Which of the following statements about electrical resistivity (𝜌) is correct?

• Resistivity is inversely proportional to conductivity.

• Resistivity decreases with increasing temperature in semiconductors.

• Metals have higher resistivity than insulators.

• Resistivity is dependent on the shape of the material.

In the four-point probe method, what is the primary advantage over the two-point probe method?

• It eliminates contact resistance effects.

• It allows measurement of magnetic properties.

• It works only for thin films.

• It does not require an applied current.

The Van der Pauw method is best suited for measuring resistivity in which type of sample?

• Cylindrical metallic rods

• Large bulk semiconductor wafers

• Irregularly shaped, homogeneous thin films

• Insulating polymers

In the Van der Pauw method, why must the contacts be placed at the perimeter of the sample?

• To minimize voltage measurement errors

• To ensure current flows through the center of the sample

• To allow the material to remain in equilibrium

• To prevent edge effects from altering conductivity

In Hall effect measurements, what information does the sign of the Hall voltage provide?

• The resistivity of the material

• The carrier concentration of the material

• The type of charge carrier (electrons or holes)

• The mobility of charge carriers

If a semiconductor sample exhibits a negative Hall voltage when subjected to a perpendicular magnetic field, what does this indicate?

• The material has no free charge carriers.

• The dominant charge carriers are electrons (n-type).

• The dominant charge carriers are holes (p-type).

• The material is an insulator.

What is the primary use of the Hall mobility (\( \mu \)) in semiconductor characterization?

• To determine the material's bandgap energy

• To measure the speed at which charge carriers move in an electric field

• To determine the thickness of thin films

• To identify the crystal structure of the material

Which of the following materials would most likely exhibit a large Hall effect?

• A highly conductive metal like copper

• A heavily doped semiconductor

• An insulator with no free carriers

• A material with low mobility and low carrier concentration

What is the primary limitation of the four-point probe method when measuring bulk materials?

• It cannot measure highly resistive materials.

• It assumes a uniform current distribution, which may not be valid for thick samples.

• It requires a high magnetic field for accurate results.

• It only works for insulating materials.

In the Van der Pauw method, why is it necessary to take multiple resistance measurements using different contact pairs?

• To determine if the material has an anisotropic resistivity.

• To ensure that the contacts remain at a constant temperature.

• To compensate for external electromagnetic interference.

• To measure the Hall voltage in addition to resistivity.