Elements of Modern Physics
314
8. If an element contains both electron and hole carriers, show that the Hall
coefficient is given by
R H =
2
2
2
(
)
h h
e e
h h
e e
n
n
e n
n
µ − µ
µ + µ
A material has 10
21
electrons/m
3
and 5 × 10
20
holes/m
3
. If µ e = 0.05 and
µ h = 0.07 in MKS units, evaluate the conductivity and the Hall coefficient
of the material.
9. Hall coefficient of A1 is – 0.3 × 10
–10
MKS units. How many conduction
electrons does each atom contribute?
10. The conductivity of germanium is 0.7Ω
–1
m
–1
at 0° C and 2Ω
–1
m
–1
at 20°C.
What is the energy gap for germanium?
11. A measurement of 0.1% change in resistivity is possible in a silicon crystal.
What is the sensitivity at room temperature of such a crystal used as a
thermistor?
12. What is the conductivity at room temperature of (i) pure silicon (ii) silicon
containing 10
–5
% of phosphorus? Mobility of electrons is 0.14m
2
/Vs, that
of holes is 0.05 m
2
/Vs and the number of charge carriers in pure silicon is
about 2 × 10
16
m
–3
, at room temperature.
13. A current of 10
–4
A flows when a forward bias of 0.2 V is applied at room
temperature. Obtain the currents if (i) forward bias of 0.4 V (ii) reverse
bias of 1 V, are applied.
14. Show that the width of the depletion region at a pn junction, when a forward
bias of V is applied, is given by
x =
1/ 2
0
0
2 (
)(
)
e
h
e h
n n V V
en n
κε
+
−
where V 0 is the equilibrium potential difference across the junction. What
is the width for a junction with n e = 10
22
m
–3
, n h = 10
22
m
–3
, κ = 14, V 0 = 0.7 V,
if a reverse bias of 2 V is applied?
15. Show that the product of electron and hole carriers is
n e n h = c 0
2
(m h *m e *T
2
)
3/2
exp [(ε v – ε c )/kT],
independent of the concentration of the impurity. Thus, if an n-type of
impurity is introduced, the number of holes decreases.
16. A silicon semiconductor is doped with 9 × 10
21
donors/m
3
and 4 × 10
21
acceptors/m
3
. If the electron mobility is 0.15 m
2
V
–1
s
–1
, estimate the
resistivity at room temperature.
314
8. If an element contains both electron and hole carriers, show that the Hall
coefficient is given by
R H =
2
2
2
(
)
h h
e e
h h
e e
n
n
e n
n
µ − µ
µ + µ
A material has 10
21
electrons/m
3
and 5 × 10
20
holes/m
3
. If µ e = 0.05 and
µ h = 0.07 in MKS units, evaluate the conductivity and the Hall coefficient
of the material.
9. Hall coefficient of A1 is – 0.3 × 10
–10
MKS units. How many conduction
electrons does each atom contribute?
10. The conductivity of germanium is 0.7Ω
–1
m
–1
at 0° C and 2Ω
–1
m
–1
at 20°C.
What is the energy gap for germanium?
11. A measurement of 0.1% change in resistivity is possible in a silicon crystal.
What is the sensitivity at room temperature of such a crystal used as a
thermistor?
12. What is the conductivity at room temperature of (i) pure silicon (ii) silicon
containing 10
–5
% of phosphorus? Mobility of electrons is 0.14m
2
/Vs, that
of holes is 0.05 m
2
/Vs and the number of charge carriers in pure silicon is
about 2 × 10
16
m
–3
, at room temperature.
13. A current of 10
–4
A flows when a forward bias of 0.2 V is applied at room
temperature. Obtain the currents if (i) forward bias of 0.4 V (ii) reverse
bias of 1 V, are applied.
14. Show that the width of the depletion region at a pn junction, when a forward
bias of V is applied, is given by
x =
1/ 2
0
0
2 (
)(
)
e
h
e h
n n V V
en n
κε
+
−
where V 0 is the equilibrium potential difference across the junction. What
is the width for a junction with n e = 10
22
m
–3
, n h = 10
22
m
–3
, κ = 14, V 0 = 0.7 V,
if a reverse bias of 2 V is applied?
15. Show that the product of electron and hole carriers is
n e n h = c 0
2
(m h *m e *T
2
)
3/2
exp [(ε v – ε c )/kT],
independent of the concentration of the impurity. Thus, if an n-type of
impurity is introduced, the number of holes decreases.
16. A silicon semiconductor is doped with 9 × 10
21
donors/m
3
and 4 × 10
21
acceptors/m
3
. If the electron mobility is 0.15 m
2
V
–1
s
–1
, estimate the
resistivity at room temperature.