NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

Applications of Admittance 

Spectroscopy in Photovoltaic 

Devices Beyond Majority-Carrier 

Trapping Defects

Preprint

Jian V. Li, Richard S. Crandall, Ingrid L. Repins, 

Alexandre M. Nardes, and Dean H. Levi 

National Renewable Energy Laboratory

Oleg Sulima 

GE Global Research

Presented at the 37th IEEE Photovoltaic Specialists Conference 

(PVSC 37)

Seattle, Washington

June 19-24, 2011

Conference Paper

NREL/CP-5200-50697

July 2011
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1 

APPLICATIONS OF ADMITTANCE SPECTROSCOPY IN PHOTOVOLTAIC DEVICES 

BEYOND MAJORITY-CARRIER TRAPPING DEFECTS

Jian V. Li,1 Oleg Sulima,

2 Richard S. Crandall,1 Ingrid L. Repins,1 Alexandre M. Nardes,1 and Dean H. Levi1

1

National Renewable Energy Laboratory, Golden, Colorado 80401 USA 2

GE Global Research, Niskayuna, New York 12309 USA

ABSTRACT

Admittance spectroscopy is commonly used to 

characterize majority- carrier trapping defects. In today’s 

practical photovoltaic devices, however, a number of other 

physical mechanisms may contribute to the admittance 

measurement and interfere with the data interpretation. 

Such challenges arise due to the violation of basic 

assumptions of conventional admittance spectroscopy 

such as single- junction, ohmic contact, highly conductive 

absorbers, and measurement in reverse bias. We exploit 

such violations to devise admittance spectroscopy- based 

methods for studying the respective origins of 

“interference”: majority- carrier mobility, non-ohmic contact 

potential barrier, minority- carrier inversion at heterointerface, and minority- carrier lifetime in a device 

environment. These methods are applied to a variety of 

photovoltaic technologies: CdTe, Cu(In,Ga)Se2, Si HIT 

cells, and organic photovoltaic materials.

INTRODUCTION

Defects are undoubtedly among the most critical physical 

issues to address for the photovoltaic (PV) industry. 

Admittance spectroscopy, among other capacitancebased techniques such as capacitance-voltage and deeplevel transient spectroscopy, is commonly used to 

characterize majority-carrier trapping defects in PV 

materials and devices. Admittance spectroscopy inspects 

the current response of a device to small AC bias voltage 

modulation and its dependence on frequency and 

temperature, presumably due to the capture and emission 

of the electrically active defects. In a simple single-junction 

device, it is possible to extract defect parameters such as 

activation energy, capture cross-section, and density of 

states [1],[2]. 

The photovoltaic community depends on maintaining the 

integrity that the signals measured by admittance 

spectroscopy and reported as defects are truly due to 

majority-carrier traps. Without that, ensuing confusion will 

certainly mislead the research effort. Unfortunately, only in 

certain simple devices can it be safely assumed that 

admittance spectroscopy reflects nothing but majoritycarrier traps. Today’s PV devices are sophisticatedly 

engineered with inclusion of building blocks such as 

polycrystalline absorbers, heterojunctions, and non-ideal 

contacts. The complex nature of these practical PV 

devices determines that other mechanisms may also 

contribute to the admittance measurement. Therefore, one 

should be careful not to attribute all admittance 

spectroscopy measurements to majority-carrier trapping 

defects.

On the other hand, there is an urgent need to evaluate a 

host of other material and device properties besides 

defects. In this work, we focus on majority-carrier mobility, 

non-ohmic contact potential barrier, minority-carrier 

inversion at certain heterojunction, and minority-carrier 

lifetime in a device environment (i.e., after the device 

fabrication is completed, rather than at the intermediate 

stage of wafer or thin-film level). Such properties are 

usually important to PV device operation and could be 

difficult to characterize by other techniques. Here, we

recognize unique opportunities for extracting these nonmajority-trap-related properties by admittance 

spectroscopy. We develop characterization methods and 

apply them to various PV technologies: CdTe, 

Cu(In,Ga)Se2 (CIGS), silicon heterojunction cells with an 

intrinsic thin (HIT) amorphous silicon layer, and poly(3-

hexylthiophene) organic photovoltaic (OPV) material.

EXPERIMENT 

We conducted admittance spectroscopy measurements 

using an Agilent 4294A impedance analyzer. The AC 

modulation voltage was nominally 35 mVrms. A Lakeshore 

331A temperature controller was used to stabilize and 

sense the cold-finger temperature (ranging from 14‒400 

K) of a close-loop He cryostat. At each temperature

setting, we recorded the sample temperature from a 

second temperature sensor attached directly to the 

sample side of the substrate. (The other side is in contact 

with the copper stage of the cold figure.) At each fixed 

temperature, we applied a series of DC bias voltages to 

the device. A logarithmic frequency scan was carried out 

at each DC bias voltage. When required, we also 

conducted current-density-voltage (JV) measurement at 

each temperature using an HP 4140 semiconductor 

parameter analyzer. 

The fabrication process of CdTe thin-film devices was 

similar to previous report [3] with the addition that gold is 

also experimented with as the back-contact metal. The 

Cu(In,Ga)Se2 thin-film device was fabricated using the 

standard process [4], except that the growth temperature 

for the Cu(In,Ga)Se2 film in this study was 435°C. This 

growth temperature was selected to produce low carrier 

density in the absorber so that its dielectric relaxation 

frequency is below 100 MHz. The Si heterojunction cells 

with an intrinsic thin layer were grown on n-type wafers. 

The samples were taken from a previously reported 

sample set, the fabrication details of which were reported 
2 

elsewhere [5]. The poly(3-hexylthiophene) (P3HT) polymer 

sample was fabricated by spin coating P3HT from solution

onto a poly(3,4-ethylenedioxythiophene) poly (styrenesulfonate) (PEDOT:PSS) layer on top of indium tin oxidecoated glass. The other contact is aluminum. 

Application of admittance spectroscopy to deep levels in 

the absorber of a typical PV device usually assumes that 

several conditions are satisfied: 1) the absorber is 

conductive enough and the dielectric relaxation frequency 

of bulk absorber material is out of the range of interest; 2) 

only one junction is present and both contacts are ohmic; 

3) only majority-carrier traps are observed; and 4) the 

junction is in reverse bias. With these simplifications, it is 

safe to consider that admittance spectroscopy reflects the 

behavior of majority-carrier trapping defects. However, the 

complex nature of most practical PV devices means that 

one or more of these conditions may often be violated in 

the admittance measurement.

Figure 1 shows the admittance spectroscopy spectrum 

taken from a CdTe solar cell using temperature derivative 

representation [6]. Three peaks are labeled. At first sight, it 

appears that there are three peaks—hence, three 

majority-carrier trapping defects. However, only peak 3 

(~0.55 eV) is a deep level due to Cu. This peak is present 

when Cu is added to the back-contact formation process. 

It is absent when the back-contact formation process is 

intentionally deprived of Cu. As we will explain in the 

following text, peaks 1 and 2 are not signatures of deep 

levels.

If the free carrier density and mobility of the absorber are 

not high enough—a probable situation in CdTe due to the 

low free carrier density—the first condition about dielectric 

relaxation may not be met. The dielectric relaxation of a 

bulk semiconductor is given by ωdr=1/ρε, where ρ is the 

resistivity and ε is the permittivity. In the case of high 

absorber resistivity or low measurement temperature, the 

dielectric relaxation frequency may fall into the range of 

interest. Indeed, peak 1 in Fig. 1 is due to dielectric 

relaxation (or freeze-out) of the CdTe absorber at low 

temperatures. The hallmark of this type of frequency 

response is the following: at a temperature lower (or 

frequency higher) than the transition point, the 

capacitance approaches the geometrical capacitance 

value (data not shown here).

In the presence of the junction depletion capacitance (Fig. 

2), the dielectric relaxation frequency of the absorber is 

modified [7] by a factor of W/t, where W is the depletion 

width and t is the absorber thickness. Because W varies 

with bias voltage, the modified dielectric relaxation 

frequency becomes bias dependent. We developed a 

method to measure mobility from the bias dependence of 

the dielectric relaxation frequency (Fig. 3) [8]. The hole 

mobility (T = 300 K) of the CIGS device measured is 0.66 

cm2

/V/s. Figure 4 shows the bias dependence of the 

square of the modified dielectric relaxation frequency in a 

P3HT sample. From there, the mobility of holes in a series 

of P3HT samples at room temperature is extracted to be in 

the range of high 10-6 to low 10-4 cm2

/V/s, consistent with 

measurements using other techniques [9]. This method 

works well on other low-mobility devices such as CdTe (at 

low temperature) [8] and a-Si.

Figure 3 Frequency dependence of the capacitance of 

a CIGS solar cell measured under various biases.

Figure 2 Band diagram and equivalent circuit of a 

solar cell with a depletion region and a neutral 

absorber connected in series.

Figure 1 The temperature differential capacitance 

measured at 43.7 kHz from a CdTe solar cell.
3 

Figure 4 Bias dependence of the square of the 

dielectric relaxation frequency from a P3HT device. 

It is also possible to violate the second condition, which 

demands that only one junction is present in the device. 

CdTe thin-film devices are prime candidates because of 

the difficulty of forming a high-quality, ohmic back contact. 

Peak 2 in Fig. 1 is actually due to the back-contact barrier. 

The activation energy extracted from Peak 2 data 

consistently agrees with that from the rollover feature seen 

in JVT curves (Fig. 5), which has been identified as 

attributable to the back-contact barrier [10]-[12]. For 

example, the CdTe device with a gold contact yielded a 

back-contact barrier height of 422 ± 5 meV from 

admittance spectroscopy and 424 ± 20 meV from the JVT 

experiment. In contrast, the back-contact barrier height for 

NREL’s devices with graphite contacts is 494 ± 9 meV 

from admittance spectroscopy and 552 ± 10 from the JVT 

experiment. The JVT experiment serves as a useful 

correlated experiment to identify the secondary potential 

barrier. 

Figure 5 The JVT curves taken from a CdTe device 

showing rollover due to the back-contact barrier.

Under most circumstances, admittance spectroscopy 

measures contributions from the response of majority 

carriers. There are usually not enough minority carriers to 

have a significant capacitance contribution. In certain 

devices with highly asymmetrical doping, especially with 

the presence of a suitable heterointerface, it is possible for 

inversion to occur in a region where the minority-carrier 

density is significant. The CdS/CIGS heterointerface is 

such an example [13]. The inversion layer reduces 

interface recombination by repelling the majority carriers.

Recently, there has also been an increasing interest in 

understanding the inversion phenomenon at the 

amorphous (a-Si) and crystalline (c-Si) interface in a HIT 

cell. We show in Figure 6 the band diagram of a HIT cell 

fabricated on n-type substrate. An activation energy of 

0.14-0.28 eV is observed in these devices. There is no 

known bulk defect of this energy in the crystalline silicon. 

After further ruling out the valence-band offset (~0.45 eV), 

we conclude that this activation energy is the 

measurement Fermi level at the a-Si/c-Si interface. The 

band bending is large enough at the interface such that 

that region is strongly inverted. The exchange of holes— 

whose density is comparable with that of electrons in the 

bulk, between the valence band and the Fermi level—can 

thus significantly contribute to an observable admittance 

spectroscopy signal. Unfortunately, there is no simple 

method to distinguish the inverted carrier-induced signal 

from that of the majority-carrier traps. We note that the 

above interpretation can be proven by calculating the band 

bending from measured carrier density and built-in 

voltage.

Figure 6 Band diagram of an n-type HIT cell showing 

the inverted region at the a-Si/c-Si interface.

Admittance spectroscopy is usually carried out with the 

device in reverse bias to avoid interference from the 

diffusion capacitance. If the diffusion capacitance cannot 

be neglected, then the basic physical assumptions of 

capacitance-voltage technique and admittance 

spectroscopy technique are violated. However, one can 

also exploit the diffusion capacitance to study the 

properties of the injected minority carriers. The diffusion 

capacitance, which depends exponentially on the forward 

bias, dominates over the depletion capacitance at 

sufficiently high forward bias. Beyond this point, the 

frequency dependence of the diffusion capacitance is 

dictated by the effective lifetime of the injected minority 

carriers [14]. Figure 7 shows such a frequency

dependence measured from a HIT cell fabricated on an ntype CZ substrate. The hole lifetime is 1/2πfpk = 82.6 μs, 

which is consistent with values measured by other 

techniques such as open-circuit voltage decay (~130 μs). 

The effective lifetime of the holes in c-Si is enhanced by 

surface passivation by the intrinsic a-Si layer. 
4 

Figure 7 Frequency dependence of capacitance (solid) 

and differential capacitance (dashed) due to minoritycarrier lifetime at 0.6 V bias in a HIT device.

CONCLUSION

In conclusion, we show that many physical mechanisms 

other than majority-carrier trapping defects contribute to 

admittance spectroscopy measurements. This contribution 

occurs because the breakdown of certain assumptions of 

conventional admittance spectroscopy, namely: single 

junction, ideal contacts, majority carrier only, and 

measurement in reverse bias. This work first identifies the 

possible physical origins of “interference” and 

distinguishes them from the real defect signatures. More 

importantly, we take advantage of such “interference” and 

devise methods to extract important material and device 

characteristics using admittance spectroscopy. We study 

several non-majority-trap-related properties that are 

commonly seen in admittance spectroscopy measurement 

of PV devices: majority-carrier mobility, freeze-out of 

majority-carrier density or mobility, contact potential barrier 

height, density of inverted minority carriers, and lifetime of 

injected minority carriers. Such properties are usually 

important to PV device operation and could be difficult to 

characterize by other techniques. The validity and 

applicability of these methods are demonstrated by 

application to a variety of PV technologies: CdTe, 

Cu(In,Ga)Se2 (CIGS), silicon heterojunction cells with an 

intrinsic thin (HIT) amorphous silicon layer, and poly(3-

hexylthiophene) organic photovoltaic devices.

ACKNOWLEDGMENT

This work was supported by the U.S. Department of 

Energy under Contract No. DE-AC36-08-GO28308 with 

the National Renewable Energy Laboratory.

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