Hot Carrier Absorbers
Work has continued in the Centre on the limiting
efficiency of hot carrier cells. It has been concluded that, in
all but the most finely tuned situations (which might not be feasible
even in principle), the populations of electrons and holes are
likely to come to equilibrium with each other (although not with
the lattice) through impact ionisation and Auger recombination,
such that they can be described by a Fermi distribution at TH .
As such, the chemical potential for these carriers approaches zero.
Hence emission cannot be suppressed appreciably below that for
a black body at TH and the conversion efficiency is
limited to 85.4% for maximal concentration and 54% for 1 sun. These
are less than the corresponding figures for the infinite tandem
of 86.8% and 68% respectively, because of the reduced number of
degrees of freedom for the parameters for the hot carrier cell.
Work in the Centre has also progressed on the theory
of slowing of carrier cooling in hot carrier absorbers. A hot electron
in the conduction band of a direct band gap material can relax
by the emission of LO phonons in a series of steps which occur
on a very short timescale (picoseconds). This will continue until
the carrier energy is closer to the band edge than the LO phonon
energy. Subsequent cooling to the band edge is via acoustic phonon
scattering and at room temperature this is within kT. For hot holes
the process is complicated by heavy and light hole bands but initial
relaxation is still mainly via LO phonons. [A. Othonos, Appl Phys
Rev 83 (1998) 1790]
For an indirect band gap material, acoustic phonons
are more likely to be involved. The critical factor being the role
of intervalley as opposed to intravalley scattering. [P.Y. Yu and
M. Cardona, Fundamentals of Semiconductors, (Springer-Verlag, 1996)]
For direct band gaps, intravalley dominates, whereas for in-direct
gap intervalley dominates because valleys away from zone centre
have lower energy states and as acoustic phonon energy is less
than optical phonon energy, acoustic emission is more probable.
However, even for direct gap material, carriers that
are well above the band edge (i.e. such that they are higher than
the valleys away from zone centre) can also scatter by acoustic
intervalley mechanisms. Hence approaches that interfere with optical
to acoustic phonon scattering have the potential to significantly
reduce carrier cooling rates and hence be useful for hot carrier
absorbers. Furthermore approaches that additionally inhibit initial
carrier scattering with LO phonons could reduce cooling rates still
further.
Several approaches have been shown to provide just
such inhibition of optical to acoustic phonon scattering:
- Slowing of carrier cooling has been observed in III-V superlattices.
The probable mechanism for this is the enhancement of a phonon “bottleneck” effect
which - because of a lack of scattering between phonon modes
- creates a hot optical phonon population that inhibits further
carrier cooling. [Westland, Ryan, Scott, Davies, Riffat, Solid
Sate Eelectronics, 31 (1988) 431] or [P.A. Snow, et.al., Superlattices
and Microstructures, 5 (1989) 595]
- Big increases in the thermoelectric figure of merit have
been observed for very short period Bi2Te3/Sb2Te3 or GaAs/AlGaAs
superlattices [Venkatasubramanian et al, Nature 413 (2001)
597]. This is caused by reduced thermal conduction attributed
to phonon reflection at the superlattice heterojunctions due
to acoustic impedance mismatch
- Phononic Bragg reflection structures have been demonstrated
using GaAs/AlGaAs superlattices of very short period (a few
nm) [M.Trigo et.al. Phys. Rev. Lett. 89 (2002) Art. No. 227402].
- Phonon dispersion curves for semiconductors depend on fairly
simple relationships between the masses of the constituent
elements. Such curves have been calculated with good agreement
to experiment, e.g. [Giannozzi et.al., Phys. Rev. B43 (1991)
7231]. These curves exhibit complete phononic band gaps between
optical and acoustic modes, with the gap size increasing with
the difference in element masses. These gaps should interfere
with inter-mode scattering and hence slow cooling.
Recent work in the Centre has led to the realisation
that approaches (1), (2) and (3) may depend on very similar mechanisms,
with phonon Bragg reflection occurring because of acoustic impedance
modulation (in analogy to refractive index modulation in photonic
band gap structures). They also effectively achieve the same result
as (4), in that for small superlattice periods Brillouin zone folding
occurs and acoustic modes are prevented from achieving their maximum
energies at the zone edges. Hence superlattice approaches can be
seen as a way of engineering the phononic band gaps of approach
(4).
The above results have allowed preliminary definition
of the properties required of a good absorber: It should be a direct
band-gap material so as to suppress intervalley acoustic phonon
cooling. This band-gap should also be narrow to increase absorption,
(although initial results suggest this is not particularly critical).
Furthermore, the first in-direct valley away from zone centre should
be at as high an energy as possible above the direct band edge,
so as to maximise the range of hot carriers for which only optical
phonon scattering is possible. Furthermore a compound semiconductor
is preferable with a large difference in element masses to maximise
the phononic band-gap, hence increasing the optical mode energy
and reducing the likelihood of optical phonon scattering with acoustic
modes.
Further quantification of such required properties
is being carried out. However, the satisfactory combination of
all these properties in a given semiconductor is most unlikely.
Hence the use of both QW and QD superlattice effects are being
investigated theoretically. These have the potential to create
the pseudo phononic band gaps discussed above; of engineering pseudo-direct
band-gaps from materials with bulk in-direct gaps; and of forcing
a higher energy for the onset of in-direct band gap valleys by
Brillouin zone folding that could further restrict acoustic mode
scattering. |
