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

VM Ayres, ECE874, F12 Lecture 24, 20 Nov 12 Chp. 05: Recombination-Generation Processes

VM Ayres, ECE874, F12 Recombination-Generation Processes These two mechanisms are important at 300K and higher temperatures: Absorption and Spontaneous emission Direct bandgap materials like GaAs: important Recombination- generation (R-G) of electrons and/or holes via a trap (a local defect). Indirect bandgap materials like Si: very important. Will show that this process is most efficient for traps near the mid-gap Chp. 05 concentrates on (b)

VM Ayres, ECE874, F12

Recombination-Generation Processes These two mechanisms are important at low temperatures: Donor or acceptor sites act as local impurity traps but are not near the mid-gap. Inefficient version of R-G mechanism. Exciton formation creates a non-dopant type of bandgap state typically close to E c or E v. When excitons form, they alter the n, p headcount. When they annihilate they can produce photons with close to the bandgap energy/wavelength. This adds extra photons but also a spread to emitted wavelengths. Important for direct bandgap optoelectonic materials like GaAs at low temps.

VM Ayres, ECE874, F12 Recombination-Generation Processes this mechanism is important at high n or p concentrations: Auger process: band-to-band recombination or trap recombination is going on when a collision with an outside n or p also occurs. The orginal n or p gets and subsequently loses a lot of extra energy. This is important for direct bandgap materials like GaAs when what you want is recombination that gives you bandgap energy/wavelength photon emission and what you get instead is a lot of thermal energy waste.

VM Ayres, ECE874, F12 Recombination-generation (R-G) via a trap (a local defect): why this is important: Rate for this steady state happening is proportional to the trap density N T J = R width = dn/dt or dp/dt

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

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

VM Ayres, ECE874, F12 Diode equation Given:  p = stay-alive time for holes on the n-side = sec

VM Ayres, ECE874, F12 This seems to be a good solid OFF.

VM Ayres, ECE874, F12 Find the depletion width W D too:

VM Ayres, ECE874, F12

J = R width time In the Depletion region; n, p and np are small: - Given:  g = generation time for holes on the n-side = same = sec

VM Ayres, ECE874, F12 You didn’t turn your device OFF as well as you thought you did by four orders of magnitude.

VM Ayres, ECE874, F12 What happened: trap-mediated recombination-generation (R-G) processes act to restore what ever the previous steady state was. In this example: in the old steady state, the n-side was largely a neutral region with: Now the same place is a depletion region W D with: Result: J gen : traps released carriers in W D : new steady state

VM Ayres, ECE874, F12 Example problem conditions: steady state

VM Ayres, ECE874, F12 General info:

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

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

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

VM Ayres, ECE874, F12 Equilibrium: 0 = 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 coefficient values don’t change too much: OK: c n, c p, n, p, n T, p T Need: n 1, p 1 (p. 145)

VM Ayres, ECE874, F : in the skipped Chp. 04 section on ionization of dopants as a function of temperature, and also traps as a function of temperature.

VM Ayres, ECE874, F12

Example problem: calculate n 1 for O in Si at 300K for the closest to mid-gap trap.

VM Ayres, ECE874, F12 Oxygen traps:.16 eV below E C.38 eV below E C.51 eV below E C Oxygen traps:.41 eV above E V

VM Ayres, ECE874, F12 Oxygen trap nearest mid-gap is:.51 eV below E C E C – E T’ =.51 eV Where is it relative to E i ? E C – E i =.56 eV eV = EV

VM Ayres, ECE874, F12 E T versus E T’. What’s the difference? E T’ includes the temperature dependence of the trap. Equation 4.69: in the skipped Chp. 04 section on ionization of traps as a function of temperature: 1 or 2 is typical E T’ is what you experimentally measure so the.51 eV below E C level on the graph is E T’ in our problem.