Semiconductors Conduction Assignment Help

Condensed Matter Physics - Semiconductors Conduction

Semiconductors Conduction

The electrical conduction in semi-conductors is caused by the motion of the electrons in the conduction band and also by motion of the holes in the valence band.

When an electric field is applied across a semiconductor, the electrons in the conduction band travel in the opposite direction to that of the applied electric field and constitute a flow of electronic current (Ie). At the same time, the holes in the valence band travel in the direction of the applied electric field and constitute a hole current (Ih). It means there are two streams of current inside a semiconductor; namely the electronic current in the semiconductor band and the hole current in the valence band. The effective current (I) in the semiconductor is the sum of these two streams of current.

i.e. I = Ie + Ih

for a pure semiconductor at room temperature, the current strength is weak.

Formation of holes

This can be understood in two ways.

(i) From the energy band diagram of the semiconductor. In the energy band diagram of the semiconductor, there is an energy gap of about 1eV between the valence and the conduction band. At zero Kelvin, the semiconductor behaves as an insulator, as no electron from the valence band can cross this energy gap and go to the conduction band. But at higher temperature, some of the electrons gain energy due to thermal agitation and move from the valence band to the conduction band. As a result of it, a vacancy is created in the valence band at a place where the electron was present before moving to the conduction band, this valency is called a hole. Since the absence of a negatively charged electron is equilivalent to the presence of an equilivalent amount of positive charge, therefore, a hole is considered as a seat of positive charge, having charge equal to that of an electron. The hole is considered as an active particle in the valence band as an electron is in the conduction band. The motion of the electrons in 
he conduction band and also the motion of holes in the valence band are responsible for the electrical conduction in semiconductors.

(ii) From the valence band study of the semiconductor. Consider a semiconductor crystal of silicon or germanium under study. We know that the Si or Ge have four valence electrons. 

Every atom of Ge tends to share one of its four nearest neighbouring atoms, and also to take share of one electron from each such neighbour. This pair of shared electrons of two atoms of Ge is said to form a covalent bond or simply a valence bond. Thus four valence electrons of a Ge atom form four covalent bonds by sharing the electrons of neighbouring four Ge atoms. Due to which the Ge atoms in the structure are strongly held by covalent bonds not in a plane as it may appear here but in space of tetrahedral angles.

At low temperature, in a Ge crystal structure, the two shared electrons in a covalent bond can be assumed to shuttle back and forth between the associated atoms, holding them together strongly.

When the temperature of Ge is raised, the thermal atoms ionises only a few atoms in the crystalline lattice. Due to which few electrons contributing to covalent bonds break and become free to move in whole of the crystal lattice. While coming out of a covalent bond, the electron leaves an empty space which is having positive charge equal to that of the electron as an open circle. It is called a hole. An electron from a neighbouring atom can break away and can be attracted by the missing electron (or hole), thus completing the covalent bond and creating a hole at another place. In our two dimensional example, we see that an electron from any of four neighbouring atoms can come to complete the bond and hole can move to any of these atoms. It is to be noted that breakage of each covalent bond produces one free electron and one hole in a crystalline lattice.

In order to create the free electron and hole in a crystalline lattice a certain amount of ionization energy Eg would be involved. This ionization energy is least for Ge, more for Si and highest for C. theoretically, it is found that the number of free electrons (ne) or holes (nh) produced as a result of an ionization is given by

ne = nh = C e-Eg/2 kT

Where C is a constant, k is a Boltzmann constant and T is the absolute temperature T increases, ne increases. - Semiconductors Conduction Assignment Help, Semiconductors Conduction Homework Help, Semiconductors Conduction Assignment Tutors, Semiconductors Conduction Solutions, Semiconductors Conduction Answers, Condensed Matter Physics Assignment Tutors

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