Effect of Au substrate and coating on the lasing characteristics of GaAs nanowires

Optically pumped lasing from highly Zn-doped GaAs nanowires lying on an Au film substrate and from Au-coated nanowires has been demonstrated up to room temperature. The conically shaped GaAs nanowires were first coated with a 5 nm thick Al2O3 shell to suppress atmospheric oxidation and band-bending effects. Doping with a high Zn concentration increases both the radiative efficiency and the material gain and leads to lasing up to room temperature. A detailed analysis of the observed lasing behavior, using finite-difference time domain simulations, reveals that the lasing occurs from low loss hybrid modes with predominately photonic character combined with electric field enhancement effects. Achieving low loss lasing from NWs on an Au film and from Au coated nanowires opens new prospects for on-chip integration of nanolasers with new functionalities including electro-optical modulation, conductive shielding, and polarization control.


1.
Design of GaAs nanowire lasers (a) Growth process and morphology of GaAs nanowire lasers The GaAs NWs were grown by metal organic vapor phase epitaxy (MOVPE) on semi-insulating GaAs (111) B substrates. During the growth process, the substrates were pre-treated with poly-Llysine (PLL) and 100 nm Au colloidal solutions before placing them inside a horizontal flow reactor 1 . The PLL acts as a thin polyelectrolyte layer to electrostatically attract and immobilize the Au colloids on the substrate, which acts as a seed for GaAs nanowire growth. The growth process was executed at a high temperature of 575 ºC in presence of AsH3 and trimethylgallium at a V/III ratio of ~1.4. The zinc doping with an acceptor concentration of NA = 2x10 19 cm -3 changes the structure of NWs from a pure wurtzite crystal to a zincblende twining superlattice (TSL) crystal. More details on the growth process and optical properties of such NWs have been reported in Ref. 2 . The scanning electron microscope (SEM) image in Fig. S1 (a) shows the TSL structure of GaAs NW with alternating dark and bright contrast on the nanowire. The grown nanowires are hexagonal and conical in shape and most of the NWs have a mean diameter of 220 nm and length of 3 µm. A small fraction of ~5% of the NWs have a length of ~8-12 µm with a bottom diameter of ~510-570 nm and a tip diameter of ~100-135 nm. The investigation of lasing from broken off NWs with lengths ranging from ~2.5 to 6 µm and a core tip diameter ranging from 200 to 320 nm is the subject in this paper.
The GaAs NWs were subsequently coated with a 5 nm-thick Al2O3 layer by atomic layer deposition (ALD) to reduce the adsorption of atmospheric ions and metal induced band bending [3][4][5] . Figure S1 (b) shows the TEM image of a single nanowire with the Au catalyst and a 5 nm-thick Al2O3 layer grown around the nanowires. Some of these nanowires were nominally coated with ~10 nm thick Au layers by e-beam evaporation. Figure 1 (b) in the paper shows the TEM image of an Au-coated NW revealing that Au nanoplatelets and nanoparticles are formed rather than a continuous film. The Au nanoparticles range from 1 to 25 nm in size.

(b)
Sample preparation Three different designs of samples were investigated (i) Al2O3/GaAs NW on a glass substrate for reference (see sketch in Fig. S2), (ii) 10 nm Au/Al2O3/GaAs NW on a glass substrate, and (iii) Al2O3/GaAs NW on 200 nm-thick Au film on a glass substrate. The Au film was deposited on the glass substrate using an Organic Molecular Beam Deposition (OMBD) system. The growth temperature and growth rate of the Au film were 1150 °C and 0.014 Ås -1 , respectively. The GaAs NWs are very fragile and break into pieces with different lengths and varying tip and base diameters when they are removed from the substrate. Two different methods were applied to transfer bare Al2O3/GaAs and coated Au/Al2O3/GaAs NWs to an Au film substrate and glass substrate: (1) Sliding the vertically oriented GaAs NWs over the glass and Au-coated substrate (method 1). (2) Using a thin brush to pick off and transfer GaAs NWs to the desired substrates (method 2). The two methods result in a significantly different nanowire density on the substrates. Figure S2 (b) shows the SEM image of GaAs NWs transferred by method 1, and Fig. S2 (c) is the SEM image of NWs transferred on an Au-coated glass substrate when method 2 was used for preparing the samples. Method 1 reveals a high NW density of more than 15 NWs within the excitation laser diameter of 40 µm, whereas method 2 provides a NW dispersion of 1 to 5 NWs within the excitation spot of the pump beam is shown as a yellow circle in Figs. S2 (b) and (c).

(c)
Size distribution and identification of lasing NWs on the substrate Due to the high density of nanowires on the samples prepared by method 1, it was impossible to reliably identify the lasing NW during lasing experiment with an optical microscope or an SEM afterwards. The much lower density provided by method 2 allowed us to unambiguously identify the lasing NW. SEM and optical microscopy investigations of samples that were prepared with method 1 and method 2 revealed 20% long (>3 µm) and thicker NWs (with a mean diameter >300 nm). Figure S3 (a) and (b) shows histograms of NW mean diameter and length, respectively, prepared with method (1). The length and tip diameter of the nanowires on three samples prepared with method 2 ranged between ~2.5 to 6 µm and ~200 to 350 nm. Most of the NWs lost their tip (including the Au catalyst) during the transfer. The short (smaller than 1 μm) broken off NW tips have mean diameters less than 150 nm which is below the optical diffraction limit and thus did not show laser emission in the experiments. In order to find the lasing NWs conveniently after the optical experiments using SEM imaging, they were deliberately dispersed near the edges of the substrate. During the lasing measurements, magnified camera images of the lasing NW at low and high power were captured to pinpoint the lasing NWs on the substrate. In the SEM, these NWs were located by correlating the images of the spot from the CCD camera to the calibrated magnification scale of the CCD image with the scale of the SEM image. Figure S4 (a) and (b) shows the CCD image of the lasing GaAs NWs on a glass substrate at 10 and 75 mW pump power, respectively. Figure S4 (c) shows the SEM image of the same spot.

Nanowire laser characterization
The optical set-up used in the lasing experiments on the three types of samples has been briefly described in the paper. Figure S5 (a) shows a power dependent emission spectrum from a single GaAs NW on glass at a cryostat temperature of Tcryo = 77 K on a logarithmic scale pumped at λp = 720 nm. At a low pump power (less than 16 mW), the spectrum reveals a broad spontaneous emission band. At a pump power of 24 mW, several spectrally wide peaks emerge in the photoluminescence spectrum, which is attributed to longitudinal resonator modes of the amplified Figure S5 Lasing NW on a glass substrate (a) Power dependent lasing spectra of GaAs NW on glass measured at the cryostat temperature of 77 K at an excitation wavelength of 720 nm. The inset shows a polar plot of the lasing emission for different longitudinal modes. The solid lines in the inset are a guide for the eye. (b) SEM of the same lasing nanowire with a length of 6.1 µm, tip diameter of 250 nm and base diameter of 560 nm. The inset shows the interference pattern of the laser emission obtained from the NW on glass. stimulated emission (ASE). These peaks get more distinct and spectrally narrower with increasing pump power and become the lasing modes. At a pump power of ~150 mW, the linewidth of the longitudinal laser modes is narrow and close to 1 nm (note the logarithmic scale). The energy position of the laser lines suggests a higher lattice and carrier temperature in the nanowires compared to the cryostat temperature due to a high non-radiative recombination rate at the NW surface. A comparison between the calculated and the experimentally observed photoluminescence spectra at 77 K cryostat temperature (see section S4) resulted in an actual NW temperature of TNW = 160 K. The polarization of the emission peaks was analyzed by placing a polarizer in front of the entrance slit of the spectrometer. The polarization of longitudinal modes at 1.46, 1.48, 1.50 and 1.52 eV at 80 mW pump power is oriented along the NW long axis as shown in the polar plots in the inset of Fig. S5 (a). Figure S5 (b) reveals the SEM image of the same lasing NW on the glass substrate. The SEM measurements of the NW gave a length L = 6.1 µm with a tip diameter of 250 nm and a base diameter of 560 nm (NW #2 in table ST1). The inset in Fig. S5 (b) depicts the camera image of the emission from the same nanowire at a pump power of 80 mW. It reveals an intense and distinct interference pattern, confirming coherent laser emission from the nanowire. The spectral distance between the longitudinal laser modes is λ ∆ =10 nm in this NW. A group refractive index ng ≈ 5.6 was deduced using the relationship The dimensions of all investigated NWs on the three types of samples characterized by SEM are summarized in tables ST1, ST2, and ST3. The experimentally determined tip and base diameters of the nanowires include the 5 nm-thick Al2O3 coating for bare NWs on glass and on Au film substrate. This adds a 10 nm/cos 30° = 11.55 nm coating length to the outer diameter (equal to two times the side length of the hexagon) of the core GaAs nanowire. In the Au-coated nanowires with λ ∆ obtained from all NWs versus the inverse NW length (1/L) of the NWs are shown in Fig. S6. As expected, the longitudinal mode distances are nearly proportional to 1/L with an average slope corresponding to a group index of 5.7. The deviations from this average value are due to the varying hybridplasmonic contributions of the lasing mode and because the dependence of group index ng(d) on the NW diameter (see section 3 (e)).

Modeling of the NW waveguide parameters using FDTD calculations
Various parameters of the lasing nanowires such as waveguide mode profiles, effective refractive indices neff, group refractive indices ng, plasmonic losses αp, absorption cross sections σabs, reflectivity losses αR and confinement factors Γ of bare NWs on glass and on Au and of Au-coated NWs were calculated with finite-difference time-domain (FDTD) simulations (Lumerical Mode Solution, and FDTD Solution packages), using material parameters of glass 6 , Al2O3 6 , GaAs 6 and Au 7 at room temperature. In these simulations, un-tapered hexagonal GaAs NW were used. The outer diameters of the NWs ranged from 100 to 600 nm and the lengths L ranged from 1 to 6 µm. The waveguide modes in uncoated and in Au-coated hexagonal GaAs NWs are similar to the guided modes in an air-clad dielectric cylinder; hence a similar mode convention is used for describing various modes. In our FDTD calculations, we consider 6 modes (HE11a, HE11b, TE01, HE21a, HE21b, TM01, see also E-intensity distributions in Fig. S7). The letters "HE" in the mode type refers to hybrid modes, "TE" represents transverse electric, and "TM" denotes transverse magnetic. The subscripts 'a' and 'b' indicate the two-polarization states of the same mode, parallel or normal to the substrate surface. The numbers "11" or "12" describe the radial order and angular symmetry of the modes 1 . In GaAs NWs on Au film, 4 of the 6 waveguide modes are plasmonic or hybrid plasmonic modes. Two modes are mainly photonic modes. We enumerate these modes according to the descending magnitude of their effective refractive index values (mode 1 to 6).

(a)
Waveguide mode calculations The FDTD calculations (see below) revealed that for a GaAs core tip diameter of less than ~320 nm (which was the case in our investigated NWs) only the first three waveguide modes needed to be considered for lasing. The electric field profiles of the guided modes in a hexagonal GaAs NW with a diameter of 300 nm in the three configurations is demonstrated in Fig. S7. In all designs, the optical gain is provided by the GaAs NW core, while the Au nanoparticle shell around the NW and the Au film for the NW on Au film substrate contribute to optical losses because of plasmonic dissipation. Figures S7 (a), (b), (c) show the supported photonic modes HE11a, HE11b, TE01 in GaAs NW coated with 5 nm thick Al2O3 on the glass substrate. It will be shown later that, depending on the tip diameter of the investigated NWs, the lasing mode is either a HE11a/b or a TE01 mode.
Guided mode simulations of Al2O3/GaAs NWs lying on a 200 nm thick Au-coated glass substrate are shown in Figs. S7 (d), (e), and (f). Mode 1 and mode 3 show a plasmonic character with the Efield being predominantly confined in the Al2O3 layer. Waveguide mode 2 shows a predominantly photonic behavior with a small plasmonic contribution at the NW/Au interface. In section 3(e) it will be shown that mode 2 is the preferred lasing mode for all investigated NWs on Au.
The profiles in Figs. S7 (g), (h), and (i) show the guided modes in the GaAs NW coated with a 5 nm-thick Al2O3 layer and a 10 nm Au-air (p = 0.33) effective medium (EM) around the NW. The modes HE11a, HE11b and TE01 in these coaxial structures are predominantly photonic.

(b)
Effective refractive index (neff, κ) Figure S8 shows the real part of the refractive index n(d) as a function of the outer diameter d (which is two times the length of a hexagon side) for various guided modes supported in an untapered Al2O3/GaAs NW on glass. (The NW diameter includes the Al2O3 layer.) The NW diameter ranges from 100 to 600 nm. The waveguide mode calculations are performed at a wavelength of λ = 880 nm (~1.41 eV), which is a typical NW lasing wavelength at room temperature. The material parameters of GaAs, Al2O3, and SiO2 in the simulations are from Palik et al. 8 . Different modes (HE11a, HE11b and TE01 are shown in Fig. S7) provide light confinement at different NW cutoff diameters. Modes with refractive indices below the index value of glass (n ~1.5) leak into the substrate. The effective refractive index increases with nanowire diameter. Lasing GaAs NWs on glass provide optical gain instead of absorption at λ = 880 nm. Therefore, the imaginary part of the refractive index was set to κ = 0 for bare NWs on glass, assuming no further losses due to scattering at the NW surface or at the NW end facets.

Figures S9 (a) and (b) show the real and the imaginary part of the refractive index n(d) and κ(d)
as a function of the outer diameter for an Al2O3/GaAs NW on Au film. The complex refractive index of the Au film at room temperature is taken from Johnson and Christy 7 . The mode cut-off diameter is reached when the refractive index falls below the value of air (nair = 1). When a GaAs NW is placed on the Au layer the imaginary part of the effective refractive index κ(d) needs to be considered. The κ values shown in Fig. S9 (b) indicate the plasmonic or Ohmic losses occurring at the metal surface. Large plasmonic losses imply high threshold gain values gth for lasing. The loss of plasmonic mode 1 (see Fig. S7) is high over the entire NW diameter range preventing plasmonic lasing. Other modes show lower plasmonic loss. Above the cutoff diameter of ~180 nm but below ~250 nm, mode 2 is a hybrid plasmonic-photonic mode with moderate plasmonic losses as indicated by the shaded area in Fig. S9 (b). Above 250 nm diameter mode 2 becomes increasingly photonic (see also Fig. S7) showing low plasmonic losses. Modes 3 to 5 remain hybrid plasmonic-photonic modes with moderate losses throughout the entire diameter range. Mode 6 has again a predominantly photonic character. Modes 2 and 6 reveal the lowest κ values for nanowire diameters above 300 nm emphasizing that these modes oscillate when the NWs are lasing.
In the case of Au-coated NWs, we performed simulations using a 10 nm-thick granular air/Au effective medium (EM) layer (see Fig. 1 in the manuscript). Since the Au clusters are in close vicinity with each other, the localized surface plasmons of individual nanoclusters can interact with each other and can be approximately treated as surface plasmon polaritons (SPPs) in an air/Au effective medium layer 9 . The complex refractive index of the composite metallic Au/air granular film is determined using effective medium (EM) theory. The effective dielectric permittivity ( e ε ) of two dimensional composites is given by 10 , where m ε is the permittivity of Au, d ε is the permittivity of the dielectric GaAs and p is the filling factor of the Au in the Au/air film. The sign in eq. (S2) needs to be chosen appropriately to result in a positive imaginary part of e ε . Using a p ~0.33 Au filling factor (estimated from the TEM image shown in Fig. 2 in the main text) we obtain a complex refractive index 2.22 0.244 n iκ + = + at a lasing wavelength of λ = 880 nm. This value has been implemented into the Lumerical program for calculating the effective refractive index, group index, facet reflection and confinement factor for Au-coated nanowires. Figures S9 (c) and (d) show the real and imaginary part of the refractive index n(d) as a function of NW diameter d for a nominally 10 nm thick EM Au-coated Al2O3/GaAs nanowire with an Au-to-air filling fraction of p = 0.33 on glass. Figure S9 (c) reveals very similar refractive indices as for GaAs NW on glass (see Fig. S8). The cut-off diameters of the GaAs core, when the refractive index of glass is reached, are somewhat smaller than for uncoated NW on glass. The imaginary part κ of the refractive index for Au coated nanowires is shown in Figure S9 (d). Au coated GaAs NWs show a higher plasmonic loss than mode 2 in GaAs NWs on Au films, suggesting higher gth values to facilitate lasing.
Due to the conical shape of the highly Zn doped GaAs nanowires the refractive index of a waveguide mode continuously changes within the nanowires as function of the nanowire diameter d. We therefore approximated the effective refractive index neff + iκ for a specific mode in a conically shaped NW by calculating the average value of functions n(d) and κ(d) i.e.
where c is the speed of light in vacuum, na is the effective refractive index of the guided mode, ε0 is the vacuum permittivity and Pz is the power flow in the propagation direction. Aa is the active area in which gain is provided. In the confinement factor calculation for GaAs NWs on glass and on Au film, the Al2O3 coating is therefore not considered as an active Aa. In Au-coated NWs both the Al2O3 and the EM Au-coating are excluded from Aa. The 6 modes supported in the three NW configurations have confinement factors that depend on the NW diameter (Figs. S10 (a), (b), and (c)) The confinement factors of the waveguide modes in bare and in Au-coated NWs on glass are again very similar, showing a rapid decrease near the mode cutoff diameter and a decrease with increasing nanowire diameter.
The confinement factors of GaAs NWs on Au film, shown in Fig. S10 (b), demonstrate a high confinement factor Γ of ~1 for the plasmonic mode 1. In addition, the confinement factor is almost independent of the NW diameter. The confinement factors for modes 2 to 6 decrease swiftly near the mode cut-off diameters and show similar values as in the bare and Au-coated NWs.
Like for the effective refractive indices we approximated the confinement factor Γ of different modes in the conically shaped NW by the average value of the function Γ(d).

(d)
Facet reflection The facet reflection of the guided modes in the NWs for the three configurations was calculated in a similar way as described in the supplemental information in Ref. 1 . Since the broken GaAs NWs are missing the NW tip with the Au catalyst, we only calculated the end facet reflections Rt and Rb at the NW top and base, respectively, at the NW/air interfaces.
The mode reflectivity in a GaAs NW on glass for different guided modes as a function of the nanowire diameter is shown in Fig. S11 (a). When the diameter of the nanowire approaches the threshold diameter, the facet reflection decreases rapidly. The estimated facet reflection in a GaAs NW on Au film as a function of its diameter is presented in Fig. S11 (b). Figure S11 (c) shows the facet reflection in an Au-coated GaAs nanowire on glass as a function of diameter. The facet reflection for all 6 modes shows a similar trend as for the modes in a NW on glass.
Because of the conical shape of the highly Zn-doped NWs the total facet reflection of the nanowires was determined by the geometrical mean of the tip Rt and base facet Rb reflectivity given by Here, Γ is the confinement factor of the waveguide, ng is the group index of the waveguide, Γ0 is the ratio of the energy in the active region of the waveguide to the energy in the whole waveguide, nb is the effective refractive index of the gain medium 11 . Figures S12 (a), (b), and (c) show the group indices as function of the outer nanowire diameter in the three types of samples. As for the effective refractive indices, we approximated the group indices of different modes in a conically shaped NW by the average value of the functions ng(d).
Figures S13 (a), (b), and (c) compare the experimentally obtained group index ng of nanowires with the theoretically calculated averaged ng values for different modes. This comparison enables the identification of lasing modes in all three design configurations. Figure 13 (a) shows the calculated group indices of modes HE11a, HE11b and TE01 and the experimental ng values of 5 lasing nanowires on glass at 77 K using eq. (S1). The dimensions of the investigated nanowires are given in table ST1. Comparison with calculated values reveals that TE01 mode is the lasing mode in all NWs on glass. Figure S13 (b) shows the calculated ng values of GaAs nanowires on Au film for 6 lasing nanowires. The ng values calculated from Lumerical calculations are in the range of 5 to 6 and correlate well with the experimentally obtained group index of mode 2. Figure S13 (c) compares the experimentally determined ng values for all investigated Au-coated nanowires on glass with the theoretically calculated results. Most of the nanowires exhibit ng values between 5 and 6.5, which is close to the ng values of the TE01 mode. NW #2 has a group index that is close to the calculated value of HE11a mode because of the small tip diameter of ~230 nm  (corresponding to a core diameter of ~200 nm), which is below the cutoff diameter of the TE01 mode.

(f)
Threshold gain calculations The threshold condition for lasing is calculated using the equation below [9] 1 1 ln where Γ is the mode confinement factor, gth is the threshold gain of the GaAs NW, L is the length of conical nanowires, is the mode reflectivity calculated by taking the geometric mean of the reflectivity at the top and bottom end facets. αp is the plasmonic loss calculated using the imaginary part κ of the effective index of NWs.
All the parameters discussed above are obtained by averaging the parameter functions between the tip and base diameter as explained earlier. With these parameters, the threshold gain values of all supporting modes are calculated and compared to each other. Waveguide modes with the lowest threshold gain are assigned to the observed laser modes. The lowest calculated threshold gain values for the three types of NWs are summarized in tables ST4, ST5 and ST6. The last row of the tables shows calculated parameters and gth values of the "average" model NW in each configuration. The calculated gth values of these "average" model NWs are compared with the threshold gain gth values obtained from the rate equation analysis of lasing nanowires described in section 8.   (g) Estimation of the absorption cross-section The absorption cross-sections σabs were estimated using a 6-sided truncated pyramid for the Al2O3/GaAs NWs on glass, on Au film and for Au-coated NWs. Tapering of the NWs was included by providing the tip and base diameter as well as the length of the truncated nanowire in the Lumerical script. In these calculations, which are important for the rate equation analysis described in section 8, an "average" model NW for each of the three configurations was considered.
The wavelength of the incident light source was λp = 720 nm. The light polarization was set parallel and perpendicular to the NW long axis to consider polarization dependent light absorption. The absorption cross-section values of both polarization directions were averaged. In the case of the EM Au-coated Al2O3/GaAs NW on glass substrate, the absorption cross section in the GaAs core was estimated by subtracting the pump pulse dissipation in the Au-coating. The latter was obtained from an EM Au-coated GaAs NW with an imaginary index value κ set to zero in the GaAs core.
Because of the high doping level of the Zn-doped GaAs NWs (p = 19 2 10 × cm -3 ) and the resulting energy position of the Fermi-level EFermi within the valence band, the optical absorption from the heavy-hole band is essentially blocked. Figure S14 demonstrates this situation at a temperature of T = 77 K where the Fermi energy is calculated to be 56 meV below the valence band minimum. Therefore, for light excitation with an energy of 1.72 eV (λp = 720 nm) nearly no electrons are present in the heavy hole-band, while the transition from the light-hole band to the conduction band is unrestricted. Therefore, the calculated absorption cross-section values σabs were corrected by a blocking factor bf of approximately bf = 0.35. At room temperature the blocking of the heavy-hole band to the conduction band is relaxed leading to a correction factor of bf = 0.6. Table ST7 summarizes the calculated absorption cross-section values σabs for the "average" NWs for the different lasing configurations at 77 K. The absorbed pump power ηp in the NW was estimated according to ηp = bf σabs /As, where As is the incident laser spot area. For the 295 K experiments the NW dimensions were estimated from the longitudinal mode distances in comparison with Fig. S6 and Fig. 6. The calculated absorption cross-section values σabs for NWs with estimated dimensions at 295 K are shown in Table ST8.
ST7: Calculated absorption cross-section values for the "average" model NWs in the three configurations at 77 K.

Samples
Average

Determination of NW temperature from photoluminescence spectra
The lattice and the carrier temperature of optically pumped NWs was estimated by comparing the photoluminescence spectra obtained at pump levels below the threshold for amplified spontaneous emission (ASE) with the calculated spontaneous emission spectrum at a specific temperature. The spontaneous emission (luminescence) spectrum of direct, bulk semiconductors is theoretically expressed by 1,12 , at the conduction and at the valence bands of the NWs were calculated using a Polylogarithm function of order 3/2 as described in 13 . n and p are the photo-excited carrier densities and 19 -3 corresponds to the density of holes provided by the Zn-acceptors 2 . In the calculation, we used the parameters given in the supplementary table 3 of Ref. 2 . We further considered a temperature induced band-gap shrinkage 2 . 2 4 ( ) 1.519 5.405 10 eV 204 The PL spectra obtained from Al2O3/GaAs NWs on glass, on Au film and from EM Au-coated NWs at low pump pulse fluences and at a specific cryostat temperature look very similar. Figure S15 shows the PL spectra from NWs on Au film and on glass obtained at cryostat temperatures of Tcryo = 77 and 295 K, respectively. The emission band at 1.48 eV at Tcryo 77 K is attributed to a Znacceptor related transition 2 . The blue full lines show the calculated PL spectra derived with eq. (S6). The calculations reveal that the temperature TNW in the NWs is ~80 to 90 K higher than Tcryo.
In these calculations, a line-shape broadening γ of 4 and 6 meV was used at both TNW = 160 and 370 K, respectively. The higher NW temperature TNW is attributed to the high rate of non-radiative surface state relaxation.

Temperature dependent measurements
A temperature-controlled, continuous nitrogen flow cryostat was used to perform lasing experiments at temperatures ranging from 77 to 295 K. Figure S16  The weakening of the high-energy laser mode k =61 at 1.50 eV is accompanied by an increase of the k = 60 mode at 1.46 eV. This is caused by the temperatureinduced shift of the gain spectrum to lower energy, which increases the overlap with lower energy modes at higher temperature.

Estimation of the real power emitted from the NWs
In both the lasing spectra and the L-L curves the NW laser intensity is given in counts per millisecond (counts/ms) as acquired by the CCD spectrometer. To estimate the real power emitted from the lasing NW, the detector head of a power meter was placed at the position of the glass fiber  entrance of the spectrometer. The sensitivity of the power meter was ~1 nW. After each pump power increase a measurement with both the spectrometer and with the power meter was performed on the same NW. To measure the power meter background correctly, the NW was moved out of the laser spot of the pump pulse using the micrometer translation stage at the cryostat. The results of these measurements are plotted as the peak power of the NW emission versus pump power (L-L) on a logarithmic scale in Fig. S17. The blue symbols represent the signal intensity obtained from the NW. Red symbols show the measured NW laser power at corresponding pump powers. Taking into account a geometrical factor of 2 / (4 ) L A f π = 0.0115 with AL = 2.54 cm 2 being the crosssectional area of the microscope objective lens with a focal length of f = 4.2 cm, we estimate that a longitudinal laser line with a peak signal intensity of 0.1 counts per millisecond corresponds to a real emitted NW laser power of approximately 1.7 µW.

Modeling of the material gain in GaAs
The gain spectrum as a function of carrier density for direct, bulk semiconductors is theoretically described by 1,12,14 f E are the three-dimensional, reduced density of states function and the Fermi-Dirac function for the conduction and valence band, respectively. As described in section 4, ( ) is the mean distance between electron hole pairs with respect to the exciton Bohr radius of = 11.6 nm. np is the electron hole-pair density (which is equal to n = p) and / B XB kT E τ = is the lattice temperature normalized with respect to the exciton binding energy. Figures S18 (a) and (b) show the calculated gain spectra at different optically excited electronhole pair concentrations, as labelled, and at NW temperatures TNW = 160 and 380 K (which corresponds to Tcryo = 77 and 295 K as explained above). In the calculations, we neglected temperature dependent changes of the ionized acceptor density A N − , which is a good approximation for degenerately doped semiconductors 17 . As expected, the gain spectrum becomes wider with increasing photoexcited carrier density and the peak gain at the corresponding carrier density shifts to lower energy with increasing temperature because of the band-gap shrinkage. The thick solid line in the gain spectra indicates the critical carrier density n = Nsat, where the energy difference between the quasi-Fermi levels is approximately equal to the energy of the exciting laser wavelength of 720 nm (~1.72 eV). At this point the GaAs NWs are starting to become transparent. Thus, the generation of photoexcited carriers is reduced. We consider this saturation effect when we calculate the NW emission power versus incident pump power (L-L plot), as described in the next section.

Rate equation analysis of NW lasing
In order to analyze the observed lasing behavior of the different NW configurations more quantitatively, we modeled the laser power output versus pump power using a coupled rate equation model for the photo-generated carrier density N and for the emitted cavity photons S, as described in Refs. 1,12 .
In eq. (S10), the first term on the right side describes the generation rate of electron-hole pairs N η ω  and V are the fraction of pump power that is absorbed, the excited photon energy and the volume of the nanowire or its active region, respectively. ηp is given by p , where abs σ is the absorption cross section of a nanowire with a particular diameter and length. As is the pump pulse spot area and bf is a blocking factor defined in section S3 (g). abs σ was calculated with FDTD simulations for a laser spot diameter of ~40 μm. To account for the saturation of photo-excited carriers at λp. = 720 nm, was multiplied with a saturation factor (1-N/Nsat). The saturation density Nsat was estimated by the material gain spectra calculated at different temperatures (see Fig. S18). The NW volume was calculated by 2 V r L π = with r being the outer radius of the "average" NW of the conically shaped GaAs NW in each configuration and with L being the length of the "average" NW. The second term in eq. (S10) describes the non-radiative recombination of excited carriers, where 2 / s A r ν = with the surface recombination velocity S v . In our calculations, we use the surface recombination velocity of 6 2.18 10 × cm s -1 as given in Ref. 2 . The third term describes the spontaneous (radiative) recombination rate for highly Zn-doped GaAs NWs. The bimolecular recombination coefficient is 11 9 ( 3.47 10 ln 1.63 10 ) . The last term in eq. (S10) describes the depletion of carriers by the emission of photons Si in longitudinal mode i. Here, g v and g(N) are the group velocity and the gain, respectively. In the calculations we used group index values ng = 4.7, 5.6, 6.2 for the "average" NWs on Au film, on glass and for Au-coated NWs, respectively.
The first term in the rate equation of emitted photons S in eq. (S11) describes photon generation by stimulated emission into longitudinal mode i. Γ is the mode confinement factor of the "average" NW which has been calculated with Lumerical MODE solutions (see section S3 (c)). g(N) is the material gain which can be expressed as Parameters g0, Ntr and Ns (with Ntr being the transparency carrier density and Ns being a shift to keep the logarithm finite at density N = 0 12 ) were determined by fitting ( ) g N with the calculated material gain spectra at the wavelength of typical laser lines. Table ST9: Parameters g0, Ns and Ntr obtained by fitting the material gain spectra at lasing energies of 1.51 and 1.41 eV at NW temperatures TNW of 160 and 380 K, respectively.
Figure S18 (c) shows extracted g(N) values from gain spectra at 160 and 380 K at typical lasing energies of 1.51 and 1.41 eV, respectively. Also shown are fits (solid lines) with parameters g0, Ns and Ntr that are summarized in table ST9. The second term in eq. (S11) considers the generation of photons due to spontaneous emission. The spontaneous emission coupling factor was adjusted in the calculations to β = 0.15 for NW on glass and to β = 0.2 for Au coated NW and for NW on Au. and Vp is the mode volume V/Γ. The obtained calculated Pout was multiplied with an adjustment factor to match the experimental data. In calculating the carrier densities N(t) and the photon density S(t) at different nanowire temperatures (TNW = 160 and 380 K) we neglected any temperature dependence of coefficients A, B, C and D. We also did not consider temperature induced changes of the ionized acceptor density NA, which are negligible for degenerately doped semiconductors 20 .