Thermal analysis of GaN-based photonic membranes for optoelectronics

Semiconductor membranes find their widespread use in various research fields targeting medical, biological, environmental, and optical applications. Often such membranes derive their functionality from an inherent nanopatterning, which renders the determination of their, e.g., optical, electronic, mechanical, and thermal properties a challenging task. In this work we demonstrate the non-invasive, all-optical thermal characterization of around 800-nm-thick and 150-$μ$m-wide membranes that consist of wurtzite GaN and a stack of In${0.15}$Ga${0.85}$N quantum wells as a built-in light source. Due to their application in photonics such membranes are bright light emitters, which challenges their non-invasive thermal characterization by only optical means. As a solution, we combine two-laser Raman thermometry with (time-resolved) photoluminescence measurements to extract the in-plane (i.e., $c$-plane) thermal conductivity $κ_{\text{in-plane}}$ of our membranes. Based on this approach, we can disentangle the entire laser-induced power balance during our thermal analysis, meaning that all fractions of reflected, scattered, transmitted, and reemitted light are considered. As a result of our thermal imaging via Raman spectroscopy, we obtain $κ_{\text{in-plane}},=,165^{+16}{-14},$Wm$^{-1}$K$^{-1}$ for our best membrane, which compares well to our simulations yielding $κ{\text{in-plane}},=,177,$Wm$^{-1}$K$^{-1}$ based on an ab initio solution of the linearized phonon Boltzmann transport equation. Our work presents a promising pathway towards thermal imaging at cryogenic temperatures, e.g., when aiming to elucidate experimentally different phonon transport regimes via the recording of non-Fourier temperature distributions.

💡 Research Summary

This paper presents a comprehensive, non‑invasive optical methodology for determining the in‑plane thermal conductivity of GaN‑based photonic membranes that incorporate In₀.₁₅Ga₀.₈₅N quantum wells as an internal light source. The membranes are ∼800 nm thick and ∼150 µm wide, dimensions that are typical for vertical‑cavity surface‑emitting laser (VCSEL) platforms. Because the membranes are bright emitters, conventional one‑laser Raman thermometry (1LR T) cannot reliably separate heating from temperature probing: the same laser both heats the sample and generates the Raman signal, making it impossible to know the exact volume over which power is deposited, especially when phonon mean free paths are comparable to the membrane thickness.

To overcome this limitation, the authors develop a two‑laser Raman thermometry (2LR T) scheme. A 325 nm laser is used solely for heating, exciting the quantum‑well stack and generating strong photoluminescence (PL). A second, 532 nm laser serves as a probe, collecting the non‑polar E₂(high) Raman mode of GaN (≈ 567 cm⁻¹). By scanning both beams independently across the membrane, spatially resolved temperature maps are obtained from the Raman shift of the E₂(high) mode. Simultaneously, time‑resolved photoluminescence (TRPL) measurements quantify how much of the heating‑laser power is reflected, scattered, transmitted, or re‑emitted as PL. This full power‑balance analysis yields the actual absorbed heating power that drives the temperature rise.

Three membrane variants are fabricated by electrochemical under‑etching of a sacrificial highly‑doped GaN layer. Samples 1 and 2 differ only in the bias voltage applied during etching (10 V vs. 6 V), which produces a rougher vs. smoother backside, respectively. Sample 3 incorporates an AlN/Al₀.₈₂In₀.₁₈N etch‑stop stack and is etched at 17 V, resulting in the smoothest backside. Atomic‑force microscopy (AFM) and scanning electron microscopy (SEM) confirm the morphological differences.

The experimental workflow proceeds as follows: (i) acquire Raman spectra at various probe‑laser positions while the heating laser is fixed; (ii) extract the E₂(high) peak shift to obtain local temperature; (iii) perform TRPL at the same positions to determine the fraction of heating‑laser photons that are converted into PL and thus leave the thermal budget; (iv) combine the Raman‑derived temperature field with the calibrated absorbed power to solve the 2‑D heat‑conduction equation and extract κ_in‑plane. For the best membrane (sample 1) the authors report κ_in‑plane = 165 W·m⁻¹·K⁻¹ with an uncertainty of +16/‑14 W·m⁻¹·K⁻¹.

To validate the measurements, ab‑initio calculations based on the linearized phonon Boltzmann transport equation (BTE) are performed on the exact layer stack, including realistic doping levels and interface roughness. The theoretical in‑plane conductivity is κ_theory = 177 W·m⁻¹·K⁻¹, in excellent agreement with experiment (≈ 7 % deviation). The authors discuss how backside roughness reduces κ by increasing phonon‑boundary scattering, while the addition of the AlN/AlInN etch‑stop layers introduces extra interface resistance, further lowering κ by ~5 %.

A key insight is the explicit accounting of the full optical power balance: reflected, scattered, transmitted, and re‑emitted light are all quantified, which eliminates the major source of systematic error in laser‑based thermometry of optically active membranes. Moreover, the spatial temperature maps reveal anisotropic heat spreading when the membrane is probed along different crystallographic directions, confirming the isotropy of κ within experimental error.

Finally, the authors outline the potential of extending 2LR T to cryogenic temperatures. At low temperatures, phonon mean free paths in GaN can exceed several micrometers, leading to non‑Fourier heat transport (ballistic or quasi‑ballistic regimes). The high spatial resolution of Raman thermometry combined with accurate power budgeting makes it possible to visualize such non‑Fourier temperature distributions, opening a pathway for experimental studies of phonon hydrodynamics in nitride semiconductors.

In summary, this work (1) introduces a robust two‑laser Raman thermometry technique coupled with TRPL for non‑invasive thermal characterization of bright, nanostructured semiconductor membranes; (2) provides quantitative measurements of in‑plane thermal conductivity for GaN‑based photonic membranes, showing good agreement with state‑of‑the‑art ab‑initio BTE simulations; (3) demonstrates how surface roughness and additional semiconductor layers affect κ, offering design guidelines for high‑power VCSELs and other optoelectronic devices; and (4) paves the way for future low‑temperature investigations of non‑Fourier heat transport in low‑dimensional nitride systems.