1. Introduction

Semiconductor nanowires have attracted extensive attention due to their unique electronic and photonic properties [1–16]. The strong two-dimensional confinement of electrons, holes and photons makes them particularly attractive as potential building blocks for nanoscale electronics and photonics [1,2]. Many applications of semiconductor nanowires in the nanoscale photonics were realized and reported, such as lasers [3–12], modulators [13], detectors [14], sensors [15], et al. Early reports on nanowire lasers were mainly focused on the homogeneous binary semiconductors such as GaN [3–6], ZnO [7,8], CdS [9,10] and GaSb [11], where the lasing wavelength corresponded to the fundamental bandgap energies of the respective homogeneous nanowire materials. In these studies, the semiconductor nanowires functioned as both the gain medium and the optical cavity. So, the photoemission of the binary semiconductors can be reabsorbed during its propagation along the nanowires and therefore the threshold of the binary semiconductor nanowire lasers is usually very high [3–11]. However, a decoupling of the gain medium with a smaller bandgap from the cavity material with a larger bandgap could offer great advantages over the homogeneous nanowire structures. On the one hand, the generated carriers can be captured into the gain medium since the cavity material has a higher conduction band bottom and a lower valence band top than the gain medium does. The enhanced confinement of electrons and holes in the gain medium enhances the photoemission efficiency. On the other hand, the photoemission of the gain medium is hardly reabsorbed during its propagation along the nanowire since the bandgap of the cavity material is larger than that of the gain medium. Therefore, not only the optical gain is enhanced but also the propagation loss due to the reabsorption of the photoemission is lowered. Recently, InGaN/GaN [12,16], InAs/InP [17], InGaAs/GaAs [18] and GaAs/AlGaAs [19] heterostructures or quantum wells have been incorporated into the nanowires successfully. However, cavity modes and lasing were achieved only in the nanowires with InGaN/GaN [12] heterostructures. In this paper, the nanowires with InGaAs/GaAs heterostructures were fabricated on the GaAs (111)B substrate using selective-area metal organic vapor phase epitaxy (SA-MOVPE) and the Fabry-Pérot microcavity modes were observed in the micro-photoluminescence (PL) spectra of these structures.

2. Fabrication

Compared with the conventional vapor-liquid-solid (VLS) growth, SA-MOVPE is more appropriate in fabricating well-defined width- and position-control semiconductor nanowires free from contamination and process-induced damage, in which (111) facet is used as the substrate and six $\left\{1\overline{1}0\right\}$ facets are used as the sidewalls for the semiconductors with zincblende crystal structures [17–21]. The fabrication procedure started with the deposition of about 30 nm SiO₂ layer on the GaAs(111)B substrate by sputtering. Then the masked pattern was formed by electron beam lithography and wet etching. Finally, the patterned substrates were loaded into a horizontal low-pressure MOVPE system (P_work = 0.1 atm) for the growth. The source materials were trimethylgallium (TMG), trimethylindium (TMI) and 5% AsH₃ in hydrogen. For the bottom and top GaAs layers, the growth temperature was 750 °C, the growth time was 20 mins and 67 mins, respectively, and the partial pressures for AsH₃ and TMG were 2.5 × 10⁻⁴ atm and 1.3 × 10⁻⁶ atm, respectively. The growth temperature and the growth time for the InGaAs layer was 600 °C and 1 min and the partial pressures for AsH₃, TMG and TMI were 6.3 × 10⁻⁵ atm, 1.3 × 10⁻⁶ atm and 1.2 × 10⁻⁷ atm, respectively. After the growth of the InGaAs layer, a GaAs layer was grown at the same growth conditions as those for the GaAs layers except that the growth temperature was changed from 750 °C to 600 °C and the growth time was changed to 2 mins.

3. Results and discussion

3.1 Structural characterization

The fabricated nanowires with InGaAs/GaAs heterostructures were characterized by the scanning electron microscope (SEM) (Fig. 1(a) ). The good uniformity of the fabricated nanowires shows the advantages of our method over the conventional VLS method in fabricating large-area uniform width- and position-control nanowires. The nanowires are hexagonal and the top and side surfaces are very smooth, which indicates the formation of six $\left\{1\overline{1}0\right\}$ facets and the top (111)B facet. Such a structure is very important for the formation of a low-loss optical microcavity since the smooth surfaces can greatly reduce the optical scattering loss. As mentioned below, the indium content in the nanowire is low, so the contrast between the InGaAs layer and the GaAs layer is very difficult to be determined by the transmission electron microscope (TEM) analysis. Another sample with the InGaAs nanowires grown on the top of the GaAs nanowires was fabricated in order to facilitate the TEM observation. After the growth of the bottom GaAs layer, only an InGaAs layer was grown at the same growth conditions as those for the InGaAs layer in the nanowires with InGaAs/GaAs heterostructures except that the growth time was changed from 1 min to 5 mins. Such a sample is also named InGaAs nanowires grown on the top of the GaAs nanowires. As shown in Fig. 1(c), rotation twins exist in this sample and the density for the rotation twins is about 2.77 × 10¹⁵cm⁻³. Electron diffraction pattern indicates that both the GaAs layer and the InGaAs layer have the zincblende crystal structures. The details about the TEM analysis can be found in Ref [21]. The height of the studied nanowires in this paper is in the range from 5.2 μm to 6.5 μm. So the corresponding thickness of the InGaAs layer is approximately in the range from 58 nm to 72 nm. So the quantum confinement effect in the axial direction is negligible. The width of the studied nanowires in this paper is in the range from 280 nm to 390 nm. So the quantum confinement effect in the radial direction is also negligible. Therefore the indium content in the free-standing nanowires can be determined by fitting their temperature-dependent PL peak positions with the Varshni formula [20]. Such a fitting indicates that the indium content is about 11%. Such a procedure has been proved to be accurate and efficient in determining the indium content in the highly uniform nanowires.²⁰ However, as testified in the previous paper [18], the indium content is dependent not only on the growth conditions but also on the length of the nanowires. Even at the same growth conditions, the indium content is lower for the longer nanowire. So the indium content in a specific nanowire with InGaAs/GaAs heterostructure probably deviates from the average value determined in the above way. However, such deviation does not affect our discussion in the below.

 

Fig. 1 (a) SEM image of the free-standing nanowires with InGaAs/GaAs heterostructures. (b) SEM image of the single nanowire with InGaAs/GaAs heterostructure dispersed onto the Si substrate with predefined Au/Ti markers. (c) TEM image of the InGaAs nanowire grown on the top of the GaAs nanowire. (d) Electron diffraction pattern of the InGaAs nanowire grown on the top of the GaAs nanowire.

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3.2 Optical Characterization and discussion

The micro-PL spectra were measured at the temperature of 20K. The excitation beam from a Millennia Pro laser (532nm) of Spectra Physics Corp. was focused to an about 46 μm diameter spot with a 50 × microscopy objective and onto the samples placed in a cryostat. The PL collected through the same microscopy objective was detected by a liquid-nitrogen-cooled charge coupled device. Figure 2 shows the micro-PL spectra of the free-standing nanowires with InGaAs/GaAs heterostructures. A peak located at the wavelength of 919 nm is believed to be from the band edge photoemission of the InGaAs layer. However, the peak is very broad (from 895 nm to 941 nm), which is mainly due to the different indium contents in the different nanowires and the nonuniform distribution of the indium contents along the axial direction of the single nanowire [18]. After the PL measurement, the nanowires with InGaAs/GaAs heterostructures were mechanically cut down and dispersed onto a silicon substrate, on which Ti/Au markers had been predefined by photolithography. This facilitated us to locate individual nanowire and to perform the SEM (Fig. 1(b)) and optical characterization on the same nanowire. In Fig. 2, the nanowire with imperfect end facets exhibits the similar PL spectra except for the appearance of the periodic peaks in the broad spectra. The lower PL intensity of the nanowire with imperfect end facets is possibly due to its lower filling ratio (FR = 0.001) than that of the free-standing nanowires (FR = 0.01). However, the nanowire with almost perfect end facets not only shows much stronger PL but also has more periodic peaks in the broad spectra. The appearance of the periodic peaks in the PL spectra of the single nanowire is due to the appearance of the bottom end facet. The top and bottom end facets act as the mirrors for the photoemission which propagates along the nanowire and therefore the Fabry-Pérot microcavity modes are formed. However, for the free-standing nanowires, there does not exist an optical interface between the nanowires and the substrate since they are both GaAs and have the same refractive indices. Therefore the photoemission that propagates along the nanowires is leakage into the GaAs substrate and the Fabry-Pérot microcavity modes cannot be formed.

 

Fig. 2 Micro-PL spectra of the nanowires with InGaAs/GaAs heterostructures with different end facets. (M: magnification)

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Figure 3 shows the PL spectra for the nanowires with different lengths dispersed onto the silicon substrate with predefined Au/Ti markers. It is clearly seen that the strongest peak locates at different positions for the nanowires with different structural parameters, which is possibly due to the different gain spectra and the different structural cavities. We also find that the mode spacing increases with a decrease in the length of the nanowire. However, as pointed out later, this is not always true since the mode spacing is dependent not only on the length of the nanowire but also on the group refractive indices of the nanowire.

 

Fig. 3 Micro-PL spectra of the nanowires with InGaAs/GaAs heterostructures with different structural parameters. (M: magnification)

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For Fabry-Pérot cavity modes, the mode spacing Δλ for a cavity with the length L is given by Δλ = λ ²/(2N _g L), where λ is the light wavelength in the vacuum, N_g is the group refractive indices. The group refractive indices of the nanowire can be achieved from the measured mode spacing in its PL spectra with the above formula. The group refractive indices of the nanowire with W = 288 nm and L = 5.66 μm are shown in the solid squares and those of the nanowire with W = 384 nm and L = 5.34 μm are shown in the solid circles in Fig. 4 . It is obvious that the group refractive indices are wavelength-dependent and increase with a decrease in the wavelength. Interestingly, we find that the nanowire with W = 288 nm and L = 5.66 μm has larger group refractive indices than the nanowire with W = 384 nm and L = 5.34 μm does.

 

Fig. 4 (a) Nanowire with a hexagonal cross section surrounded by the air used as the model for the calculation of the group refractive indices. (b) Group refractive indices of the nanowires with InGaAs/GaAs heterostructures versus wavelength. (Solid squares: experimentally determined group refractive indices of the nanowire with W = 288 nm and L = 5.66 μm; Solid line: calculated group refractive indices of the nanowire with W = 288 nm and L = 5.66 μm considering both the material dispersion and the waveguide dispersion; Dot line: calculated group refractive indices of the nanowire with W = 288 nm and L = 5.66 μm only considering the waveguide dispersion; Solid circles: experimentally determined group refractive indices of the nanowire with W = 384 nm and L = 5.34 μm; Dash line: calculated group refractive indices of the nanowire with W = 384 nm and L = 5.34 μm considering both the material dispersion and the waveguide dispersion; Dash dot line: calculated group refractive indices of the nanowire with W = 384 nm and L = 5.34 μm only considering the waveguide dispersion; Dash dot dot line: calculated group refractive indices of the nanowire only considering the material dispersion.)

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Since the refractive indices of the GaAs at 20 K are not available and the refractive indices of the GaAs are sensitive to the temperature due to the thermooptic effect [22,23], these values were achieved based on the formula n(T) = n(0K) + (dn/dT)_{0 K} × T, where (dn/dT)_{0 K} is the thermooptic coefficient and is assumed constant in the temperature rang from 0 K to 20 K. The values for n(0K) and (dn/dT)_{0 K} in reference [22] were used in the calculation. Then, first-order Sellmeir equation was used to fit the data and such fitting produces the wavelength-dependent refractive indices for the GaAs in the infrared wavelength range as n(λ) = {8.72 + 1.752[λ ²/(λ ²-0.399)]}^1/2, where λ is the light wavelength in the vacuum in micrometers. The group refractive indices only considering the material dispersion are shown in the dash dot dot line (Fig. 4). The discrepancy between these values and the experimentally determined values is obvious. The same phenomenon was also observed in the GaAs nanowires [24]. Although the nanowires were dispersed on the silicon substrate with predefined Au/Ti markers, a thin layer of SiO₂ was formed due to the natural oxidation and thermo-oxidation during the preparation of Au/Ti markers. So, the nanowire performs as a waveguide since the refractive index of the core layer (n _GaAs) is larger than the surrounding layers (n _air or n _SiO2) and the full inter-reflection condition is fulfilled for specific modes. It is well known that, in the waveguide with the cross section smaller than the wavelength, the dispersion can be classified into material dispersion, waveguide dispersion, polarization mode dispersion and carrier dispersion [25]. The carrier dispersion is negligible in our case since the excitation power density is not so high. As there is only one set of Fabry-Pérot microcavity modes observed in the micro-PL spectra, we believe that the polarization mode dispersion plays a trivial role in the experimentally determined group refractive indices of the nanowire. Since the nanowire was dispersed onto a silicon substrate with a thin oxidation layer, the fundamental quasi-TM mode, which has a dominant field element along the Y direction, is thought to be more lossy due to its long tail into the silicon substrate. So, only the fundamental quasi-TE mode, which has a dominant field element along the X direction, is considered in the following calculation.

In order to find out the effect of the waveguide dispersion on the group refractive indices of the nanowire, a nanowire with a hexagonal cross section surrounded by the air was used as the model (as shown in Fig. 4(a)) for the calculation of the effective refractive indices of the nanowires. Note that the thin oxidation layer on the top of the silicon substrate was neglected in the calculation to simplify the calculation. Finite element method (FEM) based on full vectorial solutions of Maxwell’s equations was adopted for the calculation instead of the imaginary distance beam propagation method since the nanowire is a high-index-contrast structure and the latter method is usually not efficient for the high-index-contrast structure. Firstly, the material dispersion was not included and the refractive index of the GaAs (n = 3.5115) at the wavelength of 0.88 μm was adopted in the calculation. Then the group refractive indices were calculated directly from the wavelength-dependent effective refractive indices using N _g = N _eff(λ)-λ × dN _eff(λ)/dλ (as shown in the dot line for the nanowire with W = 288 nm and L = 5.66 μm and in the dash dot line for the nanowire with W = 384 nm and L = 5.34 μm.

The group refractive indices only considering the waveguide dispersion have opposite wavelength-dependence to those only considering the material dispersion and the discrepancy between the calculated group refractive indices only considering the waveguide dispersion and the experimentally determined group refractive indices is also large. In the second calculation, the material dispersion (n(λ) = {8.72 + 1.752[λ ²/(λ ²-0.399)]}^1/2) was included and the calculated group refractive indices are shown in the solid line for the nanowire with W = 288 nm and L = 5.66 μm and in the dash line for the nanowire with W = 384 nm and L = 5.34 μm. The agreement between the calculated group refractive indices considering both the material dispersion and the waveguide dispersion and the experimentally determined group refractive indices is much better than the case only considering the material dispersion or the case only considering the waveguide dispersion. We also find that the calculated group refractive indices considering both the material dispersion and the waveguide dispersion do not completely coincide with the experimentally determined group refractive indices, which is mainly due to the shorter length of the nanowire and therefore the group refractive indices determined from the mode spacing is not so accurate. We also find that the fundamental quasi-TE mode is cutoff in the wavelength longer than 1.6 μm for the nanowire with W = 288 nm and L = 5.66 μm. However, the fundamental mode is reported to be never cutoff in Ref [27], which is mainly due to the fact that the nanowire with a cylindrical cross section was considered in Ref [27] and the nanowire with a hexagonal cross section is considered in this paper. Importantly, we find that the nanowire with smaller width has relatively larger group refractive indices than the nanowire with larger width does, which is mainly due to the enhanced confinement to the photons in the nanowire with smaller width. Based on the formula Δλ = λ ²/(2N _g L), the mode spacing is dependent not only on the length of the nanowire but also on the group refractive indices of the nanowire. Moreover, the group refractive indices are dependent on the width of the nanowire. Larger nanowire usually has smaller group refractive indices. Therefore, the mode spacing is dependent not only on the length of the nanowire but also on the width of the nanowire. Such phenomenon is neglected by many researchers and is firstly pointed out in this study.

We also find that Fabry-Pérot microcavity modes are difficult to be observed in the nanowires with the width less than about 180 nm. Note that such value is dependent not only on the index contrast between the nanowire material and the surrounding materials but also on the photoemission wavelength. The same phenomenon was also found in GaAs nanowires [24], InP nanowires [26] and other material nanowires [6]. In order to find out the underlying physical mechanism, we calculated the effective refractive indices and the corresponding field elements of the fundamental quasi-TE modes at the wavelength of 0.88 μm for the nanowires with various widths (in Fig. 5 ) using the FEM method. The effective refractive index reduces with a decrease in the width of the nanowires and approximately equals to the refractive index of the surroundings when the width of the nanowire is about 160 nm. The nanowire with the width less than 150 nm cannot support a stable optical field in the core layer. The E _x fields for the fundamental quasi-TE modes with the dominant field elements along the X direction in the nanowires with the width of 150 nm, 180 nm, 240 nm and 360 nm are also shown in this figure. With decreasing the width of the nanowires, more optical field is leakage into the surroundings. This contributes to the loss since only the fraction of the optical field inside the nanowire experiences a refractive index contrast at the end facets, thus reducing the amount of the reflection. As an approximation, the reflectivity of the optical power for the specific modes was calculated using the Fresnel formula R = (N _eff-n ₀)²/(N _eff + n ₀)², where n ₀ is the refractive index of the surroundings. The calculated results clearly indicate that the reflectivity firstly decreases slowly with a decrease in the width of the nanowire and then decreases very fast when the width of the nanowires is less than 240nm and approaches to zero when the width of the nanowire is less than 180 nm. Since the reflectivity at the end facets is very small, no feedback of the optical field exists and therefore the Fabry-Pérot microcavity modes are difficult to be observed in the nanowires with the width less than about 180 nm near the wavelength of 0.88 μm.

 

Fig. 5 Calculated effective refractive indices, reflectivity and mode field distribution of the nanowires with different widths.

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Figure 6 shows the 20 K PL spectra of the nanowire with InGaAs/GaAs heterostructure (L = 5.66 nm, D = 288nm) with the excitation power density changed from 0.0475 W/cm² to 1500 W/cm². However, the nanowire cannot achieve lasing even the excitation power density is increased to 1500 W/cm². By multiple-peaks Lorentzian fitting of the PL spectra, the width of each mode was obtained and then the quality factors of the microcavity modes was estimated using λ/Δλ. We find that the quality factors of the cavity modes are in the range from 90 to 270, which is less than those for the nanowires reported to achieve lasing [5]. Since the quality factor is directly related to the cavity loss, relatively lower mirror loss [28] and longer nanowire [5] are expected to achieve higher quality factor. As aforementioned, there are a lot of rotation twins in the nanowire, the existence of which greatly reduces the photoemission efficiency. Furthermore, the rotation twins behave as the scattering centers for the optical field and greatly enhance the scattering loss. So the growth conditions for the nanowires should be optimized to achieve single-crystal structure. Relatively shorter length of the nanowires and the existence of many rotation twins in the nanowires are the main reasons why the lasing is not achievable in the fabricated nanowires.

 

Fig. 6 Micro-PL spectra of the nanowire with InGaAs/GaAs heterostructure (L = 5.66 nm, D = 288 nm) with the excitation power density changed from 0.0475 W/cm² to 1500 W/cm². (M: magnification)

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4. Conclusion

In summary, we report on the fabrication of the nanowires with InGaAs/GaAs heterostructures on the GaAs(111)B substrate using SA-MOVPE. Fabry-Pérot microcavity modes were observed in the micro-PL spectra of the single nanowire dispersed onto the Si substrate with predefined Ti/Au markers. Although there are still some challenges to be overcome, our results point out a possible route to achieve lasing at the near-infrared wavelength in the semiconductor nanowires.