Deposition Rates in Thermal Laser Epitaxy: Simulation and Experiment

TL;DR

This work develops a nonlinear finite-element model of CW laser heating for Thermal Laser Epitaxy to predict elemental evaporation rates from a free-standing source. By coupling a Gaussian laser input with temperature-dependent heat transfer and loss mechanisms (radiation, evaporation) and including an optical-depth attenuation term, the model reproduces steady-state evaporation rates when calibrated against a melting-point reference. The authors demonstrate excellent agreement with Ta experiments and extend the approach to Pt, Mo, Ti, and Cu by extracting effective emissivity $\epsilon$ and reflectivity $\mathcal{R}$ at the laser wavelength, enabling predictive TLE process control and a pathway to determine high-temperature thermophysical and optical properties. The method highlights the dominant roles of $\kappa$, $\epsilon$, and $\mathcal{R}$ in steady-state evaporation and provides a practical calibration strategy even in the absence of comprehensive high-temperature data. Overall, this framework supports accurate deposition-rate predictions across a broad range of elements, with potential for guiding epitaxial synthesis of complex heterostructures at extreme temperatures.

Abstract

The modeling of deposition rates in Thermal Laser Epitaxy (TLE) is essential for the accurate prediction of the evaporation process and for improved dynamic process control. We demonstrate excellent agreement between experimental data and a model based on a finite element simulation that describes the temperature distribution of an elemental source when irradiated with continuous wave laser radiation. The simulation strongly depends on the thermophysical constants of the material, data of which is lacking for many elements. Effective values for the parameters may be determined with precision by means of an unambiguous reference provided by the melting point of the material, which is directly observed during the experiments. TLE may therefore be used to study the high temperature thermophysical and optical properties of the elements.

Figures (11)

• Figure 1: Cross-sectional sketch of the TLE chamber used for the measurements. The uncooled chamber was operated without substrate heating. The insets include a representation of the computational mesh of a source, along with an example of a resolved temperature distribution with a red arrow indicating the position of the incident laser. The geometry has a diameter of 3 mm and a length of 8 mm.
• Figure 2: Optical depth $\tau$ for a range of elemental vapors for a laser wavelength $\lambda = 1030$ nm as a function of temperature $T$ calculated using the expression in Eqn. \ref{['taumodel']}. The stars indicate the melting point of the indicated element. Data regarding the atomic transitions of each element was obtained from the NIST database.NIST_ASD
• Figure 3: Graph showing how the maximum steady-state source temperature at the center of the laser spot converges to a solution with an increasing number of tetrahedral elements in FEM. This simulation was performed for a cylindrical source with a diameter of 3 mm and a length of 8 mm with $P$ = 280 W and the laser spot centered on one of the end faces.
• Figure 4: Panel a) shows the simulated mass evaporation rate of a Ta source with 3 mm diameter and 8 mm length for various values of the emissivity $\epsilon$. $\mathcal{R}$ was fixed at 0.87. Panel b) shows the simulated evaporation rate of the same Ta source for various values of the reflectivity $\mathcal{R}$. $\epsilon$ was fixed at 0.07. The other parameters were fixed at $\kappa$ = 57.5 W/m K, $\rho$ = 16600 kg/m$^3$, $c$ = 140 J/kg K.
• Figure 5: Photographs of a Ta source with a diameter of 3 mm and a length of 8 mm during irradiation with an infra-red $\lambda = 1030$ nm laser beam with $\omega$ = 750 µ m. The left panel shows that the irradiated surface of the Ta source remains solid at 190 W while at 300 W, a melt pool is visible at the location where the laser beam hits the surface. The melting point for the 3 mm source of Ta was observed at 280 W.