Taurus-Medici Industry-standard device simulation tool

Overview
Taurus-Medici™ is Synopsys’ industry-standard device simulation tool that predicts electrical, thermal and optical characteristics of semiconductor devices. A wide variety of devices can be modeled in one, two or three dimensions including MOSFETs, BJTs, HBTs, power devices, IGBTs, HEMTs, CCDs, photo detectors and LEDs. With the most advanced physical models commercially available, Taurus-Medici allows device designs to be optimized for best performance without fabrication, eliminating the need for costly experiments.

Benefits

• Analyze electrical, thermal and optical characteristics of your devices through simulation without having to manufacture the actual device.
• Determine static and transient terminal currents and voltages under all operating conditions of interest.
• Understand internal device operation through potential, electric field, carrier, current density, recombination and generation rate distributions.
• Optimize device designs without fabrication and find ideal structural parameters.
• Investigate breakdown and failure mechanisms, such as leakage paths and hot carrier effects.
• Generate data for compact model generation to allow analysis of circuit designs before processing.
• Use the Physical Model and Equation Interface (PMEI) to perform simulations that incorporate user-defined physical models and equations.

Deep Submicron CMOS Simulation
With the continued scaling of CMOS devices, device design and optimization become more difficult. Previously unimportant phenomena, such as direct tunneling, can now dominate device performance and design criteria. Taurus-Medici's vast array of advanced transport and quantum models allow for the accurate simulation of deeply-scaled devices. In Figure 1-2, the impact of carrier quantization on a 2D MOSFET is examined.

Silicon on Insulator
Simulating short-channel Silicon on Insulator (SOI) devices, such as the 0.2 micron SOI MOSFET shown in Figure 3-4, require the solution of the carrier energy balance equations and the lattice heat equation to account for carrier and lattice heating effects. Taurus-Medici can model the energy exchange between the field and the carriers and also between the carriers and the lattice to provide an accurate description of the electrical and thermal characteristics of SOI devices.

Power Device Simulation
Taurus-Medici is widely used in the industry to simulate all kinds of power devices, both in 2D and 3D (Figure 5 & 6). All relevant phenomena can be simulated. The performance of new power device designs can be evaluated with Taurus-Medici without going through the manufacturing cycle. A quadtree/octree meshing capability minimizes the number of mesh points needed for the efficient simulation of large power device structures, without sacrificing the accuracy required in critical device regions.

Figure 1. Contours of the quantized electron concentration in a 2D sub-micron MOSFET computed using the Schrödinger solver. Horizontal scale is 0.6mm, vertical scale is 65Å.

Figure 2. Gate characteristics of a sub-micron MOSFET showing increase in threshold voltage due to quantum effects.

Figure 3. The top plot shows the electron temperature near breakdown. The bottom figure displays the lattice heating distribution. The heat conductivity in the oxide is much lower than in silicon, and therefore the heat propagates differently in the two materials.

Figure 4. The IV curves feature the kink effect at low gate biases and incipient breakdown around Vd=3.5V.

Electrostatic Discharge (ESD)
Taurus-Medici can be used to simulate ESD in a variety of technologies (Figures 7-9). Using the mixed mode capabilities, numeric devices can be used in place of compact models in protection circuits for analyzing the detailed behavior inside a device during an ESD event. In Figures 7-9 an advanced two-MOSFET protection circuit is simulated with the human body model (HBM).

Compound Device Simulation
Taurus-Medici includes physical models and parameters for over 30 binary, ternary, and quaternary materials and allow detailed analysis of devices such as HBTs, HEMTs, MESFETs, and LEDs (Figures 10-12). The flexibility afforded by Taurus-Medici allows design tradeoffs to be explored for optimizing device performance. All device equations can be solved fully coupled or in any combination, providing quick solutions for all simulations of interest. Quantization effects at heterojunctions can also be considered by using the available Schroedinger equation solver.

Optical Device Simulation
Taurus-Medici can simulate optical devices that convert light to electricity and vice-versa (Figures 13 and 14). For the former, a ray tracing algorithm is used to calculate transmission and absorption of light in bulk, as well as reflection and refraction at the interfaces. Arbritrary geometries can be used in 1, 2 and 3D. Spontaneous emission can be simulated by entering the optical generation rate into the continuity equations. Capabilities for stimulated emission and wave transport for laser simulation have also been developed.

Noise Analysis
The noise performance of solid-state devices is an increasingly important feature in high frequency IC design (Figures 15-17). Especially for analog applications, the noise minimization is a key issue and often defines the sensitivity or detection limit. Due to the promise of integrating whole systems on a chip, CMOS technologies are becoming more and more attractive to analog designers. While the advantages are well known, the noise performance is a major drawback of CMOS elements in comparison to bipolar transistors. Thus, a detailed analysis of the noise performance is mandatory. Noise analysis has been implemented in Taurus-Medici using the direct impedance field method. Since it is a microscopic approach based on physical device simulation, it allows for localizing the major noise sources within the device and to determine their importance for the noise voltage, current spectral densities, or correlation spectra that are measurable on the device terminals. Therefore, the noise performance of a device can be taken into account during the early IC design process to achieve high density, high frequency and high data rates. Ultimately, the device design itself can be improved with respect to the noise performance.

Figure 5. Detail from a 20 field ring device comparing conventional mesh with quadtree.

Figure 6. 3D simulation of a large resurf diode showing potential contours.

Figure 7. Protection circuit and HBM equivalent circuit. The capacitor is initially charged to 2000V and discharged into the protection circuit.

Figure 8. Contours of temperature and current flow within the protection MOSFET.

Figure 9. Peak temperature, the capacitor voltage, the total current, and the voltage at the IC input during the event.

Advanced 3D Simulation
Taurus-Medici allows you to analyze complicated 3D effects in MOSFETs and bipolar structures including channel length/width effects, breakdown, thermal instabilities, latchup and other parasitic effects ( Figures 18-19). Many devices can be modeled in 3D, including bipolar devices such as submicron BJTs, power diodes and thyristors, bipolar-MOS devices like BiCMOS and IGBT, and novel 3D devices such as the double-gate, vertical geometry FinFet. The device structure can be constructed by an analytic boundary and doping description or by physical process simulation via the seamless interface to Taurus-TSupreme4™ Synopsys’ multidimensional process simulator.

Figure 10. Energy band diagram for the structures.

Figure 11. Si1-xGex HBT structure, with mole fraction x=0.2 in the base and graded at the junctions.

Figure 12. Conduction band and quantized subbands in the channel of a HEMT. The smoothing effect of carrier quantization on the electron concentration computed using the Schrödinger solver is also shown.

Figure 13. Light absorption inside the device.

Figure 14. Electrical characteristics of a solar cell.

Physical Model and Equation Interface (PMEI)
Taurus-Medici has a physical model and equation interface (PMEI) that provides an easy and flexible way to define new physical models and partial differential equations (Figures 20-22). The PMEI allows you to either replace or compliment the hardcoded models and equations in the code with your own set of models and equations. Areas of particular importance include mobility, impact ionization and quantum models, but the PMEI is equally applicable to all partial differential equation simulations.

Simulation Features

• Simulation of arbitrarily shaped 1D, 2D and 3D structures.
• Consistently solves Poisson's equation, the electron and hole current continuity equations, the electron and hole energy balance equations, and the lattice heat equation. Steady state, transient and AC-small signal analysis with automatic I-V curve tracing and time-step algorithms.
• Ray tracing to simulate transmission, reflection and refraction across interfaces, as well as absorbtion and emission.
• Advanced adaptive mesh generation, which provides optimal grids with excellent solution and structure resolution using a minimum number of mesh points.
• Arbitrary doping from analytic functions, tables and process simulation.
• Supports multiple materials such as Si, Ge, GaAs, SiGe, AlGaAs, InP, GaInAs, GaInGaPAs and SiC, as well as arbitrary user-defined materials.
• Optional physical model and equation interface, which allows a user to define and solve new physical models and partial differential equations.
• Dynamic memory allocation - the size of the simulated problem is limited only by the capacity of the computer.
• The solution method may be controlled by the user, i.e. all available or userdefined equations can be solved individually, iteratively coupled or fully coupled.
• Large selection of fast, direct and iterative linear solvers.

Figure 15. Diffusion noise source, vector impedance field and the integrand describing the electron contribution to the thermal noise observable on the drain contact of the MOSFET (Vdrain = Vgate = 1V). Noise from the drain and source implant regions is strongly suppressed due to the low amplitude of the vector impedance field in these domains.

Figure 16. MOSFET noise figure as a function of the gate bias for50 Ohm source impedance and f=100MHz. Using drift-diffusion equations only generally leads to lower noise than simulations with energy balance equations coupled.

Figure 17. A circular BJT device. This structure contains 10720 mesh points, typically a factor of 3 less than conventional 3D device simulation with the same accuracy.

Specifications Device Models

• Complete set of device models, including SRH and Auger recombination models, bandgap narrowing, Fermi-Dirac and Boltzman statistics and gate current.
• Extensive choice of mobility models including the Philips Unified, Lombardi Surface, Shirahata, Lucent, Inversion and Accumulation layer and compositespecific mobility models.
• Mobility dependencies on impurity concentration, lattice temperature, carrier concentration, carrier energy, parallel and perpendicular electric fields, mole fraction, and stress.
• Fowler-Nordheim, hot-carrier, band-to band and direct tunneling models.
• Complete set of breakdown models, including stress dependent leakage current and temperature-dependent impact ionization.
• Quantum mechanical models including the van Dort model, the modified local density approximation (MLDA) and a Schroedinger equation solver.
• One or several physically modeled devices can be connected in a circuit with passive components and active devices with compact models (HSPICER BSIM3)

Figure 18:

3D MOSFET structure used for the investigation of channel width effects.	Potential distribution at Vg=1.8V, Vds=2.1V of a complete MOSFET structure as generated by process simulation.
Gate turn-off thyristor structure for the analysis of 3D effects at the cathode-finger termination.

Platforms and OS Support:

• Platform: Runs on Sun Solaris, Hewlett-Packard HP-UX, IBM AIX and Intel Linux
• Memory: Recommended memory range from 8MB (1D) to 1GB (3D).
• Taurus-Medici is integrated into the Taurus-Modeling. Environment, a graphical user interface for performing TCAD simulations

Figure 20. Contours of the electron concentration in a double-gate MOSFET computed using a PMEI implementation of the density-gradient method.

Figure 21. Comparison of the electron concentration under the gate computed classically and computed using the density-gradient method.

Figure 22. Simulation of mass transport driven by electromigration using PMEI. Figures a and b have different angles between grain boundaries and the direction of electric field, generating different types of voids.

For more information about Synopsys products, support services or training, visit us on the web at www.synopsys.com, contact your local sales representative or call 650.584.5000.