1. Introduction

Photonic crystals (PhCs) [1] are playing an important role in the photonic device community. Especially two dimensional (2D) realizations found a huge field of applications in photonic circuits [2–4], fibers [5], and lasers [6–10]. A substantial fraction of these implementations are based on the use of photonic defect modes. For intersubband based devices PhCs are of special interest since in- and out-coupling of light via the surface cannot directly be achieved in such devices due to their restriction to TM polarized light. Hence, there is always a need for a coupling scheme, which up to now has mainly been realized via shallow gratings for detection [11] as well as for emission [12,13]. Deep etched grating structures like a PhC quantum cascade laser [10] are under extensive investigation since they allow an increase in cavity design freedom, addressing surface emission, compactness of the device and beam shaping.

In a former publication [14] we demonstrated the possibility of a PhC characterization via intracavity mode detection by a GaAs/AlGaAs QWIP incorporated in a photonic crystal slab. The devices were illuminated under varying angles of incidence via their surface and whenever the in-plane wave vector end energy of an incoming wave matches a PhC mode, the light is coupled into the cavity. The TM polarized excited modes are absorbed by the QWIP and cause spectral enhancements in the photocurrent. Each PhC mode is therefore represented by a peak in the photocurrent spectrum, similar to the resonant features in the reflectivity measurements shown by Astratov et al. [15] By tracing these peaks the band structure can be mapped including its polarization behavior. The agreement with theoretical calculations is excellent and it is therefore interesting whether this technique can be extended to the characterization of defect modes. We therefore introduced a single missing hole defect to a triangular PhC of air holes. Most applications use a triangular array of air holes since these structures provide viable band gaps for TE polarized light and are favorable over pillar structures that can not easily be electrically contacted. QWIPs rely on intersubband transitions and are therefore solely sensitive to radiation polarized perpendicular to the detecting region, hence TM polarized light. The TE band gaps and defect modes lying within can therefore not be utilized. Nevertheless the defect structure still gives rise to localized modes that may potentially be used.

2. Device description

2.1 Photonic crystal and defects

The samples used in our earlier publication [14] included similar defects than those in this work but closely laying band edge peaks anticipated a clear distinction of defect modes. For larger air filling factors the band edge modes are separated well from each other and the defect states in between can be resolved. A number of devices were processed with different air fill factors as well as different defect geometries. The parameters r/a, representing the size of the PhC holes and r_D/r, representing the size of the defect surrounding holes are depicted in the inset of Fig. 1. The diameters of the six holes surrounding the missing hole were varied in order to tune the defect mode. Their positions within the lattice remained unchanged. The defect structure was repeated with a period of 7a forming a 7×7 defect superlattice which increases the defect related signals. Although coupling between them is unlikely because of the long distance between the defects, it can not be excluded due to the lack of a TM band gap for this lattice type. In fact Simulations performed with different supercell sizes show that the defect mode frequencies converge to a value we consider as the isolated defect frequency only for relatively large supercells of around 20×20. The results we deduce from our measurements and calculations on 7×7 supercells typically differ by 1–2% from those values.

 

Fig. 1. SEM pictures of a finished and wire bonded device. The dotted parallelogram marks the unit cell of the 7×7 defect superlattice. This unit cell was also used for 2D simulations of the defect mode. The inset shows a close up of the defect structure including the relevant dimensions a, r and r_D. The defect is build by a single missing hole with the six nearest neighboring holes being varied in diameter but not being displaced.

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2.2 Waveguide

The vertical structure of the device is made up by a surface-plasmon [16] / plasmon enhanced [17] waveguide. The surface-plasmon cladding realized via the top contact allows a thin waveguide with a high confinement of the optical mode to the detecting region. This is however compromised by higher losses caused in the metal film. The reduced waveguide thickness eases the deep etching process significantly since the PhC holes need to penetrate the entire waveguide structure in order to keep its the guiding ability. The lower cladding is provided by a highly doped GaAs layer and the under laying highly doped substrate. The high doping level shifts the plasma frequency together with the according drop in refractive index into the mid-IR region.

3. Fabrication

3.1 Growth

The detecting region is formed by 50 periods of a standard GaAs/Al0.19Ga0.81As bound-to-quasibound QWIP [18] and was grown by molecular beam epitaxy. The well and barrier widths are w=6.6 nm and b=54 nm respectively. The wells are delta doped to an equivalent sheet density of 3×10¹¹ cm^-2. Starting from the highly doped (2×10¹⁸ cm^-3) substrate the layer sequence is as follows: 540 nm GaAs (2×10¹⁸ cm^-3) acts as a lower cladding followed by an undoped 216 nm Al_0.19Ga_0.81As spacer layer and the detecting region (2.796 µm). Subsequently another 216 nm Al_0.19Ga_0.81As spacer layer (undoped) was grown before the contact facilitating layers: 108 nm GaAs (1×10¹⁸ cm^-3) and 5 nm In_0.53Ga_0.47As (1×10¹⁹ cm^-3). All layer thicknesses and Al contents were extracted from X-ray diffraction measurements after growth.

3.2 Device processing

The fabrication was carried out in a mix and match processing, where direct e-beam lithography was used to define the PhC pattern and standard UV contact lithography was done on top of that to define insulation openings as well as extended contact pads. As a first step Ge/Au/Ni/Au (15/30/14/60 nm) was evaporated, followed by a 300 nm SiN_x layer. The e-beam written pattern is transferred via SF₆ reactive ion etching (RIE) to the SiN_x which - after removal of the PMMA - serves as a hard mask for Ar RIE of the top contact. In this way we circumvent a metal deposition after the deep etching step which could potentially short circuit the device. After the patterning of the metal contact the PhC was deep etched by SiCl₄/N₂ RIE [19] where hole depths of ~5.5 µm were achieved. A SiN_x insulation, Ti/Au contact pads and a Ge/Au/Ni/Au (15/30/14/60 nm) backside contact finish the processing. In addition to the PhC devices plain mesa structures (70×100 µm with a cleaved facet) with equal contacts were fabricated to optically and electrically characterize the QWIP.

4 Results and Discussion

4.1 Measurement setup

The chips were mounted in a liquid He flow cryostat fixed to a temperature of 10 K. The devices where biased and excited via a mid-IR broadband source. The unpatterned mesa samples where excited via their cleaved facet since a 45° wedge is not feasible due to the highly doped and therefore absorbing substrate. The PhC devices where illuminated at surface normal incidence or at specific angles of incidence and under different incoming polarizations. The angular resolution is ±5°, given by an 1 inch diaphragm and a 6 inch parabolic mirror used to focus the light on the sample. The photocurrent was spectrally resolved by a fourier transform infrared spectrometer in step-scan mode.

4.2 Band structure and defect mode mapping

The plain reference samples show a typical QWIP response with a main responsivity between 700 and 1000 cm^-1 (dotted line in Fig. 2(a)). The spectra of the surface excited PhCs still show this behavior, due to non-resonant diffraction at the small apertures given by the PhC holes. In addition to this background like signal several peaks are visible that are related to a resonant interaction with the PhC. In Fig. 2(a) photocurrent spectra taken from devices with and without a defect are compared. The samples are otherwise identical having a r/a ratio of 0.3 and a lattice constant of a=3 µm. Two peaks appear for both devices: the strongest at 1533 cm^-1 can be identified with the flat band edge at the Γ-point at a/λ₀=0.454. The weaker peak at 1289 cm^-1 is superposition of two signals that match the photonic bands crossing the Γ-point at a/λ₀=0.378 and 0.365. The additional peak at 1594 cm^-1 is an artifact caused by folding of the QWIP response main peak at 797 cm^-1. The good agreement of the angular- and polarization dependence of the peaks with a 2D plain wave expansion method (PWEM) (shown in Fig. 2(b)) assures our attributions. The according PWEM calculations where carried out using slightly higher r/a figures than extracted from scanning electron microscope (SEM) pictures, in order to account for a slight underetch not visible from a top view SEM investigation. The effective refractive index of n_eff=3.2 results from a 1D waveguide calculation without air holes.

In between this photonic band related peaks only the device with the defect structure (r_D/r=0.753) shows an additional, clearly visible peak at 1439 cm^-1 that arises from a defect state. Also the peak in the shoulder of the strongest feature at 1500 cm^-1 is caused by the defect. Fig. 2(c) shows the band structure mapping of a different device (r/a=0.326, r_D/r=0.753) including the defect. The bands still show very good agreement with our simulations and the energetically position of the defect state remains unchanged for varying angles of incidence. This behavior is expected for localized defect states since a strong localization in real space appears with a range of in-plane k-vectors in the reciprocal space. The quality factor of this and the following defect modes is Q≈50. Also the band edge related peaks have comparable line widths. An examination of the size variation of the hole diameters via SEM shows a variance of ±1.5% (±16.4 nm). This small variation causes a shift in the energetically position of the modes which appears as broadening. The according quality factors are calculated to range between 30 and 60 for band edge as well as for defect modes. It is worth mentioning that a variation of only the six defect surrounding holes would result in Q≈220 but due to the lack of a TM band gap the defect modes are more extended and the influence of the whole PhC has to be taken into account. Despite the fact of good agreement with experimental data there is a second possible explanation as broadening may be caused by the QWIP itself since it introduces a serious amount of losses to the cavity. This is a clear difference to other characterization methods that are typically performed on isolated defects. The examination of the high quality factors of single defects is therefore limited, since the usage of only one single defect instead of the supercell and a lowering of the QWIP absorbance may improve the line width but at the same time deteriorates the signal strength.

 

Fig. 2. (a) A comparison of photocurrent spectra of the unpatterned reference sample (dashed line), a PhC device with (solid line) and without (chain dotted line) the defect. Two peaks at a/λ₀=0.432 and 0.450 are caused by defect mode supported in-coupling. (b) Polarization dependent band structure mapping of a device without defect. Solid lines refer to calculated PhC modes of even symmetry, dotted lines refer to odd PhC modes. The experimental data points are marked as + for TM (π) incident and as - for TE (σ) incident light. Peaks that appear in either polarization are shown as open circles. (c) The same measurement for a device with defects (r/a=0.326 and r_D/r=0.753).

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4.3 Defect mode tuning

Further measurements were concerned with the frequency tuning of the defect modes as well as with their assignment to simulations. A range of samples was investigated all processed in one step with equal periodicity of a=3 µm and equal air filling of r/a=0.365. This value was again confirmed via angle and polarization resolved measurements (not shown) with which the band structure was mapped out and compared to a PWEM calculation. The nominal defect hole diameters where varied from r_D/r=0 to 1 in steps of 0.1. The actual values where extracted after processing via SEM. The PhCs where investigated in the frequency range from a/λ₀=0.4 to 0.54 where the third and fourth band cross the Γ-point. For higher lying modes the responsivity of the detector is too low, at smaller energies a clear assignment of the peaks is difficult due to their overlap with the response function of the QWIP. The technique could easily be adopted though to characterize energetically lower lying defect modes by either changing the design of the QWIP or by processing PhCs with smaller periods. In the photocurrent spectra a clear evidence of four different defect states is visible. Photocurrent spectra are shown in Fig. 3(a) for different defect sizes. Again the two peaks related to the photonic bands at a/λ₀=0.376, 0.409 and 0.545 can be identified. Their positions remain vastly unchanged with r_D/r. The additional defect peaks in between experience a blue-shift with increasing defect size, causing more and more modes to appear. The shifting is caused by the leaking of the defect modes into the defect surrounding holes. For larger defect holes a larger portion of the light is pushed into the air holes and feels a lower refractive index. The frequency is therefore blue-shifted.

 

Fig. 3. The graph shows three photocurrent spectra taken for three different defect sizes r_D/r. The modes experience a blue-shift with increasing defect size. The four resolved defect modes were attributed to simulated modes which are represented by their electric field pattern (large) and energy density (small).

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In contrast to the band structure related features we could not observe a polarization dependence of the defect peaks. Scattering as an origin for the coupling to the defect modes is a possible reason for the unpolarized response or the close energetic position of two modes of opposite mirror parity [20]. Also the earlier discussed size variations of the hole may cause a distortion. The lack of polarization dependence in connection with the broadness of the peaks aggravates an easy attribution to distinct defect modes. Nevertheless the tuning of the defect modes could be used for an assignment to calculated modes in terms of best agreement between experimental and theoretical data. The result is shown in Fig. 4 and electric field patterns of the modes we suggest as the excited ones are shown in Fig. 3: a hexapol, a dodecapol (12-fold), and two types of monopols. The simulations were carried out with the MIT photonic bands program [21] employing a PWEM using a supercell. The supercell size was 7×7 reproducing the actually fabricated structure (Fig. 1). Additionally a finite element algorithm was used with an identical unit cell and periodic boundary conditions. Both simulations yield similar results. It is noticeable that only a fraction of the defect modes which result from the simulation were actually excited. An analysis of the surface loss related Q_⊥ may give more information since it determines the coupling strength between the defect mode and an out of plane propagating wave.

 

Fig. 4. The dependence of measured defect mode frequencies (scatter plots) is compared to the simulation results. The broken lines mark the position of the flat band regions at the Γ-point. Solid lines represent the calculated energy shift of the four defect states shown in Fig. 3.

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5. Summary

In conclusion we showed that with a QWIP processed to a 2D PhC slab and characterized under surface incident light the photonic band structure can be mapped out as well as the frequencies of localized defect modes can be determined. In our actual structure of a triangular PhCs - which does not employ a photonic band gap for the polarization used - we were able to detect four defect modes. They were attributed by their energy dependence over defect size which was compared to those of simulated modes.