# Transport, Interfaces, and Modeling in Amorphous Silicon Based Solar Cells: Syracuse University Annual Technical Report change as comment in properties2/11/03-2/10/04

NREL Subcontract NDJ-2-30630-24 with *Syracuse University.\
*Deliverable D.2.5 . Submitted: May 11. 2004.

Bolko von Roedern, NREL Technical Monitor; Vicki Riddell, NREL
Subcontract Administrator.

Eric A. Schiff, principal investigator; Rafik Middya, research assistant
professor; Kai Zhu, graduate fellow. Steluta Dinca, Thorsten Dylla,
Jianjun Liang, Weining Wang, graduate assistants. Mr. Dylla was a
visitor from Forschungszentrum Jülich.

## Summary

In this report we present the status of three projects:

1.  Amorphous Silicon Solar Cell Characteristics and Modeling

2.  Hole Drift Mobility Measurements in Microcrystalline and Amorphous
    Silicon

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

We first present brief summaries, and then offer more detailed
discussion of most projects.

### Solar Cell Characteristics & Modeling

We believe that we can demonstrate that the low hole drift-mobility of
a-Si:H largely determines the electrical properties of as-deposited
a-Si:H cells at solar illumination intensity and near room-temperature.
We think it is fair to say that, despite 20 years of work on the
characterization of amorphous silicon and amorphous silicon solar cells,
there has been no definitive, quantitative model for how the cells work
-- even under restriced conditions such as the as-deposited state. Our
hope for future work is that we can leverage the success of this model
to gain deeper insight into the light-soaked state.

The main activities in the last year have been to: (i) Obtain an
improved set of *J-V* measurements on as-deposited a-Si:H solar cells to
serve as the target for cell modeling, and (ii) to explore the range of
validity of the "hole drift-mobility only" model for the as-deposited
properties.

The improved set of measurements involves the use of a thickness series
of cells and of a near-infrared laser to obtain uniformly absorbed
illumination. Measurements were recorded over a wide range of
illumination intensities.

The more definitive set of measurements shows good agreement with the
"hole mobility only" model for intensities ranging from 1% of AM1.5 up
to AM1.5. For low intensities the this model is not very successful. It
seems likely that measurements in this regime are more sensitive to deep
levels such as dangling bonds.

### Hole Drift Mobility Measurements

There have been two main drift-mobility projects projects underway in
the last year. One project is the measurement of hole drift mobilities
in microcrystalline silicon; the particular samples are similar to those
used in 8.7% cells demonstrated by Forschungszentrum Jülich. The
material is predominately crystalline, but retains a significant
amorphous fraction (as judged by Raman meaurements). The results show
fairly low hole drift-mobilities (about 1 cm^2^/Vs), and suggest that
the low value is dominated by disorder effects reminiscent of those that
limit hole drift in a-Si:H. This hole mobility is consistent with the
thicknesses of order 2 microns that are used in optimized solar cells
with microcrystalline Si absorbers.

The second project involves development of techniques for measuring hole
drift-mobilities on substrate cells deposited onto stainless steel (or
other opaque materials). Standard time-of-flight methods for hole
measurements require illumination through the *n*^+^ layer, which is not
possible in these cells. Because of the importance of measurements on
cells with opaque substrates, we decided to try to develop a new method.
We are developing a technique based on measurements of photocurrents
with both strongly absorbed illumination (sensitive primarily to
electron properties) and weakly absorbed illumination (sensitive to both
electron and hole motion). This project has been progressing rather
slowly, and will not be described further at this time.

### Polymer *p*-layer

Hole conducting polymers are an interesting alternative to silicon-based
*p*-layers for a-Si:H, in that one can obtain highly variable bandgaps
and band alignments relative to a-Si:H. Our hope in these studies has
been to demonstrate high open-circuit voltages in a-Si:H cells using
polymers, which would be of fundamental interest (in establishing
*V~OC~* device physics), and could conceivably be of technological
significance.

In prior work we have obtained open-circuit voltages up to 0.73 V using
"PEDOT:PSS," which is a commercially available hole-conducting polymer.
PEDOT:PSS uses water as its solvent; we generally deposit the polymer
onto a-Si:H, and we have been concerned that oxide formation has led to
reduced *V~OC~*. In our present work we have been exploring doped
polyaniline as the hole-conducting polymer, which uses a non-aqueous
solvent.

The work described in this report is actually done on c-Si substrates,
and is preliminary to work on a-Si:H based *n/i* structures. We were
able to fabricate fairly good c-Si/polyaniline diodes; the open-circuit
voltage under tungsten halogen illumination was about 0.4 V.

## Characterization & Modeling of a-Si:H Solar Cells

The solar conversion efficiency of as‑deposited *pin* a-Si:H solar cells
can be explained surprisingly well from hole mobility and optical
absorption measurements on the intrinsic layer material. We first
realized this fact about 18 months ago; at the right, we have reproduced
a figure illustrating the agreement between measurements (on United
Solar cells) and the model \[[^1]\].

The surprise in this model is its simplicity. As has been summarized not
long ago in the monograph of Schropp and Zeman \[[^2]\], the standard
model for undoped a-Si:H incorporates four (or more) classes of
electronic states: valence bandtails, conduction bandtails, and two or
more dangling bond levels. Perhaps 20 or more parameters are required if
all possibly relevant electronic transport and trapping processes are
treated, and veteran scientists might well despair of gaining insight
from the daunting exercise of matching so many parameters to such simple
measurements.

The hole drift-mobility in a-Si:H can generally be explained
satisfactorily using an electronic density-of-states model with an
exponential valence bandtail; these bandtail parameters are the main
ones in the model. In Fig. 2 we illustrate the density-of-states; note
that no defect levels are incorporated. Additionally, the conduction
bandtail in this model is sufficiently narrow that it is unimportant
near room-temperature; only the conduction band "effective
density-of-states" *N~C~* has a noticeable effect on the solar cell
parameters, and even this effect is weak.

The relative simplicity of the proposed model is certainly refreshing,
and we decided to make a more stringent comparison of cell properties
with this model's predictions. As experts will no doubt recognize,
graphs of power vs. thickness such as we did for Fig. 1 depend heavily
upon optical properties, and one doesn't know for sure that mistakes in
estimating optical effects are not being cancelled by mistakes in
estimating electronic properties. For this purpose we wanted to obtain a
set of cell measurements using intense, near-infrared, monochromatic
laser illumination that was uniformly absorbed in the cell. Under
white-light illumination, a good deal of the power generated by a
single-junction cell is due to strongly absorbed illumination; models
for such cells are quite sensitive to the absorption spectrum of the
intrinsic and p-layers, but are less sensitive to transport and
recombination properties of the intrinsic layer than are measurements
with uniformly absorbed illuminatin.

Baojie Yan and Jeff Yang of United Solar Ovonic LLC agreed to
collaborate on these experiments, and sent us a series of samples with
thickness varying from 200 nm to 900 nm. AM1.5 measurements were done at
United Solar before the samples were sent to Syracuse. At Syracuse, we
have done intensity-dependent cell measurements using illumination from
a 685 nm laser (absorption length about 1500 nm). The model calculations
used the AMPS-PC engine developed by Steve Fonash's group at Penn State
University; we used exactly the same electronic modeling parameters that
we proposed previously \[Error: Reference source not found\].
Temperature-dependent measurements are underway as well, but will not be
reported here.

In Fig. 3 we show quantum efficiency measurements as a function of
*i*-layer thickness (ie. the short-circuit (particle) photocurrent
density *J~sc~*/*e* normalized by the incident photon flux *F*). The
laser wavelength  = 685 nm). The solid lines are the results of
"bandtail only" simulation. The simulations indicate that, for the
lowest flux *F* = 610^13^ cm^-2^s^-1^, *J~sc~* corresponds well to the
integrated absorption of photons throughout the intrinsic-layer. The
curvature noticeable for larger thicknesses is the effect of the finite
absorption coefficient  = 6.210^3^ cm^‑1^. As the flux is further
increased (a few hundred times), there is a small additional decrease in
the quantum efficiency for the thickest samples. This effect is due to
recombination inside the *i*-layer, and is consistent with the poor
fill-factors we measured (and predicted) for these thicker samples at
large flux.

In Fig. 4 we have graphed the fill-factor and open-circuit voltage
measurements (symbols) and simulations (solid lines) as a function of
the incident photon flux. For the fill-factors, results are shown for
four different cell thicknesses. We have not shown fill-factor results
for the thickest sample; although this sample was only slightly thicker
than the thickest one in the illustration, it had a markedly lower
fill-factor, and was plainly below the trend of the thickness series. We
have shown only a single sample to illustrate the intensity-dependence
of the open-circuit voltage *V~OC~*; the *V~OC~* measurements have very
little dependence on thickness, and for simplicity, we have shown these
results separately in Fig. 5.

For the higher intensities, the fill-factor declines markedly with
thickness (from 0.76 to less than 0.4). The decline corresponds fairly
accurately with the results of the simulations, and we are therefore
fairly confident in the following qualitative explanation for the effect
of thickness \[[^3]\]. We start with the fact that holes have far
smaller drift-mobilities than electrons; it thus takes much longer
(following their photogeneration) for them to drift to the *p/*i
interface than it takes for electrons to drift to the *n/i* interface.
However, for thin cells, the internal electric field remains fairly
large throughout the cell (even under maximum power conditions and at
larger intensities). Even holes that are photogenerated close to the
*n/i* interface are rapidly collected -- both because of the larger
internal field, and because of the relatively small distance between the
*n/i* and the *p/i* interfaces. It is worth noting that the model
predicts slightly larger fill-factors for thin cells than we measured;
we don't know the reason for this (small) discrepancy.

For thicker cells, the internal electric field no longer extends across
the cell, and some holes photogenerated in the "back" of the cell (ie.
closer to the *n/i* interface) are lost to recombination. This
"collapse" of the field \[[^4]\] is just a consequence of the buildup of
slowly-moving, positively charged holes near the *p/i* interface. We
gain some confidence in this view because we find that reducing the
incident flux by a couple of orders of magnitude noticeably improves the
fill-factor. The qualitative explanation for this effect is that, for
lower incident flux, there are fewer drifting holes, and less positive
space-charge to collapse the voltage. The simulations agree fairly well
with the measurements for fluxes in the range 10^15^ -- 10^17^.

For lower flux (less than 10^15^ cm^-2^s^-1^), the measured fill-factors
become smaller; this is counter to the trend at high intensities, where
the fill-factor decreases with increasing intensity. Furthermore, there
is little difference in fill-factor for varying thickness. We do not
presently have a successful model for these low-flux effects.

The bottom panel of Fig. 4 shows the intensity-dependence of the
open-circuit voltage *V~OC~*. The "bandtail only" model provides a good
description of the measurements down to a flux of about 10^15^
cm^-2^s^-1^; this is essentially the same range over which the model
describes the fill-factor. The corresponding photogeneration rates range
from 5x10^18^ to 5x10^20^ cm^-3^s^-1^. For lower intensities, the
bandtail model deviates markedly from the measurements. Previous work by
the Penn State group has shown that this low-intensity region is quite
strongly affected by light-soaking \[[^5]\]; we presume that a full
description of the solar cell behavior will require the addition of
defects to the present "bandtail only" model.

In Fig. 5, we show the thickness-dependence of the open-circuit voltage
*V~OC~* at several flux levels. *V~OC~* is nearly independent of
thickness; this essential result also emerges from the bandtail-only
simulations, although there are some subtle differences in the
behaviors. For thicker samples, it is relatively easy to understand
thickness-independence in terms of a "quasi-Fermi level" model \[Error:
Reference source not found,[^6]\]. In this model, the center region of
the intrinsic layer has no drift or diffusion currents; the center
region is essentially a neutral photoconductor with distinct electron
and hole quasi-Fermi levels *E~Fn~* and *E~Fp~*, respectively. The
sample zones near the *p/i* interface essentially acts as an electrode
to measure the hole quasi-Fermi level of the middle, and the *n/i*
interface serves the same role for the electron quasi-Fermi level.

### Work in Progress & Future Plans

For the moment, let us accept the validity of the basic idea proposed
here: that hole drift mobilities and valence bandtails are the main
elements determining the solar conversion efficiency of a-Si:H based
solar cells in their a-deposited state. It is also plain that the
conversion efficiency in the light-soaked state is markedly reduced from
the as-deposited state, and an understanding of the light-soaked state
is the ultimate goal for this research.

The role of the present work is to give a solid foundation for exploring
the light-soaked state. In the third phase of this project we are making
measurements on the same series of solar cells in various states of
light-soaking. Surprisingly (to us), we are unaware of any comparable
series of published measurements.

We presume that we shall need to incorporate a density of dangling bonds
that grows with light-soaking in order to account for the decline in
conversion efficiency. We also presume that as-deposited defects will be
required to accommodate the low-intensity measurements we have already
made. In the spirit of the "bandtail-only" model, we shall be seeking a
model with the bare minimum of additional complexity.

## Hole Drift-Mobility Measurements and Multiple-Trapping in Microcrystalline Silicon

### Introduction

There have been several reports of drift-mobility measurements
\[[^7],[^8],[^9],[^10]\] in microcrystalline silicon in the last decade
or so since it became clear that this material could be prepared with
properties that are interesting for solar cells \[[^11]\]. There is, of
course, an enormous range of possible structures in microcrystalline
silicon materials. For each sample there is a spectrum of sizes for the
component nano & microcrystallites. Even more poorly understood, for
each sample there is also a jumble of non-crystalline material that lies
between the crystallites. Unsurprisingly, there has also been a very
large spread in reported drift mobilities and transport properties.

In this paper we shall first summarize our recent hole drift-mobility
measurements in a particular form of microcrystalline silicon that has
been developed at Forschungszentrum Jülich as a solar cell absorber, and
for which cells with 8.7% conversion efficiency have been reported
\[[^12]\]. We shall not offer a detailed defense of the measurements
here, nor shall we offer an extended review and comparison with previous
work on microcrystalline silicon; these will be presented elsewhere.
Instead, we emphasize an unexpected aspect of the present measurements,
which is that they exhibit the features of "exponential bandtail
multiple-trapping."

Since its first successful application to amorphous semiconductors in
the early 1980's (see Tiedje's review \[[^13]\]), exponential-bandtail
multiple-trapping (usually abbreviated as simply "multiple-trapping" or
"MT") has become the standard approach to analyzing most transport
experiments in hydrogenated amorphous silicon (a-Si:H) and related
materials such as amorphous silicon-germanium alloys. The model assumes
an exponential bandtail of localized states lying at the bottom of the
conduction band, or at the top of the valence band. The application to
transport also assumes the existence of a "transport edge," with the
property that the only carriers that contribute to electrical transport
are those occupying electronic states lying above this edge (for
electrons) or below it (for holes); it has generally been assumed that
this edge is the "mobility-edge" dividing localized and extended
electronic states.

In the present work we have found that multiple-trapping obtains for our
measurements in a predominantly crystalline form of microcrystalline
silicon. This form of microcrystalline silicon is apparently a far more
ordered material than amorphous silicon, and certainly X-ray
measurements, Raman scattering, and direct microscopy indicate that most
of the volume is associated with small crystallites. One is naturally
drawn to models for electrical transport that are based on the
effective-mass theory, which would seem to apply at least within a
crystallite. Indeed this approach has been applied recently to Hall
mobility measurements in *n*‑type microcrystalline silicon \[[^14]\]. It
is thus a bit of a shock to discover that the multiple-trapping model
taken from amorphous semiconductors is a better description of
microcrystalline silicon than is an effective-mass based approach -- but
this is the implication of our measurements. The multiple-trapping
parameters in the microcrystalline material do differ in interesting
ways from those that have been reported for a-Si:H, and we shall return
to this comparison in the concluding section of this paper.

### Samples

  --------------------- ------------------------ ------------------------
  Table I: Sample                                
  Properties                                     

  *Sample*              *Raman Ratio I~C~^RS^*   *i-layer thickness* *d*
                                                 (m)

  B  (02B338)           0.71                     4.0

  D (03C245)            0.60                     3.4

  E  (03C255)           0.61                     4.3
  --------------------- ------------------------ ------------------------

The samples used for our measurements were *pin* structures prepared in
designated chambers of a multi-chamber system using plasma-enhanced
chemical vapor deposition at frequencies of 95MHz (VHF-PECVD) \[Error:
Reference source not found\]. We used ZnO coated glass as a transparent,
conductive substrate. The µc-Si:H(B) *p*-layers are about 20nm thick;
the films were doped by adding trimethylboron to the silane-hydrogen gas
mixture. The intrinsic µc-Si:H layers were prepared using a
silane-hydrogen mixture of 5-6%. The n-layer (phosphine doped) was an
amorphous a-Si:H(P) layer 30 nm thick. As top contacts we used sputtered
ZnO dots with diameters of 1-2 mm; we plasma-etched (SF~6~-gas process)
the top surface of these structures to remove the n-layer from regions
not under the ZnO.

In this paper we present measurements on three samples summarized in
Table I. To determine the extent of crystallinity, Raman spectra were
recorded from the i-layer at spots right next to the ZnO contacts. The
integrated intensity ratio I~C~^RS^ =I~C~/(I~A~+I~C~) was determined by
deconvoluting the spectra into three signal peaks at 480 cm^-1^,
500 cm^-1^ and 520 cm^‑1^. The first one can be attributed to a
disordered structure like an amorphous phase or grain boundaries (I~A~),
and the latter two are attributed to the crystalline phase (I~C~)
\[[^15]\].

### Drift-Mobilities

The transient photocurrents were measured in the *pin* diodes following
illumination by a 3 ns laser pulse (wavelength *λ* = 500 nm) through the
*n*-layer. The photocurrent transients were consistent with a
conventional interpretation in terms of hole time-of-flight. In
particular, the photocharge was independent of the applied voltage, and
a transit-time was discernible in the transient. Additionally, the
photocurrent at short times was linear in the applied voltage, which is
consistent with transport that is linear with electric field.

In Fig. 6 we present our temperature-dependence measurements of the hole
drift-mobility for 3 samples \[[^16]\] corresponding to a particular
"displacement/field" ratio *d^2^*/2*V* = 7x10^-8^ cm^2^/V of sample
thickness *d* and applied field (*V/d*). The activation energy (0.13 eV)
is illustrative only, and does not indicate any particular depth for the
bandtail traps. These average drift-mobilities, determined using
*µ~D~* = *d*^2^/(*Vt*), are much larger than typically obtained in
a-Si:H \[[^17]\], although a direct experimental comparison at the same
value for *d^2^*/*V* is not possible. We compare multiple trapping
fitting parameters shortly.

### Multiple-Trapping Fits

Our procedure for fitting to the multiple-trapping model starts with the
transient photocharge *Q*(*t*) (the time-integral of the photocurrent
*i*(*t*)). In particular, we fit to the time-dependence of the
normalized photocharge$Q(t)d^{2}/Q_{0}\left( V + V_{\text{bi}} \right)$,
where *Q*~0~ is the total photocharge of holes generated by the laser
pulse, *V* is the bias voltage, *d* is the *i*-layer thickness, and
*V~bi~* is a correction for the internal field. We have illustrated the
photocharge measurements in Fig. 2 for seven temperatures. For clarity,
we have removed sections of the transient for *Q*(*t*) \> *Q*~0~/2;
these portions of the transient are past the "transit time," and are not
used in our multiple-trapping fitting procedure. We have also removed
early-time portions of the transients that are clearly dominated by
response-times of the measurement.

The solid lines in Fig. 7 are the multiple-trapping fittings. The actual
equation that was fitted to the normalized photocharge is \[Error:
Reference source not found\]:

$L\frac{(t)}{E} = K\left( \mu_{0}\nu \right)(\nu t)^{\alpha(T)}$. (1)\
*L*(*t*) is the mean displacement for photocarriers after a delay time
*t* and with electric field *E*. The dispersion
parameter$\alpha = \text{kT}/{\Delta E}_{V}$, where *E~V~* is the width
of the exponential, valence bandtail, ~0~ is the valence band-mobility,
and is an "attempt-to-escape" frequency characterizing the rate of
release of holes from the bandtail traps. The
constant$K = \text{sin}\left( \text{απ} \right)/\left( \text{απ}(1 - \alpha) \right)$
is of order unity. The multiple-trapping parameters we chose (and that
are the basis for the solid lines shown in Fig. 2) are given in Table II
below, along with some results for a-Si:H \[Error: Reference source not
found,[^18]\].

  ------------------------------------- ------------- ----------- -----------
  Table II: Multiple-trapping fitting                             
  parameters                                                      

  *Multiple-trapping parameter*         *c-Si:H\      *a-Si:H\    *a-Si:H\
                                        *(this work)  *(ref.      *(ref.
                                                      Error:      Error:
                                                      Reference   Reference
                                                      source not  source not
                                                      found)      found)

  Valence band-mobility ~0~ (cm^2^/Vs)  1.0           0.7         0.3

  Bandtail width *E~V~* (meV)           31            45          48

  Attempt-frequency (s^-1^)             9x10^8^       1x10^12^    8x10^10^
  ------------------------------------- ------------- ----------- -----------

### Meaning of Multiple Trapping in microcrystalline silicon

One approach to analyzing mobilities in polycrystalline materials is to
invoke the effective masses that would obtain for electrons and holes in
the single crystal, and assume that the grain boundaries act as
scatterers or barriers and as the locus for traps for the carriers
\[Error: Reference source not found\]. It is instructive to use this
approach crudely to calculate an "effective-mass carrier mobility" for
holes $\mu_{h}^{e\text{.}m\text{.}}$ utilizing the expression
$\mu_{h}^{e\text{.}m\text{.}} = v_{\text{th}}l/\left( \text{kT}/e \right)$,
where *v~th~* is the "thermal velocity" for holes (about 10^7^ cm/s in
c‑Si near room-temperature) \[[^19]\] and *l* is a scattering length. If
the scattering length is identified with a typical crystallite size of 3
nm, we infer $\mu_{h}^{e\text{.}m\text{.}} = \text{120}$cm^2^/Vs, or
about 100 times larger than the estimate in Table I. The effects of
traps and barriers seem unlikely to explain the discrepancy for our
samples, since these were already (implicitly) incorporated in the
analysis that led to the estimate ~0~ = 1 cm^2^/Vs.

We suggest that, for our samples of microcrystalline silicon, the
disorder is sufficient to strongly alter the bandedge states from their
crystalline counterparts. In particular, we suggest that the bandedge
states of the crystal have been transformed into a bandtail (ie. that
the density-of-states *g*(*E*) has been altered), and that a
*mobility-edge* has formed within the bandtail \[[^20]\] (ie. states
lying deeper in the energy gap are localized).

The mobility-edge has been widely applied to amorphous semiconductors
\[Error: Reference source not found,[^21]\], and has recently been
applied to microcrystalline samples with a larger fraction of amorphous
"tissue" \[[^22]\]. Here we are suggesting that it be applied to samples
that are predominantly crystalline. In the mobility-edge model, hole
states with energy levels below the mobility-edge (*E \< E~V~*) are
completely delocalized (by definition), although with very different
wavefunctions than the effective-mass states of crystals. Hole states
lying above the mobility-edge (*E \> E~V~*) are localized. Both
analytical and computational studies of mobility-edges \[[^23],[^24]\]
indicate that the localization radius for a hole state grows very
rapidly, and may even diverge, as the state's energy approaches the
mobility-edge. It isn't clear theoretically how particular atomic-scale
features such as "strained bonds" are incorporated into the bandtail
states.

With this perspective, we first discuss the bandtail width *E~v~*. The
estimate of 31 meV for the microcrystalline material seems unremarkable
in the context of work on holes in amorphous silicon, which yield values
in the range 40 -- 50 meV. It is worth noting that disorder affects
holes and electrons very differently. The conduction bandtail in
amorphous silicon has a width around 22 meV \[Error: Reference source
not found,Error: Reference source not found\]. Electron properties in
samples quite similar to the present ones have been studied using
post-transit time-of-flight \[Error: Reference source not found\];
bandtail multiple-trapping did not apply for these transients. An
interesting possibility is therefore that electron transport may be
governed by effective masses in exactly the same material for which
holes require a mobility-edge approach.

The fact that the hole band-mobility ~0~ is about the same in the
present microcrystalline samples and in amorphous silicon seems to
support the mobility-edge interpretation, and more broadly suggests that
a value near 1 cm^2^/Vs may be a universal property of a mobility edge.
Such "universality" is also suggested by the fact that electron
band-mobilities in amorphous silicon are also around 1 cm^2^/Vs \[Error:
Reference source not found,Error: Reference source not found\].
Interestingly, a band mobility of 1 cm^2^/Vs is *not* an obvious
implication of the existing theoretical treatments of mobility-edges.

Finally, we turn to the attempt-frequency . It is quite interesting that
the value for microcrystalline silicon is substantially (about 100
times) smaller than the lower values reported for a-Si:H. However, even
for a-Si:H, there is no well-accepted physical interpretation for this
parameter. One often-mentioned interpretation is that be identified as a
"typical phonon frequency," but this association fails to explain either
the very low magnitudes or the enormous range of magnitudes that have
been reported experimentally \[[^25]\]. Yelon and Movaghar have
suggested that multi-phonon effects lead to the variations, and this
perspective has been applied by Chen, *et al.*, to drift-mobility
measurements \[[^26]\]. Another possibility originating with high-field
drift-mobility measurements in a-Si:H has been that reflects the
bandedge density-of-states *g*(*E~V~*) \[[^27]\], which suggests that
the present measurements be interpreted as indicating a substantially
lower value for *g*(*E~V~*) in microcrystalline than in amorphous
silicon. Plainly, we need more clues from experiment about the meaning
of this parameter; it seems possible that its dramatic lowering in
microcrystalline silicon could be providing it.

## Polyaniline/Si heterojunction diode

### Experimental details

We have fabricated a simple device by spin coating a layer of conductive
polyaniline onto a silicon substrate \[[^28]\]. Two kinds of silicon
substrates were used in this experiment: (i) n-type, orientation (100),
R=2 Ωcm and (ii) n-type, orientation (111), R\>3000 Ωcm. We evaporated a
large area, 50 nm thick aluminum contact to the back (unpolished) side
of the wafer. Immediately before the polymer film was applied, the
silicon wafers were etched in a 2.5% HF solution.

The polyaniline base was obtained from Sigma-Aldrich Company. The
solvent is dichloroacetic acid (DCA); the dopant is
2-acrylamido-2-methyl-1-propanesulphonic acid (AMPSA). The polyaniline
solution was made following the procedure of P. N. Adams et al
\[[^29]\]. The area of the a spin-cast doped polyaniline film was around
0.5 cm^2^. The films were annealed in air at 80 C for 24 hours after
casting. A circular, gold contact (50 nm thick) was then evaporated onto
the polyaniline film. The polyaniline films were typically 5 μm thick;
the resistivity of the doped films was about 10^-1 ^ Ωcm.

The current-voltage characteristics were measured at room temperature
with a Keithley 2400 source meter.

### Results and discussion

Fig. 8 shows two *I-V* curves for two different diodes from the same
batch, using the 2 Ωcm substrate. The *I-V* curves are highly
asymmetrical as expected for a *pn* heterostructure device; the
reproducibility is fairly good. Fig. 9 illustrates the *I-V* curves
observed in one diode at several times up to about 2 weeks after its
fabrication; the diode was stored in a dessicator when not under study.
Interestingly, the diode's forward bias current first increases, and
then recovers to nearly the initial state. We don't understand the
origin of these effects; both room-temperature curing of the polymer and
also room-temperature changes at the polymer-Si interface may be
envisioned. Aging effects have been noted for polyaniline/c-Si diodes in
previous work.\[[^30]\]

Fig. 10 illustrates the effect of changing the c-Si substrate doping
level. We presume that the higher resistance of the 3000 Ωcm substrate
affected the diode principally via the series resistance of the
substrate; obviously, this effect is modest.

We did explore the fitting of the standard diode equation to these *I-V*
curves. If the standard diode characteristic\
$I = I_{0}\text{exp}\left( \left( q/\text{nkT} \right)\left( V - \text{IR}_{S} \right) \right)$\
applies, where *q* is the electronic charge, *n* is the ideality factor,
and *R~S~* is the series resistance, then we should obtain a straight
line by a graph of *I*\*(*dV/dI*) vs *I*:

$$I\left( \text{dV}\text{dI} \right) = \text{nkT}/q + \text{IR}_{s}$$

The fit to this form for the 2 Ωcm substrate for lower currents (\< 10
mA) yielded *n*= 1.8, *R* = 49 Ω; the fit for the 3000 Ωcm yielded
n = 1.8, *R = *77 Ω.

We prepared two diodes with varying polyaniline thickness on the 2 Ωcm
substrate; the results are illustrated in Fig. 11. The illuminator was a
type ENH (250 W) tungsten-halogen bulb; the diode was illuminated
through the polyaniline. The dark currents are fairly similar; there is
slightly less dark current for the thicker diode. It is fairly evident
that these diodes suffered from significant series resistance (about 100
Ohms). Under illumination, both diodes show a saturated reverse-bias
current. It surprised us that the diode with the thicker polyaniline
film has a larger saturation current. Although we have not yet conducted
a serious analysis of these diode properties, we presume that
photocarriers generated throughout most of the polyaniline should not
contribute to the saturation current, and indeed the thicker film might
have optically filtered some of the photons. It may be that the
polyaniline film has somewhat different properties for the two
thicknesses, at least near the c-Si interface. The open-circuit voltage
for the diodes is about 0.4 V.

Two diodes were made from two different silicon substrate (as described
earlier). The polyaniline thickness of both diodes was 5 μm. The *I-V*
characteristics of the two diodes under illumination are shown is Fig.
12. We can see that the *I-V* characteristics of the two diodes are
quite different. Under forward bias, the principal effect appears to be
that the high resistivity substrate led to a significant series
resistance. Interestingly, under reverse bias the high resistivity
substrate shows a substantially larger reverse bias current. This
presumably corresponds to an increased diffusion length in the higher
resistivity substrate.

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