Lasing in Zn-doped GaAs nanowires on an iron film

In this work, we demonstrate optically pumped lasing in highly Zn-doped GaAs nanowires (NWs) lying on an iron film. The conically shaped NWs are first covered with an 8 nm thick Al2O3 film to prevent atmospheric oxidation and mitigate band-bending effects. Multimode and single-mode lasing have been observed for NWs with a length greater or smaller than 2 μm, respectively. Finite difference time domain calculations reveal a weak electric field enhancement in the Al2O3 layer at the NW/iron film interface for the lasing modes. The high Zn acceptor concentration in the NWs provides enhanced radiative efficiency and enables lasing on the iron film despite plasmonic losses. Our results open avenues for integrating NW lasers on ferromagnetic substrates to achieve new functionalities, such as magnetic field-induced modulation.


Introduction
Optical platforms based on photonic integrated circuits (PICs) can overcome the limitation of bandwidth, processing speed, and power consumption of microelectronics chips. This prospect has triggered the research on materials and designs that can manipulate light at the nanoscale and complement the functionalities of integrated circuits and devices such as transistors, amplifiers, and modulators [1][2][3]. Semiconductor nanowires (NWs), with their one-dimensional structure, high refractive index, and electromagnetic wave confinement at the nanoscale, are excellent candidates for optical platforms. They can operate as waveguides, lasers, modulators, phototransistors, and photodetectors, which are crucial elements in PICs [3][4][5][6]. Optical platforms with NW components will lead to advancements in applications such as telecommunication, sensing, and medical diagnostics [2,7,8].
An essential step towards integrating active and passive NW components in PICs is the controllability of their optical properties using an external agent. Different regulating mechanisms, such as voltage, temperature, and photons, have been used to achieve active photonic-plasmonic NW devices [9][10][11]. An alternative approach to control and manipulate their optical properties is with a magnetic field. A magnetic field with its ultrafast behavior is suitable for attaining a femtosecond level switching rate [12,13]. An applied magnetic field on NW lasers could regulate photon generation [14] and carrier movement [15] inside NWs due to magnetooptic (MO) or magneto-plasmonic (MP) effects [16], similar to Faraday, Kerr, and Hall effects.
MO interaction in a photonic NW laser is constrained by the small Verdet constant of semiconductor materials [17]. Plasmonic NW lasers use Au and Ag as substrates which have moderate plasmonic losses but possess only meager MP properties. On the other hand, ferromagnetic materials exhibit strong magnetic field effects but have much higher plasmonic losses than noble metals, thereby limiting the possibility of MP waveguides and applications [12,13].
This work demonstrates multimode and single mode lasing in hybrid photonic GaAs NWs on a plasmonic ferromagnetic Fe film. The NWs have a high Zn concentration of 2 × 10 19 cm −3 and are covered with an 8 nm thick Al 2 O 3 film to prevent oxidization and reduce band bending effects. The high acceptor concentration improves radiative recombination and decreases the transparency carrier density [18], thereby facilitating lasing despite plasmonic losses in the Fe film. The lasing experiments were theoretically supported by finitedifference time-domain (FDTD) simulations and light-output and light-input (L-L) calculations. The simulations demonstrate that the lasing modes have a weak plasmonic field enhancement within the Al 2 O 3 interlayer between the NW and Fe film. The hybrid photonic-plasmonic nature of the modes leads to moderate plasmonic losses but has the potential to enhance magnetic field induced effects [19] due to the interaction of photogenerated carriers in the NW with the emerging magnetic fields from a magnetized iron substrate or its magnetic domains.
Our results using a ferromagnetic material like Fe as a substrate provide a path for adding new magnetic field induced functionalities to hybrid photonic-plasmonic NW lasers, isolators, modulators, and interconnects, similar to MP structures [19,20] but with significantly reduced plasmonic losses.

Growth and characterization of the GaAs NWs and of the iron film
The NWs were produced by a gold catalyzed, metal-organic vapor phase epitaxy process [18,21] under the same experimental condition and with the same Zn acceptor doping level of N A = 2 × 10 19 cm −3 as described in [18] and in the supplementary document (paragraph 1). Figure 1(a) shows the SEM image of the GaAs NWs grown on GaAs (111) substrate. These NWs have an average length of 3.2 μm with a few as long as 10 μm. The bright/dark contrast on the NWs indicate a twinning superlattice structure because of the effect of Zn doping [18]. The NWs were coated with an 8 nm thick Al 2 O 3 by atomic layer deposition to minimize band bending effects (see TEM image in inset figure 1(a)).
For the experiments, the NWs were mechanically transferred with a small brush onto a ∼400 nm thick Fe film (purity of 99.995%) deposited on a silicon (100) substrate through e-beam evaporation at a rate of 2-3 Å s −1 at room temperature. The transferred NWs break into random lengths varying from 1 to 6 μm and tip diameters varying from 150 to 400 nm. Figure 1(b) shows the schematic of a GaAs NW laser lying on the Fe/Si substrate. Figure 1(c) shows the x-ray diffraction spectrum of the Fe film on Si (100) substrate, recorded using the Kα Cu radiation of wavelength λ = 1.54056 Å, in the range of 30°-90°. The spectrum shows a prominent diffraction peak at 44.6°and two smaller peaks, 65°and 82°, corresponding to the Fe (110), Fe (200), and Fe (211) Bragg reflection of a body-centered crystal structure, respectively. The strong intensity of the (110) peak indicates that the orientation of the film is predominantly in 〈110〉 direction, which is expected for e-beam evaporated Fe film [22]. The lattice constant was calculated using Bragg's and Scherrer's formula to 2.87 Å, similar to the bulk lattice constant, and the width of the peaks revealed a Fe crystallite size of ∼9 nm, indicating a polycrystalline film. Atomic force microscopy (shown in figure S1(a) of the supplementary document) shows a root mean square surface roughness of 0.35 nm for the Fe film. The profilometry of the Fe film (an example of the measure is shown in figure S1(b) in the supplementary document) returned a thickness of 380 ± 20 nm. The NWs on the Fe film were further investigated by scanning electron microscopy (SEM) to obtain their accurate dimensions. The transfer of the NWs, together with the identification and characterization of the lasing properties of the NWs are described in [23].

FDTD calculations of GaAs NW on iron films
The optical parameters of GaAs NWs such as waveguide mode profiles, effective refractive indices (n eff ), group refractive indices n g , plasmonic losses (α p ), absorption cross sections (σ abs ), reflectivity losses (α R ), and confinement factors (Γ) for six different modes were calculated using FDTD and Lumerical Mode Solution packages [23]. In the simulations, an un-tapered, hexagonal, and conical NW with a diameter of 200-600 nm surrounded with an 8 nm Al 2 O 3 layer, lying on an iron film was modeled. The material parameters of silicon, Al 2 O 3 , GaAs, and iron film at the wavelength of 880 nm in the calculations were taken from the literature [24,25]. To account for the variation of the effective refractive index and the κ value for its conical shape, the values are averaged using the functions where d t is the tip diameter, and d b is the bottom diameter of the truncated NW under investigation. Figure 2(a) shows the refractive index (real part) n(d) for Al 2 O 3 /GaAs NW on iron film. A mode cut-off for the NW was considered when the refractive index values reached ∼1 (identical to air). The imaginary refractive index κ(d) that signifies the losses due to the iron film is shown in figure 2(b). The losses for mode 1 and mode 2 were highest for NWs with a diameter of 200 nm, which decrease with diameter. Mode 2 shows the lowest losses for NWs with a tip diameter greater than 300 nm. Mode 3 has high losses, which increase exponentially from a diameter of 200-300 nm and later decrease as the diameter approaches 600 nm. Like mode 3, mode 5 presents a similar trend in the variation of the imaginary refractive index with diameter, with highest losses for 300 nm diameter NWs. Modes 2 and 6 show an analogous trend as a function of the diameter and have the least losses for NWs with a diameter larger than 400 nm, indicating a pure photonic mode. The intermediate losses in modes 4 and 5 below a diameter of 400 nm suggest a hybrid photonic lasing with plasmonic confinement in the Al 2 O 3 layer between the NW and the iron film. Modes 1 and 3 show high losses below 400 nm, indicating pure plasmonic modes.
The confinement factor of the 6 modes for the NW on the iron film is depicted in figure 2(c). Analogous to the effective index, the confinement factor was averaged considering the tip and base diameter. The confinement factor decreases suddenly for all the NWs near their cutoff. All modes show a confinement factor greater than 1 for diameters larger than 350 nm. The confinement factors of modes 2-6 decrease when the NWs reach a diameter of ∼600 nm. Mode 1 offers constant confinement of ∼1 for diameters greater than 350 nm. Mode 6 shows the highest confinement factor among all 6 modes and displays a value of ∼1.6 at a diameter of ∼400 nm. Mode 2 has the highest confinement factor of ∼1.6 at a cutoff diameter of 200 nm and decreases rapidly to ∼1 as the diameter increases to 600 nm. The facet reflection of the GaAs NWs on the iron film as a function of NW tip diameter is shown in figure 2(d). The reflectivity of the conical NWs was calculated by finding the geometric mean of R t and R b , calculated as R R R .

Results and discussion
Lasing experiments on GaAs NWs lying horizontally on a Fe film were performed in an optical setup described in [23]. The NW sample was placed inside a liquid nitrogen-cooled cryostat, and single NWs were excited with ultrashort laser pulses tuned to a wavelength λ p = 720 nm. The beam diameter on the sample was 40 μm. Excitation power dependent measurements were performed at a cryostat temperature T cryo = 77 K. The emission from each NW was sent through a polarizer to analyze the lasing modes. Figure 3(a) shows the power dependent emission from a single NW on the Fe film. At a low pump power of 4 mW, the NW emits a broad photoluminescence spectrum. With increasing pump power to 12 mW, the broad spectrum becomes narrower. At a pump power of 40 mW, the emission intensity at 1.49 eV increases exponentially, indicating the onset of amplified spontaneous emission, which converts to lasing at higher pump levels because of the increasing optical gain. Increasing the pump power also extends the gain spectrum to higher energy (see figure S18(a) in [23]) leading to a second longitudinal laser mode with an energy position at 1.52 eV. Pump power levels above 80 mW narrow the emission linewidths to a few nanometers, signifying the onset of lasing of the second longitudinal mode. Polarization dependent measurements (displayed in the inset of figure 3(a)) indicate that the two longitudinal modes at 1.49 and 1.52 eV originate from the same NW. SEM (shown in figure 4(b)) revealed that the emissionoriginates from a NW with a length of 3 μm, with a tip diameter (t d ) of 370 nm and a base diameter (b d ) of 580 nm. The mode distance Δλ of the laser emission is ∼20 nm. The expression n g = λ 2 L /2LΔλ L , where λ L is the emission wavelength, provides a group index of n g = 5.72. This index corresponds to the longitudinal mode numbers k = 41 and 42 for the 1.49 eV and 1.52 eV laser lines, respectively. Figure 3  group indices for the waveguide modes were also theoretically calculated using FDTD modeling as described in [23] and shown in figure 3(c). The assignment of the transverse lasing modes (modes 1-6) to different NWs was performed by comparing the experimentally calculated group indices of the NWs with those calculated theoretically and displayed in figure 3(d). Most of the NWs have a group index n g between 5 and 7. The NWs with tip diameters below 300 nm have an experimental group index similar to the calculated value of transverse mode 2 for NW #3 and NW #4 (see also table ST2 in the supplementary section). NWs with tip diameters between 325 and 375 nm (NW #2, #5, and #8) have an experimental group index close to the theoretical value of mode 4 (see table ST2 in the supplementary document). For NWs with a diameter greater than 375 nm (NW#1, NW#6, NW #7), mode 6 was the supported transverse laser mode, (see table ST2 in the supplementary document).
The mode assignment was further supported by calculating the threshold gain of individual NW lasers using Here, Γ is the mode confinement factor, g th is the threshold gain of the GaAs NW, L is the NW length, and R is the mode reflectivity at the end facets. α p is the ohmic loss due to Fe film, calculated using the imaginary part κ of the effective index of the NW. The optical parameters for individual NWs were obtained from FDTD simulations (see figure 2). Modes with the least threshold value were deemed as the lasing mode for the respective NW. The values of the threshold and the assigned modes are shown in table ST2 of the supplementary document.
The lasing characteristics of the NWs on Fe film were studied by evaluating the laser output versus the laser pump power, i.e. L-L plot, using the coupled rate equation for the generated carrier and photon densities. The complete information and description of the equations and the modeling parameters are described in [23]. Figures 4(a), (d), and (g) Single mode lasing was observed at 77 K for NWs with a length smaller than 2 μm. Figure 5(a) shows pump power dependent 77 K lasing spectra of a short GaAs NW with a length of 1.45 μm, a tip diameter t d of 300 nm, and a base diameter of 435 nm, as revealed in figure 5(b). The inset of figure 5(b) shows the interference pattern of the laser emission at a pump power of 60 μJ cm −2 . Figure 5(c) depicts the laser peak intensity as a function of the exciting pump fluence. The fitted L-L curve for the NW is shown as a thick black line. An approximation like the one used for longer NWs was adopted to model the emission data of this short NW. The lowest calculated threshold gain value obtained from equation (1) was 4800 cm −1 for the transverse hybrid photonic-plasmonic mode 4 (displayed in figure 5(d)). The inset of the L-L plot is the polarization-dependent measurement of the lasing mode. The linewidth versus intensity measurement in figure 5(c) shows a narrowing of the emission linewidth to ∼3 nm at a power greater than 80 μJ cm −2 , indicating lasing condition.

Conclusion
Optically pumped lasing has been demonstrated in highly Zndoped Al 2 O 3 /GaAs NWs on an Fe film at 77 K. Despite the metal loss, the NWs on Fe film show a moderately low threshold fluence of ∼20-25 μJ cm −2 , for multimode and of ∼40 μJ cm −2 for single mode lasing. Lumerical simulations and L-L modeling suggest that lasing is preferably supported by the transverse modes 2, 4 or 6 depending on the tip dimension of the NW. Modes 2 and 6 show a weak plasmonic enhancement in the Al 2 O 3 layer, whereas mode 4 corresponds to a hybrid photonic-plasmonic mode with a noticeable electric field confinement. Our investigation suggests that a ferromagnetic layer can be used to design and build magnetic field induced laser modulators with moderate plasmonic loss.