Potential resolution to the doping puzzle in iron pyrite: Carrier type determination by Hall effect and thermopower

Pyrite $\mathrm{Fe}{\mathrm{S}}_2$ has outstanding potential as an earth-abundant, low-cost, nontoxic photovoltaic, but underperforms dramatically in solar cells. While the full reasons for this are not clear, one certain factor is the inability to understand and control doping in $\mathrm{Fe}{\mathrm{S}}_2$. This is exemplified by the widely accepted but unexplained observation that unintentionally doped $\mathrm{Fe}{\mathrm{S}}_2$ single crystals are predominantly $n$ type, whereas thin films are $p$ type. Here we provide a potential resolution to this “doping puzzle,” arrived at via Hall effect, thermopower, and resistivity measurements on a large set of $\mathrm{Fe}{\mathrm{S}}_2$ single crystals and films that span five orders of magnitude in mobility. The results reveal three main findings. First, in addition to crystals, the highest mobility thin films in this study are shown to be definitively $n$ type, from both Hall effect and thermopower. Second, as mobility decreases an apparent crossover to $p$ type occurs, first in thermopower, then in Hall measurements. This can be understood, however, in terms of the crossover from diffusive to hopping transport that is clearly reflected in resistivity. Third, universal behavior is found for both crystals and films, suggesting a common $n$ dopant, possibly sulfur vacancies. We thus argue that $n$-type doping is facile in $\mathrm{Fe}{\mathrm{S}}_2$ films, that apparent $p$-type behavior in low mobility samples can be an artifact of hopping, and that the prevailing notion of predominantly $p$-type films must be revised. These conclusions have deep implications, both for interpretation of prior work on $\mathrm{Fe}{\mathrm{S}}_2$ solar cells and for the design of future studies.

Figure 1

Summary of the literature on carrier type in unintentionally doped pyrite $\mathrm{Fe}{\mathrm{S}}_2$ from Hall effect and thermopower. The room-temperature $(\sim 300\mathrm{K})$ Hall coefficient $\left(R_{\mathrm{H}}\right)$ (a) [18, 19, 20, 22, 23, 26, 27, 28, 29, 30] and Seebeck coefficient $\left(S\right)$ (b) [26, 28, 29] are plotted vs the reported Hall carrier mobility (µ) for $\mathrm{Fe}{\mathrm{S}}_2$ in various forms. The red and blue symbols indicate the apparent majority carrier type (hole and electronlike) based on the sign of $R_{\mathrm{H}}$ and $S$. Explicitly, “holelike” is associated with $R_{\mathrm{H}}>0$, $S>0$, while “electronlike” is associated with $R_{\mathrm{H}}<0$, $S<0$. Data are distinguished for thin films, synthetic single crystals, and natural single crystals.

Figure 2

Hall effect, thermopower, and apparent carrier types in the unintentionally doped $\mathrm{Fe}{\mathrm{S}}_2$ films and crystals from this study. The room-temperature $(\sim 300\mathrm{K})$ Hall coefficient $\left(R_{\mathrm{H}}\right)$ (a) and Seebeck coefficient $\left(S\right)$ (b) are plotted vs the apparent Hall carrier mobility $\left({\mu }_{\mathrm{H}}\right)$ for the polycrystalline films and synthetic single crystals in the current study. Again, the red and blue symbols indicate the apparent carrier type (hole and electronlike) based on the sign of $R_{\mathrm{H}}$ and $S$. Explicitly, holelike is associated with $R_{\mathrm{H}}>0$, $S>0$, while electronlike is associated with $R_{\mathrm{H}}<0$, $S<0$. The arrows in (a) indicate upper bounds on ${\mu }_{\mathrm{H}}$ and $R_{\mathrm{H}}$, i.e., points at the limit of detection. The vertical dashed lines and markings “I,” “II,” and “III” indicate the three regimes discussed in the text.

Figure 3

Representative raw data from Hall effect and thermopower measurements. The left panels show the magnetic field $\left(H\right)$ dependence of the zero-field-background-subtracted Hall resistivity $\left({\rho }_{xy}\right)$ in regimes I (a), II (c), and III (e). The right panels show the temperature gradient $\left(\mathrm{\Delta }T\right)$ dependence of the negative thermoelectric voltage $(-\mathrm{\Delta }V)$ in regimes I (b), II (d), and III (f). Note that $-\mathrm{\Delta }V$ is plotted, to facilitate comparison to the Hall data. Dashed lines in all cases are straight line fits. Two samples are plotted in region I (one crystal, one film), and two films are plotted in region II (one where $R_{\mathrm{H}}$ and $S$ agree on the sign of the majority carriers, one where they do not). In all cases the samples are labeled with their room temperature ${\mu }_{\mathrm{H}}$. All data are at room temperature $(\sim 300\mathrm{K})$.

Figure 4

Temperature-dependent electronic transport measurements. In the top panel the temperature $\left(T\right)$ dependence of the resistivity (ρ) is shown in (a) regime I, (b) regime II, and (c) regime III. The bottom panel shows ln $W$ vs ln $T$ generated from the data in the top panel, where $W=-dln\rho /dlnT$. Slopes of $m=1/2$ and 1 are shown, where $m$ is the exponent in $\rho ={\rho }_{0}exp{\left(T_0/T\right)}^m$. The room temperature $(\sim 300\mathrm{K})$ apparent Hall mobility $\left({\mu }_{\mathrm{H}}\right)$ for each sample is labeled. Two samples are shown in regime I (one crystal, one film), and three films are plotted in regime II, illustrating the behaviors discussed in the text.

Figure 5

Schematic density-of-states. Schematic available density-of-states $\left[D\right(E\left)\right]$ vs energy $\left(E\right)$ plot for the illustrative case of a Gaussian donor band (DB, blue) overlapping with a free-electronlike conduction band (CB, green). Five illustrative potential Fermi energy locations, $E_1$ through $E_5$, are indicated by the red dashed lines. The inset shows a density-of-states with a Coulomb gap of width ${\mathrm{\Delta }}_{\mathrm{C}}$ around a potential Fermi energy location $E_6$.