Question

1-Draw the 1s probability densitu function with respect to distance. What happen when two 1S electrons from different atoms interact?

2-Briefly explain how Kronig-Penny Model can be used to explain the existence of band structure

3-Using E-K graph explain what direct and indirect bandgap is

4-Expain how the Fermi-Dirac distribution change from 0K to 100K.

5-Explain why the number of intrinsic hole and electron are similar in the intrinsic semiconductor

6- Explain how PN junction is formed

7- State Poisson equation and explain how the voltage across an PN-junction can be derived

8- Where is the capacitance for a diode coming from?

Answer 1

2.

3. The E-k diagram of a direct bandgap semiconductor such as GaAs. The E-k curve consists of many discrete points each point corresponding to a possible state, wavefunction y k(x), that is allowed to exist in the crystal. The points are so close that we normally draw the E-k relationship as a continuous curve.

In the above E-k Diagram, we get the Valency and Conduction band shapes for every k (K is the wave number which is directly proportional to momentum and E is the total Energy).

If we define the energy band gap as the distance between the maximum point of the Valency band(VB) and the minimum point of the Conduction band(CB), we have one of two cases:

a. The max of the VB is directly under the min of the CB: This is called a direct badn gap material.

b. The max of the VB is not directly under the min of the CB: This is called an indirect band gap material.

4.

The Fermi-Dirac probability density function provides the probability that an energy level is occupied by a Fermion which is in thermal equilibrium with a large reservoir. Fermions are by definition particles with half-integer spin (1/2, 3/2, 5/2 ...).

At absolute zero temperature (T = 0 K), the energy levels are all filled up to a maximum energy which we call the Fermi level. No states above the Fermi level are filled. At higher temperature one finds that the transition between completely filled states and completely empty states is gradual rather than abrupt.

5.

5.

above igure shows that for an intrinsic semiconductor (without impurities), each electron in the conduction band is associated with a hole in the valence band. We conclude that the electron and hole densities are equal in intrinsic semiconductor.

6. P-n junctions are formed by joining n-type and p-type semiconductor materials, as shown below. Since the n-type region has a high electron concentration and the p-type a high hole concentration, electrons diffuse from the n-type side to the p-type side. Similarly, holes flow by diffusion from the p-type side to the n-type side. If the electrons and holes were not charged, this diffusion process would continue until the concentration of electrons and holes on the two sides were the same, as happens if two gasses come into contact with each other.