Modelling of disordered multimillion atom quantum dot systems
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A tight binding model which includes s, p, d, s orbitals is used to examine the electronic structures of an ensemble of dome-shaped In0.6 Ga0.4 As quantum dots. Given ensembles of identically sized quantum dots, variations in composition and configuration yield a linewidth broadening of less than 0.35 meV, much smaller than the total broadening determined from photoluminescence experiments. It is also found that the computed disorder-induced broadening is very sensitive to the applied boundary conditions, so that care must be taken to ensure proper convergence of the numerical results. Examination of local eigenenergies as functions of position shows similar convergence problems and indicates that an inaccurate resolution of the equilibrium atomic positions due to truncation of the simulation domain may be the source of the slow ground state convergence.
Disorder-induced broadening of the conduction and valence band eigenenergies is calculated for an ensemble of dome-shaped InGaAs quantum dots of diameter 20nm using an sp3d5s* tight binding model.
The effect of electron-nuclear spin interactions on qubit operations is investigated for a qubit represented by the spin of an electron localized in an InGaAs self-assembled quantum dot. The localized electron wave function is evaluated within the atomistic tight-binding model. The electron Zeeman splitting induced by the electron-nuclear spin interaction is estimated in the presence of an inhomogeneous environment characterized by a random nuclear spin configuration, by the dot-size distribution, alloy disorder, and interface disorder. Due to these inhomogeneities, the electron Zeeman splitting varies from one qubit to another by the order of 10(-6), 10(-6), 10(-7), and 10(-9) eV, respectively. Such fluctuations cause errors in exchange operations due to the inequality of the Zeeman splitting between two qubits. However, the error can be made lower than the quantum error threshold if an exchange energy larger than 10(-4) eV is used for the operation. This result shows that the electron-nuclear spin interaction does not hinder quantum-dot based quantum computer architectures from being scalable even in the presence of inhomogeneous environments.
The Nanoelectronic Modeling 3-D (NEMO 3-D) computer program has been upgraded to open-source status through elimination of license-restricted components. The present version functions equivalently to the version reported in "Software for Numerical Modeling of Nanoelectronic Devices" (NPO-30520), NASA Tech Briefs, Vol. 27, No. 11 (November 2003), page 37. To recapitulate: NEMO 3-D performs numerical modeling of the electronic transport and structural properties of a semiconductor device that has overall dimensions of the order of tens of nanometers. The underlying mathematical model represents the quantum-mechanical behavior of the device resolved to the atomistic level of granularity. NEMO 3-D solves the applicable quantum matrix equation on a Beowulf-class cluster computer by use of a parallel-processing matrix vector multiplication algorithm coupled to a Lanczos and/or Rayleigh-Ritz algorithm that solves for eigenvalues. A prior upgrade of NEMO 3-D incorporated a capability for a strain treatment, parameterized for bulk material properties of GaAs and InAs, for two tight-binding submodels. NEMO 3-D has been demonstrated in atomistic analyses of effects of disorder in alloys and, in particular, in bulk In(x)Ga(1-x)As and in In(0.6)Ga(0.4)As quantum dots.
Nanoelectronic Modeling 3-D (NEMO 3-D) is a computer program for numerical modeling of the electronic structure properties of a semiconductor device that is embodied in a crystal containing as many as 16 million atoms in an arbitrary configuration and that has overall dimensions of the order of tens of nanometers. The underlying mathematical model represents the quantummechanical behavior of the device resolved to the atomistic level of granularity. The system of electrons in the device is represented by a sparse Hamiltonian matrix that contains hundreds of millions of terms. NEMO 3-D solves the matrix equation on a Beowulf-class cluster computer, by use of a parallel-processing matrix vector multiplication algorithm coupled to a Lanczos and/or Rayleigh-Ritz algorithm that solves for eigenvalues. In a recent update of NEMO 3-D, a new strain treatment, parameterized for bulk material properties of GaAs and InAs, was developed for two tight-binding submodels. The utility of the NEMO 3-D was demonstrated in an atomistic analysis of the effects of disorder in alloys and, in particular, in bulk In(x)Ga(l-x)As and in In0.6Ga0.4As quantum dots.