Important Problems in Semiconductors and Transport Physics

ANNA UNIVERSITY SOLVED PROBLEMS

Carrier concentration in an intrinsic semiconductor

Given data

Solution

Electrical conductivity of an intrinsic semiconductor

Extrinsic semiconductor

Given data

Solution

(a) Concentration in n-type silicon

(b) Concentration in p-type silicon

Problem 3.3

A silicon material is uniformly doped with phosphorus atoms at a concentration of 2 x 10¹⁹ m^-3. The mobilitieS of holes and electrons are 0.05 and 0.12 m² V^-1 s^-1 respectively, n_i = 1.5 x 10¹⁶ m^-3 Find the electron and hole concentrations and electrical conductivity. (A.U. June 2014)

Solution

Solution

In a p-type semiconductor, the hole concentration is equal to the acceptor density.

Hall effect

Given data

Solution

We know that density of charge carriers

Substituting the given values, we have

Given data

Solution:

Hall coefficient

Electron mobility

Problem 3.7

A copper strip 2.0 cm wide and 1.0 mm thick is placed in a magnetic field with B = 1.5 weber/m² perpendicular to the strip. Suppose a current of 200 A is set up in the strip. What Hall potential difference would appear across the strip?

Given N = 8.4 x 10²⁸ electrons /m³.   (A.U. May 2015)

Given data

Solution

Note: This problem is important in the sense that it shows that Hall voltage can be also observed in metals besides semiconductor.

In semiconductors, Hall voltage is comparatively much larger; it is of the order of milli-volts as compared to the order of micro-volts in metals.

Moreover, to observe Hall voltage in metals, current of the order of amperes is needed when compared to the order of milliamperes as in the case of semiconductors.