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ECE 874: Physical Electronics

ECE 874: Physical Electronics. Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu. Lecture 27, 04 Dec 12 Chp. 06: Carrier transport  current contributions. Review of Diffusion. HW06 Prs. 6.3, 6.4, 6.7 involve diffusion

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ECE 874: Physical Electronics

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  1. ECE 874:Physical Electronics Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu

  2. Lecture 27, 04 Dec 12Chp. 06: Carrier transport current contributions VM Ayres, ECE874, F12

  3. Review of Diffusion HW06 Prs. 6.3, 6.4, 6.7 involve diffusion Review of diffusion taken from pp. 134-136, Streetman and Banerjee, available on class website VM Ayres, ECE874, F12

  4. Expected behavior of a pulse of electrons generated at x = 0 & t = 0, over later times: t1, t2, t3….. -L 0 L VM Ayres, ECE874, F12

  5. Closer look at electrons spreading out in space over time Break distance into average chunks lbar More technically, lbar is the distance an electron can go between scattering events: the mean free path VM Ayres, ECE874, F12

  6. Closer look at electrons spreading out in space over time VM Ayres, ECE874, F12

  7. Accurate description: Electrons moving right: ½(n1lbarA) Electrons moving left: ½(n2lbarA) Therefore: the net number of electrons moving from x = 0 to, for example, x = L is: Net electrons = ½(lbarA)[n1 – n2] VM Ayres, ECE874, F12

  8. Definition of electron flux fn(x): net number of electrons moving from x = 0 to x = L per time The right time to use is the average time between scattering events: the mean free time: tbar fn(x) = Net electrons = ½(lbarA)[n1 – n2] Area tbar VM Ayres, ECE874, F12

  9. Goal: re-cast n1 – n2 as a derivative: VM Ayres, ECE874, F12

  10. Now plug n1 – n2 back in to re-cast fn(x) as a derivative: And take the limit as Dx becomes very small: Dx -> 0: VM Ayres, ECE874, F12

  11. VM Ayres, ECE874, F12

  12. Converting to diffusion current Jdiff: VM Ayres, ECE874, F12

  13. Review of drift: HW06 Prs. 6.3 also involves mobility related to drift current Review of drift taken from pp. 98-100, Streetman and Banerjee, available on class website VM Ayres, ECE874, F12

  14. Force of the electric field on the electrons Decelerations due to collisions balance VM Ayres, ECE874, F12

  15. Can think of this as: the probability of staying un-scattered is exponentially decreasing Interval of time t  dt VM Ayres, ECE874, F12

  16. VM Ayres, ECE874, F12

  17. VM Ayres, ECE874, F12

  18. Use in Pr. 6.3 VM Ayres, ECE874, F12

  19. Pr. 6.3: VM Ayres, ECE874, F12

  20. Review of Poisson’s equation: VM Ayres, ECE874, F12

  21. Example problem: 5 Given equilibrium (300K). Calculate r Sketch charge density and E (x) to scale VM Ayres, ECE874, F12

  22. Given: VM Ayres, ECE874, F12

  23. Find r: where is it? VM Ayres, ECE874, F12

  24. Find r: where is it: in the depletion region: Where do you want to put the junction? VM Ayres, ECE874, F12 W

  25. Find r: where is it: in the depletion region: on both sides xp0 xn0 VM Ayres, ECE874, F12 W

  26. Find r: charge density: Also could do this directly: r = qNA = q(1 x 1018) VM Ayres, ECE874, F12

  27. Find r: charge density: Also could do this directly: r = qND = q(5 x 1015) VM Ayres, ECE874, F12

  28. Sketch charge density and E (x) to scale VM Ayres, ECE874, F12

  29. Pr. 6.7 (i): use a Taylor expansionPr. 6.9 (e): use simple diagram way of getting E, similar to Pr. 4.11 VM Ayres, ECE874, F12

  30. VM Ayres, ECE874, F12

  31. Steady state: Chp. 05: rN = rP versus equilibrium rN = 0 and rP = 0 BUT… VM Ayres, ECE874, F12

  32. Steady state: Chp. 05: rN = rP versus equilibrium rN = 0 and rP = 0 Steady state: Chp. 06: dn/dt = dp/dt = 0 Useful in Pr. 6.9 (g) VM Ayres, ECE874, F12

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