GATE Practice Problems - Hall Effect

1.       Find the magnitude of the Hall voltage V_H in an N-type silicon bar used in given figure, which has a majority carrier concentration N_D = 10¹³/cm³. Assume B_z = 0.2 Wb/m², d = 5 mm and ε_x = 5 V/cm.

 

2.       Find the magnitude of the Hall voltage V_H in an P-type silicon bar used in given figure, which has a majority carrier concentration N_A = 10¹²/cm³. Assume B_z = 0.2 Wb/m², d = 5 mm and ε_x = 5 V/cm.

3.       The Hall effect is used to determine the mobility of holes in a P-type silicon bar used in figure shown. Assume the bar resistivity is 2,00,000 Ω-cm, the magnetic field B_z = 0.1 Wb/m², and d = w = 2 mm. The measured values of the current and Hall voltage are 5 µA and 30 mV. Find mobility of holes.

 

 

4.       An N-type silicon bar whose resistivity is 1000 Ω-m is used in the figure shown, with w = 1 cm. If the current is 10 µA and the Hall voltage is 40 mV, what is the intensity B_z of the applied magnetic field?

 

5.       The hole concentration in a semiconductor specimen is shown below.

a.       Find an expression for and sketch the hole current density J_p(x) for the case in which there is no externally applied electric field.

b.      Find an expression for and sketch the built in electric field that must exist, if there is to be no net hole current associated with the distribution shown.

c.       Find the value of the potential between the points x = 0 and x = W, if P(0)/ P_o = 10³.

 

6.       Let the Hall effect could not be observed in a germanium sample, whose conduction electron mobility is 2.1 times that of holes. Find the ratio of conduction electron and hole concentrations.

7.       A germanium sample is oriented normal to 0.5 Tesla magnetic field, when a current of 1 mA is passed through it by applying a potential difference of 400 mV. Calculate Hall voltage, if concentration of majority carriers = 5.2 x 10¹⁹/m³, L = 2 cm and w = d = 1 cm.

8.       In the Hall effect experiment, a P-type semiconductor bar of width 1 cm and length of 5 cm is placed in the magnetic field of 0.5 Tesla. A potential difference of 10 volts is applied across the edges. Given V_H = 0.05 volts, σ = 2.5 x 10^-2 Ω-cm.

a.       Determine Hall coefficient, R_H.

b.      Concentration of holes, N_A.

c.       Hole mobility, µ_p.

9.       A P-type silicon semiconductor  bar with resistivity 3,00,000 Ω-cm is placed in a transverse magnetic field of 0.1 Wb/m² and d = w = 6 mm. If the measured values of current flowing through and Hall voltage are 10 µA and 60 mV respectively, find mobility of holes.

10.   A sample of silicon is doped with 10¹⁷ phosphorous atoms/cm³. Find the Hall voltage, if the sample has 100 µm thick, I_x = 1 mA and B_z = 10^-5 Wb/m²?