Mean Drift Velocity InAve

Define mean drift velocity

The average velocity of charge carriers along a conductor

Taking into account their random thermal motion and collisions

State the equation relating current to number density, cross-sectional area, drift velocity and charge.

I = nAve

Explain why n is much smaller in semiconductors than in metals.

In semiconductors, only a small fraction of electrons are free to move

Most electrons are bound in covalent bonds; only those excited across the band gap are free

Define I = nAve

current = number density cross-sectional area mean drift velocity * elementary charge

A copper wire of diameter 0.80 mm carries a current of 2.5 A. Calculate the mean drift velocity of the electrons. n = 8.5 × 10²⁸ m⁻³, e = 1.60 × 10⁻¹⁹ C.

A = πr² = π × (0.40 × 10⁻³)² = 5.03 × 10⁻⁷ m²

v = I / (n A e) = 2.5 / (8.5 × 10²⁸ × 5.03 × 10⁻⁷ × 1.60 × 10⁻¹⁹)

v = 3.7 × 10⁻⁴ m s⁻¹

A silicon semiconductor has n = 1.5 × 10¹⁶ m⁻³. When the drift velocity is 80 m s⁻¹, the current is 1.9 × 10⁻⁷ A. Calculate the cross-sectional area of the semiconductor. e = 1.60 × 10⁻¹⁹ C. [2 marks]

A = I / (n v e) = 1.9 × 10⁻⁷ / (1.5 × 10¹⁶ × 80 × 1.60 × 10⁻¹⁹)

A = 9.9 × 10⁻⁷ m² (about 1 mm²)

Explain, in terms of n, why metals are much better conductors than semiconductors at room temperature. [2 marks]

Metals have n ~ 10²⁸ m⁻³ whereas semiconductors have n ~ 10¹⁶ m⁻³

Metals have many more free charge carriers per unit volume, so can carry much larger currents for the same v and A