GATE Practice Problems on Intrinsic Semiconductors

Intrinsic Semiconductors :

1.       A potential difference of 12 volts is applied across the ends of the intrinsic silicon bar as shown below. Assume n_i = 1.5 x 10¹⁰ electrons/cm³, µ_n = 1400 cm²/V-sec and µ_p = 500 cm²/V-sec, find

a.       Electron and hole velocities

b.      Current density of electron and hole components

c.       Total current density

d.      Total current in the bar

e.      Conductivity and Resistivity of the bar

f.        Resistance of the bar

2.       A bar of silicon with intrinsic electron density of 1.4 x 10¹⁶ electrons/m³ is doped with impurity atoms until the hole density is 8.5 x 10²¹ holes/m³. The motilities of the electrons and holes are µ_n = 1400 cm²/V-sec and µ_p = 500 cm²/V-sec.

a.       Find the electron density of the extrinsic material.

b.      Is the extrinsic material is N-type or P-type?

c.       Find the extrinsic conductivity.

3.       What is the electron velocity and hole velocity in a silicon bar at room temperature, when an electric field intensity of 1800 V/m is established in it?

4.       Find electron mobility in a bar of intrinsic germanium 6 cm long has a potential difference of 12 volts applied across its ends. Assume the electron velocity in the bar is 73 m/s.

5.       A bar of intrinsic silicon 4.8 cm long has a potential difference of 60 volts applied across its ends. If the hole velocity in the bar is 77.5 m/s, what is the hole mobility?

6.       Find the hole and electron current densities, and total current density of a intrinsic silicon bar when applied electric field intensity is 500 V/m.

7.       Find the hole and electron current densities, and total current density of a intrinsic silicon bar if the electron and hole velocities are 130 m/s and 50 m/s.

8.       An intrinsic silicon bar has a cross sectional area of 3 x 10^-4 m². How long should the bar be in order that the current in it be 1.2 mA, when 9 volts is applied across its ends?

9.       An intrinsic germanium bar has 4 cm long. What should be the dimensions of the cross section if it is to be square in shape and if 3.2 mA are to flow in the bar when 60 volts potential difference is applied across its ends?

10.   Find the total resistance between ends A and B of the intrinsic germanium bar shown below.

 

11.   Find the conductivity of germanium at room temperature, if the mobility of electrons and holes are 3800 and 1800 cm²/V-sec respectively.

12.   Find the drift velocity of electrons and holes in a 1 mm length of intrinsic silicon bar at room temperature, if the applied voltage is 10 volts.

13.   If silicon was a monovalent metal, find the ratio of its conductivity to that of intrinsic silicon at room temperature.

14.   In a semiconductor, effective mass of electron is 0.07m and effective mass of hole is 0.4m, where m is mass of free electron. Assume average relaxation time for the holes is half that of electrons. Find the mobility of holes, if the mobility of electrons is 0.8 m²/V-sec.

15.   Find the electric field required to give an electron in silicon an average energy of 1 eV.

16.   For an intrinsic silicon of cross sectional area of 5 cm² and length of 0.5 cm, find the electron and hole component of current density, if the applied electric field is 20 V/cm.

17.   Find the displacement of E_Fi (intrinsic Fermi level) to the centre of forbidden band for silicon at room temperature. Assume effective mass values of electrons and holes are 1.2m and 0.56m respectively, where m is rest mass of electron.

18.   Find the temperature at which there is a 1% probability that a state with energy 0.2 eV above the Fermi level will be occupied by the electron.

19.   For germanium semiconductor, if the forbidden gap width is 0.67 eV, then the position of Fermi level at 300^oK, if the effective mass of hole is 5 times the effective mass of electron.

20.   If the effective mass of electron is 3 times the effective mass of hole, then find the relative distance of Fermi level in an intrinsic semiconductor from the centre of forbidden band at room temperature.

21.   Find the intrinsic carrier concentration of germanium at 400^oK.

22.       Find the resistivity of intrinsic silicon at 300oK. Also find the resistance, if the length of the bar is 5 cm and its cross section is 2 mm by 4 mm.

23.       Consider the intrinsic silicon at room temperature. By what percent does the conductivity increase per degree rise in temperature? Assume µ is independent of temperature T.

24.       Consider the intrinsic germanium at room temperature. By what percent does the conductivity increase per degree rise in temperature? Assume µ is independent of temperature T.