Light-Soaking Effects on the Open-Circuit Voltage of a-Si:H Solar Cells

Jianjun Liang,^1^ E. A. Schiff,^1^ S. Guha,^2^ B. Yan,^2^ and J. Yang^2^

^1^Department of Physics, Syracuse University, Syracuse, NY 13244-1130
USA

^2^United Solar Ovonic Corp., Troy, MI 48084 USA

# ABSTRACT

We present measurements on the decline of the open-circuit voltage
*V~OC~* in a-Si:H solar cells during extended illumination
(light-soaking). We used a near-infrared laser that was nearly uniformly
absorbed in the intrinsic layer of the cell. At the highest
photogeneration rate (about 2x10^21^ cm^-3^), a noticeable decline (0.01
V) occurred within about 10 minutes; *V~OC~* stabilized at 0.04 V below
its initial value after about 200 hours. We found that both the kinetics
and the magnitudes of *V~OC~* are reasonably consistent with the
predictions of a calculation combining a bandtail+defect picture for
recombination and a hydrogen-collision model for defect generation. The
version of the hydrogen-collision model that we used assumes that only
bandtail recombination drives the hydrogen collision processes. Within
this picture, the crossover between bandtail and defect recombination
occurs on the same timescale as the "light-induced annealing" process
that accounts for stabilization of the optoelectronic properties for
long light-soaking times.

# INTRODUCTION

The metastable degradation of the optoelectronic properties of a-Si:H
has been actively studied for more than 25 years. Important progress has
been made by many researchers, but a fully satisfactory picture for the
effect has never emerged. The difficulty of the metastability problem
may, at least in part, be ascribed to the fact that there are probably
two difficult, linked problems that must be understood simultaneously.
First, it is likely that photocarrier recombination drives
metastability, but - even in a single state of an a-Si:H sample - no
consensus viewpoint on these recombination processes has emerged.
Second, even if one accepts the role of recombination in mediating
metastability, there is no consensus viewpoint about how recombination
leads to metastable defect generation (or other metastabilities).

The present paper exploits the close connection between the open-circuit
voltage *V~OC~* measured in an *nip* solar cell and photocarrier
recombination in the bulk, intrinsic-layer material. In particular we
report a series of measurements of the time-dependence of *V~OC~* in
United Solar cells under near-solar illumination. In recent work
\[[^1]\] we reported the temperature-dependence of *V~OC~* at solar
illumination intensities. We concluded from these studies that, for
their as-deposited state, the recombination traffic in our samples
flowed predominantly through the valence bandtail states. For the
stabilized, light-soaked state recombination traffic appears to be split
fairly evenly between the valence bandtail and defects. We emphasize
that these conclusions apply to our materials, under near-solar
illumination, and near room-temperature; these are, of course, the
conditions of greatest practical significance for solar cells.

Using this recombination model as the starting point, we report here
that we are able to account for the time-dependent decay of *V~OC~*
using a straightforward extension of the hydrogen-collision model
\[[^2]\] for defect generation; the extension assumes that mobile
hydrogen is generated by bandtail recombination. For our materials, we
can also exclude the best known alternative model \[[^3]\].

There is at least one implications of this perspective on metastability
that deserves further investigation. It appears that there is a
coincidence of the time-scales at which crossover between bandtail and
defect recombination occurs, and at which a stabilized state of the
sample is achieved. The coincidence suggests that defect recombination
may mediate light-induced annealing.

# Measurements

For these experiments, six depositions of *nip* solar cells on stainless
steel substrates were done at United Solar Ovonic Corp.. The *n* and *p*
layers were the same in all depositions; the deposition time for the
intrinsic layer was chosen to give intrinsic layer thicknesses from 185
nm to 893 nm. The cells were not optimized for solar conversion
efficiency, but the individual layers are comparable to those used in
high-efficiency cells. Details of the deposition procedures have been
given elsewhere \[[^4]\]. As-deposited properties of the cells were
measured under a solar simulator. This paper emphasizes results for the
thickest cells, for which the white-light *V~OC~* averaged 0.98 V and
the white-light fill factors averaged 0.66.

Further studies were done using a 30 mW, 685 nm wavelength near-infrared
laser. We chose to use this laser because its wavelength is absorbed
fairly uniformly throughout the intrinsic layer of the cells, which
substantially simplifies modeling of the measurements. We were able to
achieve photocurrent densities in the cells that were comparable to
solar illumination.

Measurements of the decline of the open-circuit voltage *V~OC~* are
presented in Fig. 1. The different symbols indicate measurements for
four different laser intensities. We used four different cells on the
same substrate for these measurements; the cells had very similar
initial properties under white-light. The average photogeneration rates
*G* for each experiment are indicated in the figure; these were
calculated from the measured photocurrent density *J~p~* at *V~r~* = ‑2
V using the expression $G = J_{p}\left( - V_{r} \right)/\text{ed}$,
where *e* is the electronic charge and *d* is the thickness of the
intrinsic layer. The measurements for the highest intensity are most
comparable to solar illumination (saturated photocurrent density was 18
mA/cm^2^ with the laser, and about 15 mA/cm^2^ with the solar
simulator). We monitored the sample temperature during these
measurements, which was maintained at 294.5 K to within better than 0.1
K.

An interesting feature of the measurements is that the onset of
degradation occurs for later times at lower photogeneration rates. If we
define an "onset time" when *V~OC~* has declined by 0.01 V, it is
evident in Fig. 1 that this onset time increases by more than 1000 over
the range of photogeneration rates in the figure. For the largest
photogeneration rate it appears that *V~OC~* is approaching a saturation
value within this time window; saturation at longer times is fairly
well-established in earlier work on solar cell parameters, defect
density, and other optoelectronic properties of a-Si:H.

# A Modified H-Collision Model

In another paper \[Error: Reference source not found\] we presented
temperature-dependent measurements on the open-circuit voltage for
a-Si:H in its light-soaked and as-deposited states. These measurements
are consistent with the model that, for the as-deposited states of
a-Si:H, the photocarrier recombination traffic is predominantly through
the valence bandtail (through the process of electron capture by a
bandtail-trapped hole). Light-soaking then has a surprisingly modest
effect: the defect-density rises until recombination traffic is fairly
evenly split between the bandtails and the defects.

One important fact that has been established in several light-soaking
experiments \[Error: Reference source not found,[^5],[^6],[^7]\] is that
the defect increases as about the 1/3 power of the light-soaking time:
$N_{d} \propto t^{1/3}$ essentially from the onset of illumination until
a saturated state is achieved. The original "SJT" explanation \[Error:
Reference source not found\] for the *t*^1/3^ form assumed that
recombination traffic through the bandtails *R~t~* generated defects:

$\frac{\text{dN}_{d}}{\text{dt}} \propto R_{t}$ . (1)\
The *t*^1/3^ form then emerged from a particular recombination model
based on the assumption that most recombination traffic went through
defects. The particular model that was proposed had the property that
the fraction of the recombination traffic through the tails obeyed:\
$R_{t}/G \propto 1/N_{d}^{2}$, (SJT recombination) (2)\
where *G* is the carrier photogeneration rate and *N~d~* is the density
of defects. With this assumption, one obtains the form usually found by
experiment:

$N_{d}(t,G) = 3C_{\text{SW}}G^{2/3}t^{1/3}$ . (3)

The assumed recombination model appears to be inconsistent with the
*V~OC~*(*T*) measurements, in particular in its assumption that the
defect recombination traffic *R~d~* is predominant (i.e. that
$R_{d} \approx G$), and thus is unlikely to be the correct explanation
for the empirical form (2). The principal alternative to this model is
the "hydrogen-collision" model \[Error: Reference source not found\],
which assumes the existence of a mobile hydrogen density *H~m~*
obeying:\
$H_{m} \propto G_{H}/N_{d}$, (4)\
where *G~H~* is the rate at which light generates mobile hydrogen. A
mobile hydrogen is assumed to recombine by attaching itself to the
density of dangling bond defects *N~d~*. The rate at which new defects
are generated obeys the "hydrogen-collision" proportionality:\
$\frac{\text{dN}_{d}}{\text{dt}} \propto H_{m}^{2}$ .
(hydrogen-collision) (5)\
The empirical "*t*^1/3^" form (2) obtains if we assume that
$G_{H} \propto G$.

An interesting alternative to the assumption $G_{H} \propto G$ is
$G_{H} \propto R_{t}$. It has often been noted that the large energies
dissipated by bandtail recombination of photocarriers make it attractive
as an originating event for defect metastability; the energy dissipated
is nearly equal to the bandgap *E~G~*, and is certainly larger than
dissipation from recombination through defect levels lying near the
center of the gap. One might envision that tail-state recombination
might occasionally lead to a peculiar "hydrogen-Auger" process that
liberates hydrogen from a nearby, saturated dangling bond. However, the
$G_{H} \propto R_{t}$model looks undesirable if one assumes that the SJT
recombination model $R_{t}/G \propto 1/N_{d}$is valid. It leads to the
behavior $N_{d} \propto t^{1/5}$, and is thus largely excluded by
experiment.

Our measurements of the temperature-dependence of the open-circuit
voltage experiments have led us to suggest that $R_{t}/G$ is of order
unity through most of the light-soaking process, which suggests that we
reconsider the following, alternative version of the hydrogen-collision
equations:\
$\frac{\text{dN}_{d}}{\text{dt}} \propto H_{m}^{2} \propto \left( \frac{G_{H}}{N_{d}} \right)^{2} \propto \left( \frac{R_{t}}{N_{d}} \right)^{2}$
,\
or, collecting several proportionality constants together as *C~SW~*:\
$\frac{\text{dN}_{d}}{\text{dt}} = C_{\text{SW}}\left( \frac{R_{t}\left( N_{d} \right)}{N_{d}} \right)^{2}$
(modified H-collision) (6)\
We have indicated that *R~t~* depends upon the defect density; of
course, for *R~t~* = *G* the usual behavior of equation (3) obtains.

# Bandtail+Defect Calculations

In another paper we present the parameters and procedures of a
"bandtail+defect" calculation of the open-circuit voltage; the
calculation used the AMPS-1D computer program (©Pennsylvania State
University). In Fig. 1 we have presented (as the four lines) the
corresponding calculations for *V~OC~*(*t*) based on eq. (6), and using
the value *C~SW~* = 10^1^ cm^-3^s that is typical of direct studies of
the defect generation during light-soaking \[Error: Reference source not
found,Error: Reference source not found\]. We first used the
bandtail+defect calculation to obtain the dependence of the bandtail
recombination rate *R~t~* upon the defect density *N~d~*; we assumed a
spatially uniform density *N~d~*. The results are illustrated in Fig. 2
(lower panel). We then used this function *R~t~*(*N~d~*) to numerically
integrate eq. (6) to obtain *N~d~*(*t*); note that eq. (6) implies that
defect generation depends upon the square of *R~t~*. The bandtail+defect
calculation also yields *V~OC~* as a function of *N~d~* (upper panel of
Fig. 2), from which we finally obtained *V~OC~*(*t*).

Experimentally, *V~OC~* only declines about 0.04 V (to the value denoted
"measured saturation"). Fig. 2 indicates that this decline corresponds
to a fairly small difference between *R~T~* and *G.* For the four
intensities, the agreement between the experimental measurements and the
calculations is fairly good through the initial stages of the decay of
*V~OC~*. For longer times the measured values for *V~OC~* fall much more
slowly than predicted by eq. (6), which undoubtedly corresponds to the
onset of the "light-induced" annealing effects reported previously for
defect-density measurements \[[^8]\].

For our experiments, we used laser illumination that was nearly
uniformly absorbed; this choice was part of an effort to simplify
modeling and to avoid a non-uniform density of defects. Nonetheless, our
assumption of a spatially uniform value for *N~d~* as it grew under
light-soaking was not self-consistent with the spatial profiles of
*R~t~* that were calculated. For the larger values of the density
*N~d~*, the bandtail recombination traffic was reduced in a zone about
100-200 nm from the *p/i* interface compared to values in the middle of
the cell. We used *R~t~* values from the middle to do the numerical
integration of eq. (6). For full self-consistency we would have needed
to allow for a profile of *N~d~*. The profile would have a reduced
density of defects as the *p/i* interface was approached from the
middle. A rough analysis indicates that inclusion of this effect would
improve the agreement between the calculations and the measurements
slightly, but we have not pursued non-uniform distributions for *N~d~*
further.

# Discussion

As noted earlier, the modified H‑collision model, in conjunctionwith the
bandtail+defect recombination model, predicts some deviations from the
*t*^1/3^ form for the dependence of the defect density upon the
light-soaking time. We did not do simultaneous measurements of the
defect density during light-soaking of the present solar cells. In Fig.
3 we show the predictions of the defect density from numerical
integration of eq. (6) that corresponds to the highest photogeneration
rate we used for experiments.

The calculations show the expected *t*^1/3^ form for the earlier times.
There is a softening that occurs around 10 hours, which corresponds well
to a change in the recombination mechanism. For lower defect density,
the majority of the recombination traffic goes through the bandtail; for
larger densities, the majority goes through defects. A *t*^1/5^ form is
a good fit at longer times. Experimentally, after about 10 hours *V~OC~*
begins to show saturation behavior (cf. Fig. 1), which we attribute to
some "light-induced annealing" process. At least for the present
samples, it appears that the long-time saturation effect would obscure
direct observation of the *t*^1/5^ regime.

It is an interesting coincidence that the crossover time between the two
recombination regimes and the time at which light-induced annealing sets
in are so similar in the present sample. This apparent coincidence is
the reason offered by the present viewpoint for the fact that
open-circuit voltages decline only modestly during light soaking
(roughly by the thermal voltage *k~B~T*/*e* = 0.025 V), as well as for
the fact that most direct experiments on the kinetics of the defect
density are reasonably consistent with the *t*^1/3^ form.

It is unlikely that two entirely independent processes would appear on
the same timescale. We therefore speculate that the mechanism underlying
light-induced annealing is photocarrier recombination through defects.

This work has been supported through the Thin Film Photovoltaics
Partnership of the National Renewable Energy Laboratory (NDJ-2-30630-24
at Syracuse and ZDJ-2-30630-19 at United Solar).

[^1]: J. Liang, E. A. Schiff, S. Guha, B. Yan, and J. Yang, in P. C.
    Taylor, *et al.*, ed. *Amorphous and Nanocrystalline Silicon
    Technology -- 2005* (Mater. Res. Soc. Symp. Proc. Vol. ), *in
    press.*

[^2]: H. M. Branz, *Phys. Rev. B* **l59,** 5498 (1999).

[^3]: M. Stutzmann, W. B. Jackson, and C. C. Tsai, *Phys. Rev. B*
    **32**, 23 (1985).

[^4]: J. Yang, A. Banerjee, and S. Guha, *Appl. Phys. Lett.* **70**,
    2975 (1997).

[^5]: H. Park, J. Liu, and S. Wagner, *Appl. Phys. Lett.* **55**, 2658
    (1989).

[^6]: T. Unold, J. Hautala, and J. D. Cohen, *Phys. Rev. B* **50**,
    16985 (1994).

[^7]: P. Stradins, unpublished.

[^8]: H. Gleskova and S. Wagner, *Appl. Phys. Lett.* (1993).