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Unformatted text preview: ECE 474: Principles of Electronic Devices Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University [email protected] Lecture 28:
Chp. 04: Current StateofArt Transistors
Photogenerated carriers
Find αr for “low level injection” Excess carriers Diffusion and Drift Current
Einstein’s relation Find builtin E(x) and n(x) Lecture 28:
Chp. 04: Current StateofArt Transistors
Photogenerated carriers
Find αr for “low level injection” Excess carriers Diffusion and Drift Current
Einstein’s relation Find builtin E(x) and n(x) Example in Lecture 25:
Try to evaluate the constant of proportionality for recombination The constant of proportionality for recombination is αr. (p. 125) Doped Si @ 300K: Doped Si @ 300K + laser light: Given: τn = τp = 1 µsec. Majority carrier concentration: n0 = 1017 cm3 Minority carrier concentration: p0 = 2.25 x 103 cm3 n p δn = 101 x 1017 cm3 => increase factor: 102 ≈ 100 x 1017 cm3 => increase factor: 1016 = gop τn = (1025 cm3 s1)(1 x 106 s) = 100 x 1017 cm3 = gop τn = 100 x 1017 cm3 δp How well did my example problem meet this criteria? Badly. Now we will consider the problem from a couple of different angles: Effect of recombination. Effect of low level of injection. New Example:
Find αr but change: gop = 1015 cm3 s1 Doped Si @ 300K: Doped Si @ 300K + laser light: Given: τn = τp = 1 µsec. n p δn = 1.0 x 1017 cm3 + 1.0 x 109 cm3 ≈ 1.0 x 1017 cm3 = 2.25 x 103 cm3 + 1.0 x 109 cm3 ≈ 1.0 x 109 cm3 = gop τn = (1015 cm3 s1)(1 x 106 s) = 1.0 x 109 cm3 = gop τn = 1.0 x 109 cm3 Majority carrier concentration: n0 = 1017 cm3 Minority carrier concentration: p0 = 2.25 x 103 cm3 δp “low level injection”:
Putting extra carriers into a region OTHER than by intrinsic (thermal) or extrinsic (doping) is called “injection”. Why NOT thermal and doping: because they leave a material NEUTRAL If the extra carrier concentrations are low compared with the thermal and doped concentrations, this is called “low level injection”. Check the levels of injection in the new example on the next page. New Example:
Find αr but change: gop = 1015 cm3 s1 Doped Si @ 300K: Doped Si @ 300K + laser light: Given: τn = τp = 1 µsec. n p δn = 1.0 x 1017 cm3 + 1.0 x 109 cm3 ≈ 1.0 x 1017 cm3 = 2.25 x 103 cm3 + 1.0 x 109 cm3 ≈ 1.0 x 109 cm3 = gop τn = (1015 cm3 s1)(1 x 106 s) = 1.0 x 109 cm3 = gop τn = 1.0 x 109 cm3 Low level injection of electrons
Majority carrier concentration: n0 = 1017 cm3 Minority carrier concentration: p0 = 2.25 x 103 cm3 δp YES YES, but our material is ntype Suppose p0 was not small by comparison. “A more general expression..” p. 126 Eq’n (48) This expression still requires δn2 = small = “low level injection of electrons” YES, but our material is ntype n0
αrn0  t / τn Different Example: Start by doing this: Minority carrier concentration: n0 = (2 x 106 cm3)2/1015 cm3 = 4 x 103 cm3 Majority carrier concentration: p0 = 1.0 x 1015 cm3 Start by doing this: δn(t=0) = Δn = gop τn = (gop cm3 s1)(1 x 108 s) = 1014 cm3 Minority carrier concentration: n0 = (2 x 106 cm3)2/1015 cm3 = 4 x 103 cm3 Majority carrier concentration: p0 = 1.0 x 1015 cm3 δp(t=0) = Δp = gop τn = 1014 cm3 n p = 4 x 103 cm3 + 1014 cm3 ≈ 1014 cm3 = 1.0 x 1015 cm3 + 1014 cm3 = 1.1 x 1015 cm3 This plot assumes low level injection for electrons, δn<< p0 ?
δn(t=0) = Δn = gop τn = (gop cm3 s1)(1 x 108 s) = 1014 cm3 Minority carrier concentration: n0 = (2 x 106 cm3)2/1015 cm3 = 4 x 103 cm3 Majority carrier concentration: p0 = 1.0 x 1015 cm3 δp(t=0) = Δp = gop τn = 1014 cm3 n p = 4 x 103 cm3 + 1014 cm3 ≈ 1014 cm3 = 1.0 x 1015 cm3 + 1014 cm3 = 1.1 x 1015 cm3 ? I don’t quite agree. Lecture 28:
Chp. 04: Current StateofArt Transistors
Photogenerated carriers
Find αr for “low level injection” Excess carriers Diffusion and Drift Current
Einstein’s relation Find builtin E(x) and n(x) Example from Lectures 26 and 27:
(Si @300K, Doping yes, laser light no) 2 different ntype doping concentrations together in the same block of Si. n0 = 1017 cm3 n0 = 1013 cm3 z y x ...
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This note was uploaded on 04/14/2009 for the course ECE 474 taught by Professor Ayres during the Spring '09 term at Michigan State University.
 Spring '09
 Ayres
 Transistor

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