Part A: Explain why holes are found at the top of the valence band, whereas electrons are found at the bottom of the conduction band.
Part B: Explain why Si doped with Sb is n-type at 400K but similarly doped Ge is not.
When we apply electric field, the electrons in the otherwise empty conduction band (if no field applied) will move in the opposite of the electric field. Similarly the created holes in the otherwise filled valence band will move in the direction of the field.
The hole's energy will decrease with the increase of the electron's energy (reverse proportionally), the two carriers have opposite charge, thus the holes will seek the lowest energy state available (top of the valence band). Similarly electrons in the conduction band will rearrange so that they take the lowest energy states available (bottom of the condcution band).
It is all due to the different intrinsic carrier contentrations for Ge and Si at the same temperature of 400 K. The intrinsic carrier concentration as a function of the temperature according to |STREETMAN| is:
In accordance with the graph for intrinsic carrier concentrations for Ge, Si and GaAs as a function of inverse temperature in |STREETMAN| (Fig. 3.17) we can see that at 400 K:
- Ge has intrinsic carrier concentration
- Si has intrinsic carrier concentration
Antimony (Sb), is from group V and for Si and Ge both doped with , we can see that extrinsic carriers from Sb will be dominating ( ) in Si, resulting to an n-type semiconductor. Ge has an intrinsic carrier concentration much larger than the amount of dopant ( ), this doping will not be enough to create an n-type semiconductor, according to the definitions.