Heterostructure and Q-factor engineering for low-threshold and persistent nanowire lasing

Continuous room temperature nanowire lasing from silicon-integrated optoelectronic elements requires careful optimisation of both the lasing cavity Q-factor and population inversion conditions. We apply time-gated optical interferometry to the lasing emission from high-quality GaAsP/GaAs quantum well nanowire laser structures, revealing high Q-factors of 1250 ± 90 corresponding to end-facet reflectivities of R = 0.73 ± 0.02. By using optimised direct–indirect band alignment in the active region, we demonstrate a well-refilling mechanism providing a quasi-four-level system leading to multi-nanosecond lasing and record low room temperature lasing thresholds (~6 μJ cm−2 pulse−1) for III–V nanowire lasers. Our findings demonstrate a highly promising new route towards continuously operating silicon-integrated nanolaser elements.


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Filtered planes QW2 STEM QW1 QW region QW region Figure S1: Annular dark field (ADF) scanning transmission electron microscope (STEM) images of two quantum wells (QWs) within the same NW and corresponding fast Fourier transform (FFT) filtered images. The lines in the three respective filtered images correspond to the 220 planes in the three directions on the (111) plane. Scale bar represents 2 nm.

II. LASING DATA FOR ADDITIONAL NANOWIRES
A series of emission spectra and integrated emission as a function of excitation fluence are shown for 18 additional randomly selected example NW lasers in Figure S2 illustrating typical lasing characteristics under 620 nm excitation. These demonstrate the range of thresholds, lasing wavelengths and slope efficiency within the sample sets. It is noted that near-linear threshold behaviour is commonly observed, along with frequent single mode emission. Along with the observation of a range of lasing wavelengths, these findings support the premise of high quality laser cavities with inhomogeneous and potentially non-optimal quantum well growth. Figure S2: A series of spectra (left) and PL intensity as a function of excitation power (right) for 18 randomly selected NWs. Points and spectra in blue are before lasing is identified; points and spectra in red are above lasing threshold.

III. DAMAGE THRESHOLD MEASUREMENTS
The ratio of the lasing threshold to the damage threshold is a critical parameter determining lasing yield. Characterisation of the NW laser damage resistance was studied via power-dependent excitation measurements on ten NLs. The excitation intensity was controlled via rotation of a neutral density filter wheel through minimum to maximum intensity available. The measured output emission intensity was recorded as a function of excitation fluence to determine the point at which the output intensity drops. An example of such a plot is shown in Figure S3 where the damage threshold (D th ) is reached at ∼ 2400µJcm −2 pulse −1 ; this is at a fluence of ∼10× the lasing threshold (L th ∼ 240µJcm −2 pulse −1 ). Figure S3: Damage threshold (D th ) measured for an example NL under 620 nm excitation. For this wire, D th occurs at an excitation intensity ∼10×L th .

IV. PHOTOLUMINESCENCE EXCITATION (PLE) MEASUREMENT FOR ALL NWS
The normalized PLE spectra for all seven studied NWs are shown Figure S4. The high resolution measurement (bottom spectra) is the example displayed in the main text. Very similar behaviour is displayed for all wires demonstrating consistency, although differences in the relative height and centre positions of the three peaks (530 nm, 570 nm and 610 nm) are observed.

V. CHAMPION THRESHOLD MEASUREMENT
Under 570 nm excitation we demonstrate record low thresholds for III-V semiconductor NW lasers. The power dependent spectra and resulting intensity-in vs intensity-out curve for this champion NL are shown in Figure S5. Here emission intensity output is integrated over all wavelengths and the behaviour appears near-linear indicating that this may be a high β wire.

VI. INTERFEROMETRIC TIME CORRELATED SINGLE PHOTON COUNTING (I-TCSPC)
i-TCSPC is a technique which combines Fourier transform spectroscopy and TCSPC to obtain ultra-sensitive simultaneous measurements of time and spectrally resolved emission. Our setup is shown in the schematic in Figure  S6 and consists of a two-channel folded Michelson interferometer with the movable retro-reflector (RR) driven by a closed-loop piezo translation stage. The detectors are of the form of silicon single photon avalanche photodiodes (SPADs) connected to TCSPC hardware (HydraHarp 400) which receive a synchronisation signal from the excitation laser enabling time-resolved measurements. The sample emission from the µ-PL setup is fed into the interferometer via a single mode fibre and collimated. The measurement process involves scanning the movable mirror (RR2) through the position of zero-delay (δ=0) and storing a record of each photon arrival consisting of the delay-stage position (δ), time of arrival since excitation (τ ) and channel of photon arrival. This information enables measurement of the emission interferogram as well as time-decay. By taking the Fourier transform of the interferogram for photon arrivals within τ windows along the decay, time-resolved PL maps can be obtained (as seen in Figure 4 of the main text). The use of two channels in a folded setup enables throughput and differential interference enhancement (through subtraction of the out-of-phase channel signals).

VII. COHERENCE LENGTH MEASUREMENT AND CAVITY CALCULATIONS
The coherence length of the NLs exceeded the maximum optical delay provided by the interferometer delay-stage (200 µm). However the fixed mirror in the setup was mounted on a mechanical translation stage capable of providing up to 6 mm of delay with 5 µm precision. In order to recover the interference pattern to measure the lasing coherence length, a procedure consisting of a 200 µm i-TCSPC scan at δ=0 followed by successive 50 µm fixed mirror translations (providing 100 µm delay) and repeated measurement was used. Measurements after each fixed mirror translation were carried out under the same excitation conditions (time and power). The long-range NL interferogram was then recovered from a stitching method in post processing. Since the interference pattern is symmetrical through δ=0 µm, fixed mirror translation in only one direction was required. By reversing the data in the appropriate positions a bi-directional interferogram was recovered. By carrying out a fit to the interference visibility ( Imax(δ)−Imin(δ) Imax(δ)+Imin(δ) ) with Gaussian PL and lasing components the coherence length could be estimated from the FWHM of the lasing fit. Figure  S7 shows the bi-directional recovered interferogram (a) and interference visibility and fit (b). The PL component FWHM (∼18 µm) is similar for the interference visibility fit determined just below threshold where PL clamping occurs ensuring these values are meaningful. L coh = 980±70 µm was obtained with error propagation of the stage translation error and standard error on the fit. Note only the real half of the data is displayed in the main text. The standard laser cavity equations used for visibility and cavity Q-factor and reflectivity (R) calculations are shown below where τ coh and τ p are the coherence time and cavity lifetime respectively. Here we consider the end-facet reflectivity to be R = √ R 1 R 2 and used a NW length L= 14.5 µm deduced from an optical image of the NW in the PL regime (where the centre of emission points are taken to be the end facet positions). A GaAsP refractive index (n) of 3.4 at λ Las =780 nm was estimated from literature values for GaAsP [1].
Cavity Lifetime τ p = 2nL/c ln (1/R 1 R 2 ) Cavity Q-Factor Q = ωτ p VIII. TIME-RESOLVED SPECTRAL ANALYSIS Time-resolved spectral maps shown in Figure 4 of the main text were produced by taking the Fourier transform of the interferograms generated by photon arrivals in time-gated windows and taking the normalized absolute value of the resulting time-gated spectra. Analysis of the relative lasing/PL intensities was performed by carrying out fits of these spectra with Gaussian PL and lasing components (described by Equation 1 in main text). The relative peak area magnitudes A Las /A PL and peak PL energies (E PL ) were recorded and studied as a function of excitation power and time since excitation (τ ) to gain insight into the carrier/photon dynamics and underlying nanolasing mechanism.

IX. NEXTNANO MODELLING
One-dimensional simulations under pseudomorphic strain conditions were performed in nextnano software, to determine the band-edge positions throughout the heterostructure where absorption transitions may occur. The band-edges of the Γ and X conduction bands and the HH and LH valence band are shown in Figure S8 as a function of radial distance from the core. The magnitude of confinement for holes in the valence band quantum well is atypically larger than that of the electrons within the conduction band. This is known to occur due to strain related effects [2]. It is also notable that the light-hole heavy-hole degeneracy is lifted in the barrier due to the applied strain. Figure S8: Calculated band-edge positions within the heterostructure with Fermi level (E F) set to be the zero energy reference. Importantly the X conduction band is near isoenergetic (within kBT) throughout the structure enabling carrier transfer from barriers to quantum wells. The LH and HH band-edge energies are within close proximity throughout the structure.