We investigated the effects of the thickness and doping concentration in p and ntype polySi layers on the performance of a solar cell based on a carbon fiber in order to improve the energy conversion efficiency of the cell. The shortcircuit current density and opencircuit voltage of the carbon fiberbased solar cell were significantly influenced by the thickness and doping concentration in the p and ntype polySi layers. The solar cell efficiency was successfully enhanced to ~10.5%.
I. INTRODUCTION
Miniature and flexible solar cells have been attracting considerable attention in a variety of applications such as wireless sensor networks and robots
[1

5]
. In comparison to rigid solar cell panels, miniature and flexible solar cells are more applicable to irregular objects or to being embedded into portable devices and clothes
[1
,
2]
. Recently, fibershaped solar cells with a micrometer diameter have been developed
[6
,
7]
. Since the fibershaped solar cells are lightweight, thin and flexible, they can be easily integrated in a curved form and are suitable for portable applications
[7

10]
. The first attempt to realize fibershaped solar cells involved dyesensitized solar cells based on an optical fiber core electrode coated with a transparent conductive oxide (TCO) glass
[8]
. However, TCO glass is expensive and has a high sheet resistance, which limits its extensive application in fibershaped solar cells. To overcome this limitation, carbon fibers have been exploited to form the core electrode of a fibershaped solar cell
[9]
. A carbon fiber is a flexible, lightweight material with a submicrometer diameter, a good conductor with a very low resistance of 1.8×10
^{−5}
Ω·m, and it can endure high temperatures up to 1,500℃
[10]
. However, solar cells based on carbon fibers suffer from their inefficient photovoltaic structure
[9]
. Therefore, it is necessary to investigate the effect of the thickness and doping concentration in p and ntype polySi layers on the solar cell efficiency.
In this study, the effects of the thickness and doping concentration in p and ntype polySi layers on the efficiency of a solar cell based on a carbon fiber were theoretically analyzed by utilizing a finitedifference timedomain (FDTD) algorithm
[11
,
12]
. The solar cell efficiency (
η
) based on the carbon fiber gradually increased and finally saturated with increasing thickness of the ptype polySi layer because of the dependence of the light harvesting efficiency (
η_{lh}
) on the absorbed light intensity (
I_{abs}
), corresponding to the thickness of the ptype polySi layer (
t_{p}
). The solar cell efficiency (
η
) is directly proportional to the short circuit current density (
J_{sc}
). The shortcircuit current density (
J_{sc}
) gradually increased and was finally saturated with increasing thickness of the ptype polySi layer (
t_{p}
) because of the dependence of the light harvesting efficiency (
η_{lh}
) on the absorbed light intensity (
I_{abs}
). However, a large thickness of the ntype polySi layer (
t_{n}
) degrades the quantum efficiency (
η_{qe}
) resulting in a reduction of the solar cell efficiency (
η
). Since the absorption coefficient of free electrons (
α_{fc}
) in the carbon fiberbased solar cell primarily changed depending on the doping concentration in the ptype polySi layer (
N_{p}
), the solar cell efficiency (
η
) was enhanced by reducing the doping concentration in the ptype polySi layer (
N_{p}
). Increasing the doping concentration in the ntype polySi layer (
N_{n}
) enhances the opencircuit voltage (
V_{oc}
), resulting in improvement of the solar cell efficiency (
η
). By optimizing the thickness and doping concentration in the p and ntype polySi layers, the solar cell efficiency (
η
) based on the carbon fiber was improved up to ~10.5%.
II. RESULTS AND DISCUSSION
Figure 1
shows the (a) scheme and (b) operation principle for the solar cell based on the carbon fiber. The carbon fiber in the center of the solar cell simultaneously serves as a mechanical backbone and as electrode 1. Photovoltaic conversion in the p and ntype polySi layers must be achieved. While the solar cell based on the carbon fiber is illuminated by sunlight, the p and ntype polySi layers will absorb photons whose energies are equal to the amount of the energy bandgap of the Si layer, and electronhole pairs will be produced. As the electronhole pairs reach the depletion region, the electronhole pairs will be separated by the internal electric field induced in the junction between the ptype and ntype polySi layers. The electrons and holes drift toward the ntype and ptype polySi layers, respectively, due to the internal electric field. In
Fig. 1(b)
, the electrons and holes in the metastable state are generally moved for the electron lifetime before their recombination. Since the recombination of the electron with the hole undesirably induces a shortcircuit current density loss, the path length of the electronhole pairs should be minimized to reduce the loss. This means that a large fraction of photogenerated electronhole pairs should be created within the depletion region. Since over 50% of the sunlight incident on silicon is absorbed within 3 um from its surface, the thickness of the ntype polySi layer (< 1 μm) should be much thinner than that of the ptype polySi layer (> 10 μm). After drifting into the ptype polySi layer, the holes will be collected at electrode 1. After transport in the ntype polySi layer, the electrons will be gathered at electrode 2. Since the flow of the carriers causes the photogenerated current, the electric potential is different between electrodes 1 and 2. Therefore, the solar cell based on the carbon fiber can be used to power or recharge portable devices. In the proposed carbon fiberbased solar cell, the effects of the thickness and doping concentration in the p and ntype polySi layers on the efficiency of the solar cell were theoretically analyzed by using a finitedifference timedomain (FDTD) algorithm. We assumed that the p and ntype polySi layers were fabricated by doping silicon with boron (B) and phosphorus (P), respectively.
Figure 2(a)
shows the shortcircuit current density (
J_{sc}
) as a function of the thickness of the ptype polySi layer (
t_{p}
). The absorbed light intensity (
I_{abs}
) with respect to the thickness of the Si layer (
t_{p}
) can be written as follows
[13]
(a) Structure and (b) operation principle of the solar cell based on a carbon fiber.
The (a) shortcircuit current density (J_{sc}), (b) opencircuit voltage (V_{oc}), (c) fill factor (Γ_{f}), and (d) solar cell efficiency (η) as a function of the thickness of the ptype polySi layer (t_{p}).
where
α_{s}
and
t_{p}
are the absorption coefficient and thickness of the ptype polySi layer, respectively. From Eq. (1), it is clearly evident that the absorbed light intensity (
I_{abs}
) is exponentially enhanced by increasing the thickness of the ptype polySi layer (
t_{p}
). The shortcircuit current density (
J_{sc}
) can be approximately expressed as follows
[14]
where
q
is the electron charge,
η_{lh}
,
η_{inj}
, and
η_{qe}
are the light harvesting efficiency, charge injection efficiency, and quantum efficiency, respectively, and
I_{0}
is the input intensity of the illuminating light. In Eq. (2), it is clearly evident that the shortcircuit current density (
J_{sc}
) is directly proportional to the value of
η_{lh}
[15]
. Since the light harvesting efficiency (
η_{lh}
) is dominantly determined by the absorbed light intensity (
I_{abs}
), the shortcircuit current density (
J_{sc}
) gradually increases and is finally saturated with increasing thickness of the ptype polySi layer (
t_{p}
).
Figures 2(b)
and
2(c)
show the opencircuit voltage (
V_{oc}
) and fill factor (Γ
_{f}
), respectively, as a function of the thickness of the ptype polySi layer (
t
_{p}
). The main parameter to determine the opencircuit voltage (
V_{oc}
) is the doping concentration in the p or ntype polySi layer
[16]
. This means that the opencircuit voltage (
V_{oc}
) is not severely affected by the thickness of the ptype polySi layer, as shown in
Fig. 2(b)
. The fill factor of the solar cell (Γ
_{f}
) can be given as shown below
[17]
where
J_{max}
and
V_{max}
are the maximum output current density and maximum output voltage of the solar cell, respectively. For the ideal case of the carbon fiberbased solar cell, the fill factor (Γ
_{f}
) is not significantly affected by the thickness of the ptype polySi layer, as shown in
Fig. 2(c)
, because the shortcircuit current density (
J_{sc}
) and the maximum output current density (
J_{max}
) are simultaneously affected by the thickness of the ptype polySi layer.
Figure 2(d)
shows the variation of the solar cell efficiency (
η
) as a function of the thickness of the ptype polySi layer (
t_{p}
). The solar cell efficiency (
η
) can be expressed as follows
[16]
where
P_{i}
is the intensity of sunlight. Since the solar cell efficiency (
η
) is directly proportional to the short circuit current density (
J_{sc}
), the solar cell efficiency (
η
) should gradually increase and finally become saturated by increasing the thickness of the ptype polySi layer (
t_{p}
).
Figure 3(a)
shows the shortcircuit current density (
J_{sc}
) as a function of the thickness of the ntype polySi layer (
t_{n}
). The quantum efficiency (
η_{qe}
) is the ratio of the number of photogenerated electrons collected by the solar cell to the number of photons incident on the solar cell. The quantum efficiency (
η_{qe}
) is predominantly determined by the collection efficiency of the photogenerated electron. This collection efficiency is affected by the diffusion length of electrons (
L
) and the thickness of the ntype polySi layer (
t_{n}
). The quantum efficiency (
η_{qe}
) with respect to the thickness of the ntype polySi layer (
t_{n}
) can be approximately expressed as follows
[18]
.
The (a) shortcircuit current density (J_{sc}), (b) opencircuit voltage (V_{oc}), (c) fill factor (Γ_{f}), and (d) solar cell efficiency (η) as a function of the thickness of the ntype polySi layer (t_{n}).
From Eq. (6), it is obvious that the quantum efficiency (
η_{qe}
) is degraded with increasing thickness of the ntype polySi layer (
t_{n}
). Since the shortcircuit current density (
J_{sc}
) is directly proportional to the quantum efficiency (
η_{qe}
) in Eq. (2), the shortcircuit current density (
J_{sc}
) should be reduced by increasing the thickness of the ntype polySi layer (
t_{n}
), as shown in
Fig. 3(a)
.
Figures 3(b)
and
3(c)
show the opencircuit voltage and fill factor, respectively, as a function of the thickness of the ntype polySi layer. Similar to the case of the ptype poly Si layer, the opencircuit voltage (
V_{oc}
) and fill factor (Γ
_{f}
) are not seriously affected by the thickness of the ntype polySi layer.
Figure 3(d)
shows the solar cell efficiency (
η
) as a function of the thickness of the ntype polySi layer (
t_{p}
). Since the solar cell efficiency (
η
) is directly proportional to the shortcircuit current density (
J_{sc}
), the solar cell efficiency (
η
) should be diminished by increasing the thickness of the ntype polySi layer (
t_{n}
), as observed in
Fig. 3(d)
.
Figure 4(a)
shows the variation of the shortcircuit current density (
J_{sc}
) as the doping concentration in the ptype polySi layer (
N_{p}
) increases. The increase of the doping concentration in the ptype polySi layer (
N_{p}
) substantially produces holes in the polySi layer. The absorption coefficient of the polySi layer strongly depends on the doping concentration in the polySi layer (
N_{p}
) because the holes in the ptype polySi layer absorb photons. The absorption coefficient of the ptype polySi layer (
α_{s}
) can be written as shown below
[19]
The (a) shortcircuit current density (J_{sc}), (b) opencircuit voltage (V_{oc}), (c) fill factor (Γ_{f}), and (d) solar cell efficiency (η) as a function of the doping concentration in the ptype polySi layer (N_{p}).
where
α_{eh}
is an intrinsic absorption coefficient of Si,
α_{fc}
is the absorption coefficient of a free electron, and
N_{p}
and
N_{n}
are the doping concentrations in the ptype and ntype polySi layers, respectively. Substituting Eq. (8) into Eq. (1) yields the absorbed light intensity (
I_{abs}
) as follows.
It is obvious that the effects of the doping concentration in the ntype polySi layer (
N_{n}
) on the absorption coefficient and absorbed light intensity are negligible because of its small contribution. From Eq. (9), it is clearly evident that the absorbed light intensity (
I_{abs}
) should be reduced by increasing the doping concentration in the ptype polySi layers (
N_{p}
). Therefore, the shortcircuit current density (
J_{sc}
) is monotonously decreased by increasing the doping concentration in the ptype polySi layer (
N_{p}
), as shown in
Fig. 4(a)
.
Figure 4(b)
shows the opencircuit voltage (
V_{oc}
) as the doping concentration in the ntype polySi layer (
N_{n}
) increases. The doping concentration in the ptype polySi layer is closely related to the opencircuit voltage of the solar cell, which is a measure of the amount of recombination loss in the solar cell. Increasing the doping concentration in the ptype polySi layer reduces the electron concentration in the ptype polySi layer, resulting in suppression of the electronholerecombination. The opencircuit voltage (
V_{oc}
) with respect to the doping concentration in the ptype polySi layer can be written as follows
[20]
where k is the Boltzmann’s constant.
T
is the absolute temperature,
n_{i}
is the intrinsic carrier concentration, and
Δn
and
Δp
are the photogenerated excess electron and hole densities, respectively. From Eq. (10), it is clearly evident that increasing the doping concentration in the ptype polySi layer (
N_{n}
) slightly improves the opencircuit voltage (
V_{oc}
), as shown in
Fig. 4(b)
.
Figure 4(c)
shows the fill factor (Γ
_{f}
) as a function of the doping concentration in the ptype polySi layer. The fill factor (Γ
_{f}
) is not critically affected by the doping concentration in the ptype polySi layer (
N
_{p}
) because the opencircuit voltage (
V_{oc}
) and maximum output voltage (
V_{max}
) are simultaneously affected by the doping concentration in the ptype polySi layer (
N
_{p}
).
Figure 4(d)
shows the variation of the solar cell efficiency (
η
) as a function of the doping concentration in the ptype polySi layer (
N_{p}
). The solar cell efficiency (
η
) is gradually decreased by the doping concentration in the ptype polySi layer (
N_{p}
) because the variation of the shortcircuit current density (
J_{sc}
) is much higher than that of the opencircuit voltage (
V
_{oc}
), as shown in
Figs. 4(a)
and
4(b)
.
Figure 5(a)
shows the shortcircuit current density (
J_{sc}
) as a function of the doping concentration in the ntype polySi layer (
N_{n}
). From Eq. (9), it is clearly evident that the absorbed light intensity (
I_{abs}
) should be reduced by increasing the doping concentration in the ntype polySi layer (
N_{n}
). Therefore, the shortcircuit current density (
J_{sc}
) is slightly reduced by increasing the doping concentration in the ntype polySi layer (
N_{n}
).
Figure 5(b)
shows the variation of the opencircuit voltage (
V_{oc}
) as the doping concentration in the ntype polySi layer (
N_{n}
) increases. Increasing the doping concentration in the ntype polySi layer reduces the hole concentration in the ntype polySi layer, resulting in suppression of the electronholerecombination. The opencircuit voltage (
V_{oc}
) with respect to the doping concentration in the ntype polySi layer can be written as follows
[20]
.
The (a) shortcircuit current density (J_{sc}), (b) opencircuit voltage (V_{oc}), (c) fill factor (Γ_{f}), and (d) solar cell efficiency (η) as a function of the doping concentration in the ntype polySi layer (N_{n}).
From Eq. (11), it is clearly evident that increasing the doping concentration in the ntype polySi layer (
N_{n}
) enhances the opencircuit voltage (
V_{oc}
), as shown in
Fig. 5(a)
.
Figure 5(c)
shows the fill factor (Γ
_{f}
) as a function of the doping concentration in the ntype polySi layer (
N_{n}
). Similar to the case of the ntype polySi layer, the fill factor (Γ
_{f}
) is not significantly affected by the doping concentration in the ntype polySi layer (
N
_{n}
).
Figure 5(d)
shows the solar cell efficiency (
η
) as a function of the doping concentration in the ntype polySi layer (
N_{n}
). The solar cell efficiency (
η
) is gradually increased by the doping concentration in the ntype polySi layer (
N_{n}
) because the variation of the short circuit current density (
J_{sc}
) is much smaller than that of the opencircuit voltage (
V
_{oc}
), as observed in
Figs. 5(a)
and
5(b)
.
III. CONCLUSION
We analyzed the efficiency of the solar cell based on a carbon fiber as functions of the thickness and doping concentration in the p and ntype polySi layers. We found that the solar cell efficiency (
η
) is directly proportional to the short circuit current density (
J_{sc}
). The shortcircuit current density (
J_{sc}
) gradually increased and finally became saturated by increasing the thickness of the ptype polySi layer (
t_{p}
) because of the dependence of the light harvesting efficiency (
η_{lh}
) on the absorbed light intensity (
I_{abs}
). Therefore, the solar cell efficiency (
η
) should gradually increase and finally become saturated by increasing the thickness of the ptype polySi layer (
t_{p}
). However, the solar cell efficiency (
η
) should decrease with increasing the thickness of the ntype polySi layer (
t_{n}
) because of the degradation of the quantum efficiency (
η_{qe}
) which is closely related to the shortcircuit current density (
J_{sc}
). Since the doping concentration in the ptype polySi laser (
N_{p}
) is mainly attributed to the variation of the absorption coefficient of free electrons (
α_{fc}
) rather than that in the ntype polySi layer (
N_{n}
), the solar cell efficiency (
η
) is adequately elevated by reducing the doping concentration in the ptype polySi layer (
N_{p}
). The dependence of the opencircuit voltage (
V_{oc}
) on the doping concentration in the ntype polySi layer (
N_{n}
) should improve the solar cell efficiency (
η
) while increasing the doping concentration in the ntype polySi layer (
N_{n}
). An improvement of the solar cell efficiency based on the carbon fiber to ~10.5% was achieved when the physical parameters of the p and ntype polySi layers in the carbon fiberbased solar cell were
t_{p}
= 40 μm,
t_{n}
= 0.1 μm,
N_{p}
= 1×10
^{16}
cm
^{−3}
, and
N_{n}
= 1×10
^{19}
cm
^{−3}
.
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