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As the Si-CMOS technology approaches the end of the International Technology Roadmap for Semiconductors (ITRS), the semiconductor industry faces a formidable challenge to continue the transistor scaling according to Moore’s law. To continue the scaling of classical devices, alternative channel materials such as SiGe, carbon nanotubes, nanowires, and III-V based materials are being investigated along with novel 3D device geometries. Researchers are also investigating radically new quantum computing devices, which are expected to perform calculations faster than the existing classical Si-CMOS based structures. Atomic scale disorders such as interface roughness, alloy randomness, non-uniform strain, and dopant fluctuations are routinely present in the experimental realization of such devices. These disorders now play an increasingly impor...
Numerical calculations of nanostructure electronic properties are often based on a nonprimitive rectangular unit cell, because the rectangular geometry allows for both highly efficient algorithms and ease of debugging while having no drawback in calculating quantum dot energy levels or the one-dimensional energy bands of nanowires. Since general nanostructure programs can also handle superlattices, it is natural to apply them to these structures as well, but here problems arise due to the fact that the rectangular unit cell is generally not the primitive cell of the superlattice, so that the resulting E!k" relations must be unfolded to obtain the primitivecell E!k" curves. If all of the primitive cells in the rectangular unit cell are identical, then the unfolding is reasonably straightforward; if not, the problem becomes more difficul...
Comment: 8 pages, 4 figures; Nano Letters, Publication Date (Web): Oct. 25 2011, http://pubs.acs.org/doi/abs/10.1021/nl202725w
Often one needs to calculate the evolution time of a state under a Hamiltonian with no explicit time dependence when only numerical methods are available. In cases such as this, the usual application of Fermi’s golden rule and firstorder perturbation theory is inadequate as well as being computationally inconvenient. Instead, what one needs are conditions under which the evolution time may be obtained from the easily calculated energy uncertainty. This work derives some general conditions for obtaining the evolution time from the energy uncertainty.
While the energy bands of solids are often thought of as continuous functions of the wavevector, k, they are in fact discrete functions, due to the periodic boundary conditions applied over a finite number of primitive cells. The traditional approach enforces periodicity over a volume containing Ni primitive unit cells along the direction of the primitive lattice vector ai . While this method yields a simple formula for the allowed k, it can be problematic computer programs for lattices such as face-centred cubic (FCC) where the boundary faces of the primitive cell are not orthogonal. The fact that k is discrete is of critical importance for supercell calculations since they include only a finite number of unit cells, which determines the number of wavevectors, and have a given geometry, which determines their spacing. Rectangular supe...
Numerical calculations of nanostructure electronic properties are often based on a nonprimitive rectangular unit cell, because the rectangular geometry allows for both highly efficient algorithms and ease of debugging while having no drawback in calculating quantum dot energy levels or the one-dimensional energy bands of nanowires. Since general nanostructure programs can also handle superlattices, it is natural to apply them to these structures as well, but here problems arise due to the fact that the rectangular unit cell is generally not the primitive cell of the superlattice, so that the resulting E!k" relations must be unfolded to obtain the primitive cell E!k" curves. If all of the primitive cells in the rectangular unit cell are identical, then the unfolding is reasonably straightforward; if not, the problem becomes more difficu...
Numerical calculations of nanostructure electronic properties are often based on a nonprimitive rectangular unit cell, because the rectangular geometry allows for both highly efficient algorithms and ease of debugging while having no drawback in calculating quantum dot energy levels or the one-dimensional energy bands of nanowires. Since general nanostructure programs can also handle superlattices, it is natural to apply them to these structures as well, but here problems arise due to the fact that the rectangular unit cell is generally not the primitive cell of the superlattice, so that the resulting E(k) relations must be unfolded to obtain the primitive- cell E(k) curves. If all of the primitive cells in the rectangular unit cell are identical, then the unfolding is reasonably straightforward; if not, the problem becomes more diffic...
The valley splitting (VS) in a silicon quantum well is calculated as a function of barrier height with both the multiband sp(3)d(5)s(*) model and a simple two-band model. Both models show a strong dependence of the VS on barrier height. For example, in both models some quantum wells exhibit a sharp minimum in the valley-splitting amplitude as the barrier height is changed. From the simple two-band model we obtain analytic approximations for the phases of the bulk states involved in the valley-split doublet, and from these we show that such sharp minima correspond to parity changes in the ground state as the barrier height is increased. The two-band analytic results show a complicated dependence of the valley splitting on barrier height, with the phases essentially being determined by a competition among effective quantum wells of diffe...
While the energy bands of solids are often thought of as continuous functions of the wavevector, k, they are in fact discrete functions, due to the periodic boundary conditions applied over a finite number of primitive cells. The traditional approach enforces periodicity over a volume containingNi primitive unit cells along the direction of the primitive lattice vector ai . While this method yields a simple formula for the allowed k, it can be problematic computer programs for lattices such as face-centred cubic (FCC) where the boundary faces of the primitive cell are not orthogonal. The fact that k is discrete is of critical importance for supercell calculations since they include only a finite number of unit cells, which determines the number of wavevectors, and have a given geometry, which determines their spacing. Rectangular super...
Often one needs to calculate the evolution time of a state under a Hamiltonian with no explicit time dependence when only numerical methods are available. In cases such as this, the usual application of Fermi's golden rule and first-order perturbation theory is inadequate as well as being computationally inconvenient. Instead, what one needs are conditions under which the evolution time may be obtained from the easily calculated energy uncertainty. This work derives some general conditions for obtaining the evolution time from the energy uncertainty.
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