Ultrafast carrier dynamics and nonlinear optical response of InAsP nanowires

Junting Liu; He Yang; Vladislav Khayrudinov; Harri Lipsanen; Hongkun Nie; Kejian Yang; Baitao Zhang; Jingliang He

doi:10.1364/PRJ.430172

Abstract

Indium arsenide phosphide (InAsP) nanowires (NWs), a member of the III–V semiconductor family, have been used in various photonic and optoelectronic applications thanks to their unique electrical and optical properties such as high carrier mobility and adjustable band gap. In this work, we synthesize InAsP NWs and further explore their nonlinear optical properties. The ultrafast carrier dynamics and nonlinear optical response are thoroughly studied based on the nondegenerate pump probe and Z-scan experimental measurements. Two different characteristic carrier lifetimes (

\sim 2

and

\sim 15 ps

) from InAsP NWs are observed during the excited-carrier relaxation process. Based on the physical model analysis, the relaxation process can be ascribed to the carrier cooling process via carrier-phonon scattering and Auger recombination. In addition, based on the measured excited-carrier lifetime and Pauli-blocking principle, we discover that InAsP NWs show strong saturable absorption properties at the wavelengths of 532 and 1064 nm. Last, we demonstrate for the first time a femtosecond (

\sim 426 fs

) solid-state laser based on an InAsP NWs saturable absorber at 1.04 μm. We believe that our work provides a better understanding of the InAsP NWs optical properties and will further advance their photonic applications in the near-infrared range.

1. INTRODUCTION

In the past two decades, nanowires (NWs) have been employed as versatile building blocks [1 –3] used in various optoelectrical devices [4 –7] because of their tailored optical and electronic properties [8,9]. Semiconductor NWs exhibit many unique physical characteristics such as significant surface and size effects [10], building blocks for nanoelectronics [7], and Majorana fermions [11]. For example, the electrical and optical properties of semiconductor NWs can be tuned by controlling their sizes, shapes, and compositions [12,13]. For instance, alloyed III–V semiconductor ternary $GaAs / {In}_{x} {Ga}_{1 - x} As$ nanowires show continuous tuning of the bandgap (0.91–1.52 eV) by adjusting the ratio of In and Ga elements [12]. In addition, the bandgap of semiconductor NWs decreases with increasing size [13]. Thus, semiconductor NWs are useful and multifunctional nanomaterials working as various building blocks to advance the research of photonic and optoelectronic devices, such as solar cells [1,14], lasers [2,15], and photodetectors [3,16].

Owing to the large electron g-factor and small electron effective mass [17 –19], III–V semiconductor NWs have been applied in nanoscale optoelectronic devices [17], infrared detectors [18], and spin electronics [19]. Known as the representative of the III–V semiconductor family, InAsP NWs which were first synthesized by Pettersson in 2006 [3] show great potential for infrared photodetectors due to the high carrier mobility. Since then, great efforts have been devoted to pursuing InAsP NW-based optoelectronic devices, such as high-speed electronics [20,21] and near-infrared light emitters and detectors [22 –24]. In theory, the bandgap of InAsP NWs can be tailored from 0.35 to 1.35 eV by adjusting the alloy composition, covering the important telecommunication wavelength band from 1.3 to 1.55 μm [25]. Besides, the growth of InAsP NWs has larger tolerance for lattice mismatch than thin-film epitaxial growth, which allows adjusting the optical nonlinear sensitivity through external bending or twisting strain [26,27] and has more flexibility in substrate selection and mechanical properties. Thus, there is a demand to study the intrinsic optical properties (e.g., carrier dynamics, nonlinear optical absorption) of InAsP NWs in the near-infrared wavelength range, which remains unexplored.

In this work, we fabricate high-quality InAsP NWs by directly growing them on a quartz substrate using the Au nanoparticle-assisted vapor-liquid-solid (VLS) method. Then, the carrier dynamics of InAsP NWs is investigated by nondegenerate pump-probe measurements, which show that the excited carrier in InAsP NWs exhibits one fast ( $\sim 2 ps$ ) and one slow ( $\sim 15 ps$ ) relaxation processes. Furthermore, we study the nonlinear absorption properties of InAsP NWs by tuning the light intensity and wavelength using the Z-scan technique. We find that InAsP NWs have a large nonlinear absorption coefficient ( $β_{eff} \sim 10^{2} cm / MW$ ) and positive nonlinear refractive index ( $n_{2} \sim 10^{- 13} m^{2} / W$ ), which is much higher than the reported values of other nanomaterials including graphene, transition metal dichalcogenides (TMDs), and black phosphorus (BP). The studies on the ultrafast carrier relaxation dynamics and nonlinear optical absorption properties show the potential of InAsP NWs in the application field of optical switching. By using InAsP NWs as a saturable absorber (SA), a passively mode-locked laser at 1.04 μm is demonstrated with the shortest pulse width of 426 fs. Our results prove that InAsP NWs could be very promising candidates as excellent nonlinear optical modulators used in photonic and electronic devices.

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2. RESULTS AND DISCUSSION

A. Preparation and Characterization of InAsP NWs

InAsP NWs samples are grown on quartz substrates inside a horizontal flow atmospheric pressure metal-organic vapor phase epitaxy (MOVPE) system. The detailed process can be found in Appendix A.1. Scanning electron microscopy (SEM) is used to examine the surface morphology of the prepared NWs. Figure 1(a) depicts the as-grown InAsP NWs that have an average diameter of $\sim 50 nm$ with smooth surfaces (shown in the inset). Atomic force microscopy (AFM) image together with the height profile provides further evidence for the uniform formation of InAsP NWs. As shown in Figs. 1(b) and 1(c), the diameter of InAsP NWs is determined to be $\sim 50 nm$ (average value), which is consistent with Au particle diameter. What is more, we did the energy-dispersive X-ray spectroscopy (EDX) along the growth direction to study the crystal structure of InAsP NWs, as shown in Fig. 1(d), which illustrates the high quality of our InAsP NWs sample solely consisting of In, As, and P without additional elements and the ratio of In, As, and P elements is about 2:2:1. Figure 1(e) shows the Raman spectrum of the InAsP NWs excited by a 532 nm laser with the power of 2 mW. The peaks observed at 217.6 and $247.8 {cm}^{- 1}$ are InAs-like modes which correspond to a transverse optical ( ${TO}_{1}$ ) and a longitudinal optical ( ${LO}_{1}$ ) phonon modes. The peaks around $298.1 {cm}^{- 1}$ are InP-like modes corresponding to a transverse optical phonon mode ( ${TO}_{2}$ ), which is consistent with the previous research [28]. Photoluminescence (PL) measurement [Fig. 1(f)], performed at room temperature, reveals only one PL peak at 1280 nm, corresponding to the band-to-band transition in bulk form.

(a) SEM image of InAsP NWs on quartz substrate. The inset is a higher-resolution SEM image, which shows the NW diameter of ∼50 nm. (b) AFM image of InAsP NWs. (c) Height profiles along the line in the AFM image. (d) EDX measurement of InAsP NWs along the growth direction. (e) Raman spectrum measured using a 532 nm laser. (f) Room-temperature PL spectrum of InAsP NWs.

Figure 1.(a) SEM image of InAsP NWs on quartz substrate. The inset is a higher-resolution SEM image, which shows the NW diameter of $\sim 50 nm$ . (b) AFM image of InAsP NWs. (c) Height profiles along the line in the AFM image. (d) EDX measurement of InAsP NWs along the growth direction. (e) Raman spectrum measured using a 532 nm laser. (f) Room-temperature PL spectrum of InAsP NWs.

B. Ultrafast Carrier Dynamics of InAsP NWs

Figure 2.(a) Experimental setup of the nondegenerate pump-probe measurement. (b) Differential transmission of InAsP NWs at different pump pulse energies with a 675 nm probe laser. (c) Relationship between maximum differential transmission and initial photoinduced carrier density. (d) Linear fit to ${(n_{0} / n_{t})}^{2} - 1$ as a function of pump-probe delay time and initial photoinduced carrier density.

The photoinduced carrier dynamics relaxed from the excited states to the valence band is commonly described by a three-term rate equation [32 –34]: $- d n / d t = α n + β n^{2} + γ n^{3},$ (2)where $t$ is the relaxation time, $n$ is the excited carrier density, and $α$ , $β$ , and $γ$ are the first, second, and third terms, respectively, which represent first-order Shockley-Read-Hall (SRH) recombination, free-carrier recombination, and Auger recombination. Figure 2(c) plots the maximum bleach signal measured as a function of the pump energy density, which is modeled by the phenomenological expression [35,36] ${[\frac{Δ T}{T}]}_{\max} = \frac{A n_{0}}{B + n_{0}^{C}},$ (3)where $A$ , $B$ , and $C$ are fitting parameters. The initial charge carrier density ( $n_{0}$ ) can be calculated by $n_{0} = j α_{0}$ , where $α_{0}$ is the InAsP NWs absorption coefficient, and $j$ is the pump fluence (photons per cm²). Therefore, we can correlate differential transmission $Δ T / T$ to the density of photogenerated charge carriers using the above expression.

After converting the measured $Δ T / T$ signal into photogenerated carrier density, the third-order rate equation can be obtained by eliminating the first- and second-order terms in Eq. (2) and assuming the numbers of photogenerated electrons and holes are equal, which can be expressed as follows: $\frac{n_{0}^{2}}{n_{t}^{2}} - 1 = k n_{0}^{2} t,$ (4)where $k$ is the third-order rate constant for the recombination process. By linear fitting of Eq. (4), we obtain the initial photoinduced carrier density ( $n_{0}$ ) of $13 \times 10^{18} {cm}^{- 3}$ , as shown in Fig. 2(d). Then the Auger recombination rate of $(9.5 \pm 0.2) \times 10^{- 27} {cm}^{6} s^{- 1}$ is obtained.

C. Nonlinear Optical Response of InAsP NWs

Figure 3.Characterization of the NLO properties of the InAsP NWs. OA Z-scan measurements of the InAsP NWs at (a) 532 nm and (c) 1064 nm. CA Z-scan measurements of the InAsP NWs at (b) 532 nm and (d) 1064 nm.

The CA Z-scan technique is used to characterize the refractive index ( $n_{2}$ ) of the sample. The normalized transmittances of the closed aperture Z-scan results under different incident energies at the wavelength of 532 and 1064 nm are shown in Figs. 3(b) and 3(d). The normalized transmittance can be fitted using the following formula [43]: $T = 1 + \frac{4 k L_{eff} n_{2} I_{0} Z}{Z_{0} (Z^{2} / Z_{0}^{2} + 9) (Z^{2} / Z_{0}^{2} + 1)},$ (7)where $k = \frac{2 π}{λ}$ , and $n_{2}$ is the nonlinear refractive index. The valley–peak shapes of the normalized transmittance CA/OA Z-scan curves, which result from the Kerr effect induced self-focusing effect in InAsP NWs, suggest the positive refractive index. The obtained nonlinear refractive index is $2.39 \pm 0.03$ and $2.73 \pm 0.02 \times 10^{- 13} m^{2} / W$ at 532 and 1064 nm. The real part of the third-order nonlinear optical susceptibility ( $Re χ^{(3)}$ ) can be expressed as [40] $Re χ^{(3)} = \frac{4 ε_{0} c n_{1}^{2}}{3} n_{2} .$ (8)The $Re χ^{(3)}$ is $(7.17 \pm 0.01) \times 10^{- 7} esu$ (at 532 nm) and $(8.2 \pm 0.01) \times 10^{- 7} esu$ (at 1064 nm). As listed in Table 2, $n_{2}$ of InAsP NWs is slightly higher than that of typical 2D materials, such as graphene [35], TMDs [35,36], and MXene [38].

D. Ultrafast Photonic Applications

Because InAsP NWs exhibit strong third-order nonlinear optical response and ultrafast saturation recovery time, it is meaningful to further explore their ability on the generation of ultrashort pulses. Here, a mode-locked solid-state laser based on InAsP NWs saturable absorber is assembled. Based on the mode-locking theory, when the mode-locking pulse energy is larger than the minimum intracavity pulse energy, the stable continuous-wave (CW) laser can be demonstrated. Therefore, considering the SA parameters, the following formula should be satisfied [41]: $F_{sat, A} Δ R < \frac{{(P T_{R})}^{2}}{F_{sat, L} A_{eff, L} A_{eff, A}} = \frac{{(P T_{R})}^{2} \times m σ_{em, L} λ}{h c \times π ω_{eff, L}^{2} \times π ω_{eff, A}^{2}},$ (9)where $P$ is the intracavity pulsed laser power, $T_{R}$ is the round-trip time, and $F_{sat, A}$ and $F_{sat, L}$ are the saturation fluence of SA and laser gain medium, respectively. $A_{eff, L}$ and $A_{eff, A}$ are the effective laser mode on the laser gain medium and SA, respectively, $h$ is the Planck constant, $c$ is the light velocity, $σ_{em, L}$ is the emission cross section of the laser crystal, $ω_{eff, L}$ and $ω_{eff, A}$ are the effective laser modes radii on the laser gain medium and SA, respectively, and $m$ is a cavity constant: $m = 1$ for a ring cavity, and $m = 2$ for a linear cavity. Based on ABCD propagation matrix, a 3.5 m long Z-type resonator is designed. The setup details are given in Appendix A.4. Here, the $ω_{eff, L}$ and $ω_{eff, A}$ are calculated as 37 and 54 μm, respectively. The left-hand side of Eq. (9), $F_{sat, A} Δ R$ , is calculated to be $2.5 μJ / {cm}^{2}$ , which is smaller than the right-hand side ( $11.2 μJ / {cm}^{2}$ ). Therefore, based on the as-designed and the as-prepared InAsP NWs SA, stable CW mode-locked lasers can be obtained.

When the absorbed pump power exceeds 4.26 W, stable CW mode-locked (CWML) operation is established. Figure 4(a) depicts the relationship between the absorbed pump power and average output power. The obtained maximum average output power is 333 mW under the absorbed pump power of 7.17 W. Once the absorbed pump power exceeds 7.17 W, the CWML operation is broken. The output power instabilities (RMS) are measured to be less than 2% over 1 h. By ${sech}^{2}$ pulse shape fitting listed in Fig. 4(b), the pulse duration is measured to be 426 fs. The inset shows that the spectrum is centered at 1043 nm with a full-width-at-half-maximum (FWHM) of 3.1 nm, corresponding to the time-bandwidth product of 0.364, which is higher than the Fourier transform-limited value (0.315). It indicates that the output pulses are slightly chirped. Also, the radio-frequency spectra are recorded with different spans. As shown in Fig. 4(c), the fundamental peak is located at 42.93 MHz with a signal-to-noise ratio of 60 dB. No spurious frequency modulations are observed in a wide span of 1 GHz with a resolution bandwidth (RBW) of 75 kHz, which proves clean CWML operation based on InAsP NWs. What is more, the CWML pulse trains show good amplitude stability with a time span of 2 ms [Fig. 4(d)]. The mode-locked laser based on InAsP NWs shows a relatively short pulse width and relatively high output power, which indicates the InAsP NWs are promising SA for the ultrafast laser generation.

Figure 4.Mode-locked laser results based on InAsP NWs. (a) Average output power versus absorbed pump power. (b) The measured pulse width by autocorrelation spectroscopy is $\sim 426 fs$ . Inset: corresponding spectrum centered at 1043 nm. (c) Recorded frequency spectrum of the mode-locked laser with an RBW of 10 kHz. Inset: 1 GHz wide-span spectrum. (d) Recorded CWML pulse trains under the maximum pump power.

3. CONCLUSIONS

In summary, we fabricate InAsP NWs by using an Au nanoparticle-assisted VLS growth method. The NLO properties and ultrafast carrier dynamics of InAsP NWs have been studied by Z-scan and nondegenerate pump-probe measurements for the first time. The excited carriers of InAsP NWs exhibit two characteristic carrier lifetimes (fast $\sim 2 ps$ and slow $\sim 15 ps$ ), which can be attributed to a carrier cooling process via carrier-phonon scattering and an Auger recombination process. Besides, Z-scan measurements demonstrate that InAsP NWs have excellent NLO properties with a large nonlinear absorption coefficient of $\sim 10^{2} cm / MW$ and nonlinear refractive index of $\sim 10^{- 13} m^{2} / W$ . Furthermore, we successfully demonstrate the femtosecond mode-locked solid-state laser based on InAsP NWs SA. Our work indicates that InAsP NWs are excellent candidates for applications in photonic and electronic devices.

Acknowledgment

Acknowledgment. H.Y. acknowledges the support from EU. V.K. acknowledges the support of Aalto University Doctoral School, Walter Ahlström Foundation, Elektroniikkainsinöörien Säätiö, Sähköinsinööriliiton Säätiö, and Nokia Foundation Finnish Foundation for Technology Promotion (Tekniikan Edistämissäätiö) and Waldemar Von Frenckells foundation. H.L. and V.K. acknowledge support from the Academy of Finland Flagship Programme, Photonics Research and Innovation (PREIN), decision number: 320167. V.K. and H.Y. acknowledge the provision of facilities and technical support by Aalto University at Micronova Nanofabrication Centre.

APPENDIX A: EXPERIMENTAL METHODS

1.Growth of InAsP NWs

\sim 460

2.Nondegenerate Micro Pump-Probe Measurements

20 \times

3.Z-scan Measurement

f = 50 mm

4.CW Mode-Locking Operation

{Yb}^{3 +}

APPENDIX B: THE FITTING PARAMETERS OBTAINED FROM Z-SCAN CHARACTERIZATION

As shown in Table 3, it summarizes the fitting parameters obtained from Z-scan characterization of InAsP NWs at the wavelength of 532 and 1064 nm, which shows the strong saturable absorption properties of InAsP NWs. Table 3.

Fitting Parameters Obtained from Z-Scan Characterization of InAsP NWs under Different Excitation Energies

Wavelength (nm)	Input Energy (μJ)	$β_{eff}$ (cm/MW)	$Im χ^{(3)}$ ( $\times 10^{- 7} esu$ )	$I_{s}$ ( $GW / {cm}^{2}$ )	$Δ R$	$n_{2}$ ( $\times 10^{- 13} m^{2} / W$ )	$Re χ^{(3)}$ ( $\times 10^{- 7} esu$ )
532	0.25	$- 207.4 \pm 2.3$	$- 2.63 \pm 0.03$	$0.8 \pm 0.02$	$0.337 \pm 0.002$	$2.39 \pm 0.03$	$7.17 \pm 0.01$
	0.16	$- 205.4 \pm 1.7$	$- 2.6 \pm 0.02$	$0.81 \pm 0.04$	$0.322 \pm 0.002$	$2.46 \pm 0.02$	$7.38 \pm 0.01$
	0.055	$- 203.4 \pm 2.8$	$- 2.59 \pm 0.04$	$0.78 \pm 0.05$	$0.324 \pm 0.002$	$2.44 \pm 0.03$	$7.32 \pm 0.01$
1064	1.01	$- 144 \pm 0.7$	$- 3.7 \pm 0.02$	$0.25 \pm 0.008$	$0.192 \pm 0.002$	$2.73 \pm 0.02$	$8.2 \pm 0.01$
	0.55	$- 146 \pm 0.9$	$- 3.7 \pm 0.03$	$0.24 \pm 0.006$	$0.148 \pm 0.002$	$2.75 \pm 0.03$	$8.3 \pm 0.01$
	0.33	$- 142 \pm 1.1$	$- 3.6 \pm 0.03$	$0.24 \pm 0.006$	$0.105 \pm 0.002$	$2.76 \pm 0.02$	$8.3 \pm 0.01$

APPENDIX C: THE NONLINEAR TRANSMITTANCE CURVE OF InAsP NWS

T (Z) = 1 - \frac{Δ R}{1 + \frac{I}{I_{s}}} - A_{ns},

Figure 5.(a)–(c) Nonlinear transmittance of the InAsP NWs at the wavelength of 532 nm with different incident pulse energies. (d)–(f) Nonlinear transmittance of the InAsP NWs at the wavelength of 1064 nm with different incident pulse energies.

APPENDIX D: THE EXPERIMENTAL SETUP OF THE MODE-LOCKED SOLID-STATE LASER

In our experiment, a z-type resonator with the cavity length of 3.49 m is applied, as shown in Fig. 6 .

Figure 6.Experimental setup of the mode-locked solid-state bulk laser based on an InAsP NWs SA.

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