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 VM Ayres, ECE874, F12

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

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

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 VM Ayres, ECE874, F12

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

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 VM Ayres, ECE874, F12

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

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

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

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

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

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

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Use in Pr. 6.3 VM Ayres, ECE874, F12

Pr. 6.3: VM Ayres, ECE874, F12

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

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

Given: VM Ayres, ECE874, F12

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

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

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

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

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

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

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 VM Ayres, ECE874, F12

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

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