Beam-Offset Thermoreflectance with Bayesian Optimization to Measure the Anisotropic Thermal Properties of Semiconductor Superlattices

Abstract

The directional nature of heat conduction in semiconductor superlattices--marked by significant differences between in-plane and cross-plane pathways--poses substantial challenges for precise thermal property assessment. Conventional frequency-domain thermoreflectance (FDTR) techniques, while proficient at evaluating cross-plane thermal conductivity, suffer from restricted capability in resolving in-plane transport due to inherent phase-delay constraints and inadequate lateral resolution. In this investigation, we establish a non-contact beam-offset FDTR (BO-FDTR) approach that concurrently determines both directional thermal conductivities within layered semiconductor architectures. Our methodology implements spatial separation between excitation and detection beams while utilizing coupled normalized amplitude and phase responses as analytical inputs, thereby improving discrimination between anisotropic thermal parameters. We combine this experimental configuration with a Bayesian optimization scheme incorporating Gaussian Process Regression (BO-GPR) to reduce estimation inaccuracies, attaining measurement uncertainties under 1% to 2% at 95% confidence intervals. This technique demonstrates particular efficacy for intricate multilayer nanostructures, furnishing a structured protocol for superlattice thermal evaluation. Experimental characterization of an AlAs/GaAs superlattice (period thickness 52 nm) delivers thermal conductivity values of 14.7 W m-1 K-1 (cross-plane) and 37.4 W m-1 K-1 (in-plane). Our findings indicate that integrating frequency sweeps with varied beam offset locations yields superior measurement precision, exceeding conventional single-variable methods and confirming thermal assessment validity across both geometric arrangements.

Figures (11)

• Figure 1: Schematic of the sample structure and experimental configuration for beam-offset thermoreflectance measurements. The sample consists of a gold transducer layer deposited on a GaAs/AlAs superlattice with total thickness $d_1 = 0.52µm$ and an undoped GaAs substrate with thickness $d_2 = 520µm$. The superlattice period is $\Lambda = 52nm$, corresponding to 10 bilayers. A modulated pump laser beam at wavelength $\lambda = 532nm$ with Gaussian spatial profile generates thermal waves via the intensity distribution. The beam offset $\Delta r$ between pump and probe beams enables depth-resolved thermal characterization of the multilayer structure.
• Figure 2: Comparative study of Normalized Amplitude and Phase between 2-layer model ($k = 2~\text{Wm}^{-1}\text{K}^{-1}$, $\alpha = 10^{-6}~\text{m}^{2}\text{s}^{-1}$) vs 3-layer model, $k = 2~\text{Wm}^{-1}\text{K}^{-1}$, $\alpha = 10^{-6}~\text{m}^{2}\text{s}^{-1}$ from Pawlak2020
• Figure 3: Schematic of the beam-offset frequency-domain thermoreflectance (BO-FDTR) setup. Key components include: AOM - Acousto-optic modulator (Crystal Technology Inc.) for pump beam modulation; M1 - steering mirror; LIA - lock-in amplifier for phase-sensitive detection; and a Standa 214377 rotational stage for controlled beam offset adjustment.
• Figure 4: Sensitivity of in-plane and cross-plane measurement to modulation frequency for AlAs/GaAs superlattice samples, showing TR phase response from analytical model at different offset position vs pump modulation frequency. The analysis covers the frequency range from 1kHz to 1.250MHz.
• Figure 5: Sensitivity of in-plane and cross-plane measurement to beam offsets $\Delta r = 0$ to $1.5~\mu$m.. for AlAs/GaAs superlattice samples, showing TR phase response from analytical model at different pump modulation frequency covers the frequency range from 10kHz to 2.0MHz.