The aim of the present paper was to determine the index variation in the GaN/AlN heterostructures related to the population/depletion of the quantum well fundamental state leading to the absorption variation in the spectral domain around 1.5 µm. The variation of the refractive index was deduced from the shift of the position of the beating interference maxima of different order modes in a guided wave configuration. The obtained index variation with bias from complete depletion to full population of the quantum wells is around -5 × 10−3. This value is similar to the typical index variation achieved in InP and is an order of magnitude higher than the index variation obtained in silicon.
©2012 Optical Society of America
Thanks to the progress achieved in terms of epitaxial growth of ultrathin layers, III-nitride semiconductors (GaN, AlN, InN and their alloys) have emerged within the last ten years as excellent materials for intersubband (ISB) photonics devices in the near-infrared spectral range [1,2]. The large conduction band offset provided by their heterostructures, of the order of 1.75 eV for GaN/AlN, allows tuning the ISB transitions between electron confined levels of III-nitride quantum wells (QW) particularly in the 1.3-1.55 µm wavelength window used for fiber optics telecommunications . A number of GaN-based devices operating at telecommunication wavelengths have been demonstrated such as multi Tbit/s all-optical switches benefiting from the ultrafast ISB absorption recovery time in nitride QWs [4,5] or electro-optical modulators relying on electron depletion under a Schottky gate , charge transfer between coupled QWs [7,8] or bias-controlled QW depletion . It was also predicted that the Stark shift of the ISB resonance wavelength under an applied electric field could lead to efficient and fast electro-optical modulation devices . All these devices rely on light amplitude modulation induced by ISB absorption. Based on Kramers-Kronig relations, the ISB absorption should also translate into a variation of the refractive index at wavelengths close to the resonance which can be used for phase modulation. This has been experimentally verified at long infrared wavelengths using the Stark shift of ISB transitions in GaAs/AlGaAs step QWs . Very few theoretical works have addressed the potential of ISB refractive index modulation in GaN-based QWs . The refractive index nonlinearities in GaN/AlN waveguides have been observed, opening prospects for all-optical cross-phase modulators . In view of optical networks, switching and routing devices, fast electrical control of ISB phase modulation at 1.3-1.55 µm wavelength would be desirable but has not been demonstrated so far.
In this paper, we report on the investigation of ISB phase and amplitude electro-modulation at telecommunication wavelengths in waveguides containing GaN/AlN QWs. The ISB electro-absorption arises from the population (depletion) of the ground state of the active QWs under positive (negative) bias. We show that the ISB absorption exhibits a Stark shift to short wavelengths when increasing the bias voltage. By analyzing the spectral pattern of the beating between the propagating optical modes at various biases, we derive the electro-refractive index variation as a function of wavelength. The obtained index variation with bias from complete depletion to full population of the QWs is around -5 × 10−3. This value is similar to the typical index variation achieved in InP and is an order of magnitude higher than the index variation obtained in silicon. The results are consistent with the combined effect of resonant ISB dispersion and the Stark shift of the resonances.
2. Design and fabrication
The investigated structure was grown by Plasma-Assisted Molecular Beam Epitaxy (PAMBE) on a 1 μm thick AlN-on-sapphire substrate. The active region consists of three periods of 1.3 nm thick GaN wells with 3 nm thick AlN barriers. The wells are n-doped with Si at 2×1019 cm−3. The active region is sandwiched between two 500 nm thick Al0.5Ga0.5N bottom and top contact layers n-doped with Si at 5×1018 cm−3. These layers also act as waveguide. The sample was processed in the form of 50-μm-wide 800-nm-deep ridge waveguides using inductively coupled plasma reactive ion etching. Ti/Al/Ni/Au metals were deposited to form the top and bottom contacts. The top contact was designed to cover only part of the ridge in order to minimize the propagation losses due to plasmon absorption in the metal. The sample was then diced and the facets were mechanically polished to form optical waveguides with a length of 1.675 mm.
The operating principle of the device is shown Fig. 1 . The QWs are designed to exhibit the ISB transition at 1.5 µm. Under negative applied bias, the three QWs are depleted and the waveguide structure is transparent, while under positive applied bias the electron population of the wells gives rise to ISB absorption at 1.5 μm wavelength. Simulations show that at zero bias, the first well in growth order is populated, while the two other wells are depleted. This results in a residual ISB absorption at zero bias.
This type of wide-strip waveguide structure is commonly used for the investigations of absorption modulation [9,14,15]. Its great advantage is the relative simplicity of technological fabrication not requiring critical alignment steps and allowing rapid prototyping and testing. However, this kind of structures is not well adapted for measuring refractive index variation: The method based on Fabry-Perot resonances consisting in tracking the shift of the interference fringes as a function of modulation voltage  cannot be used in this case since the high number of lateral higher order modes blurs the Fabry-Perot interference. The determination of the refraction index in a wide-strip structure is nonetheless possible when the waveguide is also multimode in the vertical direction with a small number of higher orders modes. In this case, even if the total number of modes in the waveguide is further increased, pronounced interference fringes are obtained since the behavior of this wide-strip waveguide is akin that of a slab waveguide with only few higher order modes. The interference pattern is due to the beating effects between different order co-propagating slab modes in the quasi-slab waveguide structure. Tracking the evolution of the interference fringes with applied voltage allows the determination of the refractive index variation using the procedure described below.
3. Experiment and results
The waveguide samples were characterized using a wideband superluminescent electrical diode (SLED) centered at 1.54 µm and laser diodes tunable in 1.25-1.65 µm spectral range. A lensed optical fiber was used to couple the light into the wide-strip waveguide. The light transmitted through the waveguide was measured using an optical spectrum analyzer in the case of SLED source and wide area Ge photodetector in the case of the tunable laser. The device was operated under DC bias conditions. The thermal load at 10 V positive bias is 196 mW for a total waveguide surface of 0.084 mm2 and less than 25 mW at 5 V positive bias. All experiments were performed at room temperature.
First, the ISB absorption in the QWs was characterized by measuring the waveguide transmission spectra using the tunable laser at various bias values for transverse electric- (TE) and transverse magnetic- (TM) polarized light (Fig. 2(a) ). For TE-polarized light, marked oscillations are visible in the spectra but the average transmission level is approximately constant. The transmission not corrected for the coupling losses is around −20 dB and it does not display significant variations as a function of bias. In contrast, in the case of TM-polarized light the absorption increases when the bias changes from −10 to +5 V as a result of the population of the ground state of the QWs. The difference between TE- and TM-polarization stems from the ISB absorption selection rules. Indeed, the ISB transition couples only with TM-polarized radiation . The ISB absorption at 0 V is peaked at 1.545 µm with a full width at half maximum (FWHM) of 170 nm. The ISB absorption peak shifts with applied bias from 1.576 µm at −10 V to 1.514 µm at +5 V due to the dependence of the ISB transition energy on the electric field in the QWs (quantum confined Stark effect). This effect has already been observed in electro-optical modulators based on coupled QWs . The transmission level far from the ISB absorption is about −24 dB, which is slightly lower than for TE-polarized light due to the polarization dependent waveguide losses [18,19].
Figure 2(a) shows that the oscillation pattern changes significantly with bias for TM polarization while for TE polarization no significant change is observed. In order to analyze in detail the oscillation pattern, transmission spectra for TM-polarization have been acquired with a higher spectral resolution in the spectral region corresponding to the ISB absorption (Fig. 2(b)). The difference in the transmission between the data on Fig. 2(a) and 2(b) stems from the smaller waveguide output collection area when using the spectrum analyzer with a fibered input. For Fig. 2(b), the light collection region corresponds to the upper lobe intensity distribution visible in Fig. 3(c) , where maximal intensity modulation occurs. In the case of data displayed in Fig. 2(a), the transmitted light is collected from the entire waveguide output area. At negative bias, oscillations with a ≈10 nm period are essentially observed. However, when applying positive bias, shorter period oscillations (≈5 nm) appear on the long wavelength side of the spectrum.
As explained above, these oscillations are due to the beating interference between different order modes occurring in this type of quasi-slab waveguides. Indeed, slab mode calculations show that the investigated structure supports one fundamental and two higher order modes, as illustrated by Fig. 3(a).
The vertical multimode behavior of the investigated structure can be verified looking at the intensity distribution at the waveguide output using an IR camera (Figs. 3(b) and 3(c)). The intensity of the light distribution changes with bias, the change being maximal in the region corresponding to the AlGaN claddings and AlN/GaN QWs. This is related to the attenuation induced by the ISB absorption in the QWs. To identify the contribution of the different order modes in the formation of the beating interference pattern, it is convenient to perform a Fourier analysis of transmission spectra.
The Fourier distributions of the spectral response for TE and TM polarization at different bias are represented in Figs. 4(a) and 4(b), respectively. For TM polarization under negative bias, the Fourier distribution presents only a pronounced peak at τ1=0.69 THz−1. Since the maximum overlap of the input fiber occurs for the fundamental mode, the peak at τ1 corresponds to the 10 nm period beating interference between the fundamental and the first higher order modes (M0 and M1). At positive bias, an additional group of peaks centered around τ2=1.77 THz−1 corresponds to the 5 nm period beating interference between the fundamental and the second higher order modes (M0 and M2). The enhancement of this peak is explained by the larger confinement factor in the active region, which results in stronger dependency of the two low order modes M0 and M1 on the ISB absorption, since M2 extends farther into the sapphire substrate (Fig. 3(a)). As a consequence, the relative weight of the M2 increases with positive bias and the contribution of the M0-M2 beating interference becomes visible in the spectral response. The general decrease of the transmission level is responsible for the noise increase in the Fourier distribution at positive bias.
In the case of TE polarization [Fig. 4(a)], there is only one notable peak in the Fourier distribution centered at τTE=0.52 THz−1 regardless bias. This result further supports that the change of the interference beating pattern observed for TM polarization is indeed related to the relative changes in attenuation of the various vertical modes.
One major result following from this study is that the evolution of the transmission spectra with bias can be used to determine the electrorefractive index variation. A close examination of the TM transmission spectra of Fig. 2(b) reveals a manifest red shift of the interference maxima for increasing bias. This shift is a consequence of the index variation induced by the ISB absorption in the QWs, as expected from the Kramers-Kronig relation. To illustrate this effect, Fig. 5(b) displays the ISB absorption extracted from the transmission measurements of Fig 2(b), together with its Lorentzian fit and the associated refractive index dispersion. At a given wavelength, the refractive index is expected to change with bias due to the following effects: (i) the increase of the ISB absorption magnitude due to the QW population and (ii) the spectral shift of the ISB absorption maximum with bias.
The relation between the index variation Δneff0 of the fundamental mode M0 and the shift Δλ of the beating interference maximum is:Eq. (1) derivation can be found in Appendix B.
The difference of the M0 and M1 group index can be found directly from Fourier distribution according to the expression:20,21] using AlGaN refractive index values from reference . Details on Eq. (2) derivation can be found in Appendix A.
To determine the refractive index variation associated with the ISB transition we have carefully analyzed the wavelength position of the interference maxima and its variation with bias. The obtained index variation as a function of bias is shown in Fig. 5(a) for different wavelengths, using zero bias as a reference. The refractive index change is maximum at 1.462 µm wavelength – it is around -5×10−3 in the –5 V to 5 V bias range. The index variation decreases with increasing wavelength in qualitative agreement with the refractive index dispersion at +5 V shown in Fig. 5(b) (the grey rectangle corresponds to the experimentally explored spectral range). This resonant wavelength dependence means that the observed effect is essentially related to the population/depletion of the quantum well fundamental state leading to the absorption variation in the spectral domain around 1.5 µm. It is neither related to a thermo-optic effect caused by the dissipated electrical power, which is negligible in the −5 V to 5 V bias range, nor to the Pockels effect induced by the internal electrical field . Several waveguide devices were measured and the same qualitative behavior was observed. The magnitude of the observed index variation fluctuates from waveguide to waveguide within a factor of 2. This can be due to the inhomogeneities related to the growth process, which translates into different peak wavelength and spectral broadening of the intersubband absorption at different positions on the wafer. This can also be related to processing issues.
It is worthwhile mentioning that although the wavelength peak position experiences a red shift (Δλ>0) under positive bias, the resulting index variation plotted in Fig. 5(a) is negative. This behavior stems from the fact that as given by the modal calculations, while in Eq. (1).
It is important to note that the measured absolute value, 5×10−3, is similar to the typical index variation achieved in InP-based modulators [24–26] and is an order of magnitude higher than the index variation obtained in silicon [16,27]. Moreover, larger refractive index changes can be achieved by increasing either the number of QWs or the doping level as well as by tuning the operation wavelength to the maximum of the refractive index dispersion curve.
4. Summary and conclusion
The aim of our work was to determine the index variation in the GaN/AlN heterostructures related to the population/depletion of the QW fundamental state leading to the absorption variation in the spectral domain around 1.5µm. The experiments were performed using wide-strip waveguide structure. It was shown that the determination of the refraction index in a wide-strip structure is possible when the waveguide is multimode in the vertical direction with a small number of higher order modes. The variation of the refractive index was deduced from the shift of the position of the beating interference maxima of different order modes. The obtained index variation with bias from complete depletion to full population of the QWs is around -5 × 10−3. This value is similar to the typical index variation achieved in InP and is an order of magnitude higher than the index variation obtained in silicon. The remarkable feature is that maximum index variation is obtained at the wings of the ISB transition line where absorption is reduced with respect to the peak value. These results represent the first experimental evidence of an index variation due to ISB transitions at telecommunication wavelengths in GaN/AlN heterostructures. This index variation mechanism opens prospects for the realization of ISB phase modulators by inserting the active region in a Mach-Zehnder interferometer.
Appendix A: Group index determination
Then in a linear approximation:
Note that for Eq. (8) we use the fact that for a phase index having a linear dependence on the wavelength the group index is constant.
The Eq. (2) follows then in a straightforward way:
Appendix B: Refractive index variation with bias
The application of bias ΔV to GaN/AlGaN heterostructure produces a variation of the effective index Δneff and a shift Δλ of the interference maximum wavelength. In a linear approximation the condition for the beating interference maximum following from Eq. (3) is:
By taking into account Eq. (3) it follows that:
Then using the relation between the phase and group index given by the Eq. (7) we obtain:
The electrorefractive variation of the refractive index Δneff is accordingly:
Since in a linear approximation:Eq. (1) follows directly from Eqs. (13) and (14).
This work was supported by EC FP7 FET-OPEN STREP “Unitride” under grant agreement #233950. The AlN-on-sapphire template was provided by DOWA Electronics Materials Inc. The authors are very grateful to Prof. Gad Bahir from Technion Israel Institute of Technology for insightful comments.
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