Evans M. Harrell

A physical short-channel threshold voltage model for undoped symmetric double-gate MOSFETs

A compact, physical, short-channel threshold voltage model for undoped symmetric double-gate MOSFETs has been derived based on an analytical solution of the two-dimensional (2-D) Poisson equation with the mobile charge term included. The new model is verified by published numerical simulations with close agreement. Applying the newly developed model, threshold voltage sensitivities to channel length, channel thickness, and gate oxide thickness have been comprehensively investigated. For practical device designs the channel length causes 30-50% more threshold voltage variation than does the channel thickness for the same process tolerance, while the gate oxide thickness causes the least, relatively insignificant threshold voltage variation. Model predictions indicate that individual DG MOSFETs with good turn-off behavior are feasible at 10 nm scale; however, practical exploitation of these devices toward gigascale integrated systems requires development of novel technologies for significant improvement in process control.

On trace identities and universal eigenvalue estimates for some partial differential operators

In this article, we prove and exploit a trace identity for the spectra of Schrodinger operators and similar operators. This identity leads to universal bounds on the spectra, which apply to low-lying eigenvalues, eigenvalue asymptotics, and to partition functions (traces of heat operators). In many cases they are sharp in the sense that there are specific examples for which the inequalities are saturated. Special cases corresponding to known inequalities include those of Hile and Protter and of Yang. Introduction In this article, we prove and exploit an identity for the spectra of self-adjoint operators H modeled on the Dirichlet Laplacian or, more generally, on Schrodinger operators of the form (p−A(x))2 + V (x), (1) where p = 1i ∇ is the usual momentum operator in convenient units and A(x) is the magnetic vector potential. We recover and extend several known inequalities involving sums, differences, and ratios of eigenvalues. Let λj , j = 1, . . . , denote the ordered eigenvalues of the Dirichlet Laplacian on a bounded d-dimensional domain with zero Dirichlet boundary conditions, and recall that Hile and Protter [HiPr80] proved that: d 4 ≤ 1 n n ∑ j=1 λj λn+1 − λj , (2) thereby extending an earlier inequality of Payne, Polya, and Weinberger [PaPoWe56]. In the last few years it has become clear that these and many similar relationships can be realized as special cases of abstract variational bounds involving the interplay among commutators of −∇2, a Cartesian coordinate xj , and the corresponding derivative ∂/∂xj. For this analysis and various extensions of (2) see [Ha88], [Ho90], [Ha93], [HaMi95]. While inequalities of this type have been fairly sharp for low-lying eigenvalues, they have been mostly disappointing for higher eigenvalues. Yang [Ya91], however, Received by the editors September 28, 1995. 1991 Mathematics Subject Classification. Primary 35J10, 35J25, 58G25.

Classical dynamical systems

1 Introduction.- 1.1 Equations of Motion.- 1.2 The Mathematical Language.- 1.3 The Physical Interpretation.- 2 Analysis on Manifolds.- 2.1 Manifolds.- 2.2 Tangent Spaces.- 2.3 Flows.- 2.4 Tensors.- 2.5 Differentiation.- 2.6 Integration.- 3 Hamiltonian Systems.- 3.1 Canonical Transformations.- 3.2 Hamiltons Equations.- 3.3 Constants of Motion.- 3.4 The Limit t ? I +- ?.- 3.5 Perturbation Theory: Preliminaries.- 3.6 Perturbation Theory: The Iteration.- 4 Nonrelativistic Motion.- 4.1 Free Particles.- 4.2 The Two-Body Problem.- 4.3 The Problem of Two Centers of Force.- 4.4 The Restricted Three-Body Problems.- 4.5 The N-body Problem.- 5 Relativistic Motion.- 5.1 The Hamiltonian Formulation of the Electrodynamic Equation of Motion.- 5.2 The Constant Field.- 5.3 The Coulomb Field.- 5.4 The Betatron.- 5.5 The Traveling Plane Disturbance.- 5.6 Relativistic Motion in a Gravitational Field.- 5.7 Motion in the Schwarzschild Field.- 5.8 Motion in a Gravitational Plane Wave.- 6 The Structure of Space and Time.- 6.1 The Homogeneous Universe.- 6.2 The Isotropic Universe.- 6.3 Me according to Galileo.- 6.4 Me as Minkowski Space.- 6.5 Me as a Pseudo-Riemannian Space.

The mathematical theory of resonances whose widths are exponentially small

It is shown how the rigorous justification of resonance widths in Paper I [5] can be simplified by exploiting Langers trick of expanding the independent variable rather than the dependent variable [9].

Singular perturbation potentials

Abstract This is a perturbative analysis of the eigenvalues and eigenfunctions of Schrodinger operators of the form −Δ + A + λV, defined on the Hilbert space L2(Rn), where Δ = Σ i=1 n ∂ 2 ∂X i 2 , A is a potential function and V is a positive perturbative potential function which diverges at some finite point, conventionally the origin. λ is a small real or complex parameter. The emphasis is on one-dimensional or separable problems, and in particular the typical example is the “spiked harmonic oscillator” Hamiltonian, −d 2 dx 2 + x 2 + l(l + 1) x 2 + λ|x| −α , where α is a positive constant. When this kind of perturbation is very singular, the first-order Rayleigh-Schrodinger perturbative correction, (u0, Vu0), where u0 is the unperturbed eigenfunction, diverges. This analysis constructs explicitly calculable terms in a modified perturbation series to a finite order, by using linear operator theory in concert with approximation methods for differential equations. Along the way a connection between a W-K-B type approximation and Bessel functions is exploited.

Universal inequalities for the eigenvalues of Laplace and Schrodinger operators on submanifolds

We establish inequalities for the eigenvalues of Schrodinger oper- ators on compact submanifolds (possibly with nonempty boundary) of Euclidean spaces, of spheres, and of real, complex and quaternionic projective spaces, which are related to inequalities for the Laplacian on Euclidean domains due to Payne, Polya, and Weinberger and to Yang, but which depend in an explicit way on the mean curvature. In later sections, we prove similar results for Schrodinger operators on homogeneous Riemannian spaces and, more generally, on any Rie- mannian manifold that admits an eigenmap into a sphere, as well as for the Kohn Laplacian on subdomains of the Heisenberg group. Among the consequences of this analysis are an extension of Reillys inequality, bounding any eigenvalue of the Laplacian in terms of the mean curvature, and spectral criteria for the immersibility of manifolds in homogeneous spaces.

On the rate of asymptotic eigenvalue degeneracy

The gap between asymptotically degenerate eigenvalues of one-dimensional Schrödinger operators is estimated. The procedure is illustrated for two examples, one where the solutions of Schrödingers equation are explicitly known and one where they are not. For the latter case a comparison theorem for ordinary differential equations is required. An incidental result is that a semiclassical (W-K-B) method gives a much better approximation to the logarithmic derivative of a wave-function than to the wave-function itself; explicit error-bounds for the logarithmic derivative are given.

Commutator Bounds for Eigenvalues, with Applications to Spectral Geometry

We prove a purely algebraic version of an eigenvalue inequality of Hile and Protter, and derive corollaries bounding differences of eigenvalues of Laplace– Beltrami operators on manifolds. We significantly improve earlier bounds of Yang and Yau, Li, and Harrell.

Elimination of chaos in an intracavity-doubled Nd:YAG laser

We predict theoretically a stable configuration for the operation of a multimode, intracavity-doubled, diode-pumped Nd:YAG laser. Experimental results are presented that demonstrate the elimination of chaotic amplitude fluctuations by rotatory alignment of the KTP crystal.

On the Placement of an Obstacle or a Well so as to Optimize the Fundamental Eigenvalue

We investigate how to place an obstacle B within a domain