Mihail Nedjalkov

Modeling Thermal Effects in Nanodevices

In order to investigate the role of self-heating effects on the electrical characteristics of nanoscale devices, we implemented a 2D Monte Carlo device simulator that includes the self-consistent solution of the energy balance equations for both acoustic and optical phonons. The acoustic and optical phonon temperatures are fed back into the electron transport solver through temperature-dependent scattering tables. The electrothermal device simulator was used in the study of different generations of nanoscale fully depleted silicon-on-insulator devices that are either already in production or will be fabricated in the next five to ten years. We find less degradation due to self-heating in very short channel device structures due to the increasing role of nonstationary velocity-overshoot effects which are less sensitive to the local temperature.

Wigner quasi-particle attributes—An asymptotic perspective

Wigner quantum mechanics is reformulated in a discrete momentum space and analyzed within a Monte Carlo approach for solving integral equations and thus associated with a particle picture. General quantum phenomena may thereby be modeled in terms of quasi-particles involving attributes such as drift, generation, sign, and annihilation on a phase space grid. The model is examined in an ultimate regime, where classical and quantum dynamics become equivalent. The peculiarities of the transport in this asymptotic regime are analyzed within simulations, benchmarking the behavior of the Wigner function.

A benchmark study of the Wigner Monte Carlo method

Abstract. The Wigner equation is a promising full quantum model for the simulation of nanodevices. It is also a challenging numerical problem. Two basic Monte Carlo approaches to this model exist exploiting, in the time-dependent case, the so-called particle affinity and, in the stationary case, integer particle signs. In this paper we extend the second approach for time-dependent simulations and present a validation against a well-known benchmark model, the Schrödinger equation. Excellent quantitative agreement is demonstrated by the compared results despite the very different numerical properties of the utilized stochastic and deterministic approaches.

A Monte Carlo Method Seamlessly Linking Quantum and Classical Transport Calculations

A Monte Carlo method for carrier transport is presented, which simultaneously takes into account quantum interference and dissipation effects. The method solves the space-dependent Wigner equation including semi-classical scattering through the Boltzmann collision operator. To this equation a particle model is assigned, which interprets the non-local potential operator as a generation term for numerical particles of positive and negative statistical weight. A numerical technique to control the avalanche of numerical particles is discussed. Since the Wigner equation simplifies to the Boltzmann equation in classical device regions, the solutions of the quantum kinetic equation and the classical one are linked in a natural way. This approach allows the simulation of a quantum region embedded in an extended classical region. Results of this approach are demonstrated for a resonant tunneling diode.

Femtosecond relaxation of hot electrons by phonon emission in presence of electric field

Abstract The femtosecond relaxation of an initial distribution of electrons which interact with phonons in presence of applied electric field is studied numerically. The evolution at such a time scale cannot be described in terms of Boltzmann transport. Here, the Barker–Ferry equation is utilized as a quantum-kinetic model of the process. The numerical treatment of the original formulation of the Barker–Ferry equation becomes difficult since coordinates and time variables are coupled by the field. A transformation which decouples coordinates and time variables in the equation is proposed. A randomized iterative Monte Carlo algorithm is developed to solve the transformed equation. The quantum character of the equation is investigated. An instantaneously created initial condition is favored above the physically more adequate generation term in order to point out the quantum effects. Simulation results are obtained for GaAs material at different evolution times. Effects of collisional broadening and retardation are observed already in the fieldless case. The intracollisional field effect is clearly demonstrated as an effective change of the phonon energy, which depends on the field direction and the evolution time. Moreover, the collisional broadening and retardation are affected by the applied field. The observed phenomena are understood from the structure and the properties of the model equation.

The stationary Monte Carlo method for device simulation. I. Theory

A theoretical analysis of the Monte Carlo method for steady-state semiconductor device simulation, also known as the single-particle Monte Carlo method, is presented. At the outset of the formal treatment is the stationary Boltzmann equation supplemented by boundary conditions, which is transformed into an integral equation. The conjugate equation has been formulated in order to develop forward Monte Carlo algorithms. The elements of the conjugate Neumann series are evaluated by means of Monte Carlo integration. Using this mathematically-based approach, the single-particle Monte Carlo method is derived in a formal way. In particular, the following are recovered: the probability densities for trajectory construction, both the time averaging and the synchronous ensemble methods for mean value calculation, and the rule that the initial points of the trajectories have to be generated from the velocity weighted boundary distribution. Furthermore, the independent, identically distributed random variables of the...

Monte Carlo method for modeling of small signal response including the Pauli exclusion principle

A Monte Carlo method for small signal analysis of degenerate semiconductors is presented. The response to an electric field impulse parallel to the stationary electric field is obtained using the nonlinear Boltzmann kinetic equation with the Pauli exclusion principle in the scattering operator. After linearization of the Boltzmann equation a new Monte Carlo algorithm for small signal analysis of the nonlinear Boltzmann kinetic equation is constructed using an integral representation of the first order equation. The generation of initial distributions for two carrier ensembles which arise in the method is performed by simulating a main trajectory to solve the zero order equation. The normalization of the static distribution function is discussed. To clarify the physical interpretation of our algorithm we consider the limiting case of vanishing electric field and show that in this case kinetic processes are determined by a linear combination of forward and backward scattering rates. It is shown that at high...

Wigner transport through tunneling structures scattering interpretation of the potential operator

A stochastic method for simulation of quantum transport in nanoscale electronic devices is proposed. The interaction with the Wigner potential is interpreted as a scattering mechanism, which is a counterpart to the scattering mechanisms due to the lattice imperfections. The derived quantum Monte Carlo algorithm retains the basic features of the Single Particle Monte Carlo method used for simulation of classical devices. The method is applied for simulation of tunneling process through energy barriers.

The Role of Annihilation in a Wigner Monte Carlo Approach

The Wigner equation provides an interesting mathematical limit, which recovers the constant field, ballistic Boltzmann equation. The peculiarities of a recently proposed Monte Carlo approach for solving the transient Wigner problem, based on generation and annihilation of particles are summarized. The annihilation process can be implemented at consecutive time steps to improve the Monte Carlo resolution. We analyze theoretically and numerically this process applied to the simulation of important quantum phenomena, such as time-dependent tunneling of a wave packet through potential barriers.

Impact of Self-Heating on the Statistical Variability in Bulk and SOI FinFETs

In this paper, for the first time, we study the impact of self-heating on the statistical variability of bulk and Silicon-on-insulator FinFETs designed to meet the requirements of the 14/16-nm technology node. The simulations are performed using the Gold Standard Simulations atomistic simulator GARAND using an enhanced electrothermal model that considers the impact of the fin geometry on the thermal conductivity. In the simulations, we have compared the statistical variability obtained from full-scale electrothermal simulations with the variability at uniform room temperature and at the maximum or average temperatures obtained in the electrothermal simulations. The combined effects of line edge roughness and metal gate granularity are considered. The distributions and the correlations between key figures of merit, including the threshold voltage, ON-current, subthreshold slope, and leakage current are presented and analyzed.