Quantum Confinement Below the de Broglie Wavelength

Studies have shown that electrical, optical, and mechanical properties of Si are different in Si nanomembranes than they are in bulk Si. But what happens when Si nanomembrane thickness is reduced further than that required for quantum confinement, for example, thinner than an electron's de Broglie wavelength?

Figure 1. Electron effective mass in the conduction band under different 1-D quantum confinement. (a) Si(001); (b) Si(110)


We know that for indirect band gap semiconductors, such as Silicon, different directions will have different electron effective mass in the conduction band. Thus, once one dimensional (1D) quantum confinement happens in one direction, the conduction band valleys will shift according to the effective mass in this direction. As shown in Fig.1, this direction-dependent band shift will split the conduction band minimum to two sets of sub-bands.


Figure 2. Derivative of XAS spectrum for UTSOI (110) and UTSOI (001)


Using X-ray absorption spectroscopy (XAS) with a total electron yield measurement, we can prove the existence of quantum confinement in ultra-thin Si nanomembranes. With confinement, the six-fold degeneracy of the bulk-silicon CBM (Δ) is lifted and two unequal sub-band-ladders, Δ­2 and Δ­4, form. It reflects on the derivative of the spectra that the first peak is broader. The 2p3/2→ Δ absorption peaks  also show dramatic shift to higher energy when the membrane thickness for both Si(001) and Si(110) reduce.


Author: Feng Chen


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