Exploring the possibility of semiconducting BaSi2 for thin-film solar cell applications

Takashi Suemasu

doi:10.7567/JJAP.54.07JA01

1. Introduction

Recently, photovoltaic solar cells have been attracting considerable attention. At present, wafer-based silicon solar cells are still the main technology and have approximately 80% of the market share because of the earth's abundance of silicon and the technologies developed for their fabrication. Thin-film solar cell materials, such as chalcopyrites and CdTe, have also been gaining much attention from the viewpoint of their cost effective growth procedure and high optical absorption.¹^–⁶⁾ Thin-film Si solar cells have also been studied extensively to achieve high efficiencies by utilizing an efficient light-trapping system;⁷^–¹⁷⁾ however, achieving efficiencies as high as 20% is not easy. Thus, we consider that exploring alternative materials for thin-film solar cell applications is very important. Among such materials, we have focused on barium disilicide (BaSi₂).¹⁸^,¹⁹⁾ Both theoretical and experimental studies revealed that it has a band gap of approximately 1.3 eV²⁰⁾ and has high absorption coefficients (α) exceeding 3 × 10⁴ cm⁻¹ for photon energies higher than 1.5 eV.²¹^–²³⁾ Recent experimental results such as a large minority-carrier diffusion length (L ∼ 10 µm),²⁴^,²⁵⁾ a long minority-carrier lifetime (τ ∼ 10 µs),²⁶^–²⁸⁾ and potential variations around grain boundaries (GBs)²⁹⁾ confirmed that BaSi₂ could be a new candidate for thin-film solar cells. The obtained values of α, L, and τ are sufficiently large for thin-film solar cell applications. In BaSi₂, the conduction-band minimum is located at $\text{T}(0,1/2,1/2)$ , and the valence-band maximum is at approximately $(0,1/3,0)$ along the $\Gamma \text{--}\text{Y}(0,1/2,0)$ direction.²¹^,²³^,³⁰⁾ The direct transition occurs at approximately $(0,1/3,0)$ , and its gap value is higher than the band gap by approximately 0.1 eV. This might be the reason why the experimental studies have revealed that BaSi₂ has high absorption coefficients in spite of its indirect band gap nature.²⁰^,²²⁾ To form BaSi₂ homojunction diodes, the electrical properties of impurity (Cu, Ag, Sb, P, As, In, Al, and B)-doped BaSi₂ thin films have also been investigated.³¹^–³⁹⁾ The top of the valence band of BaSi₂ is composed mostly of the Si 3p state as determined by theoretical and experimental studies.²¹^,²³^,⁴⁰^–⁴³⁾ According to Imai and Watanabe, the substitution of Si in the BaSi₂ lattice is more favorable than the substitution of Ba from the energetic point of view.⁴⁴⁾ Among these elements, Sb and B were proved to be suitable for n⁺-BaSi₂ and p⁺-BaSi₂, respectively. Their diffusion coefficients are another important parameter that should be taken into consideration. Most impurities except B have high diffusion coefficients in BaSi₂.⁴⁵^,⁴⁶⁾ One of the most attractive features of undoped n-BaSi₂ is that we can utilize both a high α and a large L. This feature facilitates the collection of photogenerated carriers in an external circuit even though L degrades to some extent owing to extrinsic effects such as crystal imperfections and other causes. Thus, we plan to use undoped n-BaSi₂ as an active layer in a solar cell.

In this review article, we explore the possibility of BaSi₂ as a new material for thin-film solar cell applications on the basis of previously reported experimental data. First, we present the α, L, and τ values for undoped n-BaSi₂ films formed on Si(111).²²^,²⁴^–²⁸⁾ After that, the photoresponse spectra are calculated for a BaSi₂ p⁺n abrupt homojunction diode on the basis of using the one-dimensional carrier continuity equation. Individual contributions of the neutral p⁺ layer, the depletion region, and the neutral n layer to the total photoresponse are discussed. We further estimate the photocurrent density and the open-circuit voltage under AM1.5 illumination.

2. Experimental procedure

To measure α in BaSi₂, we formed a "transparent" Si(111) substrate. This is to ensure both the transparency of the substrate and the high quality of the grown film. First, 500-µm-thick high-resistivity Si(111) (ρ > 1000 Ω·cm) and 500-µm-thick fused silica wafers were bonded at room temperature (RT). Then, the Si wafer was mechanically ground and polished by chemical mechanical polishing (CMP) down to about 0.7 µm thickness. Before the substrates were loaded into the molecular beam epitaxy (MBE) chamber, oxide layers on the surface of this silicon-on-insulator (SOI) substrate were etched away using diluted hydrofluoric acid. Thermal treatment was performed at 590 °C for 20 min in ultrahigh vacuum to clean the hydrogen-terminated surface. The details of the growth procedure are described in Ref. 22. Briefly, a BaSi₂ template layer was firstly grown by reactive deposition epitaxy (RDE) at 525 °C, that is, Ba was deposited on a hot Si(111) surface. The template layer works as seed crystals for subsequent layers. Next, Ba and Si were codeposited on the template layer at 580 °C by MBE to form approximately 80-nm-thick undoped n-BaSi₂ epitaxial films at 575 °C using a Knudsen cell and an electron-beam gun, respectively. The same growth method was utilized for the epitaxial growth of semiconducting β-FeSi₂ films.⁴⁷^,⁴⁸⁾ Undoped BaSi₂ shows n-type conductivity with an electron concentration of approximately 10¹⁶ cm⁻³.²⁰^,⁴⁹⁾ This was determined by Hall measurements and capacitance–voltage analysis.

For L measurements by an electron-beam-induced current (EBIC) technique, n-Si substrates (ρ = 0.1 Ω·cm) were prepared by subjecting them to the following treatment. We grew 300-nm-thick undoped n-BaSi₂ films by RDE, followed by MBE.²⁴⁾ For EBIC measurements, Al/n-BaSi₂ Schottky diodes were formed. Front-surface Schottky contacts were formed with Al on the BaSi₂ surface via wire bonding, and a back-surface ohmic contact made of Al was formed by sputtering. EBIC observations were carried out in the edge-scan configuration under a Hitachi S4300 field-emission scanning electron microscope in the EBIC mode at RT.⁵⁰⁾ The acceleration voltage of the electron beam, V_ac, was set at 5 kV to avoid penetration of the electron beam into the Si substrate. When V_ac is 5 kV, the penetration depth of the electron beam is estimated to be less than 300 nm from the density of BaSi₂ (5.14 g/cm³). We employed a JASCO U-best 570 spectrophotometer to obtain the transmission spectra of the samples.

For τ measurements, we grew approximately 500-nm-thick BaSi₂ epitaxial films with various grain sizes (samples A–H) on high-resistivity n-Si(111) (ρ > 1000 Ω·cm) substrates by changing the growth temperature during RDE and the Ba deposition rate.⁵¹⁾ We aimed to clarify whether or not the GBs in BaSi₂ epitaxial films affect the minority carrier lifetime. Samples B and C were capped with a 3-nm-thick Ba or Si layer formed at a low temperature (100 °C). Electron backscatter diffraction (EBSD) analyses were performed to analyze the grain size of BaSi₂. τ was measured by the microwave-detected photoconductivity decay (µ-PCD) method. In this method, electron–hole pairs were generated by a 5 ns laser pulse with a wavelength of 349 nm, and photoconductivity decay was measured on the basis of the reflectivity of a microwave with a frequency of 26 GHz.²⁶⁾ The excitation laser intensity was varied from 1.1 × 10² to 1.3 × 10⁵ W/cm², corresponding to an area photon density in the range from 9.8 × 10¹¹ to 1.1 × 10¹⁵ cm⁻², assuming no reflection on the BaSi₂ surface.

3. Results and discussion

3.1. Optical absorption coefficient

The transmission spectrum for the BaSi₂/SOI structure is presented in Fig. 1(a). This spectrum was significantly influenced by an interference effect within the 0.7-µm-thick Si layer. The Si layer was very thin and flat owing to CMP, so that these interference fringes were superimposed on the spectrum. We used the equations presented in Ref. 52 to derive an interference-free transmission spectrum. As shown in Fig. 1(a), the transmission spectrum was fitted by the maximal extremes of the interference fringes (T_M) and also by their minimal extremes (T_m). Assuming that the Si layer has a certain absorption coefficient on a transparent substrate, the interference-free transmission spectrum T_α can be expressed simply as the geometric mean of T_M and T_m $(T_{\alpha } = \sqrt{T_{\text{M}}T_{\text{m}}} )$ over the entire transmission spectrum.⁵²⁾ We calculated T_α using the T_M and T_m curves, and also eliminated the absorption due to the Si layers by measuring the transmission spectrum of another SOI substrate. We finally normalized T_α by taking the reflectivity of the sample into consideration. Using T_α, we were able to obtain the absorption spectrum shown in Fig. 1(b). The absorption coefficient of BaSi₂ reached 3 × 10⁴ cm⁻¹ at 1.5 eV. Figure 1(c) shows the (αdhν)^1/2 vs hν plot used to derive the indirect optical absorption edge. Here, d is the BaSi₂ layer thickness and hν is the photon energy. The straight fitting line intersects the x-axis at 1.34 eV. Thus, the indirect absorption edge with phonon emission was at 1.34 eV. It is true that absorption coefficients below 10² cm⁻¹ are necessary to determine the precise energy gap. A much thicker BaSi₂ will enable us to measure smaller absorption coefficients precisely. At present, the obtained absorption edge agrees well with the photoresponse spectra; the photocurrent increased sharply for energies greater than 1.3 eV.⁵³⁾ Thus, the absorption edge determined above is acceptable.

$T_{\alpha } = \sqrt{T_{\text{M}}T_{\text{m}}} $ — **Fig. 1.** (a) Transmission spectrum for sample A, where $T_{\alpha } = \sqrt{T_{\text{M}}T_{\text{m}}}$ . (b) Absorption spectrum. (c) (αdhν)^1/2 versus hν plot.²²⁾
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3.2. Minority-carrier diffusion length

Figures 2(a) and 2(b) show the secondary electron (SE) and EBIC images of BaSi₂ on Si(111), respectively, with V_ac = 5 kV.²⁴⁾ To obtain Figs. 2(a) and 2(b), we used the same BaSi₂ film as reported in Ref. 24, but we formed the Schottky contact with the Al wire at different positions to measure L. In the EBIC method, the carriers generated within the diffusion length of the n-type BaSi₂ are collected by the electric field under the Schottky contact and sensed as a current in the external circuit. The brighter regions indicate a higher number of electron-beam-induced carriers collected in the BaSi₂. Figure 2(c) shows the plot of EBIC line-scan data along the broken line AA' in Fig. 2(b). The EBIC profiles show a clear exponential dependence on the distance from the metal contacts. The contribution of carriers generated within the n-Si substrate to the measured EBIC signals can be excluded as described above. In this work, L was estimated to be approximately 8.6 µm for holes in the n-BaSi₂ on Si(111), assuming that the EBIC profile varies as exp(−x/L). Here, x is the distance from the metal edge along the line, which is almost the same as that reported previously.²⁴⁾

**Fig. 2.** (a) SE and (b) EBIC images around the Al contact. (c) Experimental EBIC line-scan profile along dotted line AA' in (b).²⁵⁾
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3.3. Minority-carrier lifetime

Figure 3 shows 12 × 12 µm² EBSD crystal orientation maps and distribution histograms of the grain area fraction in samples A–H. The red, blue, and green colors indicate that three epitaxial variants of a-axis-oriented BaSi₂ exist on Si(111).²⁴⁾ The average grain area of the BaSi₂ varied in the range from 2.6 to 23.3 µm².²⁸⁾ It seems reasonable to think that the density of BaSi₂ GBs decreases when the average grain area increases. Figure 4(a) shows a typical example of the normalized µ-PCD decay curve, obtained for sample C. The decay curve can be divided into three decay modes, that is, Auger recombination and Shockley–Read–Hall (SRH) recombinations without and with the carrier-trapping effect, denoted by decay times of τ_Auger, τ_SRH, and τ_SRH-trapping, respectively. The inserted dotted lines correspond to the exponential decays of these three modes. In the SRH recombination, we assume a trap level in the band gap, where the recombination of electrons and holes occurs via this level.⁵⁴⁾ Basically, upon laser irradiation, Auger recombination occurs in the initial stage because of the high absorption coefficient of BaSi₂ for the 349 nm light, and the high excitation in the µ-PCD measurement. The initial excess carrier concentration, Δn, at the surface reaches the range of 10¹⁸ to 10²¹ cm⁻³, which was calculated from the absorption coefficient of BaSi₂ at a wavelength of 349 nm and the irradiated laser intensity. Thus, it is difficult to avoid Auger recombination in the present µ-PCD measurement. Since there is an electric field in BaSi₂ due to the difference in electron affinity between BaSi₂ (3.2 eV)⁵⁵⁾ and Si (4.0 eV), carrier separation occurs at the same time as Auger recombination, followed by SRH recombination. In this work, we used τ_SRH as a measure to investigate the minority-carrier properties of BaSi₂ films. This is because the first decay mode, Auger recombination, is not likely to happen under AM 1.5 illumination. Thus, the second decay mode is very important; τ_SRH should be sufficiently large to achieve high efficiency. τ_SRH decreased with increasing Δn. This is because Δn is orders of magnitude higher than the majority-carrier (electron) density of approximately 10¹⁶ cm⁻³ at equilibrium in undoped n-BaSi₂. Such a high carrier injection level leads to multicarrier recombination. We therefore adopted τ_SRH when Δn was about 10¹⁶ cm⁻³. For this small Δn, it was confirmed that the influence of the high-resistivity Si substrate on τ_SRH was negligible, as shown by experiments using exfoliated BaSi₂ films.⁵⁶⁾

**Fig. 3.** 12 × 12 µm² EBSD crystal orientation maps of the BaSi₂ epitaxial films and distribution histograms of BaSi₂ grain area fraction in samples A–H. The average grain area for each sample is also presented.²⁸⁾
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Fig. 4. — Download figure:
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Figure 4(b) shows the dependence of τ_SRH on the average grain area of BaSi₂ for samples A–H. For the samples without capping layers, τ_SRH values were grouped into two, that is, approximately 0.4 µs (samples A and E) and 8–10 µs (samples D and F–H). In each group, τ_SRH is almost the same, regardless of the BaSi₂ average grain area. The difference between the two groups was due to the surface conditions.²⁸⁾ BaSi₂ films with a large τ_SRH had cloudy surfaces, whereas those with a smaller τ_SRH had mirror surfaces. However, the problem was that we were not able to intentionally grow BaSi₂ films with a large τ_SRH. This problem was overcome by in situ capping with a 3 nm Ba or Si layer on BaSi₂ in samples B and C, as shown in Fig. 4(b). X-ray photoemission spectroscopy analyses revealed that the O atoms may play an important role in making τ_SRH large.²⁸⁾ Currently, we are able to form BaSi₂ films with a large τ_SRH of approximately 10 µs, regardless of the grain size of BaSi₂, by capping the surface of BaSi₂ with the Ba or Si layer. This means that τ_SRH is not influenced by GBs. This result is consistent with what we expect from the potential variations around the GBs,²⁹⁾ where the potentials are higher at GBs and thus minority carriers (holes) are not attracted towards the defective GBs.

3.4. Photoresponse spectra, photocurrent density, and open-circuit voltage

In this subsection, we attempt to deduce the expected photocurrent density in a BaSi₂ homojunction diode. Analytical expressions for the photogenerated and dark current densities can be obtained only when the dopant concentration, minority-carrier lifetime, and other parameters are assumed constant.⁵⁷^,⁵⁸⁾ We assume here a simple p⁺n abrupt junction diode, as shown in Fig. 5. When monochromatic light of energy E is incident on the front surface (p⁺), the generation rate of electron–hole pairs per unit volume per unit time at a distance x from the semiconductor surface, G(x), is given by

$\begin{equation} G(x) = \alpha\Phi_{0}(1-R)\exp(-\alpha x). \end{equation} \tag{ 1 }$

Here, Φ₀ is the number of photons incident per unit time per unit area per unit bandwidth at energy E, and R is the reflectance at the surface. These three parameters vary with E, and thus G(x) depends on E. The total photocurrent density j is given by the sum of the current density due to electrons generated within the neutral p⁺-BaSi₂ region, j_e, the current density due to electron–hole pairs generated within the depletion region, j_DL, and the current density due to holes generated within the neutral n-BaSi₂ region, j_h. The internal quantum efficiency IQE is equal to

$\begin{equation} \mathit{IQE}(E) = \frac{j}{q\Phi_{0}(1 - R)} = \frac{j_{\text{e}} + j_{\text{DL}} + j_{\text{h}}}{q\Phi_{0}(1 - R)}. \end{equation} \tag{ 2 }$

Once IQE is derived, the total photocurrent density $J_{\text{L}}$ obtained from the solar spectral range is given by

$\begin{equation} J_{\text{L}} = \int j\,dE = q\int\Phi_{0}(1 - R)\mathit{IQE}(E)\,dE. \end{equation} \tag{ 3 }$

To increase J_L, we should minimize R and maximize IQE over the solar spectral range. Therefore, IQE is a measure of the quality of the diode. Assuming that the quantum efficiency is 100% because of the electric field within the depletion region, j_DL is expressed as

$\begin{align} j_{\text{DL}}(E) &= q\int_{W_{\text{e}}}^{W_{\text{e}} + W}G(x)\,dx \\ &= q(1 - R)\Phi_{0}e^{-\alpha W_{\text{e}}}(1 - e^{-\alpha W}). \end{align} \tag{ 4 }$

Here, q is the elemental charge and W is the depletion region width.

**Fig. 5.** Dimensions and parameters in a simple p⁺n abrupt homojunction diode.
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We next derive j_e. The excess electron concentration $\Delta n_{\text{p}}$ in the neutral p⁺-type layer (0 ≤ x ≤ W_e) is given by solving the current continuity equation for electrons as follows:

$\begin{equation} D_{\text{e}}\frac{d^{2}\Delta n_{\text{p}}}{dx^{2}} - \frac{\Delta n_{\text{p}}}{\tau_{\text{e}}} + G(x) = 0. \end{equation} \tag{ 5 }$

Here, D_e is the diffusivity and τ_e is the minority-carrier (electron) lifetime. There are two boundary conditions. At the surface, we have surface recombination with a recombination velocity S_e under the condition of

$\begin{equation} D_{\text{e}}\frac{d\Delta n_{\text{p}}}{dx} = S_{\text{e}}(n_{\text{p}} - n_{\text{po}}) \quad \text{at}\quad x = 0, \end{equation} \tag{ 6 }$

where n_p and n_p0 are the electron concentrations in the neutral p⁺ layer under biased conditions and under thermal equilibrium, respectively. At the depletion edge, the electron concentration is given by

$\begin{equation} n_{\text{p}}(x = W_{\text{e}}) = n_{\text{p0}}\exp\left(\frac{qV}{k_{\text{B}}T}\right). \end{equation} \tag{ 7 }$

Here, V is the forward voltage applied across the p⁺n junction under illumination. Once n_p(x) is obtained, j_e is given by

$\begin{align} j_{\text{e}} &= qD_{\text{e}}\left(\frac{dn_{\text{p}}}{dx}\right)_{x = W_{\text{e}}}{} = -q\frac{D_{\text{e}}}{L_{\text{e}}}p_{\text{p0}}\left[\exp\left(\frac{qV}{k_{\text{B}}T}\right)-1\right]\cfrac{\cfrac{S_{\text{e}}L_{\text{e}}}{D_{\text{e}}}\cosh\biggl(\cfrac{W_{\text{e}}}{L_{\text{e}}}\biggr) + \sinh\biggl(\cfrac{W_{\text{e}}}{L_{\text{e}}}\biggr)}{\cosh\biggl(\cfrac{W_{\text{e}}}{L_{\text{e}}}\biggr)+ \cfrac{S_{\text{e}}L_{\text{e}}}{D_{\text{e}}}\sinh\biggl(\cfrac{W_{\text{e}}}{L_{\text{e}}}\biggr)}\\ &\quad + q\Phi_{0}(1 - R)\frac{\alpha L_{\text{e}}}{\alpha^{2}L_{\text{e}}^{2} - 1}\times\left\{\cfrac{\biggl(\cfrac{S_{\text{e}}L_{\text{e}}}{D_{\text{e}}} + \alpha L_{\text{e}}\biggr) - e^{-\alpha W_{\text{e}}}\biggl[\cfrac{S_{\text{e}}L_{\text{e}}}{D_{\text{e}}}\cosh\biggl(\cfrac{W_{\text{e}}}{L_{\text{e}}}\biggr) + \sinh\biggl(\cfrac{W_{\text{e}}}{L_{\text{e}}}\biggr)\biggr]}{\cosh\biggl(\cfrac{W_{\text{e}}}{L_{\text{e}}}\biggr) + \cfrac{S_{\text{e}}L_{\text{e}}}{D_{\text{e}}}\sinh\biggl(\cfrac{W_{\text{e}}}{L_{\text{e}}}\biggr)} -\alpha L_{\text{e}}e^{-\alpha W_{\text{e}}}\right\}, \end{align} \tag{ 8 }$

where L_e = (D_eτ_e)^1/2 is the diffusion length of electrons in the neutral p⁺-type layer. The first term in Eq. (8) is the dark current flowing in the opposite direction to the photocurrent.

In the same way, j_h is given by

$\begin{align} j_{\text{h}} &= -qD_{\text{h}}\left(\frac{dp_{n}}{dx}\right)_{x = W_{\text{e}} + W}{} = -q\frac{D_{\text{h}}}{L_{\text{h}}}p_{\text{n0}}\left[\exp\left(\frac{qV}{k_{\text{B}}T}\right) - 1\right]\cfrac{\cfrac{S_{\text{h}}L_{\text{h}}}{D_{\text{h}}}\cosh\biggl(\cfrac{W_{\text{b}}}{L_{\text{h}}}\biggr) + \sinh\biggl(\cfrac{W_{\text{b}}}{L_{\text{h}}}\biggr)}{\cosh\biggl(\cfrac{W_{\text{b}}}{L_{\text{h}}}\biggr) + \cfrac{S_{\text{h}}L_{\text{h}}}{D_{\text{h}}}\sinh\biggl(\cfrac{W_{\text{b}}}{L_{\text{h}}}\biggr)}\\ &\quad + q\Phi_{0}(1 - R)\frac{\alpha L_{\text{h}}}{\alpha^{2}L_{\text{h}}^{2} - 1}e^{-\alpha (W_{\text{e}} + W)}\times\left\{\alpha L_{\text{h}} - \cfrac{\cfrac{S_{\text{h}}L_{\text{h}}}{D_{\text{h}}}\biggl[\cosh\biggl(\cfrac{W_{\text{b}}}{L_{\text{h}}}\biggr) - e^{-\alpha W\text{b}}\biggr] + \sinh\biggl(\cfrac{W_{\text{b}}}{L_{\text{h}}}\biggr) + \alpha L_{\text{h}}e^{-\alpha W_{\text{b}}}}{\cosh\biggl(\cfrac{W_{\text{b}}}{L_{\text{h}}}\biggr) + \cfrac{S_{\text{h}}L_{\text{h}}}{D_{\text{h}}}\sinh\biggl(\cfrac{W_{\text{b}}}{L_{\text{h}}}\biggr)}\right\}. \end{align} \tag{ 9 }$

Here, D_h is the diffusivity and τ_h is the minority-carrier (hole) lifetime in the neutral n-type layer. The minority-carrier (hole) diffusion length L_h is expressed as (D_hτ_h)^1/2. From Eqs. (4), (8), and (9), the contributions of j_DL, j_e, and j_h to IQE, that is, IQE_DL, IQE_e, and IQE_h, respectively, are described as follows:

$\begin{align} \mathit{IQE}_{\text{DL}} &= e^{-\alpha W_{\text{e}}}(1 - e^{-\alpha W}), \end{align} \tag{ 10 }$

$\begin{align} \mathit{IQE}_{\text{e}} &= \frac{\alpha L_{\text{e}}}{\alpha^{2}L_{\text{e}}^{2} - 1}\times\left\{\cfrac{\biggl(\cfrac{S_{\text{e}}L_{\text{e}}}{D_{\text{e}}} + \alpha L_{\text{e}}\biggr) - e^{-\alpha W_{\text{e}}}\biggl[\cfrac{S_{\text{e}}L_{\text{e}}}{D_{\text{e}}}\cosh\biggl(\cfrac{W_{\text{e}}}{L_{\text{e}}}\biggr) + \sinh\biggl(\cfrac{W_{\text{e}}}{L_{\text{e}}}\biggr)\biggr]}{\cosh\biggl(\cfrac{W_{\text{e}}}{L_{\text{e}}}\biggr) + \cfrac{S_{\text{e}}L_{\text{e}}}{D_{\text{e}}}\sinh\biggl(\cfrac{W_{\text{e}}}{L_{\text{e}}}\biggr)} -\alpha L_{\text{e}}e^{-\alpha W_{\text{e}}}\right\}, \end{align} \tag{ 11 }$

$\begin{align} \mathit{IQE}_{\text{h}} &= \frac{\alpha L_{\text{h}}}{\alpha^{2}L_{\text{h}}^{2} - 1}e^{-\alpha(W_{\text{e}} + W)}\times\left\{\alpha L_{\text{h}} - \cfrac{\cfrac{S_{\text{e}}L_{\text{e}}}{D_{\text{e}}}\biggl[\cosh\biggl(\cfrac{W_{\text{b}}}{L_{\text{h}}}\biggr) - e^{-\alpha W_{\text{b}}}\biggr] + \sinh\biggl(\cfrac{W_{\text{b}}}{L_{\text{h}}}\biggr) + \alpha L_{\text{h}}e^{-\alpha W_{\text{b}}}}{\cosh\biggl(\cfrac{W_{\text{b}}}{L_{\text{h}}}\biggr) + \cfrac{S_{\text{h}}L_{\text{h}}}{D_{\text{h}}}\sinh\biggl(\cfrac{W_{\text{b}}}{L_{\text{h}}}\biggr)}\right\}. \end{align} \tag{ 12 }$

We next investigate the dependence of IQE on various parameters. For α, we used the experimental data shown in Fig. 1(b). As the diffusivity is not highly sensitive to impurities and defects,⁵⁸⁾ we set both D_e and D_h to be 0.1 cm²/s, because L_h and τ_h were approximately 10 µm in Fig. 2(c) and 10 µs in Fig. 4(b),²⁴^,²⁵^,²⁷^,²⁸⁾ respectively. When the impurity concentrations in the p⁺ and n layers, that is, N_A and N_V, are set to be 10¹⁸ and 10¹⁶ cm⁻³, respectively, W is estimated to be 0.4 µm and the built-in voltage is 1.0 V, assuming that the permittivity of BaSi₂ is approximately 15.²¹^,⁵⁹⁾ The effective densities of states at the conduction band and valence band, that is, N_C and N_V, are 2.6 × 10¹⁹ and 2.0 × 10¹⁹ cm⁻³, respectively, from the principal-axis components of the effective mass tensor for electrons and holes.²¹⁾ The square of the intrinsic carrier concentration, $n_{i}^{2}$ , is calculated to be 8 × 10¹⁶ cm⁻³ at RT. Other parameters are summarized in Table I. The complete ionization of impurity atoms is also assumed. Regarding surface recombination velocities, the BaSi₂ layer thickness dependence of τ_h revealed that the surface recombination velocity is as low as approximately 8 cm/s in undoped n-BaSi₂.²⁷⁾ Thus, we varied S_e and S_h from 8 to 100 cm/s, as shown in Table I.

Table I. Parameters of BaSi₂ homojunction diode.

Sample	N_A (cm⁻³)	W_e (µm)	L_e (µm)	S_e (cm/s)	W (µm)	N_D (cm⁻³)	W_b (µm)	L_h (µm)	S_h (cm/s)
pn-A	10¹⁸	0.1	0.1	8	0.4	10¹⁶	1.5	10	8
pn-B	10¹⁸	0.1	0.1	8	0.4	10¹⁶	2.5	10	8
pn-C	10¹⁸	0.05	0.1	8	0.4	10¹⁶	1.5	10	8
pn-D	10¹⁸	0.05	0.1	100	0.4	10¹⁶	1.5	10	8
pn-E	10¹⁸	0.05	0.1	8	0.4	10¹⁶	1.5	10	100

In Figs. 6(a) and 6(b), IQE is almost the same for samples pn-A and pn-B, although W_b increases from 1.5 µm in sample pn-A to 2.5 µm in sample pn-B. This means that W_b = 1.5 µm is sufficiently large. When W_e decreases from 0.1 to 0.05 µm, IQE increases particularly at higher energies in samples pn-C to pn-E. This is attributed to the enhancements of IQE_e and IQE_DL. Since the absorption coefficient of BaSi₂ is very high, the contributions of the surface p⁺-layer and the depletion region to IQE become pronounced when W_e decreases. This result implies that we need to design W_e to be equal to L_e or smaller. In samples pn-C to pn-E, there is no significant difference in IQE regardless of differences in S_e and S_h. This means that IQE is not very sensitive to surface conditions in a BaSi₂ homojunction solar cell.

**Fig. 6.** Calculated internal spectral responses for samples pn-A to pn-E. Individual contributions of *IQE*_e, *IQE*_DL, and *IQE*_h to the total *IQE* are shown.
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We next discuss the expected conversion efficiency of the diodes. Considering that the hole concentration in the neutral n-type layer at thermal equilibrium, p_n0, is much higher than n_p0 because of the p⁺n junction, the dark current density of the diode, J_dark, is dominant from the contribution of the n-type layer and is given by

$\begin{align} J_{\text{dark}} &= q\frac{D_{\text{h}}}{L_{\text{h}}}p_{\text{n0}}\left[\exp\left(\frac{qV}{k_{\text{B}}T}\right) - 1\right]\\ &\quad\times\cfrac{\cfrac{S_{\text{h}}L_{\text{h}}}{D_{\text{h}}}\cosh\biggl(\cfrac{W_{\text{b}}}{L_{\text{h}}}\biggr) + \sinh\biggl(\cfrac{W_{\text{b}}}{L_{\text{h}}}\biggr)}{\cosh\biggl(\cfrac{W_{\text{b}}}{L_{\text{h}}}\biggr) + \cfrac{S_{\text{h}}L_{\text{h}}}{D_{\text{h}}}\sinh\biggl(\cfrac{W_{\text{b}}}{L_{\text{h}}}\biggr)}. \end{align} \tag{ 13 }$

Thus, the reverse saturation current density J_s is expressed as

$\begin{equation} J_{\text{s}} = q\frac{D_{\text{h}}}{L_{\text{h}}}p_{\text{n0}}\times \cfrac{\cfrac{S_{\text{h}}L_{\text{h}}}{D_{\text{h}}}\cosh\biggl(\cfrac{W_{\text{b}}}{L_{\text{h}}}\biggr) + \sinh\biggl(\cfrac{W_{\text{b}}}{L_{\text{h}}}\biggr)}{\cosh\biggl(\cfrac{W_{\text{b}}}{L_{\text{h}}}\biggr) + \cfrac{S_{\text{h}}L_{\text{h}}}{D_{\text{h}}}\sinh\biggl(\cfrac{W_{\text{b}}}{L_{\text{h}}}\biggr)}. \end{equation} \tag{ 14 }$

The values of J_s and J_L, and the expected open-circuit voltage V_OC under AM 1.5 illumination for samples pn-A to pn-E are related by

$\begin{equation} V_{\text{OC}} = \frac{k_{\text{B}}T}{q}\ln\left(1 + \frac{J_{\text{L}}}{J_{\text{s}}}\right). \end{equation} \tag{ 15 }$

The results are summarized in Table II. Assuming that the fillfactor is 0.8 regardless of V_OC and R = 0, the conversion efficiency is calculated to be approximately 25% in samples pn-C and pn-D even though the total layer thickness is only 2 µm. It is true that we overestimated V_OC and J_L because R cannot be 0, and other residual effects such as series resistance and shunt resistance should be taken into consideration in actual devices. However, it is safe to conclude that BaSi₂ is indeed an attractive material for thin-film solar cell applications.

Table II. Calculated J_s, J_L, and V_OC for samples pn-A to pn-E, assuming R = 0 and FF = 0.8.

Sample	J_S (A/cm²)	J_L (A/cm²)	V_OC (V)	P_out (mW/cm²)
pn-A	2.90 × 10⁻¹⁷	3.17 × 10⁻²	0.897	22.7
pn-B	4.08 × 10⁻¹⁷	3.18 × 10⁻²	0.888	22.6
pn-C	2.90 × 10⁻¹⁷	3.55 × 10⁻²	0.900	25.6
pn-D	2.90 × 10⁻¹⁷	3.55 × 10⁻²	0.900	25.6
pn-E	1.28 × 10⁻¹⁶	3.51 × 10⁻²	0.861	24.2

4. Conclusions

We calculated the photoresponse spectra of BaSi₂ p⁺n abrupt homojunction diodes using experimentally obtained absorption coefficients, the minority-carrier diffusion length, and the minority-carrier lifetime, and discussed the influences of parameters such as emitter and base layer thicknesses and surface recombination velocities. It was found that IQE is not very sensitive to S_e, S_h, and W_b, whereas W_e significantly affects on IQE particularly in a high-energy region. This is because the absorption coefficient of BaSi₂ is high. Thus, we need to carefully consider the relationship between W_e and L_e in the emitter layer when we design W_e. A conversion efficiency of approximately 25% is expected for 2-µm-thick BaSi₂ homojunction diodes under ideal conditions.

Acknowledgements

I thank Professor N. Usami and Dr. K. O. Hara of Naogya University, and Dr. T. Sekiguchi and Dr. K. Watanabe of the National Institute for Materials Science for their help, discussions and encouragement to pursue this work. I am also particularly grateful to Dr. K. Toko, Dr. W. Du, Dr. M. Ajmal Khan, and present and past students in my laboratory of the University of Tsukuba for their experiments and fruitful discussions. This work was financially supported in part by the Core Research for Evolutionary Science and Technology (CREST) of the Japan Science and Technology Agency (JST).

Exploring the possibility of semiconducting BaSi₂ for thin-film solar cell applications

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Abstract

1. Introduction

2. Experimental procedure