Figure 2. a) Microscope image of the fully suspended AlGaN/GaN heterostructure used for in-plane thermal conductivity measurements. The separation between the heater and sensor lines is ≈75 µm. A thin ≈47 nm Al₂O₃ layer provides electrical isolation between the metal lines and the AlGaN/GaN heterostructure underneath. b) Microscope image of the suspended AlGaN/GaN heterostructure to measure the Seebeck coefficient of the 2DEG. The 2DEG mesa is contacted via Ohmic Ti/Al/Pt/Au contacts. The Seebeck 2DEG mesa is shaded white for clarity. c) Cross-section SEM image (of the A–B section in (a)) of the suspended heterostructure, with the Si substrate selectively etched out from the backside via DRIE. d) SEM image of the bulk GaN structure. The GaN thickness is ≈1.2 µm and false colored. The buffer structure, starting from the Si interface, is composed of AlN (300 nm)/Al₀.₈Ga₀.₂N (300 nm)/Al₀.₅Ga₀.₅N (400 nm)/Al₀.₂Ga₀.₈N (500 nm). Further details are in Section S1 in the Supporting Information. e) SEM image of the thin GaN structure, showing the 2DEG at the AlGaN/GaN interface and the buffer layers. The GaN thickness is ≈100–150 nm and is false colored. The other buffer layers are identical to the bulk GaN structure. f) Half-symmetric finite-element simulation of experimental structure, showing sample temperature profile when current is applied through the heater (Section S3, Supporting Information). Scale bars of (a)–(e), 200, 200, 3, 2, and 2 µm.
using sufficiently low currents to avoid self-heating (Section S2, Supporting Information). The calibration allows us to convert the electrical resistance into corresponding temperature values using the measured temperature coefficient of resistance. From the collected temperature data, we can infer the in-plane thermal conductivity of the heterostructure given the heater power ($P_H$), after accounting for errors due to heat spreading into the Al₂O₃ and external losses (Section S3, Supporting Information) through a simple analytical model in conjunction with a three-dimensional (3D) finite-element simulation. In the model, we also included estimated values of the thermal contact resistance between the electrode, insulation, and heterostructure interfaces. Overall, the errors due the insulation are found to be less than ≈6%, while errors due to external convective and radiative losses progressively increase to ≈10% at a substrate temperature of 300 °C (Section S3, Supporting Information).
The measurement of the Seebeck coefficient follows a similar procedure; a current passed through the heater electrode induces a temperature gradient in the diaphragm, resulting in a Seebeck voltage across the 2DEG mesa that spans the suspension and the substrate regions (Figure 2b). Using a similar calibration procedure for the heater line, the temperature drop
across the mesa can be used to extract the Seebeck coefficient, after accounting for external losses, Ohmic contact voltage drop, and a minor temperature drop in the substrate (Section S3, Supporting Information). Note that the measured Seebeck coefficient corresponds to the 2DEG contribution exclusively since the III–V buffer layers are semi-insulating. Lastly, electrical conductivity of the 2DEG for the bulk and thin GaN samples is estimated using circular transfer length method (CTLM) structures with varying channel lengths ($d = 20$ to $70$ µm), with the aid of simulations to obtain the thickness of the 2DEG triangular potential ($t_{2D}$) well, to be discussed in the next section.
3. Charge Profiles
The thickness and charge density of the 2DEG for the bulk and thin GaN heterostructures are simulated using a commercially available Schrödinger-Poisson solver (NextNano GmbH[19]). The simulated band structures and volumetric charge density profiles for the bulk and thin GaN heterostructures are illustrated in Figure 3. All the heterostructure layers are assumed