1.
A bar of silicon with intrinsic electron density
1.4 x 10

^{16}electronics/m^{3}is doped with impurity atoms until the hole density is 8.5 x 10^{21}holes/m^{3}. The motilities of the electronics and holes are µ_{n}= 0.14 m^{2}/V-sec and µ_{p}= 0.05 m^{2}/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 10

^{16}electrons/m^{3}and the extrinsic hole density is 0.82 x 10^{11}holes/m^{3}? (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 10

^{19}holes/m^{3}and the extrinsic hole density is 7.85 x 10^{14}holes/m^{3}? Assume that all donor atoms are ionized.
4.
One cubic centimetre of silicon has been doped
with 1.8 x 10

^{14}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 10

^{18}holes/m^{3}, 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 10

^{20}electrons/m^{3}.
7.
A bar of P-type silicon at room temperature has
a majority carrier density of 7.62 x 10

^{22}carriers/m^{3}. Its cross sectional area is 2.4 x 10^{-6}m^{2}. 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}m^{2}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 10

^{7}germanium atoms, then find the conductivity of doped semiconductor.
10.
Find the ratio of conductivity of N-type silicon
doped with 1 in 10

^{8}silicon atoms to that of intrinsic silicon at room temperature.
11.
Find the conductivity of germanium, when doped
simultaneously with 1 donor in 10

^{6}Ge atoms and 1 acceptor atom in 10^{7}Ge atoms.
12.
Calculate the electron and hole concentrations
of extrinsic silicon sample, when the conductivity is minimum. Assume µ

_{n}= 1350 cm^{2}/V-sec and µ_{p}= 450 cm^{2}/V-sec.
13.
If the resistivity of P-type silicon bar is 0.12
Ω-cm, then find electron and hole concentrations per cm

^{3}.
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 m

^{3}.
15.
Find the change in resistivity of N-type
germanium with 1 donor per 10

^{9}germanium atoms to that of intrinsic germanium.
16.
A sample of germanium is doped to the extent of 2 x 10

^{14}donors/cm^{3}and 1.5 x 10^{14}acceptors/cm^{3}. 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 10

^{14}per cm^{3}and acceptor atom density of 0.5 x 10^{14}per cm^{3}. Determine the resultant densities of free electrons and holes per cm^{3}.
18.
Determine the concentration of free electrons
and holes in a sample of Ge at 300

^{o}K, which has a concentration of 2 x 10^{14}donors/cm^{3}and 3 x 10^{14}acceptors/cm^{3}.
19.
A sample of germanium is doped with 10

^{14}donors/cm^{3}and 7 x 10^{13}acceptors per cm^{3}. 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/cm^{2}.
20.
A cylindrically shaped section of N-type silicon
has 1 mm length and 0.1 mm

^{2}cross sectional area. Find the ratio of resistance of pure germanium to that of germanium doped with 8 x 10^{13}donors/cm^{3}.
21.
In an N-type germanium, the resistivity is
measured to be 10

^{-3}Ω-m, for an impurity concentration of 10^{22}donors/m^{3}. 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 300

^{o}K, if the doping concentration is 10^{16}donors/cm^{3}.
23.
A silicon sample is doped with 10

^{17}arsenic atoms/cm^{3}.
a.
Find equilibrium hole concentration P

_{o}at 300^{o}K.
b.
Find the relative position of Fermi level with
respect to intrinsic Fermi level.

24.
A silicon sample is doped with 6 x 10

^{15}donors/cm^{3}and 2 x 10^{15}acceptors/cm^{3}. Find the position of Fermi level with respect to intrinsic Fermi level at 300^{o}K.
25.
In an N-type semiconductor, if the Fermi level
lies 0.6 eV below conduction band at 300

^{o}K. Find the new position of Fermi level at 330^{o}K.
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 10

^{8}germanium atoms. Assume effective mass of electron is half of its true mass. At what doping level (N_{D}), Fermi level coincides with conduction band edge.
28.
A silicon sample is doped with 1 donor atom per
2 x 10

^{8}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 10

^{8}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 500

^{o}K, which has a concentration of donors equal to N_{D}= 1.874 x 10^{13}atoms/cm^{3}and of acceptor atoms equal to N_{A}= 3.748 x 10^{13}atoms/cm^{3}. Show that the sample is essentially intrinsic. Explain why.
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