Using Sentaurus to Understand Superposition Failure in Thin Film Solar Cells
James E. Moore and Mark S. Lundstrom
Introduction
Ideal solar cell behavior can be described as a superposition of the dark current and a voltage independent
photocurrent (i.e. the short circuit current) according to [1].
J light (V , Gop )= J D (V )− J sc (Gop )
Measurements of thin film solar cells, however, often show superposition failure, which results in crossover
between illuminated and dark IV characteristics, making circuit modeling difficult. Superposition failure can be
explained by a violation of either of the two assumptions underlying the superposition principle. If the diode
injection current depends on photogeneration, or if the photocurrent depends on the voltage bias, superposition
failure may occur. Equation (1) can be generalized to:
J light (V , Gop )= J inj (V , Gop )− J ph (V , Gop )
Using the device simulator Sentaurus™ [2], our goal in this work is to show how the technique to separate
solar cell photo and diode injection currents introduced by Chavali [3] can be implemented in a commercial
simulation package. By simulating different solar cell structures exhibiting superposition failure, we can gain
insight into the physics behind superposition failure, which may help us design better circuit models to explain
measured data.
Theory
In this section, we will discuss the conditions under which the two assumptions underlying the
superposition principle may be invalid. Let us first investigate the assumption of bias independent photocurrent.
Photocurrent collection depends on the ability of minority carriers to reach the correct contacts of the solar cell
device where they are collected. If some minority carriers recombine in the bulk region before reaching the contacts
or at the wrong contacts then the photocurrent collection efficiency of the device will be reduced. All solar cells
separate carriers by inducing some built-in device potential Vbi,d by using two or more materials with different
workfunctions. This creates a diode and allows the separation of electrons and holes to the correct contacts using
an electric field (Fig. 1a).
When an external voltage VA is applied to the solar cell, the total potential difference across the device is
reduced. As long as VA << Vbi,d the photocurrent can usually be approximated to be voltage independent. However,
if the absorber material has a short minority carrier recombination lifetime τ, a short diffusion length will cause
photocurrent collection to depend primarily on ability of the electric field to induce drift current, and carriers
generated outside the region with an electric field may recombine before being collected. As VA increases therefore
the electric field in the device will weaken and the photocurrent will be reduced. Even for devices with low
recombination, however, voltage dependent photocurrent will decrease near VA = Vbi,d as the total potential
difference across the device approaches zero and even changes sign for VA > Vbi,d allowing some carriers to exit
the device through the wrong contacts (Fig. 1b). Most good quality devices will have long enough τ and large
enough potential difference such that Vbi,d >> Voc that this effect will not be detrimental to cell performance, but if
the collection current is significantly voltage dependent within the operating regime of the device the open circuit
voltage and fill-factor may decrease.
The second assumption of superposition principle is that the injection current of the diode is generation
independent. In most device structures photogeneration will induce a different charge distribution to that in dark.
A change in charge distribution alters the Poisson equation, which in turn will affect the solution for the total diode
current. At low bias this additional induced current is usually negligible because the generated charge distribution
is evenly distributed between electrons and holes and so does not change the band bending significantly, although
most devices will have some photogenerated charge accumulation or inversion effects at very large bias that will
affect the band bending and diode current under illumination [4]. There are also cases where the generation
dependence of the injection current becomes significant at lower bias due to charge trapping. One such example
Fig. 1 Example energy bands showing voltage dependent photocurrent collection for a p-i-n diode at a) short
circuit and b) crossover voltage (VA = Vbi,d).
is in a device such as CIGS with a window layer with minority carrier traps. In CIGS, photogenerated holes can
occupy traps in the window layer. This effect has been well documented in literature [5]. Unlike the voltage
dependent photocurrent, this effect does not usually have a significant effect on Voc, as the traps are only charged
in the dark and become neutral under illumination.
Implementation in SentaurusTM
SentaurusTM simulates the carrier distribution and carrier current for a model device by solving the
Poisson equation and the drift-diffusion and carrier continuity equations for electrons and holes:
q
p ( x )− n ( x)+ N +D ( x )− N −A ( x) ]
[
k s ϵ0
J n , p= q Dn , p ∇ (n , p)+ qμn , p E (n , p)
∂n, p
∇ J ˙n , p= q
+ Rn , p − G n , p
∂t
∇ 2 ϕ( x )= −
(
)
However, it is not ordinarily possible to extract Jinj and Jph since the solutions these equations do not distinguish
between carriers that entered the device through the contacts and those that were generated in the bulk region. We
must therefore use a more advanced technique to create a set of simulations under illuminated and dark conditions
from which these currents may be separately calculated. Our simulation package first solves the equations under
illumination for a given generation profile and range of applied voltages to find Jlight (Fig. 2). It then uses the same
Poisson solution to solve for the current in the dark, essentially “freezing” the energy bands for illuminated
conditions and then solving for the carrier profiles and currents without generation. This solution will therefore be
equivalent to the generation dependent injection current Jinj(V,Gop) for the initial generation profile under
illumination [3]. It is then straightforward to calculate the photogenerated current Jph(V,Gop) by simply subtracting
the injection current from the total illuminated current.
The implementation of this technique in Sentaurus™ is fairly simple. The Sentaurus Device Simulator™
has built-in Solve commands which allow the Poisson and electron and hole drift-diffusion equations to be solved
either as a coupled system of equations or to be solved separately. Sentaurus™ also allows the user to save and
load these solutions, so that the commands for one simulation may use the results of a previous simulation in the
solution. We can therefore solve for Jlight as usual, but save the Poisson solution to a separate file as shown in the
following example code:
set temp_filename "temp_n@node|-1@_des.sav"
Solve{ Quasistationary (
Goal {Name="p contact" Voltage= @v_max@}) {
Coupled {Poisson Electron Hole}
save(FilePrefix="light_n@node@" noOverWrite)
}
}
Given G(x), VBias
Calculates
pLight(x), nLight(x)
and φ(x) under
illumination
Calculate JLight
J
(
V
,
G
)

JV
(,
G
)

J
(
V
,
G
)
L
i
g
h
t
I
n
j
P
h
o
t
o
Set G(x) = 0
Fix φ(x)
Calculate
pDark(x),
nDark(x)
Calculate JInj
Calculate Jph
Fig. 2 Block diagram of the procedure used in the Sentaurus current separation package to calculate Jinj and Jph.
Then with the generation turned off we can solve for Jinj using the Poisson equation from the previous simulation
as follows:
Solve{
load(FilePrefix="temp_n@node|-2@")
Coupled {Electron Hole}
}
This loads the Poisson solution from the previous simulation and uses it to solve the carrier equations.
Results
We have previously simulated and reported on several different types of cell structures using the current
separation technique [5]. These structures include several devices shown in literature to show superposition failure
such as devices with Schottky barrier contacts [6], photoconductivity due to deep trap levels [3], and low built-in
potentials [7]. In this paper, we demonstrate how both photocurrent and injection current can play a role in
superposition failure by looking at two simple but interesting cases.
The first case is a very simple p-i-n structure demonstrating the effect of voltage dependent current
collection (Fig. 1). This case is a useful way to check the accuracy of our simulation, as a simple expression can
be derived for the photocurrent in this case [8]:
(
J ph (V ,G op)= qGL coth(
V − V bi
2kT
)−
2kT
V − V bi
)
We find that the simulated value for Jph matches this analytic expression very well (Fig. 3). By plotting Jlight-Jdark,
we notice a difference in current at forward bias that must come from additional injection current under
illumination. Even for this simple case there is some additional Jinj under light due to the previously discussed
photogenerated charge accumulation in high forward bias, although the effect is negligible in the operating regime
of the cell.
For the second case we will discuss the effect of the conduction band barrier in CIGS on the
photogeneration dependent injection current. This effect has been previously discussed in [9]. As before, we find
that the photogenerated current is voltage dependent with an inflection point near Vbi,d. However, there is also an
injection current caused by trapped charges generated in the CdS layer. This injection current increases sharply
near 0.6V (green curve). For the case with the smaller band offset, the injection current dominates and the effect
of the voltage dependent photocurrent is not visible in the total Jlight. However, when the band offset is increased
Jlight-Jdark
Jgen
Jph(V,Gop)
Jgen
Vbi
Fig. 3 Simulated Jlight-Jdark (blue) and Jph (red)for a p-i-n structure and comparison to analytic expression (dotted).
from 100meV to 500meV, Vbi,d proportionally decreases from 0.7V to 0.3V. The voltage dependent photocurrent
now becomes dominant at low bias, creating the well-known two diode kink effect commonly observed in this
type of device.
Conclusions
Using Sentaurus™ simulation we have demonstrated the separation of two important components of
superposition failure in solar cells. Separating the current components Jph and Jinj gives us a physical interpretation
of the difference in light and dark current that is both useful and simple to understand. These two current
components can also be used to create a physically meaningful circuit model, and in some cases can even be
represented by analytic expressions. By using this model, we hope to achieve a more accurate method of fitting
measured light and dark IV which will allow us to better understand performance losses in real solar cell devices
References
[1] N.G. Tarr and D.L. Pulfrey “An investigation of dark current and photocurrent superposition in photovoltaic devices.”
Solid State Electronics, vol. 22 pp. 265-270, 1979
[2] “Synopsys Sentaurus Semiconductor TCAD Software,” East Middlefield Road, Mountain View, CA 94043 USA.
[3] R.V.K Chavali, J.R. Wilcox, B. Ray, J.L. Gray, M.A.Alam. “Correlated Non-Ideal Effects of Dark and Light IV
Characteristics in a-Si/c-Si Heterojunction Solar Cells” IEEE Journal of Photovoltaics 2013
[4] J.E. Moore, S. Dongaonkar, R.V.K Chivali, M.A. Alam, M.S. Lundstrom “Correlation of Built-In Potential and I--V
Crossover in Thin-Film Solar Cells,” IEEE Journal of Photovoltaics Pre-print 2014
[5] G. Agostenelli, E.D. Dunlop, D.L. Batzner, A.N. Tiwari, P. Nollet, M. Burgelman, and M. Kontges “Light Dependent
Current Transport Mechanisms in Chalcogenide Solar Cells” Proceedings of the 2nd World Conference on Photovoltaic
Energy Conversion, 2003
[6] S.H. Demtsu, J.R. Sites, “Effect of back contact barrier onthin film CdTe solar cells,” Thin Solid Films, 510 pp. 320324, 2006
[7] S. Hegedus, “Current-Voltage Analysis of a-Si and a-SiGe Solar Cells including Voltage-dependent Photocurrent
Collection” Prog. in Photovoltaics vol. 5 pp. 151-168. 1997
[8] R. Sokel, R.C Hughes “Numerical analysis of transient Photoconductivity in Insulators” Journal of Applied Physics vol.
53 no. 11 pp. 7414-7424, May 1982
[9] S. Tao, J.T. McGoffin, J. Sites “"Interface-Barrier-Induced JV Distortion of CIGS Cells With Sputtered-Deposited Zn (S,
O) Window Layers." IEEE Journal of Photovoltaics vol. 4 no. 3 pp. 942-947. 2014
Jinj
Jlight
Jph
Jlight
Jinj
Jph
Fig. 4 Simulated Jinj (green) Jph (red) and Jlight(blue) for a CIGS cell with a) a 100meV band offset and b) a 500
meV band offset.