electron mobility

```svg ``` **Carrier Mobility** — the speed at which electrons or holes move through a semiconductor when an electric field is applied, directly determining transistor switching speed. **Definition** $$\mu = \frac{v_d}{E}$$ Where $v_d$ is drift velocity and $E$ is electric field. Units: cm²/(V·s) **Typical Values (Silicon at 300K)** - Electron mobility: ~1400 cm²/(V·s) - Hole mobility: ~450 cm²/(V·s) - This is why NMOS (electron carriers) is ~3x faster than PMOS (hole carriers) **Factors Affecting Mobility** - **Temperature**: Higher T → more lattice scattering → lower mobility - **Doping**: Higher doping → more impurity scattering → lower mobility - **Electric field**: Very high fields → velocity saturation (~10⁷ cm/s) - **Crystal orientation**: <100> vs <110> planes have different mobilities **Mobility Enhancement Techniques** - **Strained Silicon**: Apply tensile strain (for NMOS) or compressive strain (for PMOS) to the channel. 30-50% mobility improvement - **High-mobility channels**: Ge (2x electron, 4x hole), InGaAs (10x electron). Used in research - **FinFET fin orientation**: Choose crystal direction for optimal mobility **Why Mobility Matters** - Higher mobility → higher drive current → faster switching → higher frequency - $I_{on} \propto \mu$ — drive current directly proportional to mobility **Carrier mobility** is the physical foundation of transistor speed — every generation's performance gains partly come from mobility engineering.