A first principles pn junction device model has predicted new designs for high voltage, high efficiency InP solar cells. Measured InP material properties were applied and device parameters (thicknesses and doping) were adjusted to obtain optimal performance designs. Results indicate that p/n InP designs will provide higher voltages and higher energy conversion efficiencies than n/p structures. Improvements to n/p structures for increased efficiency are predicted. These new designs exploit the high absorption capabilities, relatively long diffusion lengths, and modest surface recombination velocities characteristic of InP. Predictions of performance indicate achievable open-circuit voltage values as high as 943 mV for InP and a practical maximum AM0 efficiency of 22.5 percent at 1 sun and 27 C. The details of the model, the optimal InP structure and the effect of individual parameter variations on device performance are presented

Barnett, Allen M.

Rhoads, Sandra L.

English

NASA Technical Reports Server

Modelling and Design of High Performance 
Indium Phosphide Solar Cells 
Sandra L. Rhoads 
AstroPower Division/Astrosystems, Inc. 
Allen M. Barnett 
University of Delaware 
Abs t rac t  
A first principles pn junction device model has predicted new designs for high voltage, high 
efficiency InP solar cells. Measured InP material properties were applied and device parameters 
(thicknesses and doping) were adjusted to  obtain optimal performance designs. Results indicate 
that p/n InP designs will provide higher voltages and higher energy conversion efficiencies than 
n/p structures. Improvements to n/p structures for increased efficiency are predicted. These new 
designs exploit the high absorption capabilities, relatively long diffusion lengths, and modest surface 
recombination velocities characteristic of InP. 
Predictions of performance indicate achievable open-circuit voltage values as high as 943 mV for 
InP and a practical maximum AM0 efficiency of 22.5% at 1 sun and 27OC. The details of the model, 
the optimal InP structure and the effect of individual parameter variations on device performance 
will be presented. 
Introduction 
The goal of this study was to derive InP solar cell designs yielding high open-circuit voltage 
without significantly sacrificing short-circuit current. It is appropriate to  begin such a study with a 
look at  today's InP solar cell designs. The widely accepted optimum design for InP solar cells is an 
n+/p/p+ structure offering a maximum open-circuit voltage of 902 mV for epitaxial structures [ref. 
11. However, from first principles, open-circuit voltages well above 900 mV should be achievable for 
a bandgap of 1.35 eV. The design requirements yielding maximum voltage and maximum energy 
conversion efficiency for InP solar cells are described. 
The highest efficiency InP solar cells were reported by Keavney and Spitzer [ref. 21. The device 
structure was an n+/p/p+ design formed by silicon ion implantation of epitaxial material. Wanlass 
et. al. [ref. 31 has also reported high efficiency InP solar cells fabricated using MOCVD. The device 
parameters and experimental results are shown in Table 1 and Table 2. These tables also include the 
device parameters and predicted performance of the near-optimum structure predicted by Goradia 
79 
https://ntrs.nasa.gov/search.jsp?R=19890015341 2020-03-20T01:43:13+00:00Z
[ref. 11. It is important to  note that all three designs are very similar. All have an ultrathin emitter 
layer, an emitter with a high carrier concentration and a base with a low carrier concentration. 
Theoretical Model 
The model used in this study is based on the diode equation. Reverse saturation current 
and short-circuit current are expressed as basic solutions to transport equations derived by many 
different authors [refs. 4,5] for the pn junction. This study uses standard modelling assumptions of 
one-dimensional carrier movement, low-level injection and uniform doping. It calculates the reverse 
saturation current contributed by the emitter and the base, and the short circuit current contributed 
by the emitter, base, and depletion region. These current equations describe the minority carrier 
behavior in each region of a solar cell structure. 
The expression for open-circuit voltage is of standard form - - proportional to the natural log 
of the ratio of short-circuit current and reverse saturation current. The expression used for fill factor 
is based on the ideal definition which expresses fill factor as a function of open-circuit voltage only 
[ref. 61. 
The reverse saturation current and short-circuit current values predicted by the equations de- 
scribed above include loss mechanisms inherent to InP according to  its material properties. These 
current values are sensitive to  surface recombination velocities, diffusion lengths, and minority carrier 
lifetimes which reflect material purity and quality. 
Additional corrections were made to short-circuit current and fill factor values to  account for 
device losses. Short-circuit current values were reduced by 6.6% for grid shading and reflection 
losses. Fill factor values were reduced by 2% to  account for series resistance losses. These specific 
percentages were determined for GaAs [ref. 71, however, electrical losses for InP solar cells are 
expected to be the same. 
For calculation of light generated current, detailed knowledge of the solar spectrum is required. 
The solar spectrum was divided into narrow bands such that photon flux and absorption coefficient 
could be considered constant within each band. The current generated within each band was cal- 
culated and then all band currents were summed together to  yield the current generated over the 
entire usable solar spectrum. 
Flux, as a function of wavelength, was obtained from the solar spectral-irradiance standard 
curve (AMO) [ref. 81 generated by measurements from aircraft. The total amount of power incident 
from the sun at  unit area in the orbit was determined to  be 135.3 mW/cm2. Optical constants for 
determination of absorption coefficient as a function of wavelength were obtained from the Handbook 
of Optical Constants [ref. 91. 
Values for minority carrier diffusion length as a function of carrier concentration were taken from 
experimental results published by Yamaguchi et a1 [ref. lo]. The data were determined from the 
relationship between photoluminescence intensity and carrier concentration in InP and that between 
solar cell photoresponse and carrier concentration in InP. Values for mobility as a function of carrier 
concentration were taken from experimental results published by Kuphal [ref. 111 for liquid phase 
epitaxial InP. Characterization was performed mainly by Van der Pauw and capacitance-voltage 
(C-V) measurements. 
80 
The results predicted by the device modelling studies are sensitive to  the material parameters 
(intrinsic carrier concentration, mobilities, diffusion lengths, lifetimes) assumed by the model. Great 
care was taken in this study to  use conservative values; the material parameter data  used in this 
study are more conservative than estimates used by others. The material parameters assumed for 
the optimum device designs predicted by this model are listed in Table 3. 
Baseline Study 
As a baseline test of this model, the device parameters used for the experimental devices by 
Wanlass et a1 were introduced to  our model using the material parameter data (such as mobility 
and diffusion length as a function of carrier concentration) discussed above. 
Figure 1 is a plot of the resulting open-circuit voltage and conversion efficiency values predicted 
for a wide range of emitter carrier concentrations. The conversion efficiencies predicted by Goradia 
and achieved by Spire [ref. 21 and SERI [ref. 31 have been added for comparison. Note that Goradia’s 
model and this model are in complete agreement for the given n+/p/p+ design. The experimental 
results indicate that the n+/p/p+ design described by Goradia is being successfully fabricated. 
Table 1 indicates that a major difference exists between Goradia’s model and this model in 
the material parameters of the p-type base. Mobility values are similar, however diffusion length 
and minority carriers lifetime values are extremely different for the same carrier concentration. 
Differences in performance are reflected in the predicted open-circuit voltage values shown in Table 
2. Goradia predicts lower reverse saturation currents are achievable - - open-circuit voltage is higher. 
InP Design Optimization Results 
Figure 1 indicates an upward trend in efficiency as emitter doping is lowered. By lowering the 
emitter doping and raising the base doping, the conversion efficiency predicted for the n/p design 
can be increased as shown in Figure 2. 
A further increase in efficiency can be realized if the emitter layer is expanded to  0.29 microns. 
In fact, as shown in Figure 3, efficiency actually increases with increasing emitter thickness up to 0.29 
microns. Figure 3 also illustrates that for the n/p+ design, efficiency is not extremely sensitive to 
wide variations in emitter thickness. The maximum efficiency for this design is 21.5%, corresponding 
to a 7% gain in efficiency over the traditional n+/p/p+ structure. This design maximizes current 
gain in the emitter while open-circuit voltage remains relatively constant. Table 3 provides device 
parameters for this optimized design. 
The maximum attainable voltage and efficiency for an InP solar cell is predicted for a p/n 
design. A 943 mV maximum is predicted for a 2 x 10Id base and emitter, however this is not a 
maximum efficiency design. A design with a more traditional emitter to  base doping ratio offers the 
maximum efficiency of 22.5%. This design is sensitive to  emitter thickness and requires an emit.ter 
less than or equal t o  0.07 microns. The details of the optimized p/n structure are given in Table 3. 
A careful comparison of n/p and p/n InP designs suggests a physical dependence of the InP solar 
cell on the properties of its p-type layer which determines the optimum device parameters. Table 
81 
3 reveals that the optimal p type  carrier concentration in both designs is identical - - 6 x 
The p type  material, whether it forms the emitter or the base, is the main contributor to reverse 
saturation current. For n/p designs, the only way to significantly reduce (by an order of magnitude) 
reverse saturation current is to increase base doping; this explains the n/p+ design being optimum 
rather than an n+/p design. As shown in Figure 5 ,  variations in emitter doping have no effect on 
total JO for n/p designs. 
For p/n designs, JO is still dominated by the p type  component. However, by increasing emitter 
doping (Figure 6) and decreasing base doping, saturation current can be brought to an absolute 
minimum. This explains why the p+/n is the absolute optimum device design for a high voltage, 
high efficiency InP solar cell. 
Another comparison of n/p and p/n designs is presented in Figures 7 and 8. Short-circuit 
current and open-circuit voltage values remain relatively unchanged within a certain range of surface 
recombination velocity values. For the n/p structure, the surface recombination limit is about 1 x lo3. 
For the p/n structure, the limit is about 1 x lo5. These values are in agreement with the physical 
constants listed for InP by Coutts [ref. 121. 
Figures 7 and 8 also uncover another difference between n/p and p/n InP designs. The reduc- 
tion in short-circuit current is less drastic for the p/n design as surface recombination exceeds its 
acceptable limit. Absorption in the n/p design occurs primarily in the emitter; an increase in sur- 
face recombination velocity drastically reduces the number of collectable carriers. The short-circuit 
current of the p/n design is less emitter-dependent. Significant absorption takes place within the 
depletion region and base layer where minority carrier diffusion lengths are longer; a larger numbnr 
of carriers are collected beyond the emitter layer. 
Conclusions 
The significance of this model is three fold. This model: 
(1) provides nontraditional designs for high voltage, high efficiency InP solar cells. 
(2) reveals that the p-type material (through reverse saturation current) is the key to high 
voltage, high efficiency InP solar cell performance. 
(3) supports the conversion efficiency predicted for the traditional n+/p/p+ InP solar cell. 
Acknowledgement 
Special-thanks is extended to Dr. Timothy J. Coutts for helpful discussions and for a copy of 
his InP review paper [ref. 121. 
82 
References 
[ 11 C. Goradia, J. V. Geier, and I. Weinberg, “Modelling and Design of High Efficiency Radiation 
Tolerant Indium Phosphide Space Solar Cells”, Proceedings o f fhe  19th IEEE PVSC,  New Orleans, 
Louisiana, (1987), p. 937. 
Appl. Phys. Lett. 52 (17), (1988), p. 1439. 
[ 31 M.W. Wanlass, T.A. Gessert, K.A. Emery, and T.J. Coutts, “Empirical and Theoretical Studies 
of the Performance of OMCVD InP Homojunction Solar Cells as a Function of Emitter Thickness 
and Doping, and Base Doping”, presented at this conference. 
(1983), p. 51)55. 
Academic Press, Inc., (1975), p.18. 
[ 2) C.J. Keavney and M.B. Spitzer, “Indium Phosphide Solar Cells Made by Ion Implantation”, 
[ 41 C. Hu and R.M. White, “Solar Cells: From Basic to Advanced Systems”, McGraw-Hill, Inc., 
[ 51 H.J; Hovel, Semiconductors and Semimeials, uol. 2 (Solar Cells), ed. Willardson and Beer, 
[ 61 M.A. Green, Solar Cells, Prentice-Hall, Inc., (1986), p. 80. 
[ 71 J.  B, McNeely, G. H. Negley, M. E. Nell, S. F. Brennan, A. M. Barnett, “Design and Fabrication 
[ 81 M.P. Thekaekara, “Extraterrestrial Solar Spectrum, 3000-6100 Aat l-AIntervals” , Applied Op- 
of GaAsP Top Solar Cells”, Proc. 18th IEEE PVSC,  (1985), p. 151. 
tics 13, No. 3, (1974), p.518. 
Academic Press, Inc., New York (1985), p. 503. 
[ 91 O.J. Glembocki and H. Pillar, in Handbook of Optical Constants of Solids, ed. E.D. Palik, 
[ 101 M. Yamaguchi, A. Yamamoto, N. Uchida and C. Uemura, “A New Approach for Thin Film 
InP Solar Cells”, Solar Cells, 19 (1986-1987) p. 85. 
[ 111 E. Kuphal, “Preparation and Characterization of LPE InP”, Journal of Crystal Growth, 54, 
117 (1981). 
[ 121 T.J. Coutts and M. Yamaguchi, “InP Based Solar Cells: A Critical Review of Their Fabrication, 
Performance and Operation”, Current Topics in Photovoltaics, 3, Academic Press, London, to be 
published, 1988. 
83 
TABLE 1 : Device parameters of the accepted n+/p/p+ 
optimum design. 
emitter: 
thickness (pm) 
doping (iim3) 
diffusion length (w) 
mobility (m-S) 
lifetime (nsi 
thickness (m) 
doping (vcm3) 
diffusion length (v) 
mobility (m-S) 
lifetime (ns) 
base: 
Goradla’s 
Model 
.04 
6 x l o ”  
1 .oo 
93.4 
4.19 
1 .s 
5 x 1ol6 
12.8 
3550 
17.9 
SPIRE 
Device 
.03 
3 x 1019 
------ 
e----- 
----- 
3.0 
2 x 10l6 
----__ 
------ 
e---- 
‘Intrinsic carrier concentration (n,2) = 1 .S x 1014 
This 
Model 
.025 
4 x 10’8 
0.36 
66.0 
0.76 
3.0 
5 x 10’6 
2.3 
3566 
57 
TABLE 2: Performance parameters for the accepted 
n+/p/p+ optimum deslgn. 
Goradia’s SPIRE SERl This 
Model Devlce Device Model 
VOC ( m y  901.6 873 882 883 
JSC (mA/an2) 36.53 35.7 33.06 36.2 
FF (%) 84.79 82.9 82.6 85.3 
AM0 Eff. (“A) 20.34 18.8 17.6 20.1 
84 
Table 3: New high voltage, high efficiency designs 
predicted by this model. 
emitter: 
thickness (pn) 
doping (1/m3) 
diffusion length (pn) 
mobility ( d - s )  
lifetime (ns) 
base: 
thickness (p) 
doping (I/c& 
diffusion length (p) 
mobility ( d - s )  
lifetime (ns) 
front surface rec. 
back surface rec. (WS) 
NIP 
.22 to .56 
2 x 10’6 
3.0 
145.0 
24.0 
5.0 
.80 
2292.0 
.11 
6 x 10” 
1 x i o 3  
1 x 107 
PIN 
.02 to .07 
6 x 10’’ 
.80 
2292.0 
.11 
5.0 
6 x 10l6 
2.7 
130.0 
22.0 
1 x 1 0 5  
1 x i 0 7  
Table 4: Predicted performance for the new designs 
described in Table 3. 
NIP 
Voc (mV) 901 
Jsc (mA/crn2) 37.7 
FF (Yo) 85.5 
PIN 
928 
38.2 
85.8 
Efficiency (AMO) 21.5% 22.5% 
85 
Fiaure 1 : Open-circuit voltage and efficiency predictions of 
this model assuming SERl’s emitter thickness, base 
doping, and base thickness. 
0.900 
n 
v, 
0 > 0.895 
0 
25 
0 0.890 
> 
U .- 
3 
2 .- 0.885 0 
C 
Q, a 
0.8EO 
4 
t -  
E X  
. w  
c 
t 
. . . ~ i 7 :  I 
j 
, . , . , , . ,  , 8 .  I , , ,  , /  . . . . . , /  
10 ” 10 ,“ 10 “ l C  
Emitter DopincJ (CM-3) 
10 ‘ e  
Fiaure 2: Higher efficiency is predicted for the N/P structure if 
the emitter concentration is reduced and the base 
concentration is increased. 
3 
v) 0.947 
U - 
0 > 
W 
Q) 
0 0.927 
1 
8 
i c, .- 3 2 0.907 0 .- 
t 4 a 
Eff - 
\ 117.C’ 
t 
I - _ _  * - - -  - & - - - - &  - - -  vo c ‘&. r 
\ 
.4 
I I , , , , , . , ? 7 . 0  
10 I’ 1 0  I’ 10 ” 
0.887 
Emitter Doping (cm-3) 
86 
Fiaure 3; The NIP+ design offers a wide range of acceptable 
emitter thicknesses yielding high efficiencies. 
-c, 5 0.93 : 
> 
Q, 
g0.92 1 
25 
W 
8 
c, 0.91 : 
2 
.- 
3 
.- 
0.90 4 
C 
Q) 
Q 
00.89 : 
i v o c  
, , I , L , , ,  I , , I I / . I ,  , I I I . 15  
Fiaure 4: The highest efficiency design predicted by this model 
is a P/N structure. 
- 23 
E 
07 
Fiaure 5: Jo of the optimum NIP+ design (Figure 2) is dominated 
by its base (P-type) component. 
n 
hl 
u 
E 
\ 10 -3': 
4 
v 
Y 
C 
Q) 
3 
0 
t 
0 
k 10 -": 
.- 2 lo  -'I: 
L 
U 
3 
0 cn 
10 -1'7- 
10 
Jo - Jo(b2se) 
. . 4 . 
. . \ . 4 
\ 
,.----c - - - - -  Jo(eni::er> . . +. 
8 I I . .  
I d  I d  ' I  10 'I 
Fiaure 6: Jo of the optimum PM design (Figure 4) is dominated 
by its emitter (P-type) component. 
l o  -3 
0 
Y 10 -'I .- 
U 1 /  0
VI 
10 -" ' 1 
I d  I' I d  10 'I 10 " 
Emitter Doping (cm-3) 
88 
Fiaure 7; Acceptable bounds for front surface recombination 
velocity for the optimum N/P+ design. 
n cv 
E 
W 
U 
C 
2 
L 
3 
0 
0.027 .- 
3 u 
0 
I 
0 
L 
v, 0.01 7 
I .- 
d 
L 
Fiaure 8: Acceptable bounds for front surface recombination 
velocity for the optimum P/N design. 
n cv 
0 
0.93 - 
cn 
\0.037 - 
Q C 
0.9; t 
E 
-Y 
W 
U 
.-I C " 
0 
0 0.8s 4 
2 
0 3 
I - 3 
4 0.027 
3 
0 
0 
0.87 *e 
3 
V 
0 
t 
Q, 
Q 
.- 
L 
I .- .- 
I 0.85 
0 
-t 
v, 0.017 0.83 
+ 
I 
89 


Modelling and design of high performance indium phosphide solar cells

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