Discuss, with the help of a proper diagram. the

Question

measurement of carrier density, resistivity and ball
mobility by Van der Pauw·method.

Answer 1

The Van der Pauw method is a widely used technique for measuring carrier density, resistivity, and Hall mobility in semiconductor materials. It is based on the principle of measuring the resistance between four equidistant electrical contacts on a sample, which are typically arranged in a square or rectangular shape.

To understand the Van der Pauw method, let's consider a square sample with four electrical contacts labeled A, B, C, and D. A constant current is passed through contacts A and B, and the voltage is measured between contacts C and D. The current is then reversed and passed through contacts C and D, and the voltage is measured between contacts A and B. This process is repeated multiple times with different combinations of contact pairs.

By analyzing the measured voltage and current data for different contact configurations, the Van der Pauw method calculates the sheet resistance (Rs) and Hall coefficient (RHall) of the sample, which can be used to determine the carrier density, resistivity, and Hall mobility.

The Van der Pauw method utilizes a unique mathematical relationship between the resistance ratio and the sheet resistance, represented by the following equation:

exp(-π (R12+R34)/(Rs)) + exp(-π (R23+R41)/(Rs)) = 1,

where R12, R23, R34, and R41 are the resistances measured between the corresponding contact pairs.

By solving this equation, the sheet resistance (Rs) can be obtained. The carrier density (n) can then be calculated using the formula:

n = 1/(q * Rs)

where q is the electronic charge.

Finally, the resistivity (ρ) can be determined using the following equation:

ρ = Rs * t,

where t is the thickness of the sample.

Hall mobility (μH) can also be determined by measuring the Hall voltage (VH) and the magnetic field (B) applied perpendicular to the sample surface. The Hall mobility is given by:

μH = VH/(q * n * B),

where VH is the Hall voltage.

In summary, the Van der Pauw method uses a combination of electrical measurements and mathematical analysis to determine the carrier density, resistivity, and Hall mobility of a semiconductor sample. The method is widely used due to its simplicity and accuracy in characterization.