Ideal

7. Ideal

8. Reverse Breakdown: What is this? Mechanisms that increase the reverse current much beyond the usual diffusion and/or recombination current(s). 1. (see Sze) Junction heating due to reverse current (this is usually not a problem except in narrow-gap semiconductors, where Eg is small or T is hight (and therefore Js is large), leading to significant power dissipation. Js increases exponentially with T, positive feedback 2. Tunneling: We looked at this earlier in the semester, but now the tunneling is from the valence band to the conduction band (at the same energy?!?) wT – tunneling distance m* - effective mass Eg – energy gap ħ – “h bar” “Zener” Tunneling Unless w is very small (a few nm)

9. wT – tunneling distance m* - effective mass Eg – energy gap ħ – “h bar” Depletion layer w=(2εV/qNB)1/2 Tunneling wT:

13. For short distances (small w) |Ɛbr|tunneling < |Ɛbr|avalanche and tunneling predominates. (high doping) For long distances (large w) |Ɛbr|tunneling > |Ɛbr|avalanche and avalanche predominates. (light doping)

15. General result for devices: For Vbr < 4 Eg/q, Tunneling (practically < 4.5-6V for silicon, depending on text) For Vbr > 6 Eg/q, Avalanche (practically > 6.5-8V for silicon) (both kinds now called Zener diodes) How can we distinguish these? Eg decreases with T, Tunneling Vbrdecreases with increasing T. Decreasing Eg should make avalanche easier, but higher T increases carrier scattering (remember those phonons!), so the end result is that Vbrincreases with increasing T in the case of Avalanche.

16. Slope?

33. A

40. What Next? • Heterojunctions • Nanotubes • Solar Cells, Photodetectors, LEDs and lasers. • MOSFET • BJT