Semiconductor nanowires bridge the gap between the nanoscale and the outside world. When the radius of the wire approaches the exciton Bohr radius, quantum confinement of an electron-hole pair leads to discrete exciton transition energies, which shapes the optical response of the wire. The combination of spectral tunability by varying the confinement and the macroscopic character along the wire axis make them to very appealing nanosystems for fundamental research, next generation solar cells, and coupling to plasmonic nanostructures. Here we investigate CdSe nanowires on a picosecond timescale by optical spectroscopy. Ultrafast nonlinear spectroscopy investigates the deviation from linear light-matter interaction and gives insight to processes such as carrier dynamics and population of the excitonic states. However, the variation of the optical response with the nanowire radius makes single wire experiments indispensable which is especially at room temperature a challenging task due to spectrally broad and fluctuating transitions.
Our sensitive pump-probe setup allows us to investigate for the first time spectrally resolved ultrafast carrier dynamics in a single CdSe nanowire . Figure 1(a) illustrates the idea of our experiment. An ultrashort laser pulse in the near-UV pumps the nanowire. The absorbed photons generate an electron-hole plasma far above the band-gap (blue arrow in the ladder scheme). After a few picoseconds, electron-hole pairs populate the energy states of the quantum system. To determine the population of these states, we try to let the nanowire absorb a second, delayed and red-detuned photon. The probability of this process depends on the difference in population of ground and excited state. The more population in the excited state, the lower the probability of further absorption: the transition bleaches, i.e., disappears, in the absorption spectrum. In our transient absorption spectra, we plot in the following the difference of the pumped and the unpumped absorption spectrum.
Figure 1(b) sketches our experimental setup. We excite at 390nm wavelength with 15fJ pulse energy and 150fs pulse duration. The probe pulses with constant energies of 130fJ are generated by an optical parametric oscillator and cover the visible and near-IR spectral region between 520 and 750nm. Amplitude modulation of the pump pulses via an acoustooptical modulator (AOM) allows us to resolve pump induced transmission changes down to 10-6 utilizing a lock-in technique. The time between pump and probe pulse is defined by a mechanical delay line. Both pulse trains are overlapped via a dichroic beam splitter and focused (NA 0.9) on the sample. The transmitted light is collected by an oil immersion objective (NA 1.3) and filtered, to remove the modulated pump light. Finally, the transmitted probe intensity is detected by a photodiode which is connected with the lock-in amplifier. We compare the transient transmission experiment with time resolved photoluminescence spectroscopy by collecting the emitted fluorescence light in backward direction.
The CdSe nanowires were synthesized by the groups of G.V. Hartland and M. Kuno at the University of Notre Dame (USA). High resolution TEM images, such as shown in Fig. 2(a), reveal an almost constant radius over large parts of each individual wire but also small radius variations. Different wires show a radius distribution ranging from 3 to 7nm, underlining the necessity of single wire experiments. The nanowire under investigation is shown in the SEM image in Fig. 2(a) and has a radius of approximatel,ey 5.8nm, determined by AFM. Maximum absorption of the pump and probe pulses is achieved by linear polarization along the wire axis. Figure 2(c) shows the measured relative transmission variations ΔT/T in the visible and near-IR spectrum. The temporal overlap of pump and probe pulse defines the excitation at 0ps on the delay axis. Positive transmittance changes (yellow) correspond to a pump-induced decrease of absorption (bleaching) in the wire, and negative transmittance changes (black) correspond to an increase of the absorption. The missing signal contrast at negative time delays, when the system is probed before being pumped, proves the excitation of an undisturbed system and a full relaxation within the repetition rate of our laser system (13ns). Directly after excitation (delay 0ps) the nonlinear response significantly changes in the spectral region between 570 and 740nm, following a dispersive line shape. However, already 4ps later, the feature has disappeared and changed into a slowly varying purely absorptive line shape with its maximum at 685nm wavelength. We attribute these phenomena to a dense electron-hole plasma after the excitation and a bleaching of excitonic transitions, as we discuss in the following.
From numerical simulations, using the bulk optical properties of CdSe and taking the experimental conditions into account, we estimate that each pump pulse creates on the order of 400 electron-hole pairs in the excitation spot due to the large absorption of the nanowire at 390nm wavelength. This corresponds to an electron-hole density of roughly 1019cm-3. The carrier plasma leads to a renormalization of the band gap energy, causing a variation of the refractive index as observed in wires of larger diameter . Figure 3(a) shows the transient transmission spectra of the section labeled "plasma" in Fig. 2(c). We observe a rising dispersive signal within the first picosecond. In the following three picoseconds a transition from the dispersive to the absorptive line shape is observed. This indicates a decaying plasma caused by a very fast and efficient Auger recombination in the strongly confined nanowire. Finally for times above 4ps no further fast changes are recognisable and the remaining electron-hole pairs are bound in excitonic states.
In order to interpret the bleaching signal at later delay times, we need to know the eigenenergies of the electron and hole states (levels in Fig. 1(a)) and their transition strengths. We use a six-band-effective mass model , neglecting Coulomb interaction and limiting us to low quantum number states. We tune the wire radius in our simulation to reproduce the position of the low energy peak in Fig. 3(b), which is the average over the time interval labeled "bleaching" in Fig. 2(c). We find best fitting for a wire radius of 5.8nm, in agreement with AFM-measurements of the investigated wire. Higher energy transitions occur between more complex electron and hole states, bunching together into four effective states, which we label ωα to ωδ . These four states fully describe our transient absorption signal by only adjusting the amplitudes of four Gaussian lines of equal width, centered on the eigenenergies, as shown by the gray line in Fig. 3(b). Furthermore, the integral over an absorption line is connected with the transition dipole moment times the number of dipoles or excitons, respectively (see  for more details). We assume a purely radiative lifetime of 3ns of the emitters, as measured for CdSe nanocrystals, and calculate the transition dipole moment for the various transitions. This allows us to estimate the number of excitons in the different states that are created by each pump pulse. We find about 50 states being filled by the pump pulse of which about 30 populate the exciton ground state ωα. Distributed over a wire section within the probe focus diameter of approximately 400nm this corresponds to an averaged exciton-exciton distance of 12nm which is on the order of the Bohr radius of 5.6 nm of bulk CdSe.
In addition to the population of different states we are able to measure their lifetimes by scanning over a larger time delay range . We find that the population of the analysed states decays with spectrally rather independent rates between 2 and 5ns-1. It is instructive to compare these findings with the luminescence properties of the wire. The emission spectrum has a slightly distorted Lorentzian lineshape with its maximum around 705nm, indicated by the vertical line in Fig. 3(b). Furthermore, we measure a photoluminescence lifetime of approximately 800ps (1.25ns-1) and obtain a quantum efficiency of the wire of approximately 25% for the assumed purely radiative decay rate of 3ns. Consequently, we expect about 8 photons being emitted from the 30 excitons in the ground state. However, in our experiment we measure a factor of 500 less photons. We propose reabsorption as cause for the low emission intensity of the nanowire: After a photon is emitted it can be reabsorbed by other unexcited parts of the nanowire. This increases the overall probability of nonradiative recombination. In contrast, Förster type energy transfer is not possible as the near surroundings of the excited dipole are shifted out of resonance due to Coulomb interaction. We support this model by classical numerical simulations, where we consider a dipolar emitter in a bulk CdSe nanowire with a radius of 6nm. We compute the emitted power and re-absorbed power of the wire by taking the off-resonant region around the emitter into account. This simple model agrees well with the experimentally found mismatch between expected and detected photon rate.
In summary, we presented the first time-resolved ultrafast nonlinear spectroscopy of the exciton dynamics in quantum confined states of an individual CdSe nanowire. We observed the spectral response of two features on different time scales. The fast response within the first 4ps was attributed to a renormalization of the band gap energy, caused by an electron-hole plasma. The slower decaying phenomenon indicated the transition bleaching of various excitonic states and is supported by a six-band effective mass model. By the integral over the transient absorption line we estimated the time dependent population of the states and found approximately 50 excitons being created by each pump pulse. The comparison with the number of emitted photons, determined by photoluminescence measurements, revealed a strong mismatch. This pointed to re-absorption processes after the emission of a photon.