1 Band diagram, generation and recombination LECTURE 4 Energy band diagram Phonons Thermal generation of electrons and holes Chemical generation (doping)

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Presentation transcript:

1 Band diagram, generation and recombination LECTURE 4 Energy band diagram Phonons Thermal generation of electrons and holes Chemical generation (doping) R-G-centre recombination

2 Potential energy What is ν ? Where is E C0 for ν = 1 ? Physically, what is E C0 ? Microscopically: Macroscopically: What is U M (x)? Sketch it for this case. x UMUM Sec VaVa

3 Energy band diagram Sec Add in the macroscopic potential energy

4 Key points from Chapter 2 Chap. 2 Electrons and holes reside in states Each state represents an energy and a crystal momentum Change in ћk is related to external forces ћk(E) ≡ m*(E)v(E) = m*v(E) in the parabolic-band approximation Each state identifies an allowable v(E) and KE In the energy band diagram, which is the faster electron and the faster hole? ECEC EVEV

5Phonons The atoms of a lattice vibrate about their mean positions. The vibrations are coupled. This leads to a dispersion relationship (Energy vs. momentum.) Note the range of phonon energies. Representation of coupling via spring analogy A quantum of lattice vibrational energy is called a phonon. Which vibrational modes are shown in (b) and (c) above? Sec

6 Thermal generation of EHP's What are these `waves'? How many simultaneous phonons are needed to generate one EHP? What is the magnitude of n i at 300K? What is a semiconductor called when E C0 and E V0 occur at different ћk ? Sec

7 Chemical generation of electrons or holes (doping) Doping is the substitutional incorporation in the lattice of selected dopant atoms. Important vocabulary: extrinsic material, donors, n-type, acceptors, p-type, majority carrier, minority carrier. Typically, doping densities are 1E16 - 1E20 cm -3. How many ppm is this? Sec

8 Doping Semiconductors What are all these processes called? Sec

9 Extrinsic carrier generation + + Why do the impurity atoms not form energy bands? What do the dashed lines in (a) and the short lines in (b) mean? Locally, in uniformly-doped material, with N D,N A > n i : -qn+qN D + = 0 or qp-qN A - = 0 (b) Sec

10 R-G-centre recombination What is the box in the bandgap? Why are the phonon arrows pointing outward? Rate of recombination for p-type material: Sec Another name for this type of recombination is SRH.