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Contract No. DE-AC36-99-GO10337 

D.L. Young, K. Ramanathan, and R.S. Crandall 

Prepared for the 31st IEEE Photovoltaics Specialists 

Conference and Exhibition 

Lake Buena Vista, Florida 

January 3-7, 2005 

February 2005 • NREL/CP-520-37359 

Unusual Capacitance Emission 

Transients in CIGS Caused by 

Large Defect Entropy Changes 
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UNUSUAL CAPACITANCE EMISSION TRANSIENTS IN CIGS 

CAUSED BY LARGE DEFECT ENTROPY CHANGES 

David L. Young, Kannan Ramanathan, and Richard S. Crandall 

National Renewable Energy Laboratory

1617 Cole, Blvd. Golden, CO 80401 

ABSTRACT 

Capacitance transient data from bias-pulse experiments on CdS/CIGS solar cells show an unusual behavior 

at high temperatures. Above 350K a minority carrier trap, 

with a larger activation energy than a majority carrier trap, 

emits faster than the lower activation-energy minority trap. 

A simple enthalpy model for trap emission cannot explain 

this counterintuitive behavior, but the more complete 

Gibbs free energy model that includes entropy can explain 

it. We show that entropy plays a major role in carrier 

emission from traps in CIGS. 

INTRODUCTION 

CdS/CuIn1-xGaxSe2 (CIGS) thin-film solar cells have 

achieved record efficiencies of greater than 19%[1] despite 

the high concentration of electronic trap levels in CIGS.[2, 

3] A variety of experimental techniques[4-6] have measured both minority- and majority-carrier traps in CIGS with 

widely varying energy levels and concentrations. It is well 

established that carrier emission from filled traps in CIGS 

generally does not follow an exponential decay, but rather, 

a stretched exponential decay, 

A(t) = Aoe−(t/τ )

β

, (1) 

-0.8

-0.6

-0.4

-0.2

0.0

0.2

Delta Capacitance

0.001 0.01 0.1 1 10

Time (s)

380 K

322K

S2213A1 CIGS

1b E1

P1

-0.8

-0.6

-0.4

-0.2

0.0

0.2

Delta Capacitance

0.001 0.01 0.1 1 10

Time (S)

322K

212 K S2213A1 CIGS

1c

P2

-0.4

-0.2

0.0

0.2

Delta Capacitance

0.001 0.01 0.1 1 10

Time (sec)

S2213A1 CIGS

400K

380K

1a

E1

P1

Fig. 1. Capacitance transients as a function of temperature. 

With τ a characteristic time constant for the decay and β

having values between 0.3 and 0.8.[7] In addition, biaspulse, trap-filling experiments show that there are energy

barriers to filling and that saturation of the traps requires 

bias pulses on the order of 100s of seconds.[7] Data also 

suggest that bias pulse length and annealing can change 

the nature of the trap being filled (e.g. from a minority to a 

majority carrier trap).[8] This latter feature suggests a trap 

metastability similar to the bipolar D defect found in aSi:H.[9] Similar to a-Si:H, it is generally found that the 

emission rates from the traps seen in CIGS follow the 

ubiquitous Meyer-Neldel rule (MNR).[10-12] Adherence to 

the MNR implies that a change in entropy plays a significant role in the thermal emission of the traps. Measuring 

the magnitude of the entropy change involved with the 

traps will greatly improve our understanding and possibly

our control of the traps. 

In this paper, we present capacitance emission transient data at elevated temperatures from CIGS/CdS solar 

cells. The data show ambipolar carrier emission; we observe both a fast-decaying minority carrier and a slower1
decaying majority carrier. The minority carrier has a 

shorter time constant for emission, but a larger activation 

energy than the majority carrier (i.e., the deeper state 

emits faster than the shallower state). This bizarre behavior is inconsistent with the notion that shallow states always thermally emit faster than deeper states. However, 

these data are consistent with the Meyer-Neldel rule, 

which predicts such counterintuitive effects for temperatures above the isokinetic temperature. For temperatures 

above the isokinetic temperature, the change in free energy is negative upon carrier emission. But below the 

isokinetic temperature, the change in free energy is positive and the emission transients are normal: the shallower 

state emits faster than the deeper state. The free-energy

sign-reversal effect has been seen in hydrogenated amorphous silicon solar cells, but this is the first time this behavior has been observed in CIGS. Our data demonstrate 

a large entropy change associated with carrier emission 

from these defects, which has implications for solar cell 

parameters, models of transport in CIGS, and the interpretation of defect spectroscopies. 

EXPERIMENT 

Thin-film ZnO/CdS/CIGS solar cells were grown on 

molybdenum-coated, soda-lime glass. The CIGS absorber layer was grown using the three-stage process by

thermal evaporation. Details of the complete cell growth 

and solar cell characterization may be found elsewhere.[1] 

Cells were contacted with pressure probes on In dots and 

placed in a commercial temperature stage in the dark. 

The capacitance of the cell was measured by a Stanford 

Research SR830 lock-in amplifier operating at 11 kHz with 

a 100 μs time constant. Capacitance transients were 

monitored by a high-speed data acquisition card with log 

time-data averaging accomplished by in-house software. 

The initial capacitance, Co, was measured while a cell was 

held at a bias of –0.3 volts. The voltage was then pulsed 

to either 0 or +0.3 volts, depending on the experiment, for 

a set amount of time and then returned to –0.3 volts. Data 

collection was triggered on the return of the bias back to –

0.3 volts. The change in capacitance (C(t) – Co) was recorded for up to 1000 s. 

DATA

Figure 1 shows capacitance transient curves for sample S2213A1 (CuIn1-xGaxSe2, x~0.3) over the temperature 

range of 400 K – 212 K using a filling pulse time of 1 s at 

zero bias. Figure 1a shows the transients between 400 K 

and 380 K, with the arrow in the figure indicating the scan 

sequence. The data show a fast-emitting minority carrier 

trap (∆C > 0)[13] labeled E1, followed by a slower-emitting 

majority-carrier trap (∆C< 0) labeled P1. All of the transients return to the original Co value (C = 0) for times 

greater than 10 s. Note that the amplitude of the E1 and 

P1 transients increase and decrease with decreasing temperature, respectively. Figure 1b is a continuation of the 

transients in Fig. 1a for temperatures between 380 K and 

320 K. Here, the transients shift from the minority- and 

majority-carrier traps at the high temperatures to a single, 

large-amplitude majority-carrier trap, labeled P2, at the 

lower temperatures. Figure 1c continues the transient 

trend with a decrease in amplitude of the majority-carrier 

trap, P2, until it is not observed below 212 K. In this contribution, we focus on the emission behavior of traps E1 and 

P1, but note that trap P2 was previously analyzed by our 

group.[7] 

For high temperatures (Fig. 1a), the transient data may

be fit with the sum of two stretched exponentials simulating the two-carrier nature (E1, P1) of the transients. Figure 2 shows a good fit to the data, along with the deconvoluted transients for the E1 and the P1 traps. A series of 

transients at different temperatures were fit in this manner 

to produce the Arrhenius plots of Fig. 3, giving the activation energies for traps E1=1.4 ± 0.04 eV and P1= 0.3 ±

0.13 eV. The unusual aspect of Fig. 3 is that the trap with 

the faster emission time, E1, has the higher activation 

energy. The crossing point of the two extrapolated line-fits 

to the Arrhenius data of Fig. 3 gives the so-called isokinetic temperature at about Tiso = 350 K. This measured 

value is similar to that measured for B-doped a-Si:H,[15] 

InGaAsN,[18] and CIGS[19] samples. Below this temperature, P1 is expected to emit faster than E1. As is evident 

in Figs. 1 a-c, P2’s influence on the transient signal interferes with the low-temperature E1 and P1 contributions to 

the transient. Nevertheless, a wealth of new information 

can be drawn from our high-temperature data. 

Fig. 2. Fit to transient data with the sum of two stretched 

exponential functions. 

MNR EMISSION RATE INVERSION 

Bias-pulse length experiments have led us to believe 

E1 and P1 are related to each other and are a result of an 

amphoteric, metastable defect. These results will be presented in a later paper. We cannot view these traps as 

simple, but rather as a much more complex entity that is 

strongly coupled to the phonons and the emitted charge. 

In this case, one must view it as a thermodynamic object 

(trap)[14] and describe transitions using 

r = τ

−1 = ν ooe−β∆G = ν ooe(∆S / kB )

e−β∆H , (2) 

2
where ∆G = ∆H-T∆S is the difference in Gibbs free energy

between initial and final states during carrier emission from 

a trap. ∆H is the change in enthalpy (emission activation 

energy, Eact), and ∆S is the change in entropy with β = 

1/kBT and kB is Boltzmann’s constant. νoo=kBT/h is the 

Eyring constant.[14] Note that the relevant quantity in determining the rate of a transition is the Gibbs free energy

and not just the activation energy. Most of the literature on 

defects in CIGS has assumed ∆S to be small enough to 

ignore. Our data show this is not the case. From Fig. 3, 

we see that at T = Tiso the emission rates are equal for 

both the minority- and majority-carrier traps. This implies 

that ∆G is the same for both traps (subscripts 1 and 2) at 

Tiso, which gives[15] 

Tiso = ( ) ∆H1 − ∆H2

( ) ∆S1 − ∆S2

. [3] 

Taking the ratio of reaction rates for two reactions gives

 

r

1

r2

= e

−β {( ) ∆H1 −∆H2 1−(T /Tiso [ )]}

, [4] 

revealing the origin of emission inversion between the two 

reactions for temperatures above and below Tiso. The 

transition with the larger ∆H (Eact) has the faster transition 

rate for T > Tiso and the slower transition rate for T < Tiso. 

Equation [2] allows a calculation of the individual entropy

changes associated with each transition reaction by noting 

that at Tiso the reaction rates must be equal for both traps 

and independent of ∆H. For the simplest case, considering only changes in entropy that scale with changes in 

enthalpy, such as phonon contributions, ∆S = ∆H/Tiso.[15] 

It should be noted that other entropy contributions to emission can and do exist[16] that do not scale with changes in 

enthalpy, but they will not be discussed in this paper. Data 

from Fig. 3 give the measured entropy changes for E1 and 

P1 to be 

-5

0

5

Ln(Tau)

3.0x10-3 2.6 2.8

1/Temperature(K)

E1, Eact = 1.4 eV 

 P1, Eact = 0.3 eV 

Tiso ~ 350 K

Fig. 3. Arrhenious plot of data for traps E1 and P1. 

∆SE1 = 48 ± 8kB ∆SP1 = 11 ± 5kB. 

The magnitude of these ∆S values are consistent with 

those found for electron and hole traps in B-doped a-Si:H 

solar cells.[15] Current theories on the origin of ∆S associate these values with the number of ways to assemble 

the required number of phonons to surmount the transition 

barrier.[17] More information on the phonon spectrum and 

the coupling potential of the lattice to the particular defects 

for CIGS are needed to corroborate our experimental ∆S 

values with the phonon assembly theory. We refer the 

reader to our recent work in this area.[16] 

DISCUSSION 

Our high-temperature transient data suggest that two 

traps, one a minority carrier and one a majority carrier, 

emit their carriers over the time scale of seconds. These 

especially long emission times are due to a barrier to 

emission related to the change in Gibbs free energy during the transition. The change in Gibbs free energy is a 

function of both the change in enthalpy (the activation energy) and the change in entropy. The large ∆S values 

calculated from our data for traps E1 and P1 confirm that 

entropy contributions to trap emission may not be ignored 

in models for these defects. Note that the large change in 

entropy values seen in our data decrease the barrier to 

emission. This characteristic is a result of the change in 

entropy scaling with the change in enthalpy. The larger 

enthalpy barrier of E1 requires a larger change in entropy

during a transition for a given change in Gibbs free energy

(∆G = ∆H – T∆S). Calculating ∆G above and below Tiso

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

Gibbs Free Energy (eV)

200 250 300 350 400 450 500

Temperature (K)

E1

P1

Fig. 4. Gibbs free energy vs. temperature for traps E1 

and P1. The arrows on the diagrams illustrate the relative energy barrier for emission. 

3
gives the relative energy barriers for E1 and P1 and reveals the physical reason why the reversal of emission 

time with activation energy above Tiso can be observed in 

materials that follow the MNR. Fig. 4 shows the Gibbs 

free energy for E1 and P1 vs. temperature, along with 

conceptual energy barrier diagrams for E1 and P1 above 

and below Tiso. Note that the Gibbs free energy changes 

sign at Tiso, which is the reason for the relative barrierheight change. 

[7] D. L. Young and R. S. Crandall, An electrostatic barrier to trap filling in CuIn1-xGaxSe2. Applied Physics Letters 

83, 2363 (2003). 

[8] M. Igalson and H. W. Schock, The metastable 

changes of the trap spectra of CuInSes - based photovoltaic devices. J. Appl. Phys. 80, 5765 (1996). 

[9] J. D. Cohen, T. M. Leen, and F. Zhong, Relaxation of 

the D cener in amorphous silicon and how this accounts 

for the observed energy distributions of deep defects 

within the mobility gap. Journal of Non-Crystalline Solids 

164-166, 327 (1993). 

SUMMARY 

Our capacitance transient data show minority- and majority-carrier trap-emission following a bias pulse for temperatures between 380 and 400 K. The data show an odd 

behavior in the emissions such that the traps with the larger activation energy emit faster than the lower activationenergy traps. This counterintuitive event is well described 

by a model that treats the defect as a thermodynamic object with a Gibbs free energy barrier to emission. The data 

show large changes in entropy are involved in the emission process, that lower the Gibbs free energy barrier to 

emission for the higher activation emissions above the 

isokinetic temperature. We believe the concept of entropy

must be included in future theoretical work to better understand defects in CIGS and related materials. 

[10] W. Meyer and H. Neldel, Z. Tech. Phys. 12, 588 

(1937). 

[11] R. Herberholz, T. Walter, C. Muller, T. Friedlmeier, 

H. W. Schock, M. Saad, M. C. Lux-Steiner, and V. Alberts, 

Meyer-Neldel Behavior of deep level parameters in heterojunctions to Cu(In,Ga)S,Se)2. Applied Physics Letters 69, 

2888 (1996). 

[12] F. R. Shapiro and J. R. Tuttle, The Meyer-Neldel 

Rule in Emission Rates from defects in copper indium 

diselenide. Solid State Communications 87, 199 (1993). 

REFERENCES 

[13] D. V. Lang, Deep-level transient spectroscopy: A 

new method to characterize traps in semiconductors. 

Journal of Applied Physics 45, 3023 (1974). [1] K. Ramanathan, M. A. Contreras, C. L. Perkins, S. 

Asher, F. S. Hasoon, J. Keane, D. Young, M. Romero, W.

Metzger, R. Noufi, J. Ward, and A. Duda, Properties of 

19.2 % Efficiency ZnO/CdS/CuInGaSe2 Thin-film Solar 

Cells. Progress in Photovoltaics: Research and Applications 11, 225 (2003). 

[14] S. Glasstone, K. J. Laidler, and H. Eyring, The Theory of Rate Processes (McGraw-Hill, New York, 1941). 

[15] R. S. Crandall, Meyer-Neldel rule in charge-trapping 

metastability in p-type hydrogenated amorphous silicon. 

Physical Review B 66, 195210 (2002). [2] T. Walter, R. Herberholz, C. Muller, and H. W.

Schock, Determination of defect distributions from admittance measurements and application to Cu(In,Ga)Se2 

based heterojunctions. J. Appl. Phys. 80, 4411 (1996). [16] D. L. Young and R. S. Crandall, Lowering of emission barrier in CuIn1-xGaxSe2 due to large entropy

changes. Applied Physics Letters Submitted (2005). [3] J. T. Heath, J. D. Cohen, and W. N. Shafarman, Bulk 

and metastable defects in CuIn1-xGaxSe2 thin films using 

drive-level capactiance profiling. Journal of Applied Physics 95, 1000 (2004). 

[17] A. Yelon, B. Movaghar, and H. M. Branz, Origin and 

consequences of the compensation (Meyer-Neldel) law.

Physical Review B 46, 12244 (1992). 

[4] M. Igalson and P. Zabierowski, Transient capacitance 

spectroscopy of defect levels in CIGS devices. Thin Solid 

Films 361-362, 371 (2000). 

[18] S. W. Johnston, R. S. Crandall, and A. Yelon, Evidence of the Meyer-Neldel rule in InGaAsN alloys and the 

problem of determining trap cature cross sections. Applied 

Physics Letters 83, 908 (2003). [5] R. Herberholz, M. Igalson, and H. W. Schock, Distinction between bulk and interface states in CuInSe2/CdS/ZnO by space charge spectroscopy. J. Appl. 

Phys. 83, 318 (1998). 

[19] J. A. AbuShama, Ph.D Thesis in Physics (Colorado 

School of Mines, Golden, 2003), p. 205. 

[6] A. E. Delahoy, A. Ruppert, and M. Contreras, Charging and discharging of defect states in CIGS/ZnO junctions. Thin Solid Films 361-362, 140 (2000). 

4
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5a. CONTRACT NUMBER

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4. TITLE AND SUBTITLE

Unusual Capacitance Emission Transients in CIGS Caused by 

Large Defect Entropy Changes 

5c. PROGRAM ELEMENT NUMBER

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NREL/CP-520-37359 

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PVA54101 

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D.L. Young, K. Ramanathan, and R.S. Crandall 

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National Renewable Energy Laboratory 

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14. ABSTRACT (Maximum 200 Words)

Capacitance transient data from bias-pulse experiments on CdS/CIGS solar cells show an unusual behavior at high 

temperatures. Above 350 K, a minority-carrier trap, with a larger activation energy than a majority-carrier trap, emits 

faster than the lower activation-energy minority trap. A simple enthalpy model for trap emission cannot explain this 

counterintuitive behavior; but the more complete Gibbs free-energy model that includes entropy can explain it. We show 

that entropy plays a major role in carrier emission from traps in CIGS. 

15. SUBJECT TERMS

PV; capacitance transient data; bias-pulse experiments; minority-carrier trap; enthalpy; carrier emission; activation 

energy; CIGS; CdS; Gibbs free-energy; 

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