# ATLAS Breaks New Ground In Device Simulation

Introduction

The device simulation capabilities offered by Silvaco
are now all integrated into * ATLAS*. This modular architecture
contains unique products, and provides users with unparalleled flexibility,
convenience and ease of use. The purpose of this article is to present
the current status of

*. The overall architecture is reviewed, and details of several new capabilities are presented.*

**ATLAS**

The ATLAS Architecture

The heart of the * ATLAS* architecture
is a development "toolkit" that includes: an input parser; a variety
of numerical capabilities (e.g. for discretization, nonlinear iteration,
and the solution of linear systems); various post-processing capabilities;
and a data base of material parameters. The individual products
that are built on this foundation work together seamlessly.

* ATLAS* presently consists of eleven
products. Eight of these are targeted at one- and two-dimensional
simulation, and three are for three-dimensional simulation. Users
need acquire only those products that are relevant to their needs,
and retain the flexibility to acquire additional functionality at
any time. The overall architecture is depicted in Figure 1.

Figure 1. The ATLAS architecture for 2-D and 3-D device simulation.

Basic Capabilities

Users have a choice of * Blaze* or

*as their base 1-D and 2-D simulator.*

**S-Pisces***handles arbitrary semiconductor materials and combinations of semiconductors (i.e. heterojunction devices).*

**Blaze***is specialized for the simulation of silicon devices. Both*

**S-Pisces***and*

**Blaze***include capabilities that other suppliers do not offer, or provide only as extra-cost options. Two examples are non-local (energy balance) transport, and the physical models required to simulate non-volatile memory devices.*

**S-Pisces**

Specialized Capabilities

The products that work in conjunction with * Blaze*
or

*are*

**S-Pisces***,*

**Giga***and*

**MixedMode, ESD, TFT, Luminous**

**Laser.***adds the ability to simulate lattice heating and heatsinks.*

**Giga***provides the ability to mix numerically-simulated devices and circuit models within a circuit simulation environment.*

**MixedMode***is a new product that works in conjunction with*

**ESD***and*

**Giga***to automate the simulation of electrostatic discharge experiments.*

**MixedMode***provides the ability to simulate amorphous and general polycrystalline materials.*

**TFT***adds the ability to simulate optoelectronic devices.*

**Luminous***adds the ability to simulate stimulated emission with coupling to electromagnetic fields.*

**Laser**

1994 Development Highlights

* ATLAS* has undergone major enhancements
and refinements during 1994. A significant development is the incorporation
of 3-D capabilities. The 2-D capabilities were available previously
in a product called

**ATLAS***. With the inclusion of 3-D capabilities the name of the product becomes simply*

**II***.*

**ATLAS**Another significant development is the implementation of a new "six-equation" solver. This includes the effects of both non-local transport (e.g. velocity overshoot) and non-isothermal effects (lattice heating). The six equation solver represents a major breakthrough in device simulation capabilities.

A new * ESD* product, which works in
conjunction with

*and*

**Giga***, automates the simulation of electrostatic discharge tests. Many other refinements, such as improved curve tracing, have also been added.*

**MixedMode**

Three-Dimensional Capabilities

Silvaco previously offered the * Thunder 3-D*
device simulator. This product worked well, but its input syntax
differed from that of

*, and the physical models were not always identical. These limitations have now been eliminated. Physical models and input syntax are now common to the 2-D and 3-D capabilities. In addition*

**S-Pisces***can determine at run time whether to perform calculations in 1-D, 2-D or 3-D.*

**ATLAS**ATLAS contains three 3-D products. These are * Device3D*,

*and*

**Interconnect3D***. The applications of each product are indicated by their names.*

**Thermal3D***is a significant improvement over earlier generations of parasitic element extractor. It handles very general, realistic topographies, and it interfaces seamlessly with*

**Interconnect3D***(and therefore to GDS2 layout data). Figure 2 shows an idealized interconnect structure that was generated automatically from layout data. The article on*

**MaskViews***elsewhere in this issue shows an example of a realistic interconnect structure that was prepared for analysis by*

**ATHENA***.*

**Interconnect3D**

Figure 2. This interconnect structure
was generated automatically

from layout. It was then provided as input to Interconnect3D.

* Thermal3D* calculates the thermal
characteristics of general 3-D structures that can extend all the
way up to the chip and subsystem levels. Figure 3 shows a temperature
distribution that was calculated for a multi-finger MESFET device,
in order to determine the extent of the temperature difference between
the central and outer fingers.

Figure 3. This temperature distribution
was calculated for a multi-finger

MESFET structure. (Symmetry considerations allow the simulation
of

only one quarter of the actual structure).

Six Equation Solver

Until the past few years device simulation was based on the solution of three equations - one each for electrons, holes and electrostatic potential. This "drift-diffusion" approximation contains two major assumptions: that transport parameters are determined by the local instantaneous electric field (the 'local' approximation), and that the lattice temperature is constant (the 'isothermal' approximation).

The 'energy balance' models that have been developed during the past few years provide a description of non-local effects such as velocity overshoot and reduced impact ionization. Energy balance models introduce two additional equations, one each for electrons and holes. Other efforts have been directed towards the elimination of the isothermal approximation. This involves solving an additional equation for the heat flux. A lot of work has been directed towards eliminating either the local approximation or the isothermal approximation. Much less effort has been directed towards the harder problem of removing both assumptions simultaneously.

Silvaco has now developed the first commercial device simulator that removes both assumptions and solves all six equations simultaneously[1]. The use of 'fully coupled' solution techniques means that efficiency, convergence and robustness are all excellent. The new 'six equation solver' is very general. It handles arbitrary materials, heterojunction devices, and very high current breakdown conditions. Small-signal AC analysis can be performed for all six equations, or for any meaningful subset.

The simultaneous solution of the energy balance equations and the lattice heating equation provides a major increase in the effectiveness of device simulation. It is already clear that 'six equation' solutions allow much more accurate simulation of submicron BJT's. Earlier generations of device simulators provide agreement with BJT measurements only after parameters such as recombination times and minority carrier mobilities are adjusted. This is unsatisfactory because it impairs predictive capabilities, and because the fitted values of parameters often exhibit anomalous, apparently unphysical, behavior. The use of 'six equation physics' substantially eliminates these problems.

Because six-equation physics is important for the
simulation of bipolar devices, it is also important for BiCMOS technologies
and (because of parasitic bipolar effects) SOI technologies. In
addition, SiO_{2} and III-V materials have much lower
thermal conductivities than silicon. This increases the relative
importance of nonisothermal and non-local transport effects in SOI,
III-V and heterojunction technologies. Six-equation physics is important
for *all* devices under conditions of high current breakdown.

An example of the capabilities of the new six equation solver is shown in Figures 4 and 5. Figure 4 shows the breakdown behavior of a SiGe PMOS transistor calculated using drift-diffusion (DD), energy balance (EB), non-isothermal drift-diffusion (NDD) and the full six equation model, and non-isothermal energy balance (NEB). In the pre-breakdown region the results are quite similar, because velocity overshoot is relatively small for holes and relatively small amounts of heating do not have a major impact on MOS devices. Results differ significantly in the breakdown region. The DD and EB models do not predict second breakdown, and the NDD model predicts breakdown too soon. Figure 5 shows the peak temperature calculated using the NDD and NEB models. The NDD model is overly pessimistic with respect to predicted thermal constraints.

Figure 4. The breakdown characteristics
of a SiGe PMOS

transistor calculated using different physical models.

Figure 5. Maximum lattice temperature
as a function of drain

voltage. Results are shown up to temperatures well above those that

would be associated with a functioning device.

The ESD Product

The six equation solver makes the simulation of
electrostatic discharge (* ESD*) protection devices much
more accurate. These devices can be simulated in a realistic test
circuit (e.g. Human Body Model) using

*. The*

**MixedMode***product automates the setup, running, and data extraction involved in simulating standard and user-defined tests on*

**ESD***protection devices.*

**ESD**

Curve Tracer

The automatic curve tracing capabilities in * ATLAS*
have been enhanced to provide improved robustness, stability, and
automatic stepping. The curve tracing works equally well for three,
four, five or six equation physics. Figure 6 shows the use of the
new curve tracing capabilities for calculating the breakdown behavior
of a Si MOSFET using six equation physics and automatic curve tracing.

Figure 6. Breakdown characteristics
of a Si MOSFET calculated

using six equation physics and automatic curve tracing.

Conclusions

This year has seen two significant developments
of * ATLAS*. The first is the inclusion of 3-D capabilities
that make

*a universal 1-D, 2-D and 3-D system. The second is the implementation of the first commercially available 'six equation' solver that accounts for non-local and non-isothermal effects simultaneously.*

**ATLAS**

Reference

[1.] Y. Apanovich, P. Blakey, R. Cottle, E. Lyumkis, B. Polsky, A. Shur, and A. Tcherniaev, "Numerical Simulation of Submicron Devices Including Coupled Non-Local Transport and Non-Isothermal Effects", to be published in IEEE Trans. on Electron Devices.