Physics Overview
MOSFET Operating Principles
The Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) is the fundamental building block of modern integrated circuits. It controls current flow through a channel region between source and drain terminals. The channel conductivity is modulated by the electric field from the gate electrode, which is separated from the channel by a thin gate oxide.
Basic Structure
A MOSFET consists of four terminals:
| Terminal | Function |
|---|---|
| Gate (G) | Controls channel conductivity via electric field |
| Source (S) | Carrier injection point |
| Drain (D) | Carrier collection point |
| Body (B) | Substrate contact, affects threshold voltage |
Key Concepts
Threshold Voltage ( )
The threshold voltage is the gate voltage required to create a conductive inversion layer (channel). It depends on several factors:
- Flat-band voltage:
- Surface potential: (for strong inversion)
- Body effect:
Where:
- : Metal-semiconductor work function difference
- : Fixed oxide charge
- : Oxide capacitance per unit area
- : Fermi potential
- : Body effect coefficient
Operating Regions
The MOSFET operates in three distinct regions depending on bias conditions:
| Region | Condition | Behavior |
|---|---|---|
| Cutoff | Channel not formed, only subthreshold leakage | |
| Linear (Triode) | , | Acts like a voltage-controlled resistor |
| Saturation | , | Channel pinched off, current nearly constant |
I-V Characteristics
The following chart shows typical MOSFET output characteristics (Id vs Vds) for different gate voltages:
The transfer characteristic (Id vs Vgs) shows how current varies with gate voltage:
Subthreshold Conduction
Below threshold, the current doesn't go to zero immediately. The subthreshold swing (SS) characterizes how sharply the transistor turns off:
Where is the body factor.
The ideal SS at room temperature is approximately 60 mV/decade, meaning a 60mV change in Vgs changes drain current by 10×.
Why 60 mV/decade?
At T = 300K, mV. Multiplied by , this gives mV. This is the theoretical minimum for conventional MOSFETs due to Boltzmann statistics of carrier injection.
Energy Band Diagram
Understanding the MOS band diagram is crucial for device physics. The diagram below shows the energy bands in inversion:
Different bias conditions create different band configurations:
| Bias Condition | Surface State | Band Bending |
|---|---|---|
| Accumulation | Majority carriers accumulate | Bands bend toward Ef |
| Flat-band | No band bending | Bands are flat |
| Depletion | Surface depleted | Bands bend away from Ef |
| Inversion | Minority carriers at surface | Strong bending, |
Capacitance-Voltage Characteristics
The MOS capacitor exhibits three distinct regions in C-V measurements:
C-V Regions Explained
Accumulation ( ): Majority carriers pile up at the surface
- (maximum capacitance)
Depletion ( ): Surface depleted of carriers
- (series combination)
Inversion ( ): Minority carriers form inversion layer
- High frequency: Inversion charge can't follow AC signal,
- Low frequency: Inversion charge responds,
Material Parameters
Silicon Properties at 300K
| Property | Symbol | Value | Unit |
|---|---|---|---|
| Band gap | 1.12 | eV | |
| Dielectric constant | 11.7 | - | |
| Intrinsic carrier concentration | cm⁻³ | ||
| Electron mobility | 1400 | cm²/V·s | |
| Hole mobility | 450 | cm²/V·s | |
| Electron saturation velocity | cm/s | ||
| Hole saturation velocity | cm/s |
Gate Dielectric Materials
| Material | Dielectric Constant ( ) | Band Gap (eV) | EOT Factor |
|---|---|---|---|
| SiO₂ | 3.9 | 9.0 | 1.0 |
| Si₃N₄ | 7.5 | 5.3 | 0.52 |
| HfO₂ | 25 | 5.8 | 0.16 |
| ZrO₂ | 25 | 5.8 | 0.16 |
High-k Dielectrics
High-k materials like HfO₂ allow thicker physical oxide for the same , reducing gate leakage while maintaining electrostatic control. The Equivalent Oxide Thickness (EOT) relates physical thickness to SiO₂ equivalent:
Temperature Effects
Temperature significantly affects MOSFET characteristics:
| Parameter | Temperature Dependence |
|---|---|
| Increases exponentially with T | |
| Decreases with T (phonon scattering) | |
| Decreases ~2 mV/K | |
| Increases exponentially with T | |
| Decreases slightly with T |
The threshold voltage temperature coefficient is approximately:
Physics Model Levels
The simulator implements three levels of physics modeling:
| Level | Model Type | Speed | Accuracy | Use Case |
|---|---|---|---|---|
| A | Analytical | Fast | Basic | Learning, quick analysis |
| B | Semi-empirical | Fast | Good | Device design, SCE analysis |
| C | Numerical | Slow | High | Research, validation |
See the detailed documentation for each level: