ECE 874: Physical Electronics Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu

Lecture 25, 26 Nov 12 Chp. 05: Recombination-Generation Processes VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

pn junction in Si at equilibrium ( no bias) Recombination-generation (R-G) via a trap (a local defect): why this is important: pn junction in Si at equilibrium ( no bias) - + p = p+ = 1019 cm-3 n = 1015 cm-3 Si W VM Ayres, ECE874, F12

Same pn junction in Si in reverse bias: - 5V - Vrev + - - - - + + + + p+ = 1019 cm-3 n = 1015 cm-3 Si W Reverse bias goal: turn the device OFF: no current flowing. VM Ayres, ECE874, F12

You didn’t turn your device OFF as well as you thought you did by four orders of magnitude. What happened: trap-mediated recombination-generation (R-G) processes act to restore what ever the previous steady state was. The trap released more carriers to try to restore the previous neutral region concentrations. VM Ayres, ECE874, F12

Two key relationships/equations: Note that n1 and p1 look just like ordinary dopant concentrations n and p except that they originate at a trap energy level ET’ VM Ayres, ECE874, F12

Two key relationships/equations in HW05: Prs. 5.3, 5.4, 5.5 Prs. 5.2, 5.3, 5.4, 5.5: All VM Ayres, ECE874, F12

Pr. 5.4: ET’ = Ei is worst case scenario: the one to check Prs. 5.2, 5.3, 5.4, 5.5: All Pr. 5.2: ET’ = Ei is given Pr. 5.3: ET’ near Ei is given Pr. 5.4: ET’ = Ei is worst case scenario: the one to check Pr. 5.5: ET’ = Ei is given Obviously there is something important about this condition VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

3b) VM Ayres, ECE874, F12

Points: p. 149: para- live NT n or p VM Ayres, ECE874, F12

Pr. 5.2 Pr. 5.3, 5.4, 5.5 3b) VM Ayres, ECE874, F12

Pr. 5.2: (a) Given a condition on the capture cross sections cp and cn (c) Given a condition on the emission cross sections ep and en But: question is about a concentration nT not an R-G rate R Saw nT in Lecture 24 in derivation of rates rN and rP under equilibrium conditions. nT is concentration of electrons in traps, pT is concentration of holes. Total concentration of filled traps NT = nT + pT. Note: in Lecture 24, we worked through an equilibrium derivation but a steady state example. Time to connect these two ideas. Prs. 5.2, 5.3, 5.4, 5.5 are all steady state problems. VM Ayres, ECE874, F12

Lecture 24: General info: Processes the change the e- headcount Processes the change the hole headcount VM Ayres, ECE874, F12

Lecture 24: Each one of these processes happens with better or worse efficiencies: Hole capture Hole emission VM Ayres, ECE874, F12

Lecture 24: General info: Processes the change the e- headcount Processes the change the hole headcount VM Ayres, ECE874, F12

Lecture 24: Equilibrium: 0 = Pierret says same things: the definition for equilibrium is that the rates for changing electrons and holes concentrations via a trap individually sum to 0. 0a) 0b) VM Ayres, ECE874, F12

Lecture 24: Equilibrium: Under equilibrium conditions you can solve for the emission coefficients in terms of the capture coefficients (p. 145). Then, assuming that even away from equilibrium, the capture/emission coefficient values don’t change too much: rN and rP are not 0, so this is not equilibrium VM Ayres, ECE874, F12

The definition of the steady state condition is: when rN = rP Under equilibrium conditions you can solve for the emission coefficients in terms of the capture coefficients (p. 145). Then, assuming that even away from equilibrium, the capture/emission coefficient values don’t change too much: The definition of the steady state condition is: when rN = rP VM Ayres, ECE874, F12

Equilibrium/Steady State: Under equilibrium conditions you can solve for the emission coefficients in terms of the capture coefficients (p. 145). Then, assume that even away from equilibrium, the capture/emission coefficient values don’t change too much. .13a) .13b) These connectors between emission and capture coefficients should be used in Pr. 5.2 (c). VM Ayres, ECE874, F12

Use NT = nT + pT to eliminate pT Solve for nT Steady State: Set rN = rP Use NT = nT + pT to eliminate pT Solve for nT VM Ayres, ECE874, F12

nT for steady state conditions: .21) Use this definition for nT under steady state conditions to answer Pr. 5.2. VM Ayres, ECE874, F12

R for steady state conditions: Can use the steady state nT definition and pT = NT - nT to eliminate nT and pT in the above. The result is: (5.24) Use this R in Prs. 5.3, 5.4 and 5.5 VM Ayres, ECE874, F12