# Investigation of low band gap silicon alloy thin film solar cell for
improving short and long wavelength response

S. M. Iftiquar, J. Yi  College of information and Communications Engineering,
Sunkyunkwan University, Suwon, South Korea<EMAIL_ADDRESS>
###### Abstract

Numerical simulation of a solar cell can provide various information that can
be useful to maximize its power conversion efficiency (PCE). In that respect
we carried out a set of numerical simulation using AFORS-HET simulation
program. Separately, in order to get a better understanding, the optical
absorption in individual layers devices were analyzed. Current-voltage
characteristic curve of a reference cell (Cell-A) was used as the starting
device. The PCE of the reference device was $8.85\%$ with short circuit
current density $J_{sc}$ of 15.43 mA/cm2 and fill factor (FF) of $68.3\%$.
However, it was noticed that the reference cell had high parasitic optical
absorption at the window layer and the device structure was also not
optimized. After suitable optimization the PCE of this device (Cell-B2)
improves to $11.59\%$ ($J_{sc}$ and FF of 13.0 mA/cm2 and $87\%$
respectively). The results show that the effective optical absorption in the
active layer can be improved significantly by optimizing the device structure.
The short wavelength response can be improved by reducing the parasitic
optical absorption by the doped window layer, while its long wavelength
response improves by raising effective absorption length of the active layer.
Furthermore, its optimum thickness, for the highest possible PCE, is found to
be dependent upon the material properties, more importantly on its defect
density.

keywords: Thin film; amorphous silicon; solar cell; light absorption; power
conversion efficiency

##  1 Introduction

Photovoltaic conversion efficiency (PCE) of an amorphous silicon thin film
solar cell is often limited by carrier recombination in mid-gap defects of the
active layer. While improved film deposition technique such as hydrogen
dilution can be used to reduce the defect density to about $10^{15}$ cm-3 and
get the PCE close to $10\%$, yet the ability to reduce the defect density by
hydrogen dilution appears as a fundamental limit to the improvement of
material quality. In addition, when high hydrogen dilution is used its flow
rate determines a reduced film deposition rate, leading to a longer time to
fabricate a device.

###  1.1 Silicon oxide window layer

Additionally, the doped window layer contributes to parasitic optical
absorption, which is a loss of light thereby the PCE get further limited.
While strategies of applying a wide band gap silicon oxide (a-SiO:H) layer can
in principle raise the PCE yet the reported PCE also appear to have limit.

Furthermore, the work function of a wider band gap a-SiO:H layer may lead to
band discontinuity, for which a suitable double layer is also suggested,
however, this second layer contributes to an increased parasitic optical
absorption. It is therefore desirable to develop strategies to improve device
performance even with a moderate defect density of the active layer and
thinner window layer.

Moderate defect density can be easily maintained with an existing plasma
enhanced chemical vapor deposition (PECVD) system, but using a thinner window
layer requires an improved PECVD system with less surface roughness or a high
degree of uniformity of the deposited film. For example, if a maximum surface
roughness of a film is 7 nm, then depositing film of thickness 7 nm or less
will result in a faulty device. However, a state of the art PECVD system can
be used to fabricate devices with film thickness 7 nm or less. In order to
analyze importance of such thin layers we carried out the investigation

###  1.2 Simulation

In this work, we demonstrate that a high device efficiency is achievable by
using a moderate quality amorphous silicon layers. This device structure has
been adapted from overall development of single junction and tandem solar cell
by using wide band gap silicon alloy and the results are obtained by freely
available AFORS-HET simulation program. More specifically, we use the Beer-
Lambert absorption law and Fresnel’s reflection to obtain incoherent optical
absorption and transmittance of individual layers in a device structure. Here
the absorbance is a key parameter and is generally known as the product of
absorption coefficient and film thickness. It is generally known that a
thicker film will absorb more light, therefore high current density can be
expected with a thicker active layer. This can be true if the carrier
transport across the film do not degrade significantly. But for amorphous
silicon based device, the degradation is prominent due to the Schockley-Read-
Hall type carrier recombination at the mid-gap defects.

###  1.3 Parasitic optical absorption

Although there have been previous observations that thin amorphous silicon
film are useful for solar cell device structure, the fact that the device
performance can actually be improved with an ultrathin amorphous silicon film
has not been well appreciated, as a large number of the reported devices
contain thicker doped window layer ($>10$ nm) and thicker active layer
($\approx 300$nm), where the device performance remains lower than that can be
achieved with an optimized one. By contrast we will see that PCE of our
optimized device is $>10\%$ even with a relatively more defective active
layer. The effect on its performance can be more prominent in a tandem device.
Comparing this with the other high efficiency thin film devices made with thin
film perovskite material, where the device efficiency can be as high as $20\%$
or more, are not limited by parasitic optical absorption of the electron or
hole collecting layers or defect density of the absorber layer. The micro or
nano-crystalline perovskite material exhibits high carrier mobility, lower
defect density, which is significantly lower in amorphous silicon based
material.

###  1.4 Perovskite solar cell

In contrast to the amorphous silicon based technology, the perovskite solar
cell require (i) spin coating of organic-inorganic precursor material, (ii)
thicker electron and hole transporting layer, (iii) small size of the
fabricated device. It is to be noted that the long term stability of these
devices is an well known issue and dimension of these devices are relatively
small because of significant non-uniformity of spin-coated layers. These
devices also exhibit a phenomena known as hysteresis, which is the difference
in current density-voltage (J-V) characteristic curves in the forward and
reverse voltage sweep. It was also reported that at a different speed of the
voltage sweep the estimated PCE also differs. Under AM1.5 illumination, the
perovskite device absorbs shorter wavelength radiation as its optical
absorption band is below 700 nm wavelength. Therefore, one of the most popular
application of the perovskite solar cell is tandem structure, with a
crystalline silicon (c-Si) heterostructure (HIT) device at the bottom sub-
cell. Under the AM1.5 illumination, it becomes easier to match the current
density of the top and bottom sub-cells to a higher value as the perovskite
solar cell can generate a very high current density. Since the perovskite
device is composed of different material than the silicon based alloy, the
interface formation between the top perovskite and the bottom HIT sub-cells
remains a challenge. On the other hand earlier research work has shown that
the silicon alloy based single and tandem devices can exhibit high PCE.

###  1.5 Various silicon alloy

Extensive research has been going on to improve performance of photovoltaic
solar cells. It includes the development of a large number of device
structures as well as developing various materials. Various silicon alloy
materials are found to be useful in thin film silicon solar cell, of which
intrinsic type hydrogenated amorphous silicon germanium (i-a-SiGe:H) [3-5] and
boron doped p-type amorphous silicon oxide (p-a-SiO:H) or p-type nano-
crystalline silicon oxide (p-nc-SiO:H) [2, 6, 7], p-type amorphous silicon
(p-a-Si:H), p-type nano-crystalline silicon (p-nc-Si:H) are few examples. One
of the primary purposes of investigating solar cell is to achieve higher power
conversion efficiency (PCE), which is generally measured under AM1.5G
insolation. Higher the PCE of a device, higher is its capability to generate
electrical energy from light.

In order to raise the PCE, the material of the layers and its device structure
requires optimization. Optical properties of the layers determine amount of
light absorbed while the electronic properties determine collection efficiency
of photo generated charge carriers. It is generally believed that adding
oxygen to the amorphous silicon network improves its optical band gap or
optical transparency [8-10], therefore the silicon oxide based doped window
layer is expected to improve light transmission into the absorber layer, hence
increase current density. For that purpose p-type silicon oxide layer is used
and optimized in various solar cells.

Although i-a-SiGe:H has been investigated for a very long time [3-5] yet a
further improvement in its optoelectronic properties appears to have reached a
saturation. The published literature suggests that the i-a-SiGe:H is more
defective material [3-5], because of which the reported performance of a
device using this photosensitive has been low [11-13]. Defects in the i-a-
SiGe:H may have insignificant effect on device performance [14]. Because of
higher optical absorption in the i-a-SiGe:H material [3-5, 15], its use in a
solar cell is expected to improve the long wavelength response of a device.

Various other approaches have also been adopted to achieve a higher PCE, like
high quality material with low defect density, high optical absorption in the
active or absorber region while reducing optical absorption loss at the doped
window layers. Optical absorption in the doped layer can be reduced by using
wide band gap materials like silicon oxide [2, 6, 7], silicon carbide.
Furthermore, intrinsic hydrogenated amorphous silicon (i-a-Si:H) ,
hydrogenated amorphous silicon oxide (i-a-SiO:H) [8, 9] have also been
investigated, among which the i-a-Si:H shows better characteristics for its
application as active layer because of its lower defect density with reference
to a-SiGe:H [3-5] or a-SiO:H [9]. In principle, lower optical gap of the
active layer is useful for absorbing long wavelength radiation while the wide
band gap material can be useful for absorbing short wavelength ones. However,
it may be possible to extend the range of absorption wavelength in the active
layer by changing design of the device as well. Here we report such an
investigation. We used an i-a-SiGe:H based solar cell, estimated its current
density-voltage characteristics (J-V curve) by numerical simulation.

Silicon based p-i-n type solar cells have been one of the most popular devices
[1, 2]. Here p-i-n indicates i-type active layer sandwiched between p-type and
n-type doped layer. Wide band gap p-type window layer can enhance device
performance partly because of a reduction in parasitic optical absorption.
Efficiently doped layers can provide higher built-in field to separate the
photo generated charge carriers. The charge carriers are generated in the
active layer. Defects in the active layer can degrade device performance.
Defect mediated Schockley-Read-Hall (SRH) recombination leads to reduced short
circuit current density ($J_{sc}$), open circuit voltage ($V_{oc}$) and fill
factor. As a result, defective active layer leads to a poor device
performance. One of the primary reasons of low power conversion efficiency of
amorphous silicon based solar cell is the high defect density of the active
layer.

This theoretical investigation was carried out with a reasonably acceptable
material properties. Here, the simulation was started with a reference device
structure (Cell-A). After that the device structure was altered and its
resulting performance was investigated.

The importance of this work is that it can give a clear indication about few
of the important issues related to device performance.

##  2 Simulation

Initial reference device structure used in the simulation is (Cell-A) as the
following: Glass/ITO/p-nc-SiO:H/p-a-SiO:H/i-a-SiGe:H/a-Si:H/n-nc-Si:H/Ag, as
shown in Fig. 1(a). Then the device structure was changed to Cell-B, by
removing the p-nc-SiO:H layer. Here the i-a-Si:H is the intrinsic hydrogenated
amorphous silicon layer, used as buffer layer to match the electronic band
structure between the i-a-SiGe:H and the n-type nano-crystalline silicon
(n-nc-Si:H) layers. Opto-electronic properties of the layers adapted for the
simulation is shown in Table I. These values are adapted from various
publications, although these values may not match exactly to experimentally
measured values reported in the literatures, but it falls under the range of
reported values.

Optical absorption transmission of each of the layers are determined by its
absorption coefficient $(\alpha)$, following Beer-Lambert’s exponential
relation. Light transmitted to the a-SiGe:H active layer ($I_{t}$) can be
expressed as:

$I_{t}=I_{0}\prod_{(x=1)}^{5}(1-R_{x})\exp(-\alpha_{x}d_{x})$ (1)

Here the symbol $\prod_{x=1}^{5}$ stands for product, with range of values for
x from 1 to 5, with x=1 for air, x=2 for glass, x=3 for ITO, x=4 for p-nc-
SiO:H, x=5 for p-a-SiO:H. Here $I_{0}$ is intensity of incident light, $R_{x}$
is Fresnel reflectivity at the interface, $d_{x}$ is film thickness while
$\alpha$ is optical absorption coefficient of respective layers. The absorbed
light ($I_{a}$) at the i-a-SiGe:H layer can be expressed as:

$I_{a}=I_{t}(1-\exp(-\alpha d))$ (2)

Here $\alpha$ is optical absorption coefficient and $d$ is thickness of the
i-a-SiGe:H layer. The above formulation can be adapted to estimate light
absorption in other layers as well.

The numerical simulation for the electronic characteristics of the device is
estimated by using freely available AFORS-HET v2.4.1 simulation program [16].
The schematic structure of the device is shown in Fig. 1(a).

In the AFORS-HET the operation of a solar cell is described by one dimensional
semiconductor equations. These semiconductor equations are Poisson’s equation
and transport equation for electrons and holes. These are also known as drift-
diffusion equation for the electrons and holes in a semiconductor. In the
AFORS-HET these equations are solved with the help of finite difference method
under different conditions. At the first stage of the simulation, the
equilibrium carrier densities were estimated under dark condition and without
external bias. Then electron-hole pairs are generated due to absorption of
incident photons. The absorption is described by Lambert-Beer expression by
taking incoherent internal passage of transmitted light. Here Shockley-Read-
Hall recombination were considered and sub-bandgap recombination was treated
as the primary mechanism of loss of photo generated carriers. The interface
currents are modeled by drift diffusion and here it is not changed by
considering zero surface charge density. The contacts between the doped layers
and transparent conducting oxides at the front and back of the device were
modeled as Schottky metal- semiconductor (MS Schottky) contacts.

The J-V characteristic curve of the Cell-A, as obtained from the simulation is
as shown in Fig. 1(b).It’s open circuit voltage ($V_{oc}$ ) was 0.84 V, short
circuit current density ($J_{sc}$ ) was 15.43 mA/cm2 , fill factor (FF) is
$68.25\%$ and PCE as $8.85\%$, which is approximately close to that reported
in [16] as 0.86 V, 15.54 mA/cm2 , $68.34\%$ and $9.13\%$ respectively (cell-D
of Table 2 of the reference [16])

Figure 1: (a) Schematic structure of the device under investigation. (b) J-V characteristic curves of the baseline simulated Cell-A.  Table 1: Parameters of the solar cell layers (Cell-A) used in the simulation. MS-Schottky contact was used at the front TCO/ p-nc-SiO:H, TCO/ p-a-SiO:H, with surface recombination velocities of the electrons and holes as $10^{7}$ cm/s. For the other interfaces ‘drift-diffusion’ interface was used with zero interface charge density. Parameters | p-ncSiO:H(p1) | p-a-cSiO:H(p2) | i-a-SiGe:H | i-a-Si:H | n-ncSi:H
---|---|---|---|---|---
Layer thickness, | 10 | 15 | 300 | 20 | 20
d (nm) |  |  |  |  |
Dielectric constant | 11.9 | 11.9 | 11.9 | 11.9 | 11.9
Electron affinity (eV) | 3.9 | 3.9 | 3.9 | 3.9 | 3.9
Band gap (eV) | 2.08 | 2.08 | 1.58 | 1.68 | 1.68
Conduction band |  |  |  |  |
density of states | $4\times 10^{20}$ | $4\times 10^{20}$ | $4\times 10^{20}$ | $4\times 10^{20}$ | $1\times 10^{20}$
(cm-3 ) |  |  |  |  |
Valence band |  |  |  |  |
density of states | $4\times 10^{20}$ | $4\times 10^{20}$ | $4\times 10^{20}$ | $4\times 10^{20}$ | $1\times 10^{20}$
(cm-3 ) |  |  |  |  |
Electron mobility | 0.2 | 0.2 | 2 | 1 | 10
(cm2 .volt-1 .s-1 ) |  |  |  |  |
Hole mobility | 10 | 10 | 0.2 | 0.1 | 0.1
(cm2 .volt-1 .s-1 ) |  |  |  |  |
Doping |  |  |  | Dop.grad. |
concentration | $1.6\times 10^{19}$ | $1.6\times 10^{18}$ |  | $(0-3)\times 10^{17}$ | $2.68\times 10^{18}$
(cm-3 ) |  |  |  |  |
Layer density | 2.328 | 2.328 | 2.328 | 2.328 | 2.328
(g.cm-3 ) |  |  |  |  |
Donor defect | $1\times 10^{16}$ | $1\times 10^{16}$ | $1\times 10^{16}$ | $1\times 10^{16}$ | $1\times 10^{16}$
density (cm -3 ) |  |  |  |  |
Acceptor defect | 0 | 0 | $3\times 10^{16}$ | $1\times 10^{16}$ | $1\times 10^{16}$
density (cm -3 ) |  |  |  |  |
Defect type | Gaussian | Gaussian | Gaussian | Gaussian | Gaussian

##  3 Results and Discussions

The standard AM1.5G insolation (100 mW/cm2 of solar spectra) was used to
estimate optical absorption of individual layers and J-V characteristic curves
of the solar cells. In order to get an idea of how the solar spectra is
absorbed at different layers Fig. 2 shows the effective part of the AM1.5G
spectra absorbed by different layers of the Cell-A. Here it can be seen that
the top p-nc-SiO:H layer has high optical absorption in the shorter wavelength
region. Although thickness of this layer is merely 10 nm, yet, because it is
at the front side of the device, it absorbs significant amount of high energy
photons. Generally, such an absorption is undesirable and several
investigations were made to reduce such an absorption loss [10, 17, 18].

###  3.1 Optical Absorption

####  3.1.1 Reference Cell-A

The purpose of this p-nc-SiO:H layer was to improve device performance. But if
two p-type layers are used, it inevitably raises total parasitic optical
absorption at the p-type window layers. Although the optical absorption at the
p2 layer is not very high , yet it can be reduced to improve device
performance. The simulated J-V characteristics curve obtained in the above
figure (Fig. 1(b)) was obtained with both the p-type layers. It is expected
that the device characteristics will improve by removing this p-nc-SiO:H
layer. So this layer was removed for subsequent simulations. The resultant
optical absorption spectra of the individual layers are shown in Fig. 3(a).

Figure 2:  Optical absorption spectra of different layers of the device,
Cell-A. The top profile shows the AM1.5G spectrum. The numbers (1,2,3,4) in
the legend correspond to the labeling of the traces. and ‘p1’, ‘p2’ and ‘i’
indicates p-nc-SiO:H, p-a-SiO:H, i-a-SiGe:H layers respectively. Here the
reported spectra was measured with 10 nm resolution.

Furthermore, AFORS-HET simulation shows that with a reduction in layer
thickness of the layers p1, p2, the band discontinuity greatly increases,
which is expected to have a deteriorating impact on device performance. On the
other hand, it was also noticed that the discontinuity reduces with a thicker
layers. It implies that with the p-type oxide double layer, there will be a
lower limit of layer thickness that can be used to achieve better device
performance. In a real device fabrication this may lead to an interpretation
that a thinner window layer is not useful to improve PCE.

####  3.1.2 Modified Cell-A, without p-nc-SiO:H (Cell-B type)

Figure 3(a) shows optical absorption of various layers of the cell (denoted as
Cell-B) after the p1 (p-nc-SiO:H) layer was removed. The Fig 3(b) shows an
increase in absorption by the i-a-SiGe:H active layer is taking place after
removing the p-nc-SiO:H layer, as expected. Therefore, the electronic
characteristics of the device are also expected to improve as well.

Figure 3:  (a) Optical absorption by the TCO, p2(p-a-SiO:H), intrinsic layer
when the p-nc-SiO:H is absent, as in Cell-B. (b) Comparison of optical
absorption by the active layer with (Cell-A) and without the p-nc-SiO:H layer
(Cell-B).

####  3.1.3 $d_{i}$ variation (Cell-B type)

One of the most popular and simple approach to improve device performance is
to find optimum thickness of the active layer. Generally it is thought that by
increasing thickness of the active layer can raise short circuit current
density ($J_{sc}$) of the cell. This is generally true if defect density of
the active layer is low. However, the $J_{sc}$ is not the only parameter used
in estimating PCE, as the PCE is estimated by using product of current density
and voltage at the maximum power point (PmaxJ, PmaxV respectively). So raising
$J_{sc}$ not necessarily can improve device performance if fill factor (FF)
and output voltage across the device degrades. To start with the related
simulation, the variation in light absorption at the active layer for its
various thicknesses ($d_{i}$) were obtained and is shown in Fig. 4(a):

Figure 4:  (a) Optical absorption by the i-a-SiGe:H layer for its various
thicknesses ($d_{i}$) of active layer of the Cell-B, as (10, 20, 30, 40, 50,
75, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 175, 200, 225, 250,
275, 280, 290, 300, 310, 320, 325, 350, 375, 400, 425, 450, 475, 500, 525,
550, 600, 625, 650, 675, 700, 750, 800, 850, 900, 950, 1000) nm. (Here, and
the subsequent, estimates are made after removing the p-nc-SiO:H layer from
the device structure.). Thickness of p-type layer was 7 nm. (b) Integrated
optical absorption in the active layer denoted as i-Absoprion for various
thickness of theactive layer, denoted as i-thickness.

This Fig. 4(a) shows that by increasing thickness of the active layer the
wavelength response of the device improves along with the increase in the
magnitude of peak absorption, Shift of the peak towards longer wavelength and
an overall increase in light absorption. It indicates that the long wavelength
response of the device changes significantly with the change in the $d_{i}$ .
Integrated light absorption, as shown in Fig. 4(b) determines $J_{sc}$. Here
it is interesting note the region where light absorption increases sharply
with the increased thickness, which is below 100 nm. Furthermore, it is worth
mentioning that here the optical absorption does not include the contribution
from the i/n buffer layer, which is also an intrinsic layer and will
contribute to the generated current of the device. For evaluating electronic
properties of the device, the contribution from the buffer layer is taken into
account.

####  3.1.4 $d_{p}$ variation (Cell-B type)

We further investigated the change in parasitic optical absorption due to
change in the thickness of the p-type window layer ($d_{p}$) of Cell-B. Fig.
5(a) shows the optical absorption by the p-type layer when its thickness was
varied from 1 nm to 25 nm. The p-type layer absorbs short wavelength part of
the spectra or high energy photons. As a result, the available light to the
intrinsic layer will also change and hence there will be a change in light
absorption by the active layer. The spectra of absorbed light by the active
layer are shown in Fig. 5(b). It shows that by changing width of the p-type
window layer the blue response (short wavelength response) of the device
changes significantly, whereas the long wavelength response remain mostly
unchanged. Integrated light absorption at the p-type and i-type layers, as
obtained from the Fig. 5(a) and 5(b), are shown in Fig. 5(c). It further
highlights that the reduced parasitic absorption at the p-layer leads to an
increased absorption at the i-layer, while sum of these two absorptions remain
nearly constant to $\approx$32 mW/cm2. Therefore this is intuitively clear
that higher optical absorption at the active layer can be achieved with a
thinner p-layer.

Figure 5:  (a) Optical absorption by the p-a-SiO:H layer, for its thicknesses
($d_{p}$) as 1, 2, 3, 4, 5, 7, 10, 15, 20, 25 nm and a corresponding optical
absorption by the active layer as shown in (b). Here the active layer
thickness ($d_{i}$) is 100nm. (c) Estimated total energy absorbed by the
p-type and i-type layer, and their sum, denoted as ‘p-layer’, ‘i-layer’ and
‘Total’ respectively in the figure.

Reducing optical absorption at the p-layer can raise absorption in the i-layer
ad hence raise PCE of the device. A simple way to reduce the absorption at the
p-layer is to reduce its thickness.

###  3.2 Electrical Characteristics

####  3.2.1 $d_{i}$ variation, without p-nc-SiO:H (Cell-B type)

As the photo generated current in a solar cell is directly related to absorbed
light by the active layer, it is expected to change the J-V characteristic
curve of the device. Fig. 6 show J-V characteristic curves of the devices when
the p-nc-SiO:H layer is present, Fig. 6(a), and when it is removed Fig. 6(b)
and the thickness of the active layer varied in a wide range, from 20 nm to
1$\mu$m. It becomes visually clear that the short circuit current density
($J_{sc}$) mostly increases with thickness of active layer, but fill factor
(FF) reduces significantly. Quantitative estimates of the solar cell
parameters are shown in Fig. 7.

Figure 6:  J-V characteristic curves of the cells (a) Cell-A type, (b) Cell-B
type, with various thicknesses of the active layer, thicknesses as mentioned
in Fig. 4, $d_{p1}$ = 15nm.

The characteristic features of the J-V curve for the Cell-A and Cell-B, is
shown in Fig 6 and Fig. 7. The open circuit voltage ($V_{oc}$) decreases
sharply when active layer thickness ($d_{i}$) was varied from 20 nm to 300 nm.
With a further increase in the thickness beyond 300 nm, the $V_{oc}$ decreases
at a slower rate. Similarly, the increase in the $J_{sc}$ is sharper until 300
nm, but the rate of increase slows down within 300 nm to 800 nm and it starts
reducing after $d_{i}>800$ nm. The FF continuously decreases with the increase
in the $d_{i}$. It implies that the $V_{oc}$ and FF decreases monotonously
with the increase in the $d_{i}$ which can be interpreted as a result of total
number of defects in the active layer. On the other hand, while the $J_{sc}$
increases primarily because of increased optical absorption, but it also
decreases for $d_{i}>800$ nm. As a result the maximum PCE was obtained with
125 nm thick active layer for Cell-A and 130 nm for Cell-B, which are much
lower than that the active layer thickness ($\approx 300$ nm) conventionally
used, yet the PCE of this device is higher than that of the starting Cell-A
($d_{i}=300$ nm).

Figure 7:  Solar cell characteristic parameters (for Cell-A,B), extracted from
the J-V curves in Fig. 6. The respective value of the reference cell is shown
as star-symbol. The maximum PCE of the Cell-B type was observed at
$d_{i}\approx 125$ nm.

The 20 nm thick active layer may appear impractical, but the result
demonstrates that a thinner device can exhibit a very high $V_{oc}$ and FF. In
this context, it is to be noted that device a thinner layer ($\approx 3$ nm
thick layer) was also investigated earlier [19]. The reason can be the average
number of defect centers encountered by photo generated charge carriers.
Defect density ($N_{dd}$ ), which is the number of defects per unit volume,
determines SRH recombination rate ($R_{SRH}$ ) so the total recombination of
the photo generated carriers ($R_{ec}$ ) will be determined by the product of
$R_{SRH}$ and volume ($V_{olume}$ ) of active layer (where$V_{olume}=di*A$, A
is surface area). Therefore

$R_{ec}=R_{SRH}V_{olume}N_{dd}=k_{1}d_{i}$ (3)

Here $k_{1}=R_{SRH}V_{olume}N_{dd}$, $N_{dd}$ is a constant when the
recombination rate, $A$ is surface area and defect density are constant. This
indicates that the total recombination of photo generated carriers is directly
proportional to thickness of active layer when the $d_{i}$ is varied.

Interestingly, the estimated PCE is highest ($9.76\%$) with $d_{i}$
($\approx$125nm)for Cell-A and $10.43\%$ with 130 nm active layer for Cell-B.
Practically the device can be made further thinner. With the $d_{i}=100$ nm
the PCE = $9.64\%$ which is 0.12 percentage point lower for a $20\%$ reduction
in $d_{i}$ from 125 nm to 100 nm or to 1/3-rd of its original value (from 300
nm to 100 nm). From the cost of material point of view, the $d_{i}$ = 100 nm
may be a preferable choice, as processing time may be an important parameter
[20] for commercial production. It is also to necessary to mention that the
PCE of the device (Cell-A) with 300 nm active layer increases marginally, from
$8.87\%$ to $9.41\%$ by removing the p-nc-SiO:H layer, although Fig. 3(b)
shows a significant increase in the optical absorption by removing this layer.
It may be primarily because the defects in the active layer, so the additional
photo generated carriers are mostly lost by recombination to travel across the
300nm thick active layer. Such an excess recombination loss can be reduced, by
using a thinner active layer. As a result devices with 125 nm or 130 nm thick
active layer shows better performance.

###  3.3  $d_{p}$ variation, without p-nc-SiO:H (Cell-B type)

Figure 8:  J-V characteristic curves of the cells with various thicknesses of
the p-a-SiO:H layer, thicknesses as mentioned in Fig. 5(b), with thin active
layer, $d_{i}$ = 100 nm.

Based on the above discussion, the J-V characteristic curves, as shown in Fig.
8 and device parameters as shown in Fig. 9 were obtained for the $d_{i}$ = 100
nm. The $J_{sc}$ increases from $\approx$ 11 mA/cm2 to $\approx$ 12.8 mA/cm2
when the $d_{p}$ was reduced from 25 nm to 1nm.

The $V_{oc}$ and FF of all the cells remain higher than the reference cell
(star symbol in Fig. 9). Although $J_{sc}$ remained lower than the reference
cell yet, the PCE came out to be higher than when the $d_{p}$ ¡20nm. The
result is interesting because it shows that obtaining a higher $J_{sc}$ may
not always lead to a higher PCE.

The effect of device structure on the short and long wavelength response may
be comparable to that expected in a device with light trapping scheme. The use
of a textured surface may have a possibility to introduce additional defects
in the deposited film [21]. This will invite two different issues, one is that
optimized device thickness inversely depends on defect density (as discussed
later in this article), the other is that the surface texture may introduce
additional non-uniformity of the film over the surface texture, whereby
depositing ultrathin layer may not be possible to result a better device
performance.

Figure 9:  Solar cell characteristic parameters extracted from the J-V curves
in Fig. 8. The respective value of the reference cell is shown as star-symbol.

###  3.4 $d_{i}$ Variation of Reference Cell type with $N_{d}=6\times 10^{15}$
cm-3

The Cell-A and Cell-B had active layer defect density ($N_{d}$ ) of $6\times
10^{16}$ cm-3 . Here, in the Cell-C type, the defect density is reduced by one
order. We denote the cells derived from Cell-A as Cell-AC, and those derived
from Cell-B as Cell-BC1. Defect density of the active layer generally has a
profound effect on device performance. Therefore, lower defect density of
active layer is always preferable.

Figure 10:  J-V characteristic curves of the (a)cells (Cell-AC type), (b)
Cell-BC1,similar to that of Fig. 6, except that here total defect density is
reduced from $6\times 10^{16}$ cm-3 to $6\times 10^{15}$ cm${-3}$ Figure 11:
Solar cell characteristic parameters extracted from the J-V curves from Fig.
10. Here the parameters are compared for devices without the p-nc-SiO:H, but
with 15 nm thick p-a-SiO:H (Cell-BC1), and with both the p-layers (Cell-AC).
In comparison to the Fig. 6, 7, all other parameters are the same except the
defect density ( defect density was reduced by one order of magnitude). The
respective value of the reference cell (Cell-A) is shown as star-symbol. The
filled-square symbol corresponds to $d_{i}=300$nm, without p-nc-SiO:H, and 7
nm thick p-a-SiO:H, with defect density $6\times 10^{15}$ cm-3 (as Cell-BC2).

Figure 12:  Variation of the open circuit voltages of the (a) Cell-B and (b)
Cell-BC, taken from Fig. 7 and 11 respectively.

Figure 13:  Energy band diagrams of (a) Cell-A and (b) Cell-B. Here the energy
is shown with reference to the p-layer conduction band (CB) mobility edge. The
VB indicates valence band mobility edge.  Figure 14:  Trend in variation in
PCE of the devices. Improvement in the PCE was estimated from the reference
device A to B, when p-nc-SiO:H was removed, but with $d_{i}$ =300 nm. All the
subsequent B-type cells were without the p-nc-SiO:H layer. The Cell-B1 was
with $d_{i}$ =100 nm, $d_{p}$ = 15nm. The Cell-B2 was with $d_{p}$ = 7nm, with
$d_{i}$ =300 nm. The Cell-AC was with the cell similar to the structure of
Cell-A, while the active layer defect density here is $6\times 10^{15}$ cm-3 .
The Cell-BC1 corresponds to the Cell-B1 while the active layer defect density
is $6\times 10^{15}$ cm-3 . and the Cell-BC2 is similar to that of Cell-BC1,
but with 7 nm thick p-a-SiO:H.

The simulated J-V characteristic curves of Cell-AC and Cell-BC are shown in
Fig.10. In comparison to the Fig. 6, a significant improvement in
characteristic curves is visible here It indicates a similar trend that the
$J_{sc}$ increases while the $V_{oc}$ decreases with the increase in the
$d_{i}$. The device parameters extracted from these curves are shown in Fig.
11, where such a trend is clearly visible. Here the parameters for the
reference device (Cell-A) are shown as a star symbol. It shows that the
$V_{oc}$, FF and PCE of the low defect device is higher than the reference
device under the same $d_{i}$ = 300nm. The changes are $V_{oc}$ = from 0.836V
to 0.953V, $J_{sc}$ = from 15.52mA/cm2 to 15.65 mA/cm2, FF = from $69.28\%$ to
$80.91\%$, PCE = from $8.99\%$ to $12.07\%$. In this condition the best
performing device has $d_{i}$ = 300nm. So if the quality of the active layer
is improved by reducing its defect density, then a thicker active layer can
give higher PCE.

It may be noted that the $V_{oc}$ increases when thickness of the active layer
decreases. The reason can be the dependence of the $V_{oc}$ on total number of
defects that exists within the active layer. A thicker active layer will have
a larger volume than that of a thinner one. As a result, for a thinner active
layer solar cell, the photo generated electron hole pairs can be collected at
the doped layer more efficiently leading to a higher $V_{oc}$ . For comparison
the variation in the $V_{oc}$ due to material defect the V oc for Cell-A and
Cell-AC (Fig. 12(a)), Cell-B and Cell-BC (Fig. 12(b)) are plotted together and
shown in Fig. 12. It shows that for a reduced defect density, the $V_{oc}$
remains higher. This also indicates that the $V_{oc}$ is inversely related to
the total number of defects that the photo generated carriers face on the
average, before being collected at the doped layers.

Figure 12 shows the variation in $V_{oc}$ with thickness of i-layer and its
defect density. The Cell-A had $p{1}$ , $p{2}$ layers, while the Cell-B had
the $p{1}$ -layer only. The results, as shown in Fig. 7, 11, indicate that the
$V_{oc}$ does not significantly depend on the $p{2}$ layer. Looking into the
figure 12, the variation in $V_{oc}$ can empirically be expressed as

$V_{oc}=K_{1}/log(d_{i})$ (4)

Similarly the $J_{sc}$ can be expressed as

$J_{sc}=K_{2}/log(d_{i})$ (5)

Here $K_{1},K_{2}$ are constant terms. It is to be noted that these two
equation will fit better for lower defect density or Cell-AC, BC, but will fit
less for the Cell-A,B.

As shown in Fig. 6-9, that by eliminating the p-nc-SiO:H layer and reducing
the thickness of the a-SiO:H layer from 15 nm to 7 nm, its PCE can be improved
significantly. So we simulated the device characteristics with only one p-a-
SiO:H layer, similar to that used in Fig. 6-9, except the defect density of
the active layer reduced from 6x1016 cm-3 to 6x1015 cm-3 and using
$d_{i}$=300nm, $d_{p}$ = 7nm (Cell-BC2). The resultant device shows
$V_{oc}$=0.965V, $J_{sc}$=16.91 mA/cm2, FF=$80.03\%$, PCE=$13.05\%$.

####  3.4.1 Energy band Diagram

The energy band diagram is expected to correlate the change in the observed V
oc with the device width although there is a difference between these two
situations, as the Fig. 13 corresponds to the measurement under dark while the
V oc was measured under light, but the similarity is that the external
electrical bias in both the situations are absent or open circuit condition.
The Cell-A and Cell-B do not exhibit any significant difference in the energy
band structure where the J sc differs in Fig. 7 (and Fig. 11), for these two
types of cells, which is expected to be due to the difference in available
light to the active layers.

However, due to the variation in cell width, a high built-in electric field
(which is the ratio between energy difference and device width) helps
collecting photo generated carriers. Figure 12 shows that the V oc also
inversely related to defect density. Another common feature visible in the
band diagram is that for a thinner cell the band discontinuity is more
prominent than that with a thicker one. Therefore, with a perfect matching of
the energy band among the layers, a further improved device performance is
expected.

The Fig. 14 shows the sumary of the improvement in PCE of the device at the
different stages. By removing the 10 nm thick p-nc-SiO:H, the PCE of the
Cell-B improved by 0.56 percentage point along with an improved blue response,
then by optimizing the active layer leads to an additional 0.89 percentage
point enhancement in the PCE (Cell-B1). A further reduction of the p-a-SiO:H
layer (to 7 nm) raises the PCE further by 1.29 percentage point along with a
further improvement in the blue response of the device (Cell-B2). By reducing
the defect density of the active layer of Cell-A from 6x1016 cm-3 to 6x1015
cm-3 (Cell-AC) leads to the PCE of $12.07\%$. Starting from the Cell-BC1 and
by reducing its $d_{p}$ to 7nm further raises of the PCE to $13.02\%$.

Here, in the AFORS HET simulation the estimated total defect density of the
active layer of the real cell is found to be (including the tail state
defects) 6x1016 cm-3, which is higher than the defect density in intrinsic
a-Si:H layer (3.2x1016 cm-3) [21].

The results indicate that even though a significant increase in optical
absorption in the active layer was initiated by removing the p-nc-SiO:H layer
and making a thinner p-layer, yet the $J_{sc}$ did not increase significantly
(Cell-B). This could be due to several reasons. One of them can be higher
midgap defects. Therefore high quality material with lower defect density is
always desirable, as can be seen in Cell-AC, BC1, BC2.

The results indicate that the solar cell with a defective material should have
a thinner active layer for a better performance [21]. This performance can be
estimated by using two separate criteria. One is effective optical absorption,
so that it absorbs a certain fraction of incident light and transmits the
rests. This criterion will be useful for the top sub-cell of a tandem device
as the transmitted light can be used by other sub-cells in a multijunction
device structure. Secondly, with a defective active layer a significant part
of the photo generated carriers will be lost by recombination. This
recombination loss can be reduced by using a thinner active layer, although a
very thin active layer is not practical.

Increasing Ge content within the film may decrease optical gap and hence
increase optical absorption in the longer wavelength region but it
simultaneously degrades short wavelength response [22], it may be because of
increased carrier loss [11] due to recombination at the dangling bond defect
sites [23]. On the other hand by adapting the approach of modifying device
structure, as described here, both the short as well as long wavelength
responses can be improved without compromising material properties.

Although this work is based on numerical simulation of solar cell, yet it
clearly demonstrates the importance of having a thinner doped window layer
with which short as well as long wavelength response of the device can be
improved. Generally it is believed that wide band gap doped window layer can
improve the short wavelength response, whereas here the results show that a
similar improvement can be achieved by using a thinner window layer. Another
important aspect of this investigation is the improvement in long wavelength
response of the device by using a thicker active layer. In this respect the
dominating belief is that a low band gap active layer is needed to achieve
this. Further investigation also indicates that a thicker active layer can
give a high PCE if its defect density remains low. Therefore, a particular
design of a solar cell is expected to be dependent on the defect density of
the active layer.

##  4 Conclusions

In conclusion, the present analysis shows that optical absorption by the
active layer is an important criterion for improving device performance. It
also shows that the short and long wavelength response can also be tuned by
adapting a suitable device structure; thinner doped window layer is always
preferable for reducing parasitic optical absorption and improving short
wavelength response. Thicker active layer can be used to raise the long
wavelength response but it should be limited to the maximum power conversion
efficiency.

##  5 References

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