Solved Problems: 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 × 10¹⁶ m^–3. If the mobility of electron and hole are 0.13 and 0.05 m² V^–1 s^–1, calculate the conductivity.

3.         The Intrinsic carrier density at room temperature in Ge is 2.37 × 10¹⁹ m³ if the electron and hole mobilities are 0.38 and 0.18 m² V^–1 s^–1 respectively, calculate the resistivity.

4.The Hall coefficient of certain silicon specimen was found to be –7.35 × 10^–5 m³ 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 × 10¹⁹ m^–3density of boran 4.5 × 10²³ atoms /m³. The electron and hole mobility are 0.4 and 0.2 m² 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 m³ 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 × 10²² 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 m² v^–1 s^–1.

11. Hall coefficient of a specimen of depend silicon found to be 3.66 × 10^–4 m³ 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 × 10¹⁹ m^–3. The electron and hole mobilities are 0.4 and 0.2 m² V^–1 s^–1 respectively. Calculate the conductivity.

Solution:

13. The electron mobility and hole mobility in Si are 0.135 m² V^–1 s^–1 and 0.048 m² V^–1 s^–1 respectively at room temperature. If the carrier concentration is 1.5 × 10¹⁶ 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 × 10¹⁹ / m^–3 at 300 K and the mobility of electron and hole are 0.39 and 0.19 m² V^–1 S^–1. (Ans: 4.31 × 10³)

Calculate the position of Fermi level E_F and the conductivity at 300 K for germanium crystal containing 5 × 10²² arsenic atoms / m³. Also calculate the conductivity if the mobility of the electron is 0.39 m² V^–1 S^–1.

(Ans : E_F is 0.16 eV below E_c   = 3210 ^–1 m^–1)

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/m² 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)m³ / coulomb. (Ans : 29.4 V and 57.7 × 10^–4 m² V^–1)

The intrinsic carrier density at room temperature in Ge is 2.37 × 10¹⁹ m³. If the electron and hole motilities are 0.38 and 0.18 m² V¹ S¹ 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 0.12m₀ and m^*_h 0.28m₀ (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 m₀ .

(Ans : 33.49 × 10¹⁸ / m³)

A silicon plate of thickness 1mm, breadth 10mm, and length 100mm is placed magnetic field of 0.5 wb/m² 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 × 10⁶ C^–1 m³)

        A N-type semiconductor has Hall coefficient = 4.16 × 10^–4 C^–1 m³. The conductivity is 108 ohm^–1 m^–1. Calculate its charge carrier density and electron mobility at room temperature.    (Ans : 0.038 m² V^–1 S^–1)