The Franz-Keldysh effect

In 1958, Franz [45] and Keldysh [46] independently theoretically predicted the absorption by a semiconductor, placed in an electric field, of light quanta which have an energy less than the width of the forbidden gap. The effect is connected with interband tunneling (Fig. 20). The valence band electron tunnels from point xl to point 3c, then it absorbs a quantum with a frequency lo Eg (Eg is the width of the forbidden gap) and further tunnels to point x2. Using the law of conservation of energy and the law of conservation of imaginary momentum (see the previous section), it is easy to show that light absorption at point 3c, which lies exactly between points acj and x2, is optimal. Consequently 

Experimental observation of the Franz Keldysh effect in real semiconductors is complicated by the possibility of absorption at u) Eg in the absence of an electric field. This absorption can result from various phenomena including exciton excitations, the influence of impurities on the 

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Isotropic media can be made birefringent by application of an electric field. This phenomenon is an electro-optic effect.5 There are in fact several electro-optic effects the Pockels effect, the electro-optic Kerr effect, the Stark effect in atoms and molecules, the Franz-Keldysh effect in semiconductors, etc. (see Table 4.6). We will limit our discussion in this section to the Pockels effect and the electro-optic Kerr effect. 

In principle, electroabsorption experiments enable excitons to be distinguished from interband transitions, as excitons are subject to the Stark effect, while interband transitions are subject to the Franz-Keldysh effect. We now describe these two effects. 

The Franz-Keldysh effects The effect of an electric field on an unbound particle-hole pair is nonperturbative, as the electron can gain an arbitrary amount of energy in the electric field by moving away from the hole. The effect of this is to reduce the band gap to zero. However, for there to be an optical... 

The Franz-Keldysh effects (Weiser and Horvath 1997) have been successfully used to distinguish the particle-hole continuum from exciton states in polydiacetylene crystals (Sebastian and Weiser 1981). 

In a more ordered polymer system, furthermore, deviation from the quadratic field dependence can be observed. This deviation accompanied by the peak broadening in the modulated spectra is often related to the Franz-Keldysh effect [57] where the... 

Under the conditions used for the electro-optical measurements on the various device structures that are reported in sections S and 6, we will expect to see a substantial electric field applied across at least a fraction of the polyacetylene layer, and we need to characterise the modulation of the %-n absorption edge with electric field. This electromodulation response is the Franz-Keldysh effect, and arises through modulation of the electron states near the band edge in the applied field. It is found to be very large in Shirakawa polyacetylene [54,55] and it has been pointed out that this is due to the strong non-linear electronic response that characterises the conjugated polymers [55]. In the low field limit, we expect to see a response that varies quadratically with the applied electric field, and that is proportional to the second differential of the absorption coefficient, a, 92a/aE2 [54]. 

As discussed above, surface fields do not play as important a role in the photochemistry of these systems. The electric field gradients are not generally sufficient to completely separate the electron and hole wavefunctions. In the event of surface charging, the field effects are better treated as a perturbation on the wavefunctions and can be modelled as a first-order Stark effect. The effect is similar to a Franz-Keldysh effect for bulk semiconductors except that there is still significant hole and electron wavefunction overlap. The oscillator strength remains similar in magnitude, albeit the frequency shifts to the red as the electron-hole pair is more... 

The electroabsorption signal Ao is always positive and shows no sign reversal in the spectrum. Such shape is not consistent with a field induced energy shift of electron states nor with a Franz-Keldysh effect of free carriers which must lead to a sign reversal of Aa. 

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