Spectrally Selective Photocapacitance Modulation in Plasmonic ...
Supporting Information
Spectrally Selective Photocapacitance Modulation in Plasmonic Nanochannels for Infrared Imaging Ya-Lun Ho, Li-Chung Huang, and Jean-Jacques Delaunay*
Department of Mechanical Engineering, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
* Address correspondence to [email protected]
Figure S1. Fabrication of the plasmonic nanochannel structure. (a) Schematic diagram showing the fabrication processes of the nanochannel structure. A resist line-and-space pattern is first fabricated by electron beam lithography. The resist pattern protects the Si device layer and serves as a mask for the reactive-ion etching process. Si nanochannels are then fabricated by reactive-ion etching and an Au layer is sputtered without removing the resist. A lift-off process is applied to remove the Si nanochannel tops made of the resist covered with their Au caps, so that the nanochannels become open. (b) Electron microscopy top-view image with low magnification shows the homogeneity of the fabricated structure. (c) High-magnification top-view of the same structure. (d) Cross-section electron microscopy images before and after the lift-off process reveal that the resist masks with Au caps of the nanochannel tops were completely removed. The fabricated nanochannel structure also shown in Fig. 1d has a period p = 1100 nm, a Si channel height h = 735 nm, a Si channel width w = 230 nm, and an Au layer thickness t = 50 nm.
Figure S2. Simulated absorptance variation with the light wavelength and the channel width. Resonances of the coupled modes show the narrow bandwidths of the absorptance at Points A and C (defined in Fig. 2a and 2b). An absorptance band with a linear relation between the resonance wavelength and the width represents the vertical channel mode, which is controlled by the dimensions of the channels. Two vertical bands at the wavelengths of ~1100 and ~1600 nm represent the conditions for horizontal SPRs. When the channel width increases (larger than 500 nm), the horizontal SPR cannot be coupled with the channel mode due to its resonance wavelength increasing with the channel width. On the other hand, to find the resonance of the coupled mode at a shorter wavelength, a narrower channel width is required to be coupled with a high-order horizontal SPR mode (Point C).
Figure S3. Electric field magnitude and phase distributions in the nanochannel structure. (a) Electric field magnitude distributions in the x- and z-direction at Point A defined in Fig. 2a. The electric field density relative to free space is shown on a normal scale. (b) Electric field phase distributions in the x- and z-direction together with the electric field directions in the nanochannels and the bottom substrate. The electric field phase distributions in both the x- and z-direction highly correspond to the electric field magnitude distributions, so that the directions of the electric field can be clearly indicated as in b.
Figure S4. Open and closed condition of nanochannel structure. (a) (Left) Electric field density distribution at λ = 1599 nm (Point A defined in Fig. 2a). (Right) Simulated time-averaged Poynting vector fields at λ = 1599 nm. (b) (Left) Electric field density distribution at λ = 1924 nm. (Right) Simulated time-averaged Poynting vector fields at λ = 1924 nm. The resonance at 1924 nm shows strong enhancement of the electric field in the channels with clear nodes and antinodes. The antinodes appear at the channel entrances and exits, thus indicating the standing SPR in the channels. As a result of the enhanced electric field in the channels, the incident light is concentrated into the channels with antinodes at the entrances, sustaining strong power flow in the channels, and leaking out through antinodes at the channel exits (open channel). The light behavior of the resonance at 1924 nm corresponds to the broad bandwidth and high transmittance. For the resonance at 1599 nm (Point A), the electric field enhancement in the channels and on the bottoms (i.e., the interface between the metallic U-cavities and the bottom substrate) provides evidence for the coupling between the channel mode and the horizontal SPR mode. The electric field enhancement on the bottoms interfaces corresponds to the condition of the horizontal SPR on the substrate surface, so that it is further restricted by the stringent resonance conditions. Different to the resonance at 1924 nm, the coupling mode of the resonance at 1599 nm changes the antinode to a node at the exit, thus hampering light transmission through the channel bottom (as a closed channel). Light is therefore trapped in the channels. Due to light trapping in the channels with horizontal SPR, the transmittance is very low and absorptance is high with a narrow bandwidth.
Figure S5. Split of the resonance dip with the incident angle. Variation of reflection spectra with the incident angle θ = 0°-3° in the wavelength λ range 1525-1675 nm. The zero-order reflectance spectra were measured with an FT-IR spectrometer (VIR-300, JASCO, Tokyo, Japan) for ppolarized incident light in air. The resonance dip bandwidths are within FWHM = 11-22 nm. When the incident angle is increased from 0° to 1.5°, a reflectance modulation larger than 0.4 is obtained, corresponding to an increase in the reflectance of the original resonance dip (λ = 1599 nm for θ = 0°) to a value larger than 0.5.
Figure S6. Electrical impedance response to light for the heavily doped n-Si. Light-to-dark contrast ratio of the impedance as a function of the operating frequency. The variation of the complex impedance resulting from the light irradiation of the heavily doped n-Si channels on SiO2 substrate is not as large as that of the lightly doped n-Si channels on Si substrate. The resistance of the n-Si/SiO2 sample exhibits a light-to-dark ratio close to 100 and the reactance light-to-dark ratio varies between 10-1 and 101.
Figure S7. Capacitance variation rate to the external bias frequency with different incident light intensity. The light-to-dark capacitance variation rates (relative to 8 mW/cm2 light irradiation) of 4 mW/cm2, 400 μW/cm2, and 20 μW/cm2 of lightly doped n-Si channels on the bottom substrate with the same material. According to the capacitance variation with external bias frequency in the inset of Fig. 5d, the variation remains stably in 103 at the operating frequency from 103 to 105 Hz. Therefore, the variation at high operating frequency (106 Hz) is obtained as 102 with light intensity of 400 μW/cm2. Based on this figure, the variation of capacitance is still obtained with low light intensity of 20 μW/cm2 at 104 Hz.
Figure S8. Photocapacitance modulation of the plasmonic nanochannel structure. Experimental reflectance spectrum and reactance variations versus incident light wavelength obtained for different operating frequencies. The nanochannel-based photocapacitor shows spectral selectivity of the impedance variation with light wavelength for a wide range of operating frequencies, as seen in Fig S8. Due to the RC time constant of the nanochannel structure, the modulation of the impedance variation decreases by two orders when the operating frequency is increased from 10 kHz to 100 kHz, keeping the incident light power constant. Although small modulations are obtained at operating frequencies higher than 100 kHz, the impedance variations show the same spectral selectivity in good agreement with that at lower frequencies and with the reflectance spectrum.
Figure S9. Simulated reflectance spectra and reactance variations versus incident light wavelength for the ranges of 1000 to 1070 nm, 640 to 750 nm, and 1200 to 1400 nm.
Details on the dimensions of the nanochannel structure in Fig. 5e The dimensions of the nanochannel structures exhibiting the narrow-band resonances at 698 (1028) nm (see Fig. 5e) were: the period of the structure p = 1000 (1000) nm, the height of the channels h = 750 (855) nm, the thickness of the Au layers t = 40 (55) nm, and the width of the Si channels w = 320 (370) nm. The structure having a resonance at 1028 nm is the same as that showing the two resonances at 1267 and 1364 nm.
Analysis of photodetection responsivity and specific detectivity In the following, we report the performance of the proposed structure evaluated at room temperature using the technique reported in [29] (J. Appl. Phys. 2014, 116, 023108). An RLC resonant circuit consisting of the nanochannel structure (capacitor in parallel with a leakage resistance of 400 k), an inductor of 4 H and a resistor of R = 5.1k was driven by a 9 kHz sinusoidal signal of amplitude V0 = 8 V (WF1973, NF corporation, Yokohama, Japan). The standby power dissipation without incident light (dark condition) is 9.8 μW, as determined by the dark voltage of 100 mV across the resistor R. The dark voltage was read directly on an oscilloscope (MSO/DPO2000B, Tektronix, Beaverton, USA). When the nanochannel structure was illuminated at the resonance and non-resonance wavelengths λ = 1028 and 1060 nm (Fig. 5e) with a power of 1.74 μW, the current values in the circuit changed by ΔI = 1.18 and 0.39 μA, respectively. The responsivities are thus 677 and 226 mA/W. The current noise was estimated from thermal noise to be Inoise = 1.82 pA/√Hz (thermal Johnson-Nyquist noise across R, Inoise = 4 / , where k is Boltzmann's constant and T is the temperature in kelvin) and the minimum light-induced change in photocapacitance ΔCmin was 4.13 × 10-18 F/√Hz. Therefore, the noise equivalent powers (NEP) are 2.69 and 8.06 pW/√Hz at λ = 1028 and 1060 nm, respectively. With an effective area of the nanochannel structure sample A = 0.075 cm2, the specific detectivities D* at room temperature are 1.02 × 1011 and 3.41 × 1010 Jones at λ = 1028 and 1060 nm, respectively. Furthermore, to clarify the photodetection of the nanochannel structure in the sub-bandgap region, a long pass filter with a cut-on wavelength of 1200 nm was used. The responsivity and specific detectivity obtained with the filter are 1.69 mA/W and 2.88 × 108 Jones, respectively.
Spectrally Selective Photocapacitance Modulation in Plasmonic Nanochannels for Infrared Imaging Ya-Lun Ho, Li-Chung Huang, and Jean-Jacques Delaunay*
Department of Mechanical Engineering, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
* Address correspondence to [email protected]
Figure S1. Fabrication of the plasmonic nanochannel structure. (a) Schematic diagram showing the fabrication processes of the nanochannel structure. A resist line-and-space pattern is first fabricated by electron beam lithography. The resist pattern protects the Si device layer and serves as a mask for the reactive-ion etching process. Si nanochannels are then fabricated by reactive-ion etching and an Au layer is sputtered without removing the resist. A lift-off process is applied to remove the Si nanochannel tops made of the resist covered with their Au caps, so that the nanochannels become open. (b) Electron microscopy top-view image with low magnification shows the homogeneity of the fabricated structure. (c) High-magnification top-view of the same structure. (d) Cross-section electron microscopy images before and after the lift-off process reveal that the resist masks with Au caps of the nanochannel tops were completely removed. The fabricated nanochannel structure also shown in Fig. 1d has a period p = 1100 nm, a Si channel height h = 735 nm, a Si channel width w = 230 nm, and an Au layer thickness t = 50 nm.
Figure S2. Simulated absorptance variation with the light wavelength and the channel width. Resonances of the coupled modes show the narrow bandwidths of the absorptance at Points A and C (defined in Fig. 2a and 2b). An absorptance band with a linear relation between the resonance wavelength and the width represents the vertical channel mode, which is controlled by the dimensions of the channels. Two vertical bands at the wavelengths of ~1100 and ~1600 nm represent the conditions for horizontal SPRs. When the channel width increases (larger than 500 nm), the horizontal SPR cannot be coupled with the channel mode due to its resonance wavelength increasing with the channel width. On the other hand, to find the resonance of the coupled mode at a shorter wavelength, a narrower channel width is required to be coupled with a high-order horizontal SPR mode (Point C).
Figure S3. Electric field magnitude and phase distributions in the nanochannel structure. (a) Electric field magnitude distributions in the x- and z-direction at Point A defined in Fig. 2a. The electric field density relative to free space is shown on a normal scale. (b) Electric field phase distributions in the x- and z-direction together with the electric field directions in the nanochannels and the bottom substrate. The electric field phase distributions in both the x- and z-direction highly correspond to the electric field magnitude distributions, so that the directions of the electric field can be clearly indicated as in b.
Figure S4. Open and closed condition of nanochannel structure. (a) (Left) Electric field density distribution at λ = 1599 nm (Point A defined in Fig. 2a). (Right) Simulated time-averaged Poynting vector fields at λ = 1599 nm. (b) (Left) Electric field density distribution at λ = 1924 nm. (Right) Simulated time-averaged Poynting vector fields at λ = 1924 nm. The resonance at 1924 nm shows strong enhancement of the electric field in the channels with clear nodes and antinodes. The antinodes appear at the channel entrances and exits, thus indicating the standing SPR in the channels. As a result of the enhanced electric field in the channels, the incident light is concentrated into the channels with antinodes at the entrances, sustaining strong power flow in the channels, and leaking out through antinodes at the channel exits (open channel). The light behavior of the resonance at 1924 nm corresponds to the broad bandwidth and high transmittance. For the resonance at 1599 nm (Point A), the electric field enhancement in the channels and on the bottoms (i.e., the interface between the metallic U-cavities and the bottom substrate) provides evidence for the coupling between the channel mode and the horizontal SPR mode. The electric field enhancement on the bottoms interfaces corresponds to the condition of the horizontal SPR on the substrate surface, so that it is further restricted by the stringent resonance conditions. Different to the resonance at 1924 nm, the coupling mode of the resonance at 1599 nm changes the antinode to a node at the exit, thus hampering light transmission through the channel bottom (as a closed channel). Light is therefore trapped in the channels. Due to light trapping in the channels with horizontal SPR, the transmittance is very low and absorptance is high with a narrow bandwidth.
Figure S5. Split of the resonance dip with the incident angle. Variation of reflection spectra with the incident angle θ = 0°-3° in the wavelength λ range 1525-1675 nm. The zero-order reflectance spectra were measured with an FT-IR spectrometer (VIR-300, JASCO, Tokyo, Japan) for ppolarized incident light in air. The resonance dip bandwidths are within FWHM = 11-22 nm. When the incident angle is increased from 0° to 1.5°, a reflectance modulation larger than 0.4 is obtained, corresponding to an increase in the reflectance of the original resonance dip (λ = 1599 nm for θ = 0°) to a value larger than 0.5.
Figure S6. Electrical impedance response to light for the heavily doped n-Si. Light-to-dark contrast ratio of the impedance as a function of the operating frequency. The variation of the complex impedance resulting from the light irradiation of the heavily doped n-Si channels on SiO2 substrate is not as large as that of the lightly doped n-Si channels on Si substrate. The resistance of the n-Si/SiO2 sample exhibits a light-to-dark ratio close to 100 and the reactance light-to-dark ratio varies between 10-1 and 101.
Figure S7. Capacitance variation rate to the external bias frequency with different incident light intensity. The light-to-dark capacitance variation rates (relative to 8 mW/cm2 light irradiation) of 4 mW/cm2, 400 μW/cm2, and 20 μW/cm2 of lightly doped n-Si channels on the bottom substrate with the same material. According to the capacitance variation with external bias frequency in the inset of Fig. 5d, the variation remains stably in 103 at the operating frequency from 103 to 105 Hz. Therefore, the variation at high operating frequency (106 Hz) is obtained as 102 with light intensity of 400 μW/cm2. Based on this figure, the variation of capacitance is still obtained with low light intensity of 20 μW/cm2 at 104 Hz.
Figure S8. Photocapacitance modulation of the plasmonic nanochannel structure. Experimental reflectance spectrum and reactance variations versus incident light wavelength obtained for different operating frequencies. The nanochannel-based photocapacitor shows spectral selectivity of the impedance variation with light wavelength for a wide range of operating frequencies, as seen in Fig S8. Due to the RC time constant of the nanochannel structure, the modulation of the impedance variation decreases by two orders when the operating frequency is increased from 10 kHz to 100 kHz, keeping the incident light power constant. Although small modulations are obtained at operating frequencies higher than 100 kHz, the impedance variations show the same spectral selectivity in good agreement with that at lower frequencies and with the reflectance spectrum.
Figure S9. Simulated reflectance spectra and reactance variations versus incident light wavelength for the ranges of 1000 to 1070 nm, 640 to 750 nm, and 1200 to 1400 nm.
Details on the dimensions of the nanochannel structure in Fig. 5e The dimensions of the nanochannel structures exhibiting the narrow-band resonances at 698 (1028) nm (see Fig. 5e) were: the period of the structure p = 1000 (1000) nm, the height of the channels h = 750 (855) nm, the thickness of the Au layers t = 40 (55) nm, and the width of the Si channels w = 320 (370) nm. The structure having a resonance at 1028 nm is the same as that showing the two resonances at 1267 and 1364 nm.
Analysis of photodetection responsivity and specific detectivity In the following, we report the performance of the proposed structure evaluated at room temperature using the technique reported in [29] (J. Appl. Phys. 2014, 116, 023108). An RLC resonant circuit consisting of the nanochannel structure (capacitor in parallel with a leakage resistance of 400 k), an inductor of 4 H and a resistor of R = 5.1k was driven by a 9 kHz sinusoidal signal of amplitude V0 = 8 V (WF1973, NF corporation, Yokohama, Japan). The standby power dissipation without incident light (dark condition) is 9.8 μW, as determined by the dark voltage of 100 mV across the resistor R. The dark voltage was read directly on an oscilloscope (MSO/DPO2000B, Tektronix, Beaverton, USA). When the nanochannel structure was illuminated at the resonance and non-resonance wavelengths λ = 1028 and 1060 nm (Fig. 5e) with a power of 1.74 μW, the current values in the circuit changed by ΔI = 1.18 and 0.39 μA, respectively. The responsivities are thus 677 and 226 mA/W. The current noise was estimated from thermal noise to be Inoise = 1.82 pA/√Hz (thermal Johnson-Nyquist noise across R, Inoise = 4 / , where k is Boltzmann's constant and T is the temperature in kelvin) and the minimum light-induced change in photocapacitance ΔCmin was 4.13 × 10-18 F/√Hz. Therefore, the noise equivalent powers (NEP) are 2.69 and 8.06 pW/√Hz at λ = 1028 and 1060 nm, respectively. With an effective area of the nanochannel structure sample A = 0.075 cm2, the specific detectivities D* at room temperature are 1.02 × 1011 and 3.41 × 1010 Jones at λ = 1028 and 1060 nm, respectively. Furthermore, to clarify the photodetection of the nanochannel structure in the sub-bandgap region, a long pass filter with a cut-on wavelength of 1200 nm was used. The responsivity and specific detectivity obtained with the filter are 1.69 mA/W and 2.88 × 108 Jones, respectively.
