Zero Valley Splitting at Zero Magnetic Field for Strained Si/SiGe Quantum Wells
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1017-DD08-23
Zero Valley Splitting at Zero Magnetic Field for Strained Si/SiGe Quantum Wells Seungwon Lee, and Paul von Allmen Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena, CA, 91109 Abstract The electronic structure for a strained silicon quantum well grown on a tilted SiGe substrate is calculated using an empirical tight-binding method. For a zero substrate tilt angle the two lowest minima of the conduction band define a non-zero valley splitting at the center of the Brillouin zone. A finite tilt angle for the substrate results in displacing the two lowest conduction band minima to finite k0 and ñk0 in the Brillouin zone with equal energy. The vanishing of the valley splitting for quantum wells grown on tilted substrates is found to be a direct consequence of the periodicity of the steps at the interfaces between the quantum well and the buffer materials.
When a strained silicon quantum well (QW) is grown on top of a relaxed SiGe buffer, the Z valley bands (direction perpendicular to the surface) are split from the X and Y valleys to lower energy [1]. The confinement of the electrons in the QW induces an additional splitting of the two Z valley states. This splitting is termed valley splitting (VS) and has been predicted, computed and measured many times over the past decades for a number of silicon structures [2-4]. Calculations within the effective mass approximation have shown that the VS is strongly suppressed if the QW is grown on a tilted substrate [2]. A first order perturbation calculation shows that the VS is zero at zero magnetic field if the steps resulting from the growth on a tilted substrate are periodically repeated [5]. However, a more involved variational calculation that includes charge density oscillations predicts that the residual VS at B=0 is non-zero [5]. The intuitive explanation is that the destructive interference between the contributions to the VS from the periodically repeated steps is incomplete because the charge density oscillations due to the steps are incommensurate with the crystal-induced oscillations. The effective mass calculation uses ad hoc parameters to describe the interface potential and the charge density oscillations (ìwashoboardî potential), which precludes a more quantitative study required for the design of quantum dot qubits. The present paper reports VS calculations for a silicon QW on a tilted substrate obtained with an empirical tight-binding method, where no ad hoc parameters are added to describe the interface and the charge oscillations. The main result is that the VS is zero at B=0 despite the charge density oscillations, at variance with Ref. [5].
The electronic structure for the QW is calculated using a parameterized tight-binding method that has been widely applied to the modeling of semiconductor bulk materials and nanostructures [6, 3, 7]. Bulk materials are described with a one-particle Schrodinger equation, and the wavefunctions are expanded on a basis set of orthogonalized atomic orbitals (Lˆwdin orbitals). The matrix elements of the
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