Advanced Physical Models
for Silicon Device Simulation
by: Andreas Schenk
in: Computational Microelectronics
ed: Siegfried Selberherr
Springer-Verlag Wien New-York
Abstract
The quality of physical models is decisive for the understanding of the physical processes
in semiconductor devices and for a reliable prediction of the behavior of a new generation
of devices. The first part of the book contains a critical review on models for silicon
device simulators, which rely on moments of the Boltzmann equation. With reference to
fundamental experimental and theoretical work, an extensive collection of widely used models
is discussed in terms of physical accuracy and application results. The second part outlines
the derivation of physics-based models for bulk mobility, band-to-band tunneling,
defect-assisted tunneling, thermal recombination, non-ideal metal-semiconductor contact,
and direct and multiphonon-assisted tunneling through insulating layers, all from a
microscopic level. The models are compared with experimental data and applied to a number
of simulation examples. This part also describes some new approaches of ``taylored
quantum-mechanics" for deriving device models from ``first principles" and the fundamental
problems therein.
Extended Abstract
Device simulation has two main purposes: to understand and to depict the physical
processes in the interior of a device, and to make reliable predictions of the
behavior of the next device generation. Towards these goals, the quality of the
physical models is decisive.
In the introductory chapter of the book we present a critical review on
models for silicon device simulators, which rely on moments of the Boltzmann equation.
With reference to fundamental experimental and theoretical work, an extensive
collection of widely used models is discussed in terms of physical accuracy and
application results. This review shows, that the quality of physical models is
sufficient for many applications. However, the basic understanding of the microscopic
processes, the uniqueness of the models, and their accuracy are still unsatisfactory.
Among the deficiencies the following items are striking:
A fundamental quantity like the intrinsic density of silicon is not precisely known.
Heavily doped silicon is scarcely understood. This holds true for the bandgap energy,
the mobility, and all recombination channels.
There is no unique theory-based bulk mobility model which covers ultra-high
doping concentrations and strong compensation. The actual recombination channel
at high doping concentrations is not really known. Furthermore, local models of
impact ionization or band-to-band tunneling have only a very limited value in
modeling the strong nonlocal effects typical for sub-quarter-micron devices.
Certain common approximations in the development of physical models, as
the WKB and the EMA approximations, become questionable in case of the large spatial
inhomogeneities resulting from todays VLSI technology, like hetero-junctions,
ultra-thin gate oxides, and narrow field peaks with the extension of a few tens of
nanometers.
The following chapters describe the derivation of physics-based models from a
microscopic level, often using new approaches. Each model is compared
with experimental data and applied to a number of simulation examples. We
demonstrate the problems when deriving those models from "first principles" and
making them suitable for a device simulator. It is shown, that demands for rapid
computation and numerical robustness require a compromise between physical accuracy
and analytical simplicity, and that the attainable accuracy is limited by the complexity
of the problems.
In Chapter 2 an analytical bulk mobility model for hydrodynamic transport equations is
developed from a microscopic level extending a variational method to the regime of nonlinear
transport. An analytical form valid for all carrier and ambient temperatures is derived.
Impurity scattering is treated including Fermi statistics and dispersive screening.
The model is applied to simulations of nin-devices and MOSFETs, and compared versus
phenomenological models.
Chapter 3 is devoted to advanced generation-recombination models. The band-to-band tunneling
rate in its most general form is derived based on a Kubo formalism. Phonon-assisted transitions
are shown to be superior over direct transitions in silicon. A simplified, but still
anisotropic version for device simulation is applied to Esaki diodes and CMOS examples.
Defect-assisted tunneling is modeled via field-enhancement factors for SRH lifetimes
starting from the fundamental level of multiphonon theory. Analytical expressions for the
field and temperature dependence of the lifetimes are found. Local versus non-local versions
of both tunneling rates are compared. Finally, the conventional SRH theory is
generalized to the case of two communicating impurity levels, resulting in a device model for
coupled defect-level recombination. Its field enhancement can explain the anomalous behavior of
LPE-grown diodes.
In Chapter 4 a new model for the non-ideal metal-semiconductor contact is presented.
Thermionic tunneling is modeled by an interpolation scheme for the transmission probability
which replaces the common WKB approximation. Analytical boundary conditions are derived, and
simulated contact currents are compared with experimental data. The optimization of a
merged pin/Schottky diode is demonstrated.
Chapter 5 describes new models for the transport across thin dielectric barriers. Direct and
Fowler-Nordheim tunneling through ultra-thin gate oxides are treated
by a new approach for the transmission coefficient, called pseudobarrier method.
The model is applied to the self-consistent simulation of gate currents in MOS capacitors with gate
oxides in the thickness range 1.5 nm - 4.2 nm.
Thanks to the CPU-time efficiency of the method, the simulation of a complete
MOSFET with dominating gate current becomes possible. Models of two-step multiphonon-assisted
tunneling and resonant tunneling via defect states in the dielectric layer are set up and
used for the simulation of the long-term charge loss in EPROMs.
In Chapter 6 a summary and an outlook are given.
Despite serious risks in forecasting the future of silicon ULSI,
at least one or two decades seem to be left for improvements of physical models.
From a principle point of view, the phenomenological transport schemes will quickly
reach their limits of validity. However, drift-diffusion simulations with physics-based
models will also continue in yielding useful "first answers", since more sound methods
have their own limitations in form of huge computation times and the necessary
expertise, at least for the industrial environment.
As there is a pressure from microelectronics industry for highly efficient and fast
simulation tools, drift-diffusion and energy-balance simulators with analytical models
will probably remain widespread in the near future.
Physics-based modeling in the sense of this work can contribute to a
better foundation.
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