Electron transport properties of degenerate n-type GaN prepared by pulsed sputtering

The physics of degenerate electrons in a partially filled conduction band of heavily doped n-type GaN has been extensively investigated because of the importance for reducing the parasitic resistance of nitride optical and electron devices.^1–3 Si is the most commonly used dopant for n-type GaN, and a room-temperature (RT) free-electron concentration of 3.6 × 10²⁰ cm⁻³ has been achieved in Si-doped GaN deposited using molecular beam epitaxy (MBE).³ Ge is also used as an alternative dopant to Si. Unlike the case of Si doping, Ge doping into GaN is known to not introduce additional tensile stress during growth.⁴ The reported free-electron concentrations in Ge-doped GaN layers deposited by metal–organic chemical vapor deposition (MOCVD) and in layers deposited by plasma-assisted MBE are 2.9 × 10²⁰ cm^−3 4 and 6.7 × 10²⁰ cm⁻³,⁵ respectively. Despite the high free-electron concentration achieved by these techniques, the minimum resistivity of the GaN films remains high (0.3–0.4 mΩ cm) at electron concentrations of ∼2 × 10²⁰ cm⁻³,^2,3 and the resistivity increases with increasing dopant concentration.^3,5 This behavior is likely caused by a decrease in the electron mobility due to diminished doping efficiency and/or by a degradation in material quality; in either case, this behavior prevents us from understanding the intrinsic electron transport properties of degenerate GaN. Hence, the development of a growth technique that offers high electron mobility as well as high carrier density should be highly sought after.

A proposed mass production technique for GaN devices called pulsed sputtering deposition (PSD) was recently developed and has attracted much attention. The use of PSD enables the growth of device-quality group-iii nitrides at much lower temperatures than those used in the conventional MOCVD process.^6–11 PSD is suitable for growing heavily impurity-doped GaN because of its highly nonequilibrium nature. In fact, heavily Si-doped GaN prepared by PSD exhibited a RT electron mobility of 110 cm² V⁻¹ s⁻¹ at an electron concentration of 2.0 × 10²⁰ cm⁻³, and the resistivity of this film was as low as 0.28 mΩ cm.¹² Also, Ge doping by PSD resulted in highly degenerate GaN with an electron concentration as high as 5.1 × 10²⁰ cm⁻³ and with the lowest resistivity reported to date (0.20 mΩ cm) for a Ge-doped GaN film.¹³ These achievements in the growth of highly conductive, heavily doped n-type GaN provide a good opportunity for systematically investigating the transport properties of degenerate GaN.

Here, we have investigated the dopant concentration dependence of the electrical properties of highly Ge- and Si-doped GaN epilayers prepared by PSD using secondary-ion mass spectrometry (SIMS) and temperature-dependent Hall-effect measurements. We also discuss the relationship between the experimental electron mobility and theoretical calculations for degenerate GaN and demonstrate the superiority of PSD for achieving highly conductive GaN.

Si-doped or Ge-doped GaN films were prepared via PSD with pulsed magnetron sputtering sources under an N₂/Ar atmosphere. The details of the growth procedure have been reported elsewhere.^12,13 To investigate their electrical properties, we deposited the n-type doped GaN epilayers onto commercially available semi-insulating C-doped GaN templates on sapphire as starting substrates. The dislocation density of the GaN templates was typically 5.0 × 10⁹ cm⁻². To obtain reliable data, we carefully determined the growth thickness by using optical measurements and cross-sectional scanning electron microscopy observations. The dopant and residual impurity concentrations were determined by SIMS. The quantitative accuracy in the dopant concentration was believed to be 20%. To fabricate van der Pauw structures for Hall-effect measurements, we processed all of the samples into cloverleaf patterns by photolithography and inductively coupled plasma reactive-ion etching. Ohmic contacts were then formed using a Ti/Al/Ti/Au (20/60/20/50 nm) stack as electrodes. The temperature-dependent Hall-effect measurements were performed using ResiTest 8400 (Toyo Corp.) with a liquid-N₂-cooled variable-temperature sample holder.

Understanding the effects of intentional dopants, residual impurities, and intrinsic defects on the electron concentration is important for clarifying the transport properties of degenerate electrons in GaN. SIMS impurity measurements revealed that the concentrations of residual impurities such as oxygen and carbon were less than 3 × 10¹⁶ cm⁻³ even at the highest doping concentration. Figure 1 shows the dependence of the RT electron concentration n(RT) on the Si or Ge dopant concentration ([Si] or [Ge]) determined by SIMS. The carrier concentration was very similar to the dopant concentration at carrier concentrations as high as 5.1 × 10²⁰ cm⁻³, which indicates that almost all of the dopant atoms in GaN act as a shallow donor and that their activation energies are negligible at RT. Moreover, this indicates that the concentrations of compensating acceptors are low. These characteristics impart PSD with an advantage over other techniques for growing heavily doped n-type GaN. In addition, the surface morphologies of our heavily doped samples remained specular, with no cracks at dopant concentrations as high as 5.1 × 10²⁰ cm⁻³. We also found that the Ge dopant resulted in a greater maximum carrier concentration compared with Si, as is often the case with other techniques such as MOCVD.⁴ Notably, despite the high doping efficiency for both Si and Ge, data points for Ge in Fig. 1 are plotted at slightly lower positions compared with those for Si. Although further study is necessary to confirm this tendency, it can be possibly related to the slightly lower electron mobility, which will be discussed later.

Figure 2 presents the RT electron mobility μ(RT) of PSD-grown Si-doped and Ge-doped GaN as a function of n(RT). The solid lines indicate the theoretical electron mobility for degenerate GaN based on a model reported by Halidou et al.¹⁴ For degenerate semiconductors, the electron mobility is known to be mainly limited by the ionized impurity scattering, even at RT. If we assume that all of the donors (N_D) and all of the acceptors (N_A) are ionized at RT, the electron mobility limited by the ionized impurity scattering limit can be analytically expressed using the compensation ratio, θ = N_A/N_D,¹⁵ 

where q is the electron charge; ε₀ε_s is the dielectric constant; m*_F is the effective mass at the Fermi energy, E_F; and k_F and k_TF are the Fermi wave vector and the Thomas–Fermi screening wave vector, respectively.¹⁶ In a degenerate semiconductor, because E_F is located within the conduction band, its nonparabolicity should be taken into account,

where E_F0 is the Fermi energy for a parabolic conduction band, α is the dimensionless nonparabolic conduction band coefficient, m_e is the effective mass at the bottom of the conduction band, and E_g is the bandgap energy. When experimental data are not available, α is often assumed to be equal to (1 − m_e/m₀)². We have also considered the bandgap renormalization due to many-body effects of free electrons: ΔE_g = −Kn^1/3, where K is the bandgap renormalization coefficient. In this calculation, the electron concentration n is simply 1/qR_H, where R_H is the Hall coefficient determined from Hall-effect measurements. This model has been used to quantitatively explain the relationship between the electron concentration and mobility for degenerate n-type GaAs.¹⁵ The parameters used in Fig. 2 and shown in Table I were taken from the literature.¹⁴ In Fig. 2, the gradual decrease in μ(RT) is qualitatively explained by this theory. However, the experimental values are substantially greater than the theoretical limit of the calculated μ(RT). For example, the electron mobility for the sample with the highest [Si] of n(RT) = 3.9 × 10²⁰ cm⁻³ is as high as 100 cm² V⁻¹ s⁻¹ and is much higher than the theoretical limit at zero compensation (θ = 0). This deviation was revealed because of the successful formation of high-quality degenerate n-type GaN by PSD. The discrepancy between the calculations and experimental results is attributed to the overestimation of the effective mass m_F^* of highly degenerate GaN, which stems from the large nonparabolic coefficients used in the previously discussed conventional calculation. Recent experimental reports have also revealed that the effective mass of degenerate wurtzite GaN can be expressed by a parabolic conduction band (α = 0) with an electron concentration as high as 1.2 × 10²⁰ cm⁻³.¹⁷ 

To improve the electron transport model of degenerate GaN with n(RT) > 1 × 10²⁰ cm⁻³, we carefully performed temperature-dependent Hall-effect measurements. Figure 3(a) shows the temperature dependence of electron mobility for the Si-doped sample with n(RT) = 3.3 × 10²⁰ cm⁻³. First, we estimated the lattice-vibration-limited electron mobility μ_Lattice, as shown in Fig. 3(a), which was calculated from the combination of the polar optical phonon, deformation potential acoustic phonon, and piezoelectric phonon scattering.¹³ Here, the dislocation scattering for degenerate GaN proposed by Look et al.¹⁸ was ignored because it is quite small in our samples. The experimental mobility data were fitted by Mattisen’s rule (μ_total⁻¹ = μ_Lattice⁻¹ + μ_I.I.⁻¹). The fitting parameters used here are the nonparabolic coefficient α and the compensation ratio θ included in Eq. (1). The experimental data and fitting results for samples with the different dopant concentrations are shown in Fig. 3(b). At low temperatures, the electron mobility was saturated and mainly limited by the ionized impurity scattering, which was almost independent of the temperature in highly degenerate samples. At higher temperatures, the slight reduction in the mobility was attributed to the lattice scattering. For all samples with different [Si] or [Ge] in Fig. 3(b), the experimental data can be well fitted by this model. The nonparabolic coefficient α and compensation ratio θ used in the fitting are plotted as a function of n(RT) in Fig. 3(c). The compensation ratio θ of the Si-doped samples was estimated to be as low as within 0 < θ < 0.1. This compensation ratio is reasonable because [Si] is approximately equal to n(RT), as shown in Fig. 1. However, the Ge-doped samples showed slightly higher θ values than the Si-doped samples. Although this phenomenon can be attributed to the greater formation energy associated with Ge atoms substituting Ga sites than with Si atoms substituting Ga sites and/or with the formation of native defects,¹⁹ further study is necessary to clarify the origin of this small amount of compensation. The fitting result also reveals that the high electron mobility of PSD samples can be explained on the basis of scattering theory with the use of the single nonparabolic coefficient α (0.31), which is much smaller than the conventional value of 0.64 based on the frequently invoked assumption that α = (1 − m_e/m₀)². This small value is, in fact, consistent with the reported notion that the conduction band of wurtzite semiconductors with wide energy bandgaps, such as GaN, ZnO, and CdS, is less nonparabolic than that of other typical semiconductor materials.²⁰ 

Finally, we briefly discuss the achievable resistivity, ρ(RT), of n-type doped GaN using the new parameter set. Figure 4 shows our experimental ρ(RT) and reported values of n-type doped GaN prepared by MOCVD, MBE, and PSD. The ρ(RT) values calculated using the lattice scattering and ionized impurity scattering with the modified nonparabolic coefficient α of 0.31 are shown as solid lines. In the case of MBE- or MOCVD-grown samples, ρ(RT) decreases as n(RT) increases to 2 × 10²⁰ cm⁻³ but reaches a minimum value of 0.3–0.4 mΩ cm; a further increase in n(RT) leads to an increase of ρ(RT) because of a reduction in μ(RT). As shown in Fig. 4, this phenomenon can be explained by the significant increase in the compensation ratio θ at doping concentrations greater than 1 × 10²⁰ cm⁻³.

In the case of the PSD samples, ρ(RT) decreases monotonically over the whole doping range, whereas the θ values remain small. Especially for the Si-doped samples, the θ values are quite small and a ρ(RT) value of 0.16 mΩ cm was achieved with a μ(RT) of 100 cm² V⁻¹ s⁻¹ at an n(RT) of 3.9 × 10²⁰ cm⁻³. To the best of our knowledge, this value is the lowest value reported for an n-type doped wurtzite GaN film. Notably, this resistivity is almost as low as that reported for transparent conductive oxides (TCO) such as indium thin oxide (ITO). The sputtered polycrystalline ITO films, which are used in the TCO applications, showed the minimum resistivity of 0.15 mΩ cm.²³ However, the μ(RT) value of 100 cm² V⁻¹ s⁻¹ is much higher than that for such ITO films, which is quite advantageous for ensuring optical transparency. Although the Ge-doped samples showed slightly lower mobility because of their higher θ values compared with those of the Si-doped samples, the highest n(RT) of 5.1 × 10²⁰ cm⁻³ with a ρ(RT) of 0.20 mΩ cm was achieved by Ge doping.

The lower compensation ratio θ of PSD samples indicates that the self-compensation effect and the incorporation of point defects were well suppressed in the PSD growth of highly n-type-doped GaN. According to first-principles calculations, the incorporation of Si or Ge atoms at N sites can be negligible under the N-rich growth condition because of the associated high formation energy.¹⁹ The use of PSD is possibly advantageous for reducing the formation of such acceptors because PSD growth proceeds under conditions where a high concentration of N radicals is generated by nitrogen-based plasma. Also, the thermodynamic equilibrium concentration of Ga vacancies decreases with reducing growth temperature,²⁴ which is also indicative of the superiority of the low-temperature PSD technique.

In conclusion, highly degenerate n-type GaN layers prepared by PSD show higher electron mobility compared with those prepared by conventional growth techniques. SIMS and Hall-effect measurements revealed that the doping efficiency of PSD n-type GaN is close to unity at electron concentrations as high as 5.1 × 10²⁰ cm⁻³ and that its electron mobility is unusually high. A record low resistivity of n-type GaN of 0.16 mΩ cm was achieved with a μ(RT) of 100 cm² V⁻¹ s⁻¹ at an n(RT) of 3.9 × 10²⁰ cm⁻³. The relationship between n(RT) and μ(RT) of degenerate electrons in such GaN can be well explained within the framework of conventional scattering theory by using a modified nonparabolic coefficient, α, of 0.31 for the conduction band. These results clearly demonstrate the strong potential for the low-temperature PSD growth of highly conductive n-type GaN.

This work was partially supported by JST ACCEL Grant No. JPMJAC1405 and JSPS KAKENHI Grant No. JP16H06414.