ECE305: Spring 2018 Exam 2 Review


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1 ECE305: Spring 018 Exam Review Pierret, Semiconductor Device Fundamentals (SDF) Chapter 3 (pp ) Chapter 5 (pp ) Professor Peter Bermel Electrical and Computer Engineering Purdue University, West Lafayette, IN USA pbermel@purdue.edu /13/018 Bermel ECE 305 S18 1
2 Key topics to review Minority carrier diffusion equation Band structures PN junctions /13/018 Bermel ECE 305 S18
3 Semiconductor equations: key cases p t D p d p dx p t p G L /13/018 Bermel ECE 305 S18 3
4 How to solve (some) Exam problems Step 1: From material information (semiconductor, doping, etc.), calculate carrier densities, Fermi level, etc. Start with the majority carriers, =, =. Then get the other carrier from = Step : Use banddiagram to calculate potential profile, electric field, = /, or = /, and =, etc. For homogenous semiconductor with a battery attached, = /. Step 3: Decide if this is driftrelated problem (resistivity, velocity, mobility, etc.), or a diffusion related problem (light turning onoff, etc.) Step 4A: For a driftproblem use = +. For, you may be given a number, or table, or diffusion coefficient, etc. Learn how to read such a table. Step 4B: For a diffusion problem, read carefully for clues to simplify the minority carrier equation. /13/018 Bermel ECE 305 S18 4
5 How to solve equations Step 4B: Two general types of minority diffusion problem. i) Determine if electron or the hole is the minority carrier. ii) If holes are the minority carriers, write the equation: p t D p d p dx p t p G L iii) iv) If steadystate, drop the timederivative. If transient, keep the time derivative. If spatially uniform, drop the diffusion term. Without light, drop the generation term. If the region is very short, drop the recombination term. Choose the solutions from the following table. Use the boundary conditions to complete solution. /13/018 Bermel ECE 305 S18 5
6 How to solve equations Transient p t D p d p dx p t p G L Steady State =, 0 = d Δ + Δ solution Δ = G + Boundary condition for B: Concentration before light was turned on? solution Δ = + + If, Δ = + + BC to determine A and B: Concentration at leftmost and rightmost points /13/018 Bermel ECE 305 S18 6
7 eq. energy band diagram E F E F 1) Begin with E F ) Draw the Ebands where you know the carrier density 3) Electrostatic potential by flipping Eband upside down. 4) Efield from slope 5) n(x), p(x) from the Eband diagram 6) rho(x) from n(x) and p(x) 7) diffusion current from (5) or from (6) E C x E C ref qv x E x 1 q de C x dx /13/018 Bermel ECE 305 S18 7
8 energy band diagram E E C x E C qv x E C E F E i E V de C x dx q dv x dx qe x x n x 0 x x p x /13/018 Bermel ECE 305 S18 8
9 Shortcut to Banddiagram Neutral Space Charge Neutral ND N A Vacuum level 1 E C E V E F /13/018 is equivalent to solving the Poisson equation Bermel ECE 305 S18 9
10 pn Junction Devices Symbols N A N P N D Finding hotspot /13/018 Bermel ECE 305 S18 10
11 What is a Diode good for.? solar cells GaAs lasers Organic LED Avalanche Photodiode GaN lasers image.google.com /13/018 Bermel ECE 305 S18 11
12 carrier densities vs. x log 10 nx,log 10 px n 0N N D p 0P N A p 0N n i N D n 0 p n i N A N x n x p x P /13/018 Bermel ECE 305 S18 1
13 the depletion approximation N r r qn D P de dx r x K S e 0 x n x p x r qn A d V Se 0 D A K q p n N N dx N D x n N A x p /13/018 Bermel ECE 305 S18 13
14 Depletion Regions in Homojunctions Neutral N Space Charge D N A Neutral x n x p N D x n N A x p x n kse 0 q N D N A N N V A D bi qv bi qndx qn n Ax k e k e s p 0 s 0 x p kse 0 q N A ND N N V A D bi Can you solve the same problem for a heterojunction? 14 /13/018 Bermel ECE 305 S18
15 Key results for PN junctions é W K Se 0 ê ë q E é 0 ê ë qv bi K s e 0 N A N D VN D N A V bi V ù bi ú û N D N A N A N D ù ú û 1/ 1/ E 0 V bi W ( ) N E x n x p x P W x n x P x n N A N A N D W V bi k T B q ln N N D A n i N D x n N A x P x p N D N A N D W /13/018 Bermel ECE 305 S18 V x x p ò x E x dx 15
16 Builtin Potential: heterojunctions qv bi 1 1 E g, qv bi E g, 1 1 qv i E 1 1 b g, N N E N AND k T ln 1 N N e A D g, kbt ln kbt ln 1 NV, NC, 1 B E g, / k B V, C, 1 T /13/018 Bermel ECE 305 S18 16
17 Interface Boundary Conditions: heterojunctions D E = (D/kεo) x n x n x p x p position position D K e E(0 ) K e E(0 ) D E K K (0 ) E(0 ) Displacement is continuous across the interface, but field need not be.. /13/018 Bermel ECE 305 S
18 equilibrium eband diagram E qv bi E C E F V A 0 I 0 E F E V W x x n /13/018 Bermel ECE 305 S18 18 x p
19 eband diagram under forward bias E V A 0 E C E F V bi V A V 0 V A > 0 E V W x x n The applied voltage drops across the junction, but /13/018 Bermel ECE 305 S18 x p 1
20 QFL s split E V 0 E C F n V bi V A V A > 0 F n > F p qv A F p E V W x x n /13/018 Bermel ECE 305 S18 x p
21 eband diagram under reverse bias E V bi V A V bi V R V 0 E C F p V A < 0 F n F n < F p E V W /13/018 x 3 p x n x
22 onesided junction N E x V A < 0 P N D >> N A x n x p >> x n V A > 0 x p x /13/018 Bermel ECE 305 S18 4
23 key points (onesided NP junctions) V bi k T B q ln N N D A n i é W K Se 0 ê ë qn A V bi V A ù ú û 1/ W µ V bi V A W µ 1 N A E 0 V bi V A W E 0 µ V bi V A E 0 µ N A /13/018 Bermel ECE 305 S18 5
24 Applying a Bias: Poisson Equation qv bi E C E F E F E V q(v bi V) qv E C F n F p E V /13/018 Bermel ECE 305 S18 6
25 Flat QuasiFermi Level up to Junction E C E V E C J n J p E V /13/018 Bermel ECE 305 S18 7
26 One Sided Minority Diffusion Can calculate current anywhere, let us solve the problem where it is the easiest q(v bi V) Steady state Acceptor doped dj n 1 n r n t q dx g n V F p E V J n qn E n dn qdn dx 0 n d n D dx /13/018 Bermel ECE 305 S18 8
27 Boundary Conditions n( x 0 ) n e p( x 0 ) n e i i ( F E ) n ( F E ) p i i n(0 ) n(0 ) n(0 ) n N i A V e G qv A 1 V G 0 ( Fn Fp ) i i np n e n e qv A p(0 ) N A q(v bi V A ) ni qva n(0 ) e N A V A F p F n N A /13/018 Bermel ECE 305 S18 9
28 Right Boundary Condition n( x W ) i n( x W ) 0 p p n N A E C V E V /13/018 Bermel ECE 305 S18 30
29 Example: One Sided Minority Diffusion d n 0 D dx N n( x, t) C Dx V /13/018 x W, n( x W ) 0 C DW p p p ni 0', ( 0) qv 1 A x n x e C N n i (, ) qv A x n x t e 1 1 N A W A p Bermel ECE 305 S18 31
30 Electron & Hole Fluxes n i ( ) qv A n x e 1 1 N A x W p J qn E qd n N N N dn qdn ni qv A J n qdn e 1 dx W N x0 p A n F n F p dp qdp ni qv A J p qdp e 1 dx W N x0' n D p /13/018 Bermel ECE 305 S18 3
31 Exam Equation Sheet /13/018 Bermel ECE 305 S18 33
32 Exam Equation Sheet /13/018 Bermel ECE 305 S18
33 Exam Fall 016 /13/018 Bermel ECE 305 S18 35
34 Exam Fall 016 /13/018 Bermel ECE 305 S18 36
35 Exam Fall 016 /13/018 Bermel ECE 305 S18 37
36 Exam Fall 016 /13/018 Bermel ECE 305 S18 38
37 Exam Fall 016 /13/018 Bermel ECE 305 S18 39
38 Exam Fall 016 /13/018 Bermel ECE 305 S18 40
39 Review Questions 1) If you apply negative bias to a terminal, which direction does the band move? ) What is the difference between Fermi & QuasiFermi levels? 3) How can we get away with solving just the MCDE in certain cases? 4) What are the most basic parameters of a pn junction, that can be used to calculate everything else? /13/018 Bermel ECE 305 S18 41
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