Mitigation of the internal p-n junction in ${\mathrm{CoS}}_2$-contacted ${\mathrm{FeS}}_2$ single crystals: Accessing bulk semiconducting transport

Pyrite ${\mathrm{FeS}}_2$ is an outstanding candidate for a low-cost, nontoxic, sustainable photovoltaic material, but efficient pyrite-based solar cells are yet to materialize. Recent studies of single crystals have shed much light on this by uncovering a $p$-type surface inversion layer on $n$-type (S-vacancy doped) crystals, and the resulting internal p-n junction. This leaky internal junction likely plays a key role in limiting efficiency in pyrite-based photovoltaic devices, also obscuring the true bulk semiconducting transport properties of pyrite crystals. Here, we demonstrate complete mitigation of the internal p-n junction in ${\mathrm{FeS}}_2$ crystals by fabricating metallic ${\mathrm{CoS}}_2$ contacts via a process that simultaneously diffuses Co (a shallow donor) into the crystal, the resulting heavy $n$ doping yielding direct Ohmic contact to the interior. Low-temperature bulk transport studies of controllably Co- and S-vacancy doped semiconducting crystals then enable a host of previously inaccessible observations and measurements, including determination of donor activation energies (which are as low as 5 meV for Co), observation of an unexpected second activated transport regime, realization of electron mobility up to $2100\mathrm{c}{\mathrm{m}}^2{\mathrm{V}}^{\text{–}1}{\mathrm{s}}^{\text{–}1}$, elucidation of very different mobilities in Co- and S-vacancy-doped cases, and observation of an abrupt temperature-dependent crossover to bulk Efros-Shklovskii variable-range hopping, accompanied by an unusual form of nonlinear Hall effect. Aspects of the results are interpreted with the aid of first-principles electronic structure calculations on both Co- and S-vacancy-doped ${\mathrm{FeS}}_2$. This work thus demonstrates unequivocal mitigation of the internal p-n junction in pyrite single crystals, with important implications for both future fundamental studies and photovoltaic devices.

Figure 1

(a) Schematic band diagram of an $n\text{−}{\mathrm{FeS}}_2$ crystal (with the surface on the extreme left). Shown are the conduction band $\left(E_{\mathrm{C}}\right)$, valence band $\left(E_{\mathrm{V}}\right)$, and Fermi $\left(E_{\mathrm{F}}\right)$ energies, along with the $n$-bulk, p-n depletion, and $p$-surface regions. Note the substantial upward band bending toward the surface. For scale, the accepted energy gap in ${\mathrm{FeS}}_2$ is $\sim 0.95\mathrm{eV}$. Temperature (T) dependence of the resistivity $\left(\rho \right)$ of ${\mathrm{FeS}}_2$ single crystals with (b) light S vacancy (${\mathrm{V}}_{\mathrm{S}}$) doping [$n\left(300\mathrm{K}\right)=6\times {10}^{14}$, $5\times {10}^{15}$, $1\times {10}^{17}\mathrm{c}{\mathrm{m}}^{\text{–}3}$], (c) moderate Co doping [$n\left(300\mathrm{K}\right)=3\times {10}^{17}$, $7\times {10}^{17}\mathrm{c}{\mathrm{m}}^{\text{–}3}$], and (d) heavy Co doping $[n\left(300\mathrm{K}\right)=1\times {10}^{18},3\times {10}^{18}\mathrm{c}{\mathrm{m}}^{\text{–}3}]$. [$n$(300 K) is the 300 K Hall electron density]. Data are shown for both In contacts (dashed lines) and ${\mathrm{CoS}}_2$ contacts (solid lines). A typical crystal is shown in (b) (adapted with permission from Ref. [16]. Copyright 2019 American Chemical Society). The insets to (c), (d) are schematics (not to scale) showing the $n$-type bulk (dark blue), $p$-type surface (red), p-n depletion region (light blue), and equivalent circuit diagrams. Note that due to heavy doping in the $p$-type surface layer, the depletion width is controlled by the $n$ doping in the crystal interior.

Figure 2

(a) Schematic composition profile of a ${\mathrm{CoS}}_2$-contacted ${\mathrm{FeS}}_2$ crystal. Time of flight secondary ion mass spectrometry (TOF SIMS) depth profiles (${log}_{10}$ scale) of (b) ${\mathrm{Co}}^{\text{–}}$ and (c) $\mathrm{Co}{{\mathrm{S}}_2}^{-}$ through the interface of an ${\mathrm{FeS}}_2$ crystal contacted with $\sim 120\mathrm{nm}$ of sulfidized ${\mathrm{CoS}}_2$ (maroon); for reference, data for $\sim 30\mathrm{nm}$ as-deposited Co contacts are also shown (black). Orange lines represent a 1D diffusion model with diffusivity $D\approx 2\times {10}^{\text{–}16}\mathrm{c}{\mathrm{m}}^2{\mathrm{s}}^{\text{–}1}$ (see the Supplemental Material, Sec. D [29], for details). The insets to (b), (c) show an XRD pattern [intensity (I) vs 2θ] and magnetization (M) vs temperature (T) for representative 120–240 nm thick ${\mathrm{CoS}}_2$ films. Expected ${\mathrm{CoS}}_2$ reflections [19, 20, 41] are marked; the peak near $30.5^{\circ }$ likely arises from the sample holder. $M\left(T\right)$ was measured in 500 Oe after field cooling in 500 Oe.

Figure 3

Schematic illustrations and band diagrams directly under contacts formed with (a) conventional In and (b), (c) interdiffused ${\mathrm{CoS}}_2$. The $n$-bulk, p-n depletion regions, $p$-surface regions, and contact layers are shown, along with the conduction band $\left(E_{\mathrm{C}}\right)$, valence band $\left(E_{\mathrm{V}}\right)$, and Fermi $\left(E_{\mathrm{F}}\right)$ energies. The different scenarios in (b), (c) correspond to shrinking of the depletion region to the point of tunneling and direct (re)inversion of the $p$-surface layer, respectively, as discussed in the text.

Figure 4

Electronic transport data on ${\mathrm{CoS}}_2$-contacted ${\mathrm{FeS}}_2$ crystals doped to room temperature Hall electron densities $\left[n\left(300\mathrm{K}\right)\right]\approx 1\times {10}^{17}\mathrm{c}{\mathrm{m}}^{\text{–}3}$ with Co [(a)–(d), red] and ${\mathrm{V}}_{\mathrm{S}}$ [(e)–(h), green]. [The ${\mathrm{V}}_{\mathrm{S}}$-doped crystal is from Fig. 1]. Shown are the temperature (T) dependence (${log}_{10}$ scale) of (a), (e) the resistivity (ρ), (b), (f) the low magnetic field Hall electron density ($n$), (c), (g) the resulting Hall mobility (μ), and (d), (h) the 9 T perpendicular to plane magnetoresistance, $\mathrm{MR}\left(9\mathrm{T}\right)=\left[\rho \left(B\right)\text{–}\rho \left(0\right)\right]/\rho \left(0\right)$. The Arrhenius fits to $n\left(T\right)$ in (b),(f) yield the shown activation energies $\left(\mathrm{\Delta }E\right)$. The power law fits to $\mu \left(T\right)$ in (c), (g) yield the shown exponents. The insets in (a), (e) are Zabrodskii plots [$lnW$ vs $lnT$, where $W=\text{–}d\left(lnR\right)/d(lnT)$], linearizing $\rho ={\rho }_{0}exp{\left(T_0/T\right)}^m$ and yielding the exponent $m$ from the slope; the black lines correspond to $m=\frac{1}{2}$, i.e., Efros-Shklovskii variable-range hopping (ES VRH). The insets to (d), (h) show the magnetic field (B) dependence of $ln\left[\rho \left(B\right)/\rho \left(0\right)\right]$ for Co- and ${\mathrm{V}}_{\mathrm{S}}$-doped crystals at 8 and 5 K, respectively; the black lines are fits to an ES VRH model yielding localization lengths $\left(L_c\right)$ of 13 and 16 nm, respectively. Colored dashed lines connect the points, and vertical black dashed lines mark the diffusive-hopping crossovers.

Figure 5

Calculated band structure (left panels) and spin-polarized density of states (DOS, right panels) for (a) Co- and (b) ${\mathrm{V}}_{\mathrm{S}}$-doped pyrite. The green horizontal line marks the Fermi energy, the zero of energy is at the valence band maximum, and the DOS is shown for the two spin states. As described in the main text and in the Supplemental Material, Sec. H [29], these calculations involve $3\times 3\times 3$ supercells containing one ${\mathrm{Co}}_{\mathrm{Fe}}$ defect [in (a)] and a tetra-S-vacancy [in (b)]. In all cases, a Hubbard $U=1.8\mathrm{eV}$ was used on Fe, as optimized in prior work [17]. For the Co in (a), as discussed in the Supplemental Material [29], the $U=3\mathrm{eV}$ result is shown.

Figure 6

Ratio of the Hall electron densities $(n_{\mathrm{H}}/n_{\mathrm{L}})$ extracted at high $\left(\left|B\right|\ge 7\mathrm{T}\right)$ and low $\left(\left|B\right|\le 1\mathrm{T}\right)$ magnetic fields in the (a) Co-doped and (b) ${\mathrm{V}}_{\mathrm{S}}$-doped ${\mathrm{FeS}}_2$ crystals in Fig. 4. The insets show transverse (Hall) resistance $\left(R_{xy}\right)$ vs B at 40 and 12 K for the Co- and ${\mathrm{V}}_{\mathrm{S}}$-doped crystals, respectively [i.e., the temperatures at which the nonlinearity in $R_{xy}\left(B\right)$ is maximum].