Surface conduction in $n$-type pyrite ${\mathrm{FeS}}_2$ single crystals

Pyrite $\mathrm{Fe}{\mathrm{S}}_2$ has long been recognized as a high potential photovoltaic material, due to its exceptionally high optical absorption, low toxicity, and the abundance and low cost of its constituents. Despite the suitable band gap (0.95 eV), minority carrier diffusion length (100–1000 nm), and short-circuit current density, power conversion efficiencies in $\mathrm{Fe}{\mathrm{S}}_2$-based solar cells have never exceeded 3% however, primarily due to low open circuit voltages $\left(V_{\mathrm{oc}}\sim 0.1\mathrm{V}\right)$. Surface phenomena have been implicated as the root cause of this low $V_{\mathrm{oc}}$, recent experiments on $n$-type crystals providing evidence for surface conduction, including $p$-type surface inversion. Here we report a detailed study of electronic transport in a large set (∼120 samples) of thoroughly characterized vapor-transport-grown $n\text{−}\mathrm{Fe}{\mathrm{S}}_2$ single crystals, with both as-prepared and mechanically polished surfaces. Abundant evidence for surface conduction is obtained from the temperature dependence of the resistance and its anisotropy, the thickness dependence of the resistivity, the sensitivity to surface preparation, and the nature of an observed surface insulator-metal transition. While the bulk transport is relatively reproducible, as-grown crystals display striking diversity in surface behavior, which is suppressed by polishing. Via detailed analyses, we demonstrate that the $\mathrm{Fe}{\mathrm{S}}_2$ surface conduction is truly two dimensional, that it can influence in-plane transport even at room temperature, and that a p-type surface inversion layer can be unambiguously established, with no possibility of artifacts from hopping conduction. A nonlinear Hall effect is also observed, allowing us to constrain a two-channel conduction model we show capable of describing all field- and temperature-dependent transport data. Combined with simple arguments, these results place limits on the thickness of the surface conduction layer, which lie below ∼3 nm. Finally, in some crystals, for unknown reasons, the as-grown surface is definitively $n$ type. These results highlight that while surface conduction is clearly important in pyrite $\mathrm{Fe}{\mathrm{S}}_2$, and is gradually yielding to understanding, additional work is clearly warranted to further understand and control it.

Figure 1

Structural characterization of $\mathrm{Fe}{\mathrm{S}}_2$ single crystals. (a) Wide angle x-ray diffraction from a representative powdered $\mathrm{Fe}{\mathrm{S}}_2$ single crystal, with the reference pyrite $\mathrm{Fe}{\mathrm{S}}_2$ pattern (PDF 00-042-1340) shown in (b); the extracted lattice parameter is shown. A photograph of a typical crystal is shown in the inset to (a), and a contact mode atomic force microscopy height image is shown in the inset to (b). (c) Wide angle x-ray diffraction from the 111 facet of a single crystal. The inset to (c) shows a rocking curve (transverse scan) through the 111 peak, with a pseudo-Voigt fit (solid red line) giving a full-width at half-maximum of 0.008°.

Figure 2

Chemical characterization of $\mathrm{Fe}{\mathrm{S}}_2$ single crystals. (a) Raman spectrum with the peak positions labeled. (b) Energy dispersive x-ray spectrum with Fe and S core transitions marked by green and yellow dotted lines, respectively, and the calculated S:Fe ratio shown. (c) Particle induced x-ray emission spectrum with Fe, S, and Ni core transitions marked by green, yellow, and red dotted lines, respectively. Detector artifact peaks are labeled in gray, and a weak Ni signal is labeled red.

Figure 3

Diversity in electronic transport properties in as-grown $\mathrm{Fe}{\mathrm{S}}_2$ crystals. (a) Temperature dependence of the resistivity ρ for $16\mathrm{Fe}{\mathrm{S}}_2$ crystals. (b) Temperature dependence of ρ for four representative samples from the larger set shown in (a). These are labeled “sample B” (blue), “sample Y” (dark yellow), “sample R” (red), and “sample G” (green). (c) Temperature dependence of the van der Pauw anisotropy $A_{\mathrm{vdP}}$ for the representative samples shown in (b), with the same color code. In (b) the crossover temperatures marked by $T_{\mathrm{cr}}$ are the points at which two-channel modeling indicates equal (50%) current flow through the bulk and surface.

Figure 4

Evidence for surface conduction in $\mathrm{Fe}{\mathrm{S}}_2$ crystals. (a) Temperature and thickness dependence of the resistivity ρ for three representative as-grown crystals. The thicknesses are labeled and color coded in green, blue, and red for samples G, B, and R, respectively. (b) Temperature dependence of ρ for eight polished $\mathrm{Fe}{\mathrm{S}}_2$ crystals. (c) The negative dimensionless temperature coefficient of resistance evaluated at 30 K [−$(T/R)$(dR/dT)] vs the 30 K sheet resistance $R_{30\mathrm{K}}$ for all crystals measured in this work. The 2D quantum resistance $h/e^2\approx 26\mathrm{k}\mathrm{\Omega }$ (i.e., the inverse of the 2D minimum metallic conductance) is marked by the red dotted line, the inverse 3D minimum metallic conductivity (for a 0.1-mm-thick crystal) being marked by the gray dotted line.

Figure 5

Nature of the $\mathrm{Fe}{\mathrm{S}}_2$ surface conduction. (a) Temperature dependence of the magnetoresistance (MR) at magnetic field $B_{\perp }=9\mathrm{T}$ for samples B and G in blue and green, respectively. The solid lines are guides to the eye. The inset shows the $B_{\perp }$ dependence of the MR at 270 K for samples B and G. (b) Resistance $\left(R\right)$ vs ln $T$ for sample B, from 1.5 to 20 K, with a straight line fit shown in black. (c) $B_{\perp }$ dependence of the sample B MR at 1.5 K. (d) Resistance $R$ for sample G vs $T^{-1/2}$, from 30 to 100 K, with a straight line fit in black. The inset shows a Zabrodskii plot (ln $W$ vs ln $T$, where $W=-d\ln R/d\ln T)$ for the same temperature range, with a straight line fit. The fit yields the parameters $m=0.57$ and $T_0=1298\mathrm{K}$. (e) $B_{\perp }$ dependence of the sample G logarithmic magnetoresistance ratio $\left[\ln (R/R_{B=0})\right]$ at 30 K, and the resulting fit (black solid line) to an Efros-Shklovskii variable range hopping model, yielding a localization length $L_{\mathrm{c}}=3.4\mathrm{nm}$.

Figure 6

Magnetic field dependence of the Hall effect. The transverse resistance $\left(R_{xy}\right)$ is shown vs the out-of-plane magnetic field $B_{\perp }$ at representative temperatures for samples B (a)–(c), G (d)–(f), Y (g)–(i), and R (j)–(l). Temperatures are shown in the upper right corner, descending from top to bottom. The solid black lines through the data are fits to the nonlinear two-channel conduction model described in the text.

Figure 7

Temperature dependence of the carrier densities, mobilities, resistivities, and Hall coefficients, along with two-channel conduction model results. (a), (e), (i), and (m) Temperature dependence of the electron or hole density $(n$ or $p)$ from fitting of the Hall effect data for samples B, G, Y, and R, respectively. In all panels, circles (triangles) represent bulk (surface) values, and closed (open) symbols represent electrons (holes). In all panels, the solid and dotted black lines represent the two-channel conduction model fits, resulting in the parameters summarized in Table 1. (b), (f), (j), and (n) Temperature dependence of the Hall mobilities (µ) for samples B, G, Y, and R, respectively. (c), (g), (k), and (o) Temperature dependence of the resistivity (ρ) for samples B, G, Y, and R, respectively. (d), (h), (l), and (p) Temperature dependence of the magnitude of the low-field Hall coefficient $\left[R_{\mathrm{H}}(B=0)\right]$, for samples B, G, Y, and R, respectively.