First-principles predictions of band alignment in strained Si/Si1-xGex and Ge/Si1-xGex heterostructures

Abstract

Accurate band offsets are essential for predictive continuum modeling of nanostructures such as quantum wells and quantum dots formed in strained Si/Si1-xGex and Ge/Si1-xGex heterostructures. Experimental offset data for these systems remain sparse away from endpoint compositions, making composition-dependent design difficult. We use atomistic first-principles density functional theory to compute valence- and conduction-band offsets across the full range 0 <= x <= 1. Random alloying is treated with special quasirandom structures, interface lineup terms are extracted from macroscopically averaged local Kohn-Sham potentials in thick periodic superlattices, valence-band spin-orbit coupling is included through species-resolved Mulliken weights, and conduction-band edges are refined using the screened hybrid Heyd-Scuseria-Ernzerhof functional. The resulting offsets show pronounced composition nonlinearity beyond the linear models explored in previous works, agree with experimental benchmarks, and reproduce the high-Ge slope change in the relaxed-alloy band gap. Analytic fitting expressions are provided for direct use in simulations, facilitating practical design of modern quantum technology devices.

Figures (4)

• Figure 1: Epitaxially constrained lattice constants used in this work. The relaxed-alloy buffer lattice constant $a_{\parallel}=a_{\mathrm{SiGe}}(x)$ is compared with the relaxed out-of-plane lattice constants $c_{\mathrm{Si}}$ and $c_{\mathrm{Ge}}$. Error bars on $a_{\parallel}$ show a representative $\pm 0.001$ Å uncertainty from EOS-fitted SQS minima. The strained-Ge series is shown up to $x=0.9$; $x=1$ is the Ge/Ge homoepitaxial limit.
• Figure 2: HSE band gap of relaxed Si$_{1-x}$Ge$_x$ across composition. Points show three-SQS means with representative standard-error bars derived from a characteristic full spread of about 50 meV. Dashed guides are overlapping quadratic fits with a crossover near $x\approx 0.82$.
• Figure 3: Interface lineup $\Delta V_{\mathrm{IF}}$ as a function of Ge concentration $x$ in Si$_{1-x}$Ge$_x$ for strained Si/Si$_{1-x}$Ge$_x$ and strained Ge/Si$_{1-x}$Ge$_x$, extracted from macroscopically averaged local Kohn--Sham potentials in thick periodic superlattices. The curves are constrained cubic fits satisfying $\Delta V_{\mathrm{IF}}(0)=0$ for Si/Si and $\Delta V_{\mathrm{IF}}(1)=0$ for Ge/Ge.
• Figure 4: Band-offset summary. (a) Strained-Si/Si$_{1-x}$Ge$_x$ valence- and conduction-band offsets versus Ge concentration, with HSE fit guides. (b) Strained-Ge/Si$_{1-x}$Ge$_x$ valence-band offset versus $x$, with theory curves and directly comparable endpoint photoemission data.Schaffler1997Virgilio2006Schwartz1989Yu1990 (a,b) Computed-point error bars combine two representative band-edge uncertainties inferred from the three-SQS gap spread with a 10 meV lineup term, added in quadrature; experimental bars are taken from the cited measurements. (c) Representative lineup extraction used to obtain $\Delta V_{\mathrm{IF}}$.