Subcontract Report 

NREL/SR-520-44101 

October 2008 

Transport, Interfaces, and 

Modeling in Amorphous Silicon 

Based Solar Cells 

Final Technical Report 

11 February 2002 – 30 September 2006 

E.A. Schiff 

Syracuse University 

Syracuse, New York 
Transport, Interfaces, and 

Modeling in Amorphous Silicon 

Based Solar Cells 

Final Technical Report 

11 February 2002 – 30 September 2006 

E.A. Schiff 

Syracuse University 

Syracuse, New York 

NREL Technical Monitor: Bolko von Roedern 

Prepared under Subcontract No. NDJ-2-30630-24 

Subcontract Report 

NREL/SR-520-44101 

October 2008 

National Renewable Energy Laboratory

1617 Cole Boulevard, Golden, Colorado 80401-3393 

303-275-3000 • www.nrel.gov 

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

Office of Energy Efficiency and Renewable Energy 

Operated by the Alliance for Sustainable Energy, LLC 

Contract No. DE-AC36-08-GO28308
This publication was reproduced from the best available copy 

Submitted by the subcontractor and received no editorial review at NREL

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TABLE OF CONTENTS 

Summary ...................................................................................................................................................... iv

Solar Cell Characteristics & Modeling..................................................................................................... iv

Drift Mobility Measurements on CIGS ..................................................................................................... v

Drift Mobility Measurements on Microcrystalline Silicon ....................................................................... v

Polymer p-layers....................................................................................................................................... vi

Optical Properties of n/i and p/i Interfaces .............................................................................................. vii

A. Characterization & Modeling of a-Si:H Solar Cells ................................................................................. 1

1. Introduction ........................................................................................................................................... 1

2. Hole-mobility Limit for pin Solar Cells ................................................................................................ 1

3. Hole Drift-Mobilities in a-Si:H ............................................................................................................. 3

4. Amorphous Silicon nip Solar Cells: Solar Illumination ........................................................................ 4

5. Amorphous Silicon Solar Cells: Uniformly Absorbed Illumination ..................................................... 6

6. Light-Soaking Kinetics of the Open-Circuit Voltage ............................................................................ 9

B. Hole Drift Mobility Measurements in CuIn1-xGaxSe2 Solar Cells........................................................... 14

1. Introduction ......................................................................................................................................... 14

2. Specimens ............................................................................................................................................ 14

3. Time-of-Flight Instrumentation ........................................................................................................... 15

4. Capacitance Measurements ................................................................................................................. 16

5. Transient photocharge measurements ................................................................................................. 16

6. Transit Time and Drift Mobility Estimates ......................................................................................... 17

7. Summary of Mobility Measurements .................................................................................................. 18

8. Discussion ........................................................................................................................................... 19

9. Appendices .......................................................................................................................................... 20

C. Hole Drift-Mobility Measurements and Multiple-Trapping in Microcrystalline Silicon ....................... 22

1. Introduction ......................................................................................................................................... 22

2. Samples ............................................................................................................................................... 23

3. Drift-Mobilities ................................................................................................................................... 23

4. Multiple-Trapping Fits ........................................................................................................................ 23

5. Meaning of Multiple Trapping in microcrystalline silicon ................................................................. 25

D. Polyaniline heterojunction diodes .......................................................................................................... 27

1. Introduction ......................................................................................................................................... 27

2. Experimental procedures ..................................................................................................................... 27

3. Results and discussion ......................................................................................................................... 27

4. Conclusions ......................................................................................................................................... 30

E. Infrared Interface Spectra in Cells .......................................................................................................... 31

References ................................................................................................................................................... 35 

 iii
Summary 

In this report we present the results for the four principal tasks of this research project: 

1. Amorphous Silicon Solar Cell Characteristics and Modeling 

2. Photocarrier Drift Mobility Measurements in hydrogenated amorphous silicon (a-Si:H), 

microcrystalline silicon (μc-Si:H), and polycrystalline copper indium-gallium diselenide (CIGS). 

3. Hole-Conducting Polymers as p-layer Materials for Amorphous and Crystal Silicon Solar Cells 

4. Infrared spectra of p/i and n/i interfaces in a-Si:H based solar cells. 

We have published thirteen papers, including four in Applied Physics Letters, which acknowledge the 

support from this subcontract. See the references [1- 13] and the associated web-links at the end of this 

report. 

Solar Cell Characteristics & Modeling 

The most important finding of our work is that the efficiency of contemporary a-Si:H solar cells is largely 

governed by the hole drift-mobility; the appropriate exceptions and details are summarized below. This 

finding is certainly surprising in the context of the field's longstanding focus on dangling bonds as the 

limitation. Much of this report will be a summary of the experiments which led to this finding, but we 

first take the liberty of discussing its implications for further improving the efficiency of a-Si:H based 

solar cells. 

There is an interesting "desert" between the best values of the hole drift mobility in a-Si:H (hole drift 

mobility about 10-2 cm2

/Vs) and in nc-Si:H (hole drift-mobility about 100 cm2/Vs); in both a-Si:H and 

nc-Si:H, the valence bandtails associated with disorder are the root cause of the low hole mobilities 

compared to crystalline silicon. It seems likely that a-Si:H materials can be grown in this desert that 

would permit better initial-state solar cells than at present. It is also fairly clear that such materials are not 

readily achieved. The "triode" materials prepared a decade ago at ETL have never been reproduced, and 

are the only occupants of the desert known to us. 

Presuming that better initial-state cells can be fabricated by optimizing the hole drift-mobility further, 

would these cells have better efficiencies following light soaking? As will be described below, we believe 

that light-soaking in a-Si:H is "self-limiting" in contemporary materials. By this phrase, we are suggesting 

the perspective that dangling bond creation under solar illumination is arrested once dangling bonds 

become significant competitors to the valence bandtail as photocarrier recombination centers. This 

hypothesis is certainly not tested as rigorously as our findings regarding the initial-state efficiency. 

Nonetheless, it implies that materials with improved hole drift mobilities would possess improved 

properties in their light-soaked state. 

What would be the use of such "improved" materials, if indeed they can be created? Presuming that the 

optical properties of a-Si:H were unchanged, improved electronic properties simply mean that the layer 

thickness of a-Si:H within the solar cell could be usefully increased. This capability would probably not 

improve current triple-junction cells, for which the a-SiGe:H layers are the critical ones. We don’t 

presently know whether the ideas of mobility-limitation and self-limitation of light-soaking are valid for 

a-SiGe:H. On the other hand, improved a-Si:H cells could be quite valuable in "micromorph" and other 

tandem cell designs, which require thicker component cells and use larger photocurrent densities. 

By way of introduction, we now list the principal findings of our work on United Solar Ovonic Corp. 

single-junction a-Si:H solar cells: 

(i) The hole drift mobility is the main electronic property of a-Si:H that determines the power density Pmax

of as-deposited cells [1,2]. Electron drift-mobilities are larger, and nearly irrelevant to the cell’s 

performance. Remarkably, the parameters describing recombination processes are fairly unimportant – 

 iv
even though recombination is the ultimate fate of photocarriers that don't contribute to power generation. 

Recombination parameters weakly affect the cell’s efficiency through its open-circuit voltage. 

(ii) Dangling bonds, which could certainly have reduced the power density below the hole-mobility limit, 

do not appear to have a strong effect on the as-deposited properties of the cells under solar illumination. 

(iii) The power density from light-soaked cells is (of course) noticeably reduced below the as-deposited 

values. In agreement with previous work, we find that the fairly modest decrease in power is primarily 

due to the increase of the dangling bond density with light-soaking. However, the photocarrier processes 

in the light-soaked cells appear to be roughly equally affected by the low hole mobility and by the 

dangling bond density; the dangling bonds don't dominate the light-soaked state for cells under solar 

illumination [2,9]. 

(iv) The time-dependence of light-soaking for the open-circuit voltage is consistent with a reasonable 

extension of the "hydrogen-collision" model, and appears to be inconsistent with the older approach 

(often associated with Stutzmann, Jackson, and Tsai) that attributes the time-dependences to changes in 

photoconductivity kinetics as light-soaking advances [8]. 

Published work from this task: 

"Hole Mobilities and the Physics of Amorphous Silicon Solar Cells," E. A. Schiff, J. Non-Cryst. Solids

352, 1087-1092 (2006). 

 "Hole Mobility Limit of Amorphous Silicon Solar Cells," Jianjun Liang, E. A. Schiff, Baojie Yan, J. 

Yang, Appl. Phys. Lett. 88 063512 (2006).

"Light-soaking Effects on the Open-circuit Voltage of Amorphous Silicon Solar Cells," J. Liang, E. A. 

Schiff, S. Guha, B. Yan, and J. Yang, in Amorphous and Nanocrystalline Silicon Science and Technology 

– 2005, edited by R. Collins, P.C. Taylor, M. Kondo, R. Carius, R. Biswas (Materials Research Society 

Symposium Proceedings Vol. 862, Pittsburgh, 2005), A13.6. 

"Temperature-dependent Open-circuit Voltage Measurements and Light-soaking in Hydrogenated 

Amorphous Silicon Solar Cells," J. Liang, E. A. Schiff, S. Guha, B. Yan, and J. Yang, in Amorphous and 

Nanocrystalline Silicon Science and Technology – 2005, edited by R. Collins, P.C. Taylor, M. Kondo, R. 

Carius, R. Biswas (Materials Research Society Symposium Proceedings Vol. 862, Pittsburgh, 2005), 

A21.8. 

“Low Mobility Solar Cells: A Device Physics Primer with Application to Amorphous Silicon,” E. A. 

Schiff, Solar Energy Materials and Solar Cells 78, 567-595 (2003).

Drift Mobility Measurements on CIGS 

We have been able to estimate the hole drift-mobility in CIGS using photocarrier time-of-flight methods. 

For cells prepared by the Noufi’s group at NREL, the hole drift-mobility has the magnitude 10-1 cm2

/Vs, 

and is not strongly temperature-dependent. For cells prepared by Bill Shafarman and his colleagues at the 

Institute of Energy Conversion (IEC), the drift-mobilities are markedly higher, but also exhibit deeptrapping effects that were not seen for the NREL cells. This latter work is an interesting complement to 

that of Dave Cohen's group, which measured hole mobilities using capacitance methods in IEC samples. 

Photocarrier time-of-flight measures mobilities in the relatively insulating, front portion of the cell. The 

capacitance techniques developed by Cohen's group measure hole mobilities in the back portion of the 

cell , and found a magnitude of 101

 cm2/Vs. We suspect the difference is due to vertical inhomogeneities 

in the CIGS materials of the cell, but this needs to be confirmed. 

Drift Mobility Measurements on Microcrystalline Silicon 

Our measurements of hole drift mobilities in microcrystalline silicon solar cells from Forschunszentrum 

Jülich were published in Applied Physics Letters [5]. We found that the hole drift-mobility was about 1 

cm2

/Vs near room-temperature. The value is much larger than found in amorphous silicon, and it accounts 

 v
for the fact that the optimum thickness of microcrystalline solar cells (using the same hole-mobility 

limited picture just described for a-Si:H cells) is substantially larger than for amorphous silicon. 

In three different papers, we have reviewed the overall picture for hole and electron drift-mobilities in 

amorphous and microcrystalline silicon [1,10]. One interesting result is that the “world champion” hole 

drift-mobility values are presently reported for “polymorphous” a-Si:H [1]. The physics of the mobility of 

microcrystalline silicon is also quite interesting. It is unsurprising that the width of the valence bandtail 

trap distribution for microcrystalline silicon (about 30 meV) is smaller than for a-Si:H (about 45 meV). It 

is intriguing that the fundamental hole band mobility is about the same for the two materials. And it is 

surprising that the attempt-to-escape frequency governing emission from the bandtail is much lower for 

microcrystalline silicon than for amorphous silicon. 

Published work from this task: 

"Hole Drift Mobility Measurements in Microcrystalline Silicon," T. Dylla, F. Finger, and E. A. Schiff, 

Appl. Phys. Lett. 87, 032103 (2005). 

"Drift-mobility measurements and mobility-edges in disordered silicons," E. A. Schiff, J. Phys.: Condens. 

Matter 16, S5265-5275 (2004). 

"Hole Drift-Mobility Measurements and Multiple-Trapping in Microcrystalline Silicon," T. Dylla, F. 

Finger, and E. A. Schiff, in Amorphous and Nanocrystalline Silicon Science and Technology – 2004, 

edited by G. Ganguly, M. Kondo, E. A. Schiff, R. Carius, and R. Biswas (Materials Research Society, 

Symposium Proc. Vol. 808, 2004), 109--114. 

"Hole Drift-Mobility Measurements in Contemporary Amorphous Silicon," S. Dinca, G. Ganguly, Z. Lu, 

E. A. Schiff, V. Vlahos, C. R. Wronski, Q. Yuan, in Amorphous and Nanocrystalline Silicon Based Films 

- 2003, edited by J.R. Abelson, G. Ganguly, H. Matsumura, J. Robertson, E. A. Schiff (Materials 

Research Society Symposium Proceedings Vol. 762, Pittsburgh, 2003), pp. 345--350. 

Polymer p-layers 

Hole conducting polymers are an interesting alternative to silicon-based p-layers for a-Si:H. In principle, 

one can obtain highly variable bandgaps and band alignments relative to a-Si:H. Our hope in these studies 

has been to demonstrate high open-circuit voltages in heterostructure a-Si:H cells using polymer p-layers, 

which would be of fundamental interest (in establishing VOC device physics), and could conceivably be of 

technological significance. The use of heterostructure p-layers has been quite successful for c-Si HIT 

cells, and, technically speaking, the present microcrystalline Si and a-SiC:H p-layers used for a-Si:H 

based solar cells are heterostructure devices. 

Our experimental work has explored doped polyaniline, cast onto the Si layer, as the hole-conducting 

polymer. We had hoped this material would be preferable for casting onto Si, since it uses a non-aqueous 

solvent (typically xylene) and might yield thinner oxide layers near the interface than polymers using 

water as the solvent. While we are able to fabricate decent diodes this way, the open-circuit voltage 

remains at least 0.1-0.2 V below values with conventional, inorganic p-layers. Furthermore, except for a 

particular variety of highly conducting polyaniline obtained from Ormecon, Inc., the illuminated diodes 

have poor photocurrent densities. 

We have obtained open-circuit voltages in a-Si:H n/i/polymer cells up to 0.73 V using “PEDOT:PSS,” 

which is a commercially available hole-conducting polymer. This value is below that obtained with 

conventional p-layers. Interestingly, an NREL/Arizona collaboration has shown that hot-wire a-Si:H cells 

deposited onto PEDOT:PSS in the pin sequence have achieved VOC's of 0.88 V, which is comparable to 

the value obtained for this material with the best conventional inorganic p-layers. However, unlike the 

inorganic p-layer, the polymer p-layer did not require an a-SiC:H buffer layer to achieve this 

performance. We did contribute the device modeling to this work, which was recently published [4]. The 

 vi
 vii

modeling illustrated the role of the conduction band offsets at the p/i interface in accounting for the 

success of both buffer layers and of the polymer p-layer. 

Returning to the polyaniline diodes, we cannot distinguish between the two possibilities of poor 

alignment of the polymer’s valence band with that of Si, or the formation of an interface region with 

completely unknown properties. However, it is fairly clear that polyaniline is unlikely to form a good 

p-layer for a-Si:H and c-Si based solar cells, and we plan to evaluate additional polymers in the coming 

year. 

Published work from this task: 

 “Polyaniline on crystalline silicon heterojunction solar cells,” Weining Wang and E. A. Schiff, Appl. 

Phys. Lett. 91, 133504 (2007). 

"Conducting polymer and hydrogenated amorphous silicon hybrid solar cells," E. L. Williams, G. E. 

Jabbour, Q. Wang, S. E. Shaheen, D. S. Ginley, and E. A. Schiff, Appl. Phys. Lett. 87, 223504 (2005). 

Optical Properties of n/i and p/i Interfaces 

In an extensive collaboration with BP Solar (G. Ganguly), we explored the optical absorption spectra of 

interface states at the n/i and p/i interfaces. The goal was to create a better understanding of the nearinterface region. For one sample series, there is a pronounced effect of the doping level for the n/i

interface, indicating a change in the character of doping near 1%. One possibility is that doping occurs via 

dopant-dangling bond complexes at higher doping levels. 

"Infrared Charge-Modulation Spectroscopy of Defects in Phosphorus Doped Amorphous Silicon," Kai 

Zhu, E. A. Schiff, and G. Ganguly, in Amorphous and Heterogeneous Silicon-Based Films- 2002, edited 

by J.R. Abelson, J.B. Boyce, J.D. Cohen, H. Matsumura, J. Robertson (Materials Research Society 

Symposium Proceedings Vol. 715, Pittsburgh, 2002), 301--306. 
A. Characterization & Modeling of a-Si:H Solar Cells 

1. Introduction 

The device physics of pin solar cells involves – at a minimum – three different materials as well as the 

interfaces between them. Since the invention of hydrogenated amorphous silicon (a-Si:H) pin solar cells 

about thirty years ago, an enormous effort by scientists around the world has generated a correspondingly 

large number of papers detailing the optoelectronic properties of the materials. There have also been a 

number of pioneering efforts to integrate this information into models for the device physics of the cells 

[14- 19]. The task of achieving useful insight when models have dozens of relevant parameters is 

daunting, and it is probably fair to say that there is no consensus understanding about how the cells work. 

In this paper we first describe the hole-mobility limit of the efficiency for pin solar cells with absorber 

layers. Such a limit, which typically applies when hole drift-mobilities are less than around 1 cm2

/Vs, is 

implicit in any of the device models for a-Si:H, but has been little explored since seminal work of 

Crandall [14]. The remarkable aspect of the hole-mobility limit is that it depends quite weakly upon 

processes that might seem more important, including photocarrier recombination and electron mobilities 

(which are assumed to be much larger than the hole mobilities). 

For intrinsic a-Si:H, we summarize the many measurements of hole drift-mobilities; these mobilities are 

very low (typically less than 10-2 cm2

/Vs), although there have been promising reports of better 

mobilities. These mobility measurements are sufficient to establish a “hole mobility limit” for singlejunction cells with an a-Si:H intrinsic layer, and we show that a-Si:H nip solar cells prepared at United 

Solar Ovonic Corp. have achieved solar conversion efficiencies that are very close to the hole mobility 

limit. This achievement is a remarkable one. It implies that dangling bond densities have been kept low 

enough that they do not dominate the drift of holes, and that the n and p layers are good enough to act as 

nearly ideal electrodes to the cell. 

These conclusions apply to the “as-deposited” state of the cells. In use, a-Si:H based solar cells are lightsoaked. Plausibly, the dangling bond density in the cells rises sufficiently to reduce the output power 

below the hole-mobility limit. The saturated degradation in the power is about 30% for thick singlejunction cells that lack optical enhancements such as back reflectors and texturing [26]; the decline is less 

in optimized cells. The conclusion that the as-deposited cells are near their hole mobility limit then 

creates a puzzle, for it seems an unlikely coincidence that the light-soaking process should saturate just 

when cells show noticeable (30% or less) degradation. We therefore speculate that the light-soaking 

process is “self-limiting” in the cells we have studied, and we discuss an obvious – but insufficient – 

mechanism for self-limitation in the concluding section. 

2. Hole-mobility Limit for pin Solar Cells 

Perhaps the most elementary model for a pin solar cell assumes uniform photogeneration G in the 

intrinsic layer, and describes transport and recombination in this layer using only hole and electron 

mobilities μp and μn and an interband recombination coefficient bR. For sufficiently low hole mobility μp

<< μn, and ideal n and p layers, this model yields a fairly simple approximation for the maximum power 

density from a thick cell [20]: 

( ) ( ) ( ( ) ) 41 23 3 = 32 VP OC pεμ eG (1) 

where the open-circuit voltage VOC is given by: 

 ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+=

VCR

OC G NNb

G kTEeV ln 0

 ; (2) 

EG is the bandgap of the material, NC and NV are the bandedge densities-of-states, e is the fundamental 

 1
charge, k is Boltzmann’s constant, and T is the temperature (in Kelvins). ε is the permittivity of the 

absorber (SI units); we use the value ε = 1.05×10-10 C2

/N-m2 that is typical of a-Si:H. 

The expression for VOC is independent of the carrier mobilities. This aspect is important, and is fairly 

readily understood from the perspective that eVOC reflects the splitting of the electron and hole quasiFermi levels EFn and EFp in the intrinsic 

layer [20]. By definition, 

( BVFp NpTkEE V −= ln ); a similar 

relation holds for EFn. These expressions are 

not directly related to mobilities. The same 

perspective accounts for VOC’s logarithmic 

dependences upon bR, NC, and NV. 

The expression for the power density P

depends directly only on the 1⁄4 power of the 

hole mobility μp and the 3⁄4 power of the 

generation rate G. It has a weak dependence 

upon recombination parameters through 

VOC. 

These analytical expressions are based on an 

approximate analysis that neglects the roles 

of diffusion. It is thus important to confirm 

them using a full numerical study of the 

same physical model. The black lines in Fig. 

1 illustrate calculations of P done using the 

AMPS-1D computer code [17] for G = 

3.3x1020 cm-3s

-1, which was selected because 

it has the same magnitude that solar illumination makes in a-Si:H. Results are shown for three values of 

the interband recombination coefficient bR [21]; the value for a-Si:H is around bR = 10-9 cm3

s

-1. The gray 

line is the analytical approximation (eq. (1)) for bR = 10-7 cm3

s

-1. Eq. (1) gives a good approximation to 

the full computer simulation over this range of hole mobilities. For larger values of μh, the power is larger 

than expected from eq. (1); the increase reflects the increased importance of ambipolar diffusion, which 

was neglected in deriving eq. (1). 

10-3 10-2 10-1 100 101

100

101

Power Density (mW/cm2

)

Hole Mobility (cm2/Vs)

 bR (cm3

s

-1)

10-9

10-8

10-7

Analytical (10-7)

Fig. 1: Calculations of the power density from a thick 

pin solar cell as a function of the hole mobility for 

uniform photogeneration 3.3x1020 cm-3s

-1. Numerical 

calculations for three values of the recombination 

coefficient bR are shown as black lines; the gray line 

is from an analytical expression (eq. (1) of the text) 

using bR = 10-7 cm3

s

-1. 

Fig. 2 presents profiles of the “collection efficiency” 1− RG (R is the recombination rate at a particular 

position x) and of the electric field as they were calculated for the maximum power point using the AMPS 

1-D code. The simulations were done for very thick absorber layers (30 μm); photocarrier collection is 

only significant in the p/i interface region that is illustrated. The profiles on the left-hand side are 

calculated for a low hole mobility 0.003 cm2

/Vs. These graphs illustrate that the electric field is confined 

to a fairly narrow region (width dC) near the p/i interface. In addition, the photocarrier collection 

efficiency is only significant within this “collection width,” from which one draws the inference that the 

field-assisted drift of holes dominates the cell. 

 2
This conclusion is consistent with the small magnitude of the ambipolar diffusion length 

( ) amb Rp L = 2 ekT τμ for this mobility; for the present model ( )

− 21

R = GbR τ . The two profiles on the 

right side of the figure illustrate the solutions for a much larger hole mobility 3 cm2

/Vs. For the smallest 

recombination coefficient bR = 10-9 cm3

s

-1, photocarrier collection is dominated by ambipolar diffusion. 

The low-mobility behavior is restored for bR = 10-7 cm3

s

-1, as can also be inferred from Fig. 1. 

3. Hole Drift-Mobilities in a-Si:H 

Fig. 3 shows the drift-mobility of holes near room-temperature for five a-Si:H samples. ECD94 is a 

plasma-deposited sample prepared around 1989; its hole drift-mobility is about the same as was reported 

for other samples prepared in the 1980’s [22]. BP03 is a plasma-deposited material prepared fairly 

recently that used hydrogen-diluted silane as the source gas [23]. Eindhoven05 was prepared using the 

expanding thermal plasma method [24], and Palaiseau03 is a “polymorphous” sample [25]. It seems 

apparent that hole drift-mobilities in a-Si:H have increased in the last decade. It is not clear at present how 

each of the changes in deposition procedures (hydrogen dilution, pressure, reactor design) has contributed 

to this improvement. 

For solar cell applications, the most significant aspect of this graph is that the magnitudes of the driftmobilities for recent samples range from 6x10-3 to 2x10-2 cm2

/Vs. Casual inspection of Fig. 1 indicates 

that the maximum power densities for cells with such mobilities are roughly the same as for a-Si:H 

single-junction solar cells; simplified cells that do not exploit “optical engineering” (light-trapping and 

advanced back reflectors) typically have an initial power density of 7 mW/cm2

 under a solar simulator 

[26]. We show results from a more accurate model for a-Si:H in the next section. 

 3

0.0 5.0 10.0

0.0

0.5

1.0

-5.0

0.0

-1.0

0.0

0.0 1.0

0.0

0.5

1.0 Lamb

Position (μm)

10-9 cm3/s

10-7

10-8

 Electric Field

(103 V/cm)

dc dc

3 cm2/Vs

 bR (cm3

/s)

10-7

10-8

10-9

0.003 cm2/Vs

Collection

Efficiency

Position (μm)

Lamb

Fig. 2: Calculations of the profiles for the photocarrier collection efficiency 1− RG and the electric field 

for a simple model of a pin solar cell; G= 3.3x1020 cm-3s

-1. Graphs on the left side of the figure are 

calculated using a hole mobility of 0.003 cm2

/Vs; the three curves show these profiles for 3 values of the 

recombination coefficient bR. Note that a factor 100 change in bR has little effect on the profiles. The 

graphs also illustrate the field-assisted collection length dC and the ambipolar diffusion length Lamb for 

bR.= 10-9 cm3

s

-1; the small effects of bR and the inequality Lamb < dc are important characteristics of the 

low-mobility limit. Graphs on the right side illustrate similar calculations for a cell with a higher hole 

mobility (3 cm2

/Vs) for which the low-mobility characteristics are less evident. 
We digress briefly to discuss the construction 

of Fig. 3. It is not common to present driftmobilities for different materials and from 

different laboratories on a single graph. The 

reason for this is the “dispersive” property of 

hole drift in a-Si:H and most other lowmobility semiconductors. Measurements of 

the photocarrier “time-of-flight” tT yield 

estimates of a drift-mobility through the 

expression: 

d Vtd T 2 2 μ ≡ , 

where d is the sample thickness and V is the 

bias voltage used in the measurement [

(3) 

27]. 

Experimentally, these drift-mobility 

estimates depend significantly upon the 

voltage that is applied; although rarely 

performed, the estimates also depend upon 

thickness. It isn’t obvious how to compare 

different materials except using the 

cumbersome approach of arranging for 

samples of identical thickness measured at 

some particular voltage. 

This voltage-dependence of μd does not 

imply that photocarrier transport is nonlinear with electric field E. The displacement x(t) of a sheet of 

carriers over a time interval t does (usually) depend linearly upon E. The voltage dependence is instead a 

consequence of “dispersive transport” [28], which is evidenced in the power-law decays of the 

photocurrent transients used to measure the transit times. It can be shown fairly generally that the driftmobility μd depends only on the “displacement field ratio” L/E [29]. Different materials can thus be 

compared – even in the presence of dispersive transport – at common values of L/E, and this was done to 

prepare Fig. 3 [30]. The lines shown in Fig. 3 are actually best-fits to the temperature-dependent hole 

drift-mobilities over the range of temperatures illustrated. 

3.0 3.5

10-3

10-2

ECD94

Eindhoven05

Hole Drift Mobility (cm2/Vs)

Reciprocal Temperature 1000/T (K-1)

L/E = 2x10-9

 cm2/V

Palaiseau03

BP03

Fig. 3: Hole drift-mobility measurements as a function 

of temperature for five a-Si:H samples evaluated at a 

displacement-field ratio L/E = 2x10-9 cm2

/V. 

Definitions of the sample codes are given in the text. 

4. Amorphous Silicon nip Solar Cells: Solar Illumination 

In order to account for the strongly temperature-dependent and dispersive character of hole driftmobilities in a-Si:H, a model incorporating an exponential valence bandtail has long been used [31]. The 

bandtail states act as traps for holes and as recombination centers; such bandtail states are provided for by 

the commonly used modeling codes including AMPS-1D [17] and ASA [32]. The simplest version of the 

valence bandtail model requires two additional parameters beyond those already introduced. These are the 

width of the bandtail ΔEV, and the valence bandtail trapping coefficient bvp that describes capture of 

mobile holes by these traps. 

 4
In Fig. 4 we present a numerical calculation 

(AMPS-1D code) of the dependence of the power 

density of a-Si:H solar cells upon the thickness of 

the intrinsic layer for solar illumination. The 

electronic parameters of the model are presented in 

Table I; they have been published previously [33]. 

The hole transport parameters μp, ΔEv, and bvp are 

consistent with two samples in the middle of the 

range of Fig. 3. The bandtail recombination 

parameter bvn = 10-9 cm3

s

-1 has been taken from two 

independent high-intensity photoconductivity 

measurements [34,35]. The valence bandtail 

density at the bandedge cm-3eV-1 is 

not independent in the present model [

0 21

gv ×= 106

20,33], but is 

required 

 for actual calculations. The bandedge parameters 

NC and NV were chosen to be consistent with 

measurements of the temperature-dependent opencircuit voltage measurements. The bandgap EG and 

the optical absorption spectra were consistent with 

direct optical measurements. Electron mobility 

parameters are given for completeness, but the 

calculations are insensitive to the precise values 

shown. 

For the present calculations, the apparent “hole 

mobility limit” is the saturated value of the power 

found for very thick cells, which is about 7 

mW/cm2

 for the present calculation. As it does 

for the simpler model of section 2, the value of 

the recombination parameter bvn does have a 

slight effect on the calculation; decreasing bvn by 

a factor 10 increases the saturated power by 6%. 

This percentage, calculated for white light 

illumination, is a bit misleading, since strongly 

absorbed green and blue photons are collected 

very readily. For red illumination, and more 

homogeneous absorption, reducing bvn tenfold 

increases the power for thick cells by 13%. 

Increasing the hole band mobility μp tenfold 

increases the power for red illumination by 95%. 

These values are reasonably consistent with the 

results for the simpler model of Fig. 1 and a 

typical mobility parameter μp = 10-2 cm2

/Vs (cf. 

Fig. 3 at T= 295 K). 

Table I: a-Si:H Solar Cell Modeling Parameters 

[33]. Solar cell performance is mainly sensitive to 

the boldfaced parameters. 

μp 0.3 cm2

/Vs Band-mobility of holes. 

ΔEv 0.04 eV Width of exponential 

valence bandtail. 

Nv 4×1020 

cm-3

Valence band effective 

density-of-states. 

bvp 1.3×10-9

cm3

s

-1

Trapping coefficient 

h+

→V0 (valence 

bandtail). 

Eg 1.74 eV Electrical bandgap. 

bvn 1.0×10-9

cm3

s

-1

Trapping coefficient e-

→V+ (valence bandtail). 

μn 2 cm2

/Vs Band-mobility of 

electrons. 

ΔEc 0.02 eV Width of exponential 

conduction bandtail 

Nc 4×1020

cm-3

Conduction band 

effective density-ofstates. 

bcn 1.3×10-9

cm3

s

-1

Trapping coefficient e-

→C0 (conduction 

bandtail) 

0 100 200 300 400 500

0

1

2

3

4

5

6

7

8

 a-Si:H (as prepared)

 a-Si:H (light-soaked)

 Hole mobility limit

Power Density (mW/cm2 

)

i-layer thickness (nm)

Fig. 4: Power output of a-Si:H nip solar cells for 

varying i-layer thicknesses (AM1.5 illumination). 

The symbols represent measurements on cells 

made at United Solar Ovonic Corp. [26]. The line 

is a computer calculation that illustrates the 

maximum power consistent with hole driftmobility measurements (see text). 

Device-makers are sometimes surprised by the 

prediction of a saturated power for larger 

thicknesses in these models, since working cells 

can show a decline in power for larger 

thicknesses. While this issue has not been 

 5
definitively studied, calculations with highly reflecting back contacts do show a peak power for some 

optimum thickness, and a decline for thicker cells [36]. 

The experimental measurements of Fig. 4 are for a series of a-Si:H single-junction nip solar cells prepared 

at United Solar Ovonic Corp. [26]. The cells are deposited directly onto stainless steel substrates, which 

have a fairly low reflectivity. Production cells that are deposited onto textured, highly reflecting back 

contacts have larger power output. On the other hand, these simpler cells are fairly well suited to 

comparison with model calculations, and as can be seen in the figure, the “as-deposited” cells agree 

reasonably well with the calculation. The light-soaked cells were exposed under open-circuit conditions 

for the unusually long time of 30,000 hours, and of course have lower power output than the as-deposited 

cells. 

5. Amorphous Silicon Solar Cells: Uniformly Absorbed Illumination 

In this section, we present temperature-dependent measurements and analyses for a series of a-Si:H nip

solar cells prepared at United Solar Ovonic Corporation that indicate that the efficiencies of these cells at 

solar intensities are mostly determined by the hole mobility of the intrinsic layer. Essentially the same 

conclusion (of mobility or space-charge limited photocurrent) was reached recently for polymer-fullerene 

blend solar cells [37] Temperature-dependent measurements are useful for exploring hole mobility effects 

in a-Si:H solar cells because the strong temperature-dependence of the hole drift-mobility in a-Si:H gives 

a fairly distinctive temperature-dependence for the cell efficiency. The statement that the efficiencies are 

near the hole mobility limit implies that the density of deep levels is sufficiently low that it has a minor 

effect on the efficiency, and that the p/i and n/i

interfaces are sufficiently good that they are 

behaving nearly ideally. We also present 

measurements for the light-soaked state, where 

deep levels do have a clearly measurable effect; 

the mobility-limitation idea remains roughly 

applicable. We conclude that improved 

efficiencies of a-Si:H solar cells will likely 

require further improvements in the hole driftmobility. 

For these experiments, six a-Si:H nip solar cells 

were deposited at United Solar Ovonic Corp. 

using RF glow discharge on stainless steel 

substrates. The n and p layers were the same in 

all depositions; the deposition time for the 

intrinsic layer was chosen to give intrinsic layer 

thicknesses from 185 nm to 893 nm. The cells 

were not optimized for the best efficiency, and 

in particular do not have a highly reflecting 

back contact. Special attention was paid to the 

hydrogen dilution in the intrinsic layer to 

maintain a good material quality throughout the 

entire intrinsic layer and to avoid 

nanocrystallite inclusion. Details of the 

deposition procedures have been given 

elsewhere [38]. As-deposited properties of the 

cells were measured under a solar simulator; 

for the thickest intrinsic layer (893 nm) a typical cell had an open-circuit voltage (VOC) of 0.982 V, a short 

circuit current density (JSC) of 14.4 mA/cm2

, a fill factor (FF) of 0.559, and a maximum power density 

(PMAX) of 7.9 mW/cm2

. 

250 300 350

0.0

0.2

0.3

0.4

0.5

0.6

0.8

0.9

1.0

 186 nm

 377

 574

 893

Normalized Power

P

max

/Js (V)

Temperature (K)

G (295 K) = 3.3 x 1020 cm-3

s

-1

Open-circuit Voltage

VOC (V)

Fig. 5. Temperature-dependent measurements of VOC

and the PMAX/Js for four as-deposited a-Si:H nip

solar cells with varying intrinsic layer thickness are 

indicated by the symbols. Measurements were done 

at constant laser flux; the average photogeneration 

rate G at 295 K was 3.3x1020 cm-3s

-1. The lines 

indicate corresponding calculations for a model 

based primarily on hole drift-mobility 

measurements. 

 6
250 300 350

0.00

0.05

0.20

0.25

0.30

0.35

0.40 Valence bandtail

 Normalized Power 

P

max/Js (V)

Temperature (K)

Deep levels

d = 893 nm

G = 3.3 x 1020 cm-3

s

-1 (295 K)

Fig. 6. Temperature-dependent calculations for PMAX/Js

of an a-Si:H nip solar cell based on a deep-level model 

are shown as the dashed line; the intrinsic layer 

thickness is 893 nm. The corresponding experimental 

measurements (symbols) and valence bandtail based 

calculations from Fig. 1 are also shown for reference. 

Further studies were done using a 30 mW, 

near-infrared (685 nm wavelength) laser. 

We chose to use this laser because its 

wavelength is absorbed fairly uniformly 

throughout the intrinsic layers of the cells, 

which simplifies modeling of the 

measurements. In Fig. 5 we present the 

temperature-dependent normalized 

maximum power density PMAX (T)/Js(T) 

and VOC(T) for four cells with differing 

intrinsic-layer thickness. Js is the 

photocurrent density measured at –2 V, 

which is a good approximation to the 

saturated reverse-bias photocurrent over 

most of the temperature-range. The 

measurements were done at constant laser 

flux. The average photogeneration rate at 

295 K was G = 3.3×1020 cm-3s

-1; G does 

vary with T due to the temperaturedependent bandgap of a-Si:H. 

As has been reported by most previous workers, VOC is nearly thickness-independent. PMAX/Js declines 

markedly with thickness, which indicates that photocarriers generated deep inside a thick cell are likely to 

recombine instead of contributing to power generation. The solid lines in Fig. 5 represent computer 

calculations (AMPS-1D code17) using what we consider to be the simplest reasonable model for an aSi:H nip solar cell. The crucial electrical parameters describe hole transport in the intrinsic layer. The 

code uses the exponential valence bandtail trapping model [39,40] to describe hole transport. The 

parameters we used are given in Table I; as described elsewhere [41], they have been chosen for 

consistency with hole drift-mobility (“time-of-flight”) measurements [42]. The electron parameters are 

given in Table I for completeness, but the calculations are fairly insensitive to them. This is expected 

because electron drift-mobilities are hundreds of times larger than hole drift-mobilities in a-Si:H [40,20] 

Deep levels were not included in the calculations of Fig. 5. We used idealized p and n layer parameters 

for which the precise values have little effect on calculated cell properties; prior experiments indicate that 

doped layers and interfaces are not limiting VOC in contemporary cells [43] The temperature-dependent 

photogeneration rate G(T) was determined from the measured, temperature-dependent photocurrent under 

reverse bias for the thinnest cell (186 nm). The temperature-dependent bandgap EG(T) was determined 

from measurements of the electroabsorption spectrum that are not shown here; this method [44] gave 

results consistent with earlier reports [45]. 

As can be seen from the figure, these calculations give a good account for the temperature-dependent 

magnitudes of VOC and PMAX/Js. The near thickness-independence of VOC and its increase with decreasing 

temperature may be roughly understood using the model that equates eVOC (e is the electronic charge) to 

the separation of electron and hole quasi-Fermi levels in the intrinsic layer [39,40] For the thicker 

samples, the decline in PMAX/Js with decreasing temperature is a consequence of the rapid decline in the 

hole drift-mobility with temperature in a-Si:H [40]. As the hole drift-mobility declines, the region from 

which holes can be collected shrinks, and leads to reduced power from a thick cell [20] At the highest 

temperatures, there is evidently a discrepancy between the model and the PMAX/Js measurements; we 

believe that this reflects the onset of the effects of deep levels (dangling bonds). 

Modelers generally include deep levels when they study a-Si:H solar cells[17,19] but we do not believe 

that deep levels dominate the values of PMAX and VOC of the as-deposited cells studied here. One reason 

for our view is that the measured drift mobilities of holes in a-Si:H essentially establish the largest values 

of PMAX that can be obtained from the cells, and Fig. 1 indicates that the actual power from cells is close to 

 7
these maximum values. If the densities of deep levels were large enough, they would lower PMAX and VOC

noticeably below the calculated values of Fig. 5. A second reason for believing that a density of deep 

levels is not dominating VOC and PMAX is illustrated in Fig. 6, where the dashed line is a calculation of 

PMAX/Js based on the assumption that deep levels do dominate hole trapping. PMAX/Js calculated using deep 

levels decreases as the temperature T increases; both the measured PMAX/Js and the calculation based on 

hole mobilities increase with T. 

For the deep level calculation in Fig. 6, we set the bandtail trap densities to zero. We used a donor-type 

(0/+) deep level that was electrically neutral in the dark. The coefficients for hole and electron capture by 

the deep level chosen to be bdp = 7.5×10-9 and bdn= 4×10-8 cm3

s

-1, respectively. Given μp = 0.3 cm2

/Vs, 

they are consistent with hole deep-trapping experiments [46]. We neglected the slight temperaturedependences. The defect density Nd is 5.7×1016 cm-3 for Fig. 2, which fits the measured power at 230 K. 

While deep levels do not seem to have a noticeable effect on the as-deposited state of these cells, a growth 

in deep-level density during illumination is the most plausible mechanism for the degradation of a-Si:H 

based solar cells during light-soaking [47]. In Fig. 7 we present the measurements for VOC and PMAX/Js for 

an 893 nm cell before and after 200 hours of light soaking at 295 K (G = 3.3×1020 cm-3s

-1). The PMAX

measured at 295 K degraded about 30%, which is comparable to the saturated degradation of thick cells 

after long-term exposure to solar 

illumination.[26] It is interesting that there 

is little difference in the light-soaked and 

the as-deposited states when measured at 

230 K. This convergence of the two states 

at lower temperatures has not, to our 

knowledge, been noted in previous solar 

cell studies. 

250 300 350

0.00

0.20

0.25

0.30

0.35

0.40

0.75

0.80

0.85

0.90

0.95

1.00

1.05

 As-deposited

 Light-soaked

Normalized Power

P

max

/Js (V)

Temperature (K)

d = 893 nm

G (295 K) = 3.3 x 1020 cm-3

s

-1

Open-circuit voltage

VOC (V)

Fig. 7. Symbols indicate temperature-dependent 

measurements of VOC and PMAX /Js for an 893-nm thick 

cell in its as-deposited and light-soaked (200 hours at 

295 K) states. The calculated line through the asdeposited measurements is from the hole drift-mobility 

based calculation of Fig. 5; for the light-soaked state, 

the calculation also includes a density of deep levels.

We were able to account for the 

convergence effect using the modeling 

procedures described above. For the lightsoaked state, we added a density of deep 

levels to the bandtail traps that were used 

to calculate the properties of the asdeposited state [48]. The deep level 

trapping coefficients bdp and bdn were 

noted earlier; the density of defects ND

was adjusted to 2×1016 cm-3 in order to fit 

the measured value of VOC at 295 K after 

light-soaking. This calculation gives a 

satisfactory account for the magnitude of 

PMAX /Js (no parameters were further 

adjusted), as well as for the temperaturedependences of VOC and of PMAX/Js. The 

measurements of VOC at lower 

temperatures are somewhat smaller than 

the calculated values. We speculate that 

this effect is due to a non-ideal p-layer. 

Heuristically, the convergence effect may be understood from the splitting of the electron and hole quasiFermi levels in the intrinsic layer. This splitting increases as T falls (as evidenced by VOC(T)). While the 

density of deep levels is constant, the density of bandtail states between the two quasi-Fermi levels 

increases with this splitting – thus accounting qualitatively for the increased importance of bandtails at 

lower T. 

 8
6. Light-Soaking Kinetics of the Open-Circuit Voltage 

Introduction 

The metastable degradation of the optoelectronic properties of a-Si:H has been actively studied for more 

than 25 years. Important progress has been made by many researchers, but a fully satisfactory picture for 

the effect has never emerged. The difficulty of the metastability problem may, at least in part, be ascribed 

to the fact that there are probably two difficult, linked problems that must be understood simultaneously. 

First, it is likely that photocarrier recombination drives metastability, but - even for a single light-soaking 

state of an a-Si:H sample - no consensus viewpoint on these recombination processes has emerged. 

Second, even if one accepts the role of recombination in mediating metastability, there is no consensus 

viewpoint about how recombination leads to degradation by defect generation or other metastabilities. 

The present section exploits the close connection between the open-circuit voltage VOC measured in an nip

solar cell and photocarrier recombination in the bulk, intrinsic-layer material. In particular we report a 

series of measurements of the time-dependent degradation of VOC in United Solar cells under near-solar 

illumination. In recent work [49] we reported the temperature-dependence of VOC at solar illumination 

intensities. We concluded from these studies that, for their as-deposited state, the recombination traffic in 

our samples flowed predominantly through the valence bandtail states. For the stabilized, light-soaked 

state recombination traffic appears to be split fairly evenly between the valence bandtail and defects. We 

emphasize that these conclusions apply to our materials, under near-solar illumination, and near roomtemperature; these are, of course, the conditions of greatest practical significance for solar cells. 

Using this recombination model as the starting point, we have been able to account for the timedependent decay of VOC using a straightforward extension of the hydrogen-collision model [50] for defect 

generation; the extension assumes that mobile hydrogen is generated by bandtail recombination. For our 

materials, we can also exclude the best known alternative model [51]. 

There is at least one implication of this perspective on metastability that deserves further investigation. It 

appears that there is a coincidence of two time-scales: (i) the time at which crossover between bandtail 

and defect recombination occurs, and (ii) the time at which a stabilized state of the sample is achieved. 

The coincidence suggests that defect recombination may mediate light-induced annealing. 

Measurements 

As-deposited properties of the cells were measured under a solar simulator. This paper emphasizes results 

for the thickest cells, for which the white-light VOC averaged 0.98 V and the white-light fill factors 

averaged 0.66. 

The present measurements were done using a 30 mW, 685 nm wavelength near-infrared laser. We chose 

to use this laser because its wavelength is absorbed fairly uniformly throughout the intrinsic layer of the 

cells, which substantially simplifies modeling of the measurements. We were able to achieve photocurrent 

densities in the cells that were comparable to solar illumination. 

Measurements of the decline of the open-circuit voltage VOC are presented in Fig. 8. The different 

symbols indicate measurements for four different laser intensities. We used four different cells on the 

same substrate for these measurements; the cells had very similar initial properties under white-light. The 

average photogeneration rates G for each experiment are indicated in the figure; these were calculated 

from the measured photocurrent density Jp at Vr = -2 V using the expression ( ) −= rp edVJG , where e

is the electronic charge and d is the thickness of the intrinsic layer. The measurements for the highest 

intensity are most comparable to solar illumination (saturated photocurrent density was 18 mA/cm2

 with 

the laser, and about 15 mA/cm2

 with the solar simulator). We monitored the sample temperature during 

these measurements, which was maintained at 294.5 K to within better than 0.1 K. 

 9
An interesting feature of the 

measurements is that the onset of 

degradation occurs for later times at lower 

photogeneration rates. If we define an 

“onset time” when VOC has declined by 

0.01 V, it is evident in Fig. 1 that this 

onset time increases by more than 1000 

over the range of photogeneration rates in 

the figure. For the largest photogeneration 

rate it appears that VOC is approaching a 

saturation value within this time window; 

saturation at longer times is fairly wellestablished in earlier work on solar cell 

parameters, defect density, and other 

optoelectronic properties of a-Si:H. 

A Modified H-Collision Model 

We presented temperature-dependent 

measurements on the open-circuit voltage 

for a-Si:H cells from the same substrate 

used for Fig. 8. These measurements for 

the as-deposited and the light-soaked 

states are consistent with the following 

model. For the as-deposited states of aSi:H, the photocarrier recombination 

traffic is predominantly through the 

valence bandtail (through the process of 

electron capture by a bandtail-trapped 

hole). Light-soaking then has a surprisingly modest effect: the defect-density rises until recombination 

traffic is fairly evenly split between the bandtails and the defects. 

10-1 101

0.84

0.86

0.88

0.90

0.92

0.94

0.96

0.98

4.0x1020

5x1019

3.5x1020

Open-circuit voltage (V)

Light-soaking time (h)

2x1021

 cm

-3

s

-1

Fig. 8: Decay of the open-circuit voltage with time at four 

different intensities; the average photogeneration rate in the 

intrinsic layer is indicated. The symbols denote the 

experimental measurements in four cells (893 nm i-layer 

thickness, laser wavelength 685 nm) on the same substrate. 

The lines represent calculations for the “extended hydrogencollision model” described in the text. 

One important fact that has been established in several light-soaking experiments [51- 54] is that the 

defect density increases as about the 1/3 power of the light-soaking time: 31

d ∝ tN essentially from the 

onset of illumination until a saturated state is achieved. The original “SJT” explanation [51] for the t

1/3

form made two assumptions. First, recombination traffic through the bandtails Rt generated defects: 

t

d R

dt

dN

∝ . (1) 

Second, for times at which the t

1/3 form applied, most recombination traffic went through defects 

. The particular model that was proposed had the property that the fraction of the recombination 

traffic through the tails obeyed: 

 

d ≈ GR

2 1 t ∝ NGR d , (SJT recombination) (2) 

where G is the carrier photogeneration rate and Nd is the density of defects. With this assumption, one 

obtains the form usually found by experiment: 

 10
( ) 3132

d = 3, SW tGCGtN . (3) 

At least for the samples we have studied, SJTrecombination does not apply over a 

significant time-regime. Recombination 

traffic mostly passes through the bandtail 

states ( ) in the as-deposited state, and 

falls only modestly even for the saturated, 

light soaked state. Although we have not 

studied the growth of the defect density 

during light-soaking with these particular 

samples, the near-universality of the 

observation of the t

1/3 form for Nd(t) suggests 

that we seek an alternative to SJTrecombination for the kinetics of lightsoaking. A similar situation also applies to 

light-soaking with intense pulses. Bandtail 

recombination is completely dominant, but 

defect growth shows a sublinear dependence 

on illumination time [

t ≈ GR

55]. 

The principal alternative to the SJT approach 

is the “hydrogen-collision” model [50], which 

assumes the existence of an illuminationinduced mobile hydrogen density Hm obeying: 

 ∝ NGH dHm . (4) 

GH is the rate at which light generates mobile 

hydrogen, and it has been assumed that the 

recombination traffic of hydrogen mostly 

flows through dangling bonds (density Nd). 

Rarely, mobile hydrogens “collide” to form a 

stable, paired hydrogen complex. Such a 

collision leaves 2 metastable dangling bond 

that are not present in the initial state; the 

defect generation rate obeys the “hydrogencollision” proportionality: 

 ( 2 2

dHm

d NGH

dt

dN

∝∝

Bandtail

Recombination

Defect

Recombination

0 5 10 15

0.0

0.5

1.0

1.5

2.0

Initial

Saturation

0.94

0.96

0.98

Rate (1021 cm-3

s

-1

)

Defect Density Nd (1015 cm

-3)

Generation

Open-circuit Voltage

V

oc (V)

Fig. 9: Bandtail recombination rate Rt and open-circuit 

voltage VOC calculated as a function of defect density 

Nd using the bandtail+defect code. The 

photogeneration rate and defect recombination rate are 

also shown. The initial experimental value of VOC

corresponds to Nd = 1x1015 cm-3, and we have 

suggested a saturation value. Note that bandtail 

recombination is comparable to G throughout this 

range of defect densities.

) (hydrogen-collision). (5) 

Note that the empirical “G2/3t

1/3” form for Nd(t) (eq. 3) obtains if we assume that GG . H ∝

The assumption GG is arguable; several experiments [ H ∝ 56] suggest that defect generation is 

mediated by photocarrier recombination, and not by direct optical processes as is suggested by this 

assumption. Given our conclusion for our samples that t GR is of order unity through most of the lightsoaking process in our samples, we have chosen to explore the modified form for the hydrogen-collision 

model: 

2 2

2

⎜

⎜

⎝

⎛ m ∝

N

G H ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∝ ⎟

⎟

⎠

⎞

∝

d

t

d

d H

N

R

dt

dN , 

 11
or, collecting several proportionality constants together as CSW: 

( ) 2

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ =

d

dt

SW

d

N

NR C

dt

dN (modified H-collision) (6) 

We have indicated that Rt depends upon the defect density; of course, for Rt = G the usual behavior of 

equation (3) obtains. 

Bandtail+Defect Calculations 

In another section of this report, as well as a conference paper [49], we present the parameters and 

procedures of a “bandtail+defect” calculation of the open-circuit voltage; the calculation used the AMPS1D computer program (©Pennsylvania State University). In Fig. 8 we have presented (as the four lines) 

the corresponding calculations for VOC(t) based on eq. (6). Assuming a spatially uniform defect density 

Nd, we used the bandtail+defect calculation to obtain the dependences of the bandtail recombination rate 

Rt and of the open-circuit voltage VOC upon the defect density Nd. These results are illustrated in Fig. 8. 

We then used the function Rt(Nd) to numerically integrate eq. (6) to obtain Nd(t); we used the value 

CSW = 101

 cm-3s that is typical of direct studies of the defect generation during light-soaking [52,53]. Once 

Nd(t) has been computed, VOC(t) is obtained from Fig.9

Experimentally, VOC only declines about 0.04 V (to the value denoted “measured saturation”). As may be 

inferred from Fig. 9, a decline by 0.04 V implies that most of the photocarrier recombination traffic still 

flows through the bandtails. 

10-2 10-1 100 101 102 103 104 1015

1016

1017

t

1/5

Defect Density (cm-3

)

Light-Soaking Time (hours)

t

1/3

G = 2x1021 cm

-3

s

-1

Fig. 10: Calculated growth of the defect density during 

light-soaking (photogeneration rate 2x1021 cm-3s

-1); the 

calculation was based on the hydrogen-collision model of 

defect generation (CSW = 10 cm-3s) and the bandtail+defect 

recombination model. The calculation shows a cross-over 

from t

1/3 to t1/5 kinetics when recombination traffic switches 

from the bandtails to the defects. 

For the four intensities, the agreement 

between the experimental 

measurements and the calculations is 

fairly good through the initial stages of 

the decay of VOC. For longer times the 

measured values for VOC fall much more 

slowly than predicted by eq. (6), which 

undoubtedly corresponds to the onset of 

the “light-induced” annealing effects 

reported previously for defect-density 

measurements [57]. 

For our experiments, we used laser 

illumination that was nearly uniformly 

absorbed; this choice was part of an 

effort to simplify modeling and to avoid 

a non-uniform density of defects. 

Nonetheless, our assumption of a 

spatially uniform value for Nd as it grew 

under light-soaking was not selfconsistent with the spatial profiles of Rt

that were calculated. For the larger 

values of the density Nd, the bandtail 

recombination traffic was reduced in a 

zone about 100-200 nm from the p/i 

interface compared to values in the 

middle of the cell. We used Rt values 

from the middle to do the numerical 

 12
integration of eq. (6). For full self-consistency we would have needed to allow for a profile of Nd. The 

profile would have a reduced density of defects as the p/i interface was approached from the middle. A 

rough analysis indicates that inclusion of this effect would improve the agreement between the 

calculations and the measurements slightly, but we have not pursued non-uniform distributions for Nd

further. 

Discussion 

As noted earlier, the modified H-collision model, in conjunction with the bandtail+defect recombination 

model, predicts some deviations from the t

1/3 form for the dependence of the defect density upon the lightsoaking time. We did not do simultaneous measurements of the defect density during light-soaking of the 

present solar cells. In Fig. 10 we show the predictions of the defect density from numerical integration of 

eq. (6) that corresponds to the highest photogeneration rate we used for experiments. 

The calculations show the expected t

1/3 form for the earlier times. There is a softening that occurs around 

10 hours, which corresponds well to a change in the recombination mechanism. For lower defect density, 

the majority of the recombination traffic goes through the bandtail; for larger densities, the majority goes 

through defects. A t

1/5 form is a good fit at longer times. Experimentally, after about 10 hours VOC begins 

to show saturation behavior (cf. Fig. 8), which we attribute to some “light-induced annealing” process. At 

least for the present samples, it appears that the long-time saturation effect would obscure direct 

observation of the t

1/5 regime. 

It is an interesting coincidence that the crossover time between the two recombination regimes and the 

time at which light-induced annealing sets in are so similar in the present sample. This apparent 

coincidence is the reason offered by the present viewpoint for the fact that open-circuit voltages decline 

only modestly during light soaking (roughly by the thermal voltage kBT/e = 0.025 V), as well as for the 

fact that most direct experiments on the kinetics of the defect density are reasonably consistent with the 

t

1/3 form. 

It is unlikely that two entirely independent processes would appear on the same timescale. We therefore 

speculate that the mechanism underlying light-induced annealing is photocarrier recombination through 

defects. 

 13
B. Hole Drift Mobility Measurements in CuIn1-xGaxSe2 Solar Cells 

1. Introduction 

Over the past decade, polycrystalline CuIn1-xGaxSe2 (CIGS) solar cells have achieved impressive 

efficiencies above 19.5% [58,

59]. Efforts to achieve greater insight into this efficiency by understanding 

the device physics are to some degree confounded by the absence of some of the foundation 

measurements that are required [60]. In this research, we applied the photocarrier time-of-flight (TOF) 

technique to determine the drift mobilities of hole photocarriers. Our measurements are apparently the 

first serious effort to do this. Our findings in brief: 

1. Hole drift mobilities are below 1 cm2

/Vs for specimens from both the National Renewable Energy 

Laboratory and the Institute for Energy Conversion (University of Delaware). 

2. The temperature-dependence is weak; the drift-mobility changed about threefold as the temperature 

fell from 295 K to 100 K in some cells, but this was the largest change. These measurements largely 

exclude shallow traps as the mechanism for the low drift-mobility, which thus appears to be a 

property of hole motion at the bandedge itself. 

3. Despite the fact that cells from NREL and from IEC both have excellent solar conversion properties, 

there are significant differences in their measured hole mobilities which need to be considered in 

modeling work. 

There have been prior measurements of hole mobilities using other techniques [61- 64] and the small 

magnitude of our TOF measurements is somewhat surprising in the context of these earlier 

measurements. We address these differences in the “Discussion” subsection below. 

We have organized this report as follows. We present our measurements for one particular sample from 

IEC in detail to illustrate our procedures. We then present a summary of the temperature-dependent 

mobility and the mobility-lifetime products for all our measurements. Finally, we compare our results 

with related work using Hall effect and admittance measurements to determine mobilities; we speculate 

that the difference between the admittance and the TOF measurements (which are about ten times 

smaller) is due to a gradient in the carrier mobility between the bottom and the top of the CIGS films. 

2. Specimens 

The CIGS thin-film solar cells used for the present measurements were provided by the National 

Renewable Energy Laboratory (NREL) and by the Institute of Energy of Conservation (IEC) at the 

University of Delaware. The cells from NREL have the following description [65]. The substrate used is 

Mo-coated soda-lime glass. The CIGS growth process is NREL's 3-stage process, which incorporates a 

slight modification in the Ga content and substrate heating profile. Essentially, the Ga content in the first 

stage (~30% relative to In) is higher than that of the third stage (~25% relative to In). Device fabrication 

follows by growth of the CdS buffer layer via chemical-bath deposition (CBD) and the ZnO window 

bilayer grown by RF sputtering. The ~50 nm-thick insulating ZnO is grown from an intrinsic ZnO target, 

whereas the ~350 nm-thick conductive layer comes from an Al2O3-doped ZnO target (2wt%). Cd-free 

devices skip the CdS deposition step and only use the bilayer ZnO, which is directly deposited on the 

CIGS absorber. These Cd-free devices use neither `wet' chemistry nor buffer layers to form the junction. 

The devices are finished with ITO-indium tin oxides electrodes evaporated for the transport properties. 

The specimen’s areas are shown in Table II, and have been estimated using a magnifying loupe with a 

built in ruler. All samples incorporate a 100 nm antireflection MgF2 coating. 

The cells from IEC have the following configuration: glass/Mo/CuIn1-xGaxSe2/CdS/ZnO/ITO/(Ni/Al 

grid). The CIGS thin films where grown using elemental thermal evaporation [66] (four source elemental 

evaporation) on top of a 0.7μm thick sputtered Mo layer. The CdS was deposited by chemical bath (CDB) 

and has a nominal thickness of 40nm. The last two layers ZnO and ITO were both deposited using RF 

sputtering, and have thicknesses of 50 nm for ZnO and 0.2 μm for ITO. Finally, the Ni/Al grids were 

 14
deposited by electron beam evaporation. The specimen areas were determined by mechanical scribing in 

order to define an active region. The structural composition and photovoltaic parameters of the specimens 

used in this research are given in Table II. The photovoltaic parameters of the cells are measured under 

standard conditions: 100 mW/cm2

, 25o C, ASTM E 892 Global. The structural composition and 

photovoltaic parameters of the specimen under study are given in Table II. 

3. Time-of-Flight Instrumentation 

The time-of-fight (TOF) measurements were done using a 3 ns pulsed nitrogen laser-pumped dye laser. 

The photocurrents were recorded and averaged (for about 100 laser shots to improve the signal-to-noise 

ratio) using a 500MHz LeCroy digital oscilloscope. The oscilloscope was interfaced to a computer for 

storage and analysis of the transient waveform. 

The specimen was illuminated trough the top layer-n. The laser wavelength was 700nm; the selected 

wavelength corresponds to a photon energy that exceeds the band gap of CIGS material, Eg = 1.12 eV. 

and the absorption coefficient [67], α=105

cm-1 of the material was large enough to ensure that the photons 

are absorbed fairly close to top for witch the absorption length is 0.13 μm (within 10% of the active 

thickness of the specimen), then the transient photocurrent corresponds to holes moving from the top to 

bottom. 

The photocharge generated by the laser was kept well below the CV-charge measured by integrating the 

displacement current waveform. The repetition rate of the laser was reduced until the transient 

photocurrent was independent of the repetition rate; a 1 Hz rate was acceptable. We applied forward and 

reverse biases across the diodes, 1μs prior to the laser pulse; the duration of the pulse was around 30 μs. 

The RC response time of the measuring circuit was comparable in some regimes to the transit time, where 

the resistance R = 100 Ω (for the amplifier and pulser) and C is the sample’s capacitance. We used fairly 

small sample areas to minimize C. 

Table II. Summary of the structural compositions and the photovoltaic parameters of the 

specimens of CuIn1-xCuxSe2. The symbols definition are as follow: Eg is the band gap, VOC

is the open circuit voltage, Jsc is the short circuit current, FF is the field factor, d is the 

physical thickness of the CIGS absorber layer, and A is the cell area (the area for the IEC 

devices was obtained by mechanical scribing). 

Sample IEC-1 IEC-2 NREL-1 NREL-2 

Cu/[In+Ga] 0.82 0.82 ~0.88 ~0.88 

Ga/[In+Ga]=x 0.30 0.30 ~0.30 ~0.30 

Eg (eV) 1.18 1.18 ~1.15 ~1.15 

VOC (V) 0.616 0.636 0.626 0.690 

JSC ( mA/cm2) 33.4 32.2 30.9 31.2

FF 72.9 76.1 68.9 77.2 

Efficiency (%) 15 15.6 13.3 16.6 

d (μm) 2 2 2.6 ~2 .5 

A(cm2) 0.0072 0.0081 0.008 0.0132 0.0132 

 15
-1.5 -1.0 -0.5 0.0 0.5

-100

-50

0

50

100

-100

-50

0

50

100

Charge 

Q (pC)

Applied bias voltage(V)

T=293K

Q

 Capacitance 

C (pF)

C

Fig 11: The symbols indicate the charge response Q

for varying voltage steps 3 microseconds after the 

step. The line through these data is a 2 term 

polynomial fit; the capacitance illustrated is obtained 

from the analytical derivative using the fitting 

parameters (IEC1, 293K, electrode area 8.1×10-3 cm2

). 

4. Capacitance Measurements 

The second measurement performed on 

these samples was capacitance, which is 

important to assess the field profile inside 

the sample. We measured the charge 

transient following a voltage step. The 

measurements of the charge 3 microseconds 

after the pulse are illustrated in Fig. 11 for 

varying pulse heights. As can be seen, there 

is a moderate nonlinearity of the chargevoltage relation, which corresponds to a 

voltage-dependent capacitance C = dQ/dV

that is also illustrated. Such nonlinearity is 

usually ascribed to depletion of defects and 

dopants by the applied bias voltage, and it is 

a complication for time-of-flight 

experiments, which are easiest to interpret 

for strictly uniform fields and negligible 

depletion.

We use the capacitance to infer an effective, 

voltage-dependent thickness for our time-offlight experiments, as we discuss in more 

detail subsequently. For Fig. 11, at -1.5 V 

the capacitance corresponds to an effective 

thickness of 1.8 μm, which is fairly close the 

physical thickness of the CIGS layer (about 

2 μm). 

0 200 400 600 800 1000

0

1

2

3

0.1 V

0.2 V

0.3 V

Photocharge Q (pC)

Time (ns)

T=293K

0.4 V

Fig 12: Transient photocharges obtained by integrating 

the photocurrents at varying bias voltages (-1.0, -0.7, -

0.5, -0.2, -0.1...+0.4) (IEC-2, 293K, electrode area of 

0.0081cm2

). 

The charge transient measurements also 

yield an electronic rise-time for our 

measurements, which convolves ordinary 

RC effects (from 50 Ohm electronics) and 

dielectric relaxation effects within the 

structure. The effects of these times on the 

transit-time measurements were small, but 

not completely negligible. 

5. Transient Photocharge 

Measurements 

In this section we present the transient 

photocharge measurements from which we 

obtained the transit time and the hole drift 

mobility estimates. The time of flight 

measures the transit time tT required to move 

the mean position of the photocharge 

distribution a distance L under the influence 

of the electric field E. Usually, the charge 

distribution is created at some time t and 

positioned by an excitation impulse-in the 

present case, the excitation impulse was a 3 

 16
ns laser pulse. As we mentioned above the laser wavelength was 700 nm, which is strongly absorbed 

within 10% (about 0.1 μm) of the effective thickness of the sample. 

As can be observed the photocharge Q(t) rises until it reaches a plateau near 1 μs for all the applied bias 

voltages. In the simplest examples of photocarrier time-of-flight experiments, the plateau photocharge is 

voltage-independent, and may be identified with the total photocharge Q0 absorbed by the sample. For 

this sample, the photocharge is voltage-dependent. This effect is well known in time-of-flight 

measurements, where it is usually attributed to “deep-trapping” of the photocarriers [68,69]. In Fig. 13, 

we have plotted the dependence of the plateau charge on voltage, along with a fitting to the “Hecht” [70] 

formula: 

 ( )( ( ( VVd ) d

VV QQ −− − − = 0

2

2

0

0 exp1 μτ )) μτ (1) 

where: μτ is the deep-trapping mobility–lifetime product for holes, d is the width of the structure, and V0

is an offset voltage related to the built-in potential VBI across the device. As noted earlier, we used the 

effective, voltage-dependent width obtained from the capacitance for this fitting. 

As was expected from the photocharge analysis the plot has two distinct regions: 

• At high voltages (fields) the photocharge shows saturation. For these voltages the holes are swept 

out to the back electrode in less than 1 μs and hence the charge is constant. 

• At low voltages (fields) the photocharge depends linearly on the voltage. In this case, holes are 

being trapped into deeper states for which the emission time is longer than the 1 um integration 

time for Q. 

The offset potential V0 inferred from this fitting (0.49 V) is smaller than the built-in potential VBI for this 

cell. A lower-limit to VBI (>0.6 V) can be set from the open-circuit voltage Voc for this cell.[71] We 

believe this difference reflects the differing profiles of the built-in potential and the potential induced by 

the voltage step; in particular, a steep built-in potential profile near the top CdS interface wouldn’t be 

detectible by the photocharge method. 

6. Transit Time and Drift Mobility Estimates 

The conventional time-of-flight technique measures a transit time tT required for the mean position of a 

carrier distribution to move some distance L in a uniform electric field E; the drift-mobility is then 

defined as μ D = ( ) tEtL . One implementation of this 

equation is to identify the transit time as the halfphotocharge risetime (the time for the photocharge to 

reach half its ultimate value Q0), and then to equate the 

distance L with half the sample thickness d (L = d/2) 

[72]. For the present research L is equal with depletion 

width w. Writing E = (V0-V)/w, the corresponding 

working equation is: 

( VV t

w

D

T

0 −= 2

2 μ ) (2) 

where again there is an offset expected due to the builtin potential of the cell. -1.0-0.8-0.6-0.4-0.2 0.0 0.2 0.4

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Photocharge Q(pC)

Voltage(V)

Fig 13: Symbols indicate 293 K 

photocharge measurements as a function of 

applied voltage. The line is a fit to the deeptrapping model with parameters Q0 = 4.57 

pC, μτ = 2.8×10-8 cm2

/Vs, and V0 = 0.49 V. 

As suggested by eq. (2), in Fig. 14 we have graphed the 

reciprocal transit-times obtained from the photocharge 

transients as a function of the size of the voltage step. 

We estimated w from the capacitance in Fig. 11. Note 

that w varies somewhat with different voltages; we 

discuss the size of a systematic error associated with 

this procedure in an appendix. The transit-time 

 17
-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4

0.0

0.5

1.0

1.5

2.0

2.5

Reciprocal transit time w2/2tt (cm2/s)

Voltage(V)

Fig. 14: Dependence of the reciprocal photocharge 

rise times (293 K) upon applied voltage at room 

temperature. The fitting line excludes the two points 

at the largest Voltages. The slope of the linear fit 

yields the mobility estimate of 0.82 cm2

/Vs. The 

voltage intercept V0= 0.303 V is related to the builtin potential VBI. 

estimates tT were obtained from the actual 

risetimes tR by making a correction for the 

electrical response time tstep (measured using 

the voltage step) and the pulse-width of the 

laser tlaser: 

 (3) 

Details are given in an appendix. The error bars 

were determined by making several risetime 

measurements at each voltage and propagating 

the risetime error into the error in w

2

/2tT. The 

large errors for more negative bias voltages 

occur because the photocharge risetime 

approaches the shortest value permitted by the 

laser pulsewidth and the electronic response 

time. 

2222

laserRT step −−= tttt

The fitting line through these measurements 

was obtained using a least-square fit; we 

excluded the two highest voltages for which 

deep-trapping effects (cf. Fig. 13) are most 

important. The slope of the fitting line yields a 

mobility of 0.8 cm2

/Vs. The offset voltage of 

the fit is 0.30 V. This value is somewhat 

smaller than found from the deep-trapping 

analysis (0.49 V); presumably, the discrepancy 

is indicative of the error in V0. 

7. Summary of Mobility Measurements 

In Fig.15 we illustrate the summary of the hole drift mobilities as a function of temperature for seven 

different cells; each substrate is represented 

by at least two cells, the only exception is 

substrate IEC-2; this substrate is represented 

by one cell. Although the measurements as a 

function of temperature are fairly wellbehaved, for nearly every cell we had 

“outlier” measurements that deviated 

substantially from the overall trends. We have 

not traced back this problem. There are also 

some differences between different cells that 

were fabricated on the same substrate. 

The temperature-dependence is quite weak 

compared to amorphous semiconductors, and 

in particular there is no consistent evidence 

for activated behavior μ D exp( ) Δ−∝ BTkE ; 

activated behavior would be expected if the 

drift-mobility were limited by traps that 

capture and bind holes with a binding energy 

ΔE, but release them within the 1 microsecond 

timescale of our experiments. 

100 150 200 250 300

0.01

0.1

1

NREL

IEC

 Temperature T(K) 

Hole Drift Mobility 

μD(cm2/Vs) 

Fig 15: Hole drift mobilities for four CIGS samples at 

varying temperature. IEC-1: ▲▼. IEC-2:◊. NREL-1: 

■□►. NREL-2: ●○

 18
0 50 100 150 200 250 300 10-2

10-1

100

101

102

103

crystals

Admittance

Hole Drift Mobility 

μD (cm2/Vs)

Temperature T(K)

TOF

Hall

Fig. 17: Survey of hole mobility measurements in 

CIGS for varying temperatures; samples are thinfilms except as noted. ■-Hall effect 

measurements. ●-Admittance measurements on 

IEC samples. ▲-IEC TOF measurements, 

▼-NREL TOF. 

As we mentioned, there does appear to be significant variation between samples from the two laboratories 

that is discernible in their drift mobilities, and in the mobility-lifetime products. In Fig. 16 we illustrate 

the variability of deep trapping mobility lifetime product with respect to temperature; in the left side of 

Fig 16 we illustrate the NREL cells, and in the right side the IEC cells. Although the measurements as a 

function of temperature are fairly well-behaved, we had one “outlier” measurement (■ IEC -1) that 

deviated substantially from the overall trends. We have not traced back this problem. On the other hand, 

we had an NREL sample which did not exhibit a measurable deep-trapping product at room temperature; 

we show this inside the shaded rectangular area in 

Fig.16. This point appears to represents an upper 

limit to the mobility-lifetime product which can 

be measured using the Time of Flight method. 

100 150 200 250 300

0.01

0.1

100 150 200 250 300

0.01

0.1

Hole μτ Product (10-6 cm2/V)

Temperature(K)

NREL

Temperature(K)

Hole μτ Product (10-6 cm2/V)

IEC

Fig. 16: Variation of the hole deep-trapping mobility-lifetime product μτ with the temperature for various

samples. The left panel shows results for NREL devices: □○◊-(NREL-1), ▼▲-(NREL-2); the right

panel shows results for the IEC devices: ■●-(IEC-1), ○-(IEC-2). 

8. Discussion 

In Fig. 17, we present most of the hole mobility 

measurements that have been done on the CIGS 

system using three different techniques: Hall 

effect, admittance, and time-of-flight. The Hall 

effect mobilities measured on epitaxial, singlecrystal films [61] are much larger than the 

mobilities for thin-films. Hall effect mobilities in 

single crystals are usually equated with the 

fundamental “band mobilities” of carriers in 

extended electronic states; they are insensitive to 

trapping effects that could affect the other 

mobility measurements. 

The admittance method mobilities [64] are based 

on measurements of the dielectric relaxation time 

τdielectric of the bottommost, undepleted region of 

the thin-films. τdielectric is simply related to the 

region’s conductivity peμ. When the density of 

mobile holes p in this region can be determined 

 19
from analysis of the capacitance, a mobility can be inferred. The fact that the thin-film admittance 

mobilities are much lower than the single-crystal Hall mobilities indicates that the hole band mobility is 

greatly depressed in the polycrystalline materials; trapping effects are excluded if the procedure is 

successful. 

The admittance measurements of the hole mobility were done on samples from the Institute of Energy 

Conversion that are comparable to the samples used to obtain the upper band (▲) of time-of-flight (TOF) 

mobilities; the TOF mobilities are about ten times smaller. TOF estimates drift-mobilities that are affected 

by multiple-trapping, so in principle trapping effects could account for the difference. However, given the 

weak temperature-dependence of the drift-mobilities, we doubt that this explanation is correct for these 

samples. A second possible origin for the difference in the admittance and TOF mobilities is their 

differing spatial sensitivities. The TOF technique is sensitive primarily to hole motion in the top half of 

the depletion layer; the admittance method is sensitive to hole motion in the bottom, undepleted region. 

We therefore suggest that these samples have a mobility gradient, with larger hole mobilities at the 

bottom than at the top. 

We now turn to the deep-trapping mobility lifetime product (μτ) measurements. One earlier experiment 

reported μτd = 6x10-6 cm2

/V for holes in polycrystalline CuGaSe2 [73], which is well above the scale of 

Fig. 16. The lower values reported here (10-8 - 10-7 cm2

/V) are just small enough that they could 

determine the depletion width of illuminated CIGS cells and be a significant factor in their solar 

conversion efficiencies. 

9. Appendices 

a. Time-of-flight in a standard depletion layer 

When the electric field is not uniform, as evidenced by a voltage-dependent capacitance, the procedure of 

substituting a depletion width calculated from a capacitance in the expression (2) for the drift mobility 

leads to a systematic error. The error can be calculated for known field distributions. For example, for the 

linearly falling electric field of the standard depletion model for semiconductors [74], one can substitute 

the depletion width for w. We now show that using eq. (2) with this additional assumption leads to 

overestimation of the drift-mobility by 44%. 

We assume that the electric field at the interface is E0, and that a sheet of carriers is generated at this 

interface at time t = 0. Then the time required for a photocarrier to move a distance x away from the 

barrier is −= ( ) (1ln − wdxEwt μ 0 ). The "transit time" tT occurs when x = w/2. Since E0 = 2(V/w), we 

get ( ) 693.02 2 VwtT = μ D ; we are neglecting the built-in potential. Denoting the “naïve” estimate of the 

drift mobility as estD 2Vtw T

2 μ , = , we obtain μ estD D μμ D 443.1

693.

1 , == ; the naïve expression, 

uncorrected for the non-uniformity of the field, overestimates the drift mobility by 44%. 

We consider 44% to be the upper limit to the systematic error for our measurements; the capacitance we 

measured (cf. Fig. 11) depended more weakly on voltage than expected for the standard depletion model. 

b. Effects of electronic risetimes and laser pulsewidth on transit-time estimation 

The risetime of the photocharge convolves several different response times: (i) the photocarrier transit 

time tT, (ii) the laser pulsewidth tlaser, and (iii) the RC response time coming from the product of the 

depletion layer capacitance C with the 100 Ohm effective resistance of the electronics (pulser and 

oscilloscope), and (iv) the dielectric relaxation time of the bottom, undepleted layer of the sample. A 

rough guide to the effects of (ii), (iii), and (iv) can obtained from the photocharge rise time at large 

reverse bias (cf. Fig. 11), where the transit time is shorter than the risetime due to the other effects. 

 20
However, because the depletion-layer capacitances of the samples increase as the bias voltage increases, 

this method is not sufficient to estimate the electronic effects for larger (more positive) bias voltages. We 

also studied the purely electronic effects (iii) and (iv) explicitly by measuring the risetime tstep of the 

charge response of the sample to the bias voltage step. We then calculated the transit time from eq. (3) 

above, which is based on the Walken and Wallman [75] approximation for convolving risetimes: 

 (3) 

The laser pulsewidth is 4 ns. We checked this expression using the photocharge risetime tR at large 

reverse-bias voltage, where tT is small, and found satisfactory agreement. 

2222

laserRT step −−= tttt

 21
C. Hole Drift-Mobility Measurements and Multiple-Trapping in 

Microcrystalline Silicon 

1. Introduction 

There have been several reports of drift-mobility measurements [76- 79] in microcrystalline silicon in the 

last decade or so since it became clear that this material could be prepared with properties that are 

interesting for solar cells [80]. There is, of course, an enormous range of possible structures in 

microcrystalline silicon materials. For each sample there is a spectrum of sizes for the component nano & 

microcrystallites. Even more poorly understood, for each sample there is also a jumble of non-crystalline 

material that lies between the crystallites. Unsurprisingly, there has also been a very large spread in 

reported drift mobilities and transport properties. 

In this paper [7,10,11] we shall first summarize our recent hole drift-mobility measurements in a 

particular form of microcrystalline silicon that has been developed at Forschungszentrum Jülich as a solar 

cell absorber, and for which cells with 8.7% conversion efficiency have been reported [81]. We shall not 

offer a detailed defense of the measurements here, nor shall we offer an extended review and comparison 

with previous work on microcrystalline silicon; these will be presented elsewhere. Instead, we emphasize 

an unexpected aspect of the present measurements, which is that they exhibit the features of “exponential 

bandtail multiple-trapping.” 

Since its first successful application to amorphous semiconductors in the early 1980’s (see Tiedje’s 

review [82]), exponential-bandtail multiple-trapping (usually abbreviated as simply “multiple-trapping” 

or “MT”) has become the standard approach to analyzing most transport experiments in hydrogenated 

amorphous silicon (a-Si:H) and related materials such as amorphous silicon-germanium alloys. The 

model assumes an exponential bandtail of localized states lying at the bottom of the conduction band, or 

at the top of the valence band. The application to transport also assumes the existence of a “transport 

edge,” with the property that the only carriers that contribute to electrical transport are those occupying 

electronic states lying above this edge (for electrons) or below it (for holes); it has generally been 

assumed that this edge is the “mobility-edge” dividing localized and extended electronic states. 

In the present work we have found that multiple-trapping obtains for our measurements in a 

predominantly crystalline form of microcrystalline silicon. This form of microcrystalline silicon is 

apparently a far more ordered material than amorphous silicon, and certainly X-ray measurements, 

Raman scattering, and direct microscopy indicate that most of the volume is associated with small 

crystallites. One is naturally drawn to models for electrical transport that are based on the effective-mass 

theory, which would seem to apply at least within a crystallite. Indeed this approach has been applied 

recently to Hall mobility measurements in n-type microcrystalline silicon [83]. It is thus a bit of a shock 

to discover that the multiple-trapping model taken from amorphous semiconductors is a better description 

of microcrystalline silicon than is an effective-mass based approach – but this is the implication of our 

measurements. The multiple-trapping parameters in the microcrystalline material do differ in interesting 

ways from those that have been reported for a-Si:H, and we shall return to this comparison in the 

concluding section of this paper. 

 22
2. Samples 

The samples used for our 

measurements were pin structures 

prepared in designated chambers of a 

multi-chamber system using plasmaenhanced chemical vapor deposition 

at frequencies of 95MHz (VHFPECVD) [81]. We used ZnO coated 

glass as a transparent, conductive 

substrate. The μc-Si:H(B) p-layers are 

about 20nm thick; the films were 

doped by adding trimethylboron to the 

silane-hydrogen gas mixture. The 

intrinsic μc-Si:H layers were prepared 

using a silane-hydrogen mixture of 5-

6%. The n-layer (phosphine doped) 

was an amorphous a-Si:H(P) layer 30 

nm thick. As top contacts we used 

sputtered ZnO dots with diameters of 

1-2 mm; we plasma-etched (SF6-gas 

process) the top surface of these structures to remove the n-layer from regions not under the ZnO. 

In this paper we present measurements on three samples summarized in Table III. To determine the extent 

of crystallinity, Raman spectra were recorded from the i-layer at spots right next to the ZnO contacts. The 

integrated intensity ratio IC

RS =IC/(IA+IC) was determined by deconvoluting the spectra into three signal 

peaks at 480 cm-1, 500 cm-1 and 520 cm-1. The first one can be attributed to a disordered structure like an 

amorphous phase or grain boundaries (IA), and the latter two are attributed to the crystalline phase (IC) 

[84]. 

3. Drift-Mobilities 

The transient photocurrents were measured in the pin diodes following illumination by a 3 ns laser pulse 

(wavelength λ = 500 nm) through the n-layer. The photocurrent 

transients were consistent with a conventional interpretation in 

terms of hole time-of-flight. In particular, the photocharge was 

independent of the applied voltage, and a transit-time was 

discernible in the transient. Additionally, the photocurrent at short 

times was linear in the applied voltage, which is consistent with 

transport that is linear with electric field. 

In Fig. 18 we present our temperature-dependence measurements 

of the hole drift-mobility for 3 samples [85] corresponding to a 

particular “displacement/field” ratio d2

/2V = 7x10-8 cm2/V of 

sample thickness d and applied field (V/d). The activation energy (0.13 eV) is illustrative only, and does 

not indicate any particular depth for the bandtail traps. These average drift-mobilities, determined using 

μD = d2

/(Vtτ), are much larger than typically obtained in a-Si:H [86], although a direct experimental 

comparison at the same value for d2

/V is not possible. We compare multiple trapping fitting parameters 

shortly. 

4. Multiple-Trapping Fits 

Our procedure for fitting to the multiple-trapping model starts with the transient photocharge Q(t) (the 

time-integral of the photocurrent i(t)). In particular, we fit to the time-dependence of the normalized 

Table III: Sample Properties 

Sample Raman 

Ratio IC

RS

i-layer 

thickness

d (μm) 

B 0.71 4.0 

D 0.60 3.4 

E 0.61 4.3 

3 4 5 6 7 8 9 10 1

10-5

10-4

10-3

10-2

10-1

100

1

 B

 D

 E

Hole Drift Mobility (cm2

V-1

s

-1

)

1000/T (K-1)

EA=0.13eV

Fig. 18: Hole drift-mobilities measured for three 

microcrystalline silicon materials (cf. Table I) determined 

with a displacement/field ratio d2

/2V = 7.8 x 10-8 cm2/V. 

 23
10-9 10-8 10-7 10-6 10-5 10-4

10-9

10-8

10-7

 T=275K

 T=250K

 T=225K

 T=200K

 T=175K

 T=150K

 T=125K

Transient Photocharge

Q(t)d2

/Q0(V-Vbi) [cm2/V]

Time [s]

μ0 = 1 cm2/Vs

ΔE = 31 meV

ν = 109 s

-1

Fig. 19: The symbols are normalized photocharge transients measured in one microcrystalline silicon 

sample (“D” in Table I); the solid lines are the corresponding calculations using the exponential 

bandtail multiple-trapping model with the parameters indicated.

photocharge () ( ) 0 +VVQdtQ bi

2 , where Q0 is the total photocharge of holes generated by the laser 

pulse, V is the bias voltage, d is the i-layer thickness, and Vbi is a correction for the internal field.We have 

illustrated the photocharge measurements in Fig. 19 for seven temperatures. For clarity, we have removed 

sections of the transient for Q(t) > Q0/2; these portions of the transient are past the “transit time,” and are 

not used in our multiple-trapping fitting procedure. We have also removed early-time portions of the 

transients that are clearly dominated by response-times of the measurement. 

The solid lines in Fig. 19 are the multiple-trapping fittings. The actual equation that was fitted to the 

normalized photocharge is [86]: 

( ) ( ) ( ) T tKEtL α ν

ν

μ ⎟

⎠

⎞ ⎜

⎝

⎛ = 0 / . (1) 

L(t) is the mean displacement for photocarriers after a delay time t and with electric field E. The 

dispersion parameterα Δ= EkT V , where ΔEV is the width of the exponential, valence bandtail, μ0 is the 

valence band-mobility, and ν is an “attempt-to-escape” frequency characterizing the rate of release of 

holes from the bandtail traps. The constant K = sin( ) ( (1−ααπαπ )) is of order unity. The multipletrapping parameters we chose (and that are the basis for the solid lines shown in Fig. 2) are given in Table 

IV below, along with some results for a-Si:H [86,87]. 

 24
Table IV: Multiple-trapping fitting parameters 

Multiple-trapping parameter μc-Si:H 

(this work) 

a-Si:H 

(ref. 86) 

a-Si:H 

(ref. 87) 

Valence band-mobility μ0 (cm2/Vs) 1.0 0.7 0.3 

Bandtail width ΔEV (meV) 31 45 48 

Attempt-frequency ν (s-1) 9x108 1x1012 8x1010 

5. Meaning of Multiple Trapping in Microcrystalline Silicon 

One approach to analyzing mobilities in polycrystalline materials is to invoke the effective masses that 

would obtain for electrons and holes in the single crystal, and assume that the grain boundaries act as 

scatterers or barriers and as the locus for traps for the carriers [83]. It is instructive to use this approach 

crudely to calculate an “effective-mass carrier mobility” for holes utilizing the expression me .. μh

( ekTlv ) th me

h =.. μ , where vth is the “thermal velocity” for holes (about 107

 cm/s in c-Si near roomtemperature) [88] and l is a scattering length. If the scattering length is identified with a typical crystallite 

size of 3 nm, we infer cm2

/Vs, or about 100 times larger than the estimate in Table I. The 

effects of traps and barriers seem unlikely to explain the discrepancy for our samples, since these were 

already (implicitly) incorporated in the analysis that led to the estimate μ0 = 1 cm2

/Vs. 

120 .. = me μ h

We suggest that, for our samples of microcrystalline silicon, the disorder is sufficient to strongly alter the 

bandedge states from their crystalline counterparts. In particular, we suggest that the bandedge states of 

the crystal have been transformed into a bandtail (i.e. that the density-of-states g(E) has been altered), and 

that a mobility-edge has formed within the bandtail [89] (i.e. states lying deeper in the energy gap are 

localized). 

The mobility-edge has been widely applied to amorphous semiconductors [82,90], and has recently been 

applied to microcrystalline samples with a larger fraction of amorphous “tissue” [91]. Here we are 

suggesting that it be applied to samples that are predominantly crystalline. In the mobility-edge model, 

hole states with energy levels below the mobility-edge (E < EV) are completely delocalized (by 

definition), although with very different wavefunctions than the effective-mass states of crystals. Hole 

states lying above the mobility-edge (E > EV) are localized. Both analytical and computational studies of 

mobility-edges [92,93] indicate that the localization radius for a hole state grows very rapidly, and may 

even diverge, as the state’s energy approaches the mobility-edge. It isn’t clear theoretically how particular 

atomic-scale features such as “strained bonds” are incorporated into the bandtail states. 

With this perspective, we first discuss the bandtail width ΔEv. The estimate of 31 meV for the 

microcrystalline material seems unremarkable in the context of work on holes in amorphous silicon, 

which yield values in the range 40 – 50 meV. It is worth noting that disorder affects holes and electrons 

very differently. The conduction bandtail in amorphous silicon has a width around 22 meV [82,90]. 

Electron properties in samples quite similar to the present ones have been studied using post-transit timeof-flight [91]; bandtail multiple-trapping did not apply for these transients. An interesting possibility is 

therefore that electron transport may be governed by effective masses in exactly the same material for 

which holes require a mobility-edge approach. 

 25
The fact that the hole band-mobility μ0 is about the same in the present microcrystalline samples and in 

amorphous silicon seems to support the mobility-edge interpretation, and more broadly suggests that a 

value near 1 cm2

/Vs may be a universal property of a mobility edge. Such “universality” is also suggested 

by the fact that electron band-mobilities in amorphous silicon are also around 1 cm2

/Vs [82,90]. 

Interestingly, a band mobility of 1 cm2

/Vs is not an obvious implication of the existing theoretical 

treatments of mobility-edges. 

Finally, we turn to the attempt-frequency ν. It is quite interesting that the value for microcrystalline 

silicon is substantially (about 100 times) smaller than the lower values reported for a-Si:H. However, 

even for a-Si:H, there is no well-accepted physical interpretation for this parameter. One often-mentioned 

interpretation is that ν be identified as a “typical phonon frequency,” but this association fails to explain 

either the very low magnitudes or the enormous range of magnitudes that have been reported 

experimentally [94]. Yelon and Movaghar have suggested that multi-phonon effects lead to the 

variations, and this perspective has been applied by Chen, et al., to drift-mobility measurements [95]. 

Another possibility originating with high-field drift-mobility measurements in a-Si:H has been that ν

reflects the bandedge density-of-states g(EV) [96], which suggests that the present measurements be 

interpreted as indicating a substantially lower value for g(EV) in microcrystalline than in amorphous 

silicon. Plainly, we need more clues from experiment about the meaning of this parameter; it seems 

possible that its dramatic lowering in microcrystalline silicon could be providing it. 

 26
D. Polyaniline heterojunction diodes 

1. Introduction 

Organic/inorganic heterostructure solar cells have been studied by various groups in the past. Among 

those studies, there were only a few reports on conducting polymer/amorphous silicon (a-Si:H) structures 

[97-

99] and conducting polymer/crystalline silicon (c-Si) structures [100,1] In this paper, we report our 

research on polyaniline (PANI)/a-Si:H heterostructure solar cells; PANI is a p-type conducting polymer 

and is stable in the air, making it suitable for various applications. We studied the open-circuit voltage 

VOC of these heterojunctions under illumination as a function of the conductivity of the PANI films. The 

measurements are consistent with the model that VOC was limited by the work functions of the PANI. We 

compare these results with our recent work on PANI/c-Si cells [1]. For these cells, VOC vs. conductivity 

data shows essentially the same relation as for a-Si:H - excepting that VOC saturates at 0.5 V for higher 

conductivity PANI. The band offsets between a-Si:H and c-Si were estimated using the two sets of 

measurements, and were in satisfactory agreement with previous estimates from photoemission 

measurements [101,102] We discuss the saturation effect for c-Si/PANI cells in light of the absence of 

saturation for the a-Si:H/PANI cells. 

2. Experimental Procedures 

Dispersions of acid-doped PANI in xylene from Sigma-Aldrich, Inc. and from Ormecon GmbH [103] 

were used. n-i a-Si:H structures were deposited onto stainless steel using a commercial plasma-enhanced 

chemical vapor deposition reactor. The thickness of the intrinsic layer is 0.80 μm. n-type, (100) 

crystalline silicon wafers were etched by 2.5% HF solution; the wafer conductivities were 2 S/cm. For 

most cells, aluminum was evaporated on the unpolished backs of the c-Si wafers to form a back contact. 

On some cells, n-type a-Si:H was deposited at NREL to form a back surface field contact. 

The two different solar cell structures were then made by spin coating the PANI dispersions onto freshly 

made a-Si:H or the polished surface of c-Si. A wide range of PANI conductivities was obtained by 

increasing the concentration of xylene of the Aldrich dispersion. The films were dried in air at 80 C for 24 

hours after casting for Aldrich’s PANI and at 100 C for 1 min for Ormecon’s PANI. A 1 mm diameter 

gold contact (50 nm thick) was evaporated onto the PANI film. The area of the PANI film was typically 

about 1 cm2

. The PANI films were 0.1-0.4 μm 

thick [104]; the conductivity of the PANI films 

was between 10-5 S/cm to 101

 S/cm depending on 

dilutions for the Aldrich dispersion, and was 102

S/cm for the Ormecon dispersion. Scanning 

electron microscopy indicated that the films were 

continuous, although with somewhat differing 

morphologies for the differing dilutions. 

-1.0 -0.5 0.0 0.5 1.0

-20

-10

0

10

20

 Dark

 Illuminated

Current density (mA/cm2

)

Voltage (V)

Fig. 20: Current density as a function of voltage 

across a PANI/c-Si diode (Ormecon dispersion, 

1.2×102

 S/cm). The white-light illuminator intensity 

was 0.1 W/cm2.

3. Results and Discussion 

The dependence of the current density upon 

voltage is shown in Fig. 20 for a PANI/n-Si 

diode (Ormecon dispersion) for the dark and for 

tungsten-halogen illumination through the PANI 

(intensity 0.1 W/cm2

). The saturated 

photocurrent density is 17 mA/cm2

, which is 

reasonably consistent with the photon flux that 

reaches the c-Si after filtering by the PANI film. 

The open-circuit voltage VOC is 0.51 V, which is 

about 0.1 V below the values observed for c-Si 

 27
based cells with metal back electrodes [105]. The 

low fill-factor of 41% is due to the lateral 

resistance of the PANI film (and the absence of a 

top metallic grid). It is of interest that the light and 

dark curves cross at about 0.6 V; while such 

“crossover” is not typical of homojunction c-Si 

diodes, it has been reported previously for 

heterojunctions such as PEDOT/a-Si:H [97,99]. 

In Fig. 21, the open-circuit-voltages VOC for the 

PANI/a-Si:H and PANI/c-Si diodes are shown as a 

function of the conductivities σ of “sibling” PANI 

films cast onto glass using the same dispersion. 

We used white-light illumination through the 

PANI with intensity 0.58 W/cm2

. 

For c-Si diodes, was almost constant (at 

= 0.52 V) above a threshold conductivity σc = 0.05 

S/cm. Below the threshold conductivity, the data 

can be fitted well by the form: 

 

Voc

sat VOC

( ) ( ) max Voc = .0 72 + B eTk ln σσ ,

 (1) 

where eTkB = 0.025 V is the ratio of the 

Boltzmann thermal energy to the electron charge 

and σmax is 102

 S/cm, which is the largest 

conductivity PANI (from Ormecon) that we used. For σ < σc, the logarithmic dependence of VOC on 

PANI conductivity is consistent with the idea that VOC is limited by the built-in potential across the 

PANI/c-Si heterojunction [106]: 

 , (2) 

where is the Fermi-level of the (n-type) c-Si and is the Fermi level of the p-type PANI film. 

Assuming that the conductivities of the PANI films are mainly determined by their Fermi levels, we write 

Si PANI

F F eVoc −=≈ EE

Si

F E

eVBI

PANI EF

( ( ) )

10-6 10-4 10-2 100 102

0.3

0.4

0.5

0.6

0.7

0.8

 Ormecon/a-Si

 Ormecon/c-Si/a-Si

 Ormecon/c-Si/Al

 Aldrich/a-Si

 Aldrich/c-Si/Al

Open Circuit Voltage Voc(V)

PANI Conductivity (S/cm)

Fig. 21: Open-circuit-voltages VOC of PANI/a-Si:H 

and PANI/c-Si solar cells for PANI films with 

widely varying conductivity. The white-light 

illumination intensity was 0.58 W/cm2

. The legend 

indicates the source of the PANI and also the back 

contact for the c-Si structures. 

TkB

PANI

F EE V

PANI σσ 00 −−=

PANI EV

exp , (3) 

where is the transport level energy for holes in the PANI films. We obtain for VOC (in the built-in 

potential limit) that: 

( ) (σ σ ) 00 ln PANI eVOC V −−= BTkE Si EF . (4) 

Eq. (4) accounts for measured slope 0.026 V of the dependence of VOC upon the natural logarithm of the 

film conductivity. 

We checked that Eq. (3) does describe the temperature-dependent conductivities of our films. The results 

are presented in Fig. 22, which shows that lower conductivity films have larger activation energies. The 

fitting curves roughly converge at a negative “Meyer-Neldel” temperature TMN ≈ -180 K and a 

conductivity S/cm. Inverse Meyer-Neldel behavior (i.e., negative values for TMN) is 

typically observed when the (temperature-dependent) Fermi-level lies in a bandtail region [

2

MN σ ×= 102

σ MN

Si PANI − EE VF

107]. 

Assuming that estimates the fundamental bandedge conductivity [ σ 00 108], we can use Eq. (4) to 

infer the difference in energy levels between Fermi level in the c-Si and the hole transport level of the 

PANI; the result eV is consistent with work function estimates in heavily doped 

PANI [

= 74.0

109]. 

 28
For a-Si:H, the data can be fitted fairly well by eq.(1) over the entire range of PANI conductivities, 

including conductivities for which the c-Si voltage was saturated. These results indicate that the saturation 

effect is not due to any intrinsic limitation of the PANI. Because the a-Si:H is part of an nip structure, the 

idea that VOC is limited by the built-in potential VBI must be modified. We shall interpret eVOC as a 

measurement of the difference between the Fermi level of the PANI and the electron quasi-Fermi level

EFn of the intrinsic a-Si:H under illumination. Device-modeling studies of a-Si:H solar cells suggest that 

the n/i interface of illuminated a-Si:H pin cells acts essentially as an ideal contact to EFn, so VOC will 

mainly be determined by properties of the p/i interface [110]. 

In Fig. 23 we illustrate these 2 differing approaches to understanding the limitation of VOC by the PANI 

work function. Fig. 23 is drawn for a particular PANI conductivity of 0.01 S/cm. The conductivity of the 

n-type silicon wafer was 0.5 S/cm, which corresponds to a Fermi level EF lying 0.25 eV below the 

conduction bandedge EC through the textbook result ( ( ) kTEEeN ) = nC −− FC μσ exp . 

For a-Si:H, we estimate from our device modeling that the electron quasi-Fermi level EFn of the intrinsic 

layer is 0.30 eV below EC. (under illumination of 0.6 W/cm2

) [110]. As can be seen from the figure, this 

analysis implies particular values for the conduction and valence band offsets between c-Si and a-Si:H. 

We obtained a conduction band offset between the two materials of 0.08 eV. Using bandgaps of 1.12 eV 

for c-Si and 1.75 eV for a-Si:H, the valence band offset is 0.55 eV. Many values for the valence band 

offset between a-Si:H and c-Si interface have been reported; our estimate of 0.55 eV seems reasonably 

consistent with the relatively recent measurements of 0.44eV±0.02 eV from photoemission experiments 

[101,102]. 

A related experiment on the effects of varying the doping level of a p-layer on a-Si:H pin structures was 

reported by Dawson, et al. [111] who used boron-doped a-Si:H. In their experiment the values for VOC

were somewhat larger (about 0.8 V) than our largest 

value, and they had little dependence on the doping 

levels of the p-layer. We suspect that this qualitative 

difference between their results with a-Si:H:B and 

the present work with PANI has to do with the much 

lower conduction band level in a-Si:H compared to 

PANI. 

-6 -4 -2 0 2 4

10-5

10-3

10-1

101

103

Ormecon

 as received

Aldrich

 2.0 %

 1.4 %

 0.6 %

 0.4 %

 0.3 %

 PANI Conductivity (S/cm)

1000/Temperature (K-1)

Fig. 22: Conductivity measurements as a function of 

reciprocal temperature 1000/T for six PANI films 

cast onto glass from dispersions with differing 

dilutions. The percentages indicated in the legend 

are the weight percentages of PANI in xylene. 

While the measurements for each sample show 

simple activated behavior, the fitting lines converge 

at a negative Meyer-Neldel temperature TMN = -180 

K.

We now return to the following feature of Fig. 21. 

For c-Si, VOC values saturated near 0.5 V for PANI 

conductivities that exceeded about 0.1 S/cm. 

However, for a-Si:H VOC increased continuously 

with increasing PANI conductivity. We have 

considered several mechanisms for the saturation 

seen in c-Si. Poor quality c-Si that intrinsically limits 

VOC is one possibility that we have previously 

excluded. In the present work, we compared VOC for 

two different back contacts: evaporated Al, and ntype a-Si:H (a “back surface field” contact). As can 

be seen in Fig. 21, the improvement obtained by 

using a-Si:H is about 0.03 V. The improvement is 

significant, but Fig. 21 suggests that a much larger 

improvement is still possible, In particular, the data 

suggest that the intrinsic properties of the highest 

conductivity PANI (from Ormecon) are able to 

support a VOC as large as 0.7 V in c-Si, as they do for 

the a-Si:H/PANI cells. 

 29
VOC saturation thus suggests to us that the PANI Fermi 

level at the c-Si interface is “pinned” at an energy 

higher than its bulk Fermi level. This pinning 

apparently doesn’t occur for a-Si:H, which is a clue as 

to the underlying physical mechanism. One 

mechanism that we have been considering for the VOC

saturation is “electrophoresis” of charged molecules in 

the PANI films near the interfaces that might lead to 

dedoping of the film. However, we can estimate the 

electric fields near the interface for c-Si and for a-Si:H 

using elementary models. For c-Si with a conductivity 

of 0.5 S/cm, and VBI of about 0.8 V across the diode, 

the interface electrical field in the dark is about 104

V/cm. The value for the interface field that we 

estimate for a-Si:H in the dark is about the same. It 

thus seems unlikely that the electrophoresis 

mechanism is correct; we are still seeking a better 

model. 

4. Conclusions 

The dependence of open-circuit-voltages VOC for 

PANI/a-Si:H and PANI/c-Si structures was studied for 

varying PANI conductivities. Generally, the open-circuit voltage VOC increases with increasing PANI 

conductivity as expected when VOC is limited by the work function of the PANI film; an analysis based on 

this idea yielded band offsets that are consistent with more direct measurements such as photoemission. 

For a-Si:H, the VOC values for the highest conductivity PANI (about 0.75 V) are lower than obtained with 

Si-based p-layers, and we consider it unlikely that PANI p-layers are of technological significance for aSi:H. For c-Si, VOC saturated at about 0.5 V for PANI conductivities greater than 0.1 S/cm. The saturation 

mechanism is not understood, and it may be possible to achieve higher VOC values comparable to the 

highest reported with other p-type materials. 

E V

E F n

E C

E V

E F

E C

0.25

0.48 0.51

0.30

0.55

0.08

c-S i P A N I a-S i:H

E F

Level Position (eV)

Fig.23. Proposed alignments of Fermi levels and 

bandedges in c-Si, PANI, and a-Si:H; 

conductivities and illumination levels are indicated 

in the text. Note that the analysis yields c-Si/a-Si:H 

conduction and valence band offsets of 0.08 and 

0.55 eV, respectively. 

 30
E. Infrared Interface 

Spectra in Cells 

For the last few years we have been 

developing an infrared modulation 

spectroscopy technique that probes 

the optical spectra of dopants and 

defects at the critical interfaces 

between the layers of amorphous 

silicon pin solar cells [112- 115]. In 

brief, the reverse bias voltage across 

a cell is sinusoidally modulated, and 

the corresponding modulation of an 

optical transmission is detected. We 

illustrate such a spectrum as Fig. 24, 

where the modulation spectrum 

ΔT/T of the optical transmission 

through a pin solar cell is shown. 

The principal feature in this 

spectrum is the large peak near 1.85 

eV; this feature, which depends 

upon the magnitude of the DC 

potential VDC across the cell, is due 

to the well-known electroabsorption

effect in the intrinsic, a-Si:H layer of 

the cell [116]. The much weaker 

infrared signal is nearly independent 

of VDC, and is attributed to the change in optical transmission as the charge state of dopants and defects 

near the interfaces is modified by the sinusoidal modulation of the electric potential across the cell. The 

electroabsorption effect is quadratic in electric field, which leads to a signal quadratic in the modulated 

field and VDC. The interface effect varies with the charge modulation at the interfaces, and is independent 

of VDC when the capacitance is also independent of VDC. 

1.0 1.5 2.0

-10

0

10

20

30

40

-1V

-2V

Δ

0V

T/T (10-6

)

Energy (eV)

Figure 24: Transmittance modulation spectrum ΔT/T for an 

amorphous silicon-based pin solar cell prepared at BP Solar. 

Spectra were taken under three different DC reverse bias voltages 

(VDC) as indicated. The larger, voltage-dependent peak near 1.85 

eV corresponds to the well established interband

electroabsorption, and depends linearly on VDC. The weaker 

infrared response is due to charging and discharging of dopant and 

defect levels near the n/i and p/i interfaces, and shows little 

dependence on VDC. Sample with 3% phosphorus doping level. 

Measured with 400Hz, 1.0 Vpp modulation. 

In work supported by this subcontract, we studied a series samples with varying phosphorus-doping level 

in the n-layer [117]. We found, for high doping levels (1% - 5%), a sharper spectral line near 0.75 eV 

with a width of 0.1 eV. This line is nearly absent in lower doping (below 1%) samples. We have 

previously attributed this line to the internal optical transitions of a “P4D” complex incorporating both a 

fourfold-coordinated phosphorus atom (P4) and a dangling bond (D) [113,118]. We have analyzed the 

present measurements to estimate the relative concentrations of “standard” dopant atoms P4 (ie. those not 

in complexes) and dopant complexes P4D. We are unaware of previous experimental estimates of this 

ratio, and we believe that they show the utility of infrared charge-modulation spectroscopy for interface 

studies. Our measurements are broadly consistent with the predictions of the model for doping developed 

by Street, although the measurements differ from this model in detail. 

In this experiment, we measured the transmittance modulation spectra for a series of samples of 

phosphorus-doped amorphous silicon (a-Si:H:P) layer with gas-phase doping levels between 0.17% - 5%. 

These samples were made as a sequence at BP Solar; the substrate for each deposition was glass coated 

with textured SnO2. The p-type layer deposited onto the SnO2 was a-SiC:H:B, followed by a-Si:H and by 

n-type a-Si:H:P. Sputtered TCO was applied to the top and used as the electrical contact. The intrinsic 

layers were around 200 nm thick as inferred from capacitance measurements. A buffer layer was 

deposited between p-type and intrinsic layers. 

 31
Fig. 25 shows the infrared chargemodulated transmittance spectra ΔT/T for 

samples with the indicated doping levels. 

Each spectrum has been normalized by its 

peak amplitude. We first noticed that for 

samples with doping levels below 1% 

there is a negative, broad peak in the 

modulation spectrum near 0.85 eV. We 

attribute this spectrum to occupancy 

modulation of isolated dopant atoms in 

the n and p layers; similar spectral 

features have been reported in 

photomodulated transmittance spectra of 

phosphorus-doped a-Si:H. We exclude 

the photodetachment of electron from D−

as possible source for this negative 

absorption spectrum. This is because the 

Fermi energy is at most 0.2 eV below 

conduction band, but D−

 is located 0.9 eV 

deep below conduction band. Depletion 

of such a deep level should be negligible. 

This argument is also supported by the 

frequency-independent spectrum with 

modulation frequency range from 200 Hz 

to 20kHz, although we won’t show this 

here. 

At high doping levels (1% and above), 

we find a sharper, positive peak at 0.75 

eV with a width of 0.1 eV. This line is 

nearly absent in low doping samples. The 

existence of a sharp absorption line suggests transitions between the ground state and a localized excited 

state of some center in phosphorus-doped a-Si:H. In our previous work we suggested the possibility that 

P4D complexes are responsible for this spectral feature [113]. Positron annihilation measurements [118] 

are also consistent with complexing at high doping levels. Fig. 26 shows a simple possible level diagram 

for a P4D complex, and corresponding absorption spectrum for an internal optical transition. As we can 

see from figure 3, when the Fermi energy is lowered, the depletion of P4D states near band edge promotes 

the internal transition to these states from deeper complex states. 

0.7 0.8 0.9 1.0 1.1

3%

1%

0.67%

0.5%

0.3%

0.17%

5%

0

0

0

0

0

0

0

0

ΔT/T (arb. units)

Energy (eV)

Fig. 25. Normalized modulated infrared absorption spectrum. 

Samples were prepared at BP Solar with varying phosphorus 

doping levels (from 0.17% to 5% as indicated). At higher 

doping levels (1% and above), there is a line spectrum at 0.75 

eV of about 0.1 eV wide. This line is essentially absent in 

samples with doping levels below 1%. This sharp line 

indicates the internal optical transitions of a complex 

incorporating four fold coordinated phosphorus and a 

dangling bond. 

Street [119] has previously noted that formation of P4D complexes is favored at high doping levels, while 

lower doping levels favor the formation of uncorrelated P4 and D-centers in essentially equal 

concentrations. In the next a few paragraphs, we will discuss briefly, based on samples studied in this 

paper, about the doping models proposed by Street [119]. The standard doping model involves nearly 

equal densities dangling bonds (D centers) and of phosphorus atoms bonded to four silicon atoms (P4

centers). The corresponding densities can be represented by [119] 

( ) ( ) 2/12/1

P4 D SiS 4 P3 == NNKNN , (1) 

where KS is the rate constant and P3 denotes a phosphorus atom with threefold coordination. The 

concentrations of pairs depends linearly on phosphorus concentration [119]: 

 32
( )( ) pair PSiP 34 4 PSiP 3 = = NNKNNKN , (2) 

where KP is the rate constant for pair generation. Low P densities favor isolated P4 and D centers; higher 

densities favor complexing. 

To analyze our spectra, we assumed that the two spectral features (broad/negative, and narrow/positive) in 

Fig. 25 originate with P4 and P4D configurations. We fit the infrared spectrum with two Gaussian peaks. 

Fig. 27 shows a typical fitting result for the sample made with 3% P. The dashed line represents the 

positive peak; the dotted line represents the negative peak. As can be seen, the sum of these two spectrum 

peaks (the solid line in the figure) fits the actual spectrum quite satisfactorily. We plotted the ratio of the 

strengths of these two spectral lines for all of our samples as the open symbols in Fig. 28. We believe that 

this value is proportional to the ratio of the densities of the two types of dopant configurations. 

From Eq. 1 and 2, we calculate the ratio of concentrations as: 

( ) ( ) 2/12/1

4 3

4

Si P

S

P

P

pair NN K

K

N

N ⎟

⎠

⎞ ⎜

⎝

⎛ = . (3) 

We fitted the resulting proportionality (to P1/2) to the measurements in Fig. 28. The fitting accounts fairly 

well for the dependence of the ratio of spectral line strengths upon the phosphorus concentration, and thus 

supports to some degree our identification of the two spectral features. There does appear to be sharper 

structure near a “critical” phosphorus level of 1% that is not reproduced by the fitting, and we hope that 

further measurements will clarify this possibility. 

EF P4D

EV

EC

0

σ (cm2)

P4

+D- ⇒ P40D0

induced

10-16

EF

sweeps down

E0

hν

Fig. 26. Optical effects resulting from a change in the Fermi energy in 

heavily phosphorus doped a-Si:H (probably at doping level of 1% and 

above). The drawing on the left indicates an internal electron excitation 

from a deep level to a shallower level of a complex, which incorporats 

four fold coordinated phosphorus and a dangling bond. The depletion of 

occupied states near the band edge of a-Si:H, as the Fermi energy is 

lowered, induces this internal transition, which account for a sharp, 

positive absorption spectrum. 

 33
0.7 0.8 0.9 1.0 1.1 1.2

-1.0

-0.5

0.0

0.5

1.0

ΔT/T (arb. units)

Energy (eV)

Figure 27: Spectrum analysis. Fit infrared spectrum with two Gaussian 

spectrum peaks. Symbols indicate the measurement; lines indicate the 

fitting results (dashed: positive Gaussian peak t 0.75 eV; dotted: negative 

Gaussian peak at 0.84 eV; solid: sum of these two peaks). 

012345

0.0

0.5

1.0

[ P D]/[P 4 4

]

Ratio of Linestrengths |A1/A2|

Vapor-phase Phosphorus (%)

Figure 28: Relative peaks strength. Symbols indicate the ratio of the strength 

of the positive peak over that of the negative peak. Line indicates the fitting 

result of Eq.3 in text. The fitting coefficient was 4.5. 

 34
 35

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AGENCY REPORT NUMBER

NREL/SR-520-44101 

12. DISTRIBUTION AVAILABILITY STATEMENT

National Technical Information Service 

U.S. Department of Commerce 

5285 Port Royal Road 

Springfield, VA 22161 

13. SUPPLEMENTARY NOTES

NREL Technical Monitor: Bolko von Roedern 

14. ABSTRACT (Maximum 200 Words)

In this report, we present the results for the four principal tasks of this research project: 1. Amorphous silicon solar cell 

characteristics and modeling; 2. Photocarrier drift mobility measurements in hydrogenated amorphous silicon, 

microcrystalline silicon, and polycrystalline copper indium-gallium diselenide; 3. Hole-conducting polymers as p-layer 

materials for amorphous and crystal silicon solar cells; and 4. Infrared spectra of p/i and n/i interfaces in a-Si:H-based 

solar cells. 

15. SUBJECT TERMS

PV; solar cells; amorphous silicon; microcrystalline silicon; CIGS; drift mobility; polymers; infrared spectra 

16. SECURITY CLASSIFICATION OF: 17. LIMITATION 

OF ABSTRACT

UL 

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a. REPORT 

Unclassified 

b. ABSTRACT 

Unclassified

c. THIS PAGE 

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Standard Form 298 (Rev. 8/98) 

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