1.A silicon wafer that has 10^16 cm^-3of boron is found to have a neutral vacancy concentration of 2*10^10 cm^-3at some processing temperature and a singly ionized vacancy concentration of10^9 cm^-3at the same temperature. Determine the temperature and the activation energy of thecharged vacancy with respect to the intrinsic level,Ei.

2.It is desired to form a denuded zone 10 um thick using an 1100 C anneal. How long will theanneal need to be? What will the oxygen concentration be in the denuded zone?

3.If the temperature gradient in Czochralski silicon is 100fC/cm,calculate the maximum pull rate.

4.A boule of single crystal silicon is pulled from the melt in a Czochralski process. The silicon isboron doped. After the boule is pulled,it is sliced into wafers. The wafer taken from the top ofthe boule has a boron concentration of 3*10^15 cm^-3. What would you expect for dopingconcentration of the wafer taken from the position corresponding to 90% of the initial chargesolidified?

5.A boule of silicon is pulled from a melt that contains 0.01% phosphorus (P) in the melt.

(a)What concentration of phosphorus (P) would you expect at the top of the boule (X=0)?

(b)If the boule is 1 m long and has a uniform cross section,at what position (or Xvalue)would you expect the concentration of phosphorus to be twice as large as it is atthetop?

(c)Now consider the melt to contain gallium as well. (Gallium is a p-type dopant for silicon,but it is not commonly used.) The concentration of gallium in the melt is such that at thetop of the boule (X=0),the concentrations of gallium and phosphorus are exactly equal.If the concentration of gallium near the bottom of the boule (X=0.9) is twice that of thephosphorus,what is the segregation coeffcient (k) for gallium?