Transport Properties of the Two-Dimensional Hole Gas for H-Terminated Diamond with an Al₂O₃ Passivation Layer

Abstract

Diamonds are thought to be excellent candidates of next-generation semiconductor materials for high power and high frequency devices. A two-dimensional hole gas in a hydrogen-terminated diamond shows promising properties for microwave power devices. However, high sheet resistance and low carrier mobility are still limiting factors for the performance improvement of hydrogen-terminated diamond field effect transistors. In this work, the carrier scattering mechanisms of a two-dimensional hole gas in a hydrogen-terminated diamond are studied. Surface roughness scattering and ionic impurity scattering are found to be the dominant scattering sources. Impurity scattering enhancement was found for the samples after a high-temperature Al₂O₃ deposition process. This work gives some insight into the carrier transport of hydrogen-terminated diamonds and should be helpful for the development of diamond field effect transistors.

1. Introduction

Due to its high critical breakdown electric field, high carrier saturation drift velocity, high thermal conductivity, and high carrier mobility, diamonds have great application potential in high power and high frequency areas [1]. A hydrogen-terminated (H-terminated) diamond surface demonstrates a relatively high surface conductivity due to the forming of a two-dimensional hole gas (2DHG) by transfer doping from adsorbates/dielectric materials in contact with a H-terminated diamond surface. The electron transfer from the diamond to the adsorbates/dielectric materials and the holes accumulate in the subsurface of the H-terminated diamond [2,3]. The 2DHG shows a sheet density of 10¹² to 10¹³ cm⁻² and a carrier mobility of less than 200 cm²/(V·s) [4,5,6].

H-terminated diamond field effect transistors (FETs) have obtained good direct current (DC) and radio frequency (RF) performances. A drain current density (I_DSmax) of 1.3 A/mm [7] and a maximum oscillation frequency (f_max) of 120 GHz [8] have been obtained for H-diamond FETs. Recently, the output power density was also improved and reached 3.8 W/mm at 1 GHz [9]. Output power densities at 2 GHz [10] and 10 GHz [11] were also reported. However, for high power and high frequency applications, the sheet resistance of the 2DHG is still at a high level and the carrier mobility is low, which leads to large parasitic resistance and limits the performance of H-terminated diamond FETs. Another issue is that, in the fabrication process of H-terminated diamond FETs, a gate dielectric, such as Al₂O₃ deposition, is needed, which is usually performed at a high temperature. The surface adsorbates would be broken during the high temperature process, which influences the electrical properties of the 2DHG of the H-terminated diamond. The atomic layer deposition (ALD) Al₂O₃ films are gate insulator and passivation films for the p-type surface conduction of the H-terminated diamond surface. Many works have investigated the effects of Al₂O₃ passivation films [12,13,14]. Kawarada et al. [12,15] suggested that the surface adsorbates desorbed below 250 °C. There are defects in the ALD Al₂O₃ films, which introduce unoccupied levels above the valence band edge of Al₂O₃. The defects could accept the electrons transferring from the H-terminated diamond and be negatively charged. Ren et al. deposited an Al₂O₃ film at 300 °C and found that O impurity or Al vacancy defects existed in the ALD Al₂O₃ dielectric. Additionally, the ALD Al₂O₃ dielectric can work as an acceptor-like transfer doping material on the H-terminated diamond surface [16]. Liu et al. deposited Al₂O₃ at 120, 200, and 300 °C. They found that, when the deposition temperature of ALD Al₂O₃ was increased from 120 to 300 °C, the polarity of the fixed charges in the ALD Al₂O₃ dielectric changes from positive to negative [17]. The low carrier mobility of the 2DHG of the H-terminated diamond has been one of the limiting factors for the development of H-terminated diamond FETs. Some works have investigated the carrier scattering mechanism of the H-terminated diamond [18,19]. The deposition of Al₂O₃ may introduce an extra scattering source to the 2DHG of the H-terminated diamond and influence its electrical properties. However, to date, no report on the scattering mechanism analysis has been conducted for the Al₂O₃/H-terminated diamond structure.

In this work, the influence of Al₂O₃ deposition by a high-temperature ALD process on the transport properties of the 2DHG in a H-terminated diamond is investigated. The sheet resistance, carrier density, and mobility of H-diamond samples with and without Al₂O₃ were measured from 90 to 300 K by a Van der Pauw–Hall method. The temperature dependence of the mobility of the 2DHG is fitted considering four scattering mechanisms: ionic impurity (IM) scattering, acoustic phonon (AC) scattering, optical phonon (OP) scattering, and surface roughness (SR) scattering for the H-diamond samples with and without Al₂O₃ deposition.

2. Experiments

Three kinds of H-terminated diamond samples were prepared, as shown in Figure 1. The samples were prepared by the microwave plasma CVD (MPCVD, Seki diamond systems, Japan) technique. For the SC-Epitaxial H-termination samples, the samples were a single crystal diamond with a H-termination formed by a homoepitaxial growth process as stated in [20]. The microwave power was 1 kW, and growth temperature was 900 °C with a chamber pressure of 100 Torr. The CH₄/H₂ ratio was 1% with total flow of 500 sccm. For the SC-H plasma treatment and PC-H plasma treatment samples, the samples were treated by MPCVD in H₂ plasma [21]. The hydrogen plasma treatment was performed at a chamber pressure of 5 kPa and a temperature of 800 °C for 40 min. The SC-H plasma treatment samples were a single crystal diamond, and the PC-H plasma treatment samples were a polycrystalline diamond with a grain size of ~100 μm. The electrical properties of the H-terminated diamond samples were measured by the Van der Pauw–Hall method in the low temperature Hall measurement system from 90 K to 300 K.

3. Results and Discussion

Figure 1 shows the relationship of carrier mobility μ vs. sheet density N_S at room temperature for the three kinds of H-terminated diamond samples. As shown in Figure 1, all the samples follow the µ∝1/Ns relationship, indicating the mobility of the 2DHG in the H-terminated diamond is limited by ionized impurity scattering [22]. The mobility values of the PC-H plasma treatment samples are comparable with the SC-Epitaxial H-termination samples and SC-H plasma treatment samples, showing that the grain boundary scattering is not dominant at this mobility level for the H-terminated diamond. This may be the reason why H-terminated diamond FETs on polycrystalline diamond samples show comparable or even better DC and RF properties than those on single crystal diamond samples [23].

To analyze the carrier transport mechanism of the 2DHG in H-terminated diamond, Van der Pauw–Hall measurements were performed. As listed in

Table 1. Room temperature electrical properties of five H-terminated single crystal diamond samples with and without Al₂O₃ deposition.

Sample Name	Before Al2O3 Deposition			After Al2O3 Deposition			Al2O3 Deposition Temperature (°C)
	Rs (Ω/sq)	Ns (1012/cm2)	μ (cm2/V·s)	Rs (Ω/sq)	Ns (1012/cm2)	μ (cm2/V·s)
A	8727	4.715	152	7360	6.18	137	450
B	9271	6.461	104	13,300	6	77.9	400
C	8332	7.512	99.7	11,500	5.37	101	300
D	7000	11.7	76.4	——			-
E	5380	14.3	80.9	——			-

, five samples with (samples A, B, and C) and without (samples C and D) ALD Al₂O₃ deposition were studied. All the five samples are a single crystal diamond. The ALD processes were performed at 450 °C, 400 °C, and 300 °C for samples A, B, and C, respectively. From Table 1, it can be seen that the carrier mobility μ of the samples A, B, and C decreased after the Al₂O₃ deposition. The changes of the sheet density N_s of the samples are dependent on the deposition temperatures of the ALD Al₂O₃, as shown in Figure 2a and Table 1. For sample C with the ALD temperature of 300 °C, the sheet density Ns decreases. For sample B with the ALD temperature of 400 °C, the sheet density Ns shows a small decrease. Additionally, for sample A with the ALD temperature of 450 °C, the sheet density N_s increases. The adsorbates on the H-terminated diamond surface formed in the air desorbed from the surface during the heating process. Additionally, the ALD Al₂O₃ is the new transfer doping layer for the formation of the 2DHG of the H-terminated diamond. The different changes of sheet density N_s of the samples A, B, and C could be due to the different electron affinities of the ALD of Al₂O₃ deposited at different temperatures [24]. Hiraiwa et al. found that the Al₂O₃ electron affinity increases with the increasing of the Al₂O₃ deposition temperature. The high electron affinity of Al₂O₃ induces a high sheet density in the H-terminated diamond.

Figure 2b shows the temperature dependences of the sheet resistance Rs of the H-terminated diamond samples with and without the ALD Al₂O₃. The sheet resistances of all the five samples decrease with temperature, which are due to the carrier mobility increases with temperature, as shown in Figure 2d. The sheet densities of the H-terminated diamond samples keep unchanged or slightly reduced with temperature, as shown in Figure 2c. The weak dependence of sheet density with temperature should be due to the electron affinity difference of the ALD Al₂O₃ and the H-terminated diamond is almost unchanged in the temperature range from 90 to 300 K. The carrier mobility of all the five samples increases with temperature. The carrier mobility of the H-terminated diamond samples with Al₂O₃ (samples A, B, and C) shows a stronger temperature dependence compared with those without (w/o) Al₂O₃ (samples D and E). The temperature dependence of the mobility of the 2DHG is fitted considering four scattering mechanisms to analyze the influences of Al₂O₃ deposition on the transport properties of the 2DHG in the H-terminated diamond.

The total relaxation time can be obtained by the Mathiessen rule:

$$\frac{1}{\tau }={\displaystyle \sum _n\frac{1}{{\tau }_n}}$$

(1)

where τ_n is the momentum relaxation time corresponding to the n_th scattering mechanism. The mobility of the 2DHG of the H-terminated diamond can be obtained by the equation $\mu =e\tau /m_c^{*}$, where $m_c^{*}$ is the conduction mass, and formulated as $m_c^{*}=(m_{lh}^{*3/2}+m_{hh}^{*3/2}+m_{so}^{*3/2})/(m_{lh}^{*1/2}+m_{hh}^{*1/2}+m_{so}^{*1/2})$ [25,26] with $m_c^{*}$ = 0.444731 m₀. The quantities m_hh^*, m_lh^*, and m_so^* are the heavy, light, and spin-orbit hole mass, respectively.

(1)

Acoustic phonon (AC) scattering

Phonons are the quanta of the lattice vibrations of materials and introduce intrinsic scatterings to carriers. Due to different modes of vibrations, phonons can be divided into acoustic phonons and optical phonons. In this work, the relaxation time limited by the acoustic phonon was calculated following the formula for 2DEG [27]:

$$\frac{1}{{\tau }_{ac}}=\frac{3m_d^{*}b{k}_{B}T{D}_{ac}^2}{16\rho u_l^2{\hslash }^3}$$

(2)

where ρ is the mass density, k_B is the Boltzmann constant, D_ac is the acoustic deformation potential, and u_l is the longitudinal acoustic phonons velocity. The parameter $b={[33\pi m_d^{*}{e}^2{p}_{s2D}/\left(2{\hslash }^2{\epsilon }_0{\epsilon }_s\right)]}^{1/3}$. In this paper, the acoustic deformation potential was considered as 8 eV. The density of state mass of diamond $m_d^{*}$ was evaluated as $m_d^{*}={(m_{lh}^{*3/2}+m_{hh}^{*3/2}+m_{so}^{*3/2})}^{2/3}$ [28] and $m_d^{*}$ = 0.907832 m₀.

(2)

Optical phonon (OP) scattering

The Debye temperature is about 2240 K for a diamond, which is very high. If the optical phonons dominate the carrier scattering, an exponential drop in carrier mobility with temperature is expected for T < 600 K. The carrier mobility can be estimated by [29]:

$${\mu }_{OP}=\frac{4\sqrt{2\pi }q\rho {\hslash }^2\sqrt{k\Theta }}{3D_0^2{(m_d^{*})}^{3/2}{m}_c^{*}}\phi (T)$$

(3)

where D₀ is the optical deformation potential. φ(T) is a temperature-dependent function, which is in an exponential relationship and drops with temperature T below the Debye temperature.

(3)

Ionic impurity (IM) scattering

Due to its deep impurity levels, the ionized impurity concentration is not a constant for diamond. This makes the ionic impurity scattering momentum relaxation time show a strong temperature dependence. The classical expression for the ionized impurity scattering momentum relaxation time is the Brooks–Herring expression [30]:

$${\tau }_{im}=\frac{16\sqrt{2m_c^{*}}\pi {\epsilon }^2}{Z^2{q}^4{N}_I}(\ln (1+b)-b/(1+b))E^{3/2}$$

(4)

where $b=8m_c^{*}{L}_D^{2}E/{\hslash }^2$ and ε is the dielectric constant of the medium. N_I is the ionized impurity concentration. Z is degree of ionization. L_D is the Debye length and E is the carrier energy. Assuming parabolic bands, by averaging over carrier momentum and neglecting the weak dependence of b on energy, the ionized impurity scattering limited relaxation time can be written as:

$${\tau }_{im}=\frac{128\sqrt{2\pi m_c^{*}}{\epsilon }^2{(kT)}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}{Z^2{q}^4{N}_I(\ln (1+b^{’})-b^{’}/(1+b^{’}))}$$

(5)

where $b^{’}=24m_c^{*}{L}_D^{2}kT/{\hslash }^2$.

(4)

Surface roughness (SR) scattering

The relaxation time of SR is expressed including the screening by the 2DHG as [31]:

$$\frac{1}{\tau }=\frac{{∆}^2{L}^2{e}^4{m}_d^{*}}{2{\left({\epsilon }_0{\epsilon }_s\right)}^2{\hslash }^3}{(\frac{N_s}{2})}^2·{\displaystyle \underset{0}{\overset{1}{\int }}\frac{u^4\exp (-k_F^2{L}^2{u}^2)}{{(u+G(q)q_{TF}/(2k_F))}^2\sqrt{1-u^2}}}du$$

(6)

where ∆ is the root-mean-square roughness of surface and L is the correlation length. u = q/2k_F, which is a dimensionless parameter, with q = 2k_Fsin(θ/2), θ∈(0, π). θ is the angle between the initial and final wave vector.

Figure 3 shows the fitting results of the carrier mobility of the 2DHG with temperature for samples B and D. It can be seen that the surface roughness (SR) scattering and ionic impurity (IM) scattering are the dominant scattering sources in the measured temperature range. For sample B with Al₂O₃ deposition, the influence of IM scattering enhances, as shown in Figure 3a. This indicates that the adsorbates on the H-terminated diamond surface formed in the air desorbed from the surface during the heating process of the Al₂O₃ deposition. The ALD Al₂O₃ as the new transfer doping layer makes the concentration of the ionized impurity N_I increase. This is consistent with the results of Liu et al. [17]. They found that there were negative charges at the Al₂O₃/H-terminated diamond interface. They thought the unoccupied levels within the Al₂O₃ dielectric near the Al₂O₃/H-terminated diamond interface were the main sources of the negatively charged acceptors at the Al₂O₃/H-terminated diamond interface. The above results indicate that the initial stage of the ALD Al₂O₃ is especially important for the H-terminated diamond. The reduction of unoccupied levels in the Al₂O₃ near the Al₂O₃/H-terminated diamond interface will be beneficial for the carrier mobility improvement of the 2DHG in the H-terminated diamond.

4. Conclusions

In summary, we studied the influence of Al₂O₃ deposition by a high-temperature atomic layer deposition process on the transport properties of the 2DHG in a H-terminated diamond. The temperature dependence of the mobility of the 2DHG is fitted considering four scattering mechanisms: ionic impurity scattering, acoustic phonon scattering, optical phonon scattering and surface roughness scattering. The surface roughness scattering and ionic impurity scattering are found to be the dominant scattering sources in the H-terminated diamond. Impurity scattering enhancement was found for the H-terminated diamond sample after the high-temperature atomic layer deposition Al₂O₃ process.