n-type conversion of SnS by isovalent ion substitution: Geometrical doping as a new doping route

Tin monosulfide (SnS) is a naturally p-type semiconductor with a layered crystal structure, but no reliable n-type SnS has been obtained by conventional aliovalent ion substitution. In this work, carrier polarity conversion to n-type was achieved by isovalent ion substitution for polycrystalline SnS thin films on glass substrates. Substituting Pb2+ for Sn2+ converted the majority carrier from hole to electron, and the free electron density ranged from 1012 to 1015 cm−3 with the largest electron mobility of 7.0 cm2/(Vs). The n-type conduction was confirmed further by the position of the Fermi level (EF) based on photoemission spectroscopy and electrical characteristics of pn heterojunctions. Density functional theory calculations reveal that the Pb substitution invokes a geometrical size effect that enlarges the interlayer distance and subsequently reduces the formation energies of Sn and Pb interstitials, which results in the electron doping.

Scientific RepoRts | 5:10428 | DOi: 10.1038/srep10428 to be a promising absorber material for low-cost thin-film solar cells. Thus, numerous n-type materials, including CdS 9,10 , SnS 2 11 , FeS 2 12 , TiO 2 13 , ZnO 14 , and amorphous-Si 15 , have been employed for fabricating heterojunction SnS-based solar cells. However, the highest energy conversion efficiency reported up to now is limited to ~4% 16,17 , which is much lower than the theoretically-predicted value of 24% 18 . The low efficiency might suffer from the unfavorable band alignments and the large lattice mismatches in the heterojunction structures 19,20 . Fabricating a homojunction solar cell with p-SnS/n-SnS structure would solve this problem.
With this line, much effort has been devoted to obtaining n-type SnS materials by substituting the Sn 2+ ions with aliovalent ions with the charge state of 3+ . Dussan et al. report that Bi 3+ -doped SnS exhibits n-type conduction when the Bi concentration is larger than 50% 21 . Whereas, a Bi 2 S 3 impurity phase, which is also n-type, was observed in their heavily Bi-doped SnS films 22 . Sajeesheesh et al. claim that n-type SnS thin films are obtained by chemical spray pyrolysis, but their result might be due to a significant n-type Sn 2 S 3 impurity phase in the films 23 . Very recently, Sinsermsuksakul et al. tried to obtain n-type SnS by Sb 3+ doping; however, except for great increase in the electrical resistance of the SnS film, no n-type conduction was observed 24 . That is, no reliable n-type SnS material has yet been reported.
In this work, we succeeded in fabricating reliable n-type SnS films by isovalent Pb 2+ doping. We found that the doping mechanism is strikingly different from the conventional doping routes such as ion substitution, off-stoichiometry, and chemical doping. Substitution for the Sn 2+ ion with a larger Pb 2+  polycrystalline disks with the target chemical composition x t = 0.18, 0.37, and 0.66 were used as ablation targets. X-ray fluorescence (XRF) spectroscopy confirmed that these x t produced thin films with x f = 0.08-0.5. The details of experimental and calculation are found in method part of this paper.

Results and discussion
First, we confirmed the film structures by X-ray diffraction (XRD). Figure 1b shows a typical out-of-plane 2θ/ω synchronous scan (top panel) and an in-plane synchronous 2θ χ /ϕ scan (bottom panel) XRD pat- film with x f = 0.5 grown at substrate temperature (T s ) = 300 °C and P = 5 Pa.
The out-of-plane XRD pattern exhibited strong 200, 400 and 800 diffractions of the orthorhombic structure, which is the same as that of pure SnS in Fig. 1a, along with a weak 011 diffraction. As seen in Figure   S1 (supplementary information), orthorhombic ( ) films were obtained at P ≤ 15 Pa (corresponding to the closed symbols in Fig. 1c); while, amorphous films were obtained when P was increased to 20 Pa (the open symbols in Fig. 1c). The in-plane synchronous 2θ χ /ϕ scan (bottom panel) shows powder-like patterns with all possible hkl diffractions, suggesting that the film did not have in-plane orientation. It was further confirmed by in-plane rocking patterns (ϕ scan at fixed 2θ χ , data not shown); all the data showed that the crystallized films did not have a preferential orientation in plane. These results indicate that the ( ) − Sn Pb S x x 1 f f films were polycrystalline films with a strong 100 preferential orientation normal to the substrate. No impurity phase was detected both in the out-of-plane and the in-plane XRD patterns. Figure 1c shows the variation of x f as functions of P, T s and x t . It is seen that all the x f values were smaller than the x t values of the corresponding targets, and the x f values decreased with increasing P. As seen for the target with x t = 0.37, the maximum amount of Pb was incorporated when the films were grown at T s = 300 °C. We, therefore, employed T s = 300 °C hereafter.
The crystallized region in Fig. 1c is classified further to three regions as indicated by the dashed lines. Region I is "p-type region" (high P ≥ 15 Pa at low x f < 0.1), where the films still exhibited p-type conduction with low hole densities (N h ) and low hole mobilities (μ h ) (measured by Hall effect, details will be discussed for Fig. 2). n-type ( ) − Sn Pb S x x 1 f f films were obtained in Region II ("n-type region", x f ≥ 0.15 at low P ≤ 10 Pa). The electron density (N e ) and mobility (μ e ) changed largely with x f and P, which will be discussed later on. Region III is the intermediate region ("highly-resistive region", low x f & low P, and high x f & high P), where the films exhibited very high resistivity > 10 5 Ω ·cm, and the Hall effect measurements did not give definite Hall voltage signs.
Here, we discuss the doping structure of Pb. Figure 1d shows the variation of the out-of-plane 400 diffraction angles 2θ 400 obtained by 2θ/ω synchronous scan as a function of x f . The 2θ 400 value shifted to lower angles as x f increased, indicating that the a-axis expanded with increasing x f . The lattice parameters obtained from the out-of-plane 400 and the in-plane 020 and 011 diffraction angles are summarized as a function of x f in Fig. 1e. As x f increased from 0 to 0.5, the a and b values increased linearly from 1.12 to 1.14 nm and from 0.403 to 0.414 nm, respectively, whereas the c value decreased from 0.426 to 0.419 nm; i.e., the interlayer distance (corresponding to the a value) increased. The solid lines in Fig. 1e represent the lattice parameters of the(Sn 1-x Pb x )S bulk sample reported by Leute et al. 25 . The a values of our films are almost the same as those of the bulk samples. However, the b and c values exhibited non-negligible deviations from the bulk values; i.e., the b-axis was expanded while the c-axis shrunken compared from the bulk values. The reason is not clear, but defects in the polycrystalline films would cause the structural difference. Figure 1e also compares the variation of the lattice parameters with those obtained by density functional theory (DFT) calculations (the open symbols) performed with the (Sn 16-n Pb n )S 16 supercell model (Pb substitution model) indicated by the black line box in Fig. 1f. Here, local density approximation (LDA) and generalized gradient approximation (GGA) functionals are compared. As will be seen later, GGA provides better description about the electronic structure; however, here we can see that the experimental results for the Pb substitution model were within the variation of the functionals (typically, the ground-state lattice parameters by DFT include errors within 2-3%). That is, this model, where the Sn sites are substituted by Pb, explains the experimental structure well, and strongly supports that the Pb dopants are successfully incorporated to the Sn sites in the SnS lattice. We also confirmed that the films are uniform in microstructures and chemical compositions, and no segregation (e.g., a Pb-rich impurity phase) was detected by atomic force microscopy (AFM), field-emission scanning electron microscopy (FE-SEM), and electron-probe microanalysis (EPMA) (supplementary information Figure S2 and Table  S1).  As shown by the red line in Fig. 2b, μ e decreased with decreasing the temperature, and the ln(μ Hal T 1/2 )-T −1 plot exhibited a good straight line in the whole T range, suggesting that the electron transport in the film was dominated by grain boundary (GB) potential barriers as proposed by Seto et al. 27 , where electron transport is disturbed by potential barriers formed due to the electrons trapped at acceptor-type defects at the GBs. The GB potential barrier height E B is estimated to be approximately 0.09 eV (the equation is given in Fig. 2b 27 ). From this result, we can estimate the potential electron mobility μ 0 (i.e., the ideal value when no GB affects the carrier transport) by extrapolating E B to zero (i.e., μ 0 = μ Hall exp(E B /kT)), which gives μ 0 ~ 1.6 × 10 2 cm 2 /(Vs). Figure 2c shows a valence band structure of a (Sn 0.5 Pb 0.5 )S film measured by ultraviolet photoemission spectroscopy (UPS). A sharp peak at 1-2 eV and a broad peak at 2.5-4.5 eV can be observed, agreeing with the projected DOS (PDOS) calculated by DFT in Fig. 2e. The valence band consists mainly of S 3p orbitals, which slightly hybridized with Sn 5s, Sn 5p, Sn 5d, Pb 6s, Pb 6p, and Pb 6d orbitals. As seen in Fig. 2d, the observed E F of the (Sn 0.5 Pb 0.5 )S film is located at 0.82 eV above VBM. From the bandgap value of 1.15 eV (will be discussed for Fig. 3), the E C -E F value is estimated to be 0.33 eV, closer to conduction band minimum (CBM).
To further confirm the n-type conduction of these films, n-type (Sn 0.5 Pb 0.5 )S/p-type Si pn heterojunction was prepared (the device structure is shown in the inset to Fig. 2f). The n-(Sn 0.5 Pb 0.5 )S film and the p-Si wafer used had N e = 2 × 10 15 and N h = 5 × 10 15 cm −3 , respectively. The current-voltage (I-V) characteristic of the pn junction (Fig. 2f)  Here, we like to discuss the origin of the n-type doping in the ( ) − Sn Pb S x x 1 f f films. It is known that Pb ions favor to take + 2 and + 4 oxidation states, and the latter would explain the n-type doping if Pb 4+ substitutes the Sn 2+ site. However, the above DFT calculations for the (Sn 32-n Pb n )S 32 supercell models indicated that the Pb substitutions at the Sn site (denoted Pb Sn ) generate no free charges because the Pb is ionized to Pb 2+ . We also confirmed by X-ray photoemission spectroscopy (XPS) that the calibrated  Here, we discuss the microscopic mechanism of the n-type doping by the Pb substitution. Firstly, we should remind that the n-type conduction was obtained only when a film was grown under the S-poor condition (i.e., at low P). We calculated the formation enthalpies (Δ H f ) of intrinsic defects in the pure SnS and the (Sn 0.5 Pb 0.5 )S models (the blue line box in Fig. 1f) under the S-poor limit condition as a function of E F by DFT calculations as shown in Fig. 4a and b, respectively. Vacancies (V S , V Sn , V Pb ), anti-site defects (Sn S , Pb S ), interstitials (Sn i , Pb i ) were examined (see Fig. 1f for the models) with the defect charge states from 2+ to 2− . These calculations employed LDA functionals not GGA in order to compare with the previously-reported results for pure SnS by Vidal et al.. 28 The present result of the pure SnS model (Fig. 4a) is almost the same as their results; i.e., the most stable charge state of V S transits from 2+ to 0 at E F ~ 0.4 eV, corresponding to the charge transfer energy level of ε 2+/0 . The most stable defect changed from V S 2+ to Sn S − & V Sn 2− at E F ~ 0.4 eV. As V S 2+ acts as a doubly-ionized donor while Sn S − and V Sn 2− are ionized acceptors, suggesting that SnS is intrinsically a compensated p-type semiconductor. For quantitative analysis, the equilibrium E F (E F,e ) at 400 °C (i.e., we assume the defect structures at the growth temperature were frozen to room temperature) was calculated by considering all the For the (Sn 0.5 Pb 0.5 )S model in Fig. 4b, although the Δ H f values of V S 2+,0 remained unchanged, that of Sn i 2+ was reduced and that of V Sn 2− increased significantly compared to those in the pure SnS, which is because the interlayer distance (corresponding to the a-axis length) and the b-axis lattice parameters were increased by the Pb substitution (as also observed experimentally in Fig. 1e). Similar ΔH f behaviors were found also for Pb i 2+ and V Pb  control in semiconductor is achieved mainly by aliovalent ion substitution, off chemical stoichiometry, chemical doping and so on. This work revealed that substitution by an isovalent ion can also induce carrier doping by a two-step indirect mechanism through a geometrical effect and subsequent formation of charged defects.
The present finding provides a novel idea for carrier doping. Even keeping the same crystal structure and the ion charges, easiness of impurity doping, in particular for atoms/ions with largely-different sizes, depends significantly on the lattice parameters and the internal atomic coordinates, which can be altered also by impurity doping. Further, although substitution doping usually requires aliovalent ion doping to alter the carrier polarity or concentration, geometrical doping has more flexibility because isovalent ion doping would also work for carrier doping.
This way of thinking would provide more flexibility to explore new doping routes, open a new way for controlling carrier polarity and density in novel semiconductors in which conventional aliovalent ion substitution is difficult. Characterization. The crystalline phase and crystal structure of the obtained films were characterized by X-ray diffraction (XRD, radiation source = Cu Kα ). Optical properties were obtained by measuring transmittance (T r ) and reflectance (R) spectra. The absorption coefficient (α) was estimated by α = ln[(1−R)/T r ]/d, where d is the film thickness. Electrical properties of the SnS films were analyzed by Hall effect measurements using the van der Pauw configuration with an AC modulation of magnetic field. The Pb content in the films (x f ) were determined by X-ray fluorescence (XRF) spectroscopy calibrated by the chemical compositions obtained by inductively-coupled plasma-atomic emission spectroscopy (ICP-AES). The valence band structures were observed by UPS (excitation source = He I, 21.2 eV), where the films were protected in an Ar atmosphere during the transfer from the PLD chamber to the UPS chamber. The oxidation state of Pb was examined by x-ray photoemission spectroscopy (XPS, Mg Kα ).

Methods
Calculation. Stable crystal/defect structures, their electronic structures, and formation energies of intrinsic defects were calculated by density functional theory (DFT) calculations with local density approximation (LDA) and generalized gradient approximation (GGA) PBE96 functionals using the Vienna Ab initio Simulation Package (VASP 5.3.3) 29 . The plane wave cutoff energy was set to 323.3 eV. A 32-atoms supercell model ((Sn 16-n Pb n )S 16 , black line in Fig. 1f) and a 4 × 6 × 5 k-mesh were used for the calculations of structural properties and electronic structures. The defect calculations were performed using a 64-atoms model ((Sn 16 Pb 16 )S 32 , blue line in Fig. 1f) and a 3 × 3 × 3 k-mesh. The procedure for calculating the defect Δ H f along with the general corrections followed the methodology reviewed by Zunger et al. 30,31 . The equilibrium Fermi levels (E F,e ) were determined using the calculated density of states (DOS) by solving semiconductor statistic equations self-consistency so as to satisfy the charge neutrality condition 32 .