### GATE Practice Problems on Extrinsic Semiconductors

1.       A bar of silicon with intrinsic electron density 1.4 x 1016 electronics/m3 is doped with impurity atoms until the hole density is 8.5 x 1021 holes/m3. The motilities of the electronics and holes are µn = 0.14 m2/V-sec and µp = 0.05 m2/V-sec.
a.       Find the electron density of the extrinsic material.
b.      Is the extrinsic material N-type or P-type?
c.       Find the extrinsic conductivity.

2.       How many free electrons are in one cubic inch of N-type silicon, if the intrinsic electron density is 1.5 x 1016 electrons/m3 and the extrinsic hole density is 0.82 x 1011 holes/m3? (one inch = 2.54 cm). Assume that all donor atoms are ionized.

3.       How many free electrons are in a bar of extrinsic germanium measuring (4 mm) x (50 mm) x (1.5 mm) if the intrinsic hole density is 2.4 x 1019 holes/m3 and the extrinsic hole density is 7.85 x 1014 holes/m3? Assume that all donor atoms are ionized.

4.       One cubic centimetre of silicon has been doped with 1.8 x 1014 atoms of arsenic. What are the electron and hole densities in the doped material? Assume that all impurity atoms are ionized.

5.       Find the current density in extrinsic semiconductor at room temperature, whose hole density is 4.5 x 1018 holes/m3, when an 8 kV/m electric field intensity is established in it?

6.       Find the total current in the extrinsic silicon bar shown below at room temperature, if the electron density in the bar is 2.6 x 1020 electrons/m3

7.       A bar of P-type silicon at room temperature has a majority carrier density of 7.62 x 1022 carriers/m3. Its cross sectional area is 2.4 x 10-6 m2. How long should the bar be in order to have a resistance between its ends of 8.2Ω?

8.       A bar of silicon 0.1 cm long has a cross sectional are of 8 x 10-8 m2 and is heavily doped with phosphorous. What should be the majority carrier density if the bar is to have a resistance of 1.5 kΩ? Assume room temperature.

9.       If donor impurity is added to the extent of 1 impurity atom in 107 germanium atoms, then find the conductivity of doped semiconductor.

10.   Find the ratio of conductivity of N-type silicon doped with 1 in 108 silicon atoms to that of intrinsic silicon at room temperature.

11.   Find the conductivity of germanium, when doped simultaneously with 1 donor in 106 Ge atoms and 1 acceptor atom in 107 Ge atoms.

12.   Calculate the electron and hole concentrations of extrinsic silicon sample, when the conductivity is minimum. Assume µn = 1350 cm2/V-sec and µp = 450 cm2/V-sec.

13.   If the resistivity of P-type silicon bar is 0.12 Ω-cm, then find electron and hole concentrations per cm3.

14.   A 1kΩ resistor is to be fabricated using a P-type silicon bar with 4 mm thick, 20 µm wide and 400 µm long. Find the required acceptor concentration per m3.

15.   Find the change in resistivity of N-type germanium with 1 donor per 109 germanium atoms to that of intrinsic germanium.

16.   A sample of germanium is doped to the extent of  2 x 1014 donors/cm3 and 1.5 x 1014 acceptors/cm3. At a temperature of sample, the resistivity of pure germanium is 80 Ω-cm. Find the total current density if the applied electric field is 5 V/cm.

17.   A block of silicon is doped with a donor atom density of 3 x 1014 per cm3 and acceptor atom density of 0.5 x 1014 per cm3. Determine the resultant densities of free electrons and holes per cm3.

18.   Determine the concentration of free electrons and holes in a sample of Ge at 300oK, which has a concentration of 2 x 1014 donors/cm3 and 3 x 1014 acceptors/cm3.

19.   A sample of germanium is doped with 1014 donors/cm3 and 7 x 1013 acceptors per cm3. At temperature of the sample, the resistivity of pure germanium is 60 Ω-cm.  Assume mobility of electron is equal to mobility of hole. Find the applied electric field if the total current density is 52.3 mA/cm2.

20.   A cylindrically shaped section of N-type silicon has 1 mm length and 0.1 mm2 cross sectional area. Find the ratio of resistance of pure germanium to that of germanium doped with 8 x 1013 donors/cm3.

21.   In an N-type germanium, the resistivity is measured to be 10-3 Ω-m, for an impurity concentration of 1022 donors/m3. Find the values of mobility and relaxation time of electron.

22.   Calculate the position of Fermi level relative to intrinsic Fermi level in silicon at 300oK, if the doping concentration is 1016 donors/cm3.

23.   A silicon sample is doped with 1017 arsenic atoms/cm3.
a.       Find equilibrium hole concentration Po at 300oK.
b.      Find the relative position of Fermi level with respect to intrinsic Fermi level.

24.   A silicon sample is doped with 6 x 1015 donors/cm3 and 2 x 1015 acceptors/cm3. Find the position of Fermi level with respect to intrinsic Fermi level at 300oK.

25.   In an N-type semiconductor, if the Fermi level lies 0.6 eV below conduction band at 300oK. Find the new position of Fermi level at 330oK.

26.   In an N-type semiconductor, Fermi level lies 0.02 eV below conduction band edge. If the donor concentration is increased by 4 times, find the new position of Fermi level.

27.   A germanium sample is doped with 1 phosphorous atom per 108 germanium atoms. Assume effective mass of electron is half of its true mass. At what doping level (ND), Fermi level coincides with conduction band edge.

28.   A silicon sample is doped with 1 donor atom per 2 x 108 silicon atoms. Assume effective mass of electron is same as its true mass. Find the temperature, at which Fermi level coincides with conduction band edge.

29.   How much donor impurity should be added to pure germanium, so that its resistivity drops to 10% of its original value?

30.   Find the concentration of holes and electrons in P-type germanium at room temperature, if the resistivity is 0.02 Ω-cm.

31.   Find the resistivity if a donor type impurity is added to the extent of 1 atom per 108 germanium atoms.

32.   A donor type impurity is added and the resistivity decreases to 9.6 Ω-cm.  Compute the ratio of donor atoms to silicon atoms per unit volume.

33.   Determine the concentration of free electrons and holes in a sample of silicon at 500oK, which has a concentration of donors equal to ND = 1.874 x 1013 atoms/cm3 and of acceptor atoms equal to NA = 3.748 x 1013 atoms/cm3. Show that the sample is essentially intrinsic. Explain why.