As semiconductor technology continues to evolve, numerical modeling of semiconductor
devices becomes an indispensible tool for the prediction of device characteristics.
The simple drift-diffusion model is still widely used, especially in the study of subthreshold
behavior in MOSFETs. The numerical solution of these two equations offers
difficulties in small devices and special methods are required for the case when dealing
with 3D problems that demand large CPU times. In this work we investigate the
convergence properties of the Bi-CGSTAB method. We find that this method shows
superior convergence properties when compared to more commonly used ILU and SIP
methods.

D. Vasileska

W. J. Gross

V. Kafedziski

D. K. Ferry

Convergence Properties of the Bi-CGSTAB Method for the
Solution of the 3D Poisson and 3D Electron Current
Continuity Equations for Scaled Si MOSFETs

Advanced MOSFET for ULSI and novel silicon-based devices require the use of ultrathin
tunneling oxides where non-uniformity is often present. We report on our
theoretical study of how tunneling properties of ultra-thin oxides are affected by
roughness at the silicon/oxide interface. The effect of rough interfacial topography is
accounted for by using the Planar Supercell Stack Method (PSSM) which can accurately
and efficiently compute scattering properties of 3D supercell structures. Our results
indicate that while interface roughness effects can be substantial in the direct tunneling
regime, they are less important in the Fowler-Nordheim regime.

D. Z.-Y. Ting

Erik S. Daniel

T. C. Mcgill

Interface Roughness Effects in Ultra-Thin Tunneling Oxides

It is argued that the Pauli master equation can be used to simulate electron transport invery small electronic devices under steady-state conditions. Written in a basis of suitablewavefunctions and with the appropriate open boundary conditions, this equationremoves some of the approximations which render the Boltzmann equationunsatisfactory at small length-scales. The main problems consist in describing theinteraction of the system with the reservoirs and in assessing the range of validity of theequation: Only devices smaller than the size of the electron wavepackets injected fromthe contacts can be handled. Two one-dimensional examples solved by a simple MonteCarlo technique are presented.

M. V. Fischetti

Theory of Electron Transport in Small SemiconductorDevices Using the Pauli Master Equation

A self-consistent eight band k.p calculation, which takes into account strain and
includes Hartree, exchange, and correlation terms (determined from a local density
approximation) is incorporated into a QW laser simulator (MINILASE-II). The
computation is performed within the envelope function approximation for a superlattice,
in which all spatially varying terms of the k.p Hamiltonian, including the
exchange and correlation energies are expanded in plane waves. The k.p eigenvalue
equation, and Poisson's equation are solved iteratively until self-consistency is attained.
Results from the k.p calculation are exported to MINILASE-II via a density of states
and an energy dependent optical matrix element factor, renormalized by a Coulomb
enhancement factor to account for electron-hole attraction. Results are presented for
the gain spectrum and modulation response for a Ga0.8 In0.2 As/Al0.1 Ga0.9 As quantum
well laser with and without the inclusion of the Coulomb enhancement factor.

F. Oyafuso

P. von Allmen

M. Grupen

K. Hess

Inclusion of Bandstructure and Many-Body Effects
in a Quantum Well Laser Simulator

A comprehensive time-dependent 1-D computer model is developed for the simulationof multi-section bistable laser diodes. Analysis of a Fabry-Perot (FP) cavity laser diodeindicates that the height and shape of the optical input pulse as well as the wavelengthplay important roles in the set/reset operation of optical switching.

Gang  Fang

Ting-Wei  Tang

Simulation of Bistable Laser Diodeswith lnhomogeneous Excitation

Numerical simulation results of noise due to current fluctuations along an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>n</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo>&#x2212;</mml:mo><mml:mi>n</mml:mi><mml:mo>&#x2212;</mml:mo><mml:msup><mml:mi>n</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:math> submicron structure are presented. The mathematical framework is based on theinterpretation of the equations describing electron transport in the semiclassicaltransport model as stochastic differential equations (SDE). According to this formalismthe key computations for the spectral density describing the noise process are reduced toa special initial value problem for the Boltzmann transport equation (BTE). Thealgorithm employed in the computation of the space dependent noise autocovariancefunction involves two main processes: the stationary self-consistent solution of theBoltzmann and Poisson equations, and a transient solution of the BTE with specialinitial conditions. The solution method for the BTE is based on the Legendrepolynomial method. Noise due to acoustic and optical scattering and the effects of nonparabolicityare considered in the physical model.

Alfredo J. Piazza

Can E. Korman

Semiconductor Device Noise Computation Basedon the Deterministic Solution of the Poissonand Boltzmann Transport Equations

In this paper we use the code Exemplar for matching a hydrodynamic 1D, time-dependentsimulator and the transport coefficients obtained by the Monte Carlosimulator Damocles. This code is based on the Least Square method and it does notrequire any a priori knowledge about the simulator (analytical form of the equationsetc.). The stationary electron flow in a one dimensional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>n</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo>&#x2212;</mml:mo><mml:mi>n</mml:mi><mml:mo>&#x2212;</mml:mo><mml:msup><mml:mi>n</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:math> submicron silicondiode is simulated.

O.  Muscato

S.  Rinaudo

P.  Falsaperla

Calibration of a One Dimensional HydrodynamicSimulator with Monte Carlo Data

To facilitate the implementation of accurate Brillouin zone integration codes fordiamond-type semiconductors such as Si we have constructed a new &#8220;irreduciblewedge&#8221; to be used in conjunction with tetrahedral k-space interpolations. This newwedge, defined by the vertices (000), (100), (110) and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> (normalized to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:mi>X</mml:mi><mml:mo>|</mml:mo></mml:mrow><mml:mtext>&#x2009;</mml:mtext><mml:mo>=</mml:mo><mml:mtext>&#x2009;</mml:mtext><mml:mn>1</mml:mn></mml:mrow></mml:math>),spans portions of the first three Brillouin zones and contains the equivalent of 1/48 of aBrillouin zone volume. Simple symmetry arguments may be used to establish theequivalency of this new wedge with the standard irreducible wedge.

John  Stanley

Neil  Goldsman

New &#8220;Irreducible Wedge&#8221; for Scattering RateCalculations in Full-Zone Monte Carlo Simulations

A quantum mechanical treatment of electron inversion layers is incorporated in the
hydrodynamic (HD) transport model used in UT-MiniMOS. A physically based, yet
computationally efficient, three-subband model is implemented in the HD simulation
tool. The three-subband model, which is based upon solutions to Schrodinger's
equation, has the important advantage of more accurately predicting the distribution of
electrons in the inversion layers than does more conventional classical models. A more
simplified quantum mechanical model with carrier heating effects included has also been
developed. Terminal currents are calculated using these quantum mechanical models
and the comparison with results from classical calculations indicates the importance of
quantum mechanical effects in the deep submicron device simulations.

Haihong Wang

Wei-Kai Shih

Susan Green

Scott Hareland

Christine M. Maziar

Al. F. Tasch

Hydrodynamic (HD) Simulation of N-Channel MOSFET's
with a Computationally Efficient Inversion Layer
Quantization Model

Smooth quantum hydrodynamic (QHD) model simulations of the resonant tunnelingdiode are presented which exhibit enhanced negative differential resistance (NDR) whencompared to simulations using the original <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>O</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mi>&#x210F;</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math> QHD model. At both 300 K and 77 K,the smooth QHD simulations predict significant NDR even when the original QHDmodel simulations predict no NDR.

Carl L. Gardner

Christian  Ringhofer

Smooth Quantum Hydrodynamic Model Simulationof the Resonant Tunneling Diode

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Articles

Convergence Properties of the Bi-CGSTAB Method for the Solution of the 3D Poisson and 3D Electron Current Continuity Equations for Scaled Si MOSFETs

Interface Roughness Effects in Ultra-Thin Tunneling Oxides

Theory of Electron Transport in Small Semiconductor Devices Using the Pauli Master Equation

Inclusion of Bandstructure and Many-Body Effects in a Quantum Well Laser Simulator

Simulation of Bistable Laser Diodes with lnhomogeneous Excitation

Semiconductor Device Noise Computation Based on the Deterministic Solution of the Poisson and Boltzmann Transport Equations

Calibration of a One Dimensional Hydrodynamic Simulator with Monte Carlo Data

New “Irreducible Wedge” for Scattering Rate Calculations in Full-Zone Monte Carlo Simulations

Hydrodynamic (HD) Simulation of N-Channel MOSFET's with a Computationally Efficient Inversion Layer Quantization Model

Smooth Quantum Hydrodynamic Model Simulation of the Resonant Tunneling Diode