled with contact material. Thus, approximately the height of the grooves and thus the metallisation can be five times its width [15]. In conventional cells, even vacuum evaporated contacts and contacts reinforced by electrodepositing, the ratio is 1:1, i.e. the metal contact height is equal to its width. The five-fold height means a reduction in the resistance of the contact finger by a factor of 5 , resulting in a significantly better fill factor. The technology of metallising consists of an electroless deposited nickel contact, which is reinforced after sintering with copper. Since this
Selected Solar Cell Types
Figure 8.2
167
Cross-section through a buried contact solar cell
technique does not require photomask processes or high vacuum evaporation technologies, and is thus significantly more economic, it is predestined for use in serial production. The double stage emitter is used for the emitter structure, whereby the highly doped n++film is restricted to the groovss. The p+ back surface field permits higher efficiencies. Owing to the low process costs, several solar cell manufacturers have bought a licence. It was shown that the manufacturing process was somewhat more economic that the widely used screen printing technique [161,[171. A further advantage of this cell is the textured back surface, which increases the confinement of light and thus the total efficiency. With this type of cell (large area), average efficiencies of 18% have been achieved in production [ 161. With specific techniques, such as an improved antireflection coating and a local back surface field, efficiencies of up to 2 1% have been achieved in the laboratory [ 181. This beneficial structure is still undergoing further development. In this case, too, attempts are being made to reduce the number of process stages, in particular the high temperature processes, thus achieving more economical solar cells [ 181.
Crystalline Silicon Solar Cells
I68 8.1.4
MIS Solar Cells
The fundamental difference between the MIS solar cell developed by Hezel and his colleagues and the conventional Si solar cell is the fact that it does not contain a p-n junction (Figure 8.3). The side of the cell facing the light is coated by a very thin (approximately 2-4 nm) thermally grown silicon dioxide film [19]. The finger grid is vacuum evaporated onto this and finally, the entire surface is coated with a silicon nitride film, which may be relatively thick due to its good transparency (some pm). This coating a dielectric - has four tasks: Protects against environmental influences. Functions as an antireflection layer. Reduces surface recombination velocity. Creates an n conducting inversion layer in the p semiconductor. A decisive step towards increasing efficiency was achieved by the use of caesium in this dielectric [20].Caesium's property of creating stable charges was reported by Sixt and Goetzberger in the early 1970s [21].
Figure 8.3
Cross-section through an MIS solar cell [ 191
One advantage of this solar cell lies in its manufacturing, which does not require any high temperature procedures. The thin SiO, layer is produced at a temperature of approximately 500°C.The number of process stages is low. A disadvantage is that the n-inversion layer has a sheet resistance which is between five and ten times higher than in conventional silicon solar cells. This necessitates a finger structure with very small distance between fingers, which means that the fingers must be very thin due to shadowing. Electrical contacting can therefore only take place using
Selected Solar Cell Types
I69
a high vacuum evaporation procedure. Furthermore, to prevent degradation the cells must be bedded under glass which has been coated to allow the absorption of ultraviolet light. After further improvements [22] 10 x 10 cm2 solar cells have been produced which achieve 15% efficiency. 8.1.5
Polycrystalline Silicon Solar Cells
Figure 8.4 shows a cross-section through a solar cell made of polycrystalline silicon, We described the manufacture of the starting material in the preceding section. The grain boundaries should be as columnar as possible, i.e. they should run vertically to the surface of the silicon wafer. It is clear that parallel grain boundaries severely detract from the formation of a good p-n junction (leakage current, high saturation current).
Figure 8.4
Cross-section through a polycrystalline silicon solar cell
Many publications have appeared on the theory of polycrystalline Si solar cells since 1977 [23]-[27]. Ref. [28] contains a model of the crystal boundaries in polycrystalline solar cells. More recent research has been more concerned with the defects in individual grains, as it has been established that these reduce efficiency [29] much more than do the grain boundaries themselves, if their average distance apart is greater than the average diffusion length by a factor of between five and ten, Such defects can be, for example, the precipitation of impurities and crystal defects such as vacancies and dislocations. One theory of the influence of the variables
I70
Crystalline Silicon Solar Cells
is that of de Pauw [30]. Three processes have been established to minimise the recombination and efficiency reduction caused by defects and grain boundaries. These are: Passivation using hydrogen ions Gettering using phosphorus Gettering using aluminium. In the first process, hydrogen ions created in an ion source and accelerated to 1000 eV are implanted into the - finished - solar cell. The precise mechanism of passivation has not yet been completely explained. However, it has been proved [31],[32], that the free valences, the so-called dangling bonds, are saturated by the stable silicon-hydrogen compounds SiH, SiOH created [33],[34]. This type of hydrogen passivation primarly increases the photocurrent [35],[36]. The second method, the gettering of impurities by phosphorus has already been described in Chapter 6. According to this, the phosphorus-silicate-glass film traps many impurities during diffusion. When the silicon wafer is cooled from its diffusion temperature (approximately 1100°C) these migrate to the surface due to their dramatic reduction in solubility with decreasing temperatures, thus becoming harmless with regard to recombination. The diffusion rate for these impurities, even in the average temperature range (400-800°C) is known to be considerable (see also Chapter 6). In [37] successful phosphorus gettering in polycrystalline material is described in detail. Various writers have described in detail the gettering of impurities by aluminium [38]-[40]. According to these, two effects are responsible for gettering. Firstly, the traps at the grain boundaries are saturated and secondly, a p-p+-BSF structure can form on the boundary, because the diffusion rate of aluminium along the grain boundaries is higher by orders of magnitude than in the crystalline material [41]. Recently, some authors have shown [42],[43], that a simultaneous gettering of phosphorus and aluminium provide the best results. A comprehensive overview of defects and their gettering is given by Schindler [44]. The efficiency of polycrystalline silicon solar cells has been continually improved in recent years. With the option of high efficiency technologies, efficiencies of approximately 16% are now being achieved [45]. On a laboratory scale, over 18% efficiency has been achieved [46], although on an area of 1 cm’. Efficiency on this type of small area cannot simply be transferred to larger cells, as in this case the distribution of crystal boundaries and defects plays a significant role.
Selected Solar Cell Types 8.1.6
Crystalline Silicon Thin Film Cells
8.1.6.I
Advantages and Requirements
I71
The cost of the solar cell still contributes more than 50% to the cost of the commercial solar module (see Figure 6.1). Of the 50% approximately twothirds can be attributed to the silicon material itself. Therefore an important target of research and development is to reduce these material costs. In numerous industrial and public institute laboratories, work on thin film solar cells made of crystalline silicon is at the centre of research and development. The thickness of this type of thin film solar cell should total around 10-50 vm. This is much larger than solar cells made of semiconducting compounds, which are described in a later section. In these, thicknesses are in the region of a few pm. Since silicon, unlike the semiconducting compounds described below, is an indirect semiconductor, its suitability for this type of thin film solar cell is limited, due to the low absorption of photovoltaically useful sunlight. There are, however, strong arguments in favour of silicon. Silicon will never present any resource problems [see Chapter 7, Section 7.1.11. The material is non-toxic both in the operation of solar cells and for disposal purposes. Solar cells made of crystalline silicon do not show any degradation of efficiency. The manufacturing technologies are closely related and linked with the technologies for the manufacture of semiconductor devices, both integrslted circuits and large area high performance semiconductor devices. Therefore the technologies for the production of solar cells from crystalline silicon can participate in the large pool of experience relating to the manufacture of extremely pure starting material and process technologies. In addition to the advantage of low material usage, calculations show that the efficiency of such a thin film solar cell can be increased. A thin film solar cell made of crystalline silicon, however, places additional demands on manufacturing technologies:
Owing to low absorption in the crystal, the light penetrating into the solar cell must be reflected several times at the inner boundaries and pass backwards and forwards in the Si crystal material, so that sufficient absorption takes place. The light must be locked in (optical confinement).
I72
Crystalline Silicon Solar Cells
The boundaries (front and back surface) of the solar cell must be very well passivated, to keep the recombination of charge carriers - in particular at the back surface (the side turned away from the light) - as low as possible [electrical confinement]. Unlike in a thick solar cell, significantly more charge carriers are created near to the back surface, where there is a much greater danger of undesired recombination on the surface. Since such a solar cell is not self supporting, the selection of a suitable substrate is one of the most important tasks, after depositing technologies. Many years ago Loferski [47] and Wolf [48] pointed out the theoretical high efficiency of thin film solar cells made of crystalline silicon. The authors of this book reported the most important requirements of this type of cell in 1984 [49]. The reader is referred to Figure 5.4 in this book, which demonstrates very clearly the potential of a thin film solar cell. A recent review is given in [50]. 21 n
20
8
W
>r '9
Y L
.a, 18 0
E W
17 16
Diffusion length I-,, (pm) in the base
15 14 0
1
1
1
I
1
I
50
100
150
200
250
300
Solar cell thickness (pm) Figure 8.5
Efficiency in relation to cell thickness, with diffusion length in the base being a parameter
Selected Solar Cell Types 8.1.6.2
I73
The Relationship between Electrical and Cell Parameters
In the following illustration, we show the efficiency in relation to the various cell parameters. These are: Solar cell thickness. Diffusion length of minority charge carriers in the base. Recombination velocity on the back and front surface. Optical confinement, i.e. the reflection characteristics of the inner surfaces. 8.I . 6.2.I
Solar Cell Thickness
Figure 8.5 shows the path of efficiency in relation to cell thickness. The parameters used in the calculation are: Resistivity of the base 1 Rcm. Surface concentration of the emitter 10” cm-3. Emitter penetration depth 1 pm. Shadowing and reflection losses on the emitter surface 8%. Reflection on the inner emitter surface 90%. Reflection on the inner back surface 95%. Surface recombination velocity at the emitter 1000 cm/s. Surface recombination velocity at the back surface 100 cm/s. All assumed parameters have been realised in high efficiency solar cells. In the investigations which follow, the above values are used, if not stated otherwise. We see from Figure 8.5, that very high efficiency values (for different diffusion lengths) can be achieved with cell thicknesses of 20-50 pm. In the calculations which follow, we have concentrated on one cell thickness of 30 pm, which can also be realised. 8.1.6.2.2 Back Surface Recombination Figure 8.6 shows the influence of back surface recombination on efficiency for different base diffusion lengths. High efficiency levels are only achievable if the diffusion length in the base is at least 3-10 times the cell thickness, and the back surface recombination velocity is less than 100 cm/s. Such values can only be realised using high efficiency technologies. Recombination at the Emitter Figure 8.7 shows that the emitter recombination must only amount to around 103-104 cm/s for high efficiency. Owing to the low penetration
8.1.6.2.3
Crystalline Silicon Solar Cells
174 21
-
.*I
20
@
I I ,
, ( ,, ' ( 4 ( I ,
'',' *,
........==.. 18 17 16 19
,300
,
-
13
-
10'
b.
'*,
102
'.
* ' * .
*'.
...
Diffusion length 45
* *., ' \'* in the base urn) 8'
i. r'.
30
15 : 14
106'
8..
103
104
105
106
Back surface recombination Sb& (cm/s) Figure 8.6
The influence of back surface recombination for cell thickness 30 pm with diffusion length in the base being a parameter
depth, only a small part of the total photocurrent is generated in the emitter. Lower recombination values could not be realised in any case, due to the high doping in the emitter. The illustration demonstrates very clearly the importance of good electrical confinement. Recombination at both surfaces must be suppressed as far as possible. 8.1.6.2.4 Optical Confjnement In Chapter 6 , Section 6.3.2 we considered this problem in detail. We once again refer you to references [28]-[30] in Chapter 6. Further details are also provided in reference [49] for this section. Figure 8.8 shows the high influence of inner surface reflection characteristics on efficiency. Efficiency increases from around 17% without inner reflection to almost 20% with very good reflection characteristics. The question of how high back surface reflection can be achieved in thin film solar cells has still not been answered. The above analyses have also been carried out for thin film solar cells with a thickness of 5 pm. The relationships which were found were naturally similar. A diffusion length of 50 pm is adequate for good
Selected Solar Cell Types
20
175
c
25 t 2!*0 16
E
W
14 c
I
12
10 10'
102
103
I05
104
106
Emitter recombination Sfront (cm/s) Figure 8.7
The influence of recombination on front and back surface (electrical confinement) on efficiency
efficiency, instead of the 300 pm required for 30 pm cell thickness. The results of the analyses are summed up here for the two dominant influences; Shack - recombination, and Rback- back surface reflection .
A.
Shack 2 lo6 cm/s (no BSF) Shack = lo4 cm/s average passivation Shack = 10' LBSF structure B.
-
RbackIOW 0.4 Rbackvery good
- 0.9
Cell thickness 30 pm
5 Irm
q = 13% q = 16% q = 20%
10% 14% 16%
q = 17%
12%
Tl
=
20%
16%
These considerations of the efficiencies of thin film silicon solar cells have been confirmed experimentally. With a 50 pm thick layer of monocrystalline silicon, grown epitaxially onto a insulating substrate, solar cells have been created in our institute with an efficiency of 19.2% [51]. As shown in Figure 8.9 an insulating SiO, layer is implanted onto a silicon substrate. On top of this a layer of approximately 45 pm thick monocrystalline silicon is epitaxially grown. Due to the insulating
Crystalline Silicon Solar Cells
176 20.0
$
0.9..
19.5
0'
19.0 #'
v
Reflection coefficient on the inside of the front surface
18.5
/
.-a, 0
/'
E
17.5 17.0 16.5 I 0.0
I
1
I
I
0.2
0.4
0.6
0.8
1.o
Reflection coefficient on the inside of the back surface Figure 8.8
Influence of optical confinement (inner surface reflection) on efficiency
intermediate layer the contacts for n++and p+ are both on the front. High efficiency technology was put to use in cell manufacture. 8.1.6.3
Manufacturing Technology for Si Thin Film Solar Cells
All concepts have in common that on a suitable substrate a thin silicon film must be deposited, which is almost always subject to an additional recrystallisation step. In addition, suitable technologies should be developed, facilitating a high optical confinement and low surface recombination velocities. 8.1.6.3.1 Substrate
Many alternatives are currently under investigation. These are: MG silicon (see Chapter 7, Section 7.1,1), or MG silicon with significantly reduced impurities by various gettering or float zone pulling processes. This material is called UMG silicon (upgraded metallurgical silicon). It can
Selected Solar Cell Types
Figure 8.9
177
Cross-section through a thin film solar cell on an insulating substrate. All contact grids are on the front surface
economically be used directly as a sheet material in addition to conventional techniques (rods, blocks, sawing). A further interesting substrate material is ceramic, as it can be manufactured to a high quality and can tolerate the high temperature processes, which are necessary for recry stallising and cell processes. Even the first silicon thin film cells by Barnett [52], in the late 1970s used a ceramic substrate material. To name further materials under investigation: graphite, steel, aluminium, glass and quartz. All these materials - except for silicon - are afflicted by the problem of thermal-mechanical mismatching. Before the active Si film can be deposited, the substrate must be provided with an intermediate layer, a buffer. This intermediate layer should first and foremost prevent the diffusion of impurities from the substrate into the active Si layer, while also acting as an optical reflector and serving as passivation for the back surface. Silicon dioxide, silicon nitrite and silicon carbide come under consideration as materials. Aluminium can be used as an optical reflector.
Techniques for Depositing the Active Si Layer Two possible concepts are followed: depositing from the liquid and from the vapour phase. Depositing from the liquid phase takes place using the so-called LPE technology (liquid phase epitaxy). For depositing from the vapour phase, PECVD technology (plasma enhanced chemical vapour deposition) has proved to be the best option. 8.1.6.3.2
Crystalline Silicon Solar Cells
I78
In the vast majority of cases the particle size of the crystallites immediately after depositing does not correspond with the requirements for high efficiency. The layer must be recrystallised, remelted. The float zone pulling process is suitable. The necessary melting heat can be created by laser or lamp techniques. 8.1.6.3.3 Cell Technology The manufacturing process for the p-n junction and for contacting differ only slightly from the technologies described in Chapter 7, Section 7.2. However, for a non-electrically conducting substrate, a front side contact of the base material must be made, doubling the shadowing losses. Figure 8.10 shows the two concepts.
Figure 8.10 Concepts for thin film silicon solar cells [53]
The intention behind Section 8.1.6 was to make a significant step forward in the economics of photovoltaics. Significant practical difficulties still stand in the way of realising an economical silicon cell [53]. For more detailed information on this field, the following entries in the reference list give a comprehensive overview [54]-[56]. 8.1.7
Multilayer Silicon Solar Cells
A few years ago an interesting new concept was suggested for crystalline
silicon thin film solar cells [56]. The principle and the manufacturing technologies are explained based on Figure 8.11. The schematic crosssection shows a multilayer structure of alternate n-and p-doped layers. The boundaries are highly doped (n") on the substrate side, whereas on the front surface, the side turned towards the light, the n-layer contains a
Selected Solar Cell Types
179
moderate surface concentration (n'). Both layers are extremely thin, at 0.1 vm. The total thickness of this cell has been selected as 10-20 pm.
Figure 8.1 1 Multilayer crystalline silicon cell [ 581 schematic and manufacturing
diagram During the manufacturing process,' the starting point is a substrate made, for example, of glass with a non-conducting coating. Then alternate layers of p and n are deposited with a concentration of approximately 10"
'
1. Glass substrate, 2. Layer separation, 3. Groove for first polarity, 4. Groove for second polarity, 5. Metallising.
iao
Crystalline Silicon Solar Cells
atoms/cm3 (e.g. using CVD), approximately 2 orders of magnitude higher than for conventional solar cells. The upper layer is covered by an insulator, e.g. of SIN or SiO,. Normal recrystallisation is only necessary to obtain grains on average > 3 pm. Then grooves are cut using a laser, as in the buried contact solar cell. It has recently been possible to cut these grooves with a minimum of slack [58]. Afterwards, diffusion of a dopant is used to give the grooves polarity. A second laser process is used to remove the doping which has just been applied on one side of the groove. Now the opposite polarity is diffused in. Finally, as in the case of the buried contact, electroless metallising takes place in the grooves. This multilayer cell gives the following advantages. As the individual layers are only a few pm thick, high efficiency can be achieved with low diffusion length or low charge carrier lifetime. At a permitted carrier lifetime of up to 0.1 pm, the doping of this layer may be up to 10l8atoms/cm3 and the grain boundaries can have dimensions less than 3 pm. Both permit depositing under less severe cleanliness requirements. The high doping leads to a low dark current, thus giving a higher open circuit voltage. A further advantage of this cell lies in its relative insensitivity to surface recombination. Most of the light is absorbed in layers away from the surface and the charge carriers created thus do not often come into contact with the surface. One very interesting aspect of the multilayer structure is the capacity to minimise lateral resistance losses by injection of the charge carriers between the layers due to lateral differences in voltage [59]. A twodimensional simulation of this effect shows that in cases where the diffusion lengths are greater than the thickness of the layer, the charge carriers are injected into the other layers, thus injection takes place [60]. Therefore a distance from the contact finger of up to 1 cm is permitted, with the result that shadowing is kept very low and the contribution to dark current by the metal-silicon interface is very low too. The optimal number of layers and thus the total thickness depends primarily o n the two factors optical confinement and surface recombination. We can see from [61] that with very good confinement of the light (Lambert's Reflection), two layers give the highest efficiency. If, however, specular reflection is only present on the back surface, then the optimal number of layers is approximately 7-8, only slightly dependent on the charge carrier lifetime. An the efficiency value of 17.6% has been reported [62]. This 32 pm thick cell consisted of five layers of high-grade silicon. The substrate was made of highly doped silicon, the surface of which was coated with an
Selected Solar Cell Types
181
insulating layer. It is hoped that with a 50 pm thick cell, efficiencies up to 20% will be achieved. Many technological hurdles must still be overcome to turn the theoretical possibilities into practical concepts [61].
THIN FILM SOLAR CELLS
8.2
Great efforts have been made in research and development in the field of thin film solar cells made of other materials, with cell thicknesses of a few pm. Thin film solar cells can be expected to provide cost reduction and energy savings in cell manufacture. All known semiconductor compounds [III-V or II-IV materials] are direct semiconductors, so the absorption of sunlight occurs within a crystal thickness of a few pm. For applications in terrestrial solar technology, however, these cells must have an efficiency of the same magnitude as those of crystalline silicon as well as high stability. Of the large variety of solar cell types investigated, we have selected the few which are at the forefront of current work due to the above criteria. We thus consider four types of cell in this section, these are cells made of amorphous silicon [a-Si], gallium arsenide [GaAs], cadmium telluride [CdTe], and copper-indium-diselenide [CuInSe,]. 8.2.1
Amorphous Silicon Solar Cells
Amorphous materials - glass is a typical example - differ from crystalline structures primarily because the strict periodicity of the lattice is not present. As a consequence, the normal selection rules for crystal do not apply. In particular, the absorption of light occurs directly. Amorphous silicon [a-Si] - a compound of silicon and hydrogen - has this characteristic. The atomic structure is as shown in Figure 8.12. The band gap of this semiconductor is approximately 1.7 eV, but varies between certain limits due to the hydrogen content. We will consider these solar cells in more detail due to their broad application in the consumer market. In 1969 the physical characteristics of amorphous silicon were described for the first time [63]. In 1977 the first solar cells were produced in the RCA laboratory by Carlson [64],[65]. They still had a very low efficiency of 2%. The rapid development which followed has led to efficiencies of approximately 13% today. The field of these solar cells is summarised in the references [66]-[68]. Hamakawa and Stafford provide very good detailed overviews [69],[70].
182
Crystalline Silicon Solar Cells
Figure 8.12 The atomic structure of amorphous silicon
VP
Figure 8.13 Production process of a-Si solar cells using glow discharge [ 6 5 ] . S: substrate; C, A: electrodes; VP: vacuum pump; RF: transmitter
Selected Solar Cell Types
183
The current production method for a-Si solar cells involves depositing the individual layers in a high frequency glow discharge reactor as shown schematically in Figure 8.13. Silane (SiH,) in a mixture with hydrogen is split into hydrogen and silicon. The a-Si can then be deposited onto glass or metal. The required p and n doping for the manufacture of solar cells is achieved by the addition of diborane (B,H,) or phosphine (PH,).In the case of evaporation onto glass the electrical contact is made using a conductive oxide film (TCO).Indium-Tin-Oxide (ITO)is often used for this purpose. Light
-------
20 nma(pc)-Si (Ge) : H :
Metal, TLO
f n c
*
Figure 8.14 The structure of an a-Si p-i-n solar cell [65]
An important discovery on the road to higher efficiency was that the diffusion length of the charge carriers was very strongly influenced by doping and was so extremely small that only a small part of charge carriers could be collected. The solution to this problem was an intrinsic layer (Figure 8.14), with a very thin (approximately 50 nm) p+- and n*- coating on either side. This requires the highest degree of cleanliness for process equipment and procedures. A wide space charge region is created in which such high fields exist that almost all of the charge carriers created here can reach the p-n junction. As the absorption in this cell structure takes place almost exclusively in the intrinsic film, the efficiency could be raised to more than 5% [71] for the first time. A further improvement was achieved by depositing a silicon-carbon compound (silicon carbide) onto the p+ side facing the light (by the addition of methane CH, during the production process). This compound (also a semiconductor with a band gap of over 2 eV) is transparent to light,
Crystalline Silicon Solar Cells
I84
and functions as a so-called window layer.2This overcame for the first time the 8% hurdle [72]. Then Hamakava [73] went one step further by creating two solar cells directly above one another by deposition (Figure 8.15). Owing to the intrinsic film, which was now only half as thick, together with better deposition techniques (low defect density) and with the use of antireflection films, efficiencies of 13% are currently achieved.
n-
I
Aluminium
I/
Figure 8.15 The structure of a a-Si solar cell with two intrinsic layers [40]
The critical problem of a-Si solar cells is their stability. The efficiency drops, is degraded. The degradation acts primarily on the fill factor and the short circuit current, whereas open circuit voltage remains almost constant. Degradation can be reversed, but only by exposing the cells to a temperature of approximately 160°C. This degradation was first researched by Staebler and Wronski [74]. This effect was named the Staebler-Wronski effect after them. Even today it has not been fully explained. The most probable explanation is that the recombination of light generated charge carriers causes weak silicon-hydrogen bonds to be broken in the amorphous material, thus creating additional defects, which lower the collective efficiency and increase serial resistance. Much research work is underway to explain the cause of this effect, so that it can at least be reduced by the use of technical measures [75]. One decisive advantage of the a-Si cell is that the necessary serial connection of cells can take place simultaneously during manufacture. As
This semiconductor with a high band gap is transparent to sunlight and functions like surface passivation
Selected Solar Cell Types
I85
shown in Figure 8.16 an entire layer of TC03 is first deposited onto a glass substrate, and then a stripe pattern created, for example by a laser beam. Then the a-Si solar cell structure is deposited in a reactor. Then the cells are structured, again using a laser, so that the subsequent evaporated metal has contact to the TCO on the back of the glass substrate. Finally, the evaporated metal coating must be separated at a suitable offset. It is thus clear that in this case five cells are connected in series. This effect is decisive in making a-Si solar cells dominate almost exclusively the small output market (clocks, pocket calculators, etc.).
Glass substrate
TLO
a-Si:H (Pin)
Metal
Figure 8.16 Integrated serial connection of a-Si solar cells
Currently, solar cells made of amorphous silicon make up some 20% of current annual production (measured in peak watts). Their use in high performance applications is still strictly limited due to the importance of efficiency (see Chapter 6), unless they are used more for architectonic reasons, e.g. in faGades.
8.2.2
Gallium-Arsenide Solar Cells
The semiconductor material GaAs has won widespread approval in electronics. As early as the beginning of the 1950s GaAs was used in some research laboratories as a substrate for future semiconductor devices. Current applications are mainly in the field of optoelectronics, such as diodes and laser. In the foreseeable future increased miniaturisation and faster data processing are predicted. The physical and technological aspects of this material have have been thoroughly investigated during more than 40 years.
’ Transparent Conductive Oxide
Crystalline Silicon Solar Cells
186
AM 1.5
Si
300K iAs Cd Ta
USb
P
S
A 2
L 3
Eg (aV)
Figure 8.17 Maximum solar cell efficiency for radiation of 1 sud1000 suns (300 K) versus energy gap
GaAs is also a very interesting material for photovoltaics. The energy gap of this semiconductor is 1.42 eV and, as we can see from Figure 8.17, it promises an almost optimal adaptation to solar radiation. Further advantages are: GaAs is also a direct semiconductor and therefore up to 90% of the sunlight is absorbed in a film thickness of 2 pm. The temperature dependency of efficiency in a GaAs solar cell is only one-third of that of silicon due to the higher energy gap. Furthermore, this binary semiconductor can be easily transformed into a ternary semiconductor by the addition of elements from the third or fifth group of the periodic table. This means that semiconductors with larger
Selected Solar Cell Types
187
band gaps can be produced, which can then act as a window layer, or with smaller band gaps for tandem solar cells. In addition GaAs solar cells have a much lower sensitivity to cosmic radiation than do Si solar cells. The GaAs solar cell is a cell with a p-n junction. There are currently three manufacturing processes in use. These are: Liquid phase epitaxy (LPE). Metal organic vapour phase epitaxy (MOVPE). Molecular beam epitaxy (MBE),carried out in an ultra high vacuum, therefore used almost exclusively in research and development laboratories. Sliding rod Graphite crucible
Thermojunction
Furnace
Temperature
HZ
Figure 8.18 Principal arrangement for liquid phase epitaxy of GaAs solar cells
In the first process (Figure 8.18) a molten mass of Ga is almost completely saturated with As in a graphite crucible at a temperature of approximately 850°C and dopants such as zinc and aluminium are added. For processing, this is placed with the crucible open at the bottom over an n-doped GaAs substrate. Firstly, a very small quantity of the n-GaAs is dissolved from the surface and secondly, during contact with the molten mass, zinc diffuses into the GaAs substrate thus doping a small part of the substrate surface to a p-material (creation of a p-n junction) and thirdly, within the dissolved layer near the surface some 85% of Ga is exchanged for A1 (Alo,85Gao,~5As), thus creating a semiconductor with a band gap of approximately 1.9 eV. Using this elegant method - in which all necessary layers are created in a single step - an efficiency of >22% can now be achieved (AM1.5) [76]. The process itself was described by Woodall and Hovel as early as 1977 [77].
188
Crystalline Silicon Solar Cells
Figure 8.19 The structure of a high efficiency GaAs solar cell [78]
To improve efficiency still further n'-GaAs is required on the back surface. Both epitaxy processes mentioned permit the creation of any chosen layer sequence and dopant level. The structure of one such cell by the MOVPE process is shown in Figure 8.19. This technique has been used to produce the highest efficiency yet of 25% under AM1.5 conditions, or with the same cell, 29% at 100 suns [78]. The use of a GaAs substrate is a large cost disadvantage. Great efforts have therefore been made to deposit GaAs on another substrate. One option is germanium, which has a thermal expansion mismatch of only 0.27% and therefore permits a relatively fault free precipitation of GaAs [79]. Cells produced in this manner are already used in satellite technology and possess an average efficiency of approximately 18% (AMO) and could have a big future in this field. Silicon would be very desirable as a substrate material for reasons of cost and better heat conductivity, but has an expansion mismatch of approximately 4%. High stress would occur in the epitaxy layer and thus high dislocation densities. A range of technologies is currently being tested to circumvent this problem using a buffer layer. The individual layers are heated several times and thus made stress free. A state is reached where the
Selected Solar Cell Types
189
efficiency at 100 suns is approximately 24% [80]. Figure 8.20 shows the layer structure of a GaAs/Si solar cell produced using MBE or LPE [81].
Figure 8.20 The structure of a GaAs solar cell on a silicon substrate [53]
Two problems stand in the way of increased use. One is the very high price of the GaAs cell, if it has to be built on a GaAs substrate. The use of another material for the substrate offers the best potential for development here. The second is a problem with acceptability since Ga and As are toxic substances. However, perhaps the GaAs cell is one which could be used in the concentrator application, where the cell price, even for a moderate concentration of > 30 fold, as previously mentioned, is of less importance. A further possibility for the use of GaAs may be in tandem solar cells (see Section 8.3 below). 8.2.3
Cadmium-Telluride Solar Cells
Of the binary semiconductors it only remains to describe solar cells made of CdTe. This material, with a band gap of 1.45 eV, is, like GaAs described above, an almost optimal semiconductor for the conversion of sunlight.
Crystalline Silicon Solar Cells
I90
The first work dates back to the 1960s and early 1970s, when an efficiency of 6% was achieved [82],[83]. Then work was put on hold until the 1980s, when it was taken up again by numerous laboratories around the world with different technologies. As well as the classical CVD technique, and high vacuum evaporation technique, other techniques were successfully developed such as electrolytic deposition and chemical spraying as well as screen printing. A good overview is provided by Bonnet [84]. Like G A S , CdTe is a direct semiconductor and therefore sunlight is totally absorbed in a layer of a few pm thickness. This also means, however, that recombination on the surface must be prevented. In CdTe solar cells n-CdS has proved successful as a window film. This heterojunction (two semiconductor materials with different band gaps) has the problem, however, that sunlight with a wavelength of -c 520 pm is absorbed in the window film. Therefore, other substances are currently being investigated. According to all tests to date, solar cells made of this material possess high stability. The best laboratory cells have achieved efficiencies of 10-14% [85],[86]. The advantage of this technology is that with different, relatively cost effective technologies, efficiencies of 10% can be achieved. However, the question of acceptability is just as critical as for GaAs, since cadmium is poisonous and its hazardous nature both in production and in accidents must be carefully considered. 8.2.4
Copper-Indium-Diselenide
Solar Cells
Of the different semiconductor compounds which are suitable for solar cells, e.g. the so-called chalcopyrite semiconductor, the copper-indiumdiselenide cell has been the most highly acclaimed. This was described as early as 1978 [87]. A good overview of this is provided by Schock [88] and Mitchell [89]. The fact that high efficiencies were being achieved for these thin film cells with no degradation being observed was partially responsible for the increase in research activity in this field. Figure 8.21 shows the structure of a cell of this type. A layer of approximately 1 pm thick molybdenum is deposited onto a glass substrate. Then the active layer of Cu-In-Se, is deposited with a thickness of 1-3 pm in a high vacuum using a multi layer evaporation process. As with all thin film cells a window film of ZnO (band gap approximately 3.2 eV) is then deposited onto a thin buffer layer of CdS with a thickness of 0.3 pm. The CuInSe, layer itself is polycrystalline, so the influences of grain boundaries and electronic states which exist in them strongly influence the characteristics of photocurrent and open circuit voltage. In addition, low defect densities are decisive for the very high efficiency of > 15% and these can only be achieved using high vacuum evaporation techniques. The
I91
Selected Solar Cell Types
- Al grid n+ window film n- buffer
p-absorber p+-absorbe r Back contact
Figure 8.21 Schematic layout of a CIS solar cell
cheaper screen printing technique has also been tested for the purposes of cost reduction. With a band gap of approximately 1 eV, CuInSe, is somewhat unfavourable. The optimal utilisation of solar radiation, however, is achieved by the addition of Ga into the In layer. This creates a quaternary semiconductor, the band gap of which increases continuously with increasing Ga concentrations. If the In is completely replaced, i.e. the structure is CuGaSe, the band gap achieved is approximately 1.7 eV. It is thus possible to achieve the optimal band gap of 1.4 eV. In addition the surface layers have recently been improved, both in the quality of the CdS buffer layer and the window film. Using this process several laboratories have been able to achieve an efficiency of up to 17% [901,[911. Of the numerous research works in the field of CIS cells, we want to mention those which attempt to replace selenium by sulphur [92]. Many encouraging results have already been achieved in this field. CIS is one of the main directions of attack for research in the field of thin film solar cells.
8.3
TANDEM SOLAR CELLS
For reasons of high utilisation of solar radiation it is desirable to connect several solar cells with different band gaps together in series. For this
I92
Crystalline Silicon Solar Cells
purpose the band gap of the solar cell material must reduce from the side turned to the sunlight to the back surface. For two cells, the optimum absorption of sunlight is achieved if the uppermost cell is made of a semiconductor with a band gap of 1.9 eV and the semiconductor material of the lower cell has a band gap of 1.2 eV. The upper cell then absorbs short wavelength light while the long wavelength light is allowed to pass through and create charge carriers in the lower cell. The total efficiency is approximated by taking the sum of the efficiencies of the individual cells.
Transparent el. contact
llI Glass
--
!‘I -a-Si-solar
/
+-
cell -Optical coupler C ,S I solar cell Metal Glass
Figure 8.22 Schematic structure of a four terminal tandem cell
However, the disadvantage of a serial connection of solar cells once again appears. The weakest current from both cells determines the total current and thus efficiency. By a suitable choice of band gaps it is possible to roughly equalize the individual currents for radiation at AM1.5, but if the intensity and spectrum of solar radiation changes a considerable reduction in efficiency must be expected. Therefore, instead of a two terminal contact each cell can be contacted individually. This involves an additional cost. A conductive, transparent intermediate layer must also be added. Furthermore, the electrical energy must now be managed by two electrical charge regulators instead of one. We see that tandem cells are connected with high costs and particularly complex technologies. Figure 8.22 shows the structure of a four terminal solar cell. Two of this type of tandem cells currently at the research and development stage are described here:
A GaAs tandem cell connected in series with a GaSb cell. A concentration of 200 suns produces an efficiency of approximately 35%[93].
A combination comprising a cell made of a-Si on a CIS cell, whereby the efficiency at one sun is 10%.
Selected Solar Cell Types
193
A multitude of different combinations is conceivable because it is possible to alter the band gap of many thin film cells. Kriihler gives a comprehensive overview of the entire field [94].
8.4
DYE-SENSITISED SOLAR CELLS
A semiconductor-electrolyte-contact cell can also be used to convert light energy into electrical energy. The photovoltaic effect of this type of layout was first observed by Becquerel in 1839.
Figure 8.23 The structure of a dye sensitised solar cell
A concept was developed by Gratzel in the late 1980s, which we will explain using the schematic drawing in Figure 8.23 [95]. Nanoporous TiO, is sintered at 500°C onto a glass plate, which is coated with a transparent conductive oxide (TCO). A tin oxide doped with fluorine, which has a sheet resistance of approximately 10 W O is used here as the conductive film. The significantly more conductive IT04 cannot, unfortunately, be used as it would not survive the sintering process. The semiconductor TiO, is not an option for photovoltaics due to its band gap of approximately 3 eV. It is transparent to sunlight; almost no absorption is possible. Therefore the porous TiO, structure is coated with a dye based on ruthenium, such that a monomolecular layer is created. The dye bonds chemically with the TiO, surface. Visible light can be absorbed in this dye.
Indium Tin Oxide.
194
Crystalline Silicon Solar Cells
Sunlight is almost completely absorbed by the surface of the TiO, colloids, which is now increased 1000-fold compared with a plain surface, despite the extremely low absorption in the dye layer. semiconductof
aye
ekcuolyte
metal
counrer.elecrro5e
Figure 8.24 Schematic representation of a regenerative dye sensitised cell to demonstrate cell voltage
The Ti0,-dye combination is placed in an electrolyte containing iodide and triiodide. This cell is sealed by a further layer of TCO coated glass, which is also platinum coated (using its catalytic effect). This is a very flat cell, which is not clear from Figure 8.23. The dye coated TiO, layer is only a few pm thick. The functionality of this cell is based on the fact that light is absorbed in the dye and thereb electrons are elevated to a higher energy level (Figure 8.24, process This level is above the conduction band edge of titanium dioxide. Electrons are injected into the conduction band of the TiO, from this state. This charge injection, however, is in competition with deactivation processes such as radiating and non-radiating recombination. To get a good yield from the injection, the junction from dye to TiO, must be such that the rate constant of charge injection is at least 100 times greater than the rate of deactivation in the dye. With newly developed dyes, charge injection of 90% is currently being achieved [96]. Unlike other solar cells, the electrons in TiO, are majority charge carriers, which are thus not dependent on diffusion length. The flow of electrons comes about because the electron loss from the dye is quickly replaced by the iodide in the electrolyte, because it becomes charged by giving up electrons, thus becoming triiodide ions These
(6).
(a)
(a).
Selected Solar Cell Types
I95
electrons are neutralised at the backplate electrodes (0). The missing electrons come through the outer circuit of TiO, The flow of current is thus ensured. These individually very complex processes can be found in publications [97]-[ 1001. Efficiencies of over 10% are currently being achieved. Despite the simple structure of the cell - it requires no high temperature processes, no expensive vacuum evaporation processes and no clean room technologies - there are still a number of questions which require answers. One significant problem is still long-term stability. A further question is the acceptability of liquid solar cells. Attempts have been underway for years to replace liquid electrolytes by a solid electrolyte. Conductive polymers are a starting point in the search for a solid electrolyte. However, up until now, no usable results have been achieved. Module manufacture is naturally an important question - parallel and serial connection - with the familiar problem of achieving as narrow a distribution of cell parameters as possible. This cell concept is still at the research stage.
(a).
References Sinton R. A. and Swanson R.W. IEEE-TED 34, 1987, p. 1380 Burgess et al., IEEE-TED 24, 1977, p. 432 Khemthong S. and Iles P. A., Solar Cells 6 , 1982, p. 6 Sinton R. A. et al., IEEE-Electron. Dev. Lett. 7 , 1986, p. 567 Swanson R. M. et al., IEEE-TED 31, 1984, p. 661 Lammert M. D. and Schwartz R. J., IEEE-TED 24, 1977, p. 337 King R. R. et al., Appl. Phys. Lett. 54, 1989, p. 15 Cuevas U. A., IEEE-Electron Dev. Lett. 11, 1990, p. 6 Verlinden P. J., Swanson R. M. and Crane R. A., Progress in Photovoltaik, Vol. 2, 1994, p. 153 Cuevas A., Luque A. et al., Solar Cells 3, 1981, p. 337 Luque A., Cuevas A. and Ruiz J. M., Solar Cells 2 , 1980, p. 151 Glum S. W., Knobloch J., Biro D. and Wettling W., Proc. 14th EC PV Solar Energy Con$, Barcelona, Spain, 1997, in print Hilbner A., Aberle A. G. and Hezel R., Proc. 14th EC PV Solar Energy Con/, Barcelona, Spain, 1997, in print
Crystalline Silicon Solar Cells
196
Green M. A,, Blakers A. W., Wenham S. R., Narayanan S., Willison M. R. Taouk M. and Szpitalak T., Proc. 18th IEEE PV Spec. Con$, Las Vegas, Nevada, USA, 1989, p. 39 Green M. A., High Efficiency Silicon Solar Cells, Trans Tech Publications, Switzerland, Germany, UK, USA, 1987, p. 170 Bruton T. M., Mason N. B. and Summers J. G., Proc. 6th Intern. PV Science and Engineering Con$, New Delhi, India, 1992 Mason N. B., Jordan D., Proc. 10th EC PV Solar Energy Conf: Lisbon, Spain, 1991, p. 280 Wenham S. R., Honsberg C. B. and Green M. A., Solar Energy Materials and Solar Cells, Vol. 34, 1994, p. 110 Hoffmann W. and Hezel R., Zeitschrft Elektrowijrme 45, 1987, p. 105 Jtiger K. et al. and Hezel R., Proc. 11th EC PV Solar Energy Con$, Montreux, Switzerland, 1992, p. 168 Sixt G. and Goetzberger A., ,4ppl. Phys. Lett. 19, 1971, p. 478 see [lo] Card H. C. and Yang E. S., IEEE-TED 24, 1977, p. 397 Fossum J. G. and Lindholm F. A., IEEE-TED 27, 1980, p. 692
BOhm M., Thesis, TU, Berlin, 1983 B6hm M., Scheer H. and Wagemann H. G., Solar Cells 13, 1984, p. 29 B6hm M., Kern R. and Wagemann H. G., Proc. 4th EC PV Solar Energy Con/. Stresa, Italy, 1982, p. 516 Wagemann H. G. and Eschrich H., Grundlagen der photovoltaischen Energiewandlung, Teubner Studienbkher, B.G. Teubner, Stuttgart, 1994, Lewalski N., Dissertation, Univ. Freiburg, 1987 De Pauw et al., Solid States Electr. 27, 1984, p. 573 Johnson N. M. et al., Appl. Phys. Lett., 40, 1982, p. 882 Ballutaud D. and Aucouturier M., Appl. Phys. Lett. 49, 1986, p. 1620 Ginley D. S. and Haaland D. M., Proc. 18th IEEE PV Spec. Con/, Las Vegas, Nevada, USA, 1985, p. 999 Kazmerski L. L., Proc. 18th IEEE PV Spec. C o n f , Las Vegas, Nevada, USA, 1985, p. 993 Hanoka J. I. et al., Appl. Phys. Lett. 42, 1983, p. 18
Selected Solar Cell Types
197
Tsuo Y. S. and Milstein J. B., Appl. Phys. Lett. 45, 1984, p. 971 Schrtiter W. and Kiihnapfel R., Appl. Phys. Lett. 56, 1990, p. 2207 Verhoef L. A. et al., Appl. Phys. Lett. 57, 1990, p. 2704 Rohatgi A . et al., Proc. 23rd IEEE-PV Spec. ConJ, Louisville, Kentucky, USA, 1 9 9 3 , ~ 111 . Bruton T. M., Knobloch J., Mitchel A. and Teale R. S . , Proc. 10th EC PV Solar Energy Conf.,Lisbon, Portugal, 1991, p. 667 Sandaresan R. et al., Appl. Phys. Lett. 55, 1984, p. 1162 Verhoef L. A. et a]., Appl. Phys. Lett. 57, 1990, p. 2704 Hartiti B., Mullert J. C., Siffert P. and Sarti D., Springer Proceedings in Physics, Vol. 54, Polycrystalline Semiconductors II, p. 230 Schindler R., Solid State Phenomena, Vols. 37-38 (1194), pp. 343-354 Schindler R. et al., Statusreport Photovoltaik, BEO, Julich, 1996, Section 15 Narasirnha S., Kamra S., Rohatgi A., Khattak C. P. and Ruby D., Proc. 25th IEEE PV Spec. Con$, Washington, DC, USA, 1995, p. 449 Spitzer M., Shewchun J., Vera E. S. and Loferski J. J., Proc. 14th IEEE PV Spec. Con$, San Diego, California, USA, 1980, p. 375 Wolf M., Proc. 14th IEEE PV Spec. Conf., San Diego, California, USA, 1980, p. 647 Goetzberger A,, Knobloch J. and VoR B., Technical Digest PVSEC-I, Kobe, Japan, 1984, p. 517 Goetzberger A., Proc. of the 26th IEEE PV Spec. Conf. Hebling C., Glunz S. W., Schetter C. and Knobloch J., Proc. 14th EC PV Solar Energy Con$, Barcelona, Spain, 1997, in print Barnett, A. M. and Rothwarf, A,, IEEE-TED, 27 (4), 1980, p. 615. Stocks, M. J., Cuevas, A. and Blakers, A. W., Progress in Photovoltaics, 4, 1996, p. 35 Statusreport Photovoltaik, BMBF, Projektrager BEO, Jiilich, 1996, Chapters 17 to 24
Wagner, B. F., Dissertation, Darmstadt, 1995. Werner H. J., Bergmann R. and Brendel R., Festkorperprobleme, Vol. 34, R. Helbig, p. 115
Crystalline Silicon Solar Cells
I98
Honsberg C. B. and Yun F. et al., Proc. 12th EC PV Solar Energy Con/:, Amsterdam, Netherlands, 1994, p. 63 Sproul A. B., Shi, 2. et al., First World Conference on Photovoltaic Energy Conversion, Hawaii, USA, 1994, p. 1410 Wenham S. R., Green M. A. et al., First World Conference on Photovoltaic Energy Conversion, Hawaii, USA, 1994, p. 1234 Honsberg C. B., Edmiston S. et al., First World Conference on Photovoltaic Energy Conversion, Hawaii, USA, 1994, p. 14 13 Stocks M. J., Cuevas A. and Blakers A. W., Progress in Photovoltaic, Research and Applications 4, 1996, p. 35 Green M. A. and Zhao J., 14th EC Proc. Solar Energy Con/: Barcelona, Spain, 1997, in print Chittik R. C. et al., J . Electrochem. Soc. 116, 1969, p. 77 Carlson D. E. and Wronski C. R., Appl. Phys. Lett. 28, 1976, p. 671 Carlson D. E., US Patent No. 4,064,521, 1977 Kfihler W., in Solarzellen, Meissner D., ed. Vieweg, 1993, p. 109 Fuhs W., Proc. 14th IEEE PV Spec. Conf., San Diego, California, USA, 1980, p. 59 Pankove J. I., Semiconductor and Semimetals, Vol. 21-A, Academic Press, 1985 Hamakawa Y., Proc. of Material Research SOC.,Vol. 49, 1985, p. 23 Stafford B. L. et al., Proc 21st IEEE PV Spec. Con/:, Kissimmee, Florida, USA, 1990, p. 1409
Hamakawa Y. et al., Appl. Phys. Lett. 35, 1979, p. 187 Okuda K., Abstracts of the 15th Conference on Solid State Devices and Materials, 1983, p. 189 Hamakawa Y., Proc. of the 14th IEEE-PV Spec. Con$, San Diego, California, USA, 1980, p. 1074 Staebler D. L. and Wronski C. R., Appl. Phys. Lett. 31, 1977, p. 292 Beyer W. and Wagner H., Forschungsverbund Sonnenenergie, Vols. 9 1-92, P. 9 Bett A. et al., Proc. of 22nd IEEE PV Spec. C o n j , Las Vegas, Nevada, USA, 1991, p. 137
Selected Solar Cell Types
I99
Woodall J. M. and Hovel H. S., Appl. Phys. Lett. 30, 1977, p. 492 Tobin S. P. et al., Proc. of 21st IEEE PV Spec. Con$, Kissimmee, Florida, USA, 1990, p. 158 Chu C. and Iles P. A,, Proc. of the 22nd IEEE PV Spec. Con$, Las Vegas, Nevada, USA, 199 1, p. 15 12 Vernon S. M. et al., Proc. of the 22nd IEEE PV Spec. Con$, Las Vegas, Nevada, USA, 1991, p. 3 5 3 Wettling W., in Solurzellen, Meissner, D., ed. Vieweg, 1993, p. 176 Cusano D. A,, Solid State Electronics 6, 1963, p. 217 Bonnet D. and Rabenhorst H., Proc. of the 9th IEEE PV Spec. Con$, Silver Spring, Maryland, USA, 1972, p. 129 Bonnet D., in Solurzellen, Hrsg. Meissner D., ed. Vieweg, 1993, p. 119 Mitchel K. W. et a\., Solar Cells 23, 1988, p. 49 Skorp J. et al., IEEE-TED 37, 1990, p. 434 Loferski J. et al., Proc. 13th IEEE PV Spec. Con$, Washington, DC, USA, 1978, p. 190 Schock H. W., in Solurzellen, Meissner D., ed. Vieweg, 1993, p. 44 Mitchell K. et al., Proc. 20th IEEE PV Spec. Con$, Las Vegas, Nevada, 1988, p. 889 Hedstrdm J. et al., Proc. 23rd IEEE PV Spec. Con$, Louisville, Kentucky, USA, 1993, p. 364 Zweibel K. et al., in Photovoltaic Insider's Report, Vol. XII, September, 1993 Tarrant R. and Ermer J., Proc. 23rd IEEE PV Spec. Con$, Louisville, Kentucky, USA, 1993, p. 372 Fraas L. M. et al., Proc. 21sf IEEE PV Spec. Con$, Kissimmee, Florida, USA, 1990, p. 190 Krtlhler W., in Solurzellen, Meissner D., ed. Vieweg, 1993, p. 109 Desilvestro J., Grtitzel M., et al., J. Am. Chem. SOC.107, 1985, p. 2988 0 Regan B., Moser J., Anderson M. and Grlitzel M., J . Phys. Chem. SOC. 94, 1990, p. 8720
Grtitzel M., Proc. Indian Acad. Sci., Vol. 107, No 6, 1995, p. 607
200
Crystalline Silicon Solar Cells
[98] Ferber J., Stangl R. and Luther J., Solar Energy, Materials and Solar Cells, in print [99] Hagfeldt A. and Gratzel M., Chem. Rev. 95, 1995, p. 49 [loo] Sadergreen S., Hagfeld, A,, et al., J . Phys. Chem. 98, 1994, p. 5552
Analytic and Measuring Techniques
Measuring individual parameters and determining their complex relationships is a fundamental prerequisite for the development and advancement of solar cells. The more precisely these relationships and dependencies can be determined, the more precisely can concepts for the improvement of parameters be implemented. Because of the familiar cost situation, two guiding principles must be followed. On the one hand, it is necessary to make the solar cell efficiency as high as possible; on the other hand, more cost effective technologies must be developed. An optimal compromise between cost reduction and efficiency must be achieved. It is for this reason that analysis is of such great importance.
9.1
CURRENT-VOLTAGE CHARACTERISTICS
As already mentioned, there is an international agreement that the efficiency of solar cells should be measured under the AM13 spectrum. In the laboratory, this radiation is approximated by a sun simulator. Figure 9.1 shows the block diagram for one such measuring set-up. The light source is a xenon ultra high pressure lamp, which gives an almost white spectrum, as the individual xenon spectral lines undergo a high level of pressure broadening. The high intensities which still occur in some spectral ranges are reduced by special filters to the extent that a good approximation of the AM1.5 spectrum is achieved. The intensity is calibrated using a specially calibrated solar cell, which must conform to certain requirements. Its short circuit current must be in strict proportion to radiation output. This means, for example, that diffusion length and surface recombination of the calibration cell in its field of application must be independent of the radiation. To increase measuring precision, the intensity variations of the light source are reduced by feedback of the measured intensity to the power
Crystalline Silicon Solar Cells
202 Sun simulator AM1.S
Figure 9.1
Block diagram of a sun simulator
supply. Even higher precision is achieved if the data from the test cell and the calibration cell, and thus the radiation intensity, are measured simultaneously. 9.1.1
Measuring the I-V Curve under Illumination
The current-voltage characteristic is measured by monitoring the current from the solar cell point by point from zero to the short circuit current using an electrical load regulator. From the current and voltage data measured the computer calculates: the open circuit voltage V,,, the short circuit current I,,, the current I, and voltage V, at the maximum power point, the fill factor FF, and the efficiency q. All cell parameters are thus available, which are required for an assessment of the quality of the cell and which the user needs, e.g. for the construction of modules. The actual analysis begins with the determination of the physical variables that are responsible for the solar cell parameters. Based on the discussion in the previous chapters, these are dependent upon
203
Analysis and Measuring Techniques
the the the the
dark currents or saturation currents in the emitter and base, diffusion lengths of the charge carriers, surface recombination velocities on the front and back surface, and serial and parallel resistances.
In addition, shadowing by contacts, surface reflection and long wavelength radiation, which is not absorbed, must also be determined. 9.1.2
Measuring the Dark Current Characteristic
The dark current characteristic, which determines the current-voltage characteristic line for the solar cell as a normal diode, can be found using the measuring system described above. The typical form of such a characteristic is shown in Figure 9.2. The individual ranges of the characteristic can be assigned different variables in the two diode model. The diode equation ( 5 . 2 . 2 4 ) is repeated here. V -IR,
V -IRs
In the starting region from 0 to approximately 0.15 V the two first terms in equation (9.1.1) are negligible and the dark current is thus mainly determined by the shunt resistance R p (in the logarithmically linear representation the linear proportionality is represented as a curved line). In the adjoining area (from 0.2 to 0.4 V) the dark current can be assigned to the second term of the two diode model. As already mentioned, in practice there is rarely a relationship with n,=2. In the range 0.4 to 0.6 V the dependency on the first term of the expression is dominant. If the dependency is according to n=1, then the saturation current lo,, which is responsible for open circuit voltage, can be determined from it. In the region around 0.6 V serial resistance has a considerable influence on the characteristic. Based on this assignment of the different parameters to the various regions of the dark current characteristic, the individual solar cell parameters can be determined using a fit programme for the measured dark current characteristic. Series resistance R, can be determined more precisely by using measurements under illumination as well as those in the dark. For the dark current measurement a higher voltage (V,) is required than the open circuit voltage ( V , J to obtain a current which has the same value as the short circuit current, because the additional voltage drop at the series resistance
Crystalline Silicon Solar Cells
204
Voltage (V) Figure 9.2
The typical shape of a dark current characteristic line
must be overcome. The series resistance can be determined from the difference between the two voltages: (9.1.2)
and thus
’
’
In most cases - but in particular in the case of high efficiency solar cells with a back surface point contact (LBSF) - this resistance is not identical with R, in illuminated conditions, because the flow of current differs substantially in the ‘light’ and ‘dark’ cases.
Analysis and Measuring Techniques
205
(9.1.3)
Determining the dark current characteristic offers another advantage. It can also serve to calculate the behaviour of solar cells - and therefore solar modules - in advance for different climatic conditions, such as radiation and temperature [ 1],[2]. Normally these dependencies can only be determined by measurements of the I-V curve under illumination. However by transferring the ratings from the dark current measurement to the measurement under light (superimposition principle), these relationships can be determined based on the much simpler temperature and intensity relationships of the dark current characteristic. Good predictions can thus be obtained about the energy yield of the solar plant. Since it is of great importance to know how the efficiency of solar cells depends upon temperature and radiation, we will include the calculation for temperature and intensity dependencies at this point .
9.I . 2.1
Dependence of Efficiency on Radiation
We assume that the short circuit voltage I,, (in the first approximation) is proportional to the level of radiation. We also replace Yo,in the formula for efficiency by
(9.1.4) Thus the formula for efficiency reads
(9.1.5) where Plight is the light input. The temperature dependency of the fill factor can be disregarded here. After some manipulation we find that for the relative change in efficiency
Crystalline Silicon Solar Cells
206
(9.1.6) where n is the air mass factor of light radiation [n = 1: one sun; n = 0.5: half a sun]. Introducing Vocwe find for the relative efficiency change (9.1.7) With the value for silicon of
kT 4 x
0.04
(9.1.8)
voc
we find as a rule of thumb A -r [YO] x 4xlnn (9.1.9) rl The efficiency of a silicon solar cell thus decreases, for example to approximately 3% (relative) at half the radiation intensity. 9.1.2.2
Dependence of Efficiency on Temperature
We here assume radiation and therefore short circuit voltage to be constant. The fill factor can also be assumed to be constant here. The relative change in efficiency is then equal to the relative change in open circuit voltage. So (9.1.10) where
20 7
Analysis a n d Measuring Techniques
(9.1.11) L p NrJ
We further assume that in the first approximation the temperature dependency of the diffusion length and the diffusion coefficients can be disregarded. I, then changes with the temperature only due to changes in n,. Then where ni2 = const. exp ( EgI kT)
(9.1.12)
we can write for the dark current density
Z, = B exp (-E, I k7')
(9.1.13)
where B contains several constant factors. Then where V,,%(kTlq)x ln(ZJ1,)
[ g]
Voc = k T ln4
+Eg
(9.1.14)
4
If we differentiate this equation for temperature - disregarding the small change in band gap with temperature - we find that by replacing B with an expression for V,,
(9.1.15)
As a rule of thumb we find that for silicon d(V,,) - -1 dT
T (Voc - 1.1)
(9.1.16)
and, with V,, being, for example, approximately 0.6 V, we find that at room temperature
Crystalline Silicon Solar Cells
208
(9.17)
The relative change in the open circuit voltage and thus efficiency is approximately 0.3% per degree.
SOLAR CELL SPECTRAL RESPONSE
9.2 9.2.1
Spectral Response of a Front Illuminated Solar Cell
Spectral response is defined as the dependence of the collected charge carriers (solar current) on the radiated photons of different wavelength ranges. In the case of so-called external spectral response the total number of radiated photons is counted, whereas in the internal case only those entering the crystal are counted. To determine this value the solar cell is illuminated with light from different spectral regions. The layout of this measuring instrument is shown in the block diagram Figure 9.3. The xenon high pressure lamp is again used as the light source. Its light is guided through different colour filters by a UV transparent fibre optic. The filter wheel is typically fitted with 19 filters, covering a wavelength range of 350-1019 nm (350 nm is the limit for short wavelength light, where sunlight is still present; 1019 nm is the approximate band edge of silicon; Ga-As cells can naturally also be measured because their band edge lies below the value for silicon). The band width of the individual filters is 8-10 nm.’ The light is first ‘chopped’, e.g. using a frequency a little above 100 Hz (integral multiples of the mains frequency must be avoided due to coupling mechanisms). After travelling through the filter the light is guided by a beam splitter onto the test cell (half of the light) and the reference cell (second half of the light). Here, too, specific requirements are made of the reference cell. In the intensity range from roughly 1/100 to 1/1000 sun the short circuit current must be proportional to the intensity of the radiated light. It may not be a
2
In more recent measuring systems the colour filter is replaced by a double monochromator. This permits a continuous ‘scanning’ of the total frequency range.
Analysis and Measuring Techniques
209
UV fibre
Reference cell
Oscilloscope
*lLz
compensation
I =
Figure 9.3
Block diagram of a measuring system for determining the spectral response of a solar cell
cell with a local back surface field, as the recombination velocity in these is dependent upon the number of charge camers generated, and strict linearity of the short circuit current is therefore no longer preserved. The short circuit current in both cells is measured by the ‘lock-in’ technique. The advantage of the ‘lock-in’ technique is that firstly a very small current (< lo-’ A) can be determined. Secondly, it is possible to irradiate the test cell with constant light - of very high intensity compared with spectral light - without influencing the measurement results. The dependencies of the solar cell parameters, e.g. surface recombination velocity and charge carrier lifetime, on radiation intensity can now be investigated. The measured values from the test and reference cells are fed into a PC and processed. To determine the internal spectral response it is also necessary to know the precise reflection conditions on the surface in relation to the wavelength. They must either be measured, or the measurement takes place with a polished surface, because then the theoretical reflection values can be included in the analysis [3],[4]. Figure 9.4 shows the internal spectral response of a high efficiency cell with a transparent emitter. The
Crystalline Silicon Solar Cells
210 100 90
3
80
v
93
8
70 60
2
50
-
1
0.9
.
1
1.0
1.1
1.2
Wavelength (nm) Figure 9.4
Internal spectral response of a high efficiency cell with a transparent emitter
illustration further shows the response of the emitter, the space charge region and the base in relation to the wavelength of the radiated light. Two predictions can be made from this 'fit'. The diffusion length in the base and the effective surface recombination on the back surface are responsible for the spectral response in the long wavelength region. In high efficiency cells the effect of these two variables cannot, however, be separated. Only if the diffusion length is less than the thickness of the cell can the spectral response in the long wavelength region give the effective recombination velocity. Secondly, the response in the short wavelength region permits predictions to be made about the surface recombination velocity of the emitter. As shown in Chapter 5 , this can only be determined for values greater than lo3 cm/s.
9.2.2
Spectral Response of a Back Surface Illuminated Solar Cell
In order to determine smaller surface recombination velocities as well, Lillington and Garlick [ 5 ] suggested a method which is described in what follows.
21 I
Analysis and Measuring Techniques Metal SiO, n+
p-base Local BSF SiO,
Figure 9.5
Structure of a solar cell for illumination from the rear side
In this case the test cell is not, as normal, illuminated on the emitter side, but on the opposite side. Figure 9.5 shows the cross-section of a cell produced especially for this purpose. This cell, which can be illuminated from both sides, is called a bifacial cell (see Chapter 8, Section 8.1.2). The back surface of this cell also has a finger grid in which the distance between fingers must be ten times greater than the diffusion length of the charge carriers in the base. This prevents the influence of high recombination under the contact fingers. In addition, it is also advantageous to apply a BSF under the metal coating to reduce recombination still further. The calculated internal spectral response of such a cell is shown in Figure 9.6. As the short wavelength light is absorbed near the surface and thus charge carriers are created some distance from the p-n junction, the surface recombination velocity S,, has a strong influence on spectral behaviour. We see from the illustration that values of S,, less than 10’ cm/s can still be detennined. The prerequisite for this, however, is that the diffusion length of minority charge carriers in the base is almost double the crystal thickness.
21 2
Crystalline Silicon Solar Cells
100
I
1
I
1
80
-
60
-
S,,
= 100 cm/s
1000
E
v5:
40
-
20
'01
0
300
500
I
I
700
900
1100
Wavelength (nm) Figure 9.6
9.3
Calculated internal spectral behaviour of a back surface illuminated solar cell
THE PCVD MEASUREMENT TECHNIQUE
We know from the above discussion that the diffusion lengths in high efficiency solar cells with values greater than the thickness are very difficult to determine. The process described in what follows offers an improvement. The measuring layout is shown in Figure 9.7. The process follows the principle of measuring the decay of short circuit current and open circuit voltage after prior illumination (Photo-CurrentVo 1t age-Decay) [61,[71. This dynamic measuring principle has the advantage over the above static process in that no absolute measurement of the light intensity is necessary and thus no knowledge of surface reflection must be available and the precise absorption coefficient need not to be known.
213
Analysis and Measuring Techniques
generator
Pre-amplifier Figure 9.7
Block diagram for a PCVD apparatus
The cell under investigation is excited, preferably by laser pulses. To be precise this measuring apparatus is operated by an Nd-YAg laser which emits light with a wavelength of 1064 nm. We thus obtain a consistently high level of charge carrier creation in the entire base (due to the very low absorption coefficient for this wavelength). A diode laser can also be implemented, which emits light at a wavelength of 904 nm. The decay of V,, and I,, is measured. From the different states and distributions of the charge carriers produced, the following variables can be determined: the the the the
effective surface recombination velocity of the emitter, emitter saturation current (with good passivation), diffusion length in the base, and effective surface recombination velocity on the back surface.
However, it is also true that only those recombination parameters that are dominant in the test cell can be relatively precisely determined.
Crystalline Silicon Solar Cells
214
However, it is still possible to determine the individual influencing variables in a high efficiency solar cell with good surface passivation. The test cell is first measured with the passivating surface. Then the silicon dioxide on the back surface is removed. A In-Ga friction contact is then deposited on the back surface, thus obtaining a surface recombination speed greater than lo6 cm/s. The cell is measured once again and the individual influencing variables can now be separated [8],[9].
9.4
TKE PCD METHOD
The measuring techniques described up to now all have in common that ohmic contacts must be attached to take measurements. Therefore a complete separation of recombination values, based upon the volume or originating from the surface, cannot be achieved. With the PCD method (Photo-Current-Decay) this is possible, since it does not require ohmic contacts [ 101. As shown in Figure 9.8 the silicon wafer under investigation is placed in a high frequency resonant circuit, operated at a frequency of 13.56 MHz
I
Nd YAg laser: 1064 nm, pulse
HF generator
Figure 9.8
HF bridge
Block diagram of a PCD measuring apparatus
Low pass filter
Analysis and Measuring Techniques
215
(the frequency permitted for research and industry) at about 1 mm distance. Its electrical conductivity results in the damping of the resonant circuit. The high frequency bridge is adjusted before measuring, such that the differential current in the bridge is close to zero. For the measurement, charge carrier pairs are created in the silicon wafer using a flash bulb or a laser. The conductivity of the silicon wafer is thus greatly increased, and the resulting detuning of the resonant circuit causes a bridge current. After the light source is switched off the conductivity of the silicon wafer returns to its original state, and the bridge current decays. The decay of this current is measured (the filter serves to suppress the upper harmonics). The data are picked up by a storage oscillograph and processed by a PC. This measuring process allows us to determine two parameters: (a) the emitter saturation current, and (b) the surface recombination velocity. 9.4.1
Determining the Emitter Saturation Current
This saturation current is becoming ever more important because the dominance of saturation current from the base decreases with the increasing diffusion length of the charge carriers and lowered surface recombination on the back surface. For very high efficiency the saturation current from the emitter region must therefore be reduced. To determine the emitter saturation current an n+ emitter is diffused from both sides into high resistivity p-Si (> 100 S2cm). The important point is that the cell is illuminated with such a high level intensity that high level injection occurs in the base, whereas the emitter remains in low injection due to its high dopant concentration. It follows from this that after the light source has been switched off, the recombination of charge carriers in the base is directly proportional to the carrier density, whereas the recombination rate in the emitter is proportional to the square of the carrier density. It is therefore possible to separate these two recombination effects. The carrier density at different times during the decay is found from the conductivity at the time, which is closely linked to the carrier density by mobility. Based on this data, the computer reports the decay transient for the carrier density. The result is given here, without going into the theory [ 101.
Crystalline Silicon Solar Cells
216 SO0
I
I
JK23.181 I oc = 3 . 3 ~ l O -A/crn2 ~ -rHi = 3 . 6 ~ 6 ~s ’ loo0 A
5 v
&
n
G=
b
500
0 1
I
I
6
11
Average carrier density (cm-3) Figure 9.9
16
*lo“
Decay transient for a test cell with face and back emitter [ 111
If we plot the reciprocal momentary decay time T,,,,~ against the corresponding average carrier density n, we find the following relationship:’ (9.4.1)
where T,,,,~
thli
s
w q
is is is is is
the momentary decay time, the high injection carrier lifetime, the surface recombination velocity, the thickness of the base, and the unit charge.
’ We have intentionally used the same designations as used in the above mentioned literature of Kane and Swanson [ 101.
Analysis and Measuring Techniques
21 7
From the gradient of the straight line we can find the saturation current in the emitter. This gradient is (9.4.2)
The value
thli can
be determined from the intercept of the axis.
9.4.2
Determination of the Surface Recombination Velocity
A test wafer is coated on both sides with the SiO, under investigation. Because there is no emitter, we determine 1hhli+ s/w direct. The SiO, film is then removed and the Si wafer submerged in a special container (teflon case with a transparent plastic sheet window) filled with hydrofluoric acid. The fact that the surface recombination velocity nears zero when a silicon surface is covered with pure hydrofluoric acid is used here.4 The measurement is now taken once again. The charge camer lifetime is determined directly and therefore so is the surface recombination speed. In this manner it is possible to determine firstly extremely low surface recombination speeds and secondly diffusion lengths that are significantly higher than crystal thickness [ 113.
9.5
MICROWAVE DETECTED PHOTOCURRENT DECAY
An improved method for determining the recombination parameters of a silicon sample is microwave detected photocurrent decay (MW-PCD) [12]-[15]. This differs from the inductive coupled PCD described in the preceding section in the detection method of changes in conductivity. The sample is located on a microwave antenna (see Figure 9.10) and is illuminated by pulses from a Nd-YAg laser (wavelength = 1064). The charge camers created in this manner An alter the conductivity Q of the sample by Ao:
In Section 9.5 the modem, safe technique is described. In this method the hydrofluoric acid is replaced by an iodinelethanol solution.
Crystalline Silicon Solar Cells
218
(9.5.1)
=401,+Pp)An
where /, and pp are the mobility of electrons and holes. The 2.8 GHz signal created by a microwave oscillator is guided via a circulator to the sample of thickness W and reflected from there. For a fairly small change in charge carrier concentration, the change in reflectivity is proportional to the change in charge carrier concentration. The reflected microwave signal is then guided via the circulator to a microwave detector, so that it is possible to observe the exponential charge carrier decay using the connected oscilloscope. If we now plot the measured transient in semilogarithmic scale, the decay constant can be determined by a fit from the mono-exponential part.
Microwave source
Circulator
Detector
Figure 9.10 Principle layout of MW-PCD (from [ 151)
This effective decay constant depends upon the volume lifetime ‘b and the recombination speeds on both surfaces S, and S, from [16],[17): 1 = -1+ D y ’ ‘cff
‘b
with tan(y W ) =
Y(S,
(Dy
+q - s,s,
(9.5.2)
The variable y must therefore be defined with an eigen value equation, which is dependent only upon the surface. For the case where S , = S, an approximation can be found which can be directly solved [18],[19]:
Analysis and Measuring Techniques
- a _ +
1
'eff
b'
[?.s
-+--
219
A[$
(9.5.3)
The term W/2S describes the surface influence at small values of S, and the term 1/D(W/n)*describes the surface influence at very large values of S.
Time us) Figure 9.11 Typical MW-PCD decay transient (from [ 151)
MW-PCD can be applied for very varied reasons. One important application, for example, is the determination of the bulk lifetime for different materials, since this variable, as shown in the previous chapters, is decisive for solar cell efficiency. For this, the influence of the surface recombination speeds must be reduced as far as is possible, so that the measured variable corresponds with T~ as well as possible. One method for minimizing S is the deposition of the wafer in an iodine/ethanol solution during the measurement [ 2 0 ] .After a dip in hydrofluoric acid the wafer is briefly rinsed and placed in a 1% iodine/ethanol solution and measured. Using this method recombination velocities of 1 cm/s can be achieved, i.e. the surface influence can be disregarded during the measurement and T~ is measured direct. In this manner it is not only possible to measure unprocessed starting material, but also the change in
Crystalline Silicon Solar Cells
220
bulk lifetime in silicon after various processing stages, since MW-PCD works without contact and is non-destructive. MW-PCD can also be used to determine surface recombination velocities. To determine the value of S for an SiO, film, for example, the effective lifetime of a SiO, wafer, passivated on both sides, is measured. The highest level of precision for the value of S is achieved for silicon with a high lifetime, since then T~~ is determined primarily by recombination on the surface. The passivating film is then removed from both sides and the wafer is measured in the iodine/ethanol solution (see above), so that tb can be measured. This value of T~ allows us, with the help of the equation (9.5.2), to determine the surface recombination velocity of the SiO, layer or other passivating mediums with a high degree of precision.
9.6
MODULATED CHARGE CARRIER ABSORPTION
The modulated free charge carrier absorption, MFCA [21], represents analternative method of determining minority charge carrier lifetime. An IR laser beam transmitted by the sample (hv > E,) is used to determine the charge carrier density [22],[23]. Owing to the free charge carrier absorption, the absorption of the IR laser beam at a not too high charge carrier density is directly proportional to the integral charge carrier density N (9.6.1)
where AZ is the change in laser intensity, I is the original laser intensity and K is the absorption constant for the free charge carrier absorption. This absorption constant increases quadratically with the laser wavelength used ~41.
The free charge carriers are not generated by pulses as is the case for most other methods of measuring lifetime, but sinusoidally. Since a phase displacement occurs between generation light and charge carrier dynamics, due to the lifetime of the charge carriers, the recombination parameters can be determined from this. The time dependent continuity equation serves as a basic equation for the derivation of the relationship between phase displacement Y and the recombination parameters:
221
Analysis and Measuring Techniques An - -- D- 8 A n - + G(x,t) at
ax2
(9.6.2)
‘b
where An is the time and position dependent excess charge carrier concentration, D is the diffusion constant, x is the depth coordinate, Tb is the bulk lifetime and G(x,r) is the generation function. The boundary conditions of this differential equation are given by the surface recombination velocities S , and S,, and the surface recombination rates U s , and Us2:
(9.6.3)
where W is the sample thickness. After a long calculation using a Fourier transformation we find the following complex function for the integral charge carrier density, in relation to the modulation frequency a:
where
L(0) =
(9.6.5)
The phase shift Y(o) is calculated from the quotients of the imaginary and real parts of the above expression, and the frequency dependent amplitude A(o) of charge carrier modulation from the amount:
Crystalline Silicon Solar Cells
222
v(w)
ImAN(w) Rem(o)
-tan-'
=
(9.6.6)
A(w) = IAN1
In the case of a negligible surface recombination velocity this expression can be greatly simplified to:
"(0)
=
- arctan(or,)
'b
Ah)
(9.6.7)
Figure 9.12 shows the calculated phase and amplitude distribution for different recombination parameters.
, .
I
.
. . . ....., . . , .....I . . . . .... 2
.....I
11)
83
O8
. -0c 08 5
P
k
m
-.-.-. -7-
.I
-
1ops.s -0loo )If. s 0 cmk
O.4
n
02
5
OD I
1
1M)
. . . , ....
,
I
lo00
.,
.,...I
. .,
loo00
.....I
1OOOOO
. , .. 1OOOOOO
Frequency (Hz)
Figure 9.12 Amplitude and phase curves for different recombination parameters (from [ 151)
Thus the higher the volume lifetime or the lower the surface recombination velocity, the earlier the increase in phase or the reduction in amplitude begins. Figure 9.13 shows the experimental realisation of the methods described above at ISE.
223
Analysis and Measuring Techniques
HeNe laser 3390 nm
!’
Laser diode
Signal
Reference signal
-
0
Figure 9.13 Layout of MFCA (from [ 151)
The IR beam ( h = 3.4 pm) emitted from a HeNe laser penetrates the sample and is detected by an InSb IR detector (A). At the same point of the sample, free charge carriers are generated by a GaAlAs laser diode ( h = 780 nm), the intensity of which is sinusoidally modulated. As the free charge carriers follow this modulation with a certain phase shift, the intensity of the transmitted IR laser beam also changes sinusoidally due to the absorption of IR light by the free charge carriers. The signal of the IR detector (A) is passed on by a current-voltage converter to the signal input of a ‘lock-in’ amplifier. The sinusoidal signal from the function generator, which also serves as a modulation source for the driver of the laser diode, is used as a reference for the ‘lock-in’ amplifier. To improve the signal to noise ratio, half of the IR beam is guided to a second similarly constructed IR detector (B) by a beam splitter and its signal is subtracted from the signal of the signal detector (A) so that in the ideal case the noise background of the HeNe laser is negligible. The phase shift between signal
224
Crystalline Silicon Solar Cells
Figure 9.14 Lifetime topography of a multicrystalline Si probe
and reference input of the ‘lock-in’ amplifier or the signal amplitude can now be measured for different frequencies using a computer and evaluated. As the sample is installed in an X-Y table and the IR detection beam focused at approximately 100 pm, it is possible to plot lifetime topography. Figure 9.14 shows the lifetime topography of an unprocessed multicrystalline silicon sample. The crystal structure is clearly recognisable in the measured lifetime. Although the lifetime is significantly reduced at the grain boundaries and in micro-crystalline regions, within the grains much better values are obtained. The degree to which this local lifetime fluctuation is reflected in the solar cell characteristics is of course of great interest. For this reason a solar cell is processed from the sample shown in Figure 9.14 and the short circuit current measured locally, Figure 9.15. The LBIC (Light Beam Induced Current) method used will be described in detail in the next section. A very good correspondence between the short circuit current and lifetime topography can be clearly recognised. This shows once again the increasing significance of lifetime for solar cell efficiency, but also the opportunity to use the MFCA method to determine the material quality in an unprocessed starting material.
Analysis and Measuring Techniques
225
Figure 9.15 Short circuit current topography of the same multicrystalline Si probe as in Figure 9.14
9.7
SHORT CIRCUIT CURRENT TOPOGRAPHY (LBIC)
The LBIC method (Light Beam Induced Current) allows us to show the local distribution of the short circuit current in a solar cell. It is particularly important to know this distribution in the case of polycrystalline solar cells. Figure 9.16 shows the block diagram for the measuring apparatus developed and constructed in our institute [25]. A tungsten halogen lamp is used as a light source, the light from which is chopped with a frequency of 2 kHz and transferred to the test cell via a fibre optic cable. The illuminated surface of the solar cell has a diameter of approximately 0.1 mm. The X-Y table has a minimum step size of 10 pm and permits tracing at 100 points per second also using a computer programme developed in our institute [26]. For a test cell with dimensions of 2 x 2 cm with a density of 200 x 200 points the measurement procedure is completed in approximately 7 min. The apparatus also allows the additional illumination of the test cell with constant light. A coloured filter wheel further permits the selection of the wavelength of the measuring light.
226
Crystalline Silicon Solar Cells Filter
Reference
Reflection
I
Fibre optic light guide Y
Lock-in
Computer
AID ,converter * +*
IEEE488 *-
Figure 9.16 Block diagram of an LBIC mapping measuring instrument
The short circuit current of the test cell is measured for each point illuminated. The level of current is then stored and converted for display on a screen or output to a colour printer in different colours. From the assignment of colours to currents we very clearly see the effective and less efficient regions of the solar cell. Figure 9.17 shows in black and white contrast the local distribution of the short circuit current in a solar cell made of polycrystalline Si material. In monocrystalline high efficiency solar cells with a local BSF structure, this apparatus can be used to clarify the influence range of the back surface point contacts. A wavelength is used which lies close to the band edge for silicon, in order to create as many charge carriers as possible on the back surface BSF structure. It can be demonstrated in this manner that the region of influence is greater than the diameter of a point contact. It extends by
Analysis and Measuring Techniques
22 7
Figure 9.17 LBIC picture of a multicrystalline Si solar cell
roughly the amount of the cell thickness [27].
9.8
THE DLTS PROCESS
We should briefly mention the DLTS process, developed by Lang [28]. We cannot and do not want to go into this any further and refer to the specialist literature [29],[30]. Using this method it is possible to determine an extremely low impurity concentration in a semiconductor according to type and quantity. It permits the determination of concentrations that lie up to five orders of magnitude below the dopant concentration. Furthermore, the process permits the determination of the energetic level and density of the states in a surface passivated with SO, [31],[32]. These investigations show that the surface recombination velocity depends upon the carrier density and thus the strength of the solar radiation.
Crystalline Silicon Solar Cells
228
References Baier J., Thesis, Univ. Freiburg, 1992 Raicu A,, Thesis, Univ. Freiburg, 1991 Hulthen R., Physica Scr: 12, 1975, p. 342 Phillip M. R. and Taft E. A,, Phys. Rev. 120, 1960, p. 37 Lillington P. R. and Garlick G. F. J., Proc. 18th IEEE PV Spec. C o n f , Las Vegas, 1985, p. 1677 Rose B. M. and Weaver H. T., Proc. 27th IEEE PVSpec. C o n f , Kissimmee, 1984, p. 626 Rose B. M. and Weaver H. T., J . Appl. Phys. 54, 1983, p. 238 Bergmann R., Dissertation, Univ. Freiburg, 1988 Warta W., Bergmann R. and Vol3 B., Proc. 8th EC PV Solar Energy C o n f , Florenz, 1988, p. 1416 Kane D. E. and Swanson R. M., Proc. 18th IEEE PV Spec. C o n f , Las Vegas, Nevada, USA, 1985, p. 578 Kopp J., Knobloch J. and Wettling W., Proc. Zlth EC PV Solar Energy ConJ, Montreux, Switzerland, 1992, p. 49 Oteredian T., Thesis, Univ. Delft, 1992 Creutzburg U., Thesis, Univ. Bremen, 1991 Schafthaler M., Brendel R., J . Appl. Phys. 77 (7), p. 3162 Glunz S., Thesis, Univ. Freiburg, 1995 Ehrhardt A., Wettling W. and Bett A., Appl. Phys. AS3, 1991, p. 123 Luke K. L. and Cheng L., J . Appl. Phys, 61, 1987, p. 2282 Grivickas V., Noreika D. and Tellefsen J. A., Sov. Phys. Collect. 29, 1989, p. 591 Sproul A. B., J . Appl. Phys. 76, 1994, p. 2851 Horanyi T. S., Pavelka T. and TUttd P., Appl. Surf Sci. 63, 1995, p. 1147 Glum S. W. and Warta W., J . Appl. Phys. 77, 1995, p. 3243 Sanii F., Schwartz R. J., Pierret R. F. and Au W. M., Proc. 20th IEEE PV Spec. C o n f , Las Vegas, Nevada, USA, 1988, p. 575 Waldmeyer J., J . Appl. Phys. 63, 1988, p. 1977
Analysis and Measuring Techniques
229
Schroder D. K., Semiconductor A4aterial and Device Characterization, John Wiley&Sons, New York Praschek S., Thesis, FH Mihchen, 1988 Wagner B., Thesis, TH Darmstadt, 1989 Aberle A., Thesis, Univ. Freiburg, 1991 Lang D. V., J. Appl. Phys. 45, 1974, p. 3023 Miller G. L., Lang D. V. and Kimmerling L. C., Ann. Rev. Mater. Sci., 1977, p. 377 Lefevre H. and Schulz M., J. Appl. Phys. 12, 1977, p. 45 Aberle A,, Glunz S. and Warta W., J. Appl. Phys. 71, 1992, p. 4422 Glunz S. W., Sproul A. B., Warta W. and Wettling W., J. Appl. Phys. 75 (3) 1994. p. 1611
Appendix A
LIST OF SYMBOLS Absorption coefficient Relative permittivity Efficiency Wavelength Electron mobility Hole mobility Electrical conductivity Lifetime Barrier height Resistivity Electric potential Activation energy Effective Richardson constant Air mass Speed of light in vacuum Capacity Diffusion constant Electron diffusion coefficient Solar constant Hole diffusion coefficient Energy Electric field strength
Energy at the bottom of the conduction band Fermi energy Energy at the top of the valence band Photon quantity Fill factor Generation rate Geometry factor Planck's constant Solar cell thickness Width of base Saturation current Saturation current in the 2 diode model Current from base Current from emitter Current generated by light Current at maximum power point Electron current Hole current Current from the space charge region Short circuit current
Crystalline Silicon Solar Cells
232
i k Ln
ND "i
"n
"0
"P
Electric current density Boltzmann constant Electron diffusion length Hole diffusion length Transport length Effective mass of electron Effective mass of hole Doping concentration Refraction index of the antireflection layers Acceptor concentration Effective density in the conduction band Donor concentration Intrinsic carrier dcnsity Number of electrons in the n-region Refraction index in air Number of electrons in the p-region Surface concentration Effective density of states in the valence band
P prn Pn
PP
R, s n
VLX "th
W
Electrical power Maximum power Number of holes in the n region Number of holes in the p region Elementary charge Total electric charge Recombination rate Various serial resistances Reflection coefficient Parallel resistance Serial resistance Surface recombination velocity of electrons Surface recombination velocity of holes Temperature Applied voltage Diffusion voltage Temperature voltage Voltage at maximum power point Open circuit voltage Thermal velocity Width of space charge region Penetration depth
Appendix B
PHYSICAL CONSTANTS 4
h m, k c
kT/q €0
Elementary charge = 1.602x 10 -I9 C Planck’s constant = 6 . 6 2 5 ~ JS Electron rest mass = 1.1096~10”’ kg Boltzmann’s constant = 1.381 x IO”’ J/K Speed of light in vacuum = 2 . 9 9 8 ~ lo8 m / s Thermal voltage = 0.02586 V (500 K) Permittivity in vacuum = 8 . 8 5 4 ~ 10‘” F/m
SELECTED SI PARAMETERS AT 300 K E, N, N,
Energy gap = 1.124 eV Effective density of states in the conduction band = 2 . 8 6 loL9 ~ cm” Effective density of states in the valence band = 3 . 1 0 ~ 1 0cm” ’~ “i Intrinsic carrier concentration = 1 . 0 8 10” ~ cm.’ P” Mobility of electrons (lO%rn” 300K) = 1110 crn2/Vs ,up Mobility of holes (1016cm”300K) = 410 cmZNs Y Density = 2.33 g / 6311.’ eSi/ e, Dielectric constant 11.9
INDEX
Index Terms
Links
A Absorption
29
coefficient
30
Acceptance problems
189
Acceptor
26
Activation energy
148
Antireflection coating
115
159
Antireflection process
114
159
Arrhenius curve
148
Auger coefficient
37
B Back surface field
92
Band gap
12
Band gap narrowing
96
Band structure
13
Barrier height
104
Bond, homopolar
10
Buffer layer
177
Busbar
113
This page has been reformatted by Knovel to provide easier navigation.
Index Terms
Links
C Capture cross-section
39
Charge carrier concentration
60
intrinsic density
19
lifetime
34
majority
25
minority
25
Cleaning techniques
155
Concentrator cell
163
Conduction band
12
Confinement, optical
33
Contact finger
97
Contact resistance
107
Contaminants
155
Continuity equation
45
Crystal momentum
30
Crystal pulling Crystal structure
136 30
Current forward bias
60
reverse bias
60
saturation
76
95
short circuit
69
90
69
201
Current-voltage characteristic CVD principle
135
Czochralski process
136
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Index Terms
Links
D Dark current characteristic
84
Dead layer
151
Defect level
27
Degradation
165
Diamond lattice
203
10
Diffusion coefficients
148
constant
27
current
27
length
41
technology
148
Diode equation
64
DLTS process
226
Donor
24
Doping
24
base
98
influence of
42
Double diffusion process Drift
25
151 22
E Efficiency EFG process
71
87
142
Einstein formula
29
Electrical conductivity
11
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Index Terms
Links
Electron
14
Emission
37
Emitter
73
penetration depth
90
two step
98
Energy gap
12
Energy level
12
Equivalent circuit
81
Error function distribution
144
Etching
155
anisotropic
118
isotropic
155
F Fermi-Dirac distribution
27
Fermi level
26
53
Field current
20
22
Field strength
58
peak
58
Field, electric
54
Fill factor
71
Float zone pulling
136
Foil material
143
Fresnel's formula
115
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Index Terms
Links
G Gaussian distribution Generation
141 20
Gettering
137
Glow discharge reactor
181
Grain boundary
139
170
H Hole
14
I Impurity conduction
24
Injection high
40
low
40
weak
60
Intrinsic conduction
20
K Kendall equation
44
L Lambert's reflection
120
Lattice absorption
30
Lift off technique
157
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Index Terms
Links
Light, monochromatic
73
Liquid phase epitaxy
187
Loss
90
due to non-absorbed light
120
optical
114
recombination
90
shadowing
121
Manufacturing costs
87
M
Masking
154
Mobility
20
Molecular beam epitaxy
187
MOVPE
187
O Occupation, probability Oxidation process
14 152
P p–n junction infinite
50 67
p and n neutral region
51
Passivation
94
PCVD method Phonon
211 32
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Index Terms
Links
Phosphor profile
150
Photocurrent Photolithography
90 156
Photon energy
30
Poisson's equation
45
Potential difference
51
Potential, electric
51
Pulling speed
142
Pyramids, inverted
119
R Rayleigh scattering
5
Recombination
20
Auger
36
by doping
42
radiative
35
SRH
80
via defect levels
37
Reflection factor
115
Refractioning procedure
135
Refractive index
116
Relative permittivity
25
Resistance base
102
parallel
83
series
79
sheet
108
85
113
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Index Terms
Links
Resistance (Cont.) shunt
79
85
S Segregation coefficient
139
Semiconductor
9
direct
30
indirect
32
Separation process
142
Shottky contact
103
Silicon columnar
139
metallurgic
133
polycrystalline
135
powder
143
Solar array
87
Solar cell physics
67
169
Solar cell amorphous
181
bifacial
166
buried contact
166
cadmium telluride
189
CIS
190
dye sensitised
193
gallium arsenide
185
IBIC
164
MIS
168
210
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Index Terms
Links
Solar cell (Cont.) real
72
tandem
191
thin film
170
Solar constant
5
Solid
9
Space charge
51
Space charge region
50
capacitance
57
width
57
Spectral response
210
SSP process
143
Sun simulator
201
Surface concentration
90
Surface recombination velocity
74
T Texturising
118
Thermionic effect
109
Thick film technology
158
Total charge Transport length Trap level Tunnel effect Two diode model
45 109 37 105 79
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Index Terms
Links
V Vacuum evaporation technology Valence band
157 12
Voltage built-in
82
diffusion
52
open circuit
70
thermal
52
91
W Window layer
184
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