Pinch-Off Voltage Explained

 

Pinch-Off Voltage (Semiconductor Physics)

Concept: Pinch-off occurs when the depletion region width becomes equal to the channel thickness, fully depleting the channel.

Step 1: Depletion Width Formula

For an abrupt junction:

W = sqrt((2 × εs × V) / (q × N))

• W = depletion width
• εs = semiconductor permittivity
• V = applied voltage (pinch-off voltage)
• q = 1.6 × 10⁻¹⁹ C
• N = doping concentration

Step 2: Pinch-Off Condition

At pinch-off:

W = a

where a = channel thickness

Step 3: Derivation

a² = (2 × εs × Vp) / (q × N)

Final Formula

Vp = (q × N × a²) / (2 × εs)

Step 4: Permittivity

εs = εr × ε0

Where:

• ε0 = 8.85 × 10⁻¹² F/m
• εr = dielectric constant

Important Observations

• Higher doping (N ↑) → higher pinch-off voltage
• Thicker channel (a ↑) → Vp increases sharply (a² dependence)
• Higher dielectric constant → lowers Vp

Vp = (1.6×10⁻¹⁹ × N × a²) / (2 × εr × 8.85×10⁻¹²)