Radiative Recombination Coefficient
In earlier work, Centre researchers have experimentally
demonstrated external luminescence quantum efficiencies (EQE) of
almost one percent from highly efficient silicon light emitting
diodes [M.A. Green et al., Nature 412,
805 (2001)] and of more than ten percent for the photoluminescence
from well-passivated high-quality float-zone silicon wafers [T.
Trupke et al., Appl. Phys. Lett. 82, 2996, (2003)].
These EQE values are orders of magnitude higher than comparable
results that had been published before.
According to these experimental studies, the EQE
is strongly dependent on the excitation conditions, i.e., on the
applied voltage in electroluminescence- (EL) and on the incident
light intensity in photoluminescence-experiments (PL). Qualitatively
this dependence arises from different dependencies of various recombination
channels on the excess carrier concentration Δn. At high excess
carrier concentrations, the total recombination rate is dominated
by Auger-recombination while Shockley-Read-Hall recombination and
surface recombination dominate the total recombination process
at low excess carrier concentrations.
One aim of the recent work in the area of light emission
from bulk silicon was to theoretically describe and to understand
the dependence of the EQE on the excess carrier concentration Δn
quantitatively.
The rate of radiative recombination in silicon is
described via the radiative recombination coefficient B(T). Unfortunately,
the data that could be found in the literature for this quantity
were very contradictory. Because reliable data for B(T) are obviously
indispensable for a quantitative analysis of the EQE, we started
with an accurate determination of the radiative recombination coefficient
as a function of temperature. Very accurate photoluminescence spectra,
which were measured with unprecedented accuracy on polished silicon
wafers using our in-house photoluminescence set-up, were used to
calculate B(T) over the temperature range 70K to 300K using the
van Roosbroeck theory [T. Trupke et al., J. Appl. Phys.
94, 4930 (2003)]. Some of the contradictory results from
the literature could be clarified in this context.
Calculated internal and external luminescence
quantum efficiencies of bulk crystalline silicon at room temperature
for different values of the effective excess carrier lifetime
for a silicon wafer with a thickness of 500 µm.
Another complication in the theoretical description
of the EQE arises from the fact that at excess carrier concentrations
exceeding ~1016cm-3 the radiative recombination coefficient
itself varies with the excess carrier concentration. P.P. Altermatt
from the Australian National University, in collaboration with
researchers from the Centre, recently derived an analytical expression
for the injection dependence of B(T) by analysing experimental
data from the literature [Appl. Phys. Lett. manuscript in preparation].
In combination with a similar expression for the Auger-recombination,
the internal quantum efficiency as a function of the excess carrier
concentration could be calculated for different values of the Shockley-Read-Hall-lifetime
(see figure above). |
