ECE 874:Physical Electronics

Prof. Virginia AyresElectrical & Computer EngineeringMichigan State Universityayresv@msu.edu

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Lecture 27, 04 Dec 12

Chp. 06: Carrier transport current contributions

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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:

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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)