6.3.2.1 Photoluminescence up-conversion
Despite exhibiting a relatively high radiative efficiency, the minority carrier lifetime of the doped nanowires was found to be only picoseconds in length. Figure 6-6(a) plots the results of up-conversion spectroscopy, mapping the emission intensity of the doped nanowires as a function of energy and time following excitation. The slight redshift and spectral narrowing seen here at early times are attributable to both thermalization and the decaying carrier density. Beyond this, emission remains centred around 1.395 eV (889 nm) and when integrated across time gives a spectrum closely resembling that seen by PL spectroscopy [Figure 6-4(e)]. The intensity of emission is further seen to decay rapidly, reducing by more than two orders of magnitude in less than 15 ps. When integrated in energy, this decay is well described by a single-exponential expression with a time constant of 3.44 ps [Figure 6-6(b)].
A lifetime of 3.44 ps accords well with previous studies of unpassivated GaAs nanowires517, 1077 and represents one of the shortest carrier lifetimes reported for a semiconductor nanowire. Given the high surface to volume ratio of the nanowire geometry and the high rates of surface recombination known to characterize bare GaAs surfaces, the ultrashort lifetimes of bare GaAs nanowires have usually been associated with non-radiative surface recombination.517, 1077 In a regime where surface recombination dominates the dynamics of recombination, the surface recombination velocity (SRV) of a nanowire may be related to the minority carrier lifetime in the following manner:
…(6-3) where is the SRV is the nanowire diameter.1096 Substituting a diameter of 300 nm into Equation 6-3 gives a SRV of 2.18 x106 cm/s. This value is similar to that calculated previously from measurements of minority carrier diffusion length in unpassivated Zn
Section 6.3 - Increasing quantum efficiency through doping
GaAs surfaces. Although the SRV will depend on multiple factors such as facet orientation and chemical termination, it is interesting to note that an increased SRV has previously been associated with doping.1078, 1097Given that the carrier lifetime measured here is both comparable to that of undoped GaAs nanowires1077 and corresponds to a reasonable value of surface recombination velocity, it may be identified as a non- radiative lifetime dominated by surface recombination. Internal quantum efficiency (IQE), , is related to both the non-radiative, , and radiative lifetimes, , in the following manner:
…(6-4)
As surface recombination is the dominant recombination pathway in GaAs nanowires, previous efforts to increase the of GaAs nanowires have focused on lengthening
through surface passivation. Here doping has however increased without
significantly affecting the non-radiative lifetime.
6.3.2.2 Transient Rayleigh scattering spectroscopy
The minority carrier lifetime of the doped nanowires was also measured by transient Rayleigh scattering (TRS)1069. Figure 6-7(a) plots the photomodulated polarisation Figure 6-6 | Measurement of carrier lifetime by PL up-conversion a) Emission of doped GaAs nanowires in energy and time. b) Integration of (a) in energy, giving a lifetime of 3.44 ps and a surface recombination velocity of 2.18 x106 cm/s.
response, , of a single doped TSL nanowire as a function of time and scattered wavelength. Delay time here reflects dispersion in the optics and source laser fibre with zero time being chosen to correspond with the onset of the fundamental band gap response at around 850 nm. The spin-orbit split-off band transition is further observed at around 700nm and appears more pronounced as approaches zero at shorter wavelengths. By considering the response at several particular wavelengths close to the band gap [as plotted in Figure 6-7(c)], the minority carrier lifetime is again observed to be picoseconds in length.
Beyond carrier dynamics, TRS spectroscopy also provides insight into band structure as carriers relax towards their equilibrium distributions following excitation.1098 Figure 6-7(d) plots TRS spectra as a function of wavelength for several particular times following excitation. Given the minority carrier lifetime of approximately 1 ps, the response at 3 ps can be expected to represent carrier concentrations and temperatures
Figure 6-7| TRS characterisation of a single doped GaAs nanowire a) photomodulated polarisation response ∆Rꞌ/Rꞌ b) a magnified view of (a) close to the band gap c) time dependant photomodulated polarisation response ∆Rꞌ/Rꞌ for several wavelengths close to the band gap d) wavelength dependant photomodulated polarisation response ∆Rꞌ/Rꞌ for several times following excitation.
Section 6.3 - Increasing quantum efficiency through doping approaching equilibrium. The minimum of this spectrum is observed at around 850 nm (1.46 eV) and corresponds to the transition between valence and conduction band edges. Blueshift here from a wavelength of 872 nm (1.42 eV) in undoped GaAs may be attributed to heavy hole doping having shifted the Fermi level to a position within the valence band. Redshift of the fundamental band gap from 872 nm (1.42 eV) to approximately 880 nm (1.41 eV), as determined from the zero crossing point [Figure 6-7(d)], may further be attributed to band gap renormalisation due to doping.
Taken together the quasi hole Fermi level can thus be taken to be +50 meV. From this energy, a heavy hole doping concentration of at least 2.4 x1019 /cm3 and a light hole doping concentration of at least 1.5 x1018 /cm3 may be calculated for a temperature of 300K. Similarly, the late time displacement of the split-off band to conduction band transition of +10 meV is indicative of a doping level of at least 1.8 x1018 /cm3.
6.3.2.3 Low-Temperature time correlated single photon counting
The efficiency advantage obtained through doping continues at low temperature. Figure 6-8(a) shows PL spectra obtained from single doped and undoped nanowires at 6 K where emission has been normalized to an excitation fluence of 5 J/cm2/pulse. Emission from the doped nanowire is again seen to be orders of magnitude brighter than that from the undoped nanowire.
In all cases the lifetime of PL emission at low temperature was found to be less than the 80 ps system response of the time correlated single photon counting (TCSPC) setup. Such short lifetimes are consistent with previous measurements1007, 1099-1102 of GaAs nanostructures at low temperature and indicate the continued dominance of a non- radiative recombination pathway. The surface recombination velocity of GaAs has been found1101-1103 to remain relatively high (>1 x105 cm/s) at cryogenic temperatures and the lifetime of GaAs nanostructures has previously been linked to surface recombination at these temperatures.1101, 1103-1105 In the case of InGaAs/InP wires, surface recombination velocity was found to vary as the square root of absolute temperature between 4 and 77 K. This suggests a capture cross section that is independent of temperature. Such behaviour can be expected for traps with a large capture cross section such as those present at the surface of unpassivated GaAs.1106, 1107