Quantum well oscillations

The versatility of the MSHG method is mainly due to its high sensitivity, which results partially from local-field enhancement effects. Consequently, the method has found a large number of applications, including the investigation of quantum well oscillations (Wierenga et al. 1995 Kirilyuk et al. 1997a) or femtosecond time-resolved spin dynamics (Scholl et al. 1997 Hohlfeld et al. 1997). 

Wierenga, H., Jong, W. D., Prins, M., Rasing, T., VoUmer, R., Kirilyuk, A., Schwabe, H., and Kirschner, J. (1995). Interface magnetism and possible quantum well oscillations in ultrathin Co/Cu films observed by magnetization induced second harmonic generation. Phys.Rev.Lett., 74 1462 -1465. 

This relation may be interpreted as the mean-square amplitude of a quantum harmonic oscillator 3 o ) = 2mco) h coth( /iLorentzian distribution of the system s normal modes. In the absence of friction (2.27) describes thermally activated as well as tunneling processes when < 1, or fhcoo > 1, respectively. At first glance it may seem surprising... 

Band gap engineetring confined hetetrostruciutres. When the thickness of a crystalline film is comparable with the de Broglie wavelength, the conduction and valence bands will break into subbands and as the thickness increases, the Fermi energy of the electrons oscillates. This leads to the so-called quantum size effects, which had been precociously predicted in Russia by Lifshitz and Kosevich (1953). A piece of semiconductor which is very small in one, two or three dimensions - a confined structure - is called a quantum well, quantum wire or quantum dot, respectively, and much fundamental physics research has been devoted to these in the last two decades. However, the world of MSE only became involved when several quantum wells were combined into what is now termed a heterostructure. 

There are well-known temperature effects, particularly dealing with the two first moments of the spectra that evoke those of the thermal average appearing in the statistical mechanics of quantum harmonic oscillator coordinates. 

When piezoelectric fields are taken into consideration, the oscillator strength of GalnN/GaN quantum wells decreases strongly with increasing well width or increasing magnitude of the field [6], This is due to the spatial separation of the electron and hole wavefimctions in the case of wide wells and strong fields. 

Since in quantum wells electrons and holes can freely move only within the quantum well plane, bound electron-hole states, i.e. excitons, become two-dimensional in nature as well. The exciton binding energy is enhanced four-fold in the ideal two-dimensional case compared to a conventional three-dimensional case. In addition, the exciton oscillator strength is also enhanced. In the optical spectra, this leads to pronounced excitonic features which are usually observed even at room temperature. 

Time-resolved photoluminescence was also used to show that the spatial separation of the electron and hole wavefunctions due to the piezoelectric fields in GalnN/GaN QWs leads to a dramatic reduction in oscillator strength, particularly for thick quantum wells [6]. Due to the reduced oscillator strength for the lowest energy state, the optical absorption spectrum of the quantum wells is expected to be dominated by highly excited states close to the strained bulk bandgap. 

The optical properties of GalnN/GaN quantum wells differ somewhat from the well-known behaviour of other III-V-based strained quantum well structures, partly due to the rather strong composition and well width fluctuations, possibly induced by a partial phase separation of InN and GaN. The even more dominant effect seems to be the piezoelectric field characteristic for strained wurtzite quantum wells, which strongly modifies the transition energies and the oscillator strengths. However, the relative influence of localisation and piezoelectric field effect is still subject to considerable controversy. 

This has the form of a double-well oscillator coupled to a transverse harmonic mode. The adiabatic approximation was discussed in great detail from a number of quantum-mechanical calculations, and it was shown how the two-dimensional problem could be reduced to a one-dimensional model with an effective potential where the barrier top is lowered and a third well is created at the center as more energy is pumped into the transverse mode. From this change in the reactive potential follows a marked increase in the reaction rate. Classical trajectory calculations were also performed to identify certain specifically quanta effects. For the higher energies, both classical and quantum calculations give parallel results. 

This rate of energy exchange between an oscillator and the thermal environment was the focus of Chapter 13, where we have used a quantum harmonic oscillator model for the well motion. In the y -> 0 limit of the Kramers model we are dealing with energy relaxation of a classical anharmonic oscillator. One may justifiably question the use of Markovian classical dynamics in this part of the problem, and we will come to this issue later. For now we focus on the solution of the mathematical problem posed by the low friction limit of the Kramers problem. 

FIGURE 3.8 The quantum harmonic oscillator eigen-function probabilities (density) representation (thick continuous curves) for ground state ( = 0), and few excited vibronic states ( = 2, 5, and 10) for the working case of HI molecule (respecting the coordinated centered on its mass center) the classical potential is as well illustrated (by the dashed curve in each instant) for facihtating the correspondence principle discussion. 

Figure 4.9 Quantum well and potential energy surfaces relevant for charge transfer. Arrows indicate fluctuations about the generalized reaction coordinate leadingto changes in the energy levels of the quantum wells, which corresponds to oscillations along the potential energy surface.

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