Quantum confinement in semiconductor random alloys: a case study on Si/SiGe/Si

Abstract

Local composition fluctuations in random alloys become crucial when one or more dimensions are reduced to the nanoscale. Using extended Hückel theory, we study the semiconductor random alloy SiGe sandwiched between Si due to its relevance for transistor devices. We evaluate the effects of the alloy composition, layer thickness, and local fluctuations of the Ge concentration on the band alignment and the band gap. The results are compared with the finite quantum well model. That model captures the essential physics and can act as a computationally faster alternative.

Figures (18)

• Figure 1: The supercell of a 3 nm SiGe layer used for the structural relaxation, with randomly distributed Si and Ge atoms and an average Ge concentration of 30% (top). It is divided into 36 sub-cells (bottom) of appropriate size for EHT calculations.
• Figure 2: The band alignment of the structure depicted on the bottom of Figure \ref{['fig:supercell']} and its atom-projected density of states (dos). The band gap of the layer, $E_{\text{gap}}(x,t)$, is larger than the corresponding band gap of the bulk material, $E_{\text{gap}}(x,\text{bulk})$, due to quantum confinement.
• Figure 3: Band gap $E_{\text{gap}}$ (a), conduction band edge $E_{\text{c}}$ (b), and valence band edge $E_{\text{v}}$ (c) of SiGe layers of varying thickness $t$ and Ge content $x$. The colorbar scale in (b) was adjusted to better visualize the change in conduction band energy, which is one order of magnitude smaller than the change in the valence band.
• Figure 4: Conduction band (a) and valence band (b) edges as a function of the Ge content $x$ interpolated by a parabolic fit. Results of thin layers and the bulk material are compared to Jungemann and Meinerzhagen Jungemann2003_chapter6. We include the standard deviation from our ensemble of 36 different atomic structures.
• Figure 5: Infinite and finite square well and the ground state wave function. The wave function penetrates the walls of the finite well with exponential decay, giving rise to the concept of an effective layer thickness $t_{\text{eff}}>t$.