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Abstract
We report the first experimental parametric analysis of subwavelength monolithic high-contrast grating (MHCG) mirrors. To date, subwavelength grating mirrors have been fabricated by suspending a thin grating membrane in the air or placing it on a low refractive index material – a scheme that requires sophisticated processing and makes the gratings sensitive to mechanical stress, impeding current injection, and heat dissipation if used in active devices. Inherently MHCGs are well suited for optoelectronic devices because they can be fabricated in all possible material systems. Here we demonstrate above 90% optical power reflectance, strong polarization discrimination. Based on experimental analysis aided by numerical simulations, we demonstrate the possibility of tuning the spectral characteristics of MHCGs reflectance for more than 200 nm via modification of the duty cycle of the MHCG stripes. We show our MHCG tuning method is convenient to define the properties of MHCG devices during the device processing.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Numerous devices require mirrors with high optical power reflectance (R) including: vertical-cavity surface-emitting lasers (VCSELs) [1]; resonant-cavity light-emitting diodes (RCLED) [2,3]; resonant cavity solar cells with enhanced efficiency [4]; wavelength selective photodetectors [5]; Fabry-Pérot filters [6]; modulators [7]; and reflection filters [8].
Presently, mirrors with high optical power reflectance are achieved using distributed Bragg reflectors (DBRs) composed of numerous layer pairs of quarter-wavelength optical thickness with a large difference in the refractive indices of the two alternating DBR materials [1]. For example, an R = 0.95 (95%) power reflectance DBR mirror designed at 1 µm wavelength can be made of 10 pairs of GaAs and Al0.9Ga0.1As layers . The total thickness of such a DBR mirror stack is ∼1.4 µm. The DBRs made of arsenide-based materials are very common as high reflectivity (HR) mirrors for high quality factor resonant optical cavity device applications for visible, and for near and mid infrared radiation. The fabrication of DBRs of other groups of semiconductor materials, as for example nitride-, phosphide-, antimonide-, or selenide-based are more problematic due to low refractive index contrast between alloys of similar lattice constant. The DBRs targeted for infrared applications at wavelengths longer than 2 µm, however, are challenging to grow by epitaxy due to their relatively large thickness, which could reach tens of micrometers depending on the DBR design wavelength. In contrast, DBRs made of dielectric materials of very high refractive index contrast require a smaller number of DBR periods to achieve very high power reflectance over a broad wavelength range [9]. However, the main disadvantage of dielectric DBRs is that they are not monolithically integrated with the rest of a semiconductor device – which can be problematic for their use in high volume manufacturing. In numerous applications, microcavities require both a large quality factor (Q) enabled by HR mirrors, and the possibility of introducing light from outside of the microcavity. In the case of DBR mirrors this is particularly troublesome due to the typically broad HR band of DBRs which reflects (blocks) most all the incoming light.
An interesting alternative mirror that enables a ten-fold thickness reduction with respect to a conventional DBR mirror is the subwavelength high contrast grating (HCG) proposed by Chang-Hasnain [10] and Victorovich [11]. A properly designed HCG may possess an extremely high power reflectance, reaching 100% (R = 1.0), strong polarization discrimination, and phase tuning of the reflected light. Typical HCGs consist of high-refractive-index (HRI) stripes that are suspended in air (membrane) or placed on a substrate made of a low-refractive index material (LRI) [12–15]. In those structures high optical reflection is governed by a destructive interference of two, surface-normal grating modes traveling perpendicularly to the HCG stripes and confined in the grating due to the low refractive index of the surroundings [16–17].
In [18,19] and later in [20,21] the concept of a different variation of an HCG – the monolithic high-contrast grating (MHCG) – was proposed. The MHCG does not require a low refractive index region beneath the HCG stripes. In particular, the stripes can be etched made of the same material as the layer beneath them. A MHCG mirror can be as thin as a quarter of the wavelength of the reflected radiation. Furthermore, MHCGs may be fabricated of any transparent material that has a refractive index higher than 1.75 and can provide 100% power reflectance with a large HR stopband that is comparable to the stopband of typical GaAs/AlGaAs DBRs [20].
In contrast to membrane HCGs, MHCGs are inherently robust and immune to mechanical damage. They also do not require sophisticated critical-point drying membrane release during processing. The MHCG parameters can be precisely controlled by a standard electron beam lithography (EBL) or via nanoimprint lithography (NiL) [22] on a mass production scale. A given MHCG may also cover an arbitrarily large surface area in contrast to a large area HCG which would be fragile - perpetually at risk of collapse [23].
The manipulation of the power reflectance is possible by tuning the lateral parameters of the MHCG stripes that are produced during the device processing stage. The MHCG design may be modified to alter the MHCG’s R by changing the MHCG geometry — thus alleviating any simultaneous changes in the epitaxial structure — as is the case for monolithically grown DBRs. Polarization selectivity provides an additional degree of freedom with respect to the optical properties of DBRs – the MHCGs enable high power reflectance and low power transmittance at the same wavelength for orthogonal polarizations [20].
Recently Kim et al. reported the first polariton laser with an MHCG as the top mirror of a vertical resonant cavity [24]. It facilitates both optical pumping through the MHCG and a high Q for the light generated inside the microcavity. We concurrently reported the first electrically-injected MHCG VCSEL emitting at 980 nm [25,26].
In [21] we showed the very first demonstration of the fabrication and power reflectance measurement of a GaAs MHCG. The GaAs MHCG was designed for ∼100% power reflectance (at normal incidence) at 980 nm. We achieved about 95% power reflectance. In this paper we present the first parametric analysis of the polarization-dependent optical power reflectance of MHCGs by experimental characterization supported by numerical analysis. We show the tuning of the spectral properties of MHCGs by a simple geometric modification of the grating duty cycle (the ratio of the width of the stripes divided by the grating period, where we vary the trapezoidal bases given by the lengths F1 and F2 shown in Fig. 1) of the MHCG stripes only, while maintaining a fixed period (L) and a fixed height (h) for the MHCG stripes. The last two parameters (L and h) are the most sensitive to technological imperfection because they have a strong impact on the properties of the MHCG.
Fig. 1. A typical structure of an MHCG mirror with stripes of a trapezoidal cross-section: L – MHCG period; h – stripe height; LF1 – bottom; and LF2 - top dimensions of the trapezoidal bases. Light is incident on the MHCG from below.
2. Experiment
The experiment we discuss in this paper is constrained by the equipment we have available to produce MHCGs. Our electron beam lithography system (EBL) enabled the fabrication of 100 µm × 100 µm MHCGs (this is the maximum EBL write area for each MHCG structure). Measurements of the optical power reflectance spectra by a probe beam that could be confined to a spot significantly smaller than the grating surface was possible by our use of a tunable Ti:sapphire laser tuned in the range from 900 nm to 1040 nm. In order to reduce the inaccuracy of the MHCG fabrication, our goal was to use in our MHCG design the largest possible grating period to achieve the maximum optical power reflectance at the longest possible wavelength - in the tuning range of the Ti:sapphire laser. Thus, we designed the MHCG with a targeted optical power reflectance maximum at ∼1020 nm.
We fabricated 8 samples of 1020 nm GaAs MHCG mirrors of equal period L = 820 nm and etching depth h = 190 nm with varied duty cycle (F1) ranging from 0.2 to 0.6 in steps of 0.05. The MHCGs were fabricated on an undoped GaAs wafer. The sample was first covered with AR.P6200.09 EBL resist, exposed to the electron beam using a Raith ELPHY Plus EBL system, and then the EBL resist was developed. Then the stripe patterns were etched in an inductively coupled plasma reactive-ion etching (ICP-RIE) reactor in a standard Cl2+BCl3+Ar plasma. Afterward the dry etching, the patterned EBL resist was removed using our standard wet N-methyl-2-pyrrolidone (NMP) process. A more detailed description of our MHCG processing is provided in [25]. At the final stage, the GaAs wafer sample was thinned by mechanical lapping and then finely mechano-chemically polished from the substrate side and covered with an antireflective (AR) SiN coating – consisting of a single quarter-lambda (optically) thick layer. The resulting parameters of the processed MHCGs were investigated via a scanning electron microscope (SEM) – we collect the results in Table 1. SEM images of all fabricated MHCGs are shown in Fig. 2.
Fig. 2. SEM images of all implemented MHCGs. The photographs were taken at an angle of 25°. All spatial parameters (see Fig. 1) for Structures A through H are listed in Table 1.
Table 1. MHCG fill factors F1 and F2 of the bottom and top trapezoidal bases extracted from SEM images for Structures A-H (see Fig. 2).
The variations in the etching depth h and the period L are estimated to be Δh = 20 nm and ΔL = 30 nm based on our SEM images. The shape of the MHCG stripes at the cross-section is dominantly trapezoidal. This is a result of a low power (low bias) plasma etching, which increases the impact of the chemical part of the etching process over the physical part — thus resulting in an isotropic etch sloped stripe sidewalls. We assume the locations of the bottom and top edges of the trapezoids are given by LF1 and LF2 respectively (see Fig. 1).
Optical power reflectance measurements — at normal incidence — of the MHCG mirrors are carried out in the setup illustrated in Fig. 3. A tunable Ti:sapphire laser is used for the optical power reflectance measurements in the range from 900 nm to 1040 nm. The Ti:sapphire laser beam allows for more precise optical power reflectance measurements — but over a narrower spectral measurement range as compared to a broad, white light source. The broad source is also more difficult to focus onto a small area of an MHCG. Ti:sapphire laser probe beam is inherently polarized. The polarizer Pol together with the halfwave plate controls the power of probe beam. A beam splitter BS1 is used to separate the signal into two parts: first (the reference arm) is directed to a broad bandwidth, HR, DBR dielectric mirror (REF mirror, Thorlabs BB05-E03 of power reflectance Rref = 0.997 in the measured spectrum) which serves as a reference mirror. The second part of the laser beam is directed onto the MHCG mirror (sample arm). The MHCG mirror is placed precisely at the waist of the focused beam at zero angle of (normal) incidence. A chopper rotating at 200 Hz enables independent and simultaneous detection of signals from the reference mirror and the MHCG by a single photodetector. Our test arrangement reduces the measurement error induced by instabilities in both the laser beam intensity and any external conditions.
Fig. 3. Experimental setup used for optical power reflectance measurements. λ/2 — the halfwave plate, Pol — polarizer, BS1, BS2 — non-polarizing beam splitters, S1, S2 — lenses, REF — high reflectivity reference mirror, PDtrans, PDrefl — photodetectors.
During each chopper rotation (see Fig. 3), 3 successive stages may be distinguished in which the signal is detected from the: 1) MHCG mirror (I1) and 2) reference mirror (I2). The third stage corresponds to the blocking of both beam paths to enable the detection of the background noise level (I3). Lens S1 is used to focus the probe laser beam onto the MHCG mirror to a spot of ∼10 µm in diameter. The photodetector PDtrans is used to measure the optical signal transmitted by the MHCG mirror. Beam splitters and detectors are slightly tilted to the laser beam to avoid back reflections. All the detected optical signals are analyzed by computer software after their conversion to digital data via a 16-bit analog-to-digital converter data acquisition system (DAQ).
The radiation splitting ratio via the beam splitter BS1 depends on the radiation wavelength. Hence, an additional calibration is required to take into account the various optical elements in the path of the MHCG under test. This calibration coefficient (C) is a ration between signal from branch in which MHCG mirror is replaced by second identical reference mirror and signal from reference mirror. From both signals the background signal is subtracted. The absolute optical power reflectance is determined based on formula:
For each wavelength, R is averaged over 300 measurements with a standard deviation not larger than 0.1%. The oscillations of power reflectance spectrum at the level of 5% are related to Fabry-Perot resonance within GaAs substrate.3. Numerical model
In the calculations we reproduce the real-word cross-section shape of the MHCGs in the plane perpendicular to the stripes assuming infinite lengths of the trapezoidal stripes (see Fig. 1). We also assume semi-infinite thickness of air above the MHCG and of GaAs beneath the MHCG. At 1020 nm we use a refractive index of 3.43 for the GaAs (the stripes and the underlying material). We use the two-dimensional Plane Wave Admittance Method (PWAM) [27] to calculate the optical power reflectance of the MHCGs. In calculations we impose periodic boundary conditions which elongate the grating to infinity in the lateral direction. In our past analysis we showed that 100 MHCG periods and more reveal reflection very close to infinite grating [26]. In the calculations as well as in the experimental analysis, two orthogonal light polarizations are used, namely TE (transverse electric, where the electric field is parallel to the MHCG stripes) and TM polarization (transverse magnetic, where the electric field is perpendicular to the MHCG stripes).
A careful inspection of the SEM images of the MHCG cross-sections (see Fig. 2) indicates a deviation of the actual grating shape from a perfect trapezoid as we use in our numerical analysis. The cross-sectional shape of the stripes can be read from the SEM images in two ways: 1) by approximating the shapes as isosceles trapezoids whose parameters can be read from the SEM images (see an example in Fig. 4(a), where the estimated MHCG parameters are listed in Table 1); or 2) by reading the MHCG shapes point-by-point from the SEM images (see an example in Fig. 4(b)). For both cases, we have determined the optical power reflectance spectrum (see Fig. 5) for Structure A for TE polarization of the incident light (at normal incidence). The difference between the two approaches is not significant. For the structure read point-by-point, the optical power reflectance spectrum is slightly wider. The calculations presented hereinafter were carried out for structures approximated by trapezoids.
Fig. 4. Two approaches to defining the cross-sectional profile of an MHCG mirror based on SEM images: a) approximating the cross-section with regular isosceles trapezoids; and b) reading the profile from the SEM images point-by-point (schematic figure, showing significantly lower number of sampling points then actually used). Both pictures show the same Structure A.
Fig. 5. Optical power reflectance spectra (at normal incidence) for the MHCG Structure A for TE polarization for isosceles trapezoidal cross-sections of the MHCG stripes (blue line) and for cross-section profiles read point-by-point from the SEM images (red line). The trapezoid parameters used for the red line are indicated in Table 1.
In our MHCG modeling, we take into account the fact that the sidewalls of our MHCG grating stripes are not smooth and that the stripes may fluctuate in width. For this reason, we calculate the optical power reflectance (at normal incidence) not for a single (one fixed) period, but for ten stripes in a group that are periodically repeated. For each of these ten period groups we assume a different width of each stripe (see Fig. 6). In our model, the width of each stripe is multiplied by the value drawn from a statistical normal distribution. The standard deviation of the normal distribution — taken as 0.15 — is estimated on the basis of the SEM images of our processed MHCG structures. We draw 10 values (from the normal distribution function) and create a grating with periodic boundary conditions in which 10 stripes have different widths. For such a grating we calculate the optical power reflectance spectrum (at normal incidence). The drawing of 10 values (to form a random group of 10 stripes) is repeated 100 times – thus we create 100 different gratings based on repeating groups of 10 stripes. For each of the 100 MHCG gratings we calculate the optical power reflectance spectrum. Then we calculate the arithmetic mean of the 100 power reflectance spectra. The spectrum obtained in this way is treated as the final (simulated) result (see Fig. 7) and is showing a close correspondence to the experimental result, which will be discussed later.
Fig. 6. Schematic structure of an MHCG with varied widths (xiLF) of the stripes. We assume random values of xi and we draw these random values from a statistical normal distribution. Red dashed line represents periodic boundary conditions.
Fig. 7. Measured and calculated optical power reflectance spectra at normal incidence for MHCG Structure A. The gray lines illustrate 100 optical power reflectance spectra, each for different 10 period MHCG structures created based on a statistical normal distribution. The black line corresponds to the average optical power reflectance spectrum (calculated as the arithmetic mean of the 100 simulated spectra) and the red line is the experimental spectrum.
4. Reflectance spectra
Figure 8 illustrates simulated map of the optical power reflectance for a trapezoidal-shaped MHCGs as a function of the bottom and top trapezoid bases for fixed values of grating period L = 820 nm and grating height h = 190 nm for TE polarization and the wavelength of 1020 nm of incident light. White dots represent the optical power reflectance of the MHCG Structures A–H (see Table 1) for perfectly trapezoidal and periodic cross-sections of stripes. The dots, except for Structure A, are positioned along line expressed by the formula F1 = F2 – 0.1, reveal satisfactory control of the MHCG parameters in the MHCG processing. Based on this image we expect that the optical power reflectance at the wavelength of 1020 nm will decrease gradually from almost 95% for Structure A to above 20% for Structure H.
Fig. 8. Colorized map of the optical power reflectance for a trapezoidal-shaped GaAs MHCG as a function of fill factors of the bottom and top trapezoid bases for fixed values of period L = 820 nm and grating height h = 190 nm for TE polarized, 1020 nm incident light. The white dots correspond to the MHCG structures listed in Table 1.
In Fig. 9 we present the measured and calculated power reflectance spectra for TE (Fig. 9(a)) and TM (Fig. 9(b)) polarization of incident light for 1020 nm MHCGs. As expected, the optical power reflectance at 1020 nm for TE polarization changes gradually for Structure A that reaches power reflectance of 95% at the wavelength of 1020 nm to Structure H which is characterized by an optical power reflectance above 20%. The calculated power reflectance spectra follow the experimental characteristics very closely and hence can be helpful in an interpretation of the results out of the spectral range of the probe beam. Our MHCG calculations show that an increase in the MHCG duty cycle shifts the power reflectance spectra towards longer wavelengths and the maximum of the optical power reflectance reduces gradually to the level of 60% at the wavelength of 1200 nm. In the short wavelength range where the optical power reflectance falls below 20%, nonperfect sidewalls of MHCGs may hamper nearly 100% transmission contributing to the discrepancy between the simulation and the experiment – and this impedes our ability to draw definitive conclusions on the associated experimental results.
Fig. 9. Optical power reflectance for fabricated 1020 nm MHCGs measured and calculated for a) TE and b) TM polarization.
Figure 9(b) illustrates experimental and simulated optical power reflectance spectra for TM polarization of the Ti:sapphire laser probe beam. The image shows a significant difference in the optical power reflectance with respect to TE polarization. The polarization discrimination is equal to ∼20% at the maximum of the TM (polarized) optical power reflectance. In the case of Structure A, the maximum optical power reflectance reaches 50% at the wavelength of 950 nm. Simulations show that an increase in fill factors leads to a redshift of the reflection spectrum, while the maximum of optical power reflectance remains at the level of above 60%. Structure H reaches its maximum R at the wavelength of 1300 nm.
The beam incident to the MHCG is not entirely parallel since laser beam is focuses at the sample by the lens (S1). In our setup the maximal incident angle is 4° in GaAs, which is due to the focal length of the lens being 8 mm and the 4 mm diameter of the laser spot on the lens. Figure 10 illustrates calculated power reflectance of Structure A as a function of wavelength and angle of incidence inside GaAs. The spectral dependence of high reflection is bounded by the diffraction limit from short wavelengths:
where α is an incident angle in GaAs. The power reflectance decreases with increase in incident angle however the angular dependence reveals a plateau for small angles that is an unique feature of MHCG stripes with trapezoidal cross-section. For the wavelength of 1020 nm power reflectance is at high and constant level of nearly 1 for angle less than 4° (Fig. 10(b)) that corresponds to the maximal angle of incidence in our setup. This suggests that the measurement accuracy is not affected by focusing of the laser beam.Fig. 10. a) Colorized map of the optical power reflectance for Structure A as a function of the wavelength and angle of incidence in GaAs, and b) power reflectance versus angle of incidence in GaAs for the wavelength of 1020 nm.
5. Summary
In this paper we present the first comprehensive experimental parameter analysis of the optical power reflectance of MHCGs. We designed eight MHCGs of different duty cycle enabling high optical power reflectance of TE polarized incident light – all processed on a single GaAs wafer in a single processing procedure. The experimental characteristics were measured in the setup using a tunable Ti:sapphire laser providing excellent properties of the probe beam – although with a relatively narrow spectrum with respect to spectral width of the MHCGs. Experimental and simulated MHCG characteristics of optical power reflectance showed excellent agreement. Structure A with the smallest duty cycle designed to achieve the maximal optical power reflectance in the spectral range of the Ti:sapphire probe laser revealed 95% and 50% optical power reflectance for TE and TM polarizations, respectively. Other samples of incrementally increasing duty cycle showed a gradual reduction of the optical power reflectance in accordance with our numerical model. The power reflectance spectra anticipated by simulations show that the maximum of the power reflectance spectra can be tuned for more than 200 nm by changing the average duty cycle from 0.2 to 0.5 and their maximal optical power reflectance is in excess of 60%. In general, we notice that the wavelength for which we measured the highest optical power reflectance was longer for higher values of duty cycle. We also investigated the discrepancies between the parameters of the designed and the processed structures and revealed that the main issue was not sufficient enough control of the dry-etching process which led to sidewall roughness. We numerically investigated the impact of the random sidewall roughness on the optical power reflectance of the MHCG mirrors and we achieved a very good agreement. Sidewall roughness is the main reason for not reaching the level of 99% of power reflectance that is expected based on numerical analysis. Such high level of power reflectance can be achieved by optimization the etching process. Concurrently, MHCGs of lower power reflectivity can create composite mirrors consisting of a few DBR pairs and MHCG. The MHCG can be easily scaled to different spectral ranges by simply scaling the MHCG parameters. The MHCG can be implemented in any material system used in optoelectronics and requires no integration with other lower refractive index materials. Hence, if utilized as part of a device an MHCG can be implemented in the material of which the device is fabricated.
Funding
Narodowe Centrum Nauki (2018/29/B/ST7/01927, OPUS; 2018/29/N/ST7/02460, PRELUDIUM); German Research Foundation via the Collaborative Research Center 787.
Disclosures
The authors declare no conflicts of interest.
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