Hi can someone show me a band theory diagram for an intrinsically pure semi conductor at absolute zero?

Question

It's form my electrical science exam in a week.

Thanks!

Answer 1

This format of answering does not seem to support diagrams! I'll provide you with a table of energy gaps 'E(g)' for selected semi-conductors at T=0 K and energy versus wave vector equations for typical band structures.

Energy gaps of selected semiconductors

material ....... E(g) ev T = 0 K  or E(0)

Si ............... 1.17

Ge .............  0.75

PbS ............ 0.29

PbSe .......... 0.17

PbTe .......... 0.19

InSb ........... 0.23

GaSb ......... 0.79

AlSb .......... 1.6

InAs ........... 0.43

At room temperature most band gaps, of semiconductors, have a linear variation with temperature, given by: -

E(g) = E(0) - AT  

The electronic properties of semiconductors are completely determined by the comparatively small numbers of electrons excited into the conduction band and the holes left behind in the valance band. The electrons will be found almost exclusively in levels near the conduction band minima, while the holes will be confined to the neighbourhood of the valance band maxima. Therefore the energy versus wave vector relations for the carriers can generally be approximated by the quadratic form: -

ε(k) = ε(c) + ħ²| k₁²  + k₂² + k₃² |

.....................| __ .... __ .... __ ... | (electrons)

.................... |m₁² . m₂² . m₃² |

ε(k) = ε(v) - ħ²| k₁²  + k₂² + k₃² |

....................| __ .... __ .... __ ... | (holes)

....................|m₁² . m₂² . m₃² |

Where 'ε(c)' is the energy at the bottom of the conduction band and 'ε(v)' is the energy at the top of the valance band. The origin of k-space is set to lie at the band maximum or minimum. If there exists more than one maximum or minimum, there will be one such term for each point so that there are a set of orthogonal  principle axis( for each such point).

For silicon.

The crystal has the diamond structure, so the first Brillouin zone is the truncated octahedron appropriate to a face centred Bravais lattice. The conduction band has six symmetry related minima at points in the <100> directions, about 80 % of the way to the zone boundary. by symmetry each of the six ellipsoids must be an ellipsoid of revolution about a cube axis. They are quite cigar shaped, being elongated along the axis. There are two degenerate valance band maxima, both located at k = 0.

For germanium.

The crystal structure is that of silicon but the conduction band minima occur at the zone boundaries in the <111> directions.

I hope this is of some help!