How Doping Affects Band Structure

Band Structure Diagram

Introduction

Doping is the process of intentionally adding impurities (foreign atoms) to a semiconductor material to modify its electrical properties.
In terms of band structure, doping has a significant impact on the distribution of electrons and holes within the semiconductor.

In band structure diagrams, electrons in the conduction band are represented as dots, while holes in the valence band are depicted as circles.
The Fermi level, denoted as "Ef," represents the energy level at which there is a 50% probability of finding an electron.

In n-type semiconductors, impurity atoms introduce extra electrons into the crystal lattice.
The presence of these additional electrons shifts the Fermi level closer to the conduction band.
This proximity to the conduction band makes it easier for electrons to gain enough energy to move from the valence band to the conduction band.
The abundance of electrons in the conduction band results in enhanced electrical conductivity.

In p-type semiconductors, impurity atoms create holes in the crystal lattice by accepting electrons from neighbouring atoms.
The introduction of holes shifts the Fermi level closer to the valence band.
This proximity to the valence band makes it easier for holes to be created in the valence band.
The presence of holes in the valence band enhances the material's conductivity by allowing for the movement of positive charge carriers (holes).

Band Structure Diagram

The change in Fermi level ( $\Delta E_f$ ) due to doping can be calculated using the formula: $\Delta E_f = (kT/q) * \ln(N_d/N_i)$ , where:

k is Boltzmann's constant (8.617 x 10^-5 eV/K),
T is the absolute temperature (in Kelvin),
q is the charge of an electron (1.602 x 10^-19 C),
N_d is the concentration of acceptor atoms (in p-type) or donor atoms (in n-type),
N_i is the intrinsic carrier concentration of the semiconductor.

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Summary

Doping introduces impurities into a semiconductor, affecting its electrical properties.
In n-type semiconductors, additional electrons shift the Fermi level closer to the conduction band, enhancing electron conductivity.
In p-type semiconductors, holes are created, shifting the Fermi level closer to the valence band, allowing for hole conductivity.
The change in Fermi level due to doping can be mathematically calculated using the temperature and impurity concentrations.
Doping is a fundamental technique in semiconductor technology, enabling the design and fabrication of various electronic devices.