Physics for Information Science: Unit I: Electrical Properties of Materials
Effect of Temperature on Fermi Function
The effect of temperature on Fermi function F (E) can be discussed with respect to equation (1)
EFFECT OF TEMPERATURE
ON FERMI FUNCTION
The
effect of temperature on Fermi function F (E) can be discussed with respect to
equation (1)
(I) At 0 Kelvin
At 0 kelvin, the electrons can be filled only upto a maximum energy level called Fermi energy (EF0), above EF0 all the energy levels will be empty. It can be proved from the following conditions.
(i) When E<EF,
equation (1) becomes
[i.e 100% chance for the electron to be filled
within the Fermi energy level]
(ii) When E> EF,
equation (1) becomes
[(i.e) Zero % chance for the electron not to
be filled within the Fermi energy level]
(iii) When E=EF,
equation (1) becomes
[(i.e) 50% chance for an electron to be filled
and not to be filled within the Fermi energy level]
This clearly shows that at 0 Kelvin all the energy states below EF0 are filled and all those above it are empty.
The
Fermi function at 0 kelvin (EF0) can also be represented graphically
as shown in Fig. 1.10. It is seen from the figure that the curve has step-like
character at 0 kelvin.
(i.e)
F (E) = 1 below EF0 and
and
F (E) = 0 above E EF0
(II) At any temperature T kelvin
When
the temperature is raised slowly from absolute zero, the Fermi distribution
function smoothly decreases to zero as shown in Fig. 1.11.
Explanation: Due
to the supply of thermal energy the electrons within the range of KBT
below the Fermi level (EF0) alone takes the energy =KBT
and goes to higher energy state. Hence at any temperature (T), empty states
will also be available below EF0.
Note: Electrons lying very deep (far
below) the Fermi energy level (EF0) will not go to excited state
Also
under classical limit
When KB T<< EF;
F(E) is said to be degenerate function.
KB T>>EF; F(E) is said to be Non-degenerate function.
Physics for Information Science: Unit I: Electrical Properties of Materials : Tag: : - Effect of Temperature on Fermi Function
Physics for Information Science: Unit I: Electrical Properties of Materials
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Physics for Information Science
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