National Renewable Energy Laboratory 

Innovation for Our Energy Future 

A national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

NREL is operated by Midwest Research Institute ● Battelle Contract No. DE-AC36-99-GO10337 

Optimization of Phase-Engineered 

a-Si:H-Based Multi-Junction Solar 

Cells 

Final Technical Report 

October 2001 — July 2005 

C.R. Wronski, R.W. Collins, N.J. Podraza, 

V. Vlahos, J.M. Pearce, J. Deng, M. Albert, 

G.M. Ferreira, and C. Chen 

Pennsylvania State University 

University Park, Pennsylvania 

Subcontract Report 

NREL/SR-520-40400 

August 2006 
Optimization of Phase-Engineered 

a-Si:H-Based Multi-Junction Solar 

Cells 

Final Technical Report 

October 2001 — July 2005 

C.R. Wronski, R.W. Collins, N.J. Podraza, 

V. Vlahos, J.M. Pearce, J. Deng, M. Albert, 

G.M. Ferreira, and C. Chen 

Pennsylvania State University 

University Park, Pennsylvania 

NREL Technical Monitor: B. von Roedern 

Prepared under Subcontract No. NDJ-1-30630-01 

Subcontract Report 

NREL/SR-520-40400 

August 2006 

National Renewable Energy Laboratory

1617 Cole Boulevard, Golden, Colorado 80401-3393 

303-275-3000 • www.nrel.gov 

Operated for the U.S. Department of Energy 

Office of Energy Efficiency and Renewable Energy 

by Midwest Research Institute • Battelle 

Contract No. DE-AC36-99-GO10337
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 

Executive Summary.............................................................................................................1

Task 1. Materials Research and Device Development ......................................................1 

Task 2. Process Improvement Directed by Real Time Diagnostics ..................................2 

 2.1 Si1-xGex:H Roughness and Phase Evolution ......................................................4 

2.2 Dielectric Functions of a-Si1-xGex:H versus Ge Content, Temperature, 

and Processing: Advances in Optical Function Parameterization ...................18 

2.3 Model for Amorphous Roughening Transition in Amorphous 

Semiconductor Deposition...............................................................................24 

Task 3. Device Loss Mechanisms ...................................................................................32 

Task 4. Characterization Strategies for Advanced Materials ..........................................48 

Appendix A: Theoretical Considerations..........................................................................68 

List of Figures 

Figure 2.1: A comparison of the deposi-tion rates of pure Si:H and Si1-xGex:H alloy 

films as a function of the H2-dilution ratio .....................................................5 

Figure 2.2: Superimposed phase diagrams for Si:H (squares) and Si1-xGex:H (circles) 

films deposited at low power (0.08 W/cm2) and low total pressure 

(< 1 Torr) on oxide-covered c-Si ....................................................................5 

Figure 2.3: Superimposed phase diagrams for Si1-xGex:H films deposited on the anode 

under similar conditions at two different substrate temperatures (T=200o

C 

and T=290oC)..................................................................................................6 

Figure 2.4: Comparison of deposition rates for anode and cathode Si:H and Si1-xGex:H 

thin film series versus the H2-dilution ratio, R = [H2]/{[SiH4]+[GeH4]} .......7 

Figure 2.5: Comparison of the structural evolution of (a) Si1-xGex:H and (b) Si:H films 

deposited on c-Si substrate mounted at the anode (triangles) and cathode 

(squares) using R=80 and R=20, respectively ................................................8 

Figures. 2.6 and 2.7: Superimposed deposition phase diagrams for the cathode (squares) 

and anode (circles) Si1-xGex:H and Si:H alloy series plotted as a function of 

H2-dilution.......................................................................................................9 

Figure 2.8: Optical band gap as a function of GeH4 flow ratio G determined from real 

time spectroscopic ellipsometry....................................................................10 

Figure 2.9: Surface roughness evolution for two pairs of Si1-xGex:H films prepared 

under rf PECVD conditions that include ......................................................11 

Figure 2.10: Superimposed phase diagrams for different GeH4 flow ratios G, each 

plotted versus the H2 dilution level R ...........................................................11 

Figure 2.11: Deposition rate for cathode Si1-xGex:H as functions of 

G = [GeH4]/{[SiH4]+[GeH4].........................................................................13 

iii
Figure 2.12: A deposition phase diagram depicting the amorphous roughening 

transition (a→a) for R=10 a-Si1-xGex:H films plotted versus the alloy 

flow ratio G=[GeH4]/{[SiH4]+[GeH4]} (solid line and square points).........13 

Figure 2.13: Width of the resonance in the dielectric function (measured at 200°C 

and at a thickness of 150-300 Å) for cathode Si1-xGex:H as a function........14 

Figure 2.14: A single deposition phase diagram for R= 40 Si1-xGex:H films plotted 

versus the GeH4 flow ratio G........................................................................14 

Figure 2.15: (left) Surface roughness evolution for two Si1-xGex:H films prepared 

in the anode configuration with R=[H2]/{[SiH4]+[GeH4]} = 80 and 

G=[GeH4]/{[SiH4]+[GeH4]} = 0.167............................................................15 

Figure 2.16: (right) Deposition rate versus the combined [H2+He]-dilution ratio 

S=R+He= {[H2]+[He]}/{[SiH4]+[GeH4]} for Si1-xGex:H films prepared 

in the anode configuration with G=[GeH4]/{[SiH4]+[GeH4]}= 0.167 .........15 

Figure 2.17: Deposition phase diagrams plotted versus the combined [H2+He]- 

dilution ratio..................................................................................................16 

Figure 2.18: (Above) Alloy content x in a-Si1-xGex:H thin films and their optical 

and gaps at Tm=Ts=200°C as a function of the flow ratio ............................19 

Figure 2.19: Examples of fits (solid lines) to dielectric function spectra (points) 

of a-Si1-xGex:H measured at Tm=Ts=200°C from films of the series of 

Fig. 2.18 (R=10, cathodic deposition) at the extremes of the alloy range ....19 

Figure 2.20: Dielectric function parameters versus a-Si1-xGex:H alloy composition 

x at Tm=Ts=200°C deduced in fits such as those of Figure 2.19 for the series 

of depositions of Figure 2.18 ........................................................................21 

Figure 2.21: Dielectric function parameters versus measurement temperature Tm obtained 

in fits such as those of Figure 2.19 for an a-Si1-xGex:H alloy with =0.083 

prepared at the cathode .................................................................................21 

Figure 2.22: The slopes that describe the linear variation of the dielectric function 

parameters versus measurement temperature Tm determined as shown 

in Figure 2.21................................................................................................23 

Figure 2.23: Dielectric function parameters for a-Si1-xGex:H alloys versus H2- 

dilution ratio..................................................................................................23 

Figure 2.24: Surface roughness evolution for a series of a-Si:H films prepared by highpressure, high-rate PECVD using the following fixed parameters: 

substrate temperature ....................................................................................25 

Figure 2.25: The surface height profile at bulk layer thicknesses of db=0, 200, and 

8000 Å for a 1-D continuum model of film growth that includes 

smoothening due to surface diffusion...........................................................25 

Figure 2.26: Fit (solid line) to experimental data (squares) for a-Si:H with R=40 from 

Figure 2.24 using a the 1-D continuum model of Figure 2.25......................28 

Figure 2.27: Amorphous roughening transition thickness obtained from real time 

SE and the critical diffusion length obtained from the 1-D model...............28 

Figure 3.1: JD-V characteristics for a p-i-n cell with 0.4 μm thick R=0 bulk i-layer and 

200 Å R=40 p/i interface layer in the annealed state and after both 1 sun 

illumination and carrier injection induced degradation ................................34 

Figure 3.2: n(V) characteristics corresponding to the results of Figure 3.1 ....................35 

iv
Figure 3.3: Degradation of fill factor with 1 sun illumination and carrier injection for 

the cell of Figure 3.1. ....................................................................................36 

Figure 3.4: Thickness dependence of 1 sun Voc and JD-V characteristics for p-i-n cells 

having the same structure but different thickness of R=0 bulk i-layers .......38 

Figure 3.5: Degradation of 1 sun Voc under 1 sun illumination at 25oC for the cell 

in Figure 3.4 with the 0.4 μm thick i-laye ....................................................38 

Figure 3.6: JD-V characteristics of the cell in Figure 3.5 in the annealed state and 

after 100 hours of 1 sun illumination............................................................39 

Figure 3.7: Degradation of Voc for a p-i-n cell with a 0.4 μm thick R=10 bulk i-layer 

and a 200 Å thick R=40 p/i interface, measured under light intensities 

from 1 to 10-4 sun..........................................................................................40 

Figure 3.8: JD-V characteristics of the cell in Figure 3.7 in the annealed state 

and after light induced degradation...............................................................40 

Figure 3.9: (a) Change of current at 0.4 V and 25oC for a p-i-n cell under injection 

currents of different intensities and 1 sun illumination; 

(b) Change of current at 0.4 V and 75oC for a p-i-n cell under injection 

currents of different intensities .....................................................................43 

Figure 3.10: (a) Changes relative to the initial value for the currents in Figure 3.9(a); 

(b) Changes relative to the initial value for the current in Figure 3.9(b) ......44 

Figure 3.11:(a, b) Normalization of the degradation kinetics under different intensities 

according to I2t = constant for the corresponding figures in Figure 3.10 .....45 

Figure 4.1: 1 Sun and 10 second intermittent probe photocurrents for carrier generation 

rate G=8x1015cm-3s

-1 during the first 30 minutes of degradation..................49 

Figure 4.2: Probe photocurrents for G=8x1015cm-3s

-1 during 1 sun degradation 

for 5 minutes and subsequent relaxation in the dark for 1 hour....................49 

Figure 4.3: Intermittent probe photocurrents for G=1x1015cm-3s

-1 normalized 

to their degraded state after 30 minutes of 1 sun illumination obtained 

at different stages of this study .....................................................................50 

Figure 4.4: Continuous probe currents for G=8x1015cm-3s

-1 normalized to their 

degraded state after 30 minutes of 1 sun illumination ..................................50 

Figure 4.5: Continuous probe currents normalized to their degraded states after 

30 minutes of 1 sun illumination for carrier generation rates from 

1x1015 to 4x1017cm-3s

-1 .................................................................................51 

Figure 4.6: Bulk recombination currents in p-i-n solar cells at 0.3, 0.4 and 0.5 V 

forward bias after 30 minutes of 1 sun illumination.....................................51 

Figure 4.7: The continuous probe photocurrents for G=8x1015cm-3s

-1 normalized to 

their degraded states after different 1 sun illumination times.......................52 

Figure 4.8: Reciprocal of 1 sun and probe photocurrents for 1 sun degradation ............55 

Figure 4.9: Evolution of forward bias current at 0.4 V for a p-i-n cell during the 

degradation with 1 sun and far forward bias current of 30 mA/cm2

.............55 

Figure 4.10: Evolution under 1 sun illumination of reciprocals of probe photocurrents 

relative to 1 minute value..............................................................................56 

Figure 4.11: Reciprocal of 1 sun and probe photocurrents for 1 sun ................................56 

Figure 4.12: An example of for the subgap absorption and its derivative kN(E), clearly 

identifying three distributions of states around midgap................................59 

v
Figure 4.13: (a) Real and (b) imaginary parts of the dielectric functions of the pure 

a-Si:H and μc-Si:H phases for an R=20 deposition on c-Si .........................62 

Figure 4.14: Depth profile in the volume fraction of the microcrystalline phase (points) 

throughout the mixed-phase (a+μc)-Si:H growth regime for the R=20 Si:H 

deposition on c-Si from Figure 4.13 .............................................................62 

Figure 4.15: (a) Surface roughness thickness versus bulk layer thickness for the 

R=20 Si:H deposition of Figs. 4.13 and 4.14; 

(b) schematic of the cone growth model.......................................................62 

Figure 4.16: Cone angle θ and nucleation density Nd versus the nucleation transition 

thickness........................................................................................................62 

Figure 4.17: Depth profiles of the microcrystal volume fraction fμc in the i-layer for 

three 4000 Å thick two-step R=40/20 i-layer structures on R=0 a-Si:H 

substrates.......................................................................................................65 

Figure 4.18: Experimental (symbols) and simulated (lines) dark J-V characteristics 

for four Si:H p-i-n solar cells........................................................................65 

Figure A.1: Schematic band diagram for the I-layer of a p-i-n cell under forward ............ 

bias in the dark..............................................................................................74 

Figure A.2: Schematic band diagram for the I-layer of a p-i-n cell under forward 

bias in the illumination..................................................................................74 

List of Tables

Table 4.1: Correlation of RTSE and device modeling results for Si:H p-i-n cells 

with 4000 Å thick two-step R=40/20 i-layers in which the R=40 interface 

thickness is varied.........................................................................................66 

vi
Executive Summary 

The restructuring in the program brought about by the move of co-PI Robert Collins to the 

University of Toledo in the third phase of this subcontract has proceeded smoothly. One of the 

graduate students associated with the project continued working at Penn State applying the same 

single-chamber system fitted with real time spectroscopic ellipsometry (RTSE) instrumentation that 

was used during the first and second phases of the project. This student continued to perform insitu RTSE studies of the growth of a-Si1-xGex:H materials for high performance solar cells. 

Construction of a new Dual Beam Photoconductivity (DBP) apparatus has been completed, and the 

new capabilities are being utilized in studies of a-Si:H thin films. A new apparatus has also been 

constructed for in-depth studies of the mechanisms limiting the performance of a-Si:H solar cells 

and for the parallel-track studies (cells and films) of the Staebler-Wronski Effect (SWE). The 

capabilities include integration of the cell characteristics including the Q.E. at different temperatures 

on both p-i-n and n-i-p solar cells. The scope of the work under this subcontract has entailed 

investigating engineered improvements in the performance and stability of solar cells in a systematic

way. It has consisted of the following four tasks. 

Task 1. Materials research and device development 

Task 2. Process improvement directed by real time diagnostics 

Task 3. Device loss mechanisms 

Task 4. Characterization strategies for advanced materials 

The work carried out in these tasks has resulted in new and important insights into the deposition of 

a-Si:H-based materials, as well as into the nature of the SWE. Presumably, many of these insights 

have been utilized by the industrial partners in developing more systematic approaches in the 

optimization of solar cells for higher performance and stability. This effort also cleared up several 

serious misconceptions that are still being held about the nature of the p-layer in cells and the SWE 

in materials and cells. Finally, the subcontract identified future directions that should be pursued for 

greater understanding and improvements. 

Task 1. Materials Research and Device Development 

In Task 1, an understanding of n-i-p (substrate) solar cells was achieved and on the basis of 

this understanding, optimization was carried out. The inherent differences between n-i-p and p-i-n 

(superstrate) cell structures have been addressed. Phase diagrams have been developed using real 

time spectroscopic ellipsometry (RTSE) and applied to characterize thin film growth and 

microstructure, comparing the two configurations. Such an approach has been successful in 

explaining the nature of p-type Si:H films doped using BF3 and guiding the development of high 

VOC in n-i-p solar cells. The results show that in order to maximize VOC, it is necessary to deposit 

the p-layers at the maximum R value that allows the desirable thickness to be obtained without 

crossing the transition into the mixed-phase growth regime. This study also showed that previous 

work reporting the highest VOC for microcrystalline Si:H p-layers was erroneous. The possible 

mechanisms responsible for the differences in 1 sun VOC obtained with the different p-type Si:H 

layers were explored. Carrier recombination in cell structures was characterized with JD-V 

measurements, and the recombination in the p/i and i/p interface regions was identified and 

quantified. These systematic studies clearly established that the lowest p/i interface recombination is 

1
obtained with protocrystalline a-Si:H and not with layers containing any microcrystalline phase. 

(When the microcrystalline phase appears, VOC is also significantly lower than that achieved with 

the structure incorporating the optimum a-Si1-xCx:H p-layer.) The significantly lower i/p interface 

recombination in the cells with the protocrystalline Si:H p-layer is attributed in large part to the subsurface modification of the underlying intrinsic layer that occurs during the deposition of the p-layer 

contact. Evidence is found that the high concentration of atomic hydrogen present during the 

deposition of the protocrystalline Si:H p-layer is responsible for this beneficial effect. In addition, 

unlike a-Si1-xCx:H, it allows the protocrystalline p-layer to be used in fabricating solar cell structures 

without any adverse effect of exposing the i-layers to air. 

The optimization of rf and vhf PECVD materials for high rate i-layers of Si:H solar cells based 

on the deposition phase diagram was also investigated. It is found that under H2 deficient dilution 

conditions, vhf (60 MHz) PECVD provides significant advantages over rf (13.56 MHz) PECVD in 

the fabrication of higher quality a-Si:H at high rates. Under optimum conditions, however, with the 

H2-dilution ratio set just below the a→(a+μc) transition for the desired film thickness, vhf PECVD 

provides no significant advantage over rf PECVD when identical high deposition rates are 

compared. It was also found that in a high plasma power, high pressure (3 Torr) rf PECVD process 

for a-Si:H film growth, the amorphous phase roughening transition thickness remains above 1000 Å 

just below the a→(a+μc) boundary where the rate is 6.5 Å/s. This transition thickness is a factor of 

two higher than that observed under low pressure deposition conditions with almost a factor of two 

lower deposition rate for the a-Si:H. 

In fact, three manifestations of enhanced precursor surface diffusion are found with increasing 

H2-dilution ratio R under all conditions of a-Si:H deposition explored: (i) increased surface 

smoothening (both rate and amplitude) associated with the coalescence of initial nuclei in the first 

100 Å of deposition; (ii) reduced surface roughness layer thickness at the stable surface value; and 

(iii) increased surface stability as measured by the thickness of the a→a roughening transition. The 

presence of all three effects provide clear signatures of improved-device quality materials based on 

the monolayer level processes detected at the film surface. As a result, we can conclude that the 

appropriate combination of high R [at the a→ (a+μc) transition for the desired film thickness], high 

power, and high pressure give rise to reasonable device performance at rates > 6 Å/s, without 

resorting to unconventional deposition methods. 

 Because the a→(a+μc) transition decreases in thickness with increasing R, two-step and even 

multi-step i-layer processes can be designed on the basis of the phase diagram in order to optimize 

solar cells. Optimization of rf and vhf PECVD materials for high rate i-layers of a-Si:H solar cells 

based on the deposition phase diagram has been further explored. The similarities of the phase 

diagrams for both rf and vhf PECVD of Si:H on R=0 a-Si:H substrate films demonstrate that the 

two-step optimization procedure developed for the rf PECVD protocrystalline i-layers of a-Si:Hbased p-i-n and n-i-p cells also apply for vhf PECVD i-layers as well. 

Task 2. Process Improvement Directed by Real Time Diagnostics 

 In Task 2, real time spectroscopic ellipsometry was applied in the development of deposition 

phase diagrams for guiding the fabrication of hydrogenated silicon (Si:H) and hydrogenated 

amorphous silicon germanium (a-Si1-xGex:H) thin films at low temperatures (<300°C) for high 

performance solar cells. Phase diagrams have been extended to include the thickness at which a 

roughening transition is detected in the amorphous film growth regime. The three surface 

microstructural and phase transitions, including the a→a roughening transition, the a→(a+μc) 

2
roughening transition, and the (a+μc)→μc smoothening transition have been incorporated into an 

extended deposition phase diagram. Correlations of such phase diagrams for the intrinsic Si:H 

layers with the corresponding electronic properties and p-i-n device performance demonstrate that 

the optimum i-layers are obtained at the maximum possible R value for the desired thickness without 

crossing the a→(a+μc) boundary of the phase diagram into the mixed-phase growth regime. 

Because the R value at this phase boundary depends on both the nature of the substrate and the ilayer thickness, these aspects of the materials or device structure must be specified in order to 

identify the optimum conditions for i-layers deposited on amorphous film substrates (such as the p 

or n-layers of p-i-n or n-i-p solar cells). The optimum a-Si:H i-layer material has been described as 

protocrystalline Si:H -- this material ultimately evolves into (a+μc)-Si:H if the film is allowed to 

grow beyond the desired thickness for which the deposition process was optimized.

Schematic of the structure of Si:H films

prepared at different R on a-Si:H (R=0)

• In this project it is emphasized that great attention must be given to the a→(a+μc) transition and 

the thickness evolution of the crystalline phase in both films and cells. In fact, the resulting film will 

exhibit a depth profile in the crystalline content if the film crosses the transition at any point during 

the course of the deposition.

3
2.1 Si1-xGex:H Roughness and Phase Evolution

Overview 

 Extensive research on hydrogenated amorphous silicon (a-Si:H) thin films has shown that 

optimum device performance is correlated with the smoothest, most stable surfaces versus time 

during the PECVD process – in fact, less than a monolayer of roughening occurs throughout the 

deposition of optimum films as thick as 0.5 μm [2.1]. Such research requires smooth crystalline 

silicon substrates for high sensitivity to surface roughness as well as an in situ probe such as 

spectroscopic ellipsometry (SE) for real-time analysis. It has been also shown that when the 

PECVD conditions deviate from the optimum even slightly, e.g., by a reduction in the hydrogen 

dilution ratio or by an increase in plasma power from its minimum, then a roughening transition is 

observed in the a-Si:H growth regime [2.1]. This transition shifts to decreasing bulk layer thickness 

for films with increasingly deteriorated device properties. As a result, the thickness at which the 

roughening transition (denoted a → a) occurs has been entered into deposition phase diagrams, 

relevant for c-Si substrates, that provide insights into the device quality of a-Si:H and how it varies 

with deposition parameters. 

 In this study, the amorphous-phase roughening transition thickness has been determined as a 

function of process variables in plasma-enhanced chemical vapor deposition (PECVD) of 

hydrogenated amorphous silicon-germanium alloys (a-Si1-xGex:H). Among the process variables 

include the H2-dilution gas flow ratio, the alloying flow ratio, the electrode configuration (anode vs. 

cathode), the substrate temperature, and the He-dilution ratio. One clear feature of this study is a 

maximum in the amorphous roughening transition thickness (and hence surface stability) at a H2-

dilution ratio just below the transition from amorphous to mixed-phase (amorphous + 

microcrystalline) growth. A second feature for high Ge content films is a significant increase in the 

roughening transition thickness for cathode PECVD (with a self-bias of ~ −20 V). Additional 

features of interest involve suppression of the mixed-phase transition for (i) alloying with Ge, (ii) 

decreasing substrate temperature, (iii) cathodic substrate biasing, and (iv) diluting the gas with He. 

Experimental Details 

The Si1-xGex:H films in this study were deposited onto native-oxide/c-Si substrates using 

single-chamber rf (13.56 MHz) PECVD and were measured in real time using a rotatingcompensator multichannel ellipsometer [2.2]. The fixed parameters were selected for the most part 

at values used in previous studies of pure Si:H PECVD [2.1], the minimum plasma power for a 

stable plasma (P ~ 0.08 W/cm2

), a low partial pressure of the source gases {[SiH4]+[GeH4]} (~ 0.06 

Torr), and a low total pressure (ptot < 1.0 Torr). In this study, the primary phase diagram variable 

was the H2-dilution ratio R = [H2]/{[SiH4]+[GeH4]}, as usual. The other variable parameters include 

(i) alloying flow ratio G = [GeH4]/{[SiH4]+[GeH4]} which was varied from G=0 to G=0.167, 

leading to x values up to 0.4; (ii) substrate temperature which was varied over the range 200oC < Ts

< 320oC; (iii) electrode configuration (see [2.3]), either the conventional anode or the cathode the 

latter with a dc self-bias of ~ −20 V; and (iv) He-dilution defined by the flow ratio 

He=[He]/{[SiH4]+[GeH4]}which was varied from 0 to 90. The optical gap of the a-Si1-xGex:H 

reached its minimum of ~1.3 eV for the maximum G value, with smaller variations due to the other 

parameters. 

4
Results and Discussion

Comparison of Si:H and Si1-xGex:H films prepared on the anode at T=200o

C 

A comparison of the deposition rates is shown in Fig. 2.1 for Si:H and Si1-xGex:H similarlyprepared on the reactor anode at 200°C with a rf plasma power of 0.08 W/cm2

 and a source gas 

partial pressure of ~0.06 Torr. The only difference in the process for Si1-xGex:H is the replacement 

of 1/5 of the SiH4 flow by GeH4. The significantly higher rates for the alloys are attributed to the 

ease with which GeH4 is dissociated in the plasma relative to SiH4. 

 Figure 2.2 shows the superimposed deposition phase diagrams for the pure Si:H and Si1-xGex:H 

alloy thin films of Fig. 2.1. Two significant differences are observed between these diagrams, 

indicating the profound effect of alloying. First, the a→(a+μc) transition for the series of Si1-xGex:H 

alloys is shifted to much larger R compared to pure Si:H. Thus, the presence of Ge in the growth 

process suppresses the nucleation of microcrystals from the amorphous phase. Second, the a→a 

roughening transition for the a-Si1-xGex:H saturates at a low bulk layer thickness of 200 Å, even as 

the a→(a+μc) transition for thick films is approached and crossed. In contrast, for Si:H, the a→a 

roughening transition increases sharply, exceeding a bulk layer thickness of 4000 Å, as the 

a→(a+μc) transition is approached. This difference suggests that the diffusion length of film 

precursors on the surface during growth is significantly reduced for the alloys, likely due to surface 

defects that immobilize the precursors. Furthermore, because the a→a transition thickness remains 

at ~200 Å throughout the range of R from R = 40 to 70 [i.e., up to the a→(a+μc) transition for the 

bulk layer thickness desired in the device], it would appear that no significant gain in the device 

performance of the alloys can be realized by increasing the H2-dilution over this range. 

Fig. 2.2: Superimposed phase diagrams for Si:H 

(squares) and Si1-xGex:H (circles) films deposited at 

low power (0.08 W/cm2

) and low total pressure 

(< 1 Torr) on oxide-covered c-Si. These substrates 

were mounted on the anode and held at 200°C. The 

(up, down) arrows indicate that the transition occurs 

(above, below) the designated value. 

Fig. 2.1: A comparison of the deposition rates of pure Si:H and Si1-xGex:H 

alloy films as a function of the H2-

dilution ratio. These films were 

prepared on native oxide-covered c-Si 

substrates mounted on the reactor 

anode and held at 200°C. 

5
Fig. 2.3: Superimposed phase diagrams for 

Si1-xGex:H films deposited on the anode under 

similar conditions at two different substrate 

temperatures (T=200oC and T=290oC). The 

temperature increase shifts the onset of the 

mixed phase transition to lower R, and 

generally results in an increased bulk layer 

thickness for the a→ a transition. 

In the next paragraphs, the effect of other deposition characteristics and parameters on the 

Si1-xGex:H phase diagram will be demonstrated, including substrate temperature, electrode 

configuration, and He dilution in an attempt to increase the a→a transition to bulk layer thicknesses 

much greater than the 200 Å observed in Fig. 2.2. 

Comparison of Si1-xGex:H films prepared on the anode at varying substrate temperature 

Previous phase diagram studies of pure Si:H prepared at elevated deposition rates (~3.5 Å/s) 

are relevant to the present studies of Si1-xGex:H, since higher plasma power levels and gas phase 

GeH4 incorporation each lead to significantly reduced a→a transition thicknesses [2.4]. In attempts 

to improve the situation for Si:H, previous phase diagram studies have shown that by increasing the 

substrate temperature to 260°C, the a→(a+μc) transition shifts to lower R, and as a result the R value 

for optimum a-Si:H must be decreased in order to maintain deposition within the amorphous regime 

of the phase diagram for the desired thickness. This decrease in R leads to a decrease in the a→a 

transition thickness even below that obtained for maximal R, high-rate deposition at 200°C. In 

essence, the detrimental effect of crystallite nucleation overcomes any possible improvement in the 

growth process due to enhanced surface diffusion. 

In contrast to the case of pure Si:H, the broad range of R for a-Si1-xGex:H over which the a→a 

transition thickness remains constant (40 ≤ R ≤ 70) suggests that, in elevating the temperature above 

200°C, improvements can be made in the maximal R condition [that is, in spite of the expected shift 

to lower R in the a→(a+μc) transition]. This suggestion is borne out in the phase diagram for 

Si1-xGex:H prepared at T=290°C, shown in Fig. 2.3 for comparison with the corresponding diagram 

from Fig. 2.2 for Si1-xGex:H prepared at T=200°C. First, Fig. 2.3 reveals the expected shift in the 

a→(a+μc) transition to lower R with the increase in substrate temperature, from R=80 to 60 for a 

5000 Å thick film. Second with the increase in temperature, the a→a transition shifts to higher db

from ~ 200 to more than 400 Å, indicating an enhancement in surface diffusion, and an expected 

modest improvement in material characteristics for solar cells. 

6
 

Fig. 2.4: (Above) Comparison of deposition rates for anode and cathode Si:H and Si1-xGex:H thin 

film series versus the H2-dilution ratio, R = [H2]/{[SiH4]+[GeH4]}. The alloy flow ratio G = 

[GeH4]/{[SiH4]+[GeH4]} was fixed at G = 0 and G = 0.167, respectively. 

Additional phase diagrams have also been developed for processes at 260°C and 320°C, as 

well as for a two step, 200°C/320°C process, the latter in order to enhance the nucleation density on 

the substrate and characterize the surface diffusion processes with greater confidence. Furthermore, 

a phase diagram versus temperature has been established for R=60. In all these studies, under no 

conditions of substrate temperature has the a→a transition been found to exceed ~ 500 Å. 

Comparison of Si:H and Si1-xGex:H films prepared on the cathode 

Having exhausted the potential of substrate temperature optimization to improve Si1-xGex:H 

surface stability under standard conditions, other less conventional approaches were considered. On 

the basis of previous successes by Paul et al. for a-Ge:H [2.3] and Ganguly et al. for a-Si:H [2.5], 

depositions were performed on the cathode of the reactor with a self-bias of ~ −20 V. The substrate 

temperature of T=200o

C was maintained indirectly from the anode through radiative and conductive 

heating, the latter through the deposition gas. Because cathodic deposition is new to the phase 

diagram studies, depositions of pure Si:H on the cathode were also performed and the results will be 

reported for convenience together with those for Si1-xGex:H in the following paragraph and in Figs. 

2.4-2.7. 

Higher deposition rates for cathodic films (under otherwise identical conditions) are expected 

due to higher gas dissociation rates by the more energetic ions crossing the cathode sheath. This 

expectation is been borne out in the comparisons of the deposition rates for cathodic and anodic 

Si1-xGex:H [2.6] and for pure Si:H depicted in Fig. 2.4. Figure 2.5(a) depicts the dramatic 

differences in the microstructural evolution in a comparison of R=80 Si1-xGex:H films deposited on 

7
the cathode and anode. The anodic Si1-xGex:H film exhibits an a→a roughening transition at db = 

200 Å and an a→(a+μc) transition at db = 700 Å. In contrast, the cathodic Si1-xGex:H remains 

amorphous throughout, exhibiting a strong smoothening effect that leads to a stable surface with ds ~ 

7 Å that presists to a thickness of db~1500 Å, a factor of three higher than the best anodic result. 

Figure 2.5(b) shows the similarly dramatic differences between R=20 pure Si:H films deposited at 

the cathode and anode. The anodic Si:H film exhibits an initial strong smoothening effect in the 

amorphous growth regime to a roughness thickness of ds ~ 2 Å at a bulk layer thickness of 150 Å. 

The film evolves through an a→(a+μc) transition almost immediately thereafter (db = 230 Å), 

however, and then through an (a+μc)→μc transition at db = 1400 Å, the latter characterized by a 

smoothening effect due to the coalescence of isolated crystallites. The cathodic Si:H film shows a 

similar smoothening effect, but in contrast exhibits sub-monolayer level roughness (ds ~ 2 Å) 

throughout the growth of a 3500 Å thick film at which point the a→(a+μc) transition occurs. In this 

case, the extensive growth period with monolayer level smoothness, a key characteristic of 

protocrystallinity, is unique to the Si:H cathodic deposition. 

Results for cathodic Si1-xGex:H deposition at 200°C such as those of Fig. 2.5(a) have been have 

been used to construct the phase diagram shown in Fig. 2.6, along with that for anodic deposition 

from Figs. 2.2 and 2.3. This comparison reveals two important effects. First, a significant shift in 

the a→(a+μc) transitions to higher R is observed for deposition on the cathode versus anode. 

Second, the a→a transition shifts to much larger thicknesses of 2000 Å for deposition on the cathode 

as the a→(a+μc) is approached. Such behavior suggests significant improvement in the precursor 

surface diffusion under cathodic conditions. It is possible that low energy ion impact in the top 1-2 

monolayers of the film is sufficient to enhance the processes of H-elimination, leading to a more 

compact surface. This may also lead to a suppression of microcrystallite nucleation which has been 

proposed to involve clusters of specific Si-H bonding structures in the top 1-2 monolayers [2.7]. 

The high H2-dilution R > 60 ensures a low defect density as H-elimination proceeds. The results for 

cathodic Si:H depositions have been used to construct the phase diagram of Fig. 2.7 which reveals 

a) b) 

Fig. 2.5: Comparison of the structural evolution of (a) Si1-xGex:H and (b) Si:H films deposited on 

c-Si substrate mounted at the anode (triangles) and cathode (squares) using R=80 and R=20, 

respectively. 

8
Figs. 2.6 and 2.7: Superimposed deposition phase diagrams for the cathode (squares) and anode 

(circles) Si1-xGex:H and Si:H alloy series plotted as a function of H2-dilution, R. The alloy flow 

ratio G = [GeH4]/{[SiH4]+[GeH4]} was fixed at 0.167 and 0, respectively. The broken lines denote 

the amorphous roughening transition (a → a), and the solid lines denote the amorphous-to-mixed 

phase transition [a → (a+μc)]. 

similar qualities. Again, compared to the anodic depositions, the cathodic conditions shift the 

a→(a+μc) transitions to higher R. This effect is advantageous in that an extended protocrystalline 

regime becomes available at higher dilution levels, even though the a→a transition thickness is 

reduced somewhat at the a→(a+μc) transition for a thick layer. 

Comparison of Si1-xGex:H films prepared on the cathode with varying G 

Figure 2.8 depicts the optical band gaps of the Si1-xGex:H samples versus the GeH4 flow ratio 

G for Si1-xGex:H films prepared with a cathodic electrod configuration. The results shown as the 

points and solid lines were obtained from real time spectroscopic ellipsometry data collected at the 

deposition temperature (T=200oC) and deduced from extrapolations of ε2

1/2 versus E, assuming a 

constant dipole matrix element (see inset). The gaps of the films prepared at R values just before the 

[a→ (a+μc)] transition (R=10 for G=0; R=40 for G=0.083; and R=90 for G=0.167) are within the 

range of 1.23 to 1.66 eV. Also shown in Fig. 2.8 are room temperature (T=20o

C) estimates based on 

an optical gap shift of ~0.08 eV (or 4.5x10−4

 eV/°C; broken line). Estimated room temperature Tauc 

gaps [extrapolations of (ε2E2

)

1/2 versus E, assuming a constant momentum matrix element], as would 

be measured by transmission spectroscopy on thick films, range from 1.35 to 1.78 eV when the band 

gap is extrapolated from photon energies close to the gap. A ~ 0.04 eV increase in gap is attributed 

to the differences in optical gap extrapolation methodology (constant momentum versus constant 

dipole matrix element) [2.8]. 

Figure 2.9 shows the surface roughness layer thickness versus bulk layer thickness during Si:H 

and Si1-xGex:H growth for two pairs of depositions, each pair at the same R but different ratios G. 

These two pairs were selected to show two trends to be emphasized in the phase diagrams presented 

9
Fig. 2.8 Optical band gap as a function of 

GeH4 flow ratio G determined from real 

time spectroscopic ellipsometry applying a 

linear extrapolation to ε2 

1/2 spectra 

obtained at the deposition temperature of 

T=200oC (main panel; points) and 

approximated to room temperature 

assuming a linear temperature coefficient 

of 4.5x104

 eV/°C (broken line). The inset 

shows a typical extrapolation that provides 

the gap. 

in Fig. 2.10. In the main part of Fig. 2.9, the role of GeH4 addition of G=0.083 is shown for R=10. 

The key effect is the shift of the roughening transition in the amorphous growth regime, denoted 

a→a, to much lower thicknesses. In the inset, the role of the same GeH4 addition is shown for R=40. 

The key effect in this case is the shift of the amorphous-to-(mixed phase microcrystalline) 

roughening transition, denoted a → (a+μc), to larger thicknesses outside the accessible range. In 

fact, for G=0 and R=40, the Si:H film passes through amorphous, mixed-phase, and single-phase 

regimes during the growth of a 4000 Å thick film, whereas for G=0.083 and R=40, the Si1-xGex:H 

film remains fully amorphous over the same range of thickness. 

 Figure 2.10 depicts three superimposed phase diagrams for G values of G=0, 0.083, and 0.167, 

but otherwise identical PECVD conditions. These phase diagrams depict the a→a roughening 

transition thickness (as in Fig. 2.9, main part) and the a→(a+μc) transition thickness (as in Fig. 2.9, 

inset, with G=0) as functions of the H2-dilution ratio R. A comparison of the overlapping phase 

diagrams yields the following three observations. 

 (i) Considering the phase diagrams collectively, the boundary defining the a → (a+μc) 

transition thickness shifts to much higher R with increasing phase diagram G value. In fact, the H2-

dilution level at which the a → (a+μc) transition occurs in an ~ 2000 Å thick film, increases from 

R=20 to R=100 as G increases from G=0 to G=0.167. 

 (ii) Considering each of the three phase diagrams individually, the a → a roughening 

transition thickness increases with increasing H2-dilution ratio right up to the R value at which the a 

→ (a+μc) transition occurs. For example with G =0.083, the a → a transition thickness increases 

from db ~ 250 Å to db ~ 3500 Å with increasing R over the amorphous growth regime. 

 (iii) Returning to the phase diagrams collectively, the maximum a → a transition thickness 

[which occurs at the R value just below the a → (a+μc) transition for a thick film] decreases with 

increasing phase diagram G value. In fact, the overall decrease from G=0 to G=0.167 is minimized 

by cathodic PECVD with a self bias of ~ −20 V, rather than conventional anodic PECVD [2.9]. 

 Here it should be recalled that in previously-described phase diagram studies at G=0.167, 

where Eg(20°C) ~ 1.25-1.35 eV, deposition conditions were set to ensure microstructural evolution 

that reflects the highest electronic quality and stability, assuming correlations established between 

10
Fig. 2.9: Surface roughness evolution for two pairs of Si1-xGex:H films prepared under rf P

conditions that include: a substrate temperature of T=200

ECVD 

f oC, a total pressure of p<1 Torr, an r

power of P=0.08 W/cm2, and a cathodic dc bias of Vdc ~ −20V. The main part shows a 

comparison of depositions with G=0 and 0.083 with the H2 dilution ratio fixed at R=10 (in the 

amorphous regime for G=0), whereas the inset shows the corresponding comparison with R=40 

(in the amorphous to microcrystalline evolution regime for G=0). 

Fig. 2.10: Superimposed phase diagrams for different GeH4 flow ratios G, each plotted versus 

the H2 dilution level R. For each phase diagram, the thicknesses of the amorphous roughening 

transition are plotted (solid line and points) along with those of the amorphous-to-(mixed-phasemicrocrystalline) transition (broken line and open points). Up- and down-arrows indicate that the 

transitions occur at thicknesses above or below the indicated values. [Left: G=0 (circles); center: 

G=0.083 (squares); and right: G=0.167 (triangles).] 

11
phase diagrams and device characteristics for a-Si:H also hold for a-Si1-xGex:H [2.9]. These 

characteristics include the largest smoothening effect during coalescence, the lowest roughness layer 

thickness when a stable surface is reached, and the largest a → a roughening transition thickness, the 

latter evident directly from the phase diagram. PECVD at the cathode with a dc self-bias of ~ −20 

V, rather than at the grounded anode, was the key process difference for optimized microstructural 

properties at G=0.167 [2.9]. The improvement is attributed to a positive influence of weak ionbombardment that can enhance near-surface dehydrogenation reactions and network ordering, but 

without causing damage through sub-surface atomic displacements [2.10]. 

 Figures 2.11-13 show the effects on the deposition rate, the a → a transition thickness, and the 

dielectric function resonance width that result due to increases in R from 10 to the value just before 

the thick-film a → (a+μc) transition. These data are plotted versus G for a-Si1-xGex:H alloys 

prepared by optimum cathode PECVD as described in the previous paragraph. The solid line in 

Fig. 2.12 represents the a → a boundary plotted versus G for fixed R=10, and the broken line 

represents the corresponding boundary but for R selected as its maximum G-dependent value 

without crossing the a → (a+μc) transition. As a result, the broken lines in Figs. 2.11-13 represent 

optimized conditions versus R for the given G plotted along the abscissa. Such optimization was 

demonstrated in detail for pure a-Si:H (G=0) by usual anode PECVD through correlations with solar 

cell performance. Here, Fig. 2.13 depicts optimization of a-Si1-xGex:H by cathode PECVD through 

the width of the resonance in the 200°C dielectric function, which can be determined from the real 

time spectroscopic ellipsometry data together with the structural evolution. Narrowing of this 

resonance indicates improvement in short-range order in the network and accompanies narrowing of 

the Urbach tail [2.11]. Thus, Figs. 2.12 and 2.13 demonstrate that the increase in a → a transition 

thickness correlates with enhanced ordering. 

 Figure 2.14 shows a phase diagram in which case all three transition thicknesses are included: 

a → a, a → (a+μc), and (a+μc) → μc; however, the latter one is only observed for G = 0, i.e., only 

for pure SiH4 depositions. For the non-zero G values, single phase microcrystalline Si1-xGex:H 

cannot be obtained, irrespective of thickness. The new phase diagram in Fig. 2.14 exhibits features 

similar to the diagrams versus R; however, the behavior vs. the abscissa is reversed: crystallite 

development occurs at low rather than high abscissa values. Finally, it should be noted that the 

phase diagram of Fig. 2.14 exhibiting structural and phase transitions versus G is expected to be 

useful in optimization of Ge grading in the i-layers of solar cells. It is clear from this figure that 

optimized grading of Ge will require simultaneous variations in H2-dilution ratio R, i.e., to higher R 

with increasing G and vice versa. These phase diagrams can direct such a process, and this will be a 

focus of future efforts. 

Comparison of Si1-xGex:H films prepared with variable He dilution 

 Figures 2.15-17 provide a comparison between the roles of H2-dilution and He-dilution for 

Si1-xGex:H alloys (G=0.167) prepared by standard anode PECVD. This study explores the 

possibility that He dilution can also improve the properties of Si1-xGex:H prepared by anode 

PECVD. Figure 2.15 shows the surface roughness evolution for a film prepared with R=80 without 

He-dilution. Under these conditions the a → a and a → (a+μc) transitions occur near bulk layer 

thicknesses of 200 and 800 Å, respectively, as depicted on the phase diagram of Fig. 2.2. The low 

value of the former transition thickness is an indication of a short precursor diffusion length on the 

film surface and poor electronic properties in spite of the proximity to the a → (a+μc) transition. As 

shown in Fig. 2.2, this situation is improved by conversion to the cathode PECVD in which case the 

12
Fig. 2.11: Deposition rate for cathode Si1-xGex:H as functions of G = [GeH4]/{[SiH4]+[GeH4]} 

for R=10 and for the maximal R value before the thick-film (0.5 μm) a → (a+μc) transition is 

crossed. 

Fig. 2.12: A deposition phase diagram depicting the amorphous roughening transition (a→a) for 

R=10 a-Si1-xGex:H films plotted versus the alloy flow ratio G=[GeH4]/{[SiH4]+[GeH4]} (solid 

line and square points). The dotted arrows represent the increase in the a → a transition possible 

with the increase in R indicated, i.e., up to the amorphous-to-(mixed-phase) transition for a thick 

film. Thus, the broken line represents the phase boundary that results versus G for optimized 

a-Si1-xGex:H films versus R. 

13
Fig. 2.13: Width of the resonance in the dielectric function (measured at 200°C and at a 

thickness of 150-300 Å) for cathode Si1-xGex:H as a function of G = [GeH4]/{[SiH4]+[GeH4]} for 

R=10 and for the maximal R value before the thick-film (0.5 μm) a → (a+μc) transition is 

crossed. Thus, the arrows indicate improvements in short-range order possible by increasing the 

R from 10 right up to the a → (a+μc) transition. 

Fig. 2.14: A single deposition phase diagram for R= 40 Si1-xGex:H films plotted versus the GeH4

flow ratio G. In this diagram, the thicknesses of the amorphous roughening transition (solid line 

and square points), the amorphous-to-(mixed-phase microcrystalline) transition (dashed line and 

circles), and the (mixed-phase)-to-(single-phase) microcrystalline transition (dotted line and 

triangles) are depicted. Up-arrows indicate that the transitions occur at thicknesses above the 

indicated value. 

14
Fig. 2.15: (left) Surface roughness evolution for two Si1-xGex:H films prepared in the anode 

configuration with R=[H2]/{[SiH4]+[GeH4]} = 80 and G=[GeH4]/{[SiH4]+[GeH4]} = 0.167. One film 

was prepared with He=[He]/{[SiH4]+[GeH4]} = 0 and the other with He =20. 

Fig. 2.16: (right) Deposition rate versus the combined [H2+He]-dilution ratio S=R+He= 

{[H2]+[He]}/{[SiH4]+[GeH4]} for Si1-xGex:H films prepared in the anode configuration with 

G=[GeH4]/{[SiH4]+[GeH4]}= 0.167. Here, results for the nine depositions without He-dilution are 

plotted from Fig. 2.1, along with two series of depositions, one in which R is fixed at 10 and the 

dominant dilution effect is He (four depositions with He increasing from 0 to 90), and the other in 

which R is fixed at 80 and the dominant dilution effect is H2 (two depositions with He = 0, 20). 

15
a → (a+μc) transition is suppressed and the a → a transition increases considerably to ~1500 Å. 

Figure 2.15 also includes the roughness evolution of a film prepared with R=80 and 

He=[He]/{[SiH4]+[GeH4]}=20. In this case, the addition of He shifts the a →(a+μc) transition to 

higher R such that the film remains amorphous throughout deposition. Furthermore the a → a 

transition shifts to somewhat higher thickness, but not nearly as much as occurs with the change in 

electrode configuration. Figure 2.16 summarizes all results for deposition rate versus the combined 

[H2+He]-dilution ratio S=R+He={[H2]+[He]}/{[SiH4]+[GeH4]}. Here, results for the nine 

depositions without He-dilution are plotted from Fig. 2.1, along with two series of depositions, one 

in which R is fixed at 10 and the dominant dilution effect is He (four depositions with He increasing 

from 0 to 90), and the other in which R is fixed at 80 and the dominant dilution effect is H2 (two 

depositions with He = 0, 20). 

 Figure 2.17 shows the phase diagrams for the same set of samples. The following two 

observations can be made. (i) Dominant H2-dilution (He=0) and He dilution (R=10) generate similar 

a → a transition thicknesses, even though higher deposition rates are achieved with dominant He 

dilution. (ii) A larger a → a transition thickness and improved properties are possible (without 

sacrificing deposition rate) by using He-dilution to suppress to a → (a+μc) transition thickness, 

enabling a larger R value, as shown for the deposition with R=80 and He=20 in Figs. 2.15 and 2.17. 

The larger amplitude of ds for this deposition in Fig. 2.15 appears to be due to a lower initial 

nucleation density, possibly a result of longer precursor diffusion length on the substrate surface. 

Fig. 2.17: Deposition phase diagrams plotted versus the combined [H2+He]-dilution ratio 

S=R+He={[H2]+[He]} /{[SiH4]+[GeH4]} for the set of Si1-xGex:H films of Fig. 2.7, prepared in 

the anode configuration with G=[GeH4]/ {[SiH4]+[GeH4]} = 0.167. The broken lines denote the a 

→ a transitions while the solid lines denote the a → (a+μc) transitions.

16
Summary 

 Si1-xGex:H phase diagrams have been developed comparing anode and cathode electrode 

configurations and the role of low-energy ion bombardment. These comparisons show that the a →

(a+μc) transitions shift to higher R for films deposited on the cathode. This opens a narrow window 

leading to a → a transitions at much higher bulk thicknesses, suggesting significant increases in 

precursor surface diffusion for a-Si1-xGex:H deposited at the cathode. Si1-xGex:H phase diagrams 

versus R have been developed under cathode deposition conditions for different flow ratios G. This 

comparison shows that: i) the a → a transitions shift to higher thicknesses with increasing R right 

up to the a → (a+μc) transitions, indicating the beneficial effect of H on precursor surface diffusion 

under all alloying conditions and ii) the dielectric function width parameter Γ decreases with 

increasing R up to the a → (a+μc) transition, indicating improvedshort-range order in the films. 

Additionally, for anode depositions with substrate temperature as a variable have indicated that the a 

→ (a+μc) transition shifts to lower R with increasing temperature. In spite of this behavior, the a →

a transitions for the highest dilution R before crossing the a → (a+μc) occur at increasingly higher 

bulk layer thickness with increasing temperature. This result indicates modest improvements in film 

quality, although not to the extent seen through the change in the electrode configuration from anode 

to cathode. Finally, the presence of He in a-Si1-xGex:H has been shown to shift the a → a 

roughening transition to higher bulk layer thicknesses, indicating enhanced surface diffusion, but the 

effect is much weaker than for H2 dilution. Similarly, He has been shown to suppress 

microcrystallite formation, shifting the a → (a+μc) transition in thin film Si1-xGex:H to higher bulk 

layer thickness, extending the protocrystalline regime. 

17
2.2 Dielectric Functions of a-Si1-xGex:H versus Ge Content, Temperature, and Processing: 

 Advances in Optical Function Parameterization 

Overview 

 Parameterizations of the optical functions of semiconductors have three important applications 

[2.11]. First, they can be used in performance simulations of optoelectronic devices that involve 

photon collection -- solar cells being an important example. In this case, the effects of deviations in 

the optical band gaps for the component i-layers on the measured quantum efficiency can be 

predicted in order to assess fabrication tolerances. Second, parameterizations can be applied in 

fitting transmittance, reflectance, ellipsometric, or optical quantum efficiency spectra acquired on 

multilayer stacks that include one or more of the layers. By using parameter databases, one can 

extract wavelength-independent parameters directly such as thicknesses, compositions (or preferably 

optical gaps), and even temperature that directly assist in evaluating the processing and material 

properties of interest in devices. Finally, parameterizations can provide succinct information useful 

for correlating with other properties for indirect assessment of the performance of the materials. For 

example, we have found that an important parameter is the energy width of the resonance in the 

dielectric function which provides information on defect density and disorder presumably due to its 

proportionality to the excited state relaxation rate. 

 We have applied an advanced model to analyze the dielectric functions ε = ε1 + iε2 of amorphous 

silicon-germanium alloys (a-Si1-xGex:H) (i) as a function of alloy content x by varying the flow ratio 

G = [GeH4]/{[SiH4]+[GeH4]} in plasma-enhanced chemical vapor deposition (PECVD), and (ii) for 

the first time as a function of the measurement temperature Tm by cooling the newly-deposited film. 

All ε spectra (1.5 – 4.5 eV) have been measured by spectroscopic ellipsometry (SE) either in real 

time during deposition or in situ post-deposition in order to avoid surface contamination. From the 

resulting extensive database, the optical properties of the alloys can be predicted for any value x and 

Tm within the ranges of the database. Such a capability is expected to be useful, for example, in real 

time control of optical gap in the PECVD process and in predicting the quantum efficiency of 

multijunction a-Si:H-based solar cells versus operating temperature. The effect on the database of 

other deposition parameters such as the electrode configuration and the H2-dilution ratio R = 

[H2]/{[SiH4]+ [GeH4]} have also been explored. The latter two studies provide useful insights into 

materials properties that can be extracted from a single spectroscopic measurement performed in real 

time during PECVD. For example, the energy width of the resonance in ε correlates closely with the 

precursor surface diffusion characteristics observed throughout growth -- both determined from real 

time SE. This result indicates that short-range ordering in the film is improved when surface 

diffusion is promoted. 

Experimental Details: 

Deposition Process 

 The primary a-Si1-xGex:H series explored in this study and presented to exemplify our 

approach was prepared by PECVD on crystalline Si (c-Si) wafers from gas flows of SiH4, GeH4, and 

H2. Most parameters were set for optimum a-Si:H [2.1] including a H2-dilution ratio of 

R = [H2]/{[SiH4]+[GeH4]} = 10, a substrate temperature of Ts = 200°C, a minimum plasma power of 

P = 0.08 W/cm2

, and a partial pressure of [SiH4]+[GeH4] of p ~ 0.05 Torr. The gas flow ratio 

18
G = [GeH4]/{[SiH4]+[GeH4]} was set at values from 0 to 0.167, corresponding to an optical gap 

range at 20°C of 1.3 to 1.8 eV, which is of interest for multijunction solar cells [2.12]. To improve 

the growth and optical characteristics of the lowest gap a-Si1-xGex:H, but at the expense of those of 

pure a-Si:H, the substrate was mounted on the cathode with a dc self-bias of ~ –20 V [2.9]. 

 This a-Si1-xGex:H series was measured in real time by spectroscopic ellipsometry (SE), and the 

structural evolution was determined throughout the growth of 0.2 - 0.8 μm thick films [2.1]. In 

addition, the dielectric function at a measurement temperature of Tm=Ts=200°C was deduced in a 

numerical inversion process that requires the bulk and surface roughness layer thicknesses. This 

inversion was performed on data collected after complete coalescence and surface smoothening 

when the bulk layer is ~ 150-300 Å thick. For this first series with variable G and R=10, selected 

samples were cooled from Tm=Ts=200°C after deposition, and the dielectric function was deduced 

by SE as a function of Tm, applying numerical inversion using the bulk and surface roughness layer 

thicknesses from the end of deposition. The calibration that provides the true Tm from a 

thermocouple reading is performed using a c-Si wafer and a similar cooling cycle, applying SE to 

deduce the critical point energies which are known functions of Tm [2.13]. 

 For the first series, Fig. 2.18 shows the variation in x and a measure of the optical band gap Eg as 

functions of G. The former is obtained ex situ by x-ray photoelectron spectroscopy and the latter in

Fig. 2.19: (Above, right) Examples of fits (solid lines) to dielectric function spectra (points) of 

a-Si1-xGex:H measured at Tm=Ts=200°C from films of the series of Fig. 2.18 (R=10, cathodic 

deposition) at the extremes of the alloy range. These spectra were deduced by inversion of real 

time SE data at bulk layer thicknesses in the range 150-300 Å.

Fig. 2.18: (Above) Alloy content x in 

a-Si1-xGex:H thin films and their optical band gaps 

at Tm=Ts=200°C as a function of the flow ratio 

G=[GeH4]/{[SiH4]+[GeH4]} using a fixed ratio 

R=[H2]/{[SiH4]+[GeH4]}=10 and a cathodic 

electrode configuration. The gaps are from 

extrapolations of ε2

1/2 to zero ordinate using ε2

obtained by inversion at thicknesses in the range o

150-300 Å. 

f 

19
real time by SE, applying an extrapolation of ε2

1/2 versus photon energy E, assuming parabolic bands 

and a constant-dipole matrix element (CD-ME, Cody’s method) [2.14]. It should be noted that the 

Tm=200°C gap of 1.17 eV at G=0.167 corresponds to a Tm=20°C Tauc gap of 1.28 eV, assuming 

parabolic bands and a constant-momentum matrix element (CM-ME) [2.8]. 

 Second and third deposition series were performed at the anode with fixed G values at the 

extrema of 0 and 0.167 in order to explore the effect of the electrode configuration, but now as a 

function of the H2-dilution ratio R. Under the G=0 conditions, the optimum a-Si:H is obtained at 

R=10 just before the amorphous-to-mixed-phase transition [a → (a+μc)] for a thick film (>0.5 μm). 

Here the amorphous phase roughening transition (a→a) thickness is maximum and the observed 

solar cell performance is the highest [2.1]. In contrast, the thick film a → (a+μc) transition for 

G=0.167 anodic depositions occurs at R=70. A fourth deposition series was performed at the 

cathode with G also fixed at 0.167 as a function of R from 10 to 140 -- under otherwise identical 

conditions as the first series. This variation in R leads to a significant improvement in the growth 

and optical characteristics for the a-Si1-xGex:H as the thick film a → (a+μc) transition is approached. 

For this fourth series, the a → (a+μc) transition occurs at R~95, which identifies the optimum 

a-Si1-xGex:H growth conditions achieved thus far in our real time SE studies, as indicated by the 

largest precursor surface diffusion length [2.9] and the highest degree of short-range order (see 

below). 

Optical Model 

The most popular dielectric function parameterization for amorphous semiconductors is based 

on a model for ε2 that includes a parabolic-band, CM-ME expression GM(E)=(E−Eg)

2

/E2 at near gap 

energies, evolving to a Lorentz oscillator L(E) = AE0ΓE/[(E0

2

−E2)

2

+Γ2E2] at high energies, 

including a total of four free parameters [2.15]. Then ε1 is given by an analytical Kramers-Kronig 

integration of ε2(E)=GM(E)L(E); E>Eg and ε2=0; E<Eg,. In fact, in determining ε1, a fifth free 

parameter is introduced, the constant contribution to the dielectric function ε∞. More recent research 

has shown that a similar approach that adopts instead a CD-ME formalism GD(E) = 

(E−Eg)

2

/[(E−Eg)

2

+Ep

2

] at near gap energies provides a superior fit with improved internal 

consistency [2.11, 2.16]. Thus, in order to couple the CD-ME expression to the Lorentz oscillator, 

the additional parameter Ep is required that controls the transition energy between the near gap 

absorption onset and the Lorentz oscillator behavior. The extra parameter of the CD-ME approach 

is compensated through improved consistency that allows fixing ε∞=1. In contrast, for the CM-ME, 

ε∞ decreases with increasing x, becoming negative for the larger values of x, unphysical behavior 

[2.11]. Fig. 2.19 shows examples of the experimental data and fits to the CD-ME approach for 

cathodic a-Si1-xGex:H prepared with the extremes of G=0, 0.167, and with R=10. 

Results and Discussion 

 Figure 2.20 depicts data plotted versus x in the best fit variable parameters in the CD-ME 

formula with ε∞ fixed at 1 (solid points). In addition, the resonance energy E0 is found to be 

constant at 3.736 eV within the confidence limits, and so is also fixed. The samples analyzed to 

obtain the results in Fig. 2.20 were from the first deposition series using the cathodic configuration 

with R fixed at 10. The results are characteristic of Tm=Ts=200°C and also a film thickness of ~150 

- 300 Å. The variations with x of interest include the expected, nearly linear decreases in the fitted 

20
Eg (distinct from the ε2

1/2 extrapolation for Eg in Fig. 2.18) and transition energy Ep. Of equal 

interest is the monotonic increase in the width parameter Γ. This is attributed to a reduction in the 

excited state lifetime due to increased disorder with alloying. In fact, assuming electron and hole 

velocities υ characteristic of the E1 excited states of c-Si and using the simple expression for the 

mean free path L = hυ/Γ (h: Planck's constant), a 2 → 3 eV dielectric function width can be 

ascribed to a 5 → 4 Å mean free path, which is consistent with the lack of long-range ordering. 

Thus, the width Γ is a very useful parameter for assessing short-range order, also found to correlate 

with the Urbach tail width [2.11]. In fact, its usefulness lies in its accessibility in a real time 

measurement. 

Fig. 2.21: Dielectric function parameters 

versus measurement temperature Tm obtained 

in fits such as those of Fig. 2.19 for an 

a-Si1-xGex:H alloy with G=0.083 prepared at 

the cathode. The dielectric functions fitted in 

this study were deduced by inversion using 

thicknesses deduced for the final film. The 

following parameters were fixed in the 

analysis: ε∞ = 1, E0 = 3.77 eV. The small 

difference in E0 compared with that of Fig. 

2.20 is attributed to the different stage of the 

growth process. 

Fig. 2.20: Dielectric function parameters 

versus a-Si1-xGex:H alloy composition x at 

Tm=Ts=200°C deduced in fits such as those of 

Fig. 2.19 for the series of depositions of Fig. 

2.18 (R=10, cathodic deposition, closed 

circles). Also shown are the corresponding 

results for films deposited on the anode under 

otherwise identical conditions. The dielectric 

functions fitted in this study were deduced by 

inversion at bulk layer thicknesses of ~150-300 

Å. The following parameters were fixed in the 

analysis: ε∞ = 1 and E0 = 3.74 eV. 

21
 Figure 2.20 also shows results at Tm=Ts=200°C for selected depositions from the second and 

third series using the anodic configuration also with R=10 (open points) for comparison with the 

otherwise identical cathodic series in the same figure (solid points). An observation of interest is 

that the conversion from the anodic to cathodic configuration leads to a reduction in Γ for the 

a-Si1-xGex:H, i.e., an improvement in order, whereas the conversion for pure a-Si:H leads to an 

increase in Γ. This is precisely the same behavior as is observed in the a→a roughening transition: 

an increase upon conversion to the cathodic configuration for a-Si1-xGex:H, but a decrease upon 

conversion for pure a-Si:H [2.9]. Evidently there is a close connection between precursor surface 

diffusion length and the resulting short-range order in the film. In fact, in previous studies, the 

narrowest width of Γ=2.0 eV at Tm=20°C has been obtained from protocrystalline Si:H which 

exhibits no a→ a roughening transition throughout the growth of a 0.5 μm thick film [2.1,2.11]. 

 Figure 2.21 shows how the dielectric function parameters vary with temperature, as obtained 

during cooling of the a-Si1-xGex:H prepared in the cathodic configuration with G=0.083 and R=10 

(sample of the first series). In this study, ε∞ =1 as usual and the resonance energy is fixed as well 

(E0=3.773 eV, appropriate for the thicker films, independent of x). All other parameters exhibit 

linear variations with T. Specifically, the optical gap Eg and transition energy Ep decrease with 

slopes of −4.2 x 10−4

 eV/°C and −8.6x10−4 eV/°C, and the width Γ increases with a slope of 5.2x10−4

eV/°C. As shown in Fig. 2.22, there are relatively weak variations in the slopes with Tm that can be 

averaged assuming linear functions of x. For example, the variations in the slopes of Eg and Ep with 

x are consistent: at larger x the slopes are larger in magnitude apparently due to stronger electronphonon interactions in the alloys. 

 As further evidence for the significance of the parameterization, in particular to extract the 

width of the resonance, Fig. 2.23 shows fitting results similar to those of Fig. 2.20, but for the fourth 

deposition series involving a variation in R under cathodic conditions with G=0.167. The vertical 

line indicates the a→(a+μc) transition for a 0.5 μm thick film. On average the gap increases by 

~0.05 eV with the increase in R up to the a→(a+μc) transition, an increase typical of that for G = 0 

depositions versus R. In addition, Γ decreases from 3.1 eV to 2.8 eV with the increase in R from 10 

to 100. For R=125 and 140, the saturations in Eg and Γ are likely to be due to the development of 

crystallites in the thin films (~150-300 Å). The decrease in Γ for R≤100 also tracks the 

corresponding increase in the a→a roughening transition thickness and even extends into the 

protocrystalline regime of the thin film (to R=100), i.e., beyond the thick-film a→(a+μc) transition. 

Summary 

In this section, we have described a recently-developed parameterization of the optical 

properties of amorphous semiconductors and its application to a-Si1-xGex:H alloys as a function of 

the alloy content x and the temperature Tm. Results at Tm=200°C in Fig. 2.20 (solid points) which 

define intercepts, along with the slopes in Fig. 2.22 allow one to apply SE for simultaneous in situ 

composition, optical gap, and temperature determination (with ε∞ = 1 and E0=3.75 eV). The same 

set of results can be used to predict the effect of optical gap variations and operation temperature 

changes on the quantum efficiency of multijunction solar cells. The results in Fig. 2.20 (open 

points) and Fig. 2.23, show how variations in electrode configuration and H2-dilution influence the 

results. Since all trends versus T can be approximated as linear functions, it is straightforward to 

predict the effects of combinations of variables. Finally, the parameter Γ, the dielectric function 

22
Fig. 2.22: The slopes that describe the 

linear variation of the dielectric function 

parameters versus measurement 

temperature Tm determined as shown in 

Fig. 2.21. Results are given for four 

a-Si1-xGex:H alloys of different 

composition x. In the overall analysis, the 

following parameters were fixed: ε∞ = 1, 

E0 = 3.75 eV. 

Fig. 2.23: Dielectric function parameters 

for a-Si1-xGex:H alloys versus H2-dilution 

ratio R=[H2]/{[SiH4]+[GeH4]} at 

Tm=Ts=200°C deduced in fits such as those 

of Fig. 2.19 for a series of depositions with 

G=0.167 prepared at the cathode. The 

dielectric functions fitted in this study were 

deduced by inversion at bulk layer 

thicknesses ~150-300 Å. The following 

parameters were fixed: ε∞ = 1, E0 = 3.74 eV. 

resonance width, shows clear correlations with the amorphous roughening transition thickness in the 

growth process, an indication that enhanced surface diffusion, which is proposed to be reflected in a 

larger a→a roughening transition (see next section), results in improved short-range order in the film 

under all the conditions of growth explored for a-Si1-xGex:H, including variations in 

G=[GeH4]/{[SiH4]+[GeH4]}, R=[H2]/{[SiH4]+ [GeH4]}, and electrode configuration.

23
2.3 Model for Amorphous Roughening Transition in Amorphous Semiconductor Deposition 

Overview 

 Real time spectroscopic ellipsometry (SE) results have demonstrated the existence of three 

regimes of surface roughness evolution during amorphous semiconductor thin film growth by 

plasma-enhanced chemical vapor deposition (PECVD) [2.1]: 

 (i) smoothening (or coalescence) of initial nucleation-generated clusters; 

 (ii) stable surface until a critical thickness; and 

 (iii) roughening of the film beyond the critical thickness. 

It should be emphasized that throughout these regimes the films remain fully amorphous. 

 Hydrogenated amorphous silicon (a-Si:H) thin films exhibiting the highest electronic 

performance also reveal in regime (i) the largest surface smoothening magnitudes and rates during 

coalescence, as well as in regime (ii) the smoothest, most stable surfaces throughout the growth of 

thick films [2.1]. In fact, for these highest quality films, the transition between regimes (ii) and (iii), 

denoted the a → a roughening transition, is not observed, presumably because it occurs at 

thicknesses greater than the final film thickness (typically > 0.5 μm). Deterioration of electronic 

properties is correlated with a reduction in the magnitude and rate of smoothening in regime (i) and 

an increase in the roughness thickness in regime (ii). Deterioration is also accompanied by a shift in 

the a → a transition to lower thicknesses. In fact, regimes (i) and (ii) may disappear when the 

electronic quality is sufficiently poor, e.g., under conditions combining high plasma power, little or 

no H2-dilution, and low temperatures. In this section, insights into the three regimes listed above 

will be obtained by applying a simple, one-dimensional (1-D) continuum model of film growth. 

This 1-D continuum model of surface profile evolution adopts an initial condition designed to be 

consistent with the nucleation characteristics measured by real time SE. Good agreement between 

the experimental results and model calculations support the contention that optimum electronic 

qualities of the films are associated with weakly reactive surfaces and long lifetime precursors that 

lead to large precursor surface diffusion lengths. 

Results and Discussion 

Experimental Data 

 Real time SE has been performed using a rotating-compensator multichannel ellipsometer [2.2] 

in order to study the evolution of the surface roughness thickness for a-Si:H films fabricated by 

PECVD on crystalline silicon (c-Si) wafer substrates. Figure 2.24 (main part) depicts examples from 

a high-pressure, high-rate PECVD series for which all films remain amorphous throughout growth 

[2.17]. The substrate temperature T, rf plasma power P, and total pressure p were fixed at the 

following values: T = 200°C, P = 0.72 W/cm2

, and p = 3 Torr, respectively. The H2-dilution ratio 

R=[H2]/[SiH4], was set at four different values ranging from 15 to 60, leading to deposition rates 

ranging from 18 Å/s (R=15) to 6.6 Å/s (R=60). These data demonstrate significant changes in the 

surface roughness evolution with R and clearly exhibit all three regimes described above. The a →

a roughening transition thickness as a function of R is included in the deposition phase diagram 

shown in the inset. This diagram also includes the amorphous-to-(mixed-phase microcrystalline) 

transition thickness obtained from depositions with R set from 70 to 100. The three regimes can be 

24
Fig. 2.24: Surface roughness evolution for a series of a-Si:H films prepared by high-pressure, 

high-rate PECVD using the following fixed parameters: substrate temperature, T=200°C; rf 

plasma power, P=0.72 W/cm2; and total pressure, p=3 Torr. The H2-dilution level R=[H2]/[SiH4] 

is set at different levels from 15 to 60. (Inset) Phase diagram compiled from Si:H films deposited 

under the same conditions over a wider range of R, including the roughening transition in the 

amorphous regime [a → a; solid line] and the amorphous-to-(mixed-phase microcrystalline) 

roughening transition [a→(a+μc); broken line]. 

Fig. 2.25: The surface height profile at bulk layer thicknesses of db=0, 200, and 8000 Å for a 1-D 

continuum model of film growth that includes smoothening due to surface diffusion and 

roughening due to an atomic size effect. An initial mean cluster radius of 24 Å is used to 

simulate initial nuclei, and the diffusion length is assumed to be λ0=45 Å.

25
better understood through a continuum surface diffusion model for the surface roughness evolution 

to be discussed briefly in the next subsection. 

Surface diffusion theory 

Continuum models have been applied to study both physical and chemical vapor deposition 

processes [2.18-2.21]. In such studies, the dynamics of the surface roughness morphology are often 

investigated by means of linear stability analysis. In this analysis, the surface roughness is 

considered to be a small perturbation from a perfectly flat surface (or from a straight line profile in a 

1-D simulation), allowing one to linearize the differential equation that describes the surface profile 

evolution. Then the time evolution of the amplitude h(λ, t) of a surface perturbation with spatial 

period λ in the in-plane direction can be described simply as 

 h(λ,t) = h0 exp[ω(λ)t], (2.1) 

where ω is a decay rate that depends on the pertinent physical mechanisms of growth. In fact, the 

relevance of this approach has been tested in real time SE studies of a-Si:H growth on 

microscopically rough transparent conducting oxide surfaces having well defined in-plane periods 

[2.22]. In depositions on such surfaces, the substrate-induced roughness is observed to decay 

exponentially with time in accordance with Eq. (2.1). In general, the decay rate ω in Eq. (2.1) can 

be described as a polynomial function of spatial frequency k=2π/λ so that [2.23] 

ω(λ) = Σm (am/λm ) . (2.2) 

In this model, the specific physical mechanisms that impact the evolutionary development of the 

surface determine the polynomial terms present as well as the polynomial coefficients am. The three 

regimes listed above can be understood qualitatively from Eqs. (2.1) and (2.2) in the following 

general way. Low amplitude surface modulations of period λ less than some critical value λ0 are 

unstable and decay versus time t (or thickness) according to Eq. (2.1), where ω(λ)<0 for λ<λ0. This 

behavior applies to short period surface modulations associated with the coalescence of initial 

nuclei. Features with λ>λ0, such that ω(λ)>0, are enhanced. This behavior applies to the later stage 

characteristics of growth, i.e., the a → a transition, in which case statistical fluctuations in nuclei 

height and radius ultimately lead to larger scale structures through space-filling competition among 

neighboring columns [2.24]. 

In one specific model [2.18,2.19], the smoothening effects can be attributed to capillarity-driven 

surface diffusion that exhibits a negative term in ω(λ) given by ω4(λ) = −16π4

 De λ−4, where 

De= Ω2

εσsDs/kBT, and Ω, ε, σs, Ds, and kBT are the atomic volume, number of atoms per area, 

surface energy density, surface diffusivity, and thermal energy, respectively. The roughening is an 

atomic size effect that exhibits a positive term in ω(λ) given by ω2(λ) =4π

2

ρJ λ−2, where ρ is the 

atomic radius and J is the deposition flux. For this effect, regions where the surface exhibits positive 

or negative curvature receive a deposition flux J greater than or less than J, respectively, as in a 

shadowing effect. Then the diffusion length corresponds to the specific period that is stable; i.e., λ0

= (4π

2

De/ρJ)1/2, since this period is too large to be dampened by diffusion. Many additional useful 

features of this model have been described previously [2.18,2.22]. 

26
Simulations of surface roughness evolution

 In applying the specific model described above, the surface perturbation is associated with the 

initial nucleation process. An appropriate 1-D model for the surface profile following nucleation 

consists of a series of contacting semicircles that simulate clusters, with radii determined by one 

Gaussian distribution, and the elevation of the semicircle diameter from the surface determined by a 

second Gaussian distribution [2.22]. This one dimensional surface profile is then allowed to evolve 

during film growth using the approach described in the previous subsection, as shown in Figure 2.25. 

As seen in the figure, the short-period perturbations in the initial surface profile arising from nuclei 

contact smoothen out during film growth in the initial stages. Generally with time (or thickness), 

however, the surface profile coarsens as can be seen by the disappearance of the smallest cluster in 

Fig. 2.25 and the development of superclusters encompassing many smaller clusers. The 

superclusters evolve from the statistical distribution of initial cluster heights and spacings. From the 

surface profile extracted at any point during film growth as in Fig. 2.25, the root-mean-square value 

of the surface roughness layer thickness, drms, can be deduced and converted to the surface roughness 

layer thickness, ds, determined from real time SE using the expression ds = 3 Å + 1.5 drms (Å). This 

expression has been obtained from a correlation of real time SE and atomic force microscopy 

measurements of the same surfaces [2.25]. 

 As an example of the final results, Figure 2.26 shows a fit (solid line) to the surface roughness 

evolution determined by real time SE for the R=40 a-Si:H film from the series of Fig. 2.24. Also 

shown are the simulated roughness evolution curves obtained using the same initial nucleation 

profile, but assigning different values to the surface diffusion length from 12 to 160 Å, above and 

below the best fit value of 45 Å. Figure 2.27 summarizes the best simulation results plotted versus R 

for all four depositions of the series of Fig. 2.24. The simulations suggest that all the films in this 

series have a mean cluster radius ~ 20 Å which describes the contact thickness; however, λ0, ranges 

from 28 Å for R=15 to 50 Å for R=60, which accounts for the significant variations with R. As 

shown in the figure, a linear correlation is found between the best fit surface diffusion length in the 

simulation, and the observed a → a transition thickness. The amorphous roughening transition is 

only sensitive to diffusion lengths above a certain value, however; below this value the roughening 

begins almost immediately in the deposition process. 

Discussion 

 The full set of roughness evolution simulations reproduce the trends of the experimental data in 

Fig. 2.24, revealing all three characteristics, namely, coalescence of initial nucleation-generated 

clusters; a stable surface until a critical thickness; and roughening of the film beyond the critical 

thickness. Here it is of interest to address whether such a simple model includes a sufficiently strong 

physical basis to account for the complex growth process of a-Si:H. In support of this simple 

approach, molecular dynamics studies of surface roughness evolution suggest that the smoothness of 

a-Si:H arises from a valley filling mechanism whereby diffusing precursors preferentially 

incorporate in valleys where dangling bonds exist in greater numbers [2.26]. This process is 

analogous to the valley filling mechanism in the simple continuum model which serves to reduce the 

surface free energy. The roughening mechanism in the simple model is similarly reasonable based 

on simple geometric constraints of film growth at the atomic level [2.27]. Furthermore the ultimate 

conclusion of the present study, namely that the highest electronic quality a-Si:H materials are 

prepared under conditions that yield the largest surface diffusion length, is consistent with previous 

27
Fig. 2.26: Fit (solid line) to experimental data (squares) for a-Si:H with R=40 from Fig. 2.24 

using a the 1-D continuum model of Fig. 2.25. In this model, initial nuclei with a mean radius of 

24 Å are assumed, along with a diffusion length of λ0=45 Å that controls the subsequent e

as in Fig. 2.25. Additional broken lines are determined using the same initial profile, but with 

different values of λ

volution 

0 from 12 to 160 Å. 

Fig. 2.27: Amorphous roughening transition thickness obtained from real time SE and the critical 

diffusion length obtained from the 1-D model of Figs. 2.25 and 2.26 plotted as a function of the H2-

dilution ratio R for the series of four a-Si:H samples of Fig. 2.24. Over this range of R, the two 

ordinate quantities are linearly related. 

28
atomic scale models for growth [2.28,2.29]. In these models, diffusion length is limited either by 

short lifetime radicals that impinge on the surface from the plasma or by surface defects such as 

dangling bonds, both of which can lead to bulk defects that degrade electronic properties and 

stability. 

 Finally, it is important to note the drawbacks of this model. First of all the simulation is 1-D and 

should be extended to 2-D for closer quantitative comparisons. Given the complexity of the surface 

processes, however, it is likely that one can say with confidence only that the surface roughness 

evolution is reflective of a competition between smoothening driven by diffusion and a roughening 

process that drives columnar growth in thin films. It is less likely, however, that the mathematical 

forms of these competing terms are so simply described as in the continuum model. As a result, the 

greatest confidence should be placed in the trends reported here, rather than the numerical values. 

One of the complexities of real surfaces is that the diffusivity and hence the diffusion length may 

depend on the stage of film evolution. In the early stage in which clusters are making contact, the 

surface is more disordered with higher defect density, and this will limit the diffusion length. After 

the coalescence process the diffusion length may increase significantly as ordering improves and the 

defect density decreases. As a result any simple model to describe the full roughness evolution from 

thin film coalescence to thick film roughening is unlikely to be sufficiently complete for detailed 

quantitative purposes. 

Summary 

 A 1-D continuum model of surface profile evolution with an initial condition designed to be 

consistent with nucleation characteristics measured by real time SE has been used in order to better 

understand the surface roughness evolution of Si:H films that remain amorphous throughout growth. 

The surface roughness evolution of such films as measured by real time SE exhibits a prominent 

roughening transition (designated a → a) at a critical thickness, and this critical thickness is found to 

correlate with the electronic properties of the film. In fact, for materials with the best electronic 

quality, the a → a transition occurs at thicknesses beyond that typically deposited for devices. 

Because of the importance of the a → a transition, it has been incorporated into deposition phase 

diagrams that have been applied successfully to optimize solar cell performance and stability. A key 

feature of modeling performed here is that the a → a transition thickness scales linearly with the 

precursor diffusion length. As a result such modeling supports previous proposals that optimum 

electronic film qualities are associated with weakly reactive surfaces, long lifetime precursors, and 

large precursor surface diffusion lengths. 

29
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31
Task 3. Device Loss Mechanisms 

Novel Methodology for characterizing solar cells 

The work carried out under Task 3 addressed the mechanisms and defects determining a-Si:H 

solar cell characteristics that had not yet been clearly resolved. The studies of a-Si:H based solar 

cells were refined with analysis using a theoretical treatment based on first principles. This treatment 

takes into account: (i) Shockley-Reed-Hall diffusion/recombination of injected carriers in the bulk 

and at the p/i interface; (ii) the drift-controlled transport of photogenerated carriers; (iii) the 

homogeneous densities of defects across the i-layers with continuous distributions of states in the 

gap; and (iv) potential barriers Vn, Vp due to the high concentration of carriers at the n, p contacts. 

The results on a wide variety of solar cell structures have been interpreted self-consistently with this 

model, described in Appendix A, thus allowing solar cell operation to be addressed systematically 

and a number of misconceptions to be rectified. In obtaining reproducible results for the JD-V 

characteristics, the contribution of external contact resistance was taken into account by using a 

three-probe technique for measuring the currents. In addition the measurements were carried out 

using a thermoelectric heating/cooling stage with which the temperature of the samples could be 

controlled to within 0.1o

C. 

The distinctly different regimes in the dark forward bias current-voltage, JD-V, characteristics 

in “state-of-the-art” a-Si:H cells have been utilized as novel powerful probes, not only for 

investigating these mechanisms, but also for characterizing the defect states in intrinsic a-Si:H 

materials when the i-layers, p/i interface regions, and p, n contacts are changed in systematic and 

controlled ways. The dependence of the bulk recombination currents on the thickness and densities 

of defects in the i-layers has been established. It was found that the “effective diode quality factors” 

of these currents do not exhibit a constant n, as has been generally considered for over 20 years. The 

characteristics exhibit voltage dependent “differential diode quality factor” n(V) equal to the inverse 

of [kT/q][d(ln JD)/dV]. This result is consistent with the model that predicts such n(V) values as a 

consequence of a continuous distribution of the states in the gap. The changes in the n(V) 

characteristics produced by the introduction of light induced defects and from differences in i-layer 

materials have been utilized in characterizing the corresponding gap states. 

The magnitudes of the currents corresponding to the recombination at the p/i interfaces have 

been directly correlated with the nature of these regions. Their n(V) characteristics are as predicted 

by the model, independent of voltage with values very close to one. The systematic decreases of p/i 

recombination have allowed, for the first time, observation of the direct dependence of 1 sun VOC on 

the thickness of the i-layers. The nature of the limitations on the carrier injection over the potential 

barriers Vn, Vp and their effects on the 1 sun fill factors have been explored and found to be 

consistent with the predictions of the model. 

The transport and recombination of carriers generated by illumination in the i-layers were also 

characterized. Superposition between JSC-VOC and JD-V characteristics is obtained over a wide 

range of currents and voltages. These results, as well as the nature of the separations obtained at 

voltages approaching 1 sun VOC, are together consistent with the recombination of carriers and the 

contributions of Vn, Vp predicted by the model. Such potential barriers can have a large effect on 

32
carrier transport at voltages approaching 1 sun VOC and hence the FF, even though the barriers are 

much smaller than those commonly postulated as being due to large densities of defects. 

The differential diode quality factors, n(V), extracted from the JD-V characteristics from the 

wide range of a-Si:H solar cell structures were investigated. From these studies the gap state 

distributions in the a-Si:H layers, and their difference in the annealed states of the R=10 and R=0 

materials was directly and reliably identified. The n(V) characteristics were also applied to results 

on both R=10 and R=0 materials in studies of the creation of 1 sun light-induced defects and the 

energy distribution of their gap states. Again distinct differences in the distributions were clearly 

identified. Characterizing the n(V) spectra after the introduction of light induced defects in the ilayer materials showed that the changes in the density of state distributions in the R=10 and R=0 

materials are also distinctly different after degradation. 

The dark forward bias current, JD-V, characteristics have been shown to be a new probe for 

characterizing carrier recombination, identifying the mechanisms limiting solar cell performance, as 

well as characterizing the defect states in the i-layers of a-Si:H solar cells. From the bias dependence 

of the differential diode quality factors, n(V), predictions can be made about the nature of the gap 

state distributions. The results obtained, in which carrier transport is clearly dominated by bulk 

recombination, show that there are distinct differences between the two types of i-layers (R=10 and 

0) in their distributions of both native and light induced defect states. It has also been reported that 

in such cell structures with protocrystalline i-layers, degradation kinetics of JD-V characteristics are 

obtained with 1 sun illumination that are similar to those due to the recombination with dark forward 

bias currents. Such “equivalence” has also been found with undiluted a-Si:H i-layers, whereby this is 

illustrated with results of the JD-V characteristics shown in Figure 3.1. More importantly this 

similarity also exists in the differential diode quality factors, n(V), which are directly related to the 

corresponding energy distributions of the defect states in the i-layer, as is illustrated in Figure 3.2. 

This ability to create and directly characterize the metastable defect states with dark current voltage 

characteristics at the same temperatures greatly enhances the ability to characterize their creation as 

well as the changes in their subsequent relaxation. 

In addition a strong similarity is obtained not only in the changes of JD-V and n(V) 

characteristics but also in that of the fill factors as illustrated in Figure 3.3. In the experimental 

apparatus constructed under the present contract, both JD-V and FF measurements can be carried out 

at well controlled temperatures for direct correlation, thus allowing direct information to be obtained 

-- not only about the nature of the metastable defects -- but also about their effects on the fill factors. 

Such studies have been undertaken in identifying and quantifying the respective contributions of the 

fast and slow defect states utilizing carrier recombination from dark currents which correspond to 1 

sun Jsc but also at far forward biases that correspond to high intensity illuminations. 

33
Votlage (V)

0.2 0.4 0.6 0.8 1.0

Current Density (A/cm

2

)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

Annealed State

Injection 30 mins

Injection 100 hours

Illumination 30 mins

Illumination 100 hours

T = 25oC

Figure 3.1: JD-V characteristics for a p-i-n cell with 0.4 μm thick R=0 bulk i-layer and 200 Å R=40 

p/i interface layer in the annealed state and after both 1 sun illumination and carrier injection 

induced degradation. The total recombination current in the case of the carrier injection is equal to 

Jsc of the cell under 1 sun illumination at the annealed state. 

34
Voltage (V)

0.0 0.2 0.4 0.6 0.8 1.0

n(V)

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

Annealed State

Injection 30 mins

Injection 10 hours

Illumination 30 mins

Illumination 10 hours

T = 25oC

Figure 3.2: n(V) characteristics corresponding to the results of Figure 3.1 

35
Illmination Time (Hours)

1 10 100 1000

Fill Factor

0.52

0.56

0.60

0.64

0.68

0.72

Injection

Illumination

T = 25oC

Figure 3.3: Degradation of fill factor with 1 sun illumination and carrier injection for the cell of 

Figure 3.1. The total recombination current in the case of the carrier injection is equal to Jsc of the 

cell under 1 sun illumination in the annealed state. 

A good understanding of the defect states in the intrinsic layers of a-Si:H solar cells and the 

limitations imposed by different device loss mechanisms on their performance and stability is 

critical in the optimization of constituent materials as well as cell structures for the further 

improvement of the already high performance of these solar cells. The conventional measurement 

techniques and analysis used in such investigations are primarily based on the analysis of light 

current-voltage (I-V) parameters such as fill factor (FF), open circuit voltage (Voc), and short circuit 

current (Jsc), measured under 1 sun illumination. These parameters are inherently complicated, being 

affected by the contributions from different parts of the cells such as bulk i-layer, p/i interface as 

well as n and p contacts, which are difficult to separate and thus to quantify. In order to overcome 

these limitations, new approaches are being developed. They include the systematic analysis of 

results obtained on carefully designed cell structures, including forward bias dark current (JD-V) 

characteristics, which are extensively used in characterizing crystalline solar cells. In the past, little 

attention was given to JD-V characteristics of a-Si:H based solar cells because of the reported lack of 

correlation between light and dark I-V’s as well as the reported predictions by the defect pool model 

for the presence of very high densities near the n and p contacts and non-uniform distributions of 

defect states across the i-layer. More recently however, equivalence between carrier recombination 

in the JD-V and light I-V characteristics has been established from the superposition between Jsc-Voc

36
and JD-V characteristics over a wide range of illumination intensities [3.1,3.2]. It has also been 

shown that in solar cells with high quality materials and optimized cell structures, the defect state 

densities are approximately uniform across the entire bulk i-layer [3.3]. Consequently, it has been 

possible through the new approaches to the analysis of JD-V characteristics to obtain valuable 

information about the contributions of p/i interface recombination and potential barriers at the p and 

n contacts, as well as bulk recombination. A key factor of the new approach is the analysis of 

differential diode quality factors, n(V), characteristics whose presence has not been previously 

recognized and allow direct information to be obtained about the nature and densities of the defect 

states in the i-layers [3.4]. The advantages of this new approach are illustrated here with successful 

application of the results on JD-V characteristics to the results on Voc’s under various illumination 

intensities in the cells. In these studies, the p/i interface recombination is minimized and the carrier 

transport is dominated by the recombination in the bulk i-layers. Excellent correlation is found 

between the JD-V characteristics and Voc’s for cells with different bulk i-layers in their annealed 

states as well as after light induced degradation. In addition, the distinct differences observed in the 

degradation kinetics of 1 sun Voc between the cells having hydrogen diluted (protocrystalline) and 

undiluted i-layers are correlated with the differences in the defect state distributions between these 

two materials as indicated by the analysis carried out previously on the differential diode quality 

factors n(V) [3.4]. 

The p (a-SiC:H)/ i (a-Si:H)/ n (μc-Si) (superstrate) a-Si:H solar cells used in this study were 

fabricated by RF plasma enhanced chemical vapor deposition at a substrate temperature of 200°C 

under conditions described previously [3.5]. The bulk i-layers in the cell structures were deposited 

using SiH4 diluted with H2, with R = [H2]/[SiH4] of either 10 (diluted) or 0 (undiluted). To minimize 

the contributions of shunts, cell structure areas of 0.02 cm2

 were used, which were defined by 

removing the uncovered top n μc-Si:H layers with reactive ion etching. The JD-V characteristics 

were measured at temperatures that were controlled to within ±0.1oC and a three-probe technique 

was used to eliminate any effects of extraneous series resistance. Care was also taken to ensure that 

the steady-state currents were measured at low biases and that no defects were introduced by double 

injection in the high forward bias regions. The annealed states were achieved by heating the cells for 

4 hours at 170°C and the light induced defects were introduced using illumination generated by ELH 

lamp which has light intensity equivalent to that of 1 sun illumination. The illumination intensities 

lower than that of 1 sun was obtained with various combinations of neutral density filters. 

It has been shown that for the cells in which bulk recombination dominates the current and the 

defect state distribution is essentially uniform across the bulk i-layer, there is a dependence of the JDV characteristics on the bulk i-layer thickness as a result of the scaling of the electric fields [3.3]. 

One natural extension to this is that because of the higher recombination in the thicker cells there 

should also be a corresponding reduction in their 1 sun Voc’s. This requires that the bulk 

recombination dominate the carrier transport not only at relatively low biases but also at high biases 

up to 1 sun Voc. That this is indeed the case is illustrated in Fig. 3.4 which shows the results on the 

thickness dependence of the 1 sun Voc as well as JD-V characteristics for p-i-n cells having the same 

structure but different thickness of R=0 bulk i-layers. In these cells the recombination at the p/i 

interfaces is minimized by having 200Å of a R=40 protocrystalline i-layer in the p/i region. It can be 

seen in the inset of Fig. 3.4 that the 1 sun Voc decreases systematically with the increasing thickness 

of the bulk i-layer. A decrease of ~30mV (from about 0.89 to 0.86V) occurs in Voc for an increase 

of a factor of 2 in the dark currents at low biases. This 30mV decrease in Voc is consistent with the 

37
dark current, whose increase for this change in voltage corresponds to the “effective” diode quality 

factor of ~1.6 for these cells. It is important to note here that these Voc’s were measured not with 

fixed illumination intensities but instead with a fixed Jsc of 10 mA/cm2

 (equivalent to 1 sun Jsc for 

the cells with 0.4μm thick i-layer). This approach was used to eliminate the effect of the changes in 

light absorption due to the differences in the i-layer thickness. In thicker cells the increases in the 

dark current at voltages corresponding to 1 sun Voc cannot be directly observed because the dark 

current becomes limited by carrier injection over the potential barriers in the i-layers adjacent to the 

p and n contacts. 

Voltage (V)

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Current Density (A/cm2) 10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

0.4 μm 

0.8 μm

1.5 μm 

Thickness (μm)

0.4 0.8 1.2 1.6

Voc (V) 0.85

0.86

0.87

0.88

0.89

 Fig. 3.4: Thickness dependence of 1 sun Voc and JD-V characteristics for p-i-n cells having the same 

structure but different thickness of R=0 bulk i-layers. 

Degradation Time (Hours)

0.1 1 10 100

Voc(V)

0.84

0.85

0.86

0.87

0.88

0.89

0.90

0.91

R=0 Bulk with R=40 p/i

Fig. 3.5: Degradation of 1 sun Voc under 1 sun illumination at 25oC for the cell in Fig. 3.4 with the 

0.4 μm thick i-layer. 

The domination of Voc by bulk recombination currents at biases corresponding to 1 sun Voc in 

the cells studied here could be further confirmed with the degradation kinetics of the 1 sun Voc. 

Shown in Fig. 3.5 is the degradation of the 1 sun Voc under 1 sun illumination at 25o

C for the cell in 

Fig. 3.4 having the 0.4 μm thick i-layer. It can be seen that there is an immediate decrease in the 1 

38
sun Voc that is a clear indication that there are no significant contributions from p/i interface 

recombination. After 100 hours of degradation there is a decrease in Voc of approximately 50 mV 

that is consistent with the changes in the JD-V characteristics of the same cell as shown in Fig. 3.6. 

In Fig. 3.6 there is an increase in the recombination current of a factor of ~3 at a bias that 

corresponds to the 1 sun Voc. 

Votlage (V)

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Current Density (A/cm2

) 10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

Annealed state

1 sun 100 hours

1 sun Voc

Fig. 3.6: JD-V characteristics of the cell in Fig. 3.5 in the annealed state and after 100 hours of 1 sun 

illumination. 

Similar correlations between the degradation of the Voc’s and JD-V characteristics are also 

obtained for the cells with R=10 protocrystalline i-layers. This is illustrated in Figs. 3.7 and 3.8 with 

results on a p-i-n cell with a 0.4 μm thick R=10 bulk i-layer and 200 Å thick R=40 p/i interface. In 

Fig. 3.7, the Voc measured under light intensities from 1 to 10-4 sun is shown as a function of the 

degradation time under 1 sun illumination. It can be seen that as the light intensity and Voc are 

lowered there are corresponding changes in both the rate and magnitude of the voltage decreases in 

reaching a degraded steady state after ~100 hours of illumination. For the illumination intensity of 

10-4 sun, corresponding to an initial Voc of 0.62 V, there is a decrease of 70 mV in Voc. For 1 sun 

illumination the degradation is less than 10 mV, a value that is also significantly smaller than the 50 

mV degradation of the 1 sun Voc for the cell with R=0 i-layer after the same time of 1 sun 

degradation. This small degradation at such a high illumination level cannot be due to the limitations 

imposed by p/i interface recombination since a similar dependence of 1 sun Voc on thickness was 

also found for the cells with R=10 i-layers. The degradation in Voc in Fig. 3.7 can be directly 

correlated with the changes in JD-V characteristics shown in Fig. 3.8. In Fig. 3.8 systematic increases 

are observed in the dark currents with illumination time just as in the corresponding Voc results. The 

changes in the currents -- which are larger at the lower biases -- correspond to the higher decreases 

in Voc measured at the lower illumination intensities. Unlike the large change in the cell with the 

R=0 i-layer, there are barely discernable changes in the dark current at the levels equivalent to 1 sun 

Jsc for the cell with the R=10 i-layer. This cannot be completely due to the carrier injection 

limitations imposed by the potential barriers since these limitations occur at similar current levels for 

both types of the cells. The difference in the 1 sun Voc degradation between the cells with the R=10 

and R=0 i-layer thus clearly points to a distinct difference in their gap state distributions upon light 

induced degradation. 

39
Degradation Time (min)

100 101 102 103 104

∆

Voc (V)

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

10-4 sun 0.62

10-3 sun 0.68

10-2 sun 0.76

10-1 sun 0.85

1 sun 0.93

Light

Intensity

Initial

 Voc (V)

R = 10 with R=40 p/i

Fig. 3.7: Degradation of Voc for a p-i-n cell with a 0.4 μm thick R=10 bulk i-layer and a 200 Å thick 

R=40 p/i interface, measured under light intensities from 1 to 10-4 sun. 

Voltage (V)

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Current (A/cm2) 10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

Annealed state

1 sun 30 mins

1 sun 10 hrs

1 sun 100 hrs

R=10 Bulk with R=40 p/i

1 sun Voc

Fig. 3.8: JD-V characteristics of the cell in Fig. 3.7 in the annealed state and after light induced 

degradation. 

Several conclusions can be drawn from the above experimental results. First, in these cells the 

currents are dominated by bulk recombination up to bias levels equivalent to 1 sun Voc. This is 

significant because the results obtained on the JD-V characteristics can then be directly applied to the 

analysis of solar cell performance. Second, there are large light induced changes in the densities and 

distributions of the defect states in both the undiluted and diluted protocrystalline i-layers associated 

with the Staebler-Wronski Effect (SWE). Thirdly, the distributions of gap states in the two i-layers 

are distinctly different, thus leading to the differences in the corresponding solar cell performance 

and stability. 

In order to understand the relation between solar cell parameters such as Voc and the 

distribution of gap states in the i-layers, it is necessary to identify the differences between the two ilayer materials. The essential features of the distributions for both the undiluted and diluted i-layers 

40
have been obtained from the analysis on the n(V) characteristics [3.4]. In both cases they are 

consistent with a Gaussian-like distribution around midgap followed by an exponentially rising 

distribution away from midgap which could also be regarded as the rising edge of a second 

Gaussian-like distribution. Similar Gaussian-like distributions have been proposed in several 

previous studies [3.6-3.9]. There is a major difference, however, between the undiluted and diluted 

i-layers whereby in the former case the rising edges of the second Gaussian-like distributions are 

much less steep. Furthermore, after the introduction of light induced defects, the distributions in 

both i-layers broaden with a much smaller broadening occurring in the case of the protocrystalline ilayer. For both cases there is also a large increase in the density of states around midgap which 

causes the large increases in the dark currents under low forward biases and the large decreases in 

the Voc’s under illumination intensities much smaller than 1 sun. On the other hand, in the case of 

the dark currents under high forward bias and Voc under sufficiently high illumination intensity, the 

splitting between the two quasi-Fermi levels is sufficiently large as to include as recombination 

centers not only the gap states around midgap but also those located further away from the midgap. 

For the cell with a protocrystalline i-layer, due to the narrower Gaussian distributions in the annealed 

and degraded states, the positions of quasi-Fermi levels at 1 sun Voc are in a region where the native 

defects away from midgap play a dominant role in the recombination. This then explains the very 

small degradation of 1 sun Voc while there is significant degradation for the Voc’s under the lower 

intensities of illuminations. On the other hand, for the cell with undiluted i-layer, due to the broad 

distribution away from midgap the contribution from the light induced defects increases the 

recombination over that of the native defect states alone and accounts for the significant degradation 

in 1 sun Voc. It is very important to note here that for cells having both undiluted and protocrystalline 

i-layers the degradation in the 1 sun Voc is much smaller than that expected if the Voc was limited 

purely by the recombination through the neutral dangling bonds, with states located around midgap 

and detected by electron-spin resonance. This is a further indication that gap states other than the 

neutral dangling bonds determine cell performance [3.10,3.11] and demonstrates the key role of the 

Gaussian-like distributions away from midgap as identified from the analysis of the n(V) 

characteristics. 

It has been shown from the JD-V characteristics that it is possible to identify and quantify the 

limitation imposed on 1 sun Voc by bulk recombination. As a consequence, it has been possible to 

relate the light induced changes in JD-V characteristics to those in 1 sun Voc for cells with undiluted 

and protocrystalline i-layers. In addition, the new approach in the analysis of JD-V characteristics in 

terms of differential diode quality factor n(V) has allowed these differences to be directly related to 

differences in the distributions of gap states in the corresponding i-layers. The results further 

demonstrate that JD-V characteristics offer a new and powerful probe for characterizing mechanisms 

limiting the performance and stability of a-Si:H solar cells as well provide direct information about 

the distribution of gap states in the intrinsic layers. They also point out a key reason why it is not 

possible to obtain correlation between solar cell characteristics and neutral dangling bond densities. 

It is therefore important to take advantage of this powerful probe in guiding a systematic approach to 

further improving performance of a-Si:H based solar cells as well as in obtaining new insights into 

SWE. 

41
Creation kinetics of metastable defects in protocrystalline intrinsic layers of p-i–n cells 

In the course of studies on the light-induced changes of the i-layers, a new phenomenon in 

SWE was observed – the thermal relaxation of defect states at 25o

C created by 1 sun illumination. 

This relaxation is readily observed at low forward biases and is sensitively dependent on the voltage 

at which it is characterized. This clearly shows that it is due to the states located close to midgap. 

Large decreases in this relaxation effect are also observed when the quasi-Fermi level splitting, and 

thus carrier recombination, is increased with higher bias, and the relaxation is eliminated for the 

splitting that occurs under 1 sun illumination. In addition, it is found that the relaxation effect 

changes with temperature -- as expected, however, in a way that cannot be readily characterized by 

any simple activation energy. These results have initiated careful studies on corresponding films as 

discussed in Task 4. Such studies confirm this relaxation effect, giving a new wrinkle to SWE, 

whose effects have not been recognized in either room temperature studies or in the models for 

creation of SW defects. 

Because of the demonstrated ability to characterize the defect states in the i-layers of solar 

cells, the potential of using the recombination under far forward bias to generate defects in studies of 

the SWE was investigated. It was found that in cell structures, for which the recombination in the 

p/i interface regions is very much less than that in the bulk, equivalence is observed in the kinetics of 

the changes in the I-V characteristics under 1 sun illumination and those for far forward bias currents 

equal to JSC. Such a method of creating SW defects was subsequently being used, adding flexibility 

to the conditions for the studies on the creation, annealing, and relaxation metastable defects. 

The creation of metastable defects in the bulk of the intrinsic layers of a-Si:H p-i-n solar cells 

by recombination of photo-generated carriers as well as those injected under far forward bias has 

been investigated. The evolution in the defects, created with volume-absorbed red light at open 

circuit voltage and with constant far forward bias currents, was characterized with the ShockleyReed-Hall recombination obtained from the dark currents under low forward bias voltages. This 

allowed the kinetics to be studied at different temperatures in the absence of isothermal annealing. It 

is found that the form of the kinetics obtained with the two methods are the same and a detailed 

study was carried out with currents from 1 to 100 mA/cm2 with carrier injection during which the 

electron and hole concentrations remain essentially constant. 

Because these measurements are carried out in about 5 seconds, they allow the recombination 

through these states to be monitored in essentially a continuous manner as well as prior to thermal 

annealing which is significant even at 25o

C, particularly in the initial stages of degradation 

[3.4,3.13]. Consequently they have been particularly useful in characterizing the changes when the 

densities of the metastable states are comparable to or less than those of the intrinsic defects. New 

information is presented on the evolution of metastable defects induced either by the recombination 

of photo-generated carriers under open-circuit voltage or by the recombination of injected carriers 

under far forward bias and constant current. In these cells the short circuit current, JSC, remains 

essentially unchanged during the degradation while the constant currents are maintained with 

essentially no change in the corresponding applied forward bias. Thus in both cases the quasi-Fermi 

level splitting, and hence the free carrier concentrations, n and p, responsible for the degradation 

remain constant. This is in contrast to the light induced changes in films where n and p continuously 

decrease due to the introduction of shorter carrier lifetimes during degradation [3.14]. 

42
 Fig. 3.9 shows the recombination currents IR at 0.4 V forward bias at 25 and 75o

C for 

metastable defects induced by carrier injection currents from 5 to 100 mA/cm2. Also included in Fig. 

3.9(a) are the results obtained at 25o

C with 1 sun illumination under open circuit conditions. A 

striking similarity can be seen in Fig. 3.9(a) between the results obtained with the 1 sun (with a 

corresponding Isc of 10 mA/cm2) and 30 mA/cm2 where the excellent superposition is obtained for 

the actual currents. The very much larger currents at 75 oC are due to the high activation energy of 

IR (half of the band gap) and not the correspondingly higher densities of metastable defects. At both 

temperatures three regimes can be clearly identified in IR similar to those reported for the changes in 

thin films. There is a region with a power-law-like time dependence, as indicated in Fig. 3.9, which 

can be represented by a t1/3 dependence, observed extensively in results on thin films [3.15,3.16]. 

Also in agreement with results on thin films is the fact that this regime, which at 25 oC covers 

changes in IR of about a factor of 3 to 4, maintains such a form at different degradation intensities 

and temperatures. This regime in Fig. 3.9 is bounded by a transition to kinetics whereby the rate of 

change in IR is greatly reduced. This transition eventually leads to a degraded steady state, as seen in 

Fig. 3.9(b) for the 30 and 100 mA/cm2 results with dependence both on the degradation intensity and 

temperature similar to that found for fill factors]. The third regime, which represents the initial 

changes in the total defect state densities, has received much less attention than the t1/3 dependence 

except in its possible contributions to stretched exponential type of kinetics [3.17]. However, in Fig. 

3.9 it does represent a significant fraction of the total changes in IR, prior to its transition into the 

regime that leads to a degraded steady state. At 25oC it covers a change in IR by a factor of between 

2 and 3 that is essentially independent of the degradation intensity. 

 

 (a) (b) 

Fig. 3.9: (a) Change of current at 0.4 V and 25oC for a p-i-n cell under injection currents of different 

intensities and 1 sun illumination; (b) Change of current at 0.4 V and 75oC for a p-i-n cell under 

injection currents of different intensities. 

43
Because the t1/3 relation covers a limited region of the entire degradation kinetics, it is 

important to characterize the evolution of just the metastable states, including when their initial 

contributions are comparable to or less than those of the intrinsic states. This can be obtained from 

the results in Fig. 3.9 by subtracting IR0, the recombination currents in the intrinsic state. Since this 

also takes into account any difference in the carrier capture cross sections that may exist between the 

intrinsic and metastable defect states ∆IR=IR−IR0 can be directly related to the densities of the 

metastable defects. The results obtained for ∆IR from Fig. 3.9(a) and (b) are shown in Figs. 3.10(a) 

and 3.10(b) respectively. It can be seen that for both temperatures and for all degradation intensities, 

∆IR has power-law-like time dependence, which is essentially t1/2 over the entire time span prior to 

the transition into the regime that eventually leads to saturation. This includes both the extensive 

initial evolution that can be seen in Fig. 3.9(a) at 25 oC as well as the region that was previously 

associated with a t1/3 dependence. This evolution of the metastable defects with a t1/2 dependence is 

present for all degradation currents I, such that the degradation is approximately linear with I. This 

naturally leads to the fact that the degree of degradation is proportional to I2

t as illustrated in Fig. 

3.11 for the results in Fig. 3.10. Such a dependence is found for films and for solar cells, the latter in 

the degradation of the fill factor [3.18]. Street [3.19], who characterized the far forward biasinduced changes in defect state densities with thermally emitted currents under reverse bias, 

observed a t1/2 dependence for the very high currents of 1 A/cm2

 where the densities of the induced 

states were indeed very much greater than those of the intrinsic state. He did not find the presence of 

a t1/3 dependence at lower values of I and attributed its absence to his interpretation of carrier 

concentrations under far forward bias responsible for inducing the metastable states. 

(a) (b) 

Fig. 3.10: (a) Changes relative to the initial value for the currents in Fig. 3.9(a); (b) Changes relative 

to the initial value for the current in Fig. 3.9(b). 

44
(a) (b) 

Fig. 3.11: (a, b) Normalization of the degradation kinetics under different intensities according to 

I

2

t = constant for the corresponding figures in Fig. 3.10. 

The similarity of the three regimes seen here to those reported for thin films, and particularly 

that represented by a t1/3 dependence, is significant since these metastable defects are induced under 

conditions under which n and p remain constant. Most of the models proposed for the mechanisms 

responsible for the creation of light induced defects are based on the kinetics represented by the t1/3 

relation found for thin films, where n, p do not remain constant during degradation. Among these 

models, the one that has received the most attention is that of Stutzmann, Jackson and Tsai (SJT) 

[3.15] who proposed that the recombination between the electrons and holes in the band tail states 

break weak bonds, thus creating dangling bond defects. Since their concentrations are directly 

proportional to that of the free carriers, the rate equation for the creation of the dangling bond 

defects is proportional to the np product, each of which is proportional to the inverse of the dangling 

bond density, ND. Consequently, in absence of any annealing, the rate equation for the increase in 

the densities of states, ND, located around midgap has a bimolecular form, which can be written as: 

2

2

1 2

D

D

N

G CnpC dt

dN == (3.1) 

where C1 and C2 are constants and G is the photo-generation rate. This yields a time dependence for 

the total density of dangling bonds: 

NtN tGC (3.2) D D

2

2

3 3 =− 3)0()(

where ND(0) is the density of the native defect states. For ND(t) >> ND (0) Eq. 3.2 yields 

3

1

3

2

D ~)( tGtN (3.3) 

45
The dependence found here for the changes in the total density of defects with n, p constant 

discounts the validity of the SJT model. The results for the evolution of just the metastable defects 

on the other hand are inconsistent with Eq. 3.2. Rather, the t1/2 and I2

t dependences seen in Figs. 3.10 

and 3.11 point to a rate equation for the creation of metastable defects, Nms : 

ms

ms

N

I

dt

dN 2

~ . (4) 

It is significant that the creation kinetics found here for the metastable defects induced by the 

recombination of photo-generated carriers and injected carriers are the same. However the rate of 

creation of the metastable defects by the recombination of carriers from identical values of Isc and I 

are not the same as seen in Fig. 3.9(a). The effect of the photo-generated carriers being field driven 

and having energies greater than the band gap, while the injected carriers are diffusive and their 

energies correspond to that of band gap, should be further investigated. This study raise serious 

questions concerning the models of SWE that are based on a rate equation having the form of Eq. 

3.1. This includes not only the SJT model but also the hydrogen collision model proposed by Branz 

[3.20] 

References 

[3.1] J. Deng, J.M. Pearce, V. Vlahos, R.W. Collins, and C.R. Wronski, Mater. Res. Soc. Symp. 

Proc. 762, A3.4 (2003). 

[3.2] J.M. Pearce, R.J. Koval, A.S. Ferlauto, R.W. Collins, C.R. Wronski, J. Yang, and S. Guha, 

Appl. Phys. Lett. 77, 3093 (2000). 

[3.3] J. Deng, J.M. Pearce, R.J. Koval, V. Vlahos, R.W. Collins, and C.R. Wronski, Appl. Phys. 

Lett. 82, 3023 (2003). 

[3.4] J. Deng, J.M. Pearce, V. Vlahos, R.W. Collins, and C.R. Wronski, Mater. Res. Soc. Symp. 

Proc. 808, A8.8 (2004). 

[3.5] R.J. Koval, J. Koh, Z. Lu, L. Jiao, R.W. Collins, and C.R Wronski, Appl. Phys. Lett. 75, 1553 

(1999). 

[3.6] K.K. Mahavadi, K. Zellama, J.D. Cohen, and J. P. Harbison, Phys. Rev. B 35, 7776 (1987). 

[3.7] L. Jiao, H. Liu, S. Semoushkina, Y. Lee, and C.R. Wronski, Proc. 25th IEEE PVSC (IEEE, 

New York, 1996), p. 1073. 

[3.8] M. Günes and C.R. Wronski, J. Appl. Phys. 81, 3526 (1997). 

[3.9] V. Nadazdy and M. Zeman, Phys. Rev. B. 69, 165213 (2004). 

[3.10] B. Von Roedern, Appl. Phys. Lett. 62, 1368 (1993). 

46
[3.11] J. Pearce, X. Niu, R. Koval, G. Ganguly, D. Carlson, R.W. Collins, and C.R. Wronski, 

Mater. Res. Soc. Proc. 664, 1231 (2001). 

[3.12] J. Deng, J.M. Pearce, V. Vlahos, M. Albert, R.W. Collins, and C.R. Wronski, Conf. Record 

31st IEEE Photovoltaic Specialists Conf., IEEE New York, 2005, p. 1404. 

[3.13] M.L. Albert, J. Deng, J.M. Pearce, X. Niu, R.W. Collins and C.R. Wronski, Mater. Res. Soc. 

Symp. Proc. 862, A13.2 (2005). 

[3.14] D.L. Staebler and C.R. Wronski, Appl. Phys. Lett. 31, 292 (1977). 

[3.15] M. Stutzmann, W.B. Jackson, and C.C. Tsai, Phys. Rev. B 32, 23 (1985). 

[3.16] P. Stradins, Solar Energy Materials and Solar Cells 78, 349 (2003). 

[3.17] D. Redfield and R. H. Bube, Appl. Phys. Lett. 54, 1037 (1989). 

[3.18] L. Yang, L. Chen, and A. Catalano, Appl. Phys. Lett. 59, 840 (1991). 

[3.19] R.A. Street, Appl. Phys. Lett. 59, 1084 (1991). 

[3.20] H.M. Branz, Solar Energy Materials and Solar Cells 78, 425 (2003). 

47
Task 4. Characterization Strategies for Advanced Materials 

Relaxation of SWE defects in a-Si:H materials 

 

The presence of the thermal annealing of light induced defect states at room temperature after 

1 sun illumination, discovered in studies of solar cells, triggered a corresponding careful study of aSi:H thin films. This study was carried out on the kinetics of fast states at 25°C created by 1 sun 

illumination in hydrogen-diluted (protocrystalline) a-Si:H films. The results were for the bulk 

properties of the a-Si:H films, which were confirmed by the similarity of their characteristics to 

those obtained for corresponding intrinsic layers in p-i-n solar cells. It is found that the kinetics 

exhibit two regimes. The first regime is in the form of a delay before the onset of an A·log(t) time 

dependence, indicative of a dispersive process. Despite the unexpected effect of a dependence of 

this first regime on the degradation/annealing history of the samples, it was possible to characterize 

the highly reproducible logarithmic dependences for different illumination times, as well as in the 

presence of different carrier generation/recombination rates. It is found that for the degradation 

times studied, the annealing kinetics associated with the second regime are independent of the 1 sun 

illumination time but are dependent on the recombination introduced by illumination levels as low as 

~10−6

 sun. From the multiple experiments carried out in this study, it is found that the initial regimes 

depend not only on the carrier generation, G, and the time of 1 sun illumination of the films, but also 

on the degradation and annealing history. The subsequent regimes, which are independent of this 

history, do depend on G with the accompanying changes in the quasi-Fermi level splitting and the 

time of 1 sun illumination -- in agreement with the results on corresponding solar cells. These results 

raise interesting questions that still need to be answered about the nature and origin of the fast 

defects in order to assess their contribution to the long term degradation and the overall stability of 

a-Si:H materials. 

 

 The experiments were performed on hydrogenated protocrystalline silicon thin films (a-Si:H) 

that were deposited at 200°C with Cr/n-type a-Si:H coplanar Ohmic contacts. The measurements 

were carried out on different films from the same deposition with the initial states obtained after 4 hr 

annealing at 170°C. The samples were mounted in a light tight enclosure on a copper platform of a 

thermoelectric stage. An ELH lamp powered by a DC constant voltage supply was used to produce 

the 1 sun illumination and the probe photocurrents. Each lamp was used up to 20 hours over which 

time the illumination remained within ±5% of its initial flux. The probe photocurrents were 

generated with volume-absorbed illumination through a 687 nm band pass filter whose maximum 

intensity matched that obtained with a solar simulator. The light flux incident on the film was 

controlled with a shutter and 5 position filter wheel that could accommodate different combinations 

of neutral density and 687 nm band pass filters. Probing was conducted using filter combinations 

that were selected to produce bulk carrier generation rates from ~1015 to 1018 cm-3s

-1. During probe 

measurements, the currents were measured over a period of 10 seconds to take into account the 

photocurrent response times. In all cases the dark currents were an insignificant portion of the total 

current measured. The experimental procedures related to filter positioning, shutter state, and data 

collection were completely automated with a personal computer thus allowing the experiments to be 

reproducibly conducted over long periods of time. 

48
 The 1 sun photoconductivity of the films decreases approximately according to the oftenreported t−0.3 dependence, which after ~2 hours of illumination undergoes a transition to a slower 

rate. In this regime a relaxation in the 1-sun photocurrents can be observed even after very short 

interruptions in the illumination. This is illustrated in Figure 4.1 where the 1 sun photocurrents are 

shown with intermittent 10 second probe illuminations of G=8x1015 cm-3s

-1. It can be seen in the 

figure that such 1 sun photocurrents, relaxation decreases with the time of illumination. The 

corresponding results for the probe photocurrents are shown after normalizing them to their values 

of 1 minute degradation. This is done because of the very large changes in the current that occurs in 

minute of 1 sun illumination when probed with low levels of illumination [4.1]. These changes are 

Time(Minutes)

0.1 1 10

Normalized Photocurrent 1

G=8x1015cm-3s

-1

1 Sun

t

-0.33

t

-0.40

Time(Minutes)

20 40 60

Photocurrent(Amps) 2e-10

3e-10

4e-10

5e-10

G=8x1015cm-3s

-1

Figure 4.2: Probe photocurrents for 

G=8x1015cm-3s

-1 during 1 sun degradation 

for 5 minutes and subsequent relaxation in 

the dark for 1 hour. 

Figure 4.1: 1 Sun and 10 second 

intermittent probe photocurrents for carrier 

generation rate G=8x1015cm-3s

-1 during the 

first 30 minutes of degradation. 

rapidly reduced by the creation of light induced defects under 1 sun illumination. The 1 minute 

photocurrents are found to be reproducible to ±10% in the different experiments and are also found 

to reflect the properties of bulk a-Si:H confirmed with results on corresponding p-i-n solar cells. 

Initial results on the cells indicated a time dependence different from the 1 sun relationship which is 

approximately ~t-0.4 as illustrated in Figure 4.1. This initial conclusion required revision and a 

subsequent detailed study on the creation of light induced defects is presented later. In Figure 4.2, 

results are presented for G=8x1015cm-3s

-1 intermittent probe currents during a 5 minute degradation 

at 1 sun. During the period between 1 and 5 minutes of 1 sun illumination, the probe photocurrent 

decreases by about a factor of two. After this short illumination, the sample was recovered in the 

dark and occasionally probed leading to a remarkable recovery in the probe photocurrents after 1 

hour to within 20% of the 1-minute value. In Figure 4.3, results are shown for the recoveries in the 

dark, after 30 minutes of 1 sun illumination, probed with G of 1x1015 and 8x1015cm-3s

-1. In both 

cases the photocurrents had degraded by about a factor of four from their 1 minute values and 

recovered after 1 hour to about 50% of these values. When the relaxation of these photocurrents is 

represented in the form of their normalized values, as is done in Figure 4.3, striking features in the 

49
annealing kinetics of the defect states are revealed. It can be seen that there are two regimes in the 

kinetics beginning with an initial delay regime before the onset of an A·log(t) dependence indicative 

of a dispersive process whereby the prefactor in both cases is A=0.9 as indicated in the figure. 

However, a difference can be seen between the times for these onsets in the two sets of results. 

 From the multiple experiments carried out at different stages of this study, it was possible to 

identify that the time of the delays was dependent on the history of the sample. Identical 

experiments conducted repeatedly on the same film exhibited a systematic change in the relaxation 

kinetics as illustrated in Figure 4.4. The results shown are for normalized photocurrents obtained 

with continuous illuminations with G=8x1015cm-3s

-1 after 30 minutes of 1 sun degradation. A 

systematic extension in delays prior to the logarithmic time dependence exhibit a 

Time(Minutes)

10 100

Normalized Photocurrent 1.0

1.5

2.0

2.5

3.0

G=1x1015cm-3s-1

G=8x1015cm-3s-1

A=0.95

Time(Minutes)

0.1 1 10 100

Normalize Photocurrents 1.0

1.2

1.4

1.6

1.8

1 hr Soak/ 5 anneals

3 hrs. Soak/9 anneals

4 hrs. Soak/11 anneals

4.5 hrs. Soak/12 anneals

A=0.6

G=8x1015

cm-3s

-1

Figure 4.3: Intermittent probe 

photocurrents for G=1x1015cm-3s

-1

normalized to their degraded state after 

30 minutes of 1 sun illumination 

obtained at different stages of this 

study. 

Figure 4.4: Continuous probe currents for 

G=8x1015cm-3s

-1 normalized to their degraded 

state after 30 minutes of 1 sun illumination. 

dependence on the sequence in which the experiments were carried out. However, the prefactors of 

the A·log(t) time dependence remain the same with a value of A=0.4. Because the A·log(t) kinetics 

are independent of the sequence of experiments, it was possible to characterize their dependence on 

G. Results obtained after 30 minutes of degradation are shown in Figure 4.5 for G from 1x1015 to 

4x1017cm-3s

-1. These results not only show the systematic decrease in A from 0.60 ≤ A ≤ 0.16 with 

increase in G, but also indicate that the delay in the onset of these kinetics also depends on G. It 

should be pointed out that the increase in G leads to photocurrents that result in both higher carrier 

recombination as well as higher quasi-Fermi level splitting. By augmenting the quasi-Fermi level 

splitting, states further removed from midgap are introduced as recombination centers. Analogous 

effects occur in p-i-n solar cells under forward bias as higher voltages are applied. The results for 

the relaxation in the bulk recombination currents after 30 minutes of degradation in corresponding pi -n solar cells are shown in Figure 4.6 for forward biases of 0.3, 0.4, and 0.5 V. Although these 

50
results cannot be readily correlated with those on the films in a quantitative way, a strong similarity 

to the results in Figure 4.5 can be seen. These results also exhibit a logarithmic time dependence 

whose prefactors systematically decrease with higher forward bias as the carrier recombination and 

quasi-Fermi level splitting increases. 

It was also possible to identify the effects of different times of degradation on the annealing 

kinetics. This is illustrated in Figure 4.7 with results for continuous probe currents of G=8x1015 

cm-3s

-1 obtained after different times of 1 sun illumination from experiments that were not carried out 

in a sequence related to these times. In Figure 4.7 it can be seen that the time to reach the 

logarithmic time regime increases in length with the duration of 1 sun degradation shown for values 

between 15 minutes to 10 hours. However, there is no change in their prefactors, which remain at 

0.4 throughout. Similar characteristics are obtained in both the delays and invariance in the 

prefactors of the logarithmic time regime for the recombination currents in p-i-n cells after 

prolonged degradation. 

 

Time(Minutes)

0.1 1 10 100

Normalized Photocurrent 1.0

1.2

1.4

1.6

1.8

G=1x1015cm-3s-1 A=0.60

G=8x1015cm-3s-1 A=0.40

G=8x1016cm-3s-1 A=0.20

G=4x1017cm-3s-1 A=0.16

Time (min)

1 10 100

Normalized Current

0.5

0.6

0.7

0.8

0.9

1.0

0.3 V

0.4 V

0.5 V

Figure 4.5: Continuous probe currents 

normalized to their degraded states after 

30 minutes of 1 sun illumination for 

carrier generation rates from 1x1015 to 

4x1017cm-3s

-1. 

Figure 4.6: Bulk recombination currents 

in p-i-n solar cells at 0.3, 0.4 and 0.5 V 

forward bias after 30 minutes of 1 sun 

illumination. 

51
Time(Minutes)

0.1 1 10 100 1000

Normalized Photocurrent 1.0

1.2

1.4

1.6

1.8

2.0

15 Minutes

30 Minutes

2 Hours

10 Hours

A~0.40

Figure 4.7: The continuous probe 

photocurrents for G=8x1015cm-3s

-1

normalized to their degraded states after 

different 1 sun illumination times. 

 The annealing kinetics of the light induced defects at 25°C created by 1 sun illumination 

reported here is consistent with the fast states identified in studies of solar cells after high intensity 

illumination [4.2]. The similarity of the annealing characteristics obtained between the forward bias 

recombination currents in p-i-n solar cells and their corresponding i-layer film measurements, 

confirm that the results reported here are reflective of the properties of bulk a-Si:H. The 

photoconductivity studies of these protocrystalline hydrogen-diluted a-Si:H films were conducted 

with sufficiently short times of 1 sun illumination (≤ 10 hours) such that the carrier recombination 

was not dominated by the slow states [4.3]. The unexpected results on the dependence of the 

annealing kinetics on the degradation and annealing history of the thin film samples were thoroughly 

investigated with multiple identical experiments and it was found that they were not experimental 

artifacts. It could also be concluded that the changes occur only in the first of the two regimes found 

in the annealing kinetics of these fast defects. The presence of the two distinctly different regimes 

and the fact that their kinetics respond differently to history and 1 sun illumination time suggest two 

processes that contribute to the annealing kinetics. The similarities in the dependences of the 

changes in the first regime, comparing the history of experiments in Figures 4.4 and the times of 

illumination in Figure 4.7, suggest that the cumulative time of degradation, rather then the repetitive 

annealing, may be responsible for this effect. The corresponding lack of dependences of the A·log(t) 

regimes on the history and time of illumination would, on the other hand, suggest that there are 

differences in the underlying mechanisms responsible for these two regimes. The fact that both 

regimes/processes are affected by carrier recombination is highly significant. What is equally 

important, however, is that this occurs for carrier generation rates that correspond to illuminations of 

≤ 10-6 sun, levels that are negligible in comparison to the illumination required to create the slow 

states that eventually dominate the long term degradation. The sensitivity to such recombination is 

52
indicated by the large decrease in A from 0.95 for the annealing in the dark seen in Figure 4.3 to 0.6 

in Figure 4.5 for carrier/generation of only 1x1015cm-3s

-1; then A systematically decreases for 

increasing values of G. The fact that these characteristics are observed with carrier generation that 

results in small quasi-Fermi level splitting about midgap indicates that the states that act as the 

recombination centers are located close to midgap. This is the region of the gap associated with the 

location of the dangling bond defect states that have been extensively characterized by ESR and 

subgap absorption [4.4]. Since those defect states anneal out at significantly higher temperatures 

than 25°C, intriguing questions are raised about the nature of these fast states and dangling bond 

defect states, as well as the mechanism for their creation. This underscores further the complexity of 

the unresolved mechanisms responsible for SWE. To answer some of these questions, studies on 

both the protocrystalline and undiluted a-Si:H films should be carried out, as well as exploration of 

temperatures above 25o C. 

Creation kinetics of SWE defects in a-Si:H films 

 Direct correlations have been obtained for the evolution of metastable defects in the intrinsic 

layers of protocrystalline p-i-n a-Si:H solar cells and in corresponding thin film material observed by 

characterizing their carrier recombination through states located around midgap. This study is 

performed using photoconductivity measurements with illumination levels from 1 to 10−6 sun for the 

thin film material and compared with the Shockley-Reed-Hall recombination in the dark under low 

forward bias for the corresponding solar cells. Because these studies were carried out in the absence 

of isothermal annealing, so as to characterize the actual creation kinetics, the contributions of 

different concentrations of the “fast/soft” and “slow/hard” defect states could be reliably analyzed. 

The same apparatus was used in relaxation studies to characterize 0.8 μm thick protocrystalline and 

undiluted thick films; the protocrystalline cell structures were characterized with SRH 

recombination at 0.4 V forward bias as in Task 3. 

In order to directly correlate the creation of metastable states in films with creation in the 

corresponding intrinsic layers of solar cells, it is important to characterize the carrier recombination 

through similar regions of the gap. In the case of the protocrystalline a-Si:H reported here, the 

kinetics of the changes in carrier recombination are the same for quasi-Fermi level splitting obtained 

with generation rates (G) from ~1016 cm-3s

-1 to that of 1 sun (~5x1020 cm-3s-1). This is illustrated in 

Fig. 4.8 for the results obtained under 1 sun illumination at 25°C, where the inverse of the 

continuous 1 sun and probe photocurrents with G=1.8x1016 cm-3s

-1 are shown to reflect the changes 

in the gap states more directly. Also, to take into account the very fast changes observed in 

photocurrents with low generation rates, the photocurrents are normalized to their values after 1 

minute. It can be seen in Fig. 4.8 that the kinetics of the changes in 1-sun and the intermittent probe 

photocurrents are the same. This is not the case, however, for non-protocrystalline films obtained 

without hydrogen dilution, demonstrating the importance of the a-Si:H microstructure, a point to be 

discussed later. 

 The same form of the kinetics is found for the recombination through midgap states in the 

intrinsic layers of the corresponding cells. This is illustrated in Fig. 4.9, which depicts the IR results 

for metastable defects induced with 1-sun illumination under open circuit conditions and with a 

forward bias current of 30 mA/cm2

. The excellent superposition in the actual values of the current 

53
also clearly shows that the recombination being characterized is in the bulk of the intrinsic layer. 

The striking similarity of the kinetics in Figs. 4.8 and 4.9 shows that with the characterization 

carried out here, it is possible to directly correlate the light induced changes in films with those in 

the intrinsic layers of the corresponding cells. This is true even though the changes in 

photoconductivity are due simply to changes in the electron lifetimes, while IR is determined by both 

electron and holes. The difference in the approach to a degraded steady state that is observed here 

may be due to this difference, as well as to the symmetry of the quasi-Fermi splitting about midgap. 

 

 The kinetics in Fig 4.9, which reflect the recombination through both the intrinsic as well as 

the created metastable gap states, show three distinct regimes with the t1/3 relation covering only a 

limited region of the kinetics. On the right side of the figure, this region is bounded by a transition 

to kinetics whereby the rate of change is greatly reduced as the degraded steady state is eventually 

reached. On the left side, the region transitions into one in which the contributions of the metastable 

defects are comparable or less than those of the intrinsic states. Because of the presence of 

“fast/soft” and “slow/hard” states [4.5,4.6], it is important to separate the contribution of the 

metastable states from that of the intrinsic defects in order to accurately characterize the evolution of 

the former. Since this also takes into account any difference in the carrier capture cross sections that 

may exist between the intrinsic and metastable states, these results can be directly related to the 

densities of the metastable defects. This was carried out in the same manner as was done with the 

recombination currents of the intrinsic layers of the p-i-n cell in Task 3, and can be obtained from 

∆IR=IR−IR0, where IR0 is the recombination current in the intrinsic state. The results obtained for 

these kinetics are shown in Fig. 4.10 for the intrinsic layer of the cells and illumination levels from 5 

to 100 mA/cm2. It can be seen that for all the illumination levels, the evolution of only the 

metastable defects has a power-law-like time dependence, which is essentially t1/2 over the entire

region prior to the transition into the saturation regime. This includes the regime previously 

associated with a t1/3 dependence. 

 Similar evolution of the metastable defects alone is obtained for the protocrystalline thin films 

under 1-sun illumination. In Fig. 4.10, results from 10 separate measurements of the probe 

photocurrents are shown after subtracting out the 1-minute values. Here the evolution of the 

metastable defects is represented by the inverse of the net probe photocurrents. In this case, a 

logarithmic-type time dependence is obtained with an exponent of 0.55±0.03. This is very close to 

the value of 0.5 for the corresponding intrinsic layers in the cells and clearly nowhere near the 1/3 

that is generally associated with the creation kinetics of these defects. It is important to note here 

that -- as is evident from the results in Fig. 4.8 -- such a dependence is also obtained for the 

recombination in the 1-sun photocurrents. Thus, in this case the light induced changes in carrier 

recombination are essentially independent of the location of the electron quasi-Fermi level as it 

changes from approximately 0.25 eV above midgap up to ~0.55 eV from the conduction band. 

 This is not the case, however, for the undiluted a-Si:H films, for which the kinetics of the 

changes in recombination obtained for photocurrents under 1-sun illumination are distinctly different 

from those present in the probe photocurrents. This is illustrated in Fig. 4.11 with the results for the 

1-sun and probe photocurrents having G=2x1016 cm-3s

-1 where the standard deviations in the 

exponent of the identified logarithmic regions are obtained from 10 measurements. The exponent 

54
for the 1-sun photocurrents of 0.32 is the same as in the case of protocrystalline a-Si:H. On the other 

hand, in the case of the probe currents, the exponent is very close to 0.5. When the contributions of 

the intrinsic states are taken into account, the evolution of the states probed with 1-sun illumination 

has the logarithmic dependence close to 0.55, while that of the probe photocurrents is close to 0.7. 

This clearly shows that the evolution of the metastable defects in this material is different from that 

in the protocrystalline a-Si:H; thus, a new “fingerprint” exists for identifying possible causes that 

lead to their differences in stability. 

 The presence of a logarithmic dependence close to 0.5 in the evolution of the light induced 

defects in films and solar cells, as well as the dependence of defect density on intensity, I, are 

significant. This logarithmic exponent and proportionality in the densities of the metastable defects 

to I2

t further confirms the presence of a rate equation for the creation of metastable defects that is of 

the form , as proposed earlier. This has a direct bearing on the various models 

proposed for SWE that rely on the rate equation of the form [4.7,4.8]. Results on 

both the protocrystalline and undiluted films are relevant for the 1-sun illumination level under 

which solar cells operate, and not for the significantly higher intensities generally used in studies on 

films. Results show that photoconductivity at intensities of 1 sun or greater do not necessarily 

reflect recombination through the states just around midgap, as is generally assumed. The results 

also reveal the kinetics in the absence of isothermal annealing, thus the actual creation kinetics are 

characterized. This in turn has allowed the contributions of different concentrations of “fast/soft” 

and “slow/hard” [4.5,4.6] metastable defect states to be reliably characterized. The origin of these 

states and the reason why their difference leads to the improved stability of protocrystalline a-Si:H is 

not understood. Improved understanding of this, as well as the dependence on microstructure, can be 

obtained from studies similar to the one reported here carried out at different temperatures on films 

and solar cells whose microstructure is changed systematically. 

ms NIdtdN ms // 2 ∝

ms NIdtdN ms

22 ∝ //

 Fig 4.9: Evolution of forward bias 

current at 0.4 V for a p-i-n cell during the 

degradation with 1 sun and far forward 

bias current of 30 mA/cm2

. 

Fig 4.8: Reciprocal of 1 sun and probe 

photocurrents for 1 sun degradation. 

55
 

Fig 4.10: Evolution under 1 sun illumination 

of reciprocals of probe photocurrents 

relative to 1 minute value. 

Fig 4.11: Reciprocal of 1 sun and 

probe photocurrents for 1 sun 

56
Accurate analysis Dual Beam Photoconductivity 

subgap absorption results from 2 to 0.5 eV 

 The light induced degradation in a-Si:H is generally associated with the creation of 

dangling bonds and the emphasis has been on determining their evolution under 

illumination. Although the neutral dangling bond (D0) defect density can be directly 

measured using electron spin resonance the most commonly used method is 

photoconductive subgap absorption as a function of photon energy, α(hυ). Generally 

α(hυ) is interpreted solely in terms of D0, dangling bond defect states where their 

densities are directly related to the magnitude, │α(hυ)│, typically for hυ from 1.1 to 1.3 

eV. Such an approach has been successfully applied in interpreting a plethora of results 

on light induced changes as well as the creation and annealing of SWE defects. Because 

results have also been reported that point to the presence of other defect states, however, 

it has become clear that α(hυ) cannot be interpreted in such a simple manner [4.9]. The 

approach taken at Penn State is to take into account the contributions to α(hυ) due to 

multiple defect states by analyzing the evolution of the entire spectra rather than just their 

magnitude at an arbitrary value. 

 

 Any interpretation of α(hυ) in terms of the density and energy distribution of 

multiple defect states is complicated by the nature of photoconductive subgap absorption, 

which is determined by N(E), the densities of electron occupied states and not directly by 

the total defect density, Ndef. Photoconductive subgap absorption is determined from the 

absorption of photons, which excite electrons into the extended states in the conduction 

band whose density is then measured as the generated photocurrent. Thus, for any given 

photon energy, α(hυ) is a measure of the number of electrons excited into the conduction 

band which are located at least within hυ of EC and is given by [4.10]: 

α(hυ) = k(hυ)

-1 ∫ N(E)NCO(E+hυ−EC)1/2dE (4.1) 

The integral takes into account the fact that the photon hυ can excite electrons with an 

energy E such that EC – E < hυ. NCO(E-EC)

1/2 is the parabolic distribution of extended 

states in the conduction band. The parameter k depends on the dipole matrix elements for 

transitions from localized to extended states which in turn depends on both hυ and E in 

theory. In practice, however, k can be taken to be constant to a good approximation for 

the different gap states [4.11]. In the case of a single type of defect state it is possible to 

relate N(E) to Ndef(E) directly because the occupation of these states is constrained by 

charge neutrality. In the case of multiple defect states, however, the electron occupation 

of each type of state is determined by the kinetics of carrier recombination, and thus 

depends -- not only on their energy distribution in the gap -- but also on their relative 

densities and carrier capture cross-sections of the states [4.12]. Despite these 

complexities, information can be obtained about the evolution of the light induced defects 

and in particular about their energy distributions. In order to relate α(hυ), which includes 

the contributions from all the electron occupied states at energies within hυ of EC, to the 

energies of the defect states relative to EC, it is necessary to take the derivative of the 

α(hυ) spectra. For the case when N(E) changes rapidly with E, relative to NCO(E−EC)

1/2, 

57
the effect of the latter on the joint density of states is small. Consequently, the derivative 

of equation 1 yields: 

 kN(E) = (hυ)d[α(hυ)]/dE – α(hυ) (4.2)

 In past studies of α(E) spectra, the nature of gap states in a-Si:H films was 

determined using a numerical model, SAM. With SAM which includes Eq. (4.2), 

experimental results on electron mobility-lifetime products over a wide range of 

generation rates and α(E) were self-consistently fit using the same “operational” 

parameters. Results were obtained showing that self-consistent fitting can only be 

achieved in the presence of different gap states. However, there are still many 

unanswered questions regarding their nature because of the number of unknown and 

adjustable parameters that are needed to describe these states in the simulations. 

 In order to experimentally characterize N(E) in any meaningful way it is critical to 

obtain α(E) spectra with both high accuracy as well as spectral resolution. The 

construction of a new dual beam photoconductivity (DBP) apparatus, which overcomes 

several deficiencies of the past one at Penn State, was completed in the last quarter of this 

phase. Among the key improvements are: 

• The range in the spectra of α(E) was extended to 0.5 eV. Currently, 

however, the signal to noise ratio from 0.5 to ~ 0.65 eV is too low for α(E) to be 

considered reliable. However, the new DBP apparatus does effectively reduce the 

lower limit of the spectra from 0.9 eV to 0.7eV. 

• The computer automation, improved signal to noise, and coupling to the 

lock-in amplifier, enables the α(E) to be obtained consistently in under 30 

minutes. 

• Improved data acquisition and monochromator resolution allows high 

resolution α(E) spectra to be obtained for reliable analysis of derivatives. 

• The ability to measure electron μτ products has been incorporated into the 

new instrument. 

• The ability to perform in-situ controlled light soaking of films has been 

established. 

• The new instrument provides the capability of controlling the quasi-Fermi 

level splitting. This allows α(E) spectra to be obtained with known splitting values 

as well as maintaining these values constant during degradation. With bias 

illumination at constant generation rates, as used in the past, this splitting 

decreases due to higher recombination, and this adds another variable in the 

measurement of the α(E) spectra.

Figure 4.12 shows an example of the subgap absorption and its derivative kN(E) clearly 

identifying three distributions of states around midgap

58
Photon Energy (eV)

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6

Absorption cm-1

0.001

0.01

0.1

1

10

30mins Soaked 100pA bias

After FFT

Photon Energy (eV)

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

Electron Occupied State (cm-3eV-1)

10-3

10-2

10-1

100

101

PSU Diluted 1um a-Si:H, 30min AM1.5 soaked 

DBP 100pA bias and 13Hz

Fig. 4.12: An example of for the subgap absorption and its derivative kN(E), clearly 

identifying three distributions of states around midgap. 

59
Virtual Interface Analysis: Evaluation of Compositional Depth Profiles in 

Mixed Phase (Amorphous + Crystalline) Silicon Films from Real Time 

Spectroscopic Ellipsometry 

Overview 

 Deposition phase diagrams have been developed that describe the microcrystal 

nucleation and coalescence thicknesses for films that evolve from amorphous Si (a-Si:H) 

to microcrystalline Si (μc-Si:H) during plasma-enhanced chemical vapor deposition 

(PECVD) from SiH4 at low temperature (T<300°C) [4.13]. In the simplest such diagram, 

the two transition thicknesses are plotted versus the H2-dilution flow ratio R=[H2]/[SiH4] 

for a given substrate. In fact, R is a key parameter controlling the phase -- from pure 

a-Si:H at low R to pure μc-Si:H at high R (e.g., R ≤ 10 and R ≥ 40, respectively, for 

native-oxide covered Si wafer substrates at 200°C). At intermediate R, the film forms 

initially as a-Si:H, but microcrystals nucleate from the amorphous phase and grow 

preferentially with accumulating thickness, eventually coalescing to form single-phase 

μc-Si:H. Optimum a-Si:H intrinsic (i) layers for solar cells are deposited using the 

maximum R possible, while avoiding microcrystal nucleation within the desired 

thickness [4.14-16]. Similarly, the optimum performance of μc-Si:H i-layers appears to 

occur at the minimum R possible, while maintaining single phase μc-Si:H throughout 

[4.17]. Owing to the importance of Si:H deposition near the phase boundaries, 

techniques are needed to determine the evolution of the μc-Si:H content as a continuous 

function of accumulated thickness. In this section, the application of real time 

spectroscopic ellipsometry (RTSE) is described for this purpose.

 The ability to characterize the phase evolution of the intrinsic (i) semiconductor 

layers incorporated into amorphous silicon (a-Si:H) and microcrystalline silicon 

(μc-Si:H) thin film solar cells is critically important for device optimization. In this 

study, a new method has been developed to extract the thickness evolution of the μc-Si:H 

volume fraction in mixed-phase amorphous + microcrystalline silicon [(a+μc)-Si:H] 

i-layers. This method applies real time spectroscopic ellipsometry (RTSE) performed 

using a rotating-compensator multichannel ellipsometer during rf plasma-enhanced 

chemical vapor deposition of the films, in conjunction with a two-layer virtual interface 

analysis of the RTSE data. In this analysis, the depth profile of the μc-Si:H volume 

fraction in the mixed phase growth regime can be determined simultaneously with the 

evolution of the surface roughness layer thickness. From this information, the 

microcrystallite nucleation density and cone angle can be estimated, the latter describing 

the preferential growth of the silicon microcrystallites. The results from RTSE analysis 

correlate well with structural and p-i-n solar cell device measurements. 

Experimental Details 

 The Si:H films studied by RTSE were prepared in a single-chamber reactor by rf 

PECVD using a substrate temperature range of 200-260°C. The deposition parameter of 

greatest interest is the H2-dilution ratio R which was varied from R=7.5 to 40. The 

substrates were crystalline Si (c-Si) wafers covered by native oxides or by 2000-3000 Å 

60
thick R=0 a-Si:H layers. The smooth surfaces of the former provide the highest 

sensitivity to the transition thicknesses, whereas the latter serve to simulate i-layer 

deposition on p-layers for p-i-n cells. The p-i-n solar cells for comparison with RTSE 

were fabricated in a load-locked multi-chamber system. Specular SnO2-coated glass 

served as the substrate for the cells, and the p-layers were prepared without H2-dilution 

from SiH4, CH4, and B(CH3)3. The phase diagrams for single- and multi-chamber Si:H 

deposition compare well as deduced from RTSE and ex situ SE, respectively. RTSE was 

performed using a rotating-compensator multichannel ellipsometer with a range of 1.5-

4.5 eV and a minimum acquisition time of ~50 ms [4.18]. This instrument employs a 

MgF2 biplate compensator in the PSCrA configuration. 

Results and Discussion 

Real time spectroscopic ellipsometry and microstructural studies 

 The volume fraction of μc-Si:H in the graded, mixed-phase growth regime is best 

determined by tracking the dielectric function of the top-most growing material 

throughout the deposition. This is an ideal application for the two-layer 

[(outerlayer)/(surface roughness)] virtual interface (VI) approach to RTSE analysis 

[4.19,4.20]. In order to apply this approach, the dielectric functions (ε1, ε2) of the singlephase a-Si:H and μc-Si:H must be obtained by RTSE in the initial and final stages of the 

same deposition, when only the pure phases are growing. Figure 4.13 compares such 

results for an R=20 Si:H film deposited on a Si wafer substrate at 200°C. This film 

evolves through single-phase a-Si:H, mixed-phase (a+μc)-Si:H, and single-phase μc-Si:H 

regimes during growth to a bulk layer thickness of db=2300 Å, as will be demonstrated in 

subsequent figures. 

 The dielectric function of the pure a-Si:H phase in Fig. 4.13 was determined by 

applying the conventional two-layer (uniform bulk)/(roughness) model to analyze the 

RTSE data collected in the a-Si:H growth regime 0≤db≤200 Å, before the microcrystal 

nucleation [4.21]. The dielectric function of the pure μc-Si:H phase was obtained from 

data collected after crystallite contact (db>1900 Å). In this case, the emphasis was on the 

top ~200 Å of the film where the dielectric function is nearly uniform with depth. The 

underlying structure, including the graded layer, is incorporated within a hypothetical 

uniform film located beneath a virtual interface to the top 200 Å. The correct roughness 

layer thickness at the very surface of the structure is required in order to extract the (ε1, 

ε2) spectra for single-phase μc-Si:H. This value was determined by embedding the VI 

analysis within a global error minimization routine. The differences between the results 

in Fig. 4.13 support an interpretation in terms of phase evolution during growth. 

 Figures 4.14 and 4.15(a) show the evolution of the μc-Si:H volume fraction fμc and 

surface roughness thickness ds for the R=20 film of Fig. 4.13, as determined using twolayer VI analysis. The profile in fμc is presented throughout the mixed-phase growth 

regime, starting and ending near the nucleation and coalescence transitions. The optical 

model consists of (i) a pseudo-substrate, incorporating the history of mixed-phase 

61
Fig. 4.14: Depth profile in the volume 

fraction of the microcrystalline phase 

(points) throughout the mixed-phase 

(a+μc)-Si:H growth regime for the 

R=20 Si:H deposition on c-Si from Fig. 

4.13 Also shown as the solid line is the 

prediction of the microcrystallite cone 

growth model depicted in Fig. 4.15(b). 

Fig. 4.13: (a) Real and (b) imaginary 

parts of the dielectric functions of the 

pure a-Si:H and μc-Si:H phases for an 

R=20 deposition on c-Si. The solid lines 

are fits using analytical models. 

62

Fig. 4.15: (a) Surface roughness 

thickness versus bulk layer thickness for 

the R=20 Si:H deposition of Figs. 4.13 

and 4.14; (b) schematic of the cone 

growth model used to estimate the 

microcrystallite nucleation density and 

cone angle. 

Fig. 4.16: Cone angle θ and nucleation 

density Nd versus the nucleation transition 

thickness db,trans for Si:H films deposited 

under different conditions on c-Si wafers and 

on R=0 a-Si:H. The values of θ and Nd are 

deduced from RTSE (circles), XTEM 

(triangles) and AFM (squares). Data are 

included from this study (closed symbols) 

and from that of Ref. [4.24] (open symbols). 
deposition, (ii) an outerlayer of thickness do, modeled as a fμc/(1−fμc) mixture of 

μc-Si:H/a-Si:H, and (iii) a topmost surface roughness layer of thickness ds, modeled as 

0.50/0.50 mixture of outerlayer/void. The dielectric function of the pseudo-substrate is 

determined as its pseudo-dielectric function (corrected only for the roughness layer). The 

dielectric functions of the two layers are determined from the component volume 

fractions and dielectric functions via Bruggeman effective medium theory [4.22]. 

 The two-layer VI analysis used to deduce the results of Figs. 4.14 and 4.15(a) 

begins as follows [4.19]. Consecutive spectra {(ψj

(e), ∆j(e)); j=1, 2, 3} (e: experimental) 

collected over a time interval ∆t = 103 s (1 s acquisition; 50 s delay) are chosen such that 

the j=2 pair, at the interval center, occurs at the nucleation transition [i.e., at the 

roughening onset established from the two-layer (uniform bulk)/(roughness) model]. 

Initially, trial values are assigned to {fμc, ds} for the interval ∆t, providing sufficient 

information for analytical removal of the roughness layer. Thus, the spectra are 

converted to those of a hypothetical one-layer (pseudo-substrate)/(outerlayer) structure 

with pseudo-dielectric functions {(<ε1>j

(e), <ε2>j(e)); j=1, 2, 3}, for usual one-layer VI 

analysis [4.23]. 

 At this point, the deposition rate (which is a known constant, r=0.28 Å/s) and the 

data set {(<ε1>j

(e), <ε2>j(e)); j=1, 2, 3} are used together to determine the derivative of 

<ε> with respect to the outerlayer thickness do, denoted <ε>'. Then using as input <ε>' 

and the outerlayer dielectric function εo determined from fμc, the common pseudosubstrate approximation is applied to predict the pseudo-dielectric function (<ε1>2

(c), 

<ε2>2

(c)) at the center of the interval (j=2) [4.23]. Finally, the roughness layer is 

reintroduced, generating the predicted pair {(ψ2

(c), ∆2(c))}. This pair is compared to the 

experimental spectra {(ψ2

(e), ∆2(e))}, and an error function is generated. Based on the 

error function values for a grid of trial (ds, fμc), a new trial pair is determined. The 

process is iterated until (ds, fμc) are found that minimize the error function. Then the 

next triplet {(ψj

(e), ∆j(e)); j=2, 3, 4} is chosen and the analysis is repeated. 

 The final results of this procedure are two functions {ds(t), fμc(t)} that can be 

converted to {ds(db), fμc(db)} because r is known throughout this process. The resolution 

of the profile fμc(db) is ~do=r∆t, which is set for ~30 Å by the 50 s delay in data 

acquisition. A similar resolution is possible without loss of signal-to-noise ratio up to a 

deposition rate of r=10 Å/s by elimination of this delay. Finally, it should be noted that 

the average of the error functions over time provides a global measure of the fit quality, 

and this can be used as a criterion to select the correct roughness thickness and dielectric 

function in the analysis of the pure μc-Si:H phase. 

 Evidently, the evolution of ds in Fig. 4.15(a) provides higher sensitivity to the 

presence of microcrystals, since it reveals a nucleation transition at ~300 Å, whereas fμc

in Fig. 4.14 is first discerned above zero at db~700 Å. The solid line in Fig. 4.14 is the 

result for fμc vs. db using a model of conical microcrystal evolution as shown in Fig. 

4.15(b). This model is based on assumptions supported by cross-sectional transmission 

electron microscopy (XTEM) and atomic force microscopy (AFM). First, it is assumed 

63
that all microcrystal nuclei originate at the nucleation transition thickness [~300 Å, from 

Fig. 4.15(a)]. Second, the area density of such nuclei is assumed to be Nd, and the nuclei 

are assumed to grow preferentially at the expense of the a-Si:H phase with a thicknessindependent cone angle, θ. Third, cones are assumed to be spherically capped with a cap 

radius rc given by rc = db − db,trans. From this geometry, Nd and θ can be deduced from 

the values of ∆db = db,coal − db,trans and ∆ds = ds,coal − ds,trans. Here, db,trans and ds,trans are 

the bulk and surface roughness layer thicknesses at the nucleation transition and db,coal

and ds,coal are the corresponding values at the coalescence transition. For the deposition 

of Figs. 4.13-15, values of θ=19° and Nd=1.1x1010

 cm−2 are determined. 

 Figure 4.16 presents results for θ and Nd versus db,trans for a series of Si:H films 

prepared on c-Si and R=0 a-Si:H surfaces under different conditions of R, T, and rf 

plasma power. Results solely from RTSE are compared with those from XTEM and 

AFM. In Fig. 4.16, the solid and open symbols represent results from this work and from 

Ref. [4.24], respectively. Evidently the nucleation density decreases significantly with 

increasing nucleation transition thickness, yet the cone angle is nearly constant between 

15° and 20°. Figure 4.16 reveals consistency between the indirect (but real time) SE and 

the direct (but ex situ) structural measurements. 

Device comparisons 

 Similar analyses to that of Figs. 4.12-15 performed for films deposited on R=0 aSi:H can be compared with the performances of the corresponding p-i-n solar cells as 

long as the p-layers in the cells are amorphous and prepared near R=0. As an example, 

Fig. 4.17 shows RTSE results for the evolution of fμc near the microcrystal nucleation 

transition for two-step (R=40 interface)/(R=20 bulk) i-layers on R=0 a-Si:H substrate 

films. These structures are distinguished by the thickness di of the R=40 i-layer, selected 

as di=400, 150, and 0 Å, whereas the total i-layer thickness is fixed at 4000 Å. Figure 

4.18 shows the dark current-voltage (J-V) curves of the corresponding Si:H p-i-n solar 

cells of this series. For the cell with the highest currents in Fig. 4.18 (inverted triangles, 

with di=400 Å), the associated two-step i-layer structure measured by RTSE exhibits the 

nucleation transition after 200 Å of R=40 deposition. For comparison purposes, the cell 

with the lowest currents (squares) was fabricated using an optimum two-step (R=40 

interface)/(R=10 bulk) a-Si:H i-layer (designated the "optimum cell") [4.16]. 

 Computer simulations of the J-V curves were also carried out, and the results are 

shown in Fig. 4.18 (solid lines). The optimum cell could be considered in terms of a 

uniform a-Si:H i-layer with a mobility gap of 1.86 eV. Results for the other three cells 

were modeled assuming an a-Si:H i-layer at the p/i interface with the same 1.86 eV 

mobility gap and a bulk μc-Si:H i-layer with a mobility gap of 1.15 eV as indicated by 

RTSE. This simple model for the solar cells reproduces the overall features of the J-V 

curves. Table 4.1 includes a comparison of the RTSE and J-V simulation results for the 

three Si:H p-i-n solar cells with two-step (R=40)/(R=20) 4000 Å i-layers of Figs. 4.17 

and 4.18. The table compares the thickness of the a-Si:H i-layer component nearest the 

p/i interface, as deduced from the device modeling, with the i-layer thickness required to 

reach fμc = 0.2, as deduced from RTSE. This good agreement suggests that once fμc

approaches ~0.2, transport is dominated by the microcrystalline phase. 

64
Summary 

 Real time spectroscopic ellipsometry (RTSE) studies of PECVD Si:H films that 

undergo amorphous-to-(mixed-phase amorphous + microcrystalline) transitions were 

performed. Novel approaches for RTSE data analysis were conceived and developed that 

provide (i) the volume fraction of the μc-Si:H phase as a function of the accumulated 

thickness, (ii) the optical properties of the films in the amorphous, mixed-phase (a+μc)-

Si:H, and single-phase μc-Si:H growth regimes, and (iii) estimates of the nucleation 

density and cone angle characterizing the evolution of the Si microcrystallites in the 

mixed-phase (a+μc)-Si:H regime. The resulting information correlates well with that 

from ex situ structural and device performance studies. 

0 500 1000 1500 2000

0.0

0.1

0.2

0.3

0.4

0.5

p-i interface Bulk layer thickness, db

 (Å)

f

μc

 di = 400 Å 

 di = 150 Å 

 di = 0 Å 

R=40 to R=20

0.0 0.2 0.4 0.6 0.8 1.0 1.2

10-12

10-10

10-8

10-6

10-4

10-2

100

 optimum cell

 di= 0 Å

 di= 150 Å

 di= 400 Å

Voltage (V)

J (mA/cm2

)

Fig. 4.17: Depth profiles of the 

microcrystal volume fraction fμc in the ilayer for three 4000 Å thick two-step 

R=40/20 i-layer structures on R=0 a-Si:H 

substrates. The thicknesses di of the 

R=40 p/i interface layer are di = 0 Å 

(circles), 150 Å (triangles), and 400 Å 

(inverted triangles). 

Fig. 4.18: Experimental (symbols) 

and simulated (lines) dark J-V 

characteristics for four Si:H p-i-n solar 

cells. The squares denote a standard 

cell that incorporates an optimized 

[R=40 (200 Å)]/[R=10 (3800 Å)] aSi:H i-layer, and the other cells 

incorporate [R=40 (di)]/[R=20 

(4000−di) Å] i-layers where di = 0 Å 

(circles), 150 Å (triangles), and 400 Å 

(inverted triangles). 

65
Table 4.1: 

Correlation of RTSE and device modeling results for Si:H p-i-n cells with 4000 Å thick 

two-step R=40/20 i-layers in which the R=40 interface thickness is varied. 

First step: 

R=40 

thickness (Å) 

Real time SE: 

db when 

fμc=0.2 (Å) 

Device Modeling: 

Heterojunction 

position from p/i (Å) 

0 1240 ± 30 1300 ± 300 

150 950 ± 30 700 ± 200 

400 330 ± 20 400 ± 100 

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67
APPENDIX A

Theoretical Considerations 

The experimental results previously reported (April 2003) showed that there are no 

large densities of defect states in i-layers adjacent to p, n contacts such as predicted by 

the defect pool model. Instead, the distributions of the defects are relatively 

homogeneous across the bulk. This conclusion greatly facilitates the analysis of the 

experimental results and serves as a fundamental basis for the correct understanding of 

the physical mechanisms governing the operation of a-Si:H solar cells. 

From the JD-V characteristics it was clearly seen that extended voltage regions exist 

in which the currents increase exponentially with the applied forward bias voltages, 

consistent with the diffusion/recombination model proposed by Lips et al.1 Furthermore, 

it has been shown that these currents increase when the density of defects is increased by 

light-induced degradation, which indicates that the recombination process is governed by 

Shockley-Reed-Hall (SRH) recombination mechanisms in which electrons and holes 

recombine through the defect states in the gap2. 

The current transport in the dark for these a-Si:H solar cells over an large range of 

forward bias voltages can be considered in terms of the diffusion of the electrons and 

holes into the bulk under the forward bias and recombination through gap states which 

have a relatively homogeneous distribution across the bulk. The recombination rate given 

by SRH theory is determined by the product of the electron and hole concentrations, n 

and p respectively, which can be expressed as: 

r = np/(sn+p)τno (A1) 

where s is the ratio of the electron to hole capture cross sections and τno is the electron 

capture time determined by the density of gap states that act as recombination centers. To 

facilitate the discussion but without losing generality, an equal electron and hole capture 

cross section (s=1) is assumed in the following discussion. 

 Even though the recombination occurring at the p/i interface and in the bulk is both 

described by the SRH recombination mechanism, their contributions to the diode quality 

factor of the dark current characteristics are distinctly different. Let us first consider the 

recombination in the bulk. When the carrier transport is diffusive, the concentrations of 

the electrons and holes in the bulk have an exponential (negative) dependence on the 

potential difference relative to the n and p contacts, respectively. The further away from 

their respective contacts, the higher the potential difference so that these carrier 

concentrations decay exponentially away from their contacts. Under forward bias, the 

potential difference is reduced across the bulk so that the carrier concentrations increase 

exponentially. Although n and p both vary rapidly across the bulk, their product is 

constant and: 

np = ni

2 exp(qV/kT) (A2) 

 

1

 K. Lips, Mat. Res. Soc. Symp. Proc. 377, 455 (1995). 2

 W. Shockley and W. T. Read, Phys. Rev. 87, 835 (1952). 

68
where ni is the intrinsic carrier concentration, determined by the band gap; q is the 

electron charge; k is the Boltzmann constant; T is the temperature; and V is the applied 

forward bias voltage. 

In the case of a single defect in the mid gap, τno is a constant. Then according to Eq. 

A1, the maximum recombination rate occurs at the location where n+p is the minimum, 

which is achieved only when n=p. At this location, from Eq. A2, it can be easily found 

that: 

n = p = ni exp(qV/2kT) (A3) 

Away from this location in the bulk, either n or p increases rapidly so that the 

recombination rate decreases rapidly resulting in a recombination profile, which has 

sharp slopes around its center. Combining equation A1 and A3, the maximum 

recombination rate rmax can be obtained: 

 rmax = [ni exp(qV/2kT)]/τn0 (A4) 

The total recombination current can be obtained by either integrating r across the 

bulk or equivalently by multiplying rmax by the width of the recombination profile. It has 

been shown that this width is proportional to the local field ε around the center of the 

recombination profile so the dark current JD has the form3: 

 JD ~ [(1/ε) ni exp(qV/2kT)]/τn0 (A5) 

Due to the fact that in these a-Si:H cells the n contact is more heavily doped than 

the p contact, the location where n=p is closer to the p contact. As will be discussed in 

more detail, the n an p contacts induce a space charge region in the i-layer adjacent to 

them so that the electric filed ε in the bulk does not scale exactly with the bulk i-layer 

thickness -- neither does JD. This conclusion has been utilized earlier in explaining the 

thickness dependence of the JD-V characteristics. More importantly, since ε is not a fastvarying function of V, Eq. A5 yields a diode quality factor of 2, which has been well 

established in the case of crystalline-Si p-n junctions at low forward bias when the 

recombination in the space charge regions dominates the total current. 

In the case of a-Si:H i-layers, which have a continuous distribution of gap states 

between valence band and conduction band, however, τno is no longer a constant. In SRH 

type recombination, the gap states that act as recombination centers are those located 

between the electron and hole quasi-Fermi levels, Fn and Fp respectively, where the 

separation is equal to the applied voltage. As the applied voltage and the splitting of the 

quasi-Fermi levels are increased there is a corresponding continuous increase in the 

number of gap states acting as recombination centers, which leads to a decrease in τno and 

a corresponding increase in the recombination. In the case of a distribution of states 

increasing exponentially around mid-gap the increase in the number of recombination 

centers enhances the current by an exponential term, which then changes the diode 

quality factor from 2 to a lower value whose offset depends on the specific exponential 

 

3

 C. van Berkel, M. J. Powell, A. R. Franklin, and I. D. French, J. Appl. Phys. 73, 5264 (1993). 

69
form in the energy distribution of the gap states. This has been confirmed numerically by 

Hack and Shur.4

 Thus, an effective diode quality factor m of 1.4 to 1.6 seen over an 

extended voltage region in the JD–V characteristics of the cells with minimized p/i 

interface recombination,5 can be explained simply by the presence of a continuous 

distribution of gap states in the a-Si:H i layer. There is therefore no necessity, as has been 

previously suggested,6 for a spatially varying density of defects in the i-layer as predicted 

by the defect pool model. 

For the case of a gap state distribution that is significantly different from 

exponential form, however, d(ln(JD))/dV does not remain constant so that the diode 

quality factor changes with the applied voltage. Consequently, there is a voltage 

dependent differential diode quality factor n(V), which is equal to the inverse of 

[kT/q][d(ln(JD))/dV]. In the results obtained for cells having either diluted or undiluted ilayers, where the recombination is dominated by that in the bulk of the i-layers, values of 

n(V) are present which are approximately constant over an extended region of voltage. 

This indicates that the distributions of the gap states around mid-gap are similar, although 

not identical, to that of an exponential form such as the Gaussian distributions suggested 

by the studies on the corresponding thin film i-layers7

. It can be pointed out here also that 

the difference in such n(V) values obtained between the two types of cells is a clear 

indication of a difference in the energy distribution of the gap states in their respective ilayers. 

In the case of recombination at the p/i interface, the concentration of holes adjacent 

to the p-contact is much larger than that of the electrons, and the electrons become the 

minority carriers. Thus, from Eq. A1, the recombination rate is determined only by the 

electron concentration at the p/i interface. The electron concentration n at p/i interface is 

an exponential function of the applied forward bias voltage V so that the recombination 

rate at the p/i interface is given by: 

 rpi = n/τnpi = [n0piexp(qV/kT)]/τnpi (A6) 

where n0pi is the electron concentration at the p/i interface in equilibrium and τnpi is the 

electron capture time at the p/i interface, which is usually smaller than that in the bulk. It 

should be noted here that n0pi can be controlled by changing the band gap of the p/i 

interface layers as has been carried out for controlling p/i recombination in the cells 

studied. The corresponding dark currents can be obtained either by summing up all the 

recombination in the thin regions adjacent to the p/i interface or by introducing an 

effective interface recombination velocity, Seff, which gives: 

 JD = qnSeff = qSeff n0pi exp(qV/kT) (A7) 

 

4

 M. Hack and M. Shur, J. Appl. Phys. 54, 5858 (1983). 5

 J. Deng, J.M. Pearce, R.J. Koval, V. Vlahos, R.W. Collins and C.R. Wronski, Appl. Phys. Lett. 82, 3023 

(2003). 

6

 M.A. Kroon and R.A.C.M.M. van Swaaij, J. Appl. Phys. 90, 994 (2001). 7

 L. Jiao, Ph.D. Thesis, The Pennsylvania State University, 1999. 

70
Thus, in the case of interface recombination dominated currents, the effective diode 

quality factors such as m* are close to one.8

 By comparing Eq. A7 with Eq. A5, it can be 

seen that the increase with voltage in the interface recombination currents is much faster 

than that of the bulk recombination currents. It is therefore not surprising that at the 

higher bias voltages the p/i interface recombination can readily dominate over the bulk 

recombination. 

To simplify the above discussion, the effects of the space charge that is present in 

the bulk on the current transport are not considered here. This space charge consists 

mainly of the trapped electrons and holes, the concentrations of which are higher than 

those of the free electrons and holes even in the highest quality a-Si:H solar cells. The 

densities of trapped electrons and holes depend on the positions of electron and hole 

quasi-Fermi level, respectively. These in turn are determined by the free electron and free 

hole concentrations -- higher free carrier concentration leads to higher trapped carrier 

concentration for the corresponding carriers. The presence of the space charge in i-layers 

affects the electric field distribution across the bulk. Due to the high electron (n0) and 

hole concentrations (p0) in the regions of i-layer adjacent to the n and p contacts, 

respectively, the space charge densities in these regions are higher than in the bulk. This 

results in potential drops Vn near the n and Vp near the p contact, which constitute 

barriers for the injection of carriers from the contacts into the bulk of the i-layer. These 

potential barriers are included in the schematic band diagram for a p-i-n cell under a 

forward bias V shown in Figure A.1. In the figure, φ represents the potential drop across 

the bulk region and φ=Vbi−V−Vn−Vp, where Vbi is the built-in voltage across the cell. 

Positive values of φ indicate that the carrier transport is diffusive while negative values 

indicate that the transport is drift-driven. In a-Si:H solar cells with low defect densities in 

their intrinsic layers, both Vn and Vp are quite small so that φ remains positive for biases 

V up to values close to Vbi. This results in the exponential dependence of the diffusive 

current JD on V over an extended voltage range so that direct correlations of JD-V 

characteristics can be made with bulk dominated recombination and consequently the 

densities of gap states in the intrinsic layers. 

The transport of photo-generated carriers is distinctly different from that of those 

injected from the contacts since with volume-absorbed light the carriers are created 

throughout the bulk of the i-layer. They are subject to a drift field, ε, which sweeps them 

out towards the contacts as a net drift current9

. In i-layers with low defect densities the 

space charge that is present has only a small effect on the electric field distribution so that 

ε≅φ/L where φ is the potential drop across the bulk of the i-layer and L its thickness. The 

photo-current JL is then determined by the densities of electrons and holes that reach the 

contacts before recombining, where the probability of undergoing recombination depends 

on their effective lifetime, τ, and transit time Ttr. This current JL can be written as 

JL=JG−JRG where JG is the photocurrent created by the generation rate of carriers, G, due 

to the absorbed photons in the bulk. JRG is the recombination current in the bulk which is 

determined by Ttr and τ. JG depends only on the intensity of the illumination and is 

independent on the electric field ε (V) while JRG depends on ε since Ttr∝1/ε. Under short 

 

8

 J. Deng, J.M. Pearce, R.J. Koval, V. Vlahos, R.W. Collins and C.R. Wronski, Appl. Phys. Lett. 82, 3023 

(2003). 

9

 D.E. Carlson and C.R. Wronski, Appl. Phys. Lett., 28, 671 (1976). 

71
circuit conditions, the effective transit time Ttr ∝ 1/Vbi. In high quality a-Si:H cells JRG is 

significantly lower than JG which is reflected by the quantum efficiencies under short 

circuit conditions of virtually 100% for carriers generated in the bulk. For JRG<<JG, 

JSC≅JG which makes JSC directly proportional to the illumination intensity as is observed 

in high quality cells.

Under a forward bias V across the i-layer, Ttr increases as does JRG. At the same 

time the balance between the drift and diffusive currents from the high densities of n0, p0

carriers is disturbed so that the net diffusion currents, Jdiff, are introduced in the opposite 

direction to the photo-generated currents, as is illustrated in Figure A.2. JL then becomes: 

 JL(V)=JG−JRG(V)−Jdiff(V) (A8) 

Since the mechanism governing this Jdiff is exactly the same as that for the diffusion 

current JD in the dark, as discussed earlier, they increase exponentially with V. For the 

same diffusive transport under illumination as that in the dark, Jdiff(V)=JD(V). Since both 

JRG and Jdiff increase with V, JL decreases until it becomes zero at V=VOC, so under open 

circuit conditions: 

 JSC ≅ JG = JRG(VOC) + Jdiff(VOC) (A9) 

 

which for Jdiff>>JRG becomes: 

 JSC ≅ Jdiff(V=VOC) = JD(V=VOC) (A10) 

At high current densities and forward bias, there are clear deviations from the 

exponential dependence on V in the dark current. This occurs when Vbi−V approaches 

Vn+Vp, which corresponds to φ approaching zero. Further increases in V invert the field 

across the i-layer, which then results in the field driven drift currents. In addition, at high 

values of JD the potential barriers associated with Vn and Vp begin to limit the carrier 

injection from the contacts into the i-layer10. The height of these barriers depends on the 

space charge, which in turn is determined by n0, p0 and the defect densities in the i-layers, 

which are small in high quality intrinsic materials. As a consequence, the effects of Vn, 

Vp do not become significant until current levels are very high. However, in low quality 

cells, where these barriers are high due to a large density of defects, their effects already 

become significant at lower current levels. 

As a consequence there is a superposition between JSC versus VOC and JD versus V, 

as reported. This occurs even though the superposition principle is not valid in a-Si:H 

solar cells for all values of V due to the voltage dependent contributions of JRG to JL. 

The absence of superposition between JSC-VOC and JD-V, however, also occurs if at 

V=VOC, JRG is comparable to or larger than Jdiff. This can occur at high illumination levels 

when VOC approaches Vbi so that the small values of φ and hence ε present across the 

bulk result in Ttr>τ, which lead to large values of JRG. At the same time the high forward 

bias currents in the JD-V characteristics encounter limitations on carrier injection imposed 

by the potential barriers Vn and Vp. Both of these effects can then contribute to a split 

 

10 F.A. Rubinelli, J.K. Arch, and S.J. Fonash, J. Appl. Phys. 72, 1621 (1992). 

72
between the two characteristics since the limitations of JRG on VOC move the JSC-VOC to 

lower values of VOC, while on the other hand the limitations on carrier injection move 

JD-V to higher values of V. Higher densities of defects in the i-layer result in larger 

values of JRG as well as Vn and Vp at the n and p contacts, so that the divergence between 

the JSC-VOC and JD-V characteristics occurs at lower voltages. 

As was discussed earlier, the potential barriers that limit the carrier injection are 

determined by both n0 and p0 as well as by the densities of defects in the i-layer 

contributing to the space charge. Any increase in density of these defects leads to larger 

Vn and Vp, which then reduces the carrier injection. The contributions to the divergence 

between JSC-VOC and JD-V due to the densities of gap states in the i-layer have been 

confirmed by introducing light induced defects. 

Although the presence of the potential barriers Vn and Vp has little effect on VOC, it 

can have deleterious effect on FF. This is because, as has been discussed above, the 

presence of these barriers lowers the average electric filed across the bulk and thus 

reduces the collection efficiency of the photo-generated carriers. This points to a 

important fact that FF is not merely determined by the defect density in the bulk but also 

affected by Vn and Vp. Consequently, FF is in general not a parameter directly 

corresponding to the i-layer defect density. Thus, when FF is used as a parameter to study 

the density of defects in the bulk i-layers, it is necessary to ensure that the contributions 

from Vn and Vp is negligible. 

73
n contactn contact

Ec

Fn

Ev

n0

p0

Fp

Diffusion

R p contact

Diffusion

V

Vp

Vn

φ

Ec

Fn

Ev

n0

p0

Fp

Diffusion

R p contact

Diffusion

V

Vp

Vn

φ

n contactn contact

Ec

Fn

Ev

n0

p0

Fp

Diffusion

R p contact

Diffusion

V

Vp

Vn

φ

Ec

Fn

Ev

n0

p0

Fp

Diffusion

R p contact

Diffusion

V

Vp

Vn

φ

Figure A.1: Schematic band diagram for the i-layer of a p-i-n cell under forward bias in 

the dark. 

∆Vp

∆Vn

φ

Ec

Fn

Ev

n0

p0

Fp

Diffusion Drift

G R

n contact

p contact

DiffusionDrift

∆Vp

∆Vn

φ

Ec

Fn

Ev

n0

p0

Fp

Diffusion Drift

G R

n contact

p contact

DiffusionDrift

Figure A.2: Schematic band diagram for the i-layer of a p-i-n cell under forward bias and 

illumination. 

74
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1. REPORT DATE (DD-MM-YYYY)

August 2006 

2. REPORT TYPE

Subcontract Report 

3. DATES COVERED (From - To)

October 2001–July 2005 

5a. CONTRACT NUMBER

DE-AC36-99-GO10337 

5b. GRANT NUMBER

4. TITLE AND SUBTITLE

Optimization of Phase-Engineered a-Si:H-Based Multi-Junction 

Solar Cells: Final Technical Report, October 2001–July 2005 

5c. PROGRAM ELEMENT NUMBER

5d. PROJECT NUMBER

NREL/SR-520-40400 

5e. TASK NUMBER

PVB65101 

6. AUTHOR(S)

C.R. Wronski, R.W. Collins, N.J. Podraza, V. Vlahos, J.M. Pearce, 

J. Deng, M. Albert, G.M. Ferreira, and C. Chen 

5f. WORK UNIT NUMBER

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

Pennsylvania State University 

University Park, Pennsylvania 

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REPORT NUMBER

NDJ-1-30630-01 

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NREL 

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14. ABSTRACT (Maximum 200 Words)

The scope of the work under this subcontract has involved investigating engineered improvements in the 

performance and stability of solar cells in a systematic way, which included the following four tasks: 1. Materials 

research and device development; 2. Process improvement directed by real time diagnostics; 3. Device loss 

mechanisms; and 4. Characterization strategies for advanced materials Our work has resulted in new and important 

insights into the deposition of a-Si:H-based materials, as well as into the nature of the Staebler-Wronski Effect 

(SWE). Presumably, many of these insights will be used by industrial partners to develop more systematic 

approaches in optimizing solar cells for higher performance and stability. This effort also cleared up several serious 

misconceptions about the nature of the p-layer in cells and the SWE in materials and cells. Finally, the subcontract 

identified future directions that should be pursued for greater understanding and improvement. 

15. SUBJECT TERMS

PV; solar cells; high performance; devices; manufacturing; materials research; real-time diagnostics; phase 

engineering; amorphous silicon; Staebler-Wronski Effect. 

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