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Assessment Task:
Kronig-Penney Model Engineering Assessment Answer

 

Questions

Kronig-Penney Model - Ge Crystal - Phosphorous Atoms - Fermi Energy - Engineering Assessment Answer Kronig-Penney Model - Ge Crystal - Phosphorous Atoms - Fermi Energy - Engineering Assessment Answer Kronig-Penney Model - Ge Crystal - Phosphorous Atoms - Fermi Energy - Engineering Assessment Answer

Long Answer and Problems

1. Give a qualitative description of the Kronig-Penney Model, referring to sketches of the potential energy diagram and the resultant E-k diagram. What is the most important result of this analysis? Use five complete, coherent sentences, along with your sketches.

2. A high quality Ge crystal has been grown with fewer than 10 parts per trillion impurity level.

a) Estimate by calculation the conductivity at room temperature (300K). Justify your calculation.

b) Estimate by calculation, the conductivity at 450K

c) If a region of the Ge was then implanted with 1 ppm (one part per million) phosphorous atoms, determine the electron concentration, hole concentration, and electrical conductivity in this region of the crystal. State any important assumptions

3. You have a metal sandwiched between silicon. On the left is n-type and on the right is p-type silicon. You want both interfaces to act as Schottky contacts.

a) Sketch the band diagram for this combination of materials when in contact. Show and label all important features: Fermi energy, conduction band edges, valence band edges, Schottky barriers. What is the magnitude of the Schottky contact potential on either side?

b) Now sketch the band diagrams for each of the three materials separately, being accurate about the relative locations of Fermi energy and magnitudes of work functions. Suggest a specific metal that may have been used to create these Schottky contacts on either side. Consult your textbook and cite the metal work function and the table from which it came.

4. A single crystal of silicon was grown with 1x1018 boron/cm3 . In subsequent processing, a region was implanted with 4x1018 phosphorous/cm3 , creating a p-n junction at the edge of this well-defined region. Assume a temperature of 300K and complete ionization of dopants. State Fermi energies with respect to the valence band edge, which is taken to be E=0 eV.

a) Calculate the Fermi energy external to the phosphorous-doped region. Is this p-type or n-type?

b) Calculate the Fermi energy within the phosphorous-doped region. Is this region p-type or n-type? (be sure to consider ³compensation doping´)

c) What is the contact potential of this junction?

d) Carefully (using a ruler) sketch the equilibrium flat band diagram for this junction (no bias applied). Be sure to indicate proper location of the Fermi energy throughout, and indicate the magnitude of the contact potential.

 

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  • Posted on : December 17th, 2018
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