Exciton radiative lifetimes in hexagonal diamond Ge and Si$_x$Ge$_{1-x}$ alloys

TL;DR

This study investigates excitonic properties and radiative lifetimes in hexagonal diamond Ge and SiGe alloys, revealing how alloying and strain influence optical emission and explaining the discrepancy with experimental photoluminescence.

Contribution

It provides a comprehensive excitonic analysis of 2H-Ge and SiGe alloys, highlighting the effects of alloying and strain on radiative lifetimes and optical properties.

Findings

Alloying with Si reduces radiative lifetime by nearly two orders of magnitude.

Uniaxial strain induces band crossover, enhancing dipole moments and decreasing lifetime to nanoseconds.

Ideal crystal excitonic effects cannot fully explain the experimentally observed strong photoluminescence.

Abstract

Recent reports of strong room-temperature photoluminescence in hexagonal diamond (2H) germanium stand in marked contrast to theoretical predictions of very weak band-edge optical transitions. Here we address radiative emission in 2H-Ge and related materials through a comprehensive investigation of their excitonic properties and radiative lifetimes, performing Bethe-Salpeter calculations on pristine and uniaxially strained 2H-Ge, 2H-Si$_x$Ge$_{1-x}$ alloys with $x=\frac{1}{6},\,\frac{1}{4},\,\frac{1}{2}$, and wurtzite GaN as a reference. Pristine 2H-Ge features sizable exciton binding energies ($\sim\!30$ meV) but extremely small dipole moments, yielding radiative lifetimes above $10^{-4}$ s. Alloying with Si reduces the lifetime by nearly two orders of magnitude, whereas a 2% uniaxial strain along the $c$ axis induces a band crossover that strongly enhances the in-plane dipole moment of the lowest-energy exciton and drives the lifetime down to the nanosecond scale. Although strained 2H-Ge approaches the radiative efficiency of GaN, its much lower exciton energy prevents a full match. These results provide the missing excitonic description of 2H-Ge and 2H-Si$_x$Ge$_{1-x}$, demonstrating that, even when excitonic effects are fully accounted for, the strong photoluminescence reported experimentally cannot originate from the ideal crystal.