Nanosecond Carrier Lifetime of Hexagonal Ge

Abstract

Hexagonal Si_1-x Ge _x with suitable alloy composition promises to become a new silicon compatible direct bandgap family of semiconductors. Theoretical calculations, however, predict that the binary end point of this family, the bulk hex-Ge crystal, is only weakly dipole active. This is in contrast to hex-Si_1-x Ge _x , where translation symmetry is broken by alloy disorder, permitting efficient light emission. Surprisingly, we observe equally strong radiative recombination in hex-Ge as in hex-Si_1-x Ge _x nanowires, but scrutinizing experiments on the radiative lifetime and the optical transition matrix element of hex-Ge remain hitherto unexplored. Here, we report an advanced spectral line shape analysis exploiting the Lasher-Stern-Würfel (LSW) model on an excitation density series of hex-Ge nanowire photoluminescence spectra covering 3 orders of magnitude. The analysis was performed at low temperature where radiative recombination is dominant. We analyze the amount of photoinduced bandfilling to obtain direct access to the excited carrier density, which allows to extract a radiative lifetime of (2.1 ± 0.3) ns by equating the carrier generation and recombination rates. In addition, we leveraged the LSW model to independently extract a high oscillator strength of 10.5 ± 0.9, comparable to the oscillator strength of III/V semiconductors like GaAs or GaN, showing that the optical properties of hex-Ge nanostructures are perfectly suited for a wide range of optoelectronic device applications.

Figure 1

(a) Scanning electron microscope image of the characterized hex-Ge nanowire shell sample. The inset shows a schematic with a partial cross-section of a single core/shell (GaAs/Ge) nanowire. (b) Band structure of the hex-Ge 2H crystal calculated using density functional theory and approximate quasi particle corrections.^, (c) Theoretically calculated and experimentally measured, low temperature, radiative lifetimes of hex-Si_xGe_1–x nanowire alloys vs Ge-composition. The radiative lifetime of GaAs is added as a benchmark. The lines connecting the data points only serve as a guide to the eye. (d) The photoluminescence intensity as a function of the Ge-composition showing a virtually constant emission at a temperature of 4 K and at an excitation density of 5.1 kW cm^–2. Reproduced and modified with permission from Fadaly et al. Nature2020, 580 (7802), 205–209. Copyright 2020 Springer Nature.

Figure 2

(a) Photoluminescence spectra of the hex-Ge nanowire shells for increasing excitation density (from bottom to top), plotted on a linear scale and fitted with the LSW model. The fits are shown as the red curves. (b) Identical PL spectra as in (a), plotted on a logarithmic scale. (c) Extracted bandgaps from the LSW model for all individual PL spectra shown in (a), displaying the evolution of the bandgap versus excitation density. (d) Evolution of the extracted carrier temperature with excitation. (e) Urbach broadening energy vs excitation.

Figure 3

Integrated photoluminescence intensity of hex-Ge nanowire shells as a function of the excitation density at (4 K) for both the experimental data and the LSW fits. The slope of the Light-In–Light-Out curve of 0.90 ± 0.02 is displayed in red and is close to unity, as expected for a material in the radiative limit.

Figure 4

(a) LSW results for the bandgap energy as a function of the minority carrier density. The solid line shows a fit with the Lindefelt model eq 11 to the data where the bandgap is decreasing (cyan markers), showing that the LSW results on hex-Ge can be described with a conventional model for bandgap renormalization in semiconductors. (b) Extracted carrier temperature from the LSW model versus the dissipated power density multiplied with the NW length. The solid line presents a fit with the linear heat transfer formula. (c) Extracted Urbach broadening energy γ vs temperature. The solid line is a fit to the data using eq 12 for temperatures above 77 K (cyan markers), showing that the results on hex-Ge can again be described by conventional theory.