Question

5. (20 points) A Silicon sample contains a small amount (1018 atoms/cm) of phosphorous (P) impurity. (a) What is the majority charge carrier at room temperature? (b) Calculate the resistivity of this material at room temperature. Please show any assumption used in calculation. The mobility of this charge carrier is 700 cm /Vs at room temperature. (e) Show schematically the temperature effects on the mobility, concentration and conductivity of this semiconductor. 6. (20 points) For Mºsc, show schematically (a) the band structures of metal and p- type semiconductor before contact and (b) how they will be changed after contact. (c) For both schematics, clearly label Er. (d) Also, on the diagram for after contact, please indicate the barrier using a bold line and label "depletion region". 7. (20 points) (a) What voltage is required to develop a charge of 2.5 x 108 C on two capacitor plates 20mm x 20mm separated by 0.01mm of (1) vacuum and (2) Nylon? (b) Will the Nylon survive the field? Justify (using the calculation) your answers. The relative permittivity (8,) of Nylon is 4. The dielectric strength of Nylon is 240 kV/cm.

Answer 1

Q1)a) phosphorus have one electron more than the silicon.so When the pentavalent atoms such as Phosphorus or Arsenic are added to the intrinsic semiconductor, an n-type semiconductor is formed. ... Hence, free electrons are the majority charge carriers in the n-type semiconductor.

B)c)mobility dependance on temperature in extrimsic semiconductor is now concentration:

now conductivity:

Again the conductance of a semiconductor is

For an intrinsic material, we know that

Combing these two equations yields

We can once again ignore the T3/2 variation, which will be mostly negligible compared with the exponential temperature variation. Thus a plot of ln(σ) vs 1/T will have a slope of –Eg/2k, which yields a value for Eg.

In the case of doped semiconductors, we note that at high temperatures they are intrinsic in behaviour and become pseudo-intrinsic at low temperature, with and energy gap equal to the gap between the impurity level and the band edge. Therefore on a plot similar to the one mentioned above we would expect two straight-line regions with different slopes. In the region between these slopes the temperature is high enough to ionize the donors fully but not high enough to ionize an appreciable number of electrons from the lattice. Hence, in this temperature rage the carrier density will not be greatly influenced by temperature and the in mobility that were previously neglected will determined .

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