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Electrically Tunable, CMOS-Compatible Metamaterial Based on Semiconductor Nanopillars Matthew Morea, Kai Zang, Theodore I. Kamins, Mark L. Brongersma, and James S. Harris ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.8b01383 • Publication Date (Web): 23 Oct 2018 Downloaded from http://pubs.acs.org on October 25, 2018

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Electrically Tunable, CMOS-Compatible Metamaterial Based on Semiconductor Nanopillars Matthew Morea*,†, Kai Zang†,§, Theodore I. Kamins†, Mark L. Brongersma‡, and James S. Harris† †Department

of Electrical Engineering and ‡Geballe Laboratory for Advanced Materials,

Stanford University, Stanford, California 94305, United States ABSTRACT: With the advent of autonomous vehicles imminent, a solid-state approach to beam steering is necessary for more affordable lidar tracking systems. Capable of dynamic control of light with subwavelength components, electrically tunable metamaterials show potential in this field as well as other applications. Here, we demonstrate a nanopillar-based metamaterial composed of Ge and Al-doped ZnO (AZO), whose optical properties can be modulated by the field effect and whose fabrication process is compatible with complementary metal-oxidesemiconductor (CMOS) technology. From reflectance spectra, wavelength shifts up to 240 nm of the optical resonances are measured in our fabricated device with gate biases from -4 V to 4 V. A high differential reflectance of more than 40% in this voltage range is experimentally shown. Then, through an effective medium approximation, we can describe the nanopillar array as a macroscopic metamaterial and calculate the phase shift of this device. With optimization of the nanopillar parameters, a large phase modulation approaching 270° is possible according to simulations, which is promising for beam steering applications. KEYWORDS: Metamaterial, nanopillar, Ge, AZO, electrically tunable, phase modulation

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The field of metamaterials has grown significantly over the past decade and shows potential for a multitude of applications including the following: biochemical sensing,1,2 on-chip interconnects,3 color filters or structural color printing,4,5 and wavefront control for beam steering6,7 or ultra-thin lenses.8,9 By definition, metamaterials are tunable with different physical arrangements or dimensions of their subwavelength elements; for real-time control of their optical properties, researchers have demonstrated thermal,10 chemical,11 mechanical,12 optical,13 and electrical modulation methods.6,7,14-18 Due to the technological push toward self-driving cars recently, a major focus of these dynamic metamaterials has been shifted toward beam steering applications. The lidar systems in these prototype cars have predominantly relied on bulky and expensive rotating mechanisms to scan the surroundings for other cars and objects. Electrically tunable metamaterials offer a solid-state alternative. By arranging these metamaterials in a phased array, light can be directed at different angles by a simple change in applied bias. Among the electro-optical approaches for such active phase-tuning metamaterials, several materials have been explored: highly doped semiconductors,16 transparent conducting oxides (TCOs),6,14,18 phasechange materials,19 and two-dimensional materials like graphene or transition metal dichalcogenides.7,17 Many of these studies rely on ultrathin metasurfaces that have an exceedingly


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short interaction length with light and, to realize noticeable modulation, need highly tunable optical properties or resonant antenna structures made out of metals such as gold or silver, which lack CMOS compatibility. In this article, we present another electro-optical approach that uses an array of nanopillars as the metamaterial, a three-dimensional design for increased interaction length with light, composed of a highly-doped semiconductor, an insulator, and a TCO. We experimentally demonstrate a device that is compatible with high-volume CMOS processing and measure the electrical modulation of the resonant wavelengths and amplitudes of the mid-infrared reflectance spectra. Using the transfer matrix method (TMM) and an effective medium approximation of our metamaterial, we calculate that our nanopillar structure is capable of strong phase modulation from calculations. Our proposed structure (Figure 1a) is fabricated from epitaxially-grown n-type Ge with carrier density of 1.5×1019 cm-3 on Si wafers. With electron-beam lithography, the Ge layer is etched with an Al mask to form nanopillars of diameter around 40 to 50 nm, periodicity of 110 nm, and height of approximately 500 nm. To achieve field-effect modulation, the Ge nanopillar array is coated with a gate oxide and n-type AZO (see Figure 1c for cross section of nanopillar) by highly conformal thermal atomic layer deposition (ALD). AZO is used instead of a metal as the gate, because it offers both high optical transparency and electrical conductivity. This forms essentially a semiconductor-oxide-semiconductor (SOS) capacitor. Details of the fabrication process are described in the Methods section. Figure 1b shows a scanning electron microscope (SEM) image of the fabricated nanopillars.


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Figure 1. (a) Proposed SOS capacitor device structure with Ge nanopillars coated by a gate oxide and AZO. Electrically biasing this device affects the carrier density in the Ge nanopillar and the AZO gate layer. (b) SEM image taken at 45° tilt after complete device fabrication, showing the Ge nanopillars coated with gate oxide and AZO layers. (c) The periodic array of nanopillars is modeled as a metamaterial with effective optical properties in this work. Inset: xy-plane crosssection schematic of an individual nanopillar illustrating the conformal coating of the gate oxide and AZO around the etched Ge cylinder; this coated nanopillar along with the air around it serves as the unit cell of the metamaterial used in our simulations. As an SOS capacitor, an applied bias will modulate the carrier density of both the Ge and the AZO at their respective interface with the gate oxide. For a positive voltage, the n-type Ge will go into accumulation as the n-type AZO is depleted, while the opposite is true for a negative voltage. These changes in the carrier density (𝑁) will directly affect the plasma frequency (𝜔𝑝) and, consequently, the permittivity (𝜖) of the modulated AZO and Ge layers based on the Drude model:

𝜔𝑝 =

𝑁𝑒2

(1)

𝑚 ∗ 𝜖0


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𝜔2𝑝

(2)

𝜖(𝜔) = 𝜖∞ ― 𝜔2 + 𝑖𝜔Γ 𝑒

(3)

Γ = 𝑚∗𝜇

Here, 𝑒 is the charge of an electron, 𝑚 ∗ is the effective mass of conduction electrons, 𝜖0 is the permittivity of vacuum, 𝜖∞ is the permittivity of the material at infinite frequency, Γ is the damping factor or relaxation rate, and 𝜇 is the carrier mobility. Later, we will discuss how these subwavelength nanopillars can be approximated as a metamaterial (Figure 1c) when we calculate the phase modulation of our device. Electrical characterization is executed first mainly to sort the devices by performance in addition to determining the improvement of nanopillar-based capacitors over their planar counterparts. Based on the capacitance versus voltage (C-V) measurements (Figure 2a), the use of nanopillars enhances the capacitance of the SOS devices by a factor of 3 approximately, which corresponds directly to the increase in the exposed surface area of Ge. As with a modern fin fieldeffect transistor (FinFET), the wrap-around gate structure of our nanopillar-array capacitors provides much stronger electrical control compared to a completely flat design. For our best devices (with diameter of 200 µm), the leakage current can be less than 2 nA for a voltage range of -4 V to +4V (Figure 2b). Such low leakage current values indicate effective insulation by the gate oxide over the large area of these capacitors due to the conformal thermal ALD process. Also, in high-frequency C-V tests, our 200-µm-diameter devices can work at 100 kHz and above (as seen in Supporting Information Figure S2), limited by the 𝑅𝐶 time constant. The resistance component is determined by the contact resistances as well as the resistance through the Ge substrate or nanopillars and the thin AZO film. Because the expected depletion width is approximately 10 nm (Figure 2c), the Ge nanopillars will still have a finite neutral region (of about


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20 nm in width if the original Ge pillar diameter is 40 nm) that will allow conduction of charge during high-frequency switching. With smaller device areas to reduce the series resistance (particularly in the AZO thin film) as well as the overall capacitance, modulation speeds even in the GHz range of transistors should be possible.

Figure 2. (a) C-V measurements of devices (200-µm-diameter capacitors) with and without nanopillars (at 1 kHz). Use of nanopillars increases the effective surface area of the capacitor and significantly enhances the capacitance. The four cartoon schematics along the sides of this C-V plot represent the different states with the two on the left depicting the negative bias condition (with accumulated electrons in AZO and depleted Ge) and with those on the right showing the positive bias condition (with accumulated electrons in Ge and depleted AZO). The two cartoons on the top are for devices with nanopillars, showing the enhanced surface area compared to the two cartoons on the bottom for planar devices. (b) I-V measurements of a device (with 200 µm diameter) with nanopillars. Between -2 V and 2 V, the current is within tens to hundreds of picoamperes. (c) Simulated electron densities in Ge at the gate oxide interface for +4 V bias for accumulation mode and -4 V bias for depletion mode. The accumulation width is less than 4 nm, while the depletion width is approximately 10 nm.


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Next, we experimentally investigate the tunable optical behavior from Fourier transform infrared (FTIR) reflectance measurements. We use a microscope with a 15x Schwarzschild-type reflective objective with a numerical aperture of 0.58, which corresponds to a maximum incident angle of 35° for illumination. Our nanopillar-array capacitors have wire-bonded contacts that we connect to a DC power supply next to our FTIR microscope. Figure 3 shows the FTIR reflectance spectra at different applied voltages. Multiple reflectance minima can be observed in these optical spectra and can be partly attributed to the Fabry-Pérot resonances of the device structure, particularly within the metamaterial cavity. (See Supporting Information Figure S3 for more optical measurements to see how the diameter of the nanopillars affects the spectra.) The two major resonance features near 2.5 µm and 11.7 µm (as noted in Figure 3) are modulated in different directions due to their proximity to the plasma frequencies of AZO at the lower wavelength and Ge at the longer wavelength respectively. For increasing applied bias, the resonance near 2.5 µm is redshifted corresponding to the AZO layer’s conversion from accumulation into depletion, while the resonance around 11.7 µm undergoes a blueshift because the Ge is going from depletion to accumulation. From -4 V to 4 V, the former resonance is modulated up to 60 nm in wavelength and the latter is shifted by 240 nm. A high differential reflectance up to 40% is measured for this voltage range (Supporting Information Figure S4).


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Figure 3. Reflectance measurements from FTIR microscopy. (a) The reflectance spectra for a planar device compared to devices with nanopillars (the latter is biased at -4 V or 4 V). Two resonance features are boxed in green or blue and explored in (b) and (c) with more detail. (b) Magnified view of these resonance features and the effect of applied bias on them. (c) On the left, the shorter-wavelength resonance feature redshifts with voltage, while, on the right, the opposite behavior occurs for the longer-wavelength resonance. This distinction can be explained by the carrier accumulation or depletion in either AZO or Ge. The error bars represent the resonance wavelengths for multiple sweeps of the applied voltage for a single device.


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Not only does each resonant frequency change with electrical bias, but also the phase is modulated. By arranging multiple elements with slightly different applied biases, one could make a phased array to steer the direction of light with this subwavelength nanopillar design. To investigate the potential for such an application, we simulate this structure with the transfer-matrix method (TMM) to calculate the phase modulation with applied voltage. Because our nanopillars’ dimensions and spacing are deep-subwavelength for the mid-infrared range of interest, they can be modeled as a metamaterial with an effective medium approximation. Therefore, our devices can be approximated as a one-dimensional material stack, which allows for the TMM approach to thoroughly describe the optical behavior of our structure. Due to the high aspect ratio, the nanopillars form an anisotropic or birefringent metamaterial with 𝜖𝑥 = 𝜖𝑦 ≠ 𝜖𝑧, where the 𝑥 and 𝑦 directions are perpendicular to the nanopillar axis and the 𝑧 direction is parallel. The effective permittivity components can be described with the volume-average formula for 𝜖𝑧 and the Bruggeman formula for 𝜖𝑥 = 𝜖𝑦:20 𝜖𝑧 = (1 ― 𝑓𝑧)𝜖𝑎𝑖𝑟 + 𝑓𝑧[𝜂𝐺𝑒𝜖𝐺𝑒 + 𝜂𝑜𝑥𝑖𝑑𝑒𝜖𝑜𝑥𝑖𝑑𝑒 + (1 ― 𝜂𝐺𝑒 ― 𝜂𝑜𝑥𝑖𝑑𝑒)𝜖𝐴𝑍𝑂]

(4)

where 𝑓𝑧 is the area or volume filling ratio of the whole (coated) pillar in air (within a square period) given by 𝜋𝑟2/𝑎2 with the pillar radius 𝑟 and period 𝑎, 𝜂 is the area or volume filling ratio of the individual pillar materials (i.e., Ge, oxide, and AZO) within the area of the pillar. 𝜖𝑎 ― 𝜖 ⊥

𝜖𝑏 ― 𝜖 ⊥

𝑓𝑥𝑦𝜖𝑎 + 𝜖 ⊥ + (1 ― 𝑓𝑥𝑦)𝜖𝑏 ― 𝜖 ⊥ = 0

𝜖 ⊥ = 𝜖𝑥 = 𝜖𝑦 = ±

2

(12 ― 𝑓𝑥𝑦) (𝜖𝑎 ― 𝜖𝑏)2 + 𝜖𝑎𝜖𝑏 ― (12 ― 𝑓𝑥𝑦)(𝜖𝑎 ― 𝜖𝑏)

(5)

(6)


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where 𝑓𝑥𝑦 is the filling ratio of the inclusion material (𝜖𝑎) within the host or surrounding material (𝜖𝑏). In this Bruggeman formula, the ± sign is chosen such that imaginary part of effective permittivity is positive. Due to the multiple layers of gate oxides and AZO surrounding the Ge nanopillars, this Bruggeman equation is repeated multiple times to get the effective 𝜖𝑥 and 𝜖𝑦 components of the permittivity for our device. With this effective medium approximation and TMM code, we obtain strong agreement between the simulated reflectance results and the measured FTIR data as seen in Figure 4a. The model works well, especially for the shorter-wavelength resonance; at longer wavelengths, there is some deviation likely due to loss terms that are not considered in the optical parameters simulated here or perhaps the spread of angles for incidence and collection. The TMM code uses parameters that are close to the actual experimental values for the fabricated devices and the measurement system such as the carrier concentrations of the Ge and AZO layers in the metamaterial (1.6×1019 cm-3 and 8.7×1019 cm-3 respectively), incident angle (35°), diameter of Ge nanopillar (41 nm), and nanopillar height (430 nm). The TMM code allows us to calculate the phase shift (𝜙) for reflectance or transmission as well as the amount of phase modulation (Δ𝜙) with simulated applied bias, which we can use to evaluate the potential of these nanopillar devices for beam steering applications. First, we use the metamaterial based on the fabricated device structure. For these dimensions, the greatest phase modulation occurs for reflection in the TE polarization. A large change in the TE reflection’s phase shift happens around the reflectance resonance between 2 and 3 µm (Figure 4b). Due to this steep slope, phase modulation up to nearly 40° around this wavelength range is possible by changing the


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bias from -4 V to 4 V (Figure 4c). However, this moderate result is based on our fabricated devices, which use a structure that is not optimized for maximum phase modulation.

Figure 4. (a) The reflectance of the effective-medium stack simulated by TMM fits well to the measured FTIR reflectance. This TMM calculation uses parameters that are close to the actual experiment and assumes unpolarized incident light. (b)-(c) Simulated phase shift and modulation with incident light at angle of 35° with nanopillar dimensions based on fabricated devices as in (a), which is not optimized for phase modulation. (b) Phase shift for reflection and transmission for both TM and TE polarization. Inset provides magnified view of the TE component of the reflection phase shift at varying applied bias. The significant change in phase shift for wavelengths between 2 and 3 µm corresponds to the resonance in the reflection spectrum that can be observed in Figure 3 and Figure 4a. This steep slope allows for strong modulation of the phase. (c) Phase modulation for the reflection phase with TE-polarized light at different applied bias. These phase modulation values are with respect to the phase shifts at a negative bias of -4 V [i.e., Δ𝜙𝑟,𝑇𝐸(𝑉2) = 𝜙𝑟,𝑇𝐸(𝑉2) ― 𝜙𝑟,𝑇𝐸(𝑉1 = ―4 V)]. The phase can be modulated up to nearly 40° at a wavelength around 2.5 µm by changing the bias from -4 V to 4 V. More effective modulation can be achieved by redesigning the nanopillar array with this TMM approach. Changing the nanopillar height is an effective way to improve the phase


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modulation (Figure 5). At certain pillar heights, the metamaterial can achieve the condition of critical coupling,7 where the reflection is minimized (Figure 5a) and the phase modulation is maximized (Figures 5b and 5c). Phase modulation approaching 270° for TE polarization is achieved with nanopillar heights near 500 nm for a voltage sweep from -4 V to 4 V. Oscillations in Figure 5c may be attributed to the Fabry-Pérot resonances of the metamaterial slab, shifting in wavelength with increasing slab thickness (Figure 5d). In our device, modulation of the reflectance resonances works based on the change in the effective refractive index of the metamaterial or nanopillar layer due to the free carrier plasma dispersion effect induced in the Ge and AZO layers with applied bias. As a result, there is a phase pickup during the roundtrip of light in this Fabry– Pérot resonator that can be strongly modulated due to the sizable interaction length of light within the metamaterial layer. Further optimization can be done with other parameters such as the Ge film thickness underneath the nanopillars (Figure S5). Despite a similar wavelength shift for the reflectance resonance (Figure 5a) as in the fabricated devices (Figure 3), the phase modulation of this design is much greater due to operation near critical coupling. The electrically tunable metamaterial design presented in this paper is a proof of concept that can be reconfigured with a variety of different materials whose refractive indices can be modulated with the free carrier plasma dispersion effect or other electro-optic effects. For instance, other highly doped semiconductors, particularly TCO materials like indium tin oxide, could take AZO’s place. Due to the high aspect ratio of our design, the use of ALD for this TCO material was clearly important for conformal coverage. Regarding the inner nanopillar material, Ge could also be replaced with Si or other doped semiconductors. For CMOS-compatibility, the main choices are either Si or Ge. As noted in the Supporting Information, the index contrast between the Ge epi layer and the Si substrate results in a Fabry-Pérot resonance that helps to enhance the optical interaction with the


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nanopillars or metamaterial layer. A similar effect could be achieved by using silicon-on-insulator (SOI) wafers or possibly depositing metal back reflectors on a thinner Si substrate.

Figure 5. Simulated phase and reflectance results with incident light at angle of 35°. Nanopillar dimensions are based on fabricated devices (as in Figure 4), except the pillar height. (a) Reflectance of TE-polarized light with pillar height of 515 nm at varying applied bias. With this pillar height, the reflectance spectrum is close to the critical coupling point where reflectance is 0%, especially at a bias of 0 V. (b) The phase shift (specifically, the TE reflection component) for this metamaterial with the same dimensions as in (a). Critical coupling leads to a significant change in the phase shift profile near 0 V. (c) Phase modulation is very sensitive to the height of the nanopillars. Phase modulation exceeding 180° or π is possible for our metamaterial, depending on the nanopillar height. Plotted here is the maximum phase modulation in the 2 to 4 µm wavelength range; the optimal wavelength shifts slightly with different pillar heights as does the reflectance spectrum as seen in (d). Note that the phase shift provided in (b) is unwrapped, and, in (c), the phase modulation is defined as the difference between the phase shift at 4 V and the phase shift at -4 V within a range wrapped from -180° to 180°. (d) The reflectance curves shift and show more Fabry-Pérot resonances as the metamaterial thickness (i.e., the pillar height) increases. This explains the oscillations in (c).


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Low optical efficiency (Figure 4a and 5a) is a notable drawback of this design and other metamaterial devices that rely on critical coupling.7,14 By operating away from critical coupling, the reflectance is greater, but the phase modulation is lower. However, with a few design adjustments, the efficiency of the device could be raised while maintaining large phase modulation. One method is to reduce the thickness of the gate oxide layer in order to induce a larger change in the AZO’s carrier density and its refractive index with applied bias. Similarly, increasing the packing density of nanopillars within the array could also allow for larger modulation of the metamaterial’s effective index. Furthermore, near critical coupling, a large portion of the incident light is lost from transmission (Figure S7) due to the Si substrate’s transparency at the operating wavelength and from absorption due to the lossy AZO material. Thus, using a more reflective substrate (e.g., by incorporating a metal back reflector with a thinner Si substrate) as well as material engineering for lower absorption losses can also help to enhance optical efficiency. In conclusion, we have demonstrated a tunable metamaterial to modulate the optical reflectance and phase. Through field-effect operation, these devices would require low power and would be capable of operating at high frequencies approaching transistor speeds by decreasing total device area. Strong optical modulation of resonant frequencies made possible by the increased gate control and interaction lengths afforded by the three-dimensional nanopillar array. Wavelength shifts up to 240 nm in the mid-infrared region and a high differential reflectance of 40% were measured for a voltage range between -4 V to 4 V. Based on our fabricated devices, we used effective medium theory to model our subwavelength nanopillar array. This permits efficient calculation of the phase shift with TMM code. According to these simulations, phase modulation approaching 270° is possible, and, with further device optimization, the optical efficiency can be improved. Capable of such a large phase tuning range, these nanopillar metamaterials are a


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promising approach for beam steering and other applications, and, due to their CMOS-compatible fabrication process, they are well suited for mass production in standard semiconductor foundries.

Methods Device Fabrication Fabrication begins with epitaxial growth of 1-µm-thick, n-type Ge on lowly-doped (i.e., less than 1 ×1015 cm-3) n-type Si wafers with a reduced pressure chemical vapor deposition (RPCVD) chamber. The carrier concentration of the Ge layer is about 1.5×1019 cm-3. Next, we proceed with electron-beam lithography with the 100-keV JEOL JBX 6300 system. An array of dots is created in 130-nm-thick polymethylmethacrylate (PMMA) at various exposure doses to create a range of different diameters from 20 to 50 nm (with the optimal Ge nanopillar diameter of around 40 to 50 nm to maximize the filling ratio for the selected nanopillar periodicity). Development uses 3:1 isopropanol to methyl isobutyl ketone (MIBK) for 60 seconds. Then, 5 nm Ti for adhesion and 10 nm Al is deposited by electron beam evaporation, and liftoff is performed with heated Remover PG (MicroChem) using ultrasonication followed by acetone and isopropanol cleaning steps. An oxygen plasma descum is used to remove any residual PMMA resist and to oxidize the top layer of the Al. Etching of the Ge nanopillars is done in an inductively coupled plasma (ICP) system with a combination of Cl2, N2, and O2 (with flow rates of 80 sccm, 20 sccm, and 8 sccm respectively) at a pressure of 5 mTorr, RF power of 150 W, and ICP power of 200 W. The introduction of O2 in this etch chemistry oxidizes the Al mask to create a much more etch-resistant aluminum oxide.21 This allows for high aspect ratios exceeding 10:1 for height to diameter. The etch rate of Ge with these settings is approximately 15 nm/second. Afterwards, we deposit SiOx and SiNx with plasma-enhanced chemical vapor deposition (PECVD) and pattern it with


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photolithography and wet etching. These insulators isolate the metal contact to the AZO from the Ge layer beneath it in order to prevent shorting the capacitor when wire bonding. Subsequently, the samples are cleaned in cyclic rinses with hydrofluoric (HF) acid, hydrochloric (HCl) acid, and water and then immediately transferred to a thermal ALD chamber. Ozone oxidation is performed to create GeOx to passivate the Ge surface first, followed by a 1-nm layer of Al2O3 to protect the GeOx. The devices are transported to another thermal ALD chamber to deposit 8 nm of HfO2 (for its high dielectric constant) and 27 nm of AZO for the gate material. Thermal ALD should provide completely conformal coatings even for high-aspect-ratio features; it should not suffer from the shadowing effects that plasma-assisted ALD might have. Another lithography and etching step is done to define the area of the SOS capacitor. Finally, the metal contacts are created with photolithography, sputtering of Ti (15 nm) and Al (200 nm), and liftoff in acetone. After testing of all devices with C-V and I-V measurements with probes, the best devices are then wire bonded for optical tests. See Supporting Information Figure S1 for more SEM images, including attempts at taller nanopillars. Electrical Characterization Characterization of I-V and C-V is done with a Micromanipulator probe station to find the best devices with lowest leakage current and highest capacitance. Breakdown voltages for our devices are around 5 to 6 V (or -5 to -6 V). Also, high-frequency C-V measurements from 1 kHz to 100 kHz are performed to evaluate device capabilities. See Supporting Information Figures S2 for the high-frequency C-V results. Optical Measurements Reflectance is measured in the wavelength range of 1.5 µm to 16 µm with a Thermo Scientific Nicolet iS50 FTIR spectrometer and Nicolet Continuμm infrared microscope. Wire-bonded


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devices are biased by a DC power supply, and multiple optical measurements are taken at each voltage to confirm repeatability. Also, unbiased measurements were done to observe the effect of the nanopillar diameters on reflectance resonances. See Supporting Information Figures S3 and S4 for supplementary optical measurement results, showing the diameter dependence of the optical spectra as well as the differential reflectance at different bias voltages. TMM Code With effective medium theory to model our structure as a one-dimensional material stack, our TMM code is used to calculate reflectance, transmission, and phase at various incident angles and polarizations. Phase modulation is determined to be sensitive to the nanopillar height or metamaterial thickness. The Drude model is used to define the wavelength-dependent permittivity of the Ge and AZO layers. See Supporting Information Figure S5 for phase modulation simulated as a function of Ge film thickness, another important parameter when optimizing phase modulation. Also, see Figure S7 for simulations of the transmission and absorption components for an example device design. Other Simulations To further validate the results, other electrical and optical simulations are performed with Synopsys Sentaurus Device and Lumerical FDTD Solutions respectively. The carrier concentrations under positive and negative bias are found with Sentaurus for a capacitor based on the fabricated structure (Figure 2c). This information is then exported to Lumerical with the carrier distribution converted into optical parameters via the Drude model to define the accumulation or depletion layers of AZO and Ge in a 3D FDTD simulation of the nanopillar array. Multiple simulations are carried out for different applied biases, nanopillar heights, and other parameters to


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study the modulation of reflectance (and transmission) spectra. See Supporting Information Figure S6 for an example of these simulation results.

ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge on the ACS Publications website. It includes other fabrication details, more SEM images, electrical characterization results including high-frequency C-V, optical reflectance measurements of planar devices compared with nanopillar devices of different diameters, differential reflectance results for different applied voltages, completely simulated results with Synopsys Sentaurus and Lumerical FDTD Solutions, and additional TMM simulations for phase modulation as a function of Ge film thickness as well as simulations showing transmission and absorption components for one metamaterial design. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Present Address § Microsoft Corporation, 1 Microsoft Way, Redmond, WA 98052 Author Contributions M. M. performed all simulations, fabrication, and measurements. Other authors provided guidance on the project and comments on the manuscript. All authors have given approval to the final version of the manuscript.


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ACKNOWLEDGMENT This research was conducted with Government support under and awarded by the Department of Defense (DoD), Air Force Office of Scientific Research, National Defense Science and Engineering Graduate (NDSEG) Fellowship, 32 CFR 168a. This work was funded by the Global Climate and Energy Project at Stanford University. Device fabrication was performed at the Stanford Nanofabrication Facility (SNF) and the Stanford Nano Shared Facilities (SNSF), supported by the National Science Foundation under award ECCS-1542152. REFERENCES 1

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TOC Graphic 39x20mm (300 x 300 DPI)


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Figure 1. (a) Proposed SOS capacitor device structure with Ge nanopillars coated by a gate oxide and AZO. Electrically biasing this device affects the carrier density in the Ge nanopillar and the AZO gate layer. (b) SEM image taken at 45° tilt after complete device fabrication, showing the Ge nanopillars coated with gate oxide and AZO layers. (c) The periodic array of nanopillars is modeled as a metamaterial with effective optical properties in this work. Inset: xy-plane cross-section schematic of individual nanopillar illustrating the conformal coating of the gate oxide and AZO around the etched Ge cylinder; this coated nanopillar along with the air around it serves as the unit cell of the metamaterial used in our simulations. 98x70mm (300 x 300 DPI)


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Figure 2. (a) C-V measurements of devices (200-µm-diameter capacitors) with and without nanopillars (at 1 kHz). Use of nanopillars increases the effective surface area of the capacitor and significantly enhances the capacitance. The four cartoon schematics along the sides of this C-V plot represent the different states with the two on the left depicting the negative bias condition (with accumulated electrons in AZO and depleted Ge) and with those on the right showing the positive bias condition (with accumulated electrons in Ge and depleted AZO). The two cartoons on the top are for devices with nanopillars, showing the enhanced surface area compared to the two cartoons on the bottom for planar devices. (b) I-V measurements of a device (with 200 µm diameter) with nanopillars. Between -2 V and 2 V, the current is within tens to hundreds of picoamperes. (c) Simulated electron densities in Ge at the gate oxide interface for +4 V bias for accumulation mode and -4 V bias for depletion mode. The accumulation width is less than 4 nm, while the depletion width is approximately 10 nm. 102x75mm (300 x 300 DPI)


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Figure 3. Reflectance measurements from FTIR microscopy. (a) The reflectance spectra for a planar device compared to devices with nanopillars (the latter is biased at -4 V or 4 V). Two resonance features are boxed in green or blue and explored in (b) and (c) with more detail. (b) Magnified view of these resonance features and the effect of applied bias on them. (c) On the left, the shorter-wavelength resonance feature redshifts with voltage, while, on the right, the opposite behavior occurs for the longer-wavelength resonance. This distinction can be explained by the carrier accumulation or depletion in either AZO or Ge. The error bars represent the resonance wavelengths for multiple sweeps of the applied voltage for a single device. 205x238mm (300 x 300 DPI)


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Figure 4. (a) The reflectance of the effective-medium stack simulated by TMM fits well to the measured FTIR reflectance. This TMM calculation uses parameters that are close to the actual experiment and assumes unpolarized incident light. (b)-(c) Simulated phase shift and modulation with incident light at angle of 35° with nanopillar dimensions based on fabricated devices as in (a), which is not optimized for phase modulation. (b) Phase shift for reflection and transmission for both TM and TE polarization. Inset provides magnified view of the TE component of the reflection phase shift at varying applied bias. The significant change in phase shift for wavelengths between 2 and 3 µm corresponds to the resonance in the reflection spectrum that can be observed in Figure 3 and Figure 4a. This steep slope allows for strong modulation of the phase. (c) Phase modulation for the reflection phase with TE-polarized light at different applied bias. These phase modulation values are with respect to the phase shifts at a negative bias of -4 V [i.e., Δϕ_(r,TE) (V_2 )=ϕ_(r,TE) (V_2 )-ϕ_(r,TE) (V_1=-4 V)]. The phase can be modulated up to nearly 40° at a wavelength around 2.5 µm by changing the bias from -4 V to 4 V. 104x77mm (300 x 300 DPI)


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Figure 5. Simulated phase and reflectance results with incident light at angle of 35°. Nanopillar dimensions are based on fabricated devices (as in Figure 4), except the pillar height. (a) Reflectance of TE-polarized light with pillar height of 515 nm at varying applied bias. With this pillar height, the reflectance spectrum is close to the critical coupling point where reflectance is 0%, especially at a bias of 0 V. (b) The phase shift (specifically, the TE reflection component) for this metamaterial with the same dimensions as in (a). Critical coupling leads to a significant change in the phase shift profile near 0 V. (c) Phase modulation is very sensitive to the height of the nanopillars. Phase modulation exceeding 180° or π is possible for our metamaterial, depending on the nanopillar height. Plotted here is the maximum phase modulation in the 2 to 4 µm wavelength range; the optimal wavelength shifts slightly with different pillar heights as does the reflectance spectrum as seen in (d). Note that the phase shift provided in (b) is unwrapped, and, in (c), the phase modulation is defined as the difference between the phase shift at 4 V and the phase shift at -4 V within a range wrapped from -180° to 180°. (d) The reflectance curves shift and show more Fabry-Pérot resonances as the metamaterial thickness (i.e., the pillar height) increases. This explains the oscillations in (c). 103x77mm (300 x 300 DPI)


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