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Physics - Semiconducting Materials - Important Solved Problems(Sum): Semiconducting Materials

**SOLVED PROBLEMS**

1.**Calculate the intrinsic
concentration of charge carriers at 300 K given that m ^{*}_{e}
=0.12m _{o} ,m ^{*}_{h} =0.28m_{o} and the
value of brand gap = 0.67 eV. Solution:**

*Given:*

**2.The intrinsic carrier density is 1.5 × 10 ^{16}
m^{–3}. If the mobility of electron and hole are 0.13 and 0.05 m^{2}
V^{–1} s^{–1}, calculate the conductivity.**

**3.** **The Intrinsic carrier density at room temperature in Ge is 2.37 × 10 ^{19}
m^{3} if the electron and hole mobilities are 0.38 and 0.18 m^{2}
V^{–1} s^{–1} respectively, calculate the resistivity.**

**4.The Hall coefficient of certain silicon
specimen was found to be –7.35 × 10 ^{–5} m^{3} C^{–1}
from 100 to 400 K. Determine the nature of the semiconductor. If the
conductivity was found to be 200 ^{–1} m^{–1}. Calculate the
density and mobility of the charge carrier. **

**Solution:**

**5. In a P-type germanium, n _{i} = 2.1 ×
10^{19} m^{–3}density of boran 4.5 × 10^{23} atoms /m^{3}.
The electron and hole mobility are 0.4 and 0.2 m^{2} v^{–1} s^{–1}
respectively. What is its conductivity before and after addition of boron
atoms.**

**6. An N-type semiconductor has hall coefficient
= 4.16 × 10 ^{–4} m^{3} C^{–1}. The conductivity is 108 ^{–1}
m^{–1}. Calculate its charge carrier density ‘n_{e}’and
electron mobility at room temperature.**

**Solution:**

*Given:*

**7. In an N-type semiconductor, the
concentration of electron is 2 × 10 ^{22} m^{–3} . Its electrical
conductivity is 112 ^{–1} m^{–1}. Calculate the mobility of
electrons.**

**8.** **For an intrinsic Semiconductor with a band gap
of 0.7 eV, determine the position of EF at T = 300 K if m*h = 6m*e.**

**9.A semiconducting crystal with 12 mm long, 5
mm wide and 1 mm thick has a magnetic density of 0.5 Wbm ^{–2} applied
from front to back perpendicular to largest faces. When a current of 20 mA
flows length wise through the specimen, the voltage measured across its width
is found to be 37μV . What is the
Hall coefficient of this semiconductor?**

**Solution:**

*Given:*

**10. Find the resistance of an intrinsic Ge rod
1 mm long, 1 mm wide and 1 mm thick at 300 K. the intrinsic carrier density 2.5
×1019 m ^{–3} is at 300 K and the mobility of electron and hole are 0.39
and 0.19 m^{2} v^{–1} s^{–1}.**

**11. Hall coefficient of a specimen of depend
silicon found to be 3.66 × 10 ^{–4} m^{3} C^{–1}. The
resistivity of the specimen is 8.93 × 10^{–3} m. Find the mobility and
density of the charge carriers.**

**12. The intrinsic carrier density of a
semiconductor is 2.1 × 10 ^{19} m^{–3}. The electron and hole
mobilities are 0.4 and 0.2 m^{2} V^{–1} s^{–1}
respectively. Calculate the conductivity. **

**Solution:**

**13. The electron mobility and hole mobility in
Si are 0.135 m ^{2} V^{–1} s^{–1} and 0.048 m^{2}
V^{–1} s^{–1} respectively at room temperature. If the carrier
concentration is 1.5 × 10^{16} m^{–3}. Calculate the
resistivity of Si at room temperature.**

**ASSIGNMENT PROBLEMS**

1. Find the resistance of an intrinsic germanium
rod 1 cm long, 1mm wide and 1mm thick at 300 K. the intrinsic carrier density
is 2.5 × 10^{19} / m^{–3} at 300 K and the mobility of electron
and hole are 0.39 and 0.19 m^{2} V^{–1} S^{–1}. **(Ans: 4.31 × 10 ^{3})**

Calculate the position of
Fermi level E_{F} and the conductivity at 300 K for germanium crystal
containing 5 × 10^{22} arsenic atoms / m^{3}. Also calculate
the conductivity if the mobility of the electron is 0.39 m^{2} V^{–1}
S^{–1}.

**(Ans : E _{F} is 0.16 eV below E_{c} = 3210**

In a Hall experiment a
current of 25 A is passed through a long foil of silver which is 0.1mm thick
and 3cm wide. If the magnetic field of flux density 0.14 Wb/m^{2} is
applied perpendicular to the foil, calculate the Hall voltage development and
estimate the mobility of electrons in silver. The conductivity the Hall
coefficient is (–8.4 × 10^{–11})m^{3} / coulomb. **(Ans : 29.4 V and 57.7 × 10 ^{–4}**

The intrinsic carrier density
at room temperature in Ge is 2.37 × 10^{19} m^{3}. If the
electron and hole motilities are 0.38 and 0.18 m^{2} V^{1} S^{1}
respectively, calculate the resistivity.

**(Ans : 0471** **m)**

5. For silicon semiconductor with band gap1.12
eV, determine the position of the Fermi level at 300 K, if m^{*}_{e}
0.12m_{0} and m^{*}_{h} 0.28m_{0} **(Ans : 0.576 eV)**

For an intrinsic
semiconductor with gap width E_{g} = 0.7 eV, calculate the
concentration of intrinsic charge carriers at 300 K assuming that m^{*}_{e}
m^{*}_{h} m_{0} .

**(Ans :
33.49 × 10 ^{18} / m^{3})**

A silicon plate of thickness
1mm, breadth 10mm, and length 100mm is placed magnetic field of 0.5 wb/m^{2}
acting perpendicular to its thickness. If A 10^{–2} current flows along
its length, calculate the Hall voltage developed if the Hall coefficient is
3.66 × 10–4 m3 / coulomb. **(Ans : 3.7 ×
10 ^{6}**

**
**A N-type
semiconductor has Hall coefficient = 4.16 × 10^{–4} C^{–1} m^{3}.
The conductivity is 108 ohm^{–1} m^{–1}. Calculate its charge
carrier density and electron mobility at room temperature. **(Ans
: 0.038 m ^{2} V^{–1} S^{–1})**

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