Electrical Engineering ⇒ Topic : Graded Semiconductor and Its Potential Variation

Sunita
 
GRADED SEMICONDUCTOR AND ITS POTENTIAL VARIATION Consider a semiconductor bar shown in Figure (a) in which hole concentration is not uniform. This type of semiconductor bar is called graded semiconductor. Two points P_{1 }and P_{2} separated by a distance d have been considered. Let us calculate the potential difference V_{21} between these points
Figure (a) Semiconductor bar. Since net current is zero, ............. (1) where D_{p} is called diffusion constant for holes and its unit is m^{2}/s. Diffusion and mobility are not independent of each other and in fact are related by the Einstein relation. ................ (2) ...............(3) Using Eqs. (2) and (3), Eq. (3) can be obtained as:
............ (4) Equation (4) can also be written as: ................(5) Equation (5) is same as the Boltzmann relation in kinetic gas theory. Let us consider a PN junction diode as shown in Figure (b). Let the hole concentration at P_{1} be NA and the electron concentration at P_{2} be N_{D}. The hole concentration at P_{2} is, therefore, n_{i}^{2}/N_{D}.
Figure (b) PN junction diode. From Eq. (4), ............ (6) Equation (6) gives the barrier potential of the diode and it is denoted by the symbol V_{0}.  
 
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