Extended interface states enhance valley splitting inSi/SiO2

Abstract

Interface disorder and its effect on the valley degeneracy of the conduction band edge remains among the greatest theoretical challenges for understanding the operation of spin qubits in silicon. Here, we investigate a counterintuitive effect occurring at Si/SiO2 interfaces. By applying tight binding methods, we show that intrinsic interface states can hybridize with conventional valley states, leading to a large ground state energy gap. The effects of hybridization have not previously been explored in details for valley splitting. We find that valley splitting is enhanced in the presence of disordered chemical bonds, in agreement with recent experiments.PACS numbers: 03.67. Lx, 85.35.Gv, 71.55.Cn Introduction.-The transistor revolution has granted silicon heterostructures a special status amongst materials platforms. Yet after many years of intense study, this system still reveals new and intriguing features. This is due in part to technological advances that open the door to new physical regimes. However, the interest in Si has also been stirred by its unusual materials properties. The Si conduction band (CB) possesses six degenerate minima in the first Brillouin zone, known as valleys. Quantum well confinement and/or the application of uniaxial strain (e.g., in the case of Si/SiGe heterostructures) in the [001] direction reduces the bulk, cubic symmetry, and raises the energy levels associated with the transverse x and y valleys [1]. At very low temperatures, the CB physics is therefore governed by the spin and the z valley degrees of freedom. Control over valley degeneracy is a key concern for Si spin qubits [2][3][4].Experimental [1,5,6] and theoretical [1,7,8] investigations of the physical mechanisms of valley coupling reveal that a sharp interface between a quantum well and a quantum barrier (most commonly SiGe or SiO 2 ) can produce a sizable energy splitting between the valley states, and that roughness can suppress this effect [9,10]. Realistic theoretical estimates for the interface-induced valley splitting are on the order of 0.1-1 meV [11], in agreement with many experiments. However, they cannot explain the recent puzzling results of Takashina et al. [5]. In an asymmetrically grown Si/SiO 2 quantum well, they observe a large ground state gap of 23 meV at the buried oxide (BOX) barrier, but a more typical valley splitting at the second, thermally grown oxide barrier [12].In this work, we demonstrate that conventional CB electron states tend to hybridize with intrinsic Si/SiO 2 interface states (IS), which form in the gap. Hybridization can produce a conducting ground state that is nondegenerate, due to strong valley orbit coupling. The resulting ground state gap can be tens of meV larger than the valley splitting between pure CB states, which could explain the large values measured in Ref. 5. Such a gap would be ideal for controlling spin qubits in Si.

Spin filling of valley–orbit states in a silicon quantum dot

“…Experimental values in Si inversion layers mostly vary from 0.3-1.2 meV [23]. A very large valley splitting of 23 meV in a similar structure has also been measured [24] and is explained in [20,21]. Recently, resonant tunneling features spaced by ∼0.1 meV in a single-crystal silicon quantum dot were attributed to valley excited states [26], while measurements on Si/SiGe quantum dots revealed valley splittings in the range of 0.12-0.27 meV [12].…”

Electric field reduced charging energies and two-electron bound excited states of single donors in silicon

“…One way to sidestep this is to assume a virtual crystal (VC) model of the oxide, and to extend the TB Hamiltonian to include this region, however, to the best of our knowledge, VC models of SiO 2 are still not well established in literature. 50,51 Although a truncated TB Hamiltonian over the silicon region can be iterated with the Poisson equation over the whole domain, there could be issues relating to charge inconsistencies which would affect the convergence. We have therefore neglected an exact quantitative description of gate screening, and have used the field as the free parameter to investigate its effects approximately.…”

Coherent electrical rotations of valley states in Si quantum dots using the phase of the valley-orbit coupling

“…[71][72][73][74][75] At the same time, the interface potential gives rise to a valley-orbit coupling, which has been studied extensively in recent years, both experimentally [76][77][78][79][80][81] and theoretically. [82][83][84][85][86][87][88][89][90] Addressing specific valley eigenstates is a profound, challenging and unresolved problem. Despite apparent similarities, valley physics is significantly different from spin-1/2 physics, and a pseudospin picture of valley physics is of limited utility.…”