hydrodynamic model
**Hydrodynamic Model** is the **advanced TCAD transport framework that extends drift-diffusion by tracking carrier energy as a separate variable** — allowing carrier temperature to differ from lattice temperature and enabling accurate simulation of hot-carrier effects and velocity overshoot in deep sub-micron devices.
**What Is the Hydrodynamic Model?**
- **Definition**: A transport model that adds an energy balance equation to the standard drift-diffusion system, treating the carrier gas as a fluid with its own temperature distinct from the lattice.
- **Key Addition**: The energy balance equation tracks the rate of energy gain from the electric field against the rate of energy loss through phonon collisions, yielding a spatially varying carrier temperature (T_e).
- **Non-Equilibrium Physics**: Where drift-diffusion assumes T_e equals lattice temperature everywhere, the hydrodynamic model allows T_e to exceed lattice temperature in high-field regions, capturing hot-carrier behavior.
- **Computational Cost**: Solving the energy equation increases simulation time by 2-5x compared to drift-diffusion and introduces additional convergence challenges.
**Why the Hydrodynamic Model Matters**
- **Velocity Overshoot**: Only the hydrodynamic model captures the transient velocity overshoot phenomenon critical for accurate current prediction in sub-30nm channels.
- **Impact Ionization**: Accurate hot-carrier energy distribution is required to correctly predict avalanche multiplication and breakdown voltage in power and logic devices.
- **Hot Carrier Reliability**: Gate oxide damage from energetic carriers (hot-electron injection) depends critically on the carrier energy distribution, which only the hydrodynamic model provides.
- **Deep Sub-Micron Necessity**: Below approximately 65nm, drift-diffusion systematically underestimates on-state current because it misses velocity overshoot — the hydrodynamic model corrects this.
- **Breakdown Analysis**: Accurate simulation of NMOS drain-avalanche breakdown and snap-back phenomena requires the hot-carrier energy tracking that the hydrodynamic model provides.
**How It Is Used in Practice**
- **Mode Selection**: Hydrodynamic simulation is typically invoked for reliability analysis, breakdown voltage extraction, and short-channel device characterization where drift-diffusion is insufficient.
- **Parameter Calibration**: Energy relaxation time and thermal conductivity parameters are calibrated to Monte Carlo simulation data or measured hot-carrier emission spectra.
- **Convergence Management**: Starting from a converged drift-diffusion solution and ramping the energy balance equations incrementally improves solver stability for the hydrodynamic system.
Hydrodynamic Model is **the essential bridge between classical and quantum device simulation** — its energy-tracking capability unlocks accurate prediction of hot-carrier physics, velocity overshoot, and breakdown mechanisms that make it indispensable for reliability analysis and sub-65nm device characterization.