01-02-2013, 12:29 PM
ENERGY BANDS AND EFFECTIVE MASS
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Semiconductors, Insulators and Metals
The electrical properties of metals and insulators are well known to all of us.
Everyday experience has already taught us a lot about the electrical properties of metals and insulators.
But the same cannot be said about “semiconductors”.
What happens when we connect a battery to a piece of a silicon;
would it conduct well ? or
would it act like an insulator ?
The Band Theory of Solids
The electrons surrounding a nucleus have certain well-defined energy-levels.
Electrons don’t like to have the same energy in the same potential system.
The most we could get together in the same energy-level was two, provided thet they had opposite spins. This is called Pauli Exclusion Principle.
The difference in energy between each of these smaller levels is so tiny that it is more reasonable to consider each of these sets of smaller energy-levels as being continuous bands of energy, rather than considering the enormous number of discrete individual levels.
Each allowed band is seperated from another one by a forbidden band.
Electrons can be found in allowed bands but they can not be found in forbidden bands.
Semiconductor energy bands at low temperature
At low temperatures the valance band is full, and the conduction band is empty.
Recall that a full band can not conduct, and neither can an empty band.
At low temperatures, s/c’s do not conduct, they behave like insulators.
The thermal energy of the electrons sitting at the top of the full band is much lower than that of the Eg at low temperatures.
Conduction Electron :
Assume some kind of energy is provided to the electron (valence electron) sitting at the top of the valance band.
This electron gains energy from the applied field and it would like to move into higher energy states.
This electron contributes to the conductivity and this electron is called as a conduction electron.
At 00K, electron sits at the lowest energy levels. The valance band is the highest filled band at zero kelvin.
Conclusions
Holes contribute to current in valance band (VB) as e-’s are able to create current in conduction band (CB).
Hole is not a free particle. It can only exist within the crystal. A hole is simply a vacant electron state.
A transition results an equal number of e- in CB and holes in VB. This is an important property of intrinsic, or undoped s/c’s. For extrinsic, or doped, semiconductors this is no longer true.
[attachment=49215]
Semiconductors, Insulators and Metals
The electrical properties of metals and insulators are well known to all of us.
Everyday experience has already taught us a lot about the electrical properties of metals and insulators.
But the same cannot be said about “semiconductors”.
What happens when we connect a battery to a piece of a silicon;
would it conduct well ? or
would it act like an insulator ?
The Band Theory of Solids
The electrons surrounding a nucleus have certain well-defined energy-levels.
Electrons don’t like to have the same energy in the same potential system.
The most we could get together in the same energy-level was two, provided thet they had opposite spins. This is called Pauli Exclusion Principle.
The difference in energy between each of these smaller levels is so tiny that it is more reasonable to consider each of these sets of smaller energy-levels as being continuous bands of energy, rather than considering the enormous number of discrete individual levels.
Each allowed band is seperated from another one by a forbidden band.
Electrons can be found in allowed bands but they can not be found in forbidden bands.
Semiconductor energy bands at low temperature
At low temperatures the valance band is full, and the conduction band is empty.
Recall that a full band can not conduct, and neither can an empty band.
At low temperatures, s/c’s do not conduct, they behave like insulators.
The thermal energy of the electrons sitting at the top of the full band is much lower than that of the Eg at low temperatures.
Conduction Electron :
Assume some kind of energy is provided to the electron (valence electron) sitting at the top of the valance band.
This electron gains energy from the applied field and it would like to move into higher energy states.
This electron contributes to the conductivity and this electron is called as a conduction electron.
At 00K, electron sits at the lowest energy levels. The valance band is the highest filled band at zero kelvin.
Conclusions
Holes contribute to current in valance band (VB) as e-’s are able to create current in conduction band (CB).
Hole is not a free particle. It can only exist within the crystal. A hole is simply a vacant electron state.
A transition results an equal number of e- in CB and holes in VB. This is an important property of intrinsic, or undoped s/c’s. For extrinsic, or doped, semiconductors this is no longer true.