Michael D. Hack

Physics of amorphous silicon based alloy field‐effect transistors

In this paper we develop a new theory to describe the characteristics of amorphous silicon based alloy field‐effect transistors. We show that the transition from below to above threshold operation occurs when the Fermi level in the accumulation region moves from the deep to tail localized states in the energy gap. The current‐voltage and capacitance‐voltage characteristics are related to the basic material parameters such as the distribution of localized states in the energy gap, band mobility, device geometry, channel doping, and series resistances. Our analysis shows that an on current in excess of 2×10−7 A/μm gate width can be obtained with a 10‐μm gate length. We also demonstrate that even in the above threshold regime the field‐effect mobility is dependent on the gate voltage. Our theory can be used to optimize the design of amorphous silicon based alloy field‐effect transistors.

Comparison of full multiple spawning, trajectory surface hopping, and converged quantum mechanics for electronically nonadiabatic dynamics

We present calculations employing the simplest version of the full multiple spawning method, FMS-M or minimal FMS, for electronically nonadiabatic quantum dynamics using three model potential energy matrices with different strengths and ranges for the diabatic coupling. We first demonstrate stability of the branching probabilities and final energy distributions with respect to the parameters in the FMS-M method. We then compare the method to a variety of other semiclassical methods, as well as to accurate quantum mechanical results for three-dimensional atom–diatom reactions and quenching processes; the deviations of the semiclassical results from the accurate quantum mechanical ones are averaged over nine cases. In the adiabatic electronic representation, the FMS-M method provides some improvement over Tully’s fewest switches trajectory surface hopping method. However, both methods, irrespective of electronic representation, systematically overpredict the extent of reaction in comparison to the exact qua...

Continuous surface switching: An improved time-dependent self-consistent-field method for nonadiabatic dynamics

We present a new semiclassical method for electronically nonadiabatic collisions. The method is a variant of the time-dependent self-consistent-field method and is called continuous surface switching. The algorithm involves a self-consistent potential trajectory surface switching approach that is designed to combine the advantages of the trajectory surface hopping approach and the Ehrenfest classical path self-consistent potential approach without their relative disadvantages. Viewed from the self-consistent perspective, it corresponds to “on-the-fly histogramming” of the Ehrenfest method by a natural decay of mixing; viewed from the surface hopping perspective, it corresponds to replacing discontinuous surface hops by continuous surface switching. In this article we present the method and illustrate it for three multidimensional cases. Accurate quantum mechanical scattering calculations are carried out for these three cases by a linear algebraic variational method, and the accurate values of reactive pro...

The treatment of classically forbidden electronic transitions in semiclassical trajectory surface hopping calculations

A family of four weakly coupled electronically nonadiabatic bimolecular model photochemical systems is presented. Fully converged quantum mechanical calculations with up to 25 269 basis functions were performed for full-dimensional atom–diatom collisions to determine the accurate scattering dynamics for each of the four systems. The quantum mechanical probabilities for electronically nonadiabatic reaction and for nonreactive electronic deexcitation vary from 10−1 to 10−5. Tully’s fewest-switches (TFS) semiclassical trajectory surface-hopping method (also called molecular dynamics with quantum transitions or MDQT) is tested against the accurate quantal results. The nonadiabatic reaction and nonreactive deexcitation events are found to be highly classically forbidden for these systems, which were specifically designed to model classically forbidden electronic transitions (also called frustrated hops). The TFS method is shown to systematically overestimate the nonadiabatic transition probabilities due to the...

A natural decay of mixing algorithm for non-Born–Oppenheimer trajectories

We present a new method called the natural decay of mixing (NDM) method for introducing decoherence effects into the semiclassical Ehrenfest self-consistent potential method. The NDM method is similar in spirit to two recently developed methods, the continuous surface switching (CSS) and continuous surface switching II (CSS2) methods, but, like the pure semiclassical Ehrenfest method, it involves only a single variable that serves as both the weight of an electronic state and its electronic population. We demonstrate how this allows the NDM method to be applied to systems where the CSS and CSS2 methods cannot be applied, and also to cases where the CSS and CSS2 methods would be prohibitively expensive. The method is tested for electronically nonadiabatic processes, both reactive and nonreactive, and in a wider context it contributes to the rapidly blossoming fields of quantum measurement and hybrid quantum/classical algorithms for the dynamics of complex systems.

Validation of trajectory surface hopping methods against accurate quantum mechanical dynamics and semiclassical analysis of electronic-to-vibrational energy transfer

The validity of the quasiclassical trajectory surface hopping method is tested by comparison against accurate quantum dynamics calculations. Two versions of the method, one including electronic coherence between hops and one neglecting this effect, are applied to the electronically nonadiabatic quenching processes Na(3p)+H2(ν=0, j=0 or 2) → Na(3s)+H2(ν′,j′). They are found to agree well, not only for quenching probabilities and final-state distributions, but also for collision lifetimes and hopping statistics, demonstrating that electronic coherence is not important for this system. In general the accurate quantum dynamical calculations and both semiclassical surface hopping models agree well on the average, which lends credence to applications of semiclassical methods to provide insight into the mechanistic details of photochemical processes proceeding on coupled potential surfaces. In the second part of the paper the intimate details of the trajectories are analyzed to provide such insight for the prese...

Electronically nonadiabatic trajectories: Continuous surface switching II

This paper presents several criteria that should be satisfied by any method such as the original continuous surface switching method that attempts to combine elements of the trajectory surface hopping method with elements of the self-consistent potential method for semiclassical electronically nonadiabatic molecular dynamics calculations. We present an improved, functionally simpler algorithm for the continuous surface switching method for nonadiabatic trajectory calculations. We show that this new algorithm satisfies nine criteria of reasonableness, whereas the original method satisfied only five of these; and we show that the accuracy of the new algorithm is somewhat better than the accuracy of the original method.

Photodissociation of LiFH and NaFH van der Waals complexes: A semiclassical trajectory study

The photodissociation of Li⋯FH and Na⋯FH van der Waals complexes is studied using Tully’s fewest-switches surface-hopping and the natural decay of mixing semiclassical trajectory methods for coupled-state dynamics. The lifetimes of the predissociated excited-state complex (exciplex), as well as the branching ratio into reactive and nonreactive arrangements and the internal energy distribution of the products are reported at several excitation energies. The semiclassical trajectory methods agree with each other only qualitatively, and the results are strongly dependent on the choice of electronic representation. In general, the lifetime of the LiFH exciplex is shorter and less dependent on the excitation energy than the lifetime of the NaFH exciplex. The semiclassical dynamics of LiFH and NaFH are interpreted in terms of the features of their coupled potential energy surfaces.

Coupled quasidiabatic potential energy surfaces for LiFH

We present high-level ab initio calculations for the global adiabatic potential energy surfaces of the ground state (X 2A′) and several excited states (A 2A′, B 2A″, C 2A′, D 2A′, and Ẽ 2A″) of LiFH, including the valleys leading to Li+HF and LiF+H. The ab initio calculations were carried out using the multireference singles and doubles configuration interaction method with 99 reference configuration state functions (CSFs) for the 2A′ states and 39 reference CSFs for the 2A″ states. The basis set consisted of 140 contracted Gaussian functions, including specifically optimized diffuse functions, and calculations were performed on a dense grid of ∼3500 nuclear geometries which allowed us to construct an accurate analytic representation of the two lowest-energy LiFH potential energy surfaces. An analytic 2×2 quasidiabatic potential energy matrix was obtained by fitting physically motivated functional forms to the ab initio data for the two lowest-energy adiabatic states and explicitly including long-rang...

Flat‐band voltage and surface states in amorphous silicon‐based alloy field‐effect transistors

We propose a new technique to determine both the flat‐band voltage and the characteristic energy of the deep localized states in amorphous silicon‐based alloy field‐effect transistors from their current‐voltage characteristics. We also analyze the effects of surface states and show that they become important when their density is greater than 1011 cm−2 eV−1.