Continuity Equation

Assignment 1 (Numerical)

Q1

In an N-type semiconductor, the Fermi level is 0.3 eV below the conduction level at a room temperature of 300 K. If the temperature is increased to 360 K, determine the new position of the Fermi level.

Q2

In a P-type semiconductor, the Fermi level is 0.3 eV above the valance band at a room temperature of 300 K. Determine the new position of the Fermi level for temperatures of (a) 350 K and (b) 400 K.

Q3

In a P-type semiconductor, the Fermi level lies 0.4 eV above the valence band. Determine the new position of Fermi level if the concentration of acceptor atoms is multiplied by a factor of (a) 0.5 and (b) 4. Assume kT = 0.025 eV.

Q4

The electron and hole mobility of Silicon are 0.17 m²/Vs and 0.035 m²/Vs respectively at room temperature. If the current density is known to be 1.1x10¹⁶ per cubic meter, calculate the resistivity of silicon.

Assignment 1 (Theory)

1.   Draw the energy level diagram of hydrogen atom explaining all the associated spectral series. Also, give the expression for the wavelength associated with each series.

2.     Explain the significance of thermal voltage.

3.     Differentiate between conductor, semiconductor and insulator.

4.     Explain in detail the formation of energy bands in solids?

5.     Distinguish between direct and indirect band gap semiconductors.

6.     Compare the properties of intrinsic and extrinsic semiconductors.

7.     Differentiate between Drift and Diffusion currents?

8.     Explain the effect of temperature on extrinsic semiconductor?

9.     What are the factors which can affect the resistivity of semiconductors?

10. Define the following terms: Doping, Diffusion, Donor, Acceptor, Collision Time, Relaxation Time, Mean Free Path.

11.  Define the Fermi Dirac Function. Explain the Fermi level in a semiconductor having impurities.

12.  Compare the properties of Silicon and Germanium. Why Si is preferred over Ge.

13.  What is mass action law? Also, explain law of electrical neutrality.

14.  Derive an expression for the concentration of free holes in valence band in an intrinsic semiconductor.

15.  Show that the Fermi level of an intrinsic semiconductor lies much closed to the middle of the band gap. How does the intrinsic carrier density depend upon the band gap?

16.  How does the position of Fermi level changes with doping and temperature. Obtain the expression for the position of Fermi level in extrinsic semiconductors (both P-type and N-type).

17.  Define the term Carrier Lifetime. Explain how the hole density changes in an N-type semiconductor due to generation and recombination kept under illumination with necessary expressions.

18.  Establish from first principles, the continuity equation, valid for transport of carriers in a semi-conductor.