Faceting of Si and Ge crystals grown on deeply patterned Si substrates in the kinetic regime: phase-field modelling and experiments

Abstract

The development of three-dimensional architectures in semiconductor technology is paving the way to new device concepts for various applications, from quantum computing to single photon avalanche detectors. In most cases, such structures are achievable only under far-from-equilibrium growth conditions. Controlling the shape and morphology of the growing structures, to meet the strict requirements for an application, is far more complex than in close-to-equilibrium cases. The development of predictive simulation tools can be essential to guide the experiments. A versatile phase-field model for kinetic crystal growth is presented and applied to the prototypical case of Ge/Si vertical microcrystals grown on deeply patterned Si substrates. These structures, under development for innovative optoelectronic applications, are characterized by a complex three-dimensional set of facets essentially driven by facet competition. First, the parameters describing the kinetics on the surface of Si and Ge are fitted on a small set of experimental results. To this goal, Si vertical microcrystals have been grown, while for Ge the fitting parameters have been obtained from data from the literature. Once calibrated, the predictive capabilities of the model are demonstrated and exploited for investigating new pattern geometries and crystal morphologies, offering a guideline for the design of new 3D heterostructures. The reported methodology is intended to be a general approach for investigating faceted growth under far-from-equilibrium conditions.

Near‐Infrared Light Trapping and Avalanche Multiplication in Silicon Epitaxial Microcrystals

“…A scanning electron microscopy (SEM) image of a microcrystal array is shown in Figure 1a, demonstrating the high fill factor and the morphological uniformity achieved due to the fine resolution of EBL patterning coupled with the stable and reproducible growth conditions in LEPECVD (as shown in, e.g., refs. [32,39,40,44]. Transmission electron microscopy (TEM) analysis was performed to study the evolution of crystal defects in such 3D microstructures.…”

“…For all cases shown in Figure 1c the microcrystal top surface is predominately formed by {001}, {111}, and {113} facets, however, the relative size of the different facets depends on the characteristic dimensions of the pattern as analyzed in detail in refs. [39,40]. For our purposes we will consider two main groups of microcrystals that can be classified as "predominantly faceted" or "predominantly flat".…”

“…The modeling of microcrystal growth can be addressed by the rate equations approach, detailed in refs. [39,40], taking into account the combined effect of the local deposition flux, subject to mutual shielding between adjacent microcrystals, and the facetdependent incorporation rates, fitted from experimental data (see Supporting Information). The time integration of the rate equations, here limited to the 2D {110} cross-section for numerical convenience, offers a reliable reconstruction of the evolution of the microcrystal profile during growth, consistent with both experiments and more advanced 3D simulations.…”

Ge and Si Microcrystal Photodetectors with Enhanced Infrared Responsivity*

“…Micro-crystal formation is based on the selfassembly of Ge or Si crystals on a Si substrate, deeply patterned by optical lithography and reactive ion etching. 3D micro-crystals, several micrometer tall and characterized by a limited lateral expansion, are obtained by using optimized growth parameters [6]. Due to crystal faceting, enhanced light absorption, as compared to conventional epitaxial layers, is expected.…”