Semiconductors, and semiconductor devices

“ Anything that's computerized or uses radio waves depends on semiconductors. ”

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Semiconductors Clockwise from top: A chip, an LED and a transistor are all made from semiconductor material. Header Date of Notes April 3rd April 6th Century Other Blah

A semiconductor is a material that has electrical conductivity between that of a conductor and that of an insulator.

Semiconductors

In the band theory of solids the highest occupied energy band is known as the valence band, while the lowest unoccupied band is known as the conduction band. At absolute zero, the valence band is completely full and the conduction band is empty. These bands are usually separated by a gap of order 1eV. The behavior of a semiconductor is dominated by electrons in states close to the top of the valence band and the bottom of the conduction band. Since we are dealing with states close to a maximum or minimum energy we can take the dispersion curve $\epsilon (k)$ to be parabolic to a good approximation. Therefore for the conduction band we have

$\epsilon _{c}=E_{G}+{\frac {\hbar ^{2}k^{2}}{2m_{e}}}$

and for the valence band

$\epsilon _{v}=-{\frac {\hbar ^{2}k^{2}}{2m_{h}}}$

where $E_{G}$ is the gap energy and $m_{h}$ is the mass of a hole. A hole is a fictitious particle created when an electron jumps from the valence band to the conduction band at some finite temperature.

To figure out the energy of a hole we consider a valence band with just one electron missing.SEE FIG 5.1/5.2 IN HOOK & HALL

$\Delta \epsilon =\epsilon _{c}-\epsilon _{v}\!$

$\Delta \epsilon =E_{G}+{\frac {\hbar ^{2}k^{2}}{2m_{e}}}-(-{\frac {\hbar ^{2}k^{2}}{2m_{h}}})$

$\Delta \epsilon =(E_{G}+{\frac {\hbar ^{2}k^{2}}{2m_{e}}})+{\frac {\hbar ^{2}k^{2}}{2m_{h}}}$

The first term in the parentheses is the energy of an electron in the conduction band. Therefore, the second term is the energy required to create the hole.

$\epsilon _{h}={\frac {\hbar ^{2}k^{2}}{2m_{h}}}$

Holes can also carry current because they have charge $+e$, however they travel in the opposite direction of an electron.

Doping

Doping is where ions of one substance are placed onto a lattice of another. Doping contributes electrons to a donor that go into a bound state just under the conduction band. This bound state is known as the impurity band. These electrons can then be excited into the conduction band.

Semiconductor Devices

A chip, an LED and a transistor are all made from semiconductor material.

MOSFET

Metal Oxide Semiconductor Field Effect Transistor