# Presentation: 872946

## Mixed-Level Circuit and Device Simulation

***Karti Mayaram***
*Department of ECE*
*Oregon State University*
*Corvallis, OR 97331*

## Outline

**Introduction**
**Mixed-level (coupled) circuit/device simulation**
**Advantages and applications**
**Simulator architecture and algorithms**
**Radio frequency (RF) simulation issues**
**Extensions to microsystem simulation**

## The Modeling Hierarchy

- High-level
- models

- Lumped-
- element
- models

- Compact
- models

- Numerical
- models

**Speed**

**Accuracy**

**VHDL-AMS**

**RLC**

**BSIM3**

**PISCES**

## Circuit/Device Simulation

- Circuit/Device Simulation

**Circuit simulation**
- Analytical (compact) models used: inaccurate under certain conditions
- Simulation of multiple devices in a circuit
**Device simulation**
- Based on device physics: accurate
- Simulation of a single device, no circuit embedding
**Coupled circuit/device simulation**
- Accurate
- Simulation of complete systems

## Coupled Circuit/Device Simulator

**Compact models for electronic components (BJTs, MOSFETs, ...)**
**Accurate numerical models for various components **
**Analysis capabilities supported by the circuit simulator**

## Coupled Circuit/Device Simulator

**Circuit Simulator**

- DC

- Transient

- AC

**Analyses**

- BJT

- Diode

- MOSFET

**Compact Models**

- R

- C

**Numerical Models**

**Geometry Structure**

**Designer**

- BJT

- Diode

- MOSFET

## Advantages

**Simulate critical devices at the device level within a circuit**
- Solve partial differential equations describing devices coupled to a circuit simulator
**Predict performance of circuits in absence of compact models for devices**
**Evaluate influence of process variations on circuit performance**

## Application Example – Single Event Upset in SRAM Cell

**Critical transistor modeled at the physical (numerical) level**
**Other transistors modeled with compact models**
**Alpha particle strike simulated with circuit boundary conditions**

## Application Examples

**Delay analysis of BiCMOS driver circuits**
**Simulation of power devices**
**Determination of switch-induced error in MOS switched-capacitor circuits**
**Simulation of RF circuits**
**Simulation of single-event-upset in SRAMs**
**Validation of analytical models**

## Coupled Device and Circuit Simulator (CODECS)

- Coupled Device and Circuit Simulator (CODECS)

**Device-level simulator (PDE solver)**
- Poisson’s and current-continuity equations
- Accurate terminal conductances and capacitances provided to circuit-level simulator
**Circuit-level simulator (SPICE3)**
- Compact model evaluation
- Simulation engine

## Architecture of CODECS

**Circuit Simulator**

**Circuit matrix and RHS**

**Compact model**
**evaluator**

**Compact models**

**Device simulator**

**Numerical models**

**Analysis stage**
**Solution vector**

## Equation Formulation

**Modified nodal admittance matrix formulation for circuit equations**
- 	x is the vector of unknown node voltages and voltage source currents
**Device equations after space discretization can also be expressed as **
- 	u is the vector of unknown electrostatic potential, electron and hole concentration at each grid point

## Equation Solution

**With voltage boundary conditions for numerical devices and Newton’s method**

- Full Newton: block LU decomposition used
- Two-level Newton: solve devices to convergence

## Various Equation Solution Methods

**Two-level Newton**
**Modified two-level Newton **
- Two-level Newton with improved initial guess
**Full Newton**
**Block iterative algorithm**
**Two-level Newton has better convergence but higher computational cost**
- Use two-level Newton scheme for DC analysis
- Use full Newton scheme for transient analysis

## DC Analysis Iterations

| Circuit | m2lev | 2lev | full Newton | blockIt |
| --- | --- | --- | --- | --- |
| RTLinv | 8 | 8 | 8 | - |
| Osc | 8 | 8 | 9 | - |
| VCO | 8 | - | 10 | - |
| Invchain | 9 | - | - | - |
| Astable | 9 | - | - | - |
| MECL | 51 | 51 | - | - |

- - No convergence in 100 iterations

## Transient Analysis Iterations

| Circuit | m2lev | 2lev | full Newton | blockIt |
| --- | --- | --- | --- | --- |
| Osc | 16916 | 16916 | 18333 | 23836 |
| VCO | 5093 | 5109 | 5864 | 7028 |
| Invchain | 1563 | 1578 | 1716 | 2324 |
| Astable | 5930 | 6305 | 6369 | 9087 |
| MECL | 2450 | 2450 | 2609 | 3236 |
| Cpump | 1644 | 1661 | 1850 | 2661 |

## RF Simulation Issues

**Accurate and efficient steady-state simulation of RF ICs required for**
- Distortion, power, frequency, and noise
- Gain and impedance characteristics
**Simulation techniques**
- Time-domain shooting method
- Harmonic-balance method

## RF Simulation Issues

**Distributed effects in devices important for RF applications**
- Use physical models in absence of accurate compact models
- Coupled device and circuit simulation

## Time-Domain Periodic Steady-State Analysis

**X**

**t**

**Period T**

**0**

**T**

**Two-point boundary value problem**

## Frequency Multiplier Example

**Shooting method: 6 periods**
**Conventional transient: 1500 periods**

## Harmonic Balance Method

**Truncated Fourier series approximation of x(t)**

**For 2s+1 time samples x****0****...x****2s**

## MOSFET Tuned Amplifier

**2D numerical MOSFET with 31x19 mesh points**
**10 harmonics**
**# iterations = 6 **
**Result verified by transient simulation**

## Periodic Steady-State Analysis: Performance Results

| Circuit | Shooting Method |  | Harmonic balance |  |
| --- | --- | --- | --- | --- |
|  | # Iter | Time (sec) | # Iter | Time (sec) |
| Simple rectifier | 2 | 28 | 16 | 37 |
| DC power supply | 6 | 81 | 39 | 45 |
| CB amplifier | 4 | 254 | 53 | 385 |
| X3 freq. multiplier | 6 | 10 | 8 | 32 |
| MOS CS amplifier | 3 | 554 | 6 | 36 |

## Simulation of Microsystems

**Microdevice simulation**
- Finite-element methods (FEM)
- Fast integral methods
**Simulation of complete systems**
- Lumped equivalent circuit representations
- Macromodels derived from FEM analysis
- Analog hardware description language (AHDL) descriptions

## Limitations of High-Level Models

- Beam bending

- Comb structure

- reach substrate

- reach limit stops

**Typically derived for small-signal conditions**
**Not suitable for systems with feedback**
**Cannot predict behavior outside range**

## Coupled Circuit/Microdevice Simulator

**Circuit Simulator**

- DC

- Transient

- AC

**Analyses**

- BJT

- Diode

- MOSFET

**Compact Models**

- R

- C

- Micro Devices

**Macro Models**

**Numerical Models**

**Geometry Structure**

**Designer**

- Pump

- Valve

## Micro Fluidic Simulation Example

**Constant flow system**

## Simulator Interaction 

**Channel**

**Control electronics**

- Fluid in

- Fluid out

- NEKTAR

- SPICE

**Flow sensor**

**  ****Actuation**

## Coupled System Simulation: 4 Physical Domains

- Flow sensor: Flow to Temperature (thermal domain)

- Circuit: Temperature to Voltage
- (electrical domain)

- Piezo-actuator:
- Voltage to Displacement
- (structure domain)

- Micropump: Displacement to Flow
- (fluid domain)

**Coupled System Simulation: 4 Physical Domains**

## Conclusions

**Coupled circuit/device simulations required for accurate simulation of circuits/systems**
**Provides a direct link between technology changes and circuit performance**
**Also useful for developing accurate compact models**
**Need faster solution methods for PDEs**
**Different coupling algorithms need to be developed for various problem domains **