Lattice mismatch, mechanical properties and lattice-compensation effect in Si_1-xGe_x alloys by using first-principles calculations combined with virtual crystal approximation

Highlights

• Calculation by first-principles calculations combined with virtual crystal approximation.

• Lattice parameters of Si_1-xGe_x alloy with any concentration ratio.

• Mechanical properties including elastic constants and moduli of Si_1-xGe_x alloys.

• Lattice-compensation effect in Si_1-x-yGe_xB_y ternary alloys.

Abstract

Si and Ge are two key semiconductor elements to construct CMOS-based devices and IC transistors, while the lattice mismatch of these two elements may decrease the quality and stability of heterojunction bipolar transistors based on Si_1-xGe_x alloy. In this work, by using the first-principles calculations and the virtual crystal approximation (VCA) in material structures, we studied the lattice mismatch and the fundamental mechanical parameters in Si_1-xGe_x alloys. The numerical results are consistent with those reported in some previous works. Moreover, the lattice-compensation effect induced by B-doping in Si_1-xGe_x alloy is also studied, confirming further that the VCA is an efficient way to study the multi-component alloy systems doped by other kinds of atoms. Our work puts forward a feasible theoretical method to study the lattice constants, the lattice mismatch, the mechanical properties and the lattice-compensation effects in multi-component alloy systems.

Introduction

To design high-quality heterojunction bipolar transistors and COMS-based devices, one efficient way is to enhance the carrier mobility in the strain-induced layer of integrated circuit (IC) transistors [1], [2]. Usually, two typical semiconducting elements, Ge and Si, are adopted to construct the Si_1-xGe_x alloy in these devices, where x denotes the mole ratio of Ge [3], [4], [5], [6], [7]. Owing to the advantage that these two elements are soluble with each other at any proportion, Si_1-xGe_x alloys form a series of substitutional solid solutions distributed continuously with changing the parameter x. Thus, these alloy candidates have long been regarded as the most important raw materials to construct semiconducting devices. For example, we usually apply the alloy Si_1-xGe_x to design the critical component, i.e., the strain-inducing layer in bipolar transistors, because their carrier mobility determines the signal sensitivities and accuracies of the transistors.

Although Si and Ge are face-centered cubic crystals, they host different lattice constants, which induce the lattice mismatch in the related semiconducting devices. On one hand, lattice mismatch serves as one important way to produce the strain-inducing layers between the epitaxial film and the substrates in COMS-based devices. For example, artificially induced lattice mismatch can be used to increase the carrier mobility in the channels of IC transistors, which is helpful to enhance the device sensitivity. On the other, the lattice mismatch between semiconductor layers may severely limit device application. As the lattice mismatch is beyond its appropriate value, the mismatch dislocation occurs usually in alloy materials, decreasing the device stability of IC transistors. It is noted that the lattice constant of single Ge crystal (a_Ge = 0.5658 nm) is larger than that of single Si crystal (a_Si = 0.5431 nm) about 4.2%, indicating that the mismatch dislocation occurs easily in Si_1-xGe_x alloy, as illustrated in Fig. 1. Thus, controlling the right lattice mismatch in the Si_1-xGe_x alloys is of great importance for obtaining high-quality semiconducting materials towards high-efficient IC transistors. Furthermore, once the relationships between the lattice constants of Si_1-xGe_x alloys and the concentration of Ge is understood, the lattice mismatch induced strain can be determined quantitatively in the epitaxial films [8], helping the experimentalists to perform the device optimizations of IC transistors [9].

In this work, by using first-principles calculations in combination with the virtual crystal approximation (VCA) method, we study the influence of the concentration of Ge on the lattice mismatch in the Si_1-xGe_x alloys and explore their fundamental mechanical properties. Our theoretical results show that the lattice constants of the Si_1-xGe_x alloy obtained by our theoretical calculations are well consistent with the previous results from Vegard's law [10] and the experimental results from Dismukes et al. [11], [12]. Moreover, some mechanical parameters including the elastic stiffness constants, bulk, shear and Young's modulus and Poisson's ratio of the Si_1-xGe_x alloy are also obtained and discussed. Finally, by using the same theoretical methods, the B-doped Si_1-xGe_x alloys, i.e., the SiGeB ternary alloys are studied. The B-doping induced lattice-compensation effect is also discussed. These numerical results show that our first-principles calculations combined with the VCA can be applied as an efficient way to study the lattice mismatch, the mechanical properties and the lattice-compensation effects of multi-component alloy systems.

The reminder of this paper is organized as follows. In Section 2, the model of Si_1-xGe_x alloy within VCA and the related theoretical methods are introduced in details. In Section 3, the numerical results of the lattice mismatch and some mechanical parameters are obtained and then, the lattice-compensation effect induced by B-doping in Si_1-xGe_x alloy is discussed in details. Finally, the main results are summarized in the last section.