Films minces à base de Si nanostructuré pour des cellules ...

Shockley-Queisser limit of 31% [Shockley 61]. The possible solution to these problems
would be in attaining a semiconductor with a tunable direct bandgap structure
insensitive to SWE, which is almost completely achieved in quantum conned Si.
1.4.1 Quantum Connement Eect (QCE)
tel-00916300, version 1 - 10 Dec 2013
QCE refers to the dramatic size dependent eects that the semiconductors like
Si show when their charge carriers (electron-hole pairs = excitons) are spatially
conned in nanometer sized volumes. At these dimensions, the bulk properties of
the solid becomes severely distorted and the behaviour of a conned exciton follows
'a particle in a box' model [Brus 83]. The simplest case of this model concerns the
1D system which represents a situation where a particle of mass m is conned by two
walls of innite potential energy at x = 0 and x = L. The particle is free to move
within this space and possesses non-zero discrete energy levels. After mathematical
derivations by solving Schrödinger equation, the permitted energy levels for a 1D
model is given as
E n = n 2 h 2 /8mL 2 for n=1,2,3... Eqn (1.1)
Applying the same principles to a particle conned in 3D (i.e.) conned in x, y
and z directions by potential wells at L x ,L y and L z , the energy levels are given as
E nx,n y,n z
= (h 2 /8m) [ (n 2 x/L 2 x) + (n 2 y/L 2 y) + (n 2 z/L 2 z) ] Eqn (1.2)
From equations (1.1) and (1.2), it can be seen that the size of the box has an
inverse relationship with the energy of the particle. Thus, as the size of the box
shrinks which indirectly refers to the particle size, there is an enhancement in the
energy gap. This is the reason behind the enlargement of bandgap as the particle
size decreases in nanometric particles which becomes more pronounced below a
particular limit specic to the particle, known as the exciton Bohr radius (typically
< 10 nm). The particles with radii larger than this limit are said to be in the 'weak
connement regime' and those that have radii smaller than the exciton Bohr radius
are said to be in the 'strong connement regime'. Another associated phenomena
with the exciton connement is the breakdown of momentum conservation rule.
When the excitons are conned by a box, it follows the Heisenberg's uncertainity
principle and their position in k space is blurred. Therefore, there is an overlap
between the tail of electron and hole wavefunctions even in an indirect bandgap
semiconductor, giving rise to quasi-direct transitions (Fig. 1.9a). The optical quasidirect
transitions without the intervention of phonons are similar to the case of
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