Heterojunction and graded band gap type solar cells are theoretically investigated. A computer program is developed to account for energy band gap variations and the resulting built-in electric fields which result from heterojunctions and graded energy band gaps. This program is used in studying solar cell operation under various optical irradiation conditions. Results are summarized

Hauser, J. R.

Sutherland, J. E.

English

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https://ntrs.nasa.gov/search.jsp?R=19750023496 2020-03-22T20:32:09+00:00Z
A Theoretical Study of Heterojunction and
Graded Band Gap Type Solar Cells
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Semi-Annual Status Reoort on
NASA Grant No.
NSG 1116
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J. R. Hauser and J. E. Sutherland
North Carolina State University
Electrical Engineering Department
Box 5275, Raleigh, NC 27607
September 1975
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Summary of Research
The basic objective of this research is a theoretical study of
heterojunction and graded band gap type solar cells. There is strong
theoretical and experimental evidence to suggest that heterojunction
and graded band gap solar cells can be fabricated with higher
efficiencies than obtainal)le with conventional silicon solar cells.
In this research, a comput,.r program is being developed to account for
energy band gap variations and vhe resulting built-in electric zields
which result from heterojunctions and graded energy band gaps. This
program is then to be used in studying solar cell operation under various
optical irradiation conditions. This report summarizes work which has
been accomplished to date on these objectives and plans for tt.e remainder
of the present grant period.
The basic equations describing heterojunetiors and graded band gap
solar cells can be written. as
J	 d nn = unn dx 	 (1)
dE
Jp = upp -p	 (2)
aJ
at = - U t Ge t 1 2xn	 ( 3)q
aJ
- U + G  - q ax
	
(4)	 4
ax
(c E)
 
= - q(p - n + N)
	 (5)
ax	 I
where 
EFn 
and E Fp are the electron and hole quasi-Fermi levels. These
are related to n and p as
2(6)
(1)
n = nio exp[(q,. + EFn + An)/kT]•
p = nio exp[ -(qV + E Fp - Ap)/kT],
where A
n	 p
and A are functions of position accounting for the electron
affinity, energy band gap and effective mass variations. In explicit form
these are given as
An = x c + kT tn(N 
c 
/n io ) -	 0 1
	
,	 (B)
Ap
 = - hv + 
kq 
Ln(Nv/n io ) + qVo ,	 (9)
where x  is the electron affinity, x  = x  + E  and V  is a constant
reference potential.
During the first six months of the present grant an existing
.emiconductor device analysis program has been modified to solve the
above set of device equations as well as to accept the modified geometry
of desired heterojunction solar cells. A block diagram of the sclar cell
analysis program indicating the parts which have been modified is shown
in Figure 1.
The incorporation of the graded bandgap and heterojunction equations
into the analysis program has been somewhat more involved and has taken
longer than originally anticipated. This has bean due in part to the fact
that the cells to be analyzed which are Ga xAl l-xAs cells, have both a direct
and an indirect minimum in the energy band structure. This means there are
really two classes of electrons with different mobilities and different
diffusion constants. Nowever,we have been able to demonstrate theoretically
that the basic set of equations as described above still applies to the
total density of electrons if appropriate averages of mobility, effective
mass and An values are used. Presently a paper is being prepared on this
phase of the work and will be submitted for jou_^nal publication..
3Real Applied	 Calculate"	 1 first Order
Voltage	
:?evice Parameters
Calculate trial Po7ential*	 Calculate Step
and trial Quasi-Fer"ni	 Size Across
Levels	 Device
Calculate Optical	 -alculate Mobility
	 1alculate'
Carrier	 from doping
	 Quasilinearization
Generation*
	
Coefficients (A,B)
Vd
Fead Devi :eEr t 	 stru::tureParameters
Nonlinear equation iter,ve
Calculate
Corrected
mn
s
 
d
r
Calculate Corrections
to 'L, sn , mp at each
point along device
Calculate Carrier*
YES	 Densities, Current
Densities, Total
Current and Efficiency
i
L
	
	 Accuracy
Sufficient
Printing and plotting
of results
YEL	 ,
---	
.epea,	 h0	 ind
Figure 1. Flow Diagram of Solar Cell Anal-Isis Pr-gram. *Indicates
sections of program which have been modified for heterojurction
and graded Land gap cells.
I
4At the present time the major modifications of the device analysis
program have been completed. The basic diode analysis program without
optical carrier generation has been tested on three basic types of
heterojunction and graded band gap devices as shown in Figure 2. In
case (a) the composition was •varied linearly from pure AlAs at x=0 to
pure GaAs at the p-n diode interface. Two types of abrupt heterojunctions
have been tested as shown in (b) and (c). In all three cases the program
has been found to lead to convergent solutions up to terminal voltages of
1.0 volt.
Figures 3 and 4 show calculated electron and hole densities in a
device of the type shown in Figure 2(c). For this particular device, the
heterojunction occurs 6 uM from the nt surface as seen in Figure 4 while
the p-n junction occurs at 6.5 uM. As can be seen from the plots, very
abrupt changes occur in P. and p across the heterojunction. This is for
pure AlAs on one side of the interface and pure GaAs on the other side.
Since this represents the more severe case of the Ga xAll-xAs system, no
difficulty is expected to be encountered with less abrupt heterojunctions.
The program subroutine which calculates the spatial variation of
the heterojunction/graded
separate to the main device
satisfactorily although some
is of interpolating the optical
optical generation rate has been modified for
band gap GaxAl l-xAs material and has been run
analysis program. This appears to be working
minor improvements need to be made in the meal
absorption coefficient between GaAs and AlAs.
In summary, the work is progressing satisfactorily. The major parts
of the prograrming work have been accomplished. The next step in the wort:
is to combine the optical generation data with the analysis program to solve
for the properties of heterojunction polar cells. No major problems are
expected to be encountered in accomplishing this work.
F
c
F
V
z
10
S
F.	 'I,x
AI As	 GaAs	
E
la1 Linearly goaded device
i
(b) Abrupt heterojunetion with p-n junction at interface
E c
E v
---- _ „; $ A LAs -- -',..k	 100% GaAs
-	 r
(r) kbruut heterojunction with p--n junction below interface
Figure 2. Tnree test types of heterojunction/graded band gap devices.
i	 I
6
i
I
p
10"
101,
U
^— 101 1H
Z
w0
i 05
102
r
V = 1.0 V	 r//
/ r
0.9
0.6
^	 r
^-	 0.7 r
/	 r/
/ r r	 0.o	 r/r	 r
r	 /
0.5
r	 /
I	 /
r/	
r	
0.4
r /	 1	 ^/	 ^	 1
jo	
U log
M
0	 25	 50	 75	 100	 125
LENGTH ("M)
Figure 3. Electron and hole dencitien at various applied voltages.
Surface of cell is at right at 125 wM.
_ I	 _ V = 1.0 V
0.9
0.8
^I
— 0.7
0.6
0.5
_ 0.4
10' `
U
105
102
l
~ 1011
H
CoZW0
I J
W
10°
(r
CL
U
n 1
► I E i
t m n-1 .R
7
10?0
P	
I	 _J
10"
0	 2.0	 4.0	 6.0	 8.0	 10.
LENGTH FROM N* SURFHCE ( LAM)
Figure 4. Expanded view of surface region. Heterojunction is at 6 UM,
p-n junction at 6.5 uM.


A theoretical study of heterojunction and graded band gap type solar cells

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