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Unformatted text preview: 1 Chapter 9: Quantum well optics and devices Optical spectra of quantum wells The energy levels and density of states of a quantum well look like: Consider the absorption of a photon. Assume that the well is made of a direct band gap semiconductor such as GaAs. The dominant optical transitions will be zero phonon and g2 vertical g3 in wavevector space. This means that the valence and conduction band states have the same values of k x , k y and k z so that g2 k x = g2 k y = g2 k z = 0 Consider k z first. Since k z = n g3 / L z where L z is the width of the well then g2 k z = 0 implies g2 n = 0 Next considering k x and k y , we expect vertical transitions on the diagram above which connect curves of equal n . The absorption spectrum should therefore follow the density of states g4 a series of steps: Energy Energy n = 1 n = 2 n = 3 n = 4 n = 1 n = 2 n = 3 n = 4 E g E g (k x 2 + k y 2 ) 1/2 g(E) m h */ g3 g2 2 m e */ g3 g2 2 C.B. V.B. z z y x 2 This works out quite well except that excitonic effects show up strongly as a peak close to each step. These are more important in quantum wells than in bulk because the coulomb binding energy between electron and hole for a twodimensional geometry is greater than in a 3dimensional geometry g4 it can be proved that a 2D hydrogen atom has 4 times smaller Bohr radius and 4 times greater binding energy than a normal 3D hydrogen atom. This can be understood qualitatively by realising that the barriers of the quantum well prevent the particles separating from one another along the z axis and this increases the overall energy of interaction. This increased overlap of electron and hole wavefunctions also results in a shrinkage in the x and y directions. For bulk GaAs the exciton binding energy is E B 3D = 4 meV. Thus for a perfectly 2D GaAs quantum well we would expect E B 2D = 16 meV . For a typical quantum well with finite potential barriers  so not perfectly 2D  E B is found to be about 10 meV . Since the value of kT at 300K is about 25 meV the excitons have low stability against thermal dissociation and therefore the width of the lines in the spectra are quite large at 300K g5g5 Stability of excitons. At T = 300K an exciton in a quantum well has a measured lifetime before ionisation by thermal excitation of about g4 ~ 0.3x1012 s 3D 2D g2 + 1s g2 g2 + free g4 ~ 0.3 1012 s E E g E g E B g4 ~ 0.3 1012 s 3 This implies a finite spectral linewidth from the Heisenberg uncertainty relation...
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This note was uploaded on 11/07/2009 for the course ELEC ece212 taught by Professor None during the Spring '09 term at York University.
 Spring '09
 none
 Electromagnet

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