Quantifying the Relationship Between Strain and Bandgap in Thin Ga$_2$Se$_2$

TL;DR

The paper addresses how strain modulates the bandgap in 2D Ga2Se2 and how to deterministically design strain-induced bandgap profiles. The authors pattern substrates to create biaxial and uniaxial regions, map local strain with AFM-constrained COMSOL simulations, and map PL shifts with hyperspectral imaging, validating gauge factors against DFT. They report beta_exp = -275.4 meV/% and alpha_exp = -116.1 meV/% that align with DFT predictions, and show a simple model DeltaE approx beta_exp*(epsilon_1+epsilon_2)/2 + alpha_exp*|epsilon_1-epsilon_2|/2 can predict multiaxial bandgap shifts with <10% error. This work enables deterministic, spatially-resolved bandgap engineering in Ga2Se2 with implications for scalable quantum emitter arrays.

Abstract

We present a rigorous analysis that combines theory, simulation, and experimental measurements to quantify the relationship between strain and bandgap in two dimensional gallium selenide (Ga$_2$Se$_2$). Experimentally, we transfer thin Ga$_2$Se$_2$ flakes onto patterned substrates to deterministically induce multiaxial localized strain. We quantify the local strain using a combination of atomic force microscopy (AFM) measurements and COMSOL Multiphysics simulation. We then experimentally map the strain-induced bandgap shifts using high-resolution hyperspectral PL imaging to generate a robust and statistically significant dataset. We systematically fit this data to extract gauge factors that relate the bandgap shift to the local uniaxial and biaxial strain. We then compute the uniaxial and biaxial strain gauge factors via density functional theory (DFT) and find excellent agreement with the experimentally-determined values. Finally, we show that a simple model that computes bandgap shifts from the local uniaxial and biaxial strain predicts the observed multiaxial bandgap shift with less than 10\% error. The combined results provide a framework for deterministic realization of tailored bandgap profiles induced by controlled strain applied to Ga$_2$Se$_2$, with implications for the future realization of localized quantum emitters for quantum photonic applications.

Figures (6)

• Figure 1: (a,b) Optical image of bare nanopatterned substrate with ring structures (a) and ridge structures (b). Optical image (c) and measured peak shift (d) for 2D Ga$_2$Se$_2$ suspended over a ring of $\sim$11 $\mu$m diameter. (e) Measured PL spectra as a function of position along the line indicated in (c).
• Figure 2: (a) AFM scan across the edge of a transferred flake, (b) Line profile of the AFM scan in (a) from which the Ga$_2$Se$_2$ thickness is extracted. (c) AFM scan of the membrane suspended over a ring structure. (d) Cross sectional line scans from the AFM data (black) and COMSOL simulations using various experimental loads (colors).
• Figure 3: (a) biaxial strain and (b) uniaxial strain in one example ring structure. The purple ring indicates the position of the ring structure on the substrate. (c) The experimental peak shift as a function of biaxial strain from the suspended center region of 16 ring samples (4523 data points in total). The colors of the points indicate different samples. The fit to the experimental data is shown by the red line and the DFT results are shown by the blue line.
• Figure 4: (a) the biaxial and (b) uniaxial strain of a sample suspended over a ridge structure. The purple lines indicates the position of the ridge structure on the substrate. (c) The experimental peak shift as a function of uniaxial strain from 7 ridge samples (2803 data points in total). The colors of the points indicate different samples. The DFT results are shown in blue while the experimental fit is in red.
• Figure 5: (a,d) Optical images of ring and ridge structures. The experimentally-measured PL peak shift along the green cross sections are plotted in (b,e) and those along the purple cross sections are plotted in (c,f). In all cases the black lines show the PL peak shift computed using Equation \ref{['PL peak shift']}.