Verilog-A Physical constants

Introduction¶

Verilog-A is widely used in analog and mixed-signal simulation because it provides an intuitive method to model physical behavior directly using mathematical and semiconductor physics principles. One of the significant advantages of Verilog-A is its access to built-in physical constants, defined in the standard constants.vams include file. These constants form the foundation of most compact and behavioral device models, helping ensure that simulations faithfully reflect real-world behavior.

What Are Verilog-A Physical Constants?¶

Physical constants in Verilog-A represent universal scientific quantities such as:

• Electron charge
• Boltzmann constant
• Permittivity of vacuum
• Speed of light
• Planck’s constant

These constants remain the same across all simulations, ensuring physics-based consistency and reliability in modeling.

They are available through the standard include:

`include "constants.vams"

Most semiconductor foundries require this include in every Verilog-A model used in a Process Design Kit (PDK).

Categories of Verilog-A Physical Constants¶

Verilog-A provides constants across major fields of applied physics:

These constants simplify implementation by preventing the need for manual value entry.

Common Constants in constants.vams¶

These names remain consistent across compliant simulators (Spectre, HSPICE, ADS, etc.)

How Constants Support Device Physics¶

Physical models require precise scientific constants for accurate behavior. Examples include:

Diode Current Equation¶

Using Boltzmann constant:

Vt = `P_K * $temperature / `P_Q; // Thermal voltage
Id = Is * (limexp(V(anode,cathode) / Vt) - 1);

This provides temperature-aware current flow behavior.

Gate Oxide Capacitance in MOSFET¶

Cox = `P_EPS0 * Eps_ox / Tox;

Describes the relationship between oxide thickness and gate control strength.

Thermal Noise in a Resistor¶

Applies Johnson-Nyquist noise:

$$i_n^2 = \frac{4kT}{R}$$

Verilog-A implementation:

I(p,n) <+ white_noise(4*`P_K*$temperature/R, "thermal_noise");

Here, P_K ensures correct temperature dependence.

Temperature Relationships¶

Temperature-dependent behavior makes analog simulation representative of real operation. Built-in variable $temperature pairs with constants for:

• Conductivity change
• Threshold voltage variation
• Junction leakage growth

Example:

Eg_T = Eg0 - alpha*(($temperature^2)/(beta + $temperature));

These physics-based effects are critical for CMOS PDK modeling.

Constants for High-Frequency Modeling¶

RF and microwave compact models depend on electromagnetic constants:

• P_EPS0 — dielectric interactions
• P_C — propagation delay
• P_MU0 — inductive energy in magnetic fields

Example: Transmission line characteristic impedance

Zo = sqrt(L / C); // Using physical L, C derived from EPS0 and MU0

Emerging Quantum Modeling in Verilog-A¶

As semiconductor technologies scale below 5 nm, modeling quantum behavior becomes necessary:

• Electron tunneling
• Quantum confinement
• Density-of-states corrections

Planck’s constant and reduced Planck’s constant support such developments:

E_quantum = `P_HBAR * omega;

This enables modern compact models such as BSIM-CMG and HiSIM-HV.

Why Using Built-In Constants Is Better¶

Standardized constants support:

• Foundry-compatible PDK models
• Model portability between simulators
• Greater numerical stability

Best Practices for Using Physical Constants¶

Good practices remove ambiguity and reinforce simulation correctness.