Corresponding Author: Y Tabar, Tel: +221778943232 © 2018 Science IN. All rights reserved
Theoretical Study of Spectral Responses of Homojonctions Based on CuInSe
2Deposited on Substrate With or Without A Window Layer:
Effect of An Electric Field
Y. Tabar
·
M. L. Sow·
E. M. Keita·
A. A. Correa·
B. MbowLaboratory of Semiconductors and Solar Energy, Physics Department, Faculty of Science and Technology, University Cheikh Anta DIOP-Dakar-SENEGAL.
ABSTRACT
The aim of this work is to make a comparative study of the spectral response between the two models of solar cells, namely a homojonction deposited on substrate without a window layer: CuInSe2(N)/ CuInSe2(P) /CdTe(P+) and a homojonction deposited on substrate with a window layer: CdS (N+)/CuInSe2(N)/
CuInSe2(P)/CdTe(P+). In this case we will calculate the respective different expressions of the spectral response by solving the continuity equations governing the variation of the minority carriers in each region for each model and using the boundary conditions. A simulation of this quantum efficiency with the energy is done, keeping the same values of geometrical parameters. The results show that the homojonction model with a window layer and deposited on substrate gives the best quantum efficiency. The window layer decreases the losses at the surface and at the window-emitter interface and increases in the base the collection of electrons. We will then study the influence of an internal electrical field due to a doping gradient on a homojonction deposited on substrate with or without a window layer. We note that the internal quantum efficiency rises with the increasing of the additional electric field in the window layer. We also note that the best quantum efficiency is obtained with a homojonction deposited on substrate for an internal electric field of 2.10⁵Vcm-1. We remark a concordance of our results to those found in literature.
ARTICLE HISTORY Received 17-07-2018 Revised 10-09-2018 Accepted 26-09-2018 Published 26-11-2018 KEYWORDS
Thin films, CuInSe2, CdS, CdTe,
Internal quantum efficiency, Window layer and substrate effects,
Electric field
© 2018 JMSSE and Science IN. All rights reserved
Introduction
The ternary compound CuInSe₂ (CIS) of the family I-III-VI₂ presented a considerable interest [1] in solar applications for some years [2-4]. This material is presently considered as the most promising because of its forbidden band (Eg=
1.04eV). Its higher absorption coefficient α (α=10⁴-10⁵ cm⁻¹) [5-6] allows it to absorb in a wide range of the solar spectrum, from the visible to the nearest infrared. It may also change the type of conduction (N or P) without doping foreign atoms [7].
However the conversion efficiency remains limited despite the good performance of this material. It is in order to improve the quantum efficiency that we will study a homojonction of CuInSe₂ with a CdS window layer. The whole things will be deposited on a CdTe substrate. The CdS window layer will be transparent in the incident radiation [8-9] and the substrate will return the uncollected carriers to the space charge region so that they can participate in the photocurrent.
The effect of an additional electric field due to the doping gradient on a homojonction deposited on a substrate with or without a window layer was also studied in this work.
Theoretical Study
Homojunction deposited on substrate CuInSe2(N)/
CuInSe2 (P) / CdTe (P+) Modelling
In order to simulate a homojunction model corresponding to an N-P junction deposited on a doped substrate P+, we assume that the junction is between the two first layers and
that the thickness of the substrate is infinitely large compared to the others geometrical parameters.
Figures 1 and 2 respectively represent the diagram and the band diagrams of a homojunction model N-P deposited on a P+ type substrate. In Fig. 2: e2, e3 and e4 respectively represent the thicknesses of the emitter, the base and the substrate and w represents the thickness of the space charge region. In figure 1 we have x’2 = e2, x3=e2+ w + e3
and H = e2+ w + e3+ e4.
N P P+
Emitter Base
SCR Substrate
CuInSe2 CuInSe2 CdTe
x’2 w
x3
H
Figure 1: Diagram of the structure:CuInSe2(N)/
CuInSe2(P)/CdTe (P⁺)
e2 w e3 e4
CuInSe2 Eg=1,04eV
ZCE
CuInSe2 Eg=1,04eV
CdTe Eg=1,5eV N
P
P+
0 x
Emitter
Base
Substrate
Figure 2: Energy band diagram of the structure:
CuInSe2 (N)/CuInSe2(P)/CdTe (P⁺)
Quantum efficiency in the emitter layer
The continuity equation governing the variation of the holes density in the N-type emitter under static mode is given by equation (1) [10-13]:
0 2
) 2 1 2 ( 2 2
2 2
2 2
Dp x e R N Lp
p dx
p
d
(1)
Where 𝐿𝑝₂is the diffusion length of the holes in the emitter [14], 𝛼2 the absorption coefficient of CuInSe₂,
𝐷𝑝₂ the diffusion coefficient of the holes in the emitter, N:
incident photon number and R: reflection coefficient.
The general solution of equation (1) is in the form:
x Ke xLp Be xLp Ae x
p ( ) 2 2 2
2
with
) 1 (
) 1 (
2 2 2 2
2 2 2
Dp Lp
Lp R K N
The constants A and B were determined from the boundary conditions given by equations (2) and (3) [10-12]:
2 2 2
2 Sp p
dx p
Dp d
for x = 0 (2)
p2 0 for x = x’2 (3) 𝑆𝑝2is the surface recombination velocity of the emitter.
The expression of the internal quantum efficiency in the emitter is given by:
(1 )
2
2 qN R
Jp
p
(4)
2 '2 sinh 2
2 2 2 '2 cosh
'2 2 2 '2 cosh 2
2 2 2 '2 sinh 2
2 2 2 2
'2 2 2 2
2 1 2 2
2 2 2
Lp x Dp
Lp Sp Lp x
x Lp e
x Dp
Lp Sp Lp x Dp
Lp Sp Lp
x e Lp
Lp Lp p
(5)
Where, Jp2 is the photocurrent of the holes in the region 2.
This equation (5) describes the contribution of the generated holes in the emitter following photon absorption.
Quantum efficiency in the space charge region
From the current and continuity equations we calculated the current density in the space charge region to deduce the expression of the internal quantum efficiency in the space charge region. The contribution of the minority carriers in the internal quantum efficiency [15] is described by equation (6):
'2 2
1 2 x
w e zce e
(6)
Quantum efficiency in the base
The continuity equations representing the variations of generated electrons in the base and in the substrate are given by equations (7) and (8):
x Dn e
w x e
R N Ln
n dx
n
d 3
3
1) '2 3)(
( 2 ) 1 3 ( 2 3
3 2
3
2
(7)
x Dn e
x e w x e R N Ln
n dx
n
d 4
4
)3 4 (3 1) '2 3)(
(2 ) 1 4 ( 2 2
4 2
4
2
(8)
4 is the absorption coefficient of CdTe,Ln4 is the diffusion length of electrons in the substrate,Dn4 is the diffusion coefficient of electrons in the substrate.
The general solutions of equations (7) and (8) are of the type:
x e K xLn e B xLn e A x
n 3
1 3 1 3 ) 1
3(
(9)
x e K xLn e B xLn e A x
n 4
2 4 2 4 ) 2
4(
(10)
With A1 , A2 , B1and B2are constant values and K1 and K2
are given by:
3( 32 32 1)
1) '2 3)(
( 2 2 ) 3 1 3 (
1
Ln Dn
w x e
Ln R N
K
(11)
) 2 1 4 2 ( 4 4
)3 4 ( 3 1) '2 3)(
( 2 2 ) 4 1 4 (
2
Ln Dn
x e
w x e
Ln R N
K
(12)
The constants values are determined from the boundary conditions given by equations (13 to 16) [10-12]:
30
n for xx'2w1 (13)
dx n Dn d dx
n
Dn3d 3 4 4 for xx3 (14)
4
3 n
n
for xx3 (15)
40
n for xH (16)
The internal quantum efficiency
b describing the contribution of electron in the base is given by the result (17):
2 ) ' 3(
) 3 2 ) ' ( sinh(
4 3
3 ) 4 3 2 ) ' ( c osh(
) 3 2 ) ' ( c osh(
4 3
3 ) 4 3 2 ) ' ( sinh(
3 ) 3 2 ) ' ( sinh(
4 3
3 ) 4 3 2 ) ' ( c osh(
) 2 1 4 2 (4 3 3
4) 1 4 )(
2 1 3 2 (3 4 ) 4 3 4
4 3 3 (3
2 ) ' 3( 3 3
) 2 1 3 2 (3
1) '2 3)(
(2 3 3
w x e
Ln w x H Ln Dn
Ln Dn Ln
w x H
Ln w x H Ln Dn
Ln Dn Ln
w x H
H e
Ln w x H Ln Dn
Ln Dn Ln
w x H
Ln Ln
Ln Ln Ln Ln Dn
Ln Dn Ln
w x e Ln
Ln w x e Ln b
(17) The expression of the total internal quantum efficiency resulting from the contribution of the different regions of the solar cells model is given by equation (18):
total f zceb
(18)
Homojunction with window and deposited on substrate CdS(N+)/CuInSe2(N)/CuInSe2(P)/CdTe(P+) Modelling
The figures below represent the modelling of a homojonction with window layer deposited on CdTe substrate. In Fig. 4 e1, e2, e3 and e4 respectively represent the thicknesses of the window layer, the emitter, the base
and the substrate and w is the thickness of the space charge region. In Fig. 3 x1= e1, x2= e1 + e2, x3= e1+ e2 + w + e3 and H = e1 + e2 + w + e3 + e4.
N+ N P P+
Window Emitter Base
SCR Substrate
CdS CuInSe2 CuInSe2 CdTe
x1
x2 w
x3
H Figure 3: Diagram of structure CdS(N+)/CuInSe2(N)/CuInSe2(P)/CdTe(P+)
e1 e2 w e3 e4
N+ CdS
Eg=2,42eV
CuInSe2 Eg=1,04eV
SCZ
CuInSe2 Eg=1,04eV
CdTe
Eg=1,5eV
N
P
P+
0 x
Window
Emetter
Base
Substrate
Figure 4: Energy band diagram of structure CdS(N+)/CuInSe2(N)/CuInSe2(P)/CdTe(P+) Internal quantum efficiency in the window layer
The quantum efficiency in the window layer for a homojonction with window layer and deposited on substrate is the same that the emitter for the model of homojonction deposited on substrate. We have just replaced x1, α1, Lp1, Dp1 and Sp1respectively by x’2, α2, Lp2, Dp2 and Sp2.
The expression of the internal quantum efficiency in the window layer becomes:
1 sinh 1 1
1 1 1 cosh 1
1 cosh 1 1
1 1 1 sinh 1 1 1 1
1 1 1 1 1 1 1 1 1 2 1 2 1
1 1 1
Lp x Dp
Lp Sp Lp
x
Lp x Dp
Lp Sp Lp x x Dp e
Lp Sp Lp x e Lp Lp
Lp p
(19) Internal quantum efficiency in the emitter
The continuity equation governing the variation of the holes in the emitter [4] is given by:
2 0 2
)1 2 ( 1 ) 1 2 ( 2 2
2 2
2 2
x
Dp e x e R N Lp
p dx
p
d
(20)
2is the absorption coefficient of CuInSe2, 𝐿𝑝2is the diffusion length of the holes in the emitter, 𝐷𝑝2diffusion coefficient of the holes in the emitter.The general solution of equation (15) is of the type:
xLp K e x
e B xLp e A x
p 2
3 2 3 2 3 2
(21)
with A3 et B3constant values andK3 is given by
2( 22 22 1)
)1 2 ( 1 2 ) 2 1 2 (
3
Lp Dp
x e
Lp R N
K
(22)
The constant values are determined from the boundary conditions that are [3-6] :
dx p Dp d p dx Sp
p
Dp2d 2 2 2 2 1
for xx1 (23)
2 0
p for xx2 (24)
Sp is the recombination velocity at the window-emitter 2
interface. The expression of the internal quantum efficiency in the emitter
e is given by:
2 1 sinh 2 2
2 2 2
1 cosh 2
2 2 2 2
2 1 sinh 2 2
2 2 2
1 cosh 2
2 2 2
1 cosh2 2
2 2 2
1 sinh 2 1 2 2
2 2 2 2
2 2 2 1 2
)1 2 (1 2 2
Lp x x Dp
Lp Sp Lp
x x
f
x e Lp
Lp x x Dp
Lp Sp Lp
x x
x e Lp
x x Dp
Lp Sp Lp
x x x e Dp
Lp Sp Lp
Lp x e Lp
e
(25) Quantum efficiency in the space charge region
The expression of the internal quantum efficiency in the space charge region is given by [15]:
w
e x x e x
scr e ) 1 2
1 ( 2 . 2 1
1
(26)
Quantum efficiency in the base
The continuity equations for the electron variations in the base and the substrate are given by [12]:
x Dn e
w x e x e R N Ln
n dx
n
d 3
3
1) )(2 3 (2 1. 2) (1 ).
1 3 ( 2 3
3 2
3
2
(27)
e x Dn
e x w e x
e x R N Ln
n dx
n
d 4
4
)3 4 (3 1) )(2 3 (2 )1 2 (1 ) 1 4 ( 2 2
4 2
4
2
(28)
4is the absorption coefficient of the CdTe, Ln is the 4 diffusion length of the electrons in the substrate, 𝐷𝑛4diffusion coefficient of electrons in the substrate.
The general solutions of equations (23) and (24) are of the type:
x e K xLn e B xLn e A x
n 3
3 4 3 4
) 4 3(
(29)
x e K xLn e B xLn e A x
n 4
5 4 5 4 ) 5
4(
(30)
With
A
4,A
5,B
4 andB
5 constants and K4, K5 are given by:3( 32 32 1)
1) )(2 3 ( 2 )1 2 (1 2 ) 3 1 3 (
4
Ln Dn
w x e
x e
Ln R N
K
(31)
4(42 42 1)
)3 4 (3 1) )(2 3 (2 )1 2 (1 2 ) 4 1 4 (
5
Ln Dn
x e w x e x e Ln R N
K
(32)
