Towards understanding junction degradation in cadmium telluride solar cellsMarco Nardone

Citation: Journal of Applied Physics 115, 234502 (2014); doi: 10.1063/1.4883368 View online: http://dx.doi.org/10.1063/1.4883368 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/115/23?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Effect of chlorine activation treatment on electron beam induced current signal distribution of cadmium telluridethin film solar cells J. Appl. Phys. 114, 163518 (2013); 10.1063/1.4827204 Hybrid polymer solar cell based on cadmium selenide quantum dots AIP Conf. Proc. 1536, 213 (2013); 10.1063/1.4810176 Organic/inorganic hybrid pn-junction between copper phthalocyanine and CdSe quantum dot layers as solar cells J. Appl. Phys. 112, 044507 (2012); 10.1063/1.4747835 Enhanced performance of hybrid solar cells using longer arms of quantum cadmium selenide tetrapods Appl. Phys. Lett. 99, 223515 (2011); 10.1063/1.3662839 Single-crystal II-VI on Si single-junction and tandem solar cells Appl. Phys. Lett. 96, 153502 (2010); 10.1063/1.3386529

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

129.1.90.94 On: Mon, 07 Jul 2014 15:58:02

Towards understanding junction degradation in cadmium telluride solar cells

Marco Nardonea)

Department of Environment and Sustainability, Bowling Green State University, Bowling Green, Ohio 43403,USA

(Received 6 April 2014; accepted 3 June 2014; published online 17 June 2014)

A degradation mechanism in cadmium telluride (CdTe/CdS) solar cells is investigated using

time-dependent numerical modeling to simulate various temperature, bias, and illumination stress

conditions. The physical mechanism is based on defect generation rates that are proportional to

nonequilibrium charge carrier concentrations. It is found that a commonly observed degradation

mode for CdTe/CdS solar cells can be reproduced only if defects are allowed to form in a

narrow region of the absorber layer close to the CdTe/CdS junction. A key aspect of this

junction degradation is that both mid-gap donor and shallow acceptor-type defects must be

generated simultaneously in response to photo-excitation or applied bias. The numerical

approach employed here can be extended to study other mechanisms for any photovoltaic

technology. VC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4883368]

I. INTRODUCTION

The stability of thin-film photovoltaic modules remains

rather unpredictable compared to their crystalline counter-

parts.1 That uncertainty needs to be minimized if such low-

cost alternatives are to provide a significant portion of solar

electricity on a global scale.2 Similar reliability issues will

be faced by more advanced technologies that have yet to hit

the market. Predicting degradation is complicated by the fact

that it depends not only on the type of stress (light, tempera-

ture, bias, atmospheric conditions, and combinations thereof)

but also on fabrication details and transient effects. Inherent

nonuniformities (more pronounced in thin films) lead to vari-

able degradation even in devices that have been fabricated

and stressed in identical conditions. A better understanding

of the fundamental mechanisms of degradation is required to

improve stability and reduce the uncertainty in product life-

times. Understanding cell-level degradation is an essential

aspect of this challenge.

A common yet unexplained degradation mode in cad-

mium telluride (CdTe) cells is significant losses in open cir-

cuit voltage (Voc) and fill factor (FF) while the short circuit

current (Jsc) tends to remain stable (or increases in some

cases).3–5 In this work, numerical modeling is employed to

investigate a mechanism of defect generation caused by

excess charge carrier concentrations. This type of mecha-

nism has been widely investigated for other types of semi-

conductors, but remains relatively unexplored in CdTe. Our

time-dependent simulation tool is used to predict the tempo-

ral changes in performance metrics (i.e., observed degrada-

tion “modes”) under various conditions of bias, illumination,

and temperature. As such, our results serve as a semi-

quantitative guide towards understanding the underlying

cause of this particular degradation mode. We focus on

CdTe here, but our approach can be extended to any type of

PV device.

Over the past several decades, experimental studies

have uncovered important correlations between device rec-

ipes, stress conditions, and performance degradation in thin-

film PV including CdTe solar cells,3–18 hydrogenated amor-

phous silicon (a-Si:H),19–22 and Cu(In,Ga)Se2 (CIGS).23–25

The degree of understanding varies with each technology

but, in all cases, more quantitative analyses are required to

link observed correlations with underlying mechanisms.

Since we focus on CdTe devices here, an overview of experi-

mental data is provided for context.

In what follows, we will only consider uniform degrada-

tion mechanisms—those that can be described purely in one

dimension. They determine the evolution of performance in

terms of temporal changes in device parameters, such as dop-

ant/defect concentrations, carrier concentrations, and contact

barriers, as functions of position along the transversal direction

of the device while ignoring the lateral directions. Though

cells are never 1D, we may glean some important physics

from this approach. Superimposed and coupled with that 1D

perspective are nonuniform degradation mechanisms. Their

effects are 3D by nature and are related to shunting and weak

micro-diodes (regions of low Voc, but not shunted).11,26–29

Such nonuniformities are unavoidable in thin film technology

due to their unique physics and can have a significant impact

on device degradation by robbing current from a large area of

the cell or creating hot spot (runaway) instabilities.30

Nonuniform degradation is beyond the scope of the present

work.

In the previous work, 1D numerical modeling was used to

fit experimental data on photo-induced degradation in a-

Si:H22,31 to a model based on defect generation proportional to

recombination rate.32 The same model is considered herein for

the case of CdTe and shown to be an unlikely mechanism for

these devices. Numerical methods have also been employed to

study the metastable behavior of intrinsic defects in CIGS.33

To our knowledge, the work presented here is the first to

employ an explicit time-dependent solver for this type of prob-

lem; that capability is enabled by our customization of the lat-

est version of COMSOL Multiphysics.34 This simulation toola)marcon@bgsu.edu

0021-8979/2014/115(23)/234502/9/$30.00 VC 2014 AIP Publishing LLC115, 234502-1

JOURNAL OF APPLIED PHYSICS 115, 234502 (2014)

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

129.1.90.94 On: Mon, 07 Jul 2014 15:58:02

enables coupling to other physical processes such as ion diffu-

sion or tunneling/hopping transport. Broadly speaking, such

couplings will allow us to explore what stability phenomena

can or cannot be explained by a 1D, time-dependent model.

Extensions to 2D and 3D are also possible.

Ultimately, device stability is measured in terms of the

efficiency variation over time, gðtÞ ¼ VocjJscjFF=Ps, where

Ps is the input solar power. Degradation “modes” are the

observed temporal changes in performance, including the

metrics of Voc, Jsc, and FF, as well as JV curve features such

as rollover and dark/light crossover. Quantitative physical

models should elucidate the link between the observed

modes and the underlying degradation mechanism(s).

This paper is organized as follows. The general numeri-

cal modeling approach is presented in Sec. II and it is appli-

cation to a specific case of CdTe-based PV is described in

Sec. III, which includes details of the baseline cell, an over-

view of experimental findings, and a description of the deg-

radation mechanisms investigated herein. The results of the

degradation simulations are presented in Sec. IV. A discus-

sion of the results in the context of experimental observa-

tions for CdTe is presented in Sec. V followed by concluding

remarks in Sec. VI.

II. MODELING APPROACH

Studying degradation requires the use of a time-

dependent model. Changes in device parameters evolve over

time in response to stress-related conditions. For example,

the models considered here track the formation of defects as

a function of excess charge carriers, the concentrations of

which depend on light, bias, and temperature (cf. Sec. III C).

The time-dependent degradation model is coupled to the

semiconductor equations and the set of partial differential

equations are solved numerically for the dependent variables

of electron concentration, n, hole concentration, p, electric

potential V, and the degradation parameter of interest (defect

concentration, N, in this case). From there, any of the typical

performance metrics are readily calculated as functions of

time.

The simulation tool employed here is based on the cus-

tomization of COMSOL Multiphysics 4.4 (most recent ver-

sion).34 The semiconductor module in v4.4 is the first that

employs the numerical methods necessary for handling heter-

ostructures in a robust way. The Poisson equation is solved in

conjunction with the continuity equations for electron and

hole drift-diffusion currents. Either finite volume or finite ele-

ment spatial discretization methods can be employed. The

most reliable approach is to use the finite volume method

with the Scharfetter-Gummel scheme for the continuity equa-

tions. (It is typically used in semiconductor modeling soft-

ware.) The stationary solver is based on Newton’s method

which can be set to solve the system of equations as fully

coupled or segregated. Time-dependent problems are solved

using the backward differentiation formulas (BDF) method

and small signal analysis can be used to simulate capacitance

diagnostics which require the application of a small AC bias.

A review of the applicable numerical methods is available in

Ref. 35.

There are several advantages of using this platform over

existing PV software, including higher dimensional capabil-

ities, coupling to other physics modes (e.g., optical, thermal,

etc.), time-dependent and small signal analysis solvers, con-

trol of the fundamental equations, and seamless links to aux-

iliary software such as MatLab. However, it is not set up for

PV applications and our customization has added: (i) calcu-

lation of the photo-generation rate based on solving

Maxwell’s equations for any incident spectrum; (ii) calcula-

tion of defect occupancies based on capture/emission statis-

tics; and (iii) proper accounting of charged defects in the

space charge term of the Poisson equation. The input param-

eters are those that are typical of semiconductor modeling

(e.g., band gaps, electron affinities, doping, etc.) and our cus-

tomized PV outputs include standard measures such as band

diagrams, carrier concentrations, JV, and QE, (CV and Cf are

in the process of being added). While existing PV software,

such as AMPS36 and SCAPS,37 remain invaluable to the PV

research community, the COMSOL package adds many use-

ful features at a reasonable cost.

Our approach is to conduct a systematic study of degra-

dation by comparing the model predictions to available ex-

perimental data. We investigate the effects of a specific

degradation mechanism by varying stress conditions and cal-

culating the predicted time-dependent metrics, g(t), Voc(t),Jsc(t), and FF(t). The other standard PV measures can be

exhaustively analysed as well for comparison with data for

real devices stressed under similar conditions. As with all

simulators, given the large number of parameters, it is impor-

tant to employ a judicious alteration of input values. Another

issue is that more than one degradation mechanism may be

at play in real devices and distinguishing their effects may

be difficult; the approach described here may help to deter-

mine the contributions from concurrent mechanisms.

A key concern is the convergence of the numerical

solver; it becomes more of an issue as defect concentrations

increase. The COMSOL package has proven to be very reli-

able in most circumstances and the ability to ramp-up any

parameter to minimize the effects of nonlinearities in the

equations allows one to work around most convergence

issues.

III. CASE STUDY

A. Baseline cell and stress conditions

This case study focuses on CdTe PV cells based on the

Gloeckler baseline model. The cell has a superstrate structure

with layers SnO2/CdS/CdTe of thicknesses 500 nm, 25 nm,

and 4000 nm, respectively [see Ref. 38 for a detailed list of pa-

rameters]. Fig. 1 shows the basic structure and band diagram.

The correspondence between light and dark JV curves calcu-

lated using COMSOL and the well-established PV software

package SCAPS37 is shown in Fig. 2. Performance metrics for

this cell are: g¼ 16.0%, Voc¼ 0.87 V, Jsc¼ 24.1 mA/cm2, and

FF¼ 76.2%.

We also consider a slight variation of the baseline cell

by adding a 100 nm-thick layer between the CdS and CdTe

to represent the CdTe1�xSx material that forms during the

common CdTe cell fabrication process.39,40 Small

234502-2 Marco Nardone J. Appl. Phys. 115, 234502 (2014)

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

129.1.90.94 On: Mon, 07 Jul 2014 15:58:02

variations within that layer can have significant impacts on

device performance because that is where the greatest opti-

cal absorption and electric field occur. The morphology and

electronic properties in that region are unclear, but for sim-

plicity in our model, the only difference between that layer

and the bulk CdTe is that the shallow acceptor and deep do-

nor concentrations both increase from the baseline values of

Na¼Nd¼ 2� 1014 cm�3 to Na¼Nd¼ 1016 cm�3; we expect

smaller grain sizes and greater average defect concentra-

tions here. Performance metrics for this modified cell

are: g¼ 15.3%, Voc¼ 0.853 V, Jsc¼ 24.5 mA/cm2, and

FF¼ 73.2%.

The reference (“equilibrium”) condition for this study

was in the dark, with zero bias, at T¼ 300 K. Stress was

simulated either in the dark or under AM1.5G light at an in-

tensity of 100 mW/cm2. Reverse, zero, open-circuit, and for-

ward bias values were applied to the device at a range of

temperatures. Various combinations of the stress conditions

were evaluated, as discussed in Sec. IV.

B. Overview of experimental data

Concisely summarizing the observations is difficult

because all data related to degradation must be viewed in the

context of the device details, fabrication processes, and stress

conditions. For example, forward bias stress is the most det-

rimental, while short circuit conditions are the most benign.

Reverse bias can also be significant, especially related to

shunting. Similar bias dependence is observed in light and

dark conditions.6,8 It is also well established that Cu-rich

back contacts provide cells with better initial performance

but they tend to degrade more quickly than cells without

Cu.7,12 Devices with other types of back contacts (without

Cu) exhibit varying degrees of stability.14 Overall, there is

typically a wide statistical dispersion of degradation data for

similar cells. Performance improvements have also been

observed.5,11,16

Some of the common observations that can be accounted

for by the mechanism described here are as follows:

• Under short circuit or forward bias, the degradation mode

is usually strong FF loss, followed by Voc, with minimal

or no loss in Jsc. JV-curve rollover and crossover are also

typically observed.3–5

• For degraded Cu-containing cells, replacing the back con-

tact leads to partial recovery of FF loss and elimination of

rollover without improvement in Voc loss, suggesting that

Voc loss is primarily in the junction region.4

• Degradation increases with temperature with an apparent

activation energy of approximately Ea� 1 eV.6

• The same degradation modes can be caused by exposure

to electron beam, light, or bias.9,11

The range of observations can be perplexing and contra-

dictory statements are common, but we emphasize that they

depend on the details of cell processing. Our purpose is not

to present a mechanism that accounts for all the disparate

data but rather to present an effective method of analysis to

be used in conjunction with a controlled dataset. Moreover,

it will be shown that the physical model employed below can

account for several of the general trends of CdTe cell degra-

dation and is worthy of further investigation.

C. Physical model

We will consider a set of models based on excess charge

carriers as the driver of degradation. Basically, excess charge

carriers (electrons and/or holes) cause new defects to form,

which increases recombination and alters the built-in field.

In turn, those changes affect charge carrier concentrations

and a feedback loop is established. This type of degradation

mechanism is well-know in many types of semiconductors,41

but has not received much attention with respect to CdTe

(with the exception of Ref. 9).

The defect generation rate can be linear or quadratic in

the nonequilibrium charge carrier concentration. The linear

rate equation is given by

FIG. 1. Device structure and energy band diagram for the baseline cell under

AM1.5G, 1-sun light at short circuit conditions. Energy is referenced to the

vacuum level.

FIG. 2. Light and dark JV curves for the baseline cell38 calculated using

both COMSOL and SCAPS. COMSOL is able to reproduce the SCAPS

simulation.

234502-3 Marco Nardone J. Appl. Phys. 115, 234502 (2014)

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

129.1.90.94 On: Mon, 07 Jul 2014 15:58:02

dN

dt¼ an� bN; (1)

where a and b are, respectively, defect creation and annihila-

tion rates, and n can represent either electron or hole concen-

trations. The term with b accounts for annealing effects that

lead to saturation or reversal of defect formation. Both a and

b are material parameters that are temperature activated and

depend on the type of defect being considered.

The coupling of Eq. (1) with n can be established through

the quasi-stationary approximation, dn/dt¼G�CnNn� 0,

where G is the generation rate, and Cn is the recombination

coefficient. Solving the coupled equations results in an

exponential time dependence for N(t) that saturates at

N1 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiaG=Cnb

p. To simplify our discussion, consider the

short time approximation, when saturation is insignificant (bt� 1). In that case, the linear model yields the following

defect generation rate

N ¼ N0 1þ t=s½ �1=2; (2)

where N0 is the initial defect concentration and the character-

istic degradation time is s ¼ N20Cn=ð2aGÞ.

We will also consider two forms of higher order

kinetics: (i) quadratic in electron concentration, and (ii) pro-

portional to the recombination rate or electron-hole product

np. In the approximation of low annealing, the rate equation

for the quadratic model is

dN

dt¼ an2: (3)

Defect generation proportional to n2 (electrons or holes) can

be associated with the formation of certain types of defects,

such as negative-U, AX, or DX centers, which have been

studied using first principles methods in CIGS42 and

CdTe.43–45

The recombination-based model is predominantly men-

tioned in the literature for a:Si–H, where defect generation is

enabled by the energy released during recombination of free

electrons and holes. The generation rate (again, neglecting

annealing) is then given by32

dN

dt¼ aCnp � aR; (4)

where C is the overall transition probability for np annihila-

tion and R is the recombination rate. Note that the units of aare different in the different models. The quasi-stationary

balance conditions give the carrier concentrations as

n¼G/CnN and p¼G/CpN, yielding the defect generation

rate

N ¼ N0 1þ t=s½ �1=3: (5)

The characteristic time is different in this case and depends

more strongly on the generation rate: s ¼ N20CnCp=ð3aG2Þ.

The result of Eq. (5) can be reduced to the more familiar de-

pendence in the a-Si:H literature, NðtÞ � cswG2=3t1=3, where

csw is the Staebler-Wronski coefficient. It fits the degradation

data for a-Si:H well over a limited range.32 More comprehen-

sive defect rate equations and the notion of dispersive behav-

ior in disordered systems have led to stretched exponential

time dependence which fits a wider range of data related to a-

Si:H.41

The analytical treatment assumes that recombination

coefficients are independent of defect concentrations and

their occupancies. That assumption is not required in the nu-

merical approach because the solver calculates recombina-

tion rate, R, based on the Shockley-Read-Hall (SRH) model

with occupation statistics of defect states. Another critical

point is that the numerical approach considers the spatial de-

pendence of all parameters, while the analytical estimates

assume spatially uniform values. This is an important differ-

ence because the location of new defects can be just as im-

portant as concentration with respect to the degradation rate

and observed mode. In other words, a numerical approach is

required to predict the losses in g, Voc, Jsc, FF, and other

metrics, which will help to elucidate underlying mechanisms

and connect reliability issues to fabrication parameters.

At this point, the microscopic nature of the defects,

including the associated lattice reconfigurations and density

of states in the band gap, will not be considered; this work

focuses on the predictions of the degradation model based on

the evolution of generic defects. Specific defect parameters

could be included, but at this point the number of tunable pa-

rameters should be minimized. A discussion of microscopic

models and experimental evidence for a wide variety of

semiconductors (both crystalline and noncrystalline) is pro-

vided in the review by Redfield and Bube.41

IV. RESULTS

In this section, we present the results of four different

scenarios. The first three consider only mid-gap, donor-type

defect generation in the CdTe layer according to: (i) the lin-

ear model of Eq. (1); (ii) the quadratic model of Eq. ((3); and

(iii) the recombination model of Eq. (4). Model (iv) is based

on Eq. (1) with generation of both mid-gap defects (donor-

type) and shallow acceptors at equal rates in a 100-nm thick

layer near the CdS/CdTe interface. That thin region is impor-

tant because it is where most of the photo-current is gener-

ated and alloying during fabrication creates interdiffused

CdTeS that can dominate junction properties (cf. Sec.

III A).46 In all cases, annealing is considered to be insignifi-

cant (bt � 1). All light stress conditions refer to AM1.5G,

1-sun.

Our temperature values and time scales for the following

analysis remain arbitrary because we are not fitting a specific

dataset. Rather, we are searching for degradation trends that

best match available data in a qualitative way. This serves as

a starting point for establishing our methodology. Future

work will apply this approach to experimental data at various

temperatures, thereby determining time scales and the mag-

nitude of the defect generation rate, a. This point is discussed

further in Sec. V.

For our first model, the predicted modes of degradation

using Eq. (1) for voltage bias V¼Voc, under light and in the

dark are presented in Figs. 3(a) and 3(b), respectively.

234502-4 Marco Nardone J. Appl. Phys. 115, 234502 (2014)

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

129.1.90.94 On: Mon, 07 Jul 2014 15:58:02

Performance metrics were normalized to the baseline values

and the defect generation rate was set to a¼ 1 s�1 (a serves as

a fitting parameter so an arbitrary rate can be used here with-

out loss of generality). Bias in the dark was held at V¼ 0.86 V

(resulting in a forward current of J� 10 mA/cm2).

Fig. 3(a) indicates that by the time efficiency decreases

by 18% under illumination, FF decreases by about 11%

while Voc and Jsc exhibit nearly equal losses of 3%–4%. The

dark results show a very similar trend but with 12.5% loss in

efficiency in the same time period as the light stress case. As

expected from the data, degradation caused by light and bias

stresses are the same, only the rate is accelerated in the light

due to the high concentration of photo-excited carriers. In

other words, allowing the dark conditions to continue for a

longer time would likely render the two scenarios equivalent.

This may have important practical applications since it

would allow for accelerated life testing with dark bias rather

than light, eliminating the need for cooling or a light source.

The latter would only apply to the type of degradation mech-

anism studied here (i.e., driven by injected carriers).

A useful feature of the numerical approach is the exten-

sive predictive capability. For example, Fig. 4 shows the

defect evolution and recombination rates within the CdTe

layer according to Eq. (1) over the course of light stressing.

The graphs clearly indicate how both mid-gap defect concen-

trations and recombination rates increase in correspondence

with the nonequilibrium minority carrier concentration pro-

file; most of the defects are formed near the CdTe/CdS junc-

tion. That defect profile causes the degradation modes

illustrated in Fig. 3(a).

Light and dark stress conditions were also evaluated at

short circuit SC and reverse bias (RB, V¼�0.5 V) conditions.

The results are summarized in Fig. 5 with t¼ 500 s and

a¼ 1 s�1 in each case. Again it is evident that performance

loss is slightly accelerated in the light compared to the dark

but the trends are the same. The greatest degradation rate

occurs under forward bias in the dark or near Voc under light.

Very little degradation was observed for the SC and RB con-

ditions, which is to be expected since excess charge carriers

are quickly swept away by the strong electric field. Significant

degradation which is often observed under reverse bias is not

seen here.

A comparison of the degradation behavior for the quad-

ratic models of Eqs. (3) and (4) is shown in Fig. 6, with stress

FIG. 3. Degradation of performance metrics predicted by Eq. (1) with

a¼ 1 s�1. Simulated for stress conditions: (a) AM1.5 G illumination, 100

mW/cm2 intensity, V¼Voc; (b) dark, V¼ 0.86 V. Results are normalized to

the baseline values g¼ 16.0%, Voc¼ 0.87 V, Jsc¼ 24.1 mA/cm2,

FF¼ 76.2%.

FIG. 4. The evolution of (a) mid-gap, donor-type defect concentration and

(b) SRH recombination rates in the CdTe layer according to Eq. (1) under

light stress. The time range corresponds to that in Fig. 3.

234502-5 Marco Nardone J. Appl. Phys. 115, 234502 (2014)

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

129.1.90.94 On: Mon, 07 Jul 2014 15:58:02

conditions of light and V¼Voc. In order to set a similar time

frame, a¼ 10�13 cm3/s and a¼ 5� 10�9 were used for Eqs.

(3) and (4), respectively. There are significant differencesbetween these two models. Efficiency loss due to Eq. (3) is

mostly through FF and Jsc, while Voc plays a smaller role. In

the recombination driven model of Eq. (4), the decline in g is

linear with predominant FF loss and minor but equal loss

contributions from Voc and Jsc.

The predicted degradation mode of our fourth model

(junction degradation) is shown in Fig. 7. As both mid-gap

and shallow defects evolve at the same rate with stress time,

Jsc remains stable while Voc and FF decline in good correla-

tion with g. Very slight increases (<1%) in Jsc have also been

predicted. This result displays the degradation features com-

monly observed for many CdTe devices subjected to forward

bias stress. It should be noted that of the numerous defect

generation models simulated (only a sample is shown in this

work), only this type of model, with self-compensation in the

junction region, leads to this type of degradation mode; varia-

tions of either Nd or Na in isolation does not result in stable

Jsc. Initial tests of the junction degradation model using Eqs.

(3) and (4) instead of Eq. (1) indicate qualitatively similar

results (not shown here). Discerning which of those models

provides a better quantitative fit will require comparison with

a specific dataset, which will be the subject of subsequent

work.

Pre- and post-stress light and dark JV curves are shown

in Fig. 8. Light-dark cross-over tends to occur at lower cur-

rent densities as degradation proceeds. Roll-over that is typi-

cally associated with back contact deterioration is not

observed here since our subject degradation mechanism

focusses on the main junction region.

V. DISCUSSION

From the above analysis, it is clear that the model with

simultaneous evolution of mid-gap donors (Nd) and shallow

acceptors (Na) in the junction region best describes an impor-

tant type of degradation commonly observed in CdTe PV

cells. The increased mid-gap defects tend to increase

FIG. 5. Efficiency change predicted by Eq. (1) as a function of bias for light

and dark conditions. Efficiency normalized to initial value g¼ 16.0%.

FIG. 6. Degradation of performance metrics for (a) the quadratic models of

Eq. (3) and (b) the recombination model Eq. (4). Stress conditions: light,

V¼Voc. Metrics are normalized to the baseline values.

FIG. 7. Degradation of performance metrics for the model of Eq. (1) with

generation of both mid-gap and shallow defects of opposite type in the junc-

tion region with a¼ 75 s�1. Stress conditions: light, V¼Voc. Metrics are

normalized to the baseline values.

234502-6 Marco Nardone J. Appl. Phys. 115, 234502 (2014)

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

129.1.90.94 On: Mon, 07 Jul 2014 15:58:02

recombination, which causes declines in Jsc, Voc, and FF.

However, an increase in acceptors tends to increase the elec-

tric field in the junction region, which increases Jsc.

Therefore, as the defects evolve Jsc is stabilized while Voc,

and FF continue to decrease. Although the microscopic na-

ture of the defect kinetics is beyond the present scope, it is

noted that similar models have been used to describe self-

compensation effects. As the Fermi level shifts due to

changes in carrier density, oppositely charged defects or

complexes form which limit the Fermi level change.45 In our

case, increased carriers are supplied by light stress or for-

ward bias, rather than extrinsic doping. Hence, it is plausible

that neutral complexes dissociate to form shallow acceptor,

deep donor pairs (e.g., AX-center44 and DX-center43 models).

Experimental observations suggest that the presence of Cu

plays an important role in the defect kinetics during degrada-

tion; the defect chemistry remains an open question.

The basic physics of the stable Jsc is as follows. In thin-

film CdTe, most of the photocurrent is generated in the

depletion region (within <1 lm of the CdTe/CdS junction)

and, hence, the built-in field E plays an important role in car-

rier collection (more so than diffusion through a quasi-

neutral region). The transit time for an excited charge carrier

to travel a distance x through the depletion region should be

shorter than the recombination time, which are respectively

given by

sdrif t ¼ x=ðlEÞ and srec ¼ ðrvthNdÞ�1: (6)

The condition for efficient carrier collection in the high-

field region, sdrift � srec, is only weakly satisfied for typical

parameters of cross-section r� 10�14–10�12 cm2, thermal ve-

locity vth� 107 cm/s, mid-gap state concentration Nd� 1014

–1015 cm–3, mobility l� 102 cm2 V�1 s�1, E � 104 V=cm,

and x� 0.1–1 lm. Numerical modeling shows that the collec-

tion efficiency is not benign to small changes in the Nd, and

Jsc is strongly affected as Nd increases, as may occur during

degradation.

The postulate advanced here is that during degradation

two opposing mechanisms act simultaneously to decrease

srec and sdrift, thereby maintaining a constant srec/sdrift. The

result is a constant Jsc while Voc and FF decrease due to

recombination. The lifetime decreases as mid-gap recombi-

nation center concentration increases, srec / 1/Nd.

Meanwhile, the built-in field increases with space charge

density according to47 DE ¼ eNax=�s, where e is the elemen-

tary charge, �s the relative permittivity, and Na is the

acceptor concentration; hence, sdrift / 1/Na. The resulting ra-

tio, srec/sdrift / Na/Nd and, hence Jsc, remain constant if both

mid-gap defects and shallow dopant-type defects increase in

a compensatory fashion as degradation proceeds.

It should be noted that the field change DE becomes

observable when it is greater than the existing built-in field

DE E. With typical values of E � 104 V=cm; �s � 10, and

x� 0.1 lm, that condition holds for Na> 1016 cm�3. A field

of E� 30 kV/cm in the interdiffused region within approxi-

mately 100 nm of the CdS/CdTe has been suggested.46

Consistent with the above estimate, our model predicts that

concentrations on the order of Na ¼ Nd � 1016 cm�3 in the

junction region are required to generate that field and initiate

the type of degradation predicted here. Fig. 9 compares our

calculations of the electric field distribution for the Gloecker

and modified baseline cells.

Another discriminating feature between the models is

the time dependence of performance loss. Referring to Fig.

6(b), the recombination model of Eq. (4) leads to a linear

decline in efficiency over time, which is not typically

observed. The same recombination based model predicted a

nonlinear decay in g(t) for a-Si:H, which was in good agree-

ment with the data.22 Therefore, while the recombination

model can account for degradation in a-Si:H cells, it may not

be appropriate for CdTe.

An important question pertains to the nature of a. Its

meaning is similar in all the models: it is the probability of

forming new defects in response to the presence of excess

charge carriers. Hence, it represents the coupling between

the electronic system and the atomic structure. As an acti-

vated material parameter, it can be represented by

FIG. 8. Pre-stress and post-stress JV curves for the model of Eq. (1). Stress

conditions are light and V¼Voc. The post-stress condition is at 16% effi-

ciency loss; the metrics are shown in Fig. 7.

FIG. 9. Electric field distributions for the Gloeckler38 and modified baseline

cells. AM1.5G, 1-sun light, V¼ 0 V.

234502-7 Marco Nardone J. Appl. Phys. 115, 234502 (2014)

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

129.1.90.94 On: Mon, 07 Jul 2014 15:58:02

a ¼ �0 expð�Ea=kTÞ; (7)

where �0� 1013 s�1 is the characteristic atomic frequency, Ea

is an activation energy, k is Boltzmann’s constant, and T is

temperature. Although the time scale used in our results was

arbitrary, it can be easily transformed to predict the equiva-

lent degradation at any time scale by using as/a¼ t/ts, where

as and ts correspond to simulated values. For example, our

result with as¼ 75 s�1 leads to a loss in g of 16% after

ts¼ 400 s (see Fig. 7). A real value of a¼ 0.015 s�1 (with

Ea¼ 1 eV and T¼ 65 C) would extend that time to t� 560 h,

which is well within the typical time frame for stress tests.

An example simulation of a more realistic time frame is

shown in Fig. 10 where values of �0¼ 1013 s�1 and Ea¼ 1 eV

where used in Eq. (7). The temperature dependence of effi-

ciency loss shown in Fig. 10 is indicative of what is typically

observed in accelerated stress testing,5 along with the degra-

dation modes of Fig. 7.

Nonuniformities play a critical role in the degradation of

thin-film PV.11,27 Mechanisms, such as shunt formation,

metal contact delamination,48 grain boundary effects, and

variations of material properties in real space and energy

space, can lead to broad statistical distributions and hot-spot

runaway effects.30 Although only uniform mechanisms were

considered in the present work, it provides a good example

of how uniform and nonuniform mechanisms can be

coupled. Specifically, small variations in the barrier Ea result

in exponential changes in defect formation rates and spatial

variations that can increase with stress time. Furthermore, as

a material parameter, the barrier may depend on the presence

of nonuniform dopant concentrations such as Cu in CdTe

cells. Overall, nonuniformities play an important role in the

different degradation rates observed in sister cells and the

statistical nature of the data. The higher dimensional capabil-

ities of the numerical tool employed here provide a means to

investigate uniform/nonuniform couplings.

Our numerical approach can be used to study other possi-

ble mechanisms specific to CdTe, including electromigration

of mobile ions leading to back contact deterioration, nonuni-

form diffusion of dopants, and lowering of the CdS bandgap

due to the presence of Cu. Such studies are essential because

many of the observations listed in Sec. III B remain quantita-

tively unexplained. In addition to specific mechanisms, one

can study the effects of alternative band structures such as a

light-modulated front barrier49 or a gull-wing singularity due

to the piezoelectric nature of CdS.50 The latter may be partic-

ularly applicable because it naturally provides defect genera-

tion in the narrow band of the field singularity at the junction

(where nonequilibrium electrons accumulate). Alternative

charge transport mechanisms, such as optimum channel hop-

ping,51 may also have important effects and can be investi-

gated with this simulation tool.

VI. CONCLUSIONS

A mechanism of junction deterioration in CdTe/CdS PV

cells has been analyzed using a new simulation tool. Our

study shows that junction degradation consisting of self-

compensatory defect evolution in response to the presence of

excess charge carriers leads to commonly observed degrada-

tion modes. Defect generation is confined to a narrow region

close to the CdTe/CdS interface. Temperature dependence of

the degradation rate appears to be governed by a thermally

activated parameter. Similar degradation modes were pre-

dicted for stress under light or in the dark with forward bias,

suggesting that stress testing may be possible in the dark

with only bias stress, thereby avoiding the need to light-

soak. Degradation under reverse bias, which is known to

occur, was not predicted with the physical model studied

here. Our numerical tool can be extended to study degrada-

tion mechanisms in PV devices of similar structure.

ACKNOWLEDGMENTS

The author gratefully acknowledges V. G. Karpov and

D. S. Albin for insightful comments and discussions.

1D. C. Jordan and S. R. Kurtz, Prog. Photovoltaics 21, 12 (2013).2See http://events.energetics.com/NISTGrandChallenges2010/pdfs/AdvPV-

WorkshopReport.pdf for Workshop Summary Report: Grand Challenges

for Advanced Photovoltaic Technologies and Measurements, July 2010.3P. V. Meyers, S. Asher, and M. M. Al-Jassim, in Proceedings of theMaterials Research Society Symposium (Cambridge University Press,

1996), pp. 317–324.4S. S. Hegedus and B. E. McCandless, Sol. Energy Mater. Sol. Cells 88, 75

(2005).5D. S. Albin, Proc. SPIE 7048, 70480N (2008).6J. F. Hiltner and J. R. Sites, AIP Conf. Proc. 462, 170–175 (1999).7K. D. Dobson, I. Visoly-Fisher, G. Hodes, and D. Cahen, Sol. Energy

Mater. Sol. Cells 62, 295 (2000).8S. S. Hegedus, B. E. McCandless, and R. W. Birkmire, in ConferenceRecord of the 28th IEEE Photovoltaic Specialists Conference, Anchorage,

Alaska, USA (IEEE, 2000), pp. 535–538.9R. Harju, V. G. Karpov, D. Grecu, and G. Dorer, J. Appl. Phys. 88, 1794

(2000).10A. O. Pudov, J. R. Sites, S. H. Demtsu, M. Gloeckler, K. L. Barth, R. A.

Enzenroth, and W. S. Sampath, in Conference Record of the 29h IEEEPhotovoltaic Specialists Conference, New Orleans, LA, USA (IEEE,

2002), pp. 760–763.11V. G. Karpov, A. D. Compaan, and D. Shvydka, Appl. Phys. Lett. 80,

4256 (2002).12C. R. Corwine, A. O. Pudov, M. Gloeckler, S. H. Demtsu, and J. R. Sites,

Sol. Energy Mater. Sol. Cells 82, 481 (2004).

FIG. 10. Normalized efficiency decline over time predicted by the model of

Eq. (1) with a from Eq. (7) and Ea¼ 1 eV. Stress conditions are light and

V¼Voc. The associated metrics for T� 340 K are shown in Fig. 7.

234502-8 Marco Nardone J. Appl. Phys. 115, 234502 (2014)

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

129.1.90.94 On: Mon, 07 Jul 2014 15:58:02

13T. J. Berniard, D. S. Albin, B. To, J. W. Pankow, M. Young, and S. E.

Asher, J. Vac. Sci. Technol. B 22, 2423 (2004).14D. L. B€atzner, A. Romeo, M. Terheggen, M. D€obeli, H. Zogg, and A. N.

Tiwari, Thin Solid Films 451-452, 536 (2004).15T. A. Gessert, S. Smith, T. Moriatry, M. Young, S. Asher, S. Johnston, and

A. L. Fahrenbruch, in Conference Record of the 31st IEEE PhotovoltaicSpecialists Conference, Lake Buena Vista, FL, USA (IEEE, 2005), pp.

291–294.16D. S. Albin, R. G. Dhere, S. C. Glynn, and W. K. Metzger, in Conference

Record of the 34th IEEE Photovoltaic Specialists Conference (PVSC),Philadelphia, PA, USA (IEEE, 2009), pp. 001903–001908.

17D. S. Albin and J. A. del Cueto, Proc. SPIE 7773, 77730N (2010).18R. L. Graham, D. S. Albin and L. A. Clark, Proc. SPIE 8112, 81120V

(2011).19D. L. Staebler and C. R. Wronski, Appl. Phys. Lett. 31, 292 (1977).20D. L. Staebler, R. S. Crandall, and R. Wilson, Appl. Phys. Lett. 39, 733

(1981).21L. Chen and L. Yang, J. Non-Cryst. Solids 137-138, 1185 (1991).22A. Klaver and R. A. C. M. M. van Swaaij, Sol. Energy Mater. Sol. Cells

92, 50 (2008).23M. Igalson, P. Zabierowski, D. Przado, A. Urbaniak, M. Edoff, and W. N.

Shafarman, Sol. Energy Mater. Sol. Cells 93, 1290 (2009).24P. Zabierowski, U. Rau, and M. Igalson, Thin Solid Films 387, 147 (2001).25J. T. Heath, J. D. Cohen, and W. N. Shafarman, J. Appl. Phys. 95, 1000

(2004).26V. G. Karpov, A. D. Compaan, and D. Shvydka, Phys. Rev. B 69, 045325

(2004).27V. G. Karpov and D. Shvydka, Proc. SPIE 7412, 74120L (2009).28T. J. McMahon, T. J. Berniard, and D. S. Albin, J. Appl. Phys. 97, 054503

(2005).29M. Nardone, M. Simon, and V. G. Karpov, Appl. Phys. Lett. 96, 163501

(2010).30V. G. Karpov, Phys. Rev. B 86, 165317 (2012).31M. N. Meytin, M. Zeman, B. G. Budaguan, and J. W. Metselaar,

Semiconductors 34, 717 (2000).32M. Stutzmann, W. B. Jackson, and C. C. Tsai, Phys. Rev. B 32, 23 (1985).33K. Decock, P. Zabierowski, and M. Burgelman, J. Appl. Phys. 111,

043703 (2012).

34COMSOL MultiphysicsVR

, 2013, Version 4.4, COMSOL, Inc., Burlington,

MA, USA.35S. Selberherr, Analysis and Simulation of Semiconductor Devices

(Springer Verlag, New York, 1984).36S. Fonash, J. Arch., J. Cuiffi, J. Hou, W. Howland, P. McElheny, A.

Moquin, M. Rogosky, T. Tran, H. Zhu, and F. Rubinelli, A Manual forAMPS-1D for Windows 95/NT—A One-Dimensional Device SimulationProgram for the Analysis of Microelectronic and Photonic Structures (The

Pennsylvania State University, 1997).37M. Burgelman, P. Nollet, and S. Degrave, Thin Solid Films 361-362, 527

(2000).38M. Gloeckler, A. L. Fahrenbruch, and J. R. Sites, in Proceedings of 3rd

World Conference on Photovoltaic Energy Conversion, Osaka, Japan

(IEEE, 2003), pp. 491–494.39D. H. Rose, F. S. Hasoon, R. G. Dhere, D. S. Albin, R. M. Ribelin, X. S.

Li, Y. Mahathongdy, T. A. Gessert, and P. Sheldon, Prog. Photovoltaics 7,

331 (1999).40B. E. McCandless, M. G. Engelmann, and R. W. Birkmire, J. Appl. Phys.

89, 988 (2001).41D. Redfield and R. H. Bube, Photoinduced Defects in Semiconductors

(Cambridge University Press, Cambridge, 1996).42S. Lany and A. Zunger, Phys. Rev. Lett. 100, 016401 (2008).43D. J. Chadi, Phys. Rev. Lett. 72, 534 (1994).44D. J. Chadi, Phys. Rev. B 59, 15181 (1999).45S. H. Wei and S. B. Zhang, Phys. Rev. B 66, 155211 (2002).46R. G. Dhere, Y. Zhang, M. J. Romero, S. E. Asher, M. Young, B. To, R.

Noufi, and T. A. Gessert, in 33rd IEEE Photovoltaic Specialists Conference,PVSC’08, San Diego, California, May 11–16 (IEEE, 2008), pp. 1–5.

47S. Sze, Physics of Semiconductor Devices, 2nd ed. (Wiley, New York,

1981).48V. G. Karpov, D. Shvydka, and Y. Roussillon, in Conference Record of the

31st IEEE Photovoltaic Specialists Conference (IEEE, 2005), pp. 437–440.49G. Agostinelli, D. L. B€atzner, and M. Burgelman, Thin Solid Films

431-432, 407 (2003).50M. Mitra, J. Drayton, M. L. C. Cooray, V. G. Karpov, and D. Shvydka,

J. Appl. Phys. 102, 034505 (2007).51M. Nardone, V. G. Karpov, D. Shvydka, and M. L. C. Attygalle, J. Appl.

Phys. 106, 074503 (2009).

234502-9 Marco Nardone J. Appl. Phys. 115, 234502 (2014)

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

129.1.90.94 On: Mon, 07 Jul 2014 15:58:02