Description
The four probe method is a widely used laboratory technique for measuring the resistivity of semiconductors at different temperatures and determining the bandgap energy of the material.
Apparatus Description
The setup consists of four collinear spring-loaded probes mounted with equal spacing on a Teflon bush for electrical insulation.
A semiconductor sample, such as a germanium or silicon wafer, is placed on a heated platform or in an oven for temperature control.
Associated electronics include a constant current generator, micro- or millivoltmeter (to measure voltage), thermometer, and oven controller for varying sample temperature.
The arrangement avoids errors from probe contact resistance, making the measurement more accurate.
Measurement Procedure
Current is supplied through the outer two probes; the potential difference is measured across the inner two probes.
At each controlled temperature, voltage and current readings allow calculation of sample resistance and, using probe geometry, conversion to resistivity.
This process is repeated at multiple temperatures from room temperature up to 150–200°C.
Determination of Band Gap
Semiconductors exhibit exponential changes in resistivity with temperature, following:
ρ
(
T
)
=
A
exp
(
E
g
2
k
B
T
)
ρ(T)=Aexp(
2k
B
T
E
g
)
where
E
g
E
g
is the band gap energy,
k
B
k
B
the Boltzmann constant, and
T
T temperature.
A graph is plotted of
log
(
ρ
)
log(ρ) versus
1
/
T
1/T; the slope of this plot is proportional to the band gap energy (
E
g
E
g
), which can then be determined.
Applications
This method provides precise resistivity measurements and bandgap determination, fundamental for characterizing semiconductor properties and crucial in electronics/materials science research.
The four probe apparatus is standard in academic and industrial labs, offering reliable results even on small, thin samples.