Extrinsic semiconductors: Intrinsic semiconductors, to which some suitable impurity or doping agent or dopant has been added in extremely small amounts (about 1 part of 10⁸) are called extrinsic or impurity semiconductors.

The actual doping agents are:

Pentavalent atoms having five valence electrons like arsenic, antimony, phosphorous etc.

Trivalent atoms having three valence electrons like gallium, indium, aluminum, boron etc.

Pentavalent doping atoms are known as donor atom because it contributes or donates electrons to the conduction band of pure germanium. The trivalent atom on the other hand is called acceptor atom because it accepts one electron from germanium atoms.

Depending upon the type of impurity added, extrinsic semiconductors are classified into

1. n- type semiconductor.

2. p-type semiconductor.

They are also called doped or impure semiconductors. Germanium can be made extrinsic with the addition of a very small percentage of pentavalent elements like antimony, phosphorus, arsenic etc. The four valence electrons form covalent bonds with germanium atoms and fifth one moves freely and thus increases conductivity. These elements which thus provide excess, electrons are called 'donors' or n - type impurities. Hence the donor doped semi conductors have fewer number of holes because of more recombinations .

The impurities introduce the new energy level very near the conduction band.

When a trivalent impurity(boron, gallium or indium) is added to the semiconductor there is a vacancy in the form of a hole. These can accept electrons and such impurities are called acceptors or p-type impurities. Such impurities create a discrete energy level which is just above the valence band. Little energy is needed for the electron to leave the valence band and occupy the acceptor energy level. Thus doping with p-type impurities decreases the concentration of free electrons. Under thermal equilibrium the product of free negative and positive concentrations is a constant.

Fig 2.6 Energy Band Diagram N typeFig2.7 P type

n_p = n _i 2 (2.17 ) n_i is dependent on temperature

In an n-type semiconductors the majority carriers are electrons and minority carriers are holes. In p-type semiconductors it is just the reverse.

The general expression for current density in case of an extrinsic semiconductor when an electrical field is employed is given by

If it is an N-type semiconductor, then the above expression beomes

Where n_n and p_n represent the electron and hole densities in the N-type semiconductor after doping.

If it is a P-type semiconductor, then the expression is

where n_p and p_p represent similar quantities in P type semiconductor after doping. The conductivity is given by

In N-type semiconductors, electrons from the majority carriers although holes are also available in minority carriers. The current density in such a semiconductor is given by expression J_n. However since electron density in such extrinsic semiconductor is much more than hole density i.e n_n >> p_n, the above expressions are simplified into

In P type semiconductors, conduction is by means of holes in the valence land, which form majority carriers although electrons are available as minority carriers. Since in extrinsic semiconductors n_p << p_p, the above expression becomes

m _n = 0.05 m² V-s and e = 1.6 * 10^-19 c

being N type silicon, it is assumed that n>>>P.

s = e (n m _e + p m _n) = n_e m _e

r = 1 / (n_e m _e ) or 15 = 1/ (n x 1.6x 10^-19 x 0.14)

or h = 3.1 x 10²⁰ m^-3

n_p = n_i2 or r = n_i2 / h

= 2 x 10 ¹² m ^-3

Electrical properties of Germanium and Silicon

With increasing temperature, the conductivity increases

The energy gap is also temperature dependent

EG for Si = 1.1 eV

EG for Ge = 0.7.2 eV at room temperature

EG for Si at T

= EG(T)

= 1.21

Mobility is a function of temperature and electric field intensity