The characteristics of MBE-grown In_xAl_1−xN/GaN surface states

The InAlN/GaN heterojunction has attracted significant interest for electronics since Kuzmik reported on its promise for high electron mobility transistor (HEMT) application.¹ At 17%–18% indium composition, InAlN is lattice-matched to GaN,² avoiding strain relaxation³ and providing thermally stable structures. In addition, the spontaneous polarization at the InAlN/GaN heterojunction is two times higher than that of traditional AlGaN/GaN HEMTs,¹ thus creating a higher density of two-dimensional electron gas (2DEG) in the channel.

Surface states characteristics, among all of the properties of nitride HEMTs, are fundamentally important and key to device performance. It is generally accepted that the origin of the electrons comprising the 2DEG is surface donor states.^4,5 Thus, the density and energy distribution of surface states directly affect 2DEG properties. As for device application, studies on AlGaN/GaN HEMTs⁶ show that surface states are responsible for drain current collapse at high operating frequencies, thus decreasing output power. Due to the similarity between InAlN and AlGaN HEMTs, it is believed that surface states on InAlN HEMTs may also affect output power.

Apart from the importance of surface states, their characteristics are not well understood. For InAlN, only one study by Pandey et al. on Schottky junctions fabricated on the InAlN/AlN/GaN heterostructure indicating distributed surface states is found.⁷ The density of the surface donor state is estimated to be 2.7 × 10¹³ cm⁻² eV⁻¹ by simulating 2DEG density as a function of Schottky barrier height. There is no study on the characteristics of bare InAlN/GaN surface states properties to the author's best understanding. Thus, in this work, the characteristics of In_xAl_1−xN/GaN heterostructure surface states with different indium compositions, x, are studied.

InAlN/GaN heterostructures with various thicknesses and compositions were grown using a Veeco GEN II RF-plasma-assisted molecular beam epitaxy (PAMBE). GaN was grown at a growth temperature of 680 °C with approximately two monolayers (MLs) of Ga adlayer coverage.⁸ Three series of InAlN samples with various thicknesses were grown under N-rich conditions with the N plasma fixed at 350 W/1.0 sccm. Detailed growth conditions are listed in Table I.

The as-grown samples were prepared for characterization using standard solvent cleaning procedures followed by a 10-min etch in 10:1 buffered oxide etch (BOE) which is shown by x-ray photoelectron spectroscopy (XPS) to effectively remove the native oxide and contaminants on InAlN surfaces.

High-resolution x-ray diffraction (HRXRD) using a Philips X'Pert PRO HR XRD System with a Cu Ka1 (1.5405 Å) x-ray source and Ge (220) hybrid monochromator was used to determine the bulk In_xAl_1−xN film composition, x_b. HRXRD $(0002)$ ω-2θ scans and $(101¯5)$ reciprocal space mapping (RSM) scans are used to determine the composition of each film. The details of our films' XRD measurements and analysis can be found in a prior study.⁹ All three films show that the InAlN layers are lattice-matched or strained to the GaN substrate with bulk indium composition, x_b. Series A and B are regarded as strain-free with In compositions of 16.9% and 18.2%, respectively. The growth temperature for series C was higher at 540 °C, approaching the temperature at which In-N bonds dissociate; thus, this sample has a lower indium composition of 9.8%.

According to Goyal et al.,¹⁰ determining the bare surface barrier height (BSBH) as a function of AlGaN thickness is a reliable method for extracting surface states properties. As shown in Figure 1, the BSBH is defined as the distance between the conduction band minimum (CBM) and the Fermi level at the bare, or unprocessed, surface. The BSBH can be calculated by subtracting the valence band maximum (VBM) from the band gap. The same approach is used in this work to study InAlN surface states.

Spectroscopic ellipsometry (SE) was used to determine the InAlN dielectric functions from which the layer's band gaps can be extracted. Our SE system (Horiba Jobin Yvon) is installed on the MBE system and is equipped with a source with a photon energy range of 1.5 eV–6.0 eV. The measurements are made after the films were grown and cooled to room temperature. From SE, the dielectric function of the InAlN/GaN structure was obtained from the as-measured pseudodielectric function. By describing the dielectric function of InAlN as a Tauc-Lorentz dispersion formula with two oscillators, the dielectric function of the InAlN layer can be determined.¹¹ The dielectric function was then used to calculate the absorption coefficient, $α,$ and refractive index, $n$⁠, of the InAlN layer in each heterostructure. By plotting $(αnE)2$ as a function of photon energy, $E$⁠, and performing a linear extrapolation to zero, the band gap, $Eg$⁠, can be obtained¹² (see Figure 2 which includes the 15 nm sample from each series). The calculated band gaps are listed in Table II.

X-ray photoelectron spectroscopy (XPS) was used to determine the energy separation between the Fermi level and valence band maximum (VBM) for each sample. Using a Kratos Axis UltraTM instrument with a monochromatic Al Kα source of kinetic energy of 1486.6 eV, valence band spectrum scans were conducted with a pass energy of 20 eV. The instrument was calibrated to an Au 4f_7/2 binding energy of 84.0 eV. Each spectrum was then calibrated to the C 1 s peak at 285.0 eV. As shown in Figure 3, by extrapolating the linear portion of the leading edge of the valence band spectrum, the energy value is determined with respect to the Fermi level by calculating the intersection with a horizontal offset.¹³ Three different take-off-angles (TOAs) 15°, 30°, and 50° are used in our XPS VBM experiments. Simulation methodology similar to that proposed by Akazawa et al.¹⁴ is applied to VBM results so that the VBM value on the varying InAlN surface is calculated considering different polarization induced band bending effects with varying In compositions. Simulation details can be found in our previously published paper studying valence band offsets (VBOs).¹⁵ The measured VBM is shown in Table II. From the measured bandgaps, $Eg$⁠, and VBM, the BSBH of each sample was calculated and is included in Table II.

Since InAlN surface states have not been studied, the surface states characteristics of AlGaN films are used as a reference in analyzing our data. Two different surface states energy distributions have been revealed experimentally for AlGaN films. In the first case, surface states are distributed over a relatively large energy range with low density^5,10,16–18 (Figure 4(a)). For example, Al_0.35Ga_0.65N is found to have surface states residing 1.0–1.8 eV below the CBM. The density is found to be approximately 0.46–0.75 × 10¹³ cm⁻² eV⁻¹.⁵ In the second case, surface states reside at a single energy level with a relatively high density of at least 1.1 × 10¹³ cm⁻² (Refs. 4, 19, and 20) (Figure 4(b)). For example, Al_0.34Ga_0.66N is found to have surface states 1.65 eV below the conduction band minimum (CBM).⁴ The surface states density for this case was found to be greater than 1.35 × 10¹³ cm⁻².²⁰ These two distributions will lead to different BSBH behavior as a function of thickness.

If the surface states are distributed over a specific energy range (Figure 4(a)), when the InAlN is thin, all of the donor states are below the Fermi level. These states are therefore occupied, and thus no 2DEG formed at the heterojunction interface. The spontaneous polarization induces an internal electric field in the InAlN layer so that its bands bend upward. This causes the Fermi level to move to a lower energy within the bandgap with increasing InAlN barrier layer thickness. Eventually, the Fermi level will cross the surface states energies. The states above the Fermi level will be emptied resulting in electron donation to the 2DEG. This model is supported experimentally wherein it was shown that the 2DEG concentration in an AlGaN/GaN heterojunction increases with increasing AlGaN barrier thickness.⁵ 

The two different surface states energy distribution and density models lead to different relationships between the measured BSBH and layer thickness. When the density of surface states is relatively low once the Fermi level reaches the donor level, the BSBH changes as a function of InAlN thickness. If the surface states reside at a single, or narrow, energy level (Figure 4(b)), and the concentration of donors is high, a small movement of the Fermi level donates a large concentration of electrons to the 2DEG, and the Fermi level is pinned at the donor level resulting in constant BSBH with thickness.

From Table II, we can see that the BSBH values tend to increase as a function of InAlN thickness indicating that the Fermi level is not pinned. This implies that the surface states distribution spans a larger energy range and the density of surface states is relatively low.

An analytical physical model is used to calculate the concentration of surface states.¹⁶ This model relates the BSBH to the thickness and is given by

in which $n0$ is the density of surface states per unit area, and $Ed$ is the highest energy position defining the distribution of surface states below the CBM as shown in Figure 4. $σpz$ is the positive density surface charge at the heterojunction interface due to polarization, $q$ is the electron charge, $d$ is the InAlN barrier thickness, $εInAlN$ is the permittivity of InAlN, $and ΔEc$ is the conduction band offset (CBO) between InAlN and GaN. In this equation, the BSBH and thickness are determined from the experimental data, $and Ed$ and $n0$ are fitting parameters. Other parameters are constants with values shown in Table III. The CBO is calculated using

with the bandgaps of InAlN shown in Table II, a GaN bandgap of 3.42 eV,²¹ and the valence band offset (VBO) measured by calculating the XPS peak separation between the core level peak energies for Al 2 p, Ga 2 p, and the valence band maximum with details published elsewhere.¹⁵ The spontaneous polarization charge difference between the InAlN and GaN, $σ,$ and the InAlN permittivity, $ε,$ follows Ref. 22.

To obtain a better understanding of the model, different values of $n0$ and $Ed$ are used to relate the BSBH to the InAlN thickness as shown in Figure 5. Higher surface states density, $n0,$ (Figure 6(a)) more effectively pins the Fermi level thus leading to BSBH saturation at a smaller thickness and with a lower slope after saturation. Higher $Ed$ (Figure 6(b)) leads to a larger BSBH saturation value. The final saturated BSBH is determined by both $n0$ and $Ed$⁠; for sufficiently large InAlN thickness $d$⁠, the BSBH will saturate at a value of $Ed+σpz/qn0$⁠, which is a function of both $Ed$ and $n0$⁠.

A fit of our experimental data using Equation (1) is shown in Figure 6 and the extracted values of the surface states density, $n0,$ and energy position, $Ed,$ are listed in Table IV. The energy distribution is calculated by subtracting the saturation energy, obtained by calculating the BSBH with an InAlN thickness of 30 nm, by $Ed$⁠.

We can see that the surface states density, $n0,$ varies from 4.64 to 8.27 × 10¹³ cm⁻² eV⁻¹. This density of surface states is higher than that found for AlGaN, which is approximately 1 × 10¹³ cm⁻² eV⁻¹.¹⁷ Band models showing the surface states density and energy distribution from Table IV are plotted in Figures 7(a)–7(c) for comparison.

To date, unlike AlGaN, In_xAl_1−xN surface reconstructions have not been studied using first-principles methods based on density functional theory (DFT). Miao et al.²³ calculated the relationship between surface reconstruction and surface states distribution on Al_xGa_1−xN surfaces. Their findings suggest that surface states distribution is a function of Al incorporation, x. For InAlN, we expect similar behavior with In incorporation, x, to be a primary factor impacting the properties of surface states due to differences between the binary endpoint compounds, AlN and InN. In Figure 7, the bulk indium concentration x_b as determined using XRD is shown. We find that x_b does not seem to directly relate to the surface states distribution $n0$ and $Ed$ as suggested for AlGaN by Miao et al.

InAlN may possess a different indium composition at the surface compared with the bulk as shown by our previous study.⁹ Thus, we use XPS region scan peak intensities to calculate the surface indium composition x_s. The results are shown in Figure 7. These data show that the properties of the surface states are directly related to the surface composition x_s instead of x_b. With a larger x_s, the surface states have a higher density and narrower energy distribution. This implies that the formation of the surface states is related to the surface reconstruction.

In conclusion, the properties of the surface states at InAlN/GaN heterostructure surfaces with various indium incorporations are studied. The BSBH as a function of InAlN thickness is modeled in order to extract the surface states density and energy distribution. The results show that samples having higher surface indium composition have surface states with larger density and narrower energy distribution.

The authors would like to acknowledge the support of ONR N00014-08-1-0396, GOALI NSF NSF-ECCS-12-02132, and NSF MRSEC DMR-1121288.