Tru Physics

Extrinsic Semiconductors

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Introduction

Extrinsic semiconductors are a specialized type of semiconductors that are chemically modified (or ‘doped’) to enhance their electrical conductivity. Unlike intrinsic semiconductors, which consist solely of one type of atom, extrinsic semiconductors have been intentionally doped with impurities to create a surplus of free charge carriers, either electrons or holes.

Doping Process

The process of doping involves the addition of a small amount of impurity atoms to the intrinsic semiconductor. Depending on the type of impurity, the extrinsic semiconductor can become either an n-type (negative) or a p-type (positive) semiconductor.

n-Type and p-Type Semiconductors

An n-type semiconductor is created by doping the intrinsic semiconductor with an element that has more valence electrons than the semiconductor. The extra electron from the dopant atom is loosely bound and can easily move to the conduction band, resulting in a higher concentration of free conduction electrons.

Conversely, a p-type semiconductor is created by doping the intrinsic semiconductor with an element that has fewer valence electrons. This introduces vacancies (or ‘holes’) in the valence band, resulting in a higher hole concentration.

Fermi Level and Carrier Concentration

In extrinsic semiconductors, the Fermi level (E_F), which is the energy level at which the probability of finding an electron is 50%, shifts towards the majority carriers’ energy band. In n-type, E_F moves closer to the conduction band, while in p-type, it shifts towards the valence band.

The carrier concentrations of n-type (n) and p-type (p) extrinsic semiconductors can be represented as:

n = N_D + \dfrac{N_c \exp((E_F - E_c) / kT)}{1 + \dfrac{N_c}{N_v} \exp((E_F - E_i) / kT)}

p = N_A + \dfrac{N_v \exp((E_v - E_F) / kT)}{1 + \dfrac{N_v}{N_c} \exp((E_i - E_F) / kT)}

where N_D and N_A are the donor and acceptor impurity densities respectively, N_c and N_v are the effective densities of states in the conduction and valence bands respectively, E_c and E_v are the energies at the bottom of conduction band and top of valence band respectively, E_i is the intrinsic Fermi level, k is Boltzmann’s constant, and T is the absolute temperature.

Conductivity in Extrinsic Semiconductors

Similar to intrinsic semiconductors, the conductivity (\sigma) of extrinsic semiconductors can be defined as:

\sigma = e(n\mu_e + p\mu_h)

where e is the charge of an electron, \mu_e and \mu_h are the mobilities of electrons and holes, respectively.

Application: Transistors and Diodes

Extrinsic semiconductors form the core of most electronic devices. In a transistor, an n-type or p-type region is sandwiched between two regions of the other type, forming a p-n-p or n-p-n configuration. Diodes consist of an interface between p-type and n-type semiconductors, allowing current flow in only one direction.

Conclusion

Extrinsic semiconductors are at the heart of modern electronics. Through the process of doping, we can carefully control the properties of these materials, making it possible to design and build an extraordinary array of electronic devices, from the simplest diodes to the most complex integrated circuits.

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