To determination of the band-gap of the semiconductor using the four probe method.
In a crystalline solid as a result of interaction between tremendous numbers of atoms in the crystal the energy levels are split up and form bands of allowed energy which contains almost continuum of levels. The band which contains the valence electrons is called the valence band. The unoccupied energy levels also split up and form another band called conduction band. These energy bands are separated by a gap of forbidden energy termed as the band-gap.
The electrical conductivity in a semiconductor will be the sum of the contribution of both electron and holes. In general, it is given by the expression:
The factor T3/2 and mobility change relatively slow with T as compared to the exponential term and hence the log of resistivity r(1/s) varies linearly with 1/T.
Thus we can write:
Method used for determination of resistivity is referred to as the four-probe method. Four sharp probes are placed on a flat surface of the material to be measured, current (I) is passed through the two outer electrodes, and the floating potential (V) is measured across the inner pair. The resistivity ro of the material is measured by the expression,
Since the thickness of the crystal is small compared to the probe distances a correction factor for it has to be applied. Further the bottom surface is non-conducting in the present case, hence we can write:
The function G7(w/s) here is given by G7(0.050/0.200) or 5.89. Hence
Distance between the probes(s) = 0.200cm
Thickness of the crystal (w) = 0.050 cm
- Table for determination of determination of the resistivity of the semiconductor:
Current (I) = …..mA (constant).
K = 8.6 x 10-5 eV/deg & T is the temperature in Kelvin