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Optical and Quantum Electronics

, Volume 46, Issue 11, pp 1457–1465 | Cite as

Impurity photovoltaic effect in silicon solar cells doped with two impurities

  • Jiren Yuan
  • Honglie Shen
  • Lang Zhou
  • Haibin Huang
  • Naigen Zhou
  • Xinhua Deng
  • Qiming Yu
Article
  • 245 Downloads

Abstract

In this work, a numerical study has been carried out to investigate the impurity photovoltaic (IPV) effect for silicon solar cells doped with two impurities (indium and thallium). It is found that the conversion efficiency \(\eta \) of the IPV solar cell doped with two impurities can improve by 2.21 % absolute, which is greater than that of the IPV solar cell doped with indium (\(\Delta \eta =1.63\,\%\)), but less than that of the one doped with thallium (\(\Delta \eta =2.69\,\%\)). It is concluded that introducing two IPV impurities may not be a good selection for implementing the IPV effect since one impurity with poorer IPV effect can absorb some sub-bandgap photons while contributing fewer currents. The location of impurity energy level is critical to the IPV cell performance. For an acceptor-type IPV impurity, the optimized location of the IPV impurity energy level locates at 0.20–0.26 eV above the valence band edge. Our results may help to make better use of the IPV effect for improving solar cell efficiency.

Keywords

Impurity photovoltaic effect Silicon solar cell Conversion efficiency Indium Thallium 

1 Introduction

With the aggravation of energy crisis and environmental pollution worldwide, solar photovoltaic is considered as one of the most promising technology for our future needs of clean and renewable energy (Agrawal and Tiwari 2013; Zhang et al. 2012). At present, the main efforts in the photovoltaic technology focus on increasing the efficiency and reducing the cost of the solar cells. Some new photovoltaic technologies concentrate on the broad spectrum utilization of solar energy since the conversion efficiency of a solar cell is mainly limited by the waste of the photons with energy less than the bandgap (Luque and Marti 1997). A multi-junction solar cell, which can broaden the absorption range of the solar spectrum, is made up of several single-junction solar cells with different bandgaps (Holovsky et al. 2012; Guha et al. 2013). However, with the increase of the number of single-junction solar cell, the cell design is more complicated, and the fabrication process is very difficult and the preparation cost is rising sharply. If the energy structure of multi-bandgaps can be realized in a single-junction solar cell, it would be beneficial to the reduction of production cost. This idea can be performed by the impurity photovoltaic (IPV) effect (Keevers and Green 1994; Khelifi et al. 2008a, b; Zhao et al. 2010; Sahoo et al. 2011; Azzouzi and Chegaar 2011; Yuan et al. 2011a, 2012).

The mechanism of the IPV effect is to introduce some impurity energy levels within the bandgap. The bandgap of the host semiconductor can be divided into two sub-bandgaps by an impurity energy level. So, the solar cell based on the IPV effect can additionally absorb the photons with energies less than the bandgap. This action can enhance the spectral response for long wavelength sunlight, leading to the increase of the short-circuit current density \(J_{sc}\). Although the introduced impurities can also act as recombination centers, the open-circuit voltage \(V_{oc}\) of the solar cell does not get a significant degradation provided that a proper solar cell structure is adopted (Schmeits and Mani 1999). Thus, a positive gain of conversion efficiency may be achieved for implementing this IPV effect. In fact, several groups showed theoretically that the cell efficiency can get an increase if some IPV impurities are introduced into the host material, such as indium (Keevers and Green 1994; Sahoo et al. 2011), copper (Khelifi et al. 2008b), thallium (Zhao et al. 2010), sulphur (Azzouzi and Chegaar 2011), tellurium (Yuan et al. 2011a) and magnesium (Yuan et al. 2012). However, these works have been limited studies on one IPV impurity introduced into the solar cell. The use of a combination of several IPV impurities may yield exceptional performance than one IPV impurity. Therefore, introducing two IPV impurities in the IPV effect is necessary to have a primary understanding. To the best of our knowledge, published research results about IPV cell do not deal with this problem.

In this paper, we propose two impurities (indium and thallium) as candidates used for IPV silicon solar cells. The potential of the IPV effect in silicon solar cells doped with two impurities was investigated by using the SCAPS program (Burgelman et al. 2000, 2013). The influence of the impurity concentration on the cell performance was discussed. The cause of changing the IPV cell property was analyzed.

2 Methodologies

The operation principle of an IPV solar cell is shown in Fig. 1. Apart from the conventional Shockley–Read–Hall (SRH) mechanism (Shockley and Read 1952; Hall 1952), two impurity optical transitions are included in the model. One impurity optical transition is that a photon with energy \(h\nu _{1}\) pumps an electron from the valence band to the impurity level, and another impurity optical transition is that the second photon of energy \(h\nu _{2}\) excites the electron from there to the conduction band. In other words, two photons with energies less than the bandgap make an electron transit from the valence band to the conduction band and generate an electron–hole pair. If there is no IPV effect, electron–hole pairs are created through the absorption of photons with energy greater than the bandgap. A modified SRH model is applied due to the IPV effect. The net recombination rate \(U\) via impurity is given by (Keevers and Green 1994; Khelifi et al. 2008b)
$$\begin{aligned} U=\frac{np-\left( {n_1 +\tau _{n0} g_{nt} } \right) \left( {p_1 +\tau _{p0} g_{pt} } \right) }{\tau _{n0} \left( {p+p_1 +\tau _{p0} g_{pt} } \right) +\tau _{p0} \left( {n+n_1 +\tau _{n0} g_{nt} } \right) }, \end{aligned}$$
(1)
with
$$\begin{aligned}&\displaystyle \tau _{n0} =\frac{1}{\sigma _n^{th} \upsilon _{th} N_t },\quad \tau _{p0} =\frac{1}{\sigma _p^{th} \upsilon _{th} N_t }\end{aligned}$$
(2)
$$\begin{aligned}&\displaystyle g_{nt} =N_t \int \limits _{\lambda _g }^{\lambda _{n,\max } } {\sigma _n^{opt} } \left( {x,\lambda } \right) \phi _{ph} \left( {x,\lambda } \right) d\lambda ,\end{aligned}$$
(3)
$$\begin{aligned}&\displaystyle g_{pt} =N_t \int \limits _{\lambda _g }^{\lambda _{p,\max } } {\sigma _p^{opt} } \left( {x,\lambda } \right) \phi _{ph} \left( {x,\lambda } \right) d\lambda \end{aligned}$$
(4)
$$\begin{aligned}&\displaystyle n_1 =N_C \exp \left( {-\frac{E_C -E_t }{kT}} \right) ,\quad p_1 =N_V \exp \left( {-\frac{E_t -E_V }{kT}} \right) , \end{aligned}$$
(5)
where \(n\) and \(p\) are the electron and hole concentrations, \(\tau _{n0}\) and \(\tau _{p0}\) the lifetimes for electrons and holes, \(g_{nt}\) and \(g_{pt}\) the optical emission rates from the impurity for electrons and holes, \(N_{t}\) the impurity concentration, \(\upsilon _{th}\) the carrier thermal velocity (\(10^{7}\) cm/s), \(\sigma _n^{th} \) and \(\sigma _p^{th} \) the electron and hole thermal capture cross-sections, \(n_{1}\) and \(p_{1}\) the electron and hole concentrations when the Fermi level coincides with the impurity level, \(N_{C}\) and \(N_{V}\) the effective densities of states in conduction and valence bands, \(E_{C}\) and \(E_{V}\) the conduction and valence band edges, \(E_{t}\) the impurity energy level, \(\sigma _n^{opt} \) and \(\sigma _p^{opt} \) the electron and hole optical emission cross-sections of the impurity.
Fig. 1

Schematic structure and operation principle of the IPV solar cell

The photon flux \(\phi _{ph} (x, \lambda )\) at depth \(x\) from the incident surface for the wavelength \(\lambda \) is given by the following expression (Keevers and Green 1994):
$$\begin{aligned} \phi _{ph} \left( {x,\lambda } \right) =\phi _{ext} \frac{1+R_b e^{-4\alpha _{tot} \left( \lambda \right) \left( {L-x} \right) }}{1-R_f R_b e^{-4\alpha _{tot} \left( \lambda \right) L}}e^{-2\alpha _{tot} \left( \lambda \right) x} \end{aligned}$$
(6)
with
$$\begin{aligned}&\displaystyle \alpha _{tot} =\alpha _{e-h} +\alpha _n +\alpha _p +\alpha _{fc}\end{aligned}$$
(7)
$$\begin{aligned}&\displaystyle \alpha _n \left( \lambda \right) =f_t N_t \sigma _n^{opt} \left( \lambda \right) ,\quad \alpha _p \left( \lambda \right) =(1-f_t )N_t \sigma _p^{opt} \left( \lambda \right) \end{aligned}$$
(8)
where \(\phi _{ext}\) is the external incident photon flux, \(R_{f}\) and \(R_{b}\) the internal reflection coefficients at the front and back surface of the cell, \(L\) the total length of the cell, \(\alpha _{e-h}\) the band-to-band absorption coefficient, \(\alpha _n \) and \(\alpha _p \) the impurity absorption coefficients for electron and hole photoemission from the IPV impurity, \(\alpha _{fc} \) the absorption coefficient for free-carrier absorption, and \(f_{t}\) the occupation probability of impurity level, respectively.
The silicon solar cell is a p\(^{+}\)–n–n\(^{+}\) structure as shown in Fig. 1. For the p\(^{+}\) emitter layer, the doping concentration \(N_{A}\) is 10\(^{18}\) cm\(^{-3}\) and the thickness is 2 \(\upmu \)m; for the n base layer, the doping concentration \(N_{D}\) and the thickness are \(2\times 10^{17}\,\mathrm{cm}^{-3}, 100\,\upmu \)m, respectively; for the n\(^{+}\) layer, the doping concentration \(N_{D}\) and the thickness are \(10^{18 }\,\mathrm{cm}^{-3}, 5\,\upmu \)m, respectively. The acceptor-type IPV impurities (indium and thallium) are assumed to be only contained in n base layer. The energy level of indium in Si is at 0.157 eV above the valence band edge (Sze and Ng 2007), and that of thallium in Si is at 0.26 eV above the valence band edge (Sze and Ng 2007). The electron and hole thermal capture cross-sections for indium impurity are set as \(2\times 10^{-22}\) and \(8\times 10^{-15}\,\mathrm{cm}^{2}\) (Keevers and Green 1994), respectively. The electron and hole thermal capture cross-sections for thallium impurity are set as \(1\times 10^{-22}\) and \(5.07\times 10^{-15}\,\mathrm{cm}^{2}\) (Zhao et al. 2010), respectively. Basic parameters used for the IPV Si solar cell at 300 K are listed in Table 1 (Sze and Ng 2007). The electron and hole photoemission cross-sections of the IPV impurities are calculated in accordance with the model of Lucovsky (1965). \(\sigma _n^{opt} \) and \(\sigma _p^{opt} \) are assumed to be zero for the photons with energy above bandgap. The absorption of free carriers is ignored. The transition of carriers between impurities is accounted for. The simulated illumination is AM 1.5 G, 100 mW/cm\(^{2}\). \(R_{f}\) and \(R_{b}\) are both set to 0.999.
Table 1

Basic parameters for the silicon solar cell used in this study (at 300 K)

Parameter and unit

Value

Bandgap (eV)

1.12

Dielectric constant

11.9

Electron affinity (eV)

4.05

Effective conduction band density (cm\(^{-3}\))

\(2.80\times 10^{19}\)

Effective valence band density (cm\(^{-3}\))

\(2.65\times 10^{19}\)

Electron mobility (\(\mathrm{cm}^{2}\,\mathrm{V}^{-1}\,\mathrm{s}^{-1}\))

1,350

Hole mobility (\(\mathrm{cm}^{2}\,\mathrm{V}^{-1}\,\mathrm{s}^{-1}\))

450

Surface recombination velocity (cm/s)

10\(^{4}\)

Indium energy level \(E_{t}-E_{V}\) (eV)

0.157

Thallium energy level \(E_{t}-E_{V}\) (eV)

0.26

3 Results and discussion

Figure 2 shows the short-circuit current density \(J_{sc}\) as a function of the impurity concentration of indium and/or thallium. It can be seen that the short-circuit current density increases from 39.75 to 44.13 mA/cm\(^{2}\) with increasing the impurity concentration of indium and thallium when \(N_{t}\le N_{D}\). Note that the introduced impurity concentration of indium is as same as that of thallium, i.e. \(N_{t}\mathrm{(indium)}=N_{t}\mathrm{(thallium)}\). The \(J_{sc}\) increases from 39.62 to 42.64 mA/cm\(^{2}\) when only one impurity (indium) is introduced into the solar cell and that increases from 39.81 to 45.10 mA/cm\(^{2}\) when just thallium is introduced into the solar cell. These improvements of the short-circuit current density come from the absorption of sub-bandgap photons. It is worth notice that the gain of introducing two impurities is less than that of introducing thallium, but greater than that of introducing indium. Obviously, the improvement of introducing thallium is greater than that of introducing indium. The reason should be that thallium impurity is at an optimized energy level location for implementing the IPV effect. If the energy level location is too deep so that these impurities can act as the effective recombination centers. If the energy level location is too shallow so that some sub-bandgap photons cannot be absorbed. In our previous work (Yuan et al. 2011b), we calculated the total number of photons in the range of 1.12–0.963 eV (i.e. the conduction band edge to the indium energy level) under air mass 1.5 global spectrum. The number of the photons reaches \(4.1\times 10^{16}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}\). These subgap photons can theoretically contribute to the short-circuit current density of 6.6 mA/cm\(^{2}\). Similarly, the total number of photons in the range of 1.12–0.86 eV (\(0.86=1.12-0.26\)) can achieve \(5.5\times 10^{16}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}\). The short-circuit current density calculated can attain 8.8 mA/cm\(^{2}\). When a combination of indium and thallium works as the IPV impurity in the solar cell, the indium impurity should absorb some available subgap photons. These subgap photons would contribute much more currents if they are absorbed by the thallium impurity. As a result, the improvement of the short-circuit current density of introducing thallium is much than that of introducing indium/(indium + thallium).
Fig. 2

Short-circuit current density \(J_{sc}\) as a function of the impurity concentration of indium and/or thallium

When the impurity concentration \(N_{t}\) is larger than the doping concentration \(N_{D}\), the short-circuit current density decreases for injecting indium, thallium and the combination of indium and thallium. This is due to the overcompensation of the impurity for the base doping. This can make electron photoemission from the valence band to the impurity energy level maximized and result in the decrease of the photon flux \(\phi _{ph} \) available for the electron photoemission process from the impurity energy level to the conduction band. So, the \(J_{sc}\) decreases with increasing the impurity concentration when \(N_{t} > N_{D}\).

Figure 3 depicts the open-circuit voltage \( V_{oc}\) versus the impurity concentration. It is found that \(V_{oc}\) increases slightly first and then decreases as impurity concentration increases. The slight increase of the \(V_{oc}\) comes from the increase of the short-circuit current density \(J_{sc}\). According to the equation (Green 1982):
$$\begin{aligned} V_{\hbox {oc}} =\frac{kT}{q}\left[ {\ln \left( {\frac{J_{\hbox {sc}} }{J_0 }} \right) +1} \right] \approx \frac{kT}{q}\left[ {\ln \left( {\frac{J_{\hbox {sc}} }{J_0 }} \right) } \right] \end{aligned}$$
(9)
where \(J_{0}\) is the dark saturation current density, \(q\) is the elementary charge, \(k\) is the Boltzmann constant, \(T\) is the absolute temperature.
Fig. 3

Open-circuit voltage \(V_{oc}\) versus the impurity concentration of indium and/or thallium

\(V_{oc}\) increases slightly first with the increasing \(J_{sc}\) since \(J_{0}\) has more little change when the impurity concentration is low. But, after that \(V_{oc}\) decreases as impurity concentration increases since the recombination of the solar cell gets a more drastic increase when the impurity concentration is around the base layer doping. It can be seen that the decrease of the \(V_{oc}\) is not very much since the special cell structure p\(^{+}\)–n–n\(^{+}\) can keep a high value for the built-in voltage, safeguarding the open-circuit voltage (Schmeits and Mani 1999).

In Fig. 4, the cell efficiency is plotted versus impurity concentration of indium, thallium and indium + thallium. It is shown that conversion efficiency increases from 25.00 to 27.69 % when the thallium impurity is introduced. If the indium impurity is introduced into the Si solar cell, the cell efficiency varies from 24.87 to 26.50 %. While two impurities are introduced, the cell efficiency increases from 24.98 to 27.19 %. The improvements of the absolute conversion efficiencies for the above IPV solar cells are 2.69, 1.63 and 2.21 %, respectively. It is clear that the IPV cell for the most improvement is the one doped with thallium impurity. It can be concluded that the location of impurity levels has important impact on IPV cell performance. Hence, we plot the efficiency as a function of the energy level location of the IPV impurity, as illustrated in Fig. 5. It is observed that the efficiency is maximal when the impurity energy level locates at 0.20–0.26 eV above the valence band edge. Also, we calculated the current–voltage curve using the combination of two IPV impurities with different concentrations, as shown in Fig. 6. When the introduced impurity concentrations of indium and thallium are \(10^{16}\) and \(10^{15}\,\mathrm{cm}^{-3}\), respectively, the short-circuit current density and the conversion efficiency of the IPV cell are 42.05 mA/cm\(^{2}\) and 26.12 %, respectively. While those of indium and thallium are \(10^{15}\) and \(10^{16}\,\mathrm{cm}^{-3}\), respectively, the short-circuit current density and the conversion efficiency of the IPV cell are 44.96 mA/cm\(^{2}\) and 27.42 %, respectively. The results indicate that thallium impurity can act as a good role in the IPV solar cell. Moreover, the combination of two IPV impurities may not be a desired selection for implementing the IPV effect.
Fig. 4

Cell efficiency \(\eta \) versus impurity concentration of indium, thallium and indium + thallium

Fig. 5

Cell efficiency \(\eta \) as a function of the energy level location of the IPV impurity

Fig. 6

Current–voltage curve of introducing two IPV impurities with different concentrations

4 Conclusions

We carried out a numerical study on the IPV effect in silicon solar cells doped with indium and thallium. It is found that an increase of 2.21 % for conversion efficiency can be obtained by the IPV effect of introducing the two impurities. The improvement of the conversion efficiency of introducing two impurities is much than that of introducing indium and less than that of introducing thallium. Introducing two IPV impurities may not be a good selection for implementing the IPV effect. The energy level location of the IPV impurity has vital impact on the cell performance. When the IPV impurity is acceptor-type, the optimized location of the IPV impurity energy level locates at 0.20–0.26 eV above the valence band edge.

Notes

Acknowledgments

We acknowledge the free use of the SCAPS program developed by Prof. M. Burgelman’s group at the ELIS of the University of Gent, Belgium. We are very grateful to Prof. M. Burgelman for his helpful discussion about the IPV solar cell. This work was supported by the National Natural Science Foundation of China (Grant Nos. 61176062, 61306084, 51361022), the Priority Academic Program Development of Jiangsu Higher Education Institutions, the Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20113601120006), the Natural Science Foundation of Jiangxi Province of China (Grant No. 20122BAB202002) and the Science and Technology Project of Education Department of Jiangxi Province (Grant No. GJJ13010).

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Jiren Yuan
    • 1
    • 2
    • 3
  • Honglie Shen
    • 2
  • Lang Zhou
    • 1
  • Haibin Huang
    • 1
  • Naigen Zhou
    • 1
  • Xinhua Deng
    • 3
  • Qiming Yu
    • 3
  1. 1.School of Materials Science and EngineeringNanchang UniversityNanchang People’s Republic of China
  2. 2.College of Materials Science and TechnologyNanjing University of Aeronautics and AstronauticsNanjing People’s Republic of China
  3. 3.School of ScienceNanchang UniversityNanchang People’s Republic of China

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