Semiconductors and Diodes

The addition of small amount of foreign impurity in the host crystal is called as doping. It results in an increase in the electrical conductivity of the crystal. Doping of group 14 elements (such as Si, Ge etc.) with elements of group 15 (such as As) produces an excess of electrons in the crystals and thus, gives n-type semiconductors. Doping of groups 14 elements with group 13 elements (such as Indium) produces holes (electron deficiency) in the crystals. Thus, p-type semiconductors are produced. The symbol 'p' indicates flow of positive charge. Also, the band gap in germanium is small as Ge is a semi-conductor.

The addition of a small amount of foreign impurity in the host crystal is called doping. 

The addition of small amount of foreign impurity in the host crystal is called as doping. It results in an increase in the electrical conductivity of the crystal. Doping of group 14 elements (such as Si, Ge etc.) with elements of group 15 (such as As) produces an excess of electrons in the crystals, thus, giving n-type semiconductors. Doping of groups 14 elements with group 13 elements (such as Indium) produces holes (electron deficiency) in the crystals. Thus, p-type semiconductors are produced. The symbol 'p' indicates flow of positive charge. Positive holes are responsible for the semiconducting properties like conduction.

The electron concentration is much greater than the hole concentration, indicating an n-type semiconductor. Conductivity sigma = e(n * mu_n + p * mu_p). Computing sigma and taking its reciprocal gives the resistivity, which comes out to approximately 0.34 ohm-meter.

The band gap energy E = hc / lambda. Using h = 6.63e-34, c = 3e8, and lambda = 2480e-9 m, E = 1240 eV nm / 2480 nm = 0.5 eV.

In extrinsic semiconductors, formation of donor or acceptor level takes place in forbidden energy gap. Thus, some of the electrons in valance band acquire enough energy to jump to donor level or acceptor level present in forbidden energy gap. Thus, to obtain large number of electrons in conduction band some energy to be supplied to the electrons in valance band. For extrinsic semiconductors, it is nearly equal to $1\ eV$.

The energy bandgap of semiconductors tends to decrease as the temperature is increased.  the interatomic spacing increases when the amplitude of the atomic vibrations increases due to the increased thermal energy. This effect is quantified by the linear expansion coefficient of a material. An increased interatomic spacing decreases the potential seen by the electrons in the material, which in turn reduces the size of the energy bandgap. A direct modulation of the interatomic distance, such as by applying high compressive (tensile) stress, also causes an increase (decrease) of the bandgap.

Semiconductor materials have low but finite band gap energy, due to which there is an easy jump of electron from valence band to conduction band upon provision of external thermal energy.

The energy bandgap of semiconductors tends to decrease as the temperature is increased. This behaviour can be understood if one considers that the interatomic spacing increases when the amplitude of the atomic vibrations increases due to the increased thermal energy. This effect is quantified by the linear expansion coefficient of a material. An increased interatomic spacing decreases the potential seen by the electrons in the material, which in turn reduces the size of the energy bandgap. 

A band gap, also called an energy band, is an energy range in a solid where no electron states can exist. It generally refers to the energy difference (in electron volts) between the top of the valence band and the bottom of the conduction band in insulators and semiconductors. The energy band gaps of silicon and germanium are $1.1eV $ and $0.7eV$ respectively.

In case of a p-type semiconductor, the number of holes in valence band is grater then number of electrons in conduction band. hence, the probability of occupation of energy levels by the holes in valence band is greater than probability of occupation of energy levels by electrons in conduction band. This probability of occupation of energy levels is represented in terms of Fermi level.

The range of energy of the valence electrons of an atom is known as valence band. The range of energy in which an electron must exist in order to participate in the conduction of electricity is known as conduction band. The difference between the valence band and conduction band is known as band gap or energy gap. In conductors, the valence band overlaps with the conduction band. Which means, electrons are already ready for conduction and energy gap in a conductor is zero.

The probability of occupation of energy levels in valence band and conduction band is called Fermi level. As the temperature increases free electrons and holes gets generated. In intrinsic semiconductor, the number of holes in valence band is equal to the number of electrons in the conduction band. Hence, the probability of occupation of energy levels in conduction band and valence band are equal. Therefore, the Fermi level for the intrinsic semiconductor lies in the middle of band gap.

The energy gap of a semiconductor lies in between insulators and conductors. In case of conductors, band gap Eg $\sim 0$ eV. Whereas in case of insulators, Eg $\sim 3-4$ eV. So, Band gap in case of a semiconductor is of order $\sim 1$ eV.

The level formed due to impurity atom, in the forbidden energy gap, very near to the valency band in a p-type semiconductor is called an acceptor level.