Electron-transport properties of degenerate ZnSnN₂ doped with oxygen

Abstract

In this study, analysis of the electron mobility in ZnSnN₂ epilayers that were unintentionally doped with oxygen (ZnSnN_2−xO_x) was performed to elucidate the reason for the low mobilities of ~ 20 cm² V⁻¹ s⁻¹. While roughly 30% of the incorporated oxygen donated electrons, the rest existed as neutral impurities. Seebeck-effect measurements revealed that scattering by neutral impurities governed the electron transport. The theoretical mobility calculated taking into account the scattering by neutral impurities and ionized impurities reproduced the experimental Hall mobility. We concluded that the low electron mobility is attributed to the presence of the neutral oxygen impurities in high concentration.

Introduction

Zn–IV–N₂ (IV = Si, Ge, Sn) compounds, which are derived from wurtzite-type group III nitride by replacing the group III elements with an equal number of Zn and group IV elements, can be regarded as a pseudo group III nitride [1, 2]. It has been demonstrated that similar to the well-known In_xGa_xN system, the bandgap (E_g) of alloyed ZnSn_xGe_1−xN₂ was tunable from 3.1 to 2.0 eV by varying the Sn content (x) from 0 to 1 [3]. This makes Zn–IV–N₂ an intriguing semiconductor system, and studies on ZnSn_xGe_1−xN₂ as a counterpart to the In_xGa_1−xN system have been carried out in recent years [3, 4].

Zinc tin nitride (ZnSnN₂) is the least studied Zn–IV–N₂ compound. For example, the synthesis of ZnSnN₂ thin films [5, 6] and powders [7, 8] has been reported in only the last 5 years. Since theoretical studies showed that the E_g value of 1.0–2.0 eV for ZnSnN₂ is appropriate for a photovoltaic absorber [1, 2, 9,10,11], experimental investigations have been carried out on this material [12,13,14,15]. Indeed, ZnSnN₂ has a large optical absorption coefficient (~ 10⁵ cm⁻¹) in most of the solar spectrum [13]. In addition, p-Si/n-ZnSnN₂ and p-SnO/n-ZnSnN₂p–n junctions for photovoltaic application were successfully fabricated recently [15, 16].

ZnSnN₂ has two phases that depend on the ordering of the cation sublattice: the ordered phase, which is derived by alternately replacing the cation sublattice with Zn and Sn in the wurtzite structure; the disordered-phase, in which Zn and Sn randomly occupy the cation sublattice. Theoretical studies showed that E_g of ZnSnN₂ is dependent on the cation-sublattice ordering: E_g = 2 eV for the ordered phase and E_g = 1 eV for the disordered phase [10, 17]. Optical studies on ordered- and disordered-ZnSnN₂ thin films obtained E_g values close to the above-mentioned theoretical values [10, 12, 14, 17, 18]. Owing to intensive study from theoretical and experimental points of view, the intrinsic E_g value of ZnSnN₂ has gradually become clear.

However, even though control of the transport properties is also important for photovoltaic applications, such properties of ZnSnN₂ are not well understood. ZnSnN₂ thin films usually show degenerate n-type conductivity owing to unintentional oxygen doping [12, 18]. The oxygen impurities occupy the nitrogen sites and behave as electron donors [11]. As a result, ZnSnN₂ films have electron densities of the order of 10¹⁹–10²¹ cm⁻³ [9, 10, 12, 14, 17, 18]. The electron mobility of ZnSnN₂ thin films are usually 10 cm² V⁻¹ s⁻¹ or lower [9, 10, 12, 14, 17, 18] even though the films are single crystalline. To establish ZnSnN₂ as a photovoltaic absorber, the major challenges include suppression of the conduction electron density and enhancement of the electron mobility.

For the suppression of the conduction electron density, Floretti et al. proposed a method in which hydrogen doping takes place during film growth and subsequent annealing [19]. They successfully obtained nondegenerate Zn_1+δSn_1−δN₂ films with a carrier density of 10¹⁶ cm⁻³. On the other hand, no method for improving the electron mobility has been reported so far, and the low electron mobility remains one of the open questions of the electron-transport properties of ZnSnN₂. In the case of heavily-doped GaN epilayers with an electron density of ~ 10²⁰ cm⁻³ [20], an electron mobility above 100 cm² V⁻¹ s⁻¹ has been obtained. In comparison, the electron mobility of ZnSnN₂ appears to be unusually low, but an understanding of the limiting factor of the electron mobility in ZnSnN₂ is lacking.

In this study, detailed analysis of the electron-transport properties of epitaxially grown ZnSnN₂ thin films was carried out to elucidate the reason for the low electron mobility. Herein, we present the analysis results and discuss in detail the limiting factor of the mobility.

Results and discussion

Cation-disordered ZnSnN₂ films were grown on the (111) plane of yttria-stabilized zirconia (YSZ) single-crystalline substrates with a temperature of 300 °C; the films were grown by reactive radio-frequency magnetron sputtering using a Zn–Sn alloy target with Zn concentration of 50 at.%. In general, high growth temperature is preferable for the growth of thin films composed of larger crystalline grains with higher crystallinity. In the case of ZnSnN₂, however, the highest growth temperature is limited to ~ 300 °C, because the decomposition temperature of this compound was estimated to be ~ 350 °C [8]. Indeed, we previously confirmed that no film was grown on YSZ (111) at 350 °C [18]. Accordingly, 300 °C is the highest temperature for the growth of ZnSnN₂ thin films.

Out-of-plane and in-plane X-ray diffraction (XRD) measurements confirmed that the ZnSnN₂ films were epitaxially grown on YSZ(111) with the epitaxial relationship of $\left( {000{1}} \right)[{{2\bar{1}\bar{1}}}0]_{{{\text{ZnSnN}}_{{2}} }}$ || (111)[${\bar{{1}}}$10]_YSZ (Additional file 1: Fig. S1). The Zn/(Zn + Sn) atomic ratio in the films was determined by X-ray photoelectron spectrometry (XPS) to be in the range of 0.52–0.55. That is, slightly Zn-rich off-stoichiometric films were obtained in this study. The XPS measurements also confirmed that all the films were unintentionally doped with oxygen, forming ZnSnN_2−xO_x. The oxygen content x could be controlled by varying the nitrogen partial pressure ($P_{{{\text{N}}_{{2}} }}$) during the growth [18]. When $P_{{{\text{N}}_{{2}} }}$ was decreased from 2.0 to 1.2 Pa, x in ZnSnN_2−xO_x increased from 0.056 to 0.079 (the x values were semi-quantitatively determined by using the integrated intensity of the O 1s core spectra). The XPS spectra and elemental composition data are given in Additional files 2 and 3, respectively. Impurity substitution usually expand or shrink a unit cell, leading to a small shift of XRD peak. In the case of the ZnSnN_2−xO_x films with x < 0.08, however, significant peak shift by the incorporation of oxygen was not observed (Additional file 4: Fig. S3a), indicating that the lattice constant did not change (Additional file 4: Fig. S3b). The difference of the ionic radii of N³⁻ (146 pm) and O²⁻ (138 pm) is so small that the oxygen substitution hardly caused the change of the lattice constant.

Hall-effect measurements were carried out to determine the carrier density (n_e) and Hall mobility (μ_H) in the films. As shown in Fig. 1a, n_e increased with increasing x, indicating that the unintentionally incorporated oxygen (O_N) served as an electron donor. Temperature (T)-independent behavior of n_e can be seen in Fig. 1b, which suggests that the ZnSnN_2−xO_x films were degenerate semiconductors. The curve in Fig. 1a represents n_e calculated assuming that 30% of O_N was ionized (the ionization rate of η = 30%). The curve reasonably approximated the experimental n_e values, indicating that O_N was highly compensated at room temperature (RT). The reason for such high compensation is probably related to the Zn-rich composition of the films. The Zn excess introduces Zn_Sn acceptor-like defects in ZnSnN₂ [19]. Recent theoretical calculation suggests that electrically neutral Zn_Sn–2O_N complexes forms when Zn_Sn and O_N coexist in ZnSnN₂ [21]. The formation of the Zn_Sn–2O_N complexes implies the compensation of the O_N donors. Hence, many Zn_Sn–2O_N complexes are likely to present in the epilayers.

Fig. 1

a Electron density (n_e) and c Hall mobility (μ_H) at room temperature as functions of x in ZnSnN_2−xO_x (closed circles). The solid line in a represents the carrier density calculated based on the assumption that the ionization rate of the incorporated oxygen was 30%. The cross marks in c represent the optically derived mobility (μ_opt). Temperature dependence of bn_e and dμ_H; the circles, triangles, inverted triangles, squares, and diamonds represent the values for films with x = 0.055, 0.069, 0.071 0.074, and 0.079, respectively. All the data are included in Additional file 5

Figure 1c shows the x dependence of μ_H at RT. The unintentional oxygen doping caused the decrease in μ_H, suggesting that O_N acted as an impurity scattering center. Indeed, the μ_H values were independent of T (Fig. 1c), representing typical behavior of mobility limited by ionized- or neutral-impurity scattering in degenerate semiconductors. Furthermore, the T-independent behavior of μ_H clearly indicates that the contribution of T-dependent phonon scattering to electron transport was negligible.

Recently, Hamilton et al. reported that grain-boundary scattering is one of mobility-limiting factors in polycrystalline films in ZnSnN_2−xO_x [19]. Even in epitaxial films, grain-boundary scattering sometimes cannot be ignored, because epitaxial films frequently have a biaxially-oriented grain structure [22,23,24]. As we previously reported, ZnSnN₂ epitaxial films sputtered on YSZ (111) have a compact grain structure with lateral grain diameters of ~ 30 nm [18]. In other words, sputtered ZnSnN_2−xO_x epilayers are not single-crystalline films but rather biaxially-oriented polycrystalline films. Accordingly, grain-boundary scattering should be considered, when we analyze the electron transport properties of the sputtered ZnSnN_2−xO_x epilayers. The optically derived mobility (μ_opt) using the Drude model corresponded to the intra-grain mobility without the grain boundary contribution, whereas DC-measured μ_H included the contribution of the grain-boundary scattering. To obtain the μ_opt values, we measured the infrared reflectance spectra of the ZnSnN_2−xO_x films at near-normal incidence (~ 5°) in the wavelength range of 1–5 μm, and then fitting analysis was carried out using the Drude model. In our previous study, we showed that the frequency (ω)-dependent dielectric function of the ZnSnN_2−xO_x (ε(ω)) can be modeled by combining the Drude function (ε_D(ω)) with double Tauc–Lorentz (TL) functions [ε_TL1(ω) and ε_TL2(ω)]: i.e., ε(ω) = ε_TL1(ω) + ε_TL2(ω) + ε_D(ω). The Drude function is given by

$$\varepsilon_{{\text{D}}} \left( \omega \right) = - \frac{{\omega_{{\text{p}}} }}{{\omega^{2} - i\varGamma_{{\text{D}}} \omega }},$$

(1)

$$\omega_{{\text{p}}}^{2} = \frac{{en_{{\text{e}}} }}{{\varepsilon_{0} m^{*} }} ,$$

(2)

where ω_p is the plasma frequency, Γ_D is the scattering rate, ε₀ is the static dielectric constants of free space, and m^* is the effective mass. The TL function is given in Ref. [25]. The theoretical reflectance spectra calculated through the Fresnel formula combined with the modeled dielectric function were fitted to the experimental spectra (ω_p and Γ_D were used as the fitting parameters). In the fitting analysis, the parameters in the TL functions were fixed for simplicity at constant values that were the same as reported values in the literature [13]. We obtained good fits, as shown in Fig. 2a–d. The best-fit parameters are listed in Additional file 7: Table S2 (Additional file 7). Using the best-fit parameters, the μ_opt values were calculated using the relationship

$$\mu_{{{\text{opt}}}} = \frac{1}{{en_{{\text{e}}} }}\frac{{\varepsilon_{0} \omega_{{\text{p}}}^{2} }}{{\varGamma_{{\text{D}}} }}{ }.$$

(3)

The values of μ_opt and μ_H were almost identical, as shown in Fig. 1c, indicating that the contribution of grain-boundary scattering to the electron transport in the ZnSnN_2−xO_x epilayers was negligible. In other words, μ_H corresponded to the intra-grain mobility, implying that the electron transport properties of the ZnSnN_2−xO_x epilayers were close to those of single crystalline films.

Fig. 2

Infrared reflectance spectra of ZnSnN_2−xO_x epilayers with x = a 0.055, b 0.069, c 0.074, and d 0.079. The results of least-squares fitting using the modeled dielectric function are represented by solid lines. All the data are included in Additional file 6

Here, we compare μ_H values of the ZnSnN_2−xO_x epilayers with those of InN epilayers. Figure 3 shows n_e versus μ_H plot for the ZnSnN_2−xO_x and InN epilayers [26, 27]. The μ_H values of the present ZnSnN_2−xO_x films are in comparable level with those of the degenerate InN epilayers reported in the 1990s. Nevertheless, the μ_H values in the present study are substantially lower than those of the InN layers fabricated in 2010s. We believe that there is still room for the improvement of electron mobility, if the mobility-limiting factors are fully understood.

Fig. 3

Comparison of Hall mobility (μ_H) as a function of electron density (n_e) for ZnSnN_2−xO_x and degenerate InN epilayers [26, 27]. All the data are included in Additional file 8

To obtain insight into the intra-grain electron transport in ZnSnN_2−xO_x, the μ_H values were compared with theoretical models. We first considered ionized-impurity scattering, which generally governs the electron transport in heavily-doped degenerate semiconductors. The theoretical mobilities limited by the ionized-impurity scattering (μ_I) were calculated by using the Brooks–Herring model [28]. We used an effective mass of 0.37m₀ [18] and a static dielectric constant (ε_s) of 11[1] for the calculation. The calculated μ_I is plotted as a function of n_e in Fig. 4a. The μ_I curve gives the upper limit of the electron mobility in ZnSnN_2−xO_x; namely, the electron mobility of ZnSnN_2−xO_x potentially reaches ~ 100 cm² V⁻¹ s⁻¹. Nevertheless, the experimental μ_H values had a maximum of 20 cm² V⁻¹ s⁻¹, implying that an additional scattering source must be taken into account.

Fig. 4

a Dependence of Hall mobility on carried density. The circles represent data for the same films shown in Figs. 1 and 2. The triangles represent data for films grown under conditions similar to those employed for the grown of films shown in Figs. 1 and 2. The lines labeled μ_I and μ_N are theoretical curves of mobility limited by ionized- and neutral-impurity scatterings, respectively. The curve labeled μ_total represents the total mobility calculated from μ_total = (1/μ_I + 1/μ_N)⁻¹. b Seebeck coefficient as a function of (carrier density)^−2/3; theoretical lines for r = 3/2 (dashed line) and 0 (solid line) are also included. All the data are included in Additional file 9

Thermopower measurements were carried out for further investigation. For highly degenerate n-type semiconductors with a parabolic conduction band, Seebeck coefficient (S) is given by [28]

$$S = - \frac{{8\pi^{2} }}{3}\left( {r + \frac{3}{2}} \right)\frac{{k_{B}^{2} m^{*} T}}{{eh^{2} }}n_{e}^{{ - \frac{2}{3}}} ,$$

(4)

where r represents the scattering constant (e.g., r = 3/2 for ionized-impurity scattering, and r = 0 for neutral-impurity scattering), k_B is the Boltzmann constant, and h is the Planck constant. A plot of S versus n_e^−2/3 allows us to gain insight into the electron-transport mechanisms from the viewpoint of r values [29]. As shown in Fig. 4b, the experimental data lie close to the theoretical curve for r = 0 (solid line), whereas the experimental S values are located away from the theoretical S curve (dashed line) for the ionized-impurity scattering (r = 3/2). These trends suggest that neutral-impurity scattering was the dominant scattering mechanism. The temperature-independent behavior of μ_H is consistent with this interpretation because neutral-impurity scattering does not depend on temperature [30, 31]. Since ~ 70% of O_N was not ionized (Fig. 1a), it is reasonable to suppose that the compensated oxygen that is likely to form the Zn_Sn–2O_N complex acted as the neutral-impurity scattering centers. In fact, Hamilton et al. recently pointed out the possibility that the Zn_Sn–2O_N complexes behave as the neutral-impurity scattering centers [21].

We further analyzed the n_e–μ_H data by taking account of the neutral-impurity scattering. We hypothesized that all the compensated oxygen served as neutral-impurity scattering centers, namely, the density of the neutral impurity (n_N) was defined as n_N = (n_e/η)(1 − η). The mobility limited by the neutral-impurity scattering (μ_N) was calculated on the basis of the model developed by Mayer et al. [31]:

$$\mu_{{\text{N}}} = \frac{{e^{3} m^{*} }}{{4\pi \varepsilon_{{\text{s}}} \varepsilon_{0} A\left( w \right)\hbar^{3} }}\frac{1}{{n_{{\text{N}}} }}{ },$$

(5)

where w = (k_Fa_B)²,

$$A\left( w \right) = \frac{35.2}{{w^{\frac{1}{2}} }}\frac{{\left( {1 + e^{ - 50w} } \right)\left( {1 + 80.6w + 23.7w^{2} } \right)}}{{1 + 41.3w + 133w^{2} }}\left[ {\frac{1}{w}{\ln}\left( {1 + w} \right) - \frac{{1 + \frac{1}{2}w - \frac{1}{6}w^{2} }}{{\left( {1 + w} \right)^{3} }}} \right],$$

(6)

k_F is the Fermi wave number, and a_B is the effective Bohr radius (a_B = 1.5 nm for ZnSnN₂). Assuming that the ionization ratio of O_N was η = 30%, the total mobility was calculated using Matthiessen’s rule, μ_Total = (1/μ_N + 1/μ_I)⁻¹. The calculated n_e–μ_total curve agrees well with the experimental n_e–μ_H data, as shown in Fig. 4a. Furthermore, we grew an additional series of ZnSnN_2−xO_x epilayers under conditions similar to those mentioned above, and their n_e–μ_H data are also plotted in Fig. 4a (triangles). Again, the experimental data was found to be located near the theoretical n_e–μ_total curve. These findings led us to the conclusion that the unintentionally incorporated oxygen had an ionization rate as low as approximately ~ 30% and the unionized oxygen acted as neutral-impurity scattering centers that dominated electron transport in the heavily-doped ZnSnN_2−xO_x epitaxial films. The low μ_H values in the ZnSnN_2−xO_x epilayers resulted from the high concentration of neutral oxygen impurities. Frequently reported low electron mobilities in ZnSnN₂ epitaxial films can be explained by the same reason. Recent study showed that μ_H of ZnSnN_2−xO_x films with very high oxygen contents (x > 0.4) was as low as < 5 cm² V⁻¹ s⁻¹ [21]. That is, the more the oxygen content increases, the lower μ_H becomes. This supports the idea that electron scattering by the oxygen-related defects governs the electron-transport properties of ZnSnN_2−xO_x.

Conclusions

In summary, we analyzed the electron-transport properties of unintentionally oxygen-doped ZnSnN₂ epitaxial layers. We confirmed that the incorporated oxygen impurities behaved as electron donors with the low ionization rate of 30%. The Hall- and Seebeck-effect measurements revealed that the compensated oxygen impurities, which are likely to form the electrically neutral Zn_Sn–2O_N complexes, behaved as neutral-impurity scattering centers and further governed electron transport in the ZnSnN_2−xO_x. The low ionization rate led to the high concentration of neutral-impurity scattering centers. Therefore, we conclude that the low electron mobilities reported even in ZnSnN₂ single-crystalline films are attributed to the high concentration of neutral oxygen impurities. Suppression of the oxygen concentration in ZnSnN₂ is crucial not only to obtain nondegenerate ZnSnN₂, but also to achieve high mobility.

Methods

Thin-film growth

Reactive radio-frequency (RF) magnetron sputtering was employed to grow ZnSnN₂ epitaxial films on YSZ(111) single-crystalline substrates at the growth temperature of 300 °C. The base pressure of ~ 2 × 10^–4 Pa was established prior to the film-growth. A disk of Zn_0.5Sn_0.5 alloy was used as a target (diameter of 10 cm and purity of 3 N). An RF power of 70 W was applied to the target. A mixture of Ar and N₂ gas with various N₂/(N₂ + Ar) ≡ f(N₂) ratios was introduced into the chamber through two independent mass flow controllers with a total flow rate of 5 sccm. The total pressure in the growth chamber (P) was held at 2.0 Pa during film growth. The nitrogen partial pressure was defined as P_N2 = f(N₂) × P. The growth time was adjusted to obtain films with thicknesses of 100–300 nm. Prior to the film growth, a 5 min-long sputter-etching with pure Ar gas was performed, followed by a 5 min-long pre-sputtering under the same condition with the film growth. After the film growth, the as-grown films were immediately stored in another vacuum chamber (the pressure was about 1 Pa) for subsequent measurements.

Characterization

A Rigaku ATX-G X-ray diffractometer with Cu Kα radiation was employed to perform out-of-plane (θ/ω) and in-plane (2θ_χ/φ) scans to confirm the epitaxial growth. The compositions (Zn/(Zn + Sn) and x) of the ZnSnN₂ films were examined by XPS (PHI Versa Probe), using monochromated Al Kα (hν = 1486.6 eV) radiation. The XPS measurements were performed on 3-min Ar⁺-sputter-etched surface of the films. The relative sensitivity factor (RSF) approach was exploited to determine the compositions. It was confirmed that the compositions determined by the RSF method were consistent with those determined by Rutherford backscattering spectrometry [29, 32]. Hence, we believe that the compositions in this study are sufficiently reliable. The details of the RSF approach were already described elsewhere [18]. Electrical properties were determined by Hall-effect measurements in the van der Pauw configuration (Toyo Corp. Resitest 8200). Optical transmittance and reflectance were collected between 0.3 and 5.0 µm using a UV–Vis-NIR spectrophotometer (Shimadzu UV-3150) and FTIR spectrometer (Shimadzu IRAffinity-1).

Fitting analysis of reflectance spectra

As seen from Fig. 2a–d, free-electron reflection is clearly seen in the IR region. The well-known Drude dielectric model (Eqs. 1, 2) was employed to describe the optical response by the free electrons. In addition to the Drude model, the Tauc–Lorentz (TL) dispersion model was considered to describe the optical response across the whole spectral region. The explicit expression of the TL model is given in literature [25]. Deng et al. previously demonstrated that the dielectric response of ZnSnN₂ in the UV to visible region can be reproduced by double TL functions [13]. Hence, we modelled the dielectric function of degenerate ZnSnN_2−xO_x as a sum of double TL and Drude functions. Theoretical reflectance spectra calculated via the Fresnel formulas combined with the dielectric function above were fitted to the experimental spectra. In the fitting analysis, the parameters in the TL functions were fixed for simplicity at constant values that were the same as the values reported by Deng et al. [13]. Thus, ω_p and Γ_D in the Drude function were used as the fitting parameters.