ECE 874:Physical Electronics

Prof. Virginia AyresElectrical & Computer EngineeringMichigan State Universityayresv@msu.edu

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Lecture 24, 20 Nov 12

Chp. 05: Recombination-Generation Processes

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Recombination-Generation ProcessesThese 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-gapChp. 05 concentrates on (b)

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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 Ec or Ev. 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.

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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.

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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 NT J = R width

= dn/dt or dp/dt

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p = p+ = 1019 cm-3 n = 1015 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:

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- Vrev +

p+ = 1019 cm-3 n = 10

15 cm-3

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Si

Same pn junction in Si in reverse bias: - 5V

Reverse bias goal: turn the device OFF: no current flowing.

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Diode equation

Given: p = stay-alive time for holes on the n-side = 10-6 sec

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This seems to be a good solid OFF.

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Find the depletion width WD too:

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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 = 10-6 sec

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You didn’t turn your device OFF as well as you thought you did by four orders of magnitude.

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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 WD with:

Result: Jgen: traps released carriers in WD: new steady state

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Example problem conditions: steady state

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General info:

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General info:

Processes the change the e- headcount

Processes the change the hole headcount

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Each one of these processes happens with better or worse efficiencies:

Hole capture

Hole emission

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General info:

Processes the change the e- headcount

Processes the change the hole headcount

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Equilibrium:

0 =

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: cn, cp, n, p, nT, pT

Need: n1, p1 (p. 145)

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

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Example problem: calculate n1 for O in Si at 300K for the closest to mid-gap trap.

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Oxygen traps:

.16 eV below EC

.38 eV below EC

.51 eV below EC

Oxygen traps:

.41 eV above EV

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Oxygen trap nearest mid-gap is:

.51 eV below EC

EC – ET’ = .51 eV

Where is it relative to Ei?

EC – Ei = .56 eV - .0073 eV= 0.5527 EV

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ET versus E T’. What’s the difference?

ET’ 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

ET’ is what you experimentally measure so the .51 eV below EC level on the graph is ET’ in our problem.