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

2. Lecture 27, 04 Dec 12 Chp. 06: Carrier transport current contributions
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3. Review of Diffusion HW06 Prs. 6.3, 6.4, 6.7 involve diffusion
Review of diffusion taken from pp , Streetman and Banerjee, available on class website
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4. Expected behavior of a pulse of electrons generated at x = 0 & t = 0, over later times: t1, t2, t3….. -L L
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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
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6. Closer look at electrons spreading out in space over time
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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]
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8. fn(x) = Net electrons = ½(lbarA)[n1 – n2]
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
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9. Goal: re-cast n1 – n2 as a derivative:
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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:
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11. VM Ayres, ECE874, F12

12. Converting to diffusion current Jdiff:
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13. Review of drift:
HW06 Prs. 6.3 also involves mobility related to drift current
Review of drift taken from pp , Streetman and Banerjee, available on class website
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14. Force of the electric field on the electrons
Decelerations due to collisions
balance
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15. Can think of this as: the probability of staying un-scattered is
exponentially decreasing
Interval of time t  dt
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18. Use in Pr. 6.3
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19. Pr. 6.3:
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20. Review of Poisson’s equation:
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21. Example problem: Calculate r Sketch charge density and E (x) to scale5
Given
equilibrium (300K).
Calculate r
Sketch charge density and E (x) to scale
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22. Given:
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23. Find r: where is it?
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24. Find r: where is it: in the depletion region:
Where do you want to put the junction? W
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25. Find r: where is it: in the depletion region: on both sides
xp0
xn0 W
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26. Find r: charge density:
Also could do this directly:
r = qNA = q(1 x 1018)
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27. Find r: charge density:
Also could do this directly:
r = qND = q(5 x 1015)
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28. Sketch charge density and E (x) to scale
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29. Pr. 6. 7 (i): use a Taylor expansion Pr. 6
Pr. 6.7 (i): use a Taylor expansion Pr. 6.9 (e): use simple diagram way of getting E, similar to Pr. 4.11
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31. Steady state: Chp. 05: rN = rP versus equilibrium rN = 0 and rP = 0
BUT…
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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)
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