ECE 874:Physical Electronics
Prof. Virginia AyresElectrical & Computer EngineeringMichigan State [email protected]
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Lecture 27, 04 Dec 12
Chp. 06: Carrier transport current contributions
VM Ayres, ECE874, F12
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
Review of Diffusion
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Expected behavior of a pulse of electrons generated at x = 0 & t = 0, over later times: t1, t2, t3…..
-L L0
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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
Closer look at electrons spreading out in space over time
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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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Definition of electron flux n(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
n(x) = Net electrons = ½(lbarA)[n1 – n2]
Area tbar
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Goal: re-cast n1 – n2 as a derivative:
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Now plug n1 – n2 back in to re-cast n(x) as a derivative:
And take the limit as x becomes very small: x -> 0:
VM Ayres, ECE874, F12
VM Ayres, ECE874, F12
Converting to diffusion current Jdiff:
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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
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balance
Force of the electric field on the electrons
Decelerations due to collisions
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Can think of this as: the probability of staying un-scattered isexponentially decreasing
Interval of time t dt
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VM Ayres, ECE874, F12
VM Ayres, ECE874, F12
Use in Pr. 6.3
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Pr. 6.3:
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Review of Poisson’s equation:
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Example problem:
5
Givenequilibrium (300K).
Calculate
Sketch charge density and E (x) to scale
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Given:
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Find : where is it?
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Find : where is it: in the depletion region:
Where do you want to put the junction?
W
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Find : where is it: in the depletion region: on both sides
W
xp0 xn0
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Find : charge density:
Also could do this directly: = qNA = q(1 x 1018)
VM Ayres, ECE874, F12
Find : charge density:
Also could do this directly: = qND = q(5 x 1015)
VM Ayres, ECE874, F12
Sketch charge density and E (x) to scale
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Pr. 6.7 (i): use a Taylor expansion
Pr. 6.9 (e): use simple diagram way of getting E, similar to Pr. 4.11
VM Ayres, ECE874, F12
VM Ayres, ECE874, F12
Steady state: Chp. 05: rN = rP versus equilibrium rN = 0 and rP = 0
BUT…
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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)