Carrier-induced refractive index change observed by a whispering gallery mode shift in GaN microrods

A GaN microrod sample was grown with four sections of different doping concentrations along the c-axis. A sketch of the growth sequence is shown in figure 2. To initialize microrod growth, a high TMGa flow of 40 sccm (180 μmol min⁻¹) is applied for 20 s. To improve the optical properties, TMGa was then reduced to a flow of 10 sccm within 50 s [6, 12, 24]. Afterwards, four microrod sections each with a growth time of 5 min and with different Si doping concentrations were deposited.

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Among an ensemble of differently sized microrods, a long GaN microrod is chosen for further investigations with a height and inner diameter of 9.21 ± 0.04 and 1.75 ± 0.01 μm, respectively. The diameter along the microrod axis is constant within the error range, i.e., no tapering such as in previous reported GaN wires is present [25] (for the details of the diameter measurements see the supplementary material). The SEM image of the microrod and the corresponding panchromatic CL image are shown in figures 3(a), (b). The basis grown with a high TMGa flux has poor optical properties (strong yellow defect luminescence and weak GaN NBE emission) and is not considered for the following investigations. Details on the optical properties can be found in [6]. The upper part of the microrod grown with a low TMGa flux having improved optical properties can be separated into four sections defined in figure 2: between each section there is a thin layer of different contrast visible in the panchromatic CL map in figure 3(b). From each section a CL spectra was recorded while fixing the focused electron beam at the center of each section (see figure 3(c)). Dominating NBE emission as well as weak yellow luminescence centered at 2.2 eV and surface related emission at 2.7 eV are visible [26].

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Independent of the respective section of the microrod, WGMs are observed in the energy range from the NBE emission to the yellow defect luminescence. The spectral positions of the WGMs in the blue spectrum obtained from section 1 have been calculated using equation (1). The inner diameter used for the calculation was set to 1779.8 nm, which is in good agreement with the measured inner diameter of 1.75 ± 0.01 μm. The band gap parameter E₀ was modified in order to get the best agreement between experimental and calculated data. For the ordinary and extraordinary refractive index, E₀ was set to 3.386 and 3.429 eV to fit with the TE and TM WGMs, respectively. The calculated spectral positions of the WGMs are also in agreement with the black spectrum from section 4, but not in good agreement with the green and red spectra from sections 2 and 3, respectively, especially in the high energy range.

Figure 3(d) displays the energy shift of four selected WGMs at different energetical positions. There is a WGM shift towards higher energy with increasing silane flow and the shift is more pronounced at higher energies. The TM₁₉ WGM at ∼2.15 eV shows only a small shift of up to 6 meV whereas the TM₃₄ WGM at ∼3.34 eV is shifted by 30 meV with respect to the spectrum from section 1.

Due to the superposition of the NBE emission with WGMs, the NBE emission peak position can not unambiguously be determined. Compared to section 1, a NBE emission peak shift of ∼10 and ∼20 meV for sections 2 and 3, respectively, can roughly be estimated. However, these values are not very reliable due to the presence of WGMs at the peak and low energy edge of the NBE emission. A more precise estimation is possible when only considering the high energy edge of the NBE emission at half maximum which is not in superposition with WGMs. The shift is displayed in figure 3(d) (black line). With increasing the silane flow a shift up to 34 meV towards higher energy is observed, which can be explained by the Burstein–Moss effect.

The FWHM of the NBE emission of each spectra was determined and is shown in figure 3(d) (right axis). Values in a range between 100–160 meV are present. The carrier concentration of each section was estimated from the FWHM of the NBE emission according to [27] and are summarized in table 2. High n-type carrier concentrations up to $1.2\times {10}^{20}$ cm⁻³ were found. The estimated carrier concentrations reveal that not all the supplied Si atoms are incorporated into GaN as dopants. An increase of silane supply by a factor of 4 and 7 enhances the carrier concentration only by a factor of ∼2 and ∼3, respectively. This is attributed to the self-catalytic VLS growth of the microrods and the low solubility of Si atoms into the Ga droplet on top of rod leading to enhanced formation of SiN on the sapphire surface and on the sidewalls of the rods acting as a sink for Si [12, 13, 28]. The high carrier concentrations above 1×10¹⁹ cm⁻³ in all four sections of the microrod are in agreement with the trend showing a shift of the high energy edge of the NBE emission towards higher energies [21].

Table 2.  Summary of the carrier concentrations N obtained from FWHM of NBE emission (see figures 3(c), (d)) and from the LOPPCM-position in the Raman spectra (see figure 4). The LOPPCM-measured at 515 cm⁻¹ corresponds to contributions from sections 1, 2 and 4.

	Silane flow	${\mathrm{FWHM}}_{\mathrm{NBE}}$	${N}_{\mathrm{FWHM}}$	LOPPCM-	${N}_{\mathrm{LOPPCM}-}$
Section	($\times 0.045$ μmol min−1)	(meV)	(cm−3)	(cm−1)	(cm−3)
1	1	106.0	$3.1\times {10}^{19}$	∼515	∼5.4 × 1019
2	4	141.0	$7.6\times {10}^{19}$	∼515	∼5.4 × 1019
3	7	163.7	$1.2\times {10}^{20}$	528	2.7 × 1020
4	0	102.9	$2.8\times {10}^{19}$	∼515	∼5.4 × 1019

Micro-Raman measurements were used as an additional method to determine the carrier concentration in the microrod [29, 30]. The micro-Raman spectra in figure 4 recorded on a single microrod show the A₁(TO), E₁(TO) and ${E}_{2}^{H}$(TO) modes at 531.3 , 558.2 and 567.2 cm⁻¹, respectively. The values are comparable to Raman measurements on high-quality nonpolar and strain-free GaN substrates grown by hydride phase epitaxy [31]. The spectral position of the longitudinal optical phonon plasmon coupled mode (LOPPCM) provides information about the carrier concentration. A LOPPCM-and a LOPPCM+ peak show up below the transversal optical (TO) phonon frequency in the uncoupled mode ${\omega }_{T}$ (= 531.3 cm⁻¹) and above the LO phonon frequency in the uncoupled mode ${\omega }_{L}$ (= 734 cm⁻¹) for high and low carrier concentrations, respectively. The following equation, derived from the dielectric function, reproduces the N dependent LOPPCM ± frequency ${\omega }_{\pm }$ [32]:

$$\begin{eqnarray}&&{\omega }_{\pm }^{2}=\displaystyle \frac{1}{2}({\omega }_{L}^{2}+{\omega }_{p}^{2})\pm \sqrt{\displaystyle \frac{1}{4}{({\omega }_{L}^{2}+{\omega }_{p}^{2})}^{2}-{\omega }_{p}^{2}{\omega }_{T}^{2}},\end{eqnarray} \tag{ 3 }$$

with the plasmon frequency ${\omega }_{p}=\sqrt{4\pi {{Ne}}^{2}/({\varepsilon }_{\infty }{m}^{*})}$, e as the elementary charge, ${\varepsilon }_{\infty }=5.3$ as the optical dielectric constant of GaN and ${m}^{*}=0.216$ as the effective mass of an electron in GaN valid for high doping concentrations [33].

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Two measurement configurations have been used for the micro-Raman investigations as illustrated in the inset of figure 4 [34]. In the $x(z,-)\bar{x}$ configuration, i.e., laser excitation and detection is perpendicular to the microrod side-wall facet, the intense A₁(TO) mode at ∼531.3 cm⁻¹ covers the LOPPCM-peak. The latter is expected to be located between 500–531.4 cm⁻¹ for high carrier concentrations above 3 × 10¹⁹ cm⁻³, as for the microrod in the present study. Therefore, each section of the microrod can not be analyzed by micro-Raman with respect to the LOPPCM-peak. The A₁(TO) mode is not allowed in the $z(x,-)\bar{z}$ configuration, i.e., laser excitation and detection is perpendicular to the microrod top facet, however, all sections are probed at once. Two LOPPCM-peaks are visible at 515 and 528 cm⁻¹ corresponding to 5.4 × 10¹⁹ and $2.7\times {10}^{20}$ cm⁻³, respectively, using equation (3). The LOPPCM-at 528 cm⁻¹ originates from section 3 of the microrods, while the LOPPCM-at 515 cm⁻¹ is a superposition of all other sections. The carrier concentrations obtained from micro-Raman measurements and from the FWHM of the NBE emission are in good agreement as can be seen in table 2. Finally, there is a peak at 735.5 cm⁻¹ referred to a A₁(LO)/LOPPCM+, which is expected to stem from unintentional doped GaN located at the base of the microrod formed during the initial microrod growth. Such a peak at 735.5 cm⁻¹ (corresponds to a carrier concentration of 6 × 10¹⁶ cm⁻³ using equation (3)) can also be observed in unintentional doped GaN layers grown in the used MOVPE system (not shown here).

Concerning the WGM shift, the NBE emission shift, and the FWHM, there is no significant difference between the spectra from sections 1 and 4, i.e., there is still some Si incorporation taking place after switching off silane supply during growth of section 4. High temperature decomposition of the surface SiN might act as a source leading to a background doping effect.

Figure 5 is showing a detailed view of three selected modes at different spectral positions with a small and large WGM shift at low and high energies, respectively, as already shown in figure 3(d). The blue dashed lines are the calculated ${\mathrm{TM}}_{\mathrm{19,24,34}}$ WGMs similar to figure 3(c). The new spectral positions of the WGMs for the green and red spectra obtained from sections 2 and 3, respectively, were also calculated. For that purpose, the band gap parameter E₀ was set to 3.457 eV for the green spectra and to 3.480 eV for the red spectra, i.e., the initial E₀ used for the blue spectra was modified by +28 and +51 meV. The trend of these values is in agreement with the high energy edge shift of the NBE emission. The green dashed–dotted and red dotted lines in figure 5 are in good agreement with the new spectral positions of the WGMs in the green and red spectra. The same modification of the ordinary refractive index is also in good agreement with the observed shift of the TE WGMs (not shown here).

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It was already stated that the diameter along the microrod is constant, however, a small variation of a few nm might not be measureable via SEM. Using equations (1) and (2) it can be calculated that a diameter reduction of 10 nm for the microrod having a diameter of 1780 nm would lead to a blue shift of 11, 13, 13 and 7 meV for the TM₁₉, TM₂₆, TM₃₀, and TM₃₄ WGM, respectively (for the details of the diameter dependent WGM shift see the supplementary material). Comparing these values with the observed WGM shift in figure 3(d), which shows an increasing WGM shift with increasing N, it is clear that a diameter variation can not be responsible for the observed WGM shift.

Si is known to induce tensile strain in a GaN layer leading to a reduction of the band gap [35–37]. This is in contrast with the data presented in figure 3(d) showing a blue shift with increasing the Si doping concentration and can therefore not be considered as a reason for the observed WGM shift.

It is clear that the carrier concentration effects the refractive index change, which leads to a WGM shift. The high carrier concentration induces a Burnstein–Moss shift, i.e., an increase of the band gap. A modification of the band gap parameter E₀ in the refractive index equation (2) is therefore a proper tool to explain the WGM shift caused by different carrier concentrations.

The present study is not only limited to the GaN material system, but can also be applied to other material systems such as ZnO [38].