Direct experimental band alignment and interface charge of nonpolar m-plane (10-1̄0) and semipolar (20-2̄1) GaN/AlGaN heterojunctions

Capacitance-voltage ( $C$ - $V$ ) profiling of isotype (both layers n-type) GaN/Al $_x$ Ga $_{1-x}$ N heterojunctions grown on nonpolar m-plane $(10\overline{1}0)$ and semipolar $(20\overline{2}1)$ GaN substrates (Hurni, Kroemer, Mishra, and Speck, 2014) extracted conduction-band offsets $\Delta E_c$ that rise approximately linearly with Al fraction $x$ on m-plane (0.085–0.163 eV for $x = 0.10$ – $0.20$ ) and implied a $\Delta E_c:\Delta E_v$ partitioning of 50:50–60:40, but left the semipolar interface charge sign and magnitude uncertain, provided no statistical error bars, assumed abrupt defect-free interfaces, and inferred the valence-band offsets $\Delta E_v$ from an assumed bandgap bowing parameter. The extracted positive $(20\overline{2}1)$ interface charge (about 1.3– $2.5\times10^{11}\,\mathrm{cm}^{-2}$ ) contradicts the theoretically predicted low negative polarization charge at this orientation. The open problem is to establish the orientation-resolved band alignment of m-plane and $(20\overline{2}1)$ GaN/AlGaN heterojunctions: a determination of the valence-band offset $\Delta E_v$ for these orientations and an independent determination of the magnitude and sign of the $(20\overline{2}1)$ interface charge, thereby fixing the $\Delta E_c:\Delta E_v$ partitioning and resolving the polarization-sign contradiction.

Background

Gallium nitride (GaN) and its alloy aluminum gallium nitride ( $\mathrm{Al}_x\mathrm{Ga}_{1-x}\mathrm{N}$ ) crystallize in the hexagonal wurtzite structure. Because this structure lacks inversion symmetry along the hexagonal $c$ -axis, the material carries a spontaneous electric polarization, and any strain adds a piezoelectric component. In the conventional polar $c$ -plane (0001) growth orientation this produces fixed sheet charges of order $10^{13}\,\mathrm{cm}^{-2}$ at GaN/AlGaN interfaces, which tilt the bands (the quantum-confined Stark effect) and complicate the design of light emitters and transistors. Growth orientations whose surface normal is perpendicular to the $c$ -axis - the nonpolar $m$ -plane $(10\overline{1}0)$ and $a$ -plane $(11\overline{2}0)$ - carry no normal polarization discontinuity at all, while semipolar orientations such as $(20\overline{2}1)$ , whose normal is tilted roughly 75 degrees from the $c$ -axis, carry a strongly reduced, composition-dependent charge. Nonpolar and semipolar GaN substrates are therefore attractive for lasers, ultraviolet emitters, and mid-infrared intersubband devices (intersubband = optical transitions between quantized conduction-band states of a quantum well).

The band offsets - the discontinuities $\Delta E_c$ and $\Delta E_v$ in the conduction and valence bands across the heterojunction - determine electron and hole confinement in all of these devices. Microscopically, interface-specific dipole shifts arise from the different local bond configurations (Al-N versus Ga-N nearest neighbors) at the junction, so there is no a priori reason for offsets measured on the polar $c$ -plane to transfer unchanged to other orientations; however, the expected differences are small and require dedicated measurements.

For an isotype heterojunction (both sides doped n-type, so no p-n junction is formed), capacitance-voltage ( $C$ - $V$ ) profiling measures an apparent electron concentration $\hat{n}(w)$ versus depletion depth $w$ , a Debye-length-broadened (thermal-smearing-limited) version of the true profile. Kroemer-type integral relations invert $\hat{n}(w)$ and the donor profile $N_d(w)$ to yield the hetero-interface sheet charge $\sigma_i$ and the band-offset-induced potential drop, given the interface position $x_i$ . When $|\sigma_i|$ is large the inversion becomes highly sensitive to the assumed $x_i$ ; on $c$ -plane structures with $10^{13}\,\mathrm{cm}^{-2}$ polarization charges this sensitivity is severe, while nonpolar interfaces with nearly vanishing charge are favorable.

Before the source study, direct valence-band-offset measurements by X-ray photoelectron spectroscopy (XPS; the Kraut method combines core-level binding-energy differences with valence-band-maximum positions) existed for the polar $c$ -plane and the nonpolar $a$ -plane of the binary AlN/GaN system, with sizable scatter; optical analysis of nonpolar $a$ -plane GaN/AlGaN quantum wells had to assume a $\Delta E_c:\Delta E_v$ ratio (45:55 at one barrier composition); and the theory of strained semipolar layers (Romanov, Baker, Nakamura, and Speck) predicted that the piezoelectric polarization of pseudomorphic AlGaN on GaN vanishes near nonpolar and near 45-degree-tilted orientations, implying only a small, predicted-negative interface charge at $(20\overline{2}1)$ .

In this setting, Hurni, Kroemer, Mishra, and Speck [Applied Physics Letters 105, 232108 (2014); DOI 10.1063/1.4903180] extracted $\Delta E_c$ by $C$ - $V$ profiling from isotype GaN/Al $_x$ Ga $_{1-x}$ N junctions on bulk nonpolar $m$ -plane and semipolar $(20\overline{2}1)$ GaN substrates. For $m$ -plane samples with $x\approx 0.10$ , $0.14$ , and $0.20$ they found $\Delta E_c = 0.085$ , $0.123$ , and about $0.161$ - $0.163$ eV (approximately linear in $x$ ) with small residual interface charges ( $\sigma_i/e \approx -10^{10}$ to $-5\times10^{10}\,\mathrm{cm}^{-2}$ ), where the extraction is robust against $x_i$ uncertainty. Using an assumed bandgap bowing parameter (the coefficient $b$ of the quadratic term in the composition dependence of the alloy bandgap; $b = 0.7$ eV was assumed) and literature bandgaps, these offsets imply a conduction-to-valence offset ratio of roughly 50:50–60:40 ( $\Delta E_c:\Delta E_v$ ). On the semipolar $(20\overline{2}1)$ samples the extraction, with $x_i$ placed at the maximum of $\hat{n}(w)$ , gave a measurable positive effective interface charge $\sigma_i/e \approx 1.3$ - $2.5\times10^{11}\,\mathrm{cm}^{-2}$ - contradicting the predicted low negative polarization charge - and the reconstructed profiles matched the measured $\hat{n}(w)$ less well, leaving the semipolar $\Delta E_c$ and $\sigma_i$ less certain. A later charge-neutrality-level analysis (a model that derives barrier heights and band offsets from the Fermi level at which interface states change from valence- to conduction-like character) of polar $c$ -plane AlGaN (Reddy et al., 2015) finds a roughly 2/3:1/3 conduction:valence split, in tension with the inferred 50:50-60:40, which sharpens the need for direct nonpolar/semipolar $\Delta E_v$ measurements.

Problem Statement

Establish the band alignment and interface charge of isotype (both layers n-type doped) GaN/Al $_x$ Ga $_{1-x}$ N heterojunctions grown on nonpolar $m$ -plane $(10\overline{1}0)$ and semipolar $(20\overline{2}1)$ GaN substrates - the orientations and alloy system of the 2014 capacitance-voltage profiling study. The scientific objective is an orientation-resolved band alignment that no longer rests on the assumptions of that study: a determination of the valence-band offset $\Delta E_v$ for these orientations, fixing the $\Delta E_c:\Delta E_v$ partitioning without invoking an assumed bowing parameter and literature bandgaps; and an independent determination of the magnitude and sign of the non-zero semipolar $(20\overline{2}1)$ hetero-interface charge that, in the words of the source abstract, made the extraction of $\Delta E_c$ less reliable - thereby settling whether and how the GaN/AlGaN band lineup depends on crystallographic orientation. The tension between the measured positive $(20\overline{2}1)$ charge and the low negative polarization charge predicted by the Romanov-type semipolar theory, and the bowing-parameter dependence of the inferred 50:50-60:40 partitioning, form the background against which such a determination would address the questions left unresolved by the 2014 study.

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