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Till now we have studied classical diodes. Classical diodes are fabricated using non-degenerate semiconductor. Doping of 10 ^{17} /cc or less is non-degenerate semi-conductor. Doping in the range of 10 ^{18} /cc or more gives rise to degenerate semi-conductor.
In non-degenerate semi-conductors we have drift and diffusion of carriers. In degenerate semi-conductor apart from drift and diffusion we have band-to-band tunneling which is a purely quantum-mechanical transport mechanism.
I have talked about Quantum Mechanical tunneling in Chapter 1, Part 8. We will briefly review it in this Section.
An electron in an infinite potential well can never come out of the potential well. Electron in finite potential well with thick potential wall can come out of the potential well if by photon excitation or by thermal excitation it gains sufficient energy to cross the surface potential barrier and escape into vacuum above 0 eV energy level. These processes are known as Photoionic-emission or Thermoionic-emission. But there is a third case where the electron is trapped in a potential well with thin potential walls. The potential walls are as thin as 10A° to 100A° as shown in the Figure ( ) in Chapter 1 Part8 .In this case there is a finite probability of finding the electron outside the potential well by the process of tunneling.
The Tunneling factor is calculated to be:
Substituting the values of the different parameters, the values of Tunneling Factor is tabulated in Table 3.3.1.
Table 3.3.1.Qunatum Mechanical Tunneling Ratio for different Wall thickness and different Barrier Potential.
W | (qV _{1} -E) | Exponent term | T | Comments |
---|---|---|---|---|
10A° | 1eV | -10.2463 | 3.5×10 ^{-5} | With 10A° wall thickness and 1eV well depth there is a very low probability of finding 3.5 electron in 100,000 electrons. |
5A° | 1eV | -5.12317 | 6×10 ^{-3} | With wall thickness reduced to 5A° but well depth kept constant tunneling increases to 6 out of 1000electrons. |
1A° | 1eV | -1.02463 | 0.36 | With wall thickness reduced to 1A° but depth well kept constant tunneling increases to 36% . |
1A° | 10eV | -3.24018 | 0.04 | With wall thickness kept at 1A° but depth well increased to 10eV tunneling again decreases to 4% . |
1A° | 100eV | -10.2463 | 3.5×10 ^{-5} | With wall thickness kept at 1A° but depth well increased to 100eV tunneling drastically decreases to . 3.5 electron in 100,000 electrons. |
As the doping density is increased we encounter 4 different classes of devices:
The I-V characteristics of these four diodes are shown in Figure 3.19.
We are considering an abrupt Si-diode with symmetrical N-type and P-type doping. Therefore the the built-in potential is given by the following formula:
Depletion Width (d) is given by the following fomula:
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