Planar Hot-Electron Photodetection with Tamm Plasmons

Transcription

1 Supporting information for Planar Hot-Electron Photodetection with Tamm Plasmons Cheng Zhang, a,b Kai Wu, a,b Vincenzo Giannini, c and Xiaofeng Li a,b,* a College of Physics, Optoelectronics and Energy & Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou , China; b Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province & Key Lab of Modern Optical Technologies of Education Ministry of China, Soochow University, Suzhou , China; c Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BZ, United Kingdom. * Corresponding author: xfli@suda.edu.cn CONTENTS: S1. Optoelectronic model S2. More about Tamm plasmons S3. Analysis of SP-HE PD photoemission process S4. Angular performance of TP-HE PD S5. Multiband hot-electron photodetection 1

2 S1. Optoelectronic model a. Optical model Based on the optical constants from Palik, S1 we calculate the electric field distribution in the planar and grating nanostructures via the finite-element method (FEM) using periodic boundary conditions. The optical absorption efficiency (A) by each layer is analyzed by: S2 ω =,,, (1) where ω is the angular frequency, P in the incident power, and Q rh the volume density of the power absorption. Q rh can be calculated under Poynting theory:,,, =,,, (2) where ε i is the imaginary part of the material permittivity and E(x, y, z) the electric field at position (x, y, z). Assuming one absorbed photon generates one hot electron-hole pair and taking into account the resistive loss (P resistive ~30%) of the absorbed energy, which is dissipated without hot electrons generation due to the intrinsic lifetime of the electronic states comprising the collective oscillation, S3 the spatially dependent hot-electron generation rate (G) can be obtained: where ħ is the reduced Planck constant. b. Electrical model,,, = 1,,, ħ (3) The initial hot electron energy distribution D(E) is described (under normalization) by the multiplication of the joint density of states, which is the product of the densities of states at the initial and final energies, and their respective distribution functions: S4 S7 = [ ] [ ] where E is the energy of the excited electron, hν is the photon energy, is the parabolic electron density of states from the free electron model, and is the Fermi distribution function. The approximation does not take into account the momentum conservation rule in the electronic transitions. Based on the assumption of an isotropic initial momentum distribution and using the exponential attenuation model, the probability that a hot electron reaches the M/S interface without being dissipated by scattering is evaluated by: S8 S10,, =, exp (5) where for the system shown in Figure 1c the y direction is infinite and only the x-z plane needs to be considered, d is the distance from the generation position (x, z) of the hot electron to the M/S interface, θ is the moving angle of hot electrons, θ 1 and θ 2 are the accepting angles, i.e., only the hot electrons confined within the angles are possible to reach the M/S interface, S11 and λ e is the energy-dependent MFP of hot electrons accounting for electron electron and electron-phonon contributions in Au. S3 (4) 2

3 With the spatial distributions of the hot-electron generation, the initial distribution of hot electrons, and the probability that a hot electron reaches the M/S interface using energy-dependent MFP, the spatial distribution of the hot-electron flux reaching the interface can be calculated by:,, =,,, (6) Then the final energy distributions F(E) of hot electrons reaching the top and bottom M/S interfaces can be calculated by volume integration and normalization: =,,,, (7) With the final energy distributions F(E) of hot electrons reaching the top and bottom M/S interfaces, the probabilities of the hot electrons to be injected into the semiconductor (P 2 ), propagate through the ultra-thin intermediate layer without being scattered (P 3 ), and transmit through the opposite S/M interface (P 4 ), the internal-quantum efficiency (IQE defined as η i ) for photo-ejection from the M/S interface to the other electrode at photon energy E ph can be calculated as: S8 = (8) The detailed description of the transport process and the corresponding analytical treatment can be found in the supporting information of Ref. S8, which has been demonstrated to be consistent with experiment. The net photocurrent density from the top to bottom contacts (J Net ) can be expressed as: S12 =,,,,,, (9) where N top bot (N bot top ) is the hot-electron flux reaching the top (bottom) M/S interface and η i, top bot (η i, bot top) is the IQE of the electron transporting from the top (bottom) contact to the opposite. It should be noted that in the main manuscript, Eq. 5 shows another version for the calculation of J Net. In fact, Eq.5 in the manuscript and Eq. 9 in the supporting information are fundamentally same. Here, we introduce Eq. 9 in order to present the expression of the IQE which has been plotted in Figure 4 in the manuscript. S2. More about Tamm plasmons For further insights into the electromagnetic nature of Tamm plasmon resonance in the proposed hot-electron photodetector, the reflection spectra of the MSM+DBR structure with DBR pair numbers N DBR = 5, 8, and 11 are compared in Figure S1a. It is clear that when N DBR = 8, the strongest narrow TP is excited and the reflection dip is as low as zero at λ = 813 nm. However, with more DBR pairs, the highly-reflective DBR prevents the light incidence from penetrating into the metal; while with less DBR pairs, the low-reflective DBR cannot well confine the light. Since the semiconductor layer is very thin, the reflection coefficient of the MSM layer is close to 1 at frequencies well below Au plasma frequency. The ideal TP can be excited when the reflection coefficients of the DBR (r DBR ) and the bottom MSM layer (r MSM ) for the light incident from the TiO 2 medium meet the following condition: S13 =1 (10) The condition is satisfied near the Bragg frequency if the Bragg reflector has a large number of layers and the refractive index of the first layer (i.e., close to the metal) is greater than that of the second layer. The left panel of Figure S1b plots the profile of the electric field intensity E 2 along z direction under different wavelengths (λ), where the dashed horizontal lines position the top Au layer. It is found that the 3

4 strongest electric field occurs at λ = 813 nm in a localized region very close to the MSM/DBR interface, suggesting the excitation of TP. For a clearer illustration on the electric field distribution along the junction, the E 2 profile along z is plotted in the right panel of Figure S1b. It is shown that the significantly strengthened electric field is confined mostly in the bottom DBR layer (close to the top Au), which causes more energy to be absorbed by the top Au layer. In fact, an ideal TP can confine the energy which shows the peaked electric field on the DBR/metal interface (SPs-like property). However, this requires a perfect metal and a DBR with an infinite number of DBR pair (N DBR = ). S13 S15 In realistic situation, the location of the peaked electric field will shift slightly away from the DBR/metal interface. Figure S1. (a) Comparison of the device reflection R(λ) with different DBR pair numbers, N DBR = 5, 8, and 11. (b) Left panel: the normalized electric field E 2 along z axis and the wavelength λ for N DBR = 8; right panel: E 2 along z at λ = 813 nm. S3. SP-HE PD photoemission process Figure S2. The SP-based hot-electron photodetector (SP-HE PD) is considered in this figure. (a) the detailed optical responses; the spatial distributions of (b) the hot-electron generation rate, (c) the transport probability, and (d) the flux of hot electrons reaching the M/S interface before thermalization for excess energy of 0.9 ev with MFP = 21 nm. The device configuration of the SP-HE PD is inserted in (a). The 4

5 device parameters used here are the same as those indicated in the caption of Figure 1. The period and width of the grating are 800 and 280 nm, respectively. S4. Angular performance of TP-HE PD Furthermore, we briefly examine the performance of the TP-HE PD under an oblique incidence. In this case, both transverse electric (TE) and transverse magnetic (TM) incidences have to be considered. The contour maps of the reflection as a function of the incident wavelength (λ) and angle (θ) for TM and TE incidences are shown in Figure S3a and S3b, respectively. As can be seen that the oblique incidence blue-shifts the TP resonance under both incidences, coinciding with the predication of Ref. S8. Moreover, although with the resonance shifted, the ultra-low reflection dip can be sustained in a very wide range of incident angles. Taking θ = 0, 30, and 60 as examples, the corresponding reflection and responsivity spectra under TM and TE incidences are plotted in Figures S3c S3f. It is noted that although the reflection at θ = 60 is relatively high with a slightly degraded absorption, the responsivity shows a similar (or even higher) value due to the excitation of the high-energy hot electrons. In addition, the full width at half maximum (FWHM) of the responsivity spectrum under normal incidence is ~8 nm (normally ~15 mev), which is sharp enough for high-sensitivity narrow-band photodetection/sensing applications. S16,S17 These results show that the high photoresponsivity by TP-HE PD can be sustained simultaneously over a wide range of incident angles. Figure S3. The dependence of the device reflection spectrum R(λ) as a function of the incident angle θ for (a) TM and (b) TE incidences. (c, d) and (e, f) are R(λ) and responsivity spectra at θ = 0º, 30º, and 60º under TM and TE incidences, respectively. The rest parameters are the same as those indicated in the caption of Figure 1. S5. Multiband hot-electron photodetection Finally, the proposed TP-HE PD system can be extended for rich functionalities. For example, it is possible to realize the TP-based multiband photodetection. Figure S4a shows the contour map of the reflection as a function of λ and d TiO2. Interestingly, there exist multiple resonant bands in the optical 5

6 forbidden band of DBR if using a large d TiO2. Taking d TiO2 = 1330 nm as an example, the reflection and net absorption spectra A Net (i.e., top Au absorption minus bottom Au absorption) of the TP-HE PD are displayed in Figure S4b, where the dashed curve plots the reflection spectrum of the bare DBR. It is clear that there are three pronounced reflection dips at 693, 763, and 847 nm, respectively, corresponding to three successfully excited TPs; moreover, each TP is accompanied with a high net optical absorption over 60% (i.e., highly asymmetrical optical absorption is realized for the multiband photodetection system). The corresponding photoresponsivity spectrum is illustrated in Figure S4c, which shows three distinct responsivity peaks in the DBR forbidden band. Furthermore, the responsivity at λ = 693 nm is even greater than that of the resonance at λ = 813 nm (see Figure 4d] due to the higher energy excitation. S18 Figure S4. (a) The dependence of the device reflection spectrum R(λ) as a function of d TiO2. (b) R(λ) and net absorption A Net (λ) at d TiO2 = 1330 nm, where R(λ) for bare DBR is given and (c) the corresponding responsivity spectrum. (d) the normalized electric field E 2 along z axis and the wavelength λ in the device by integrating dual DBRs, as the inset shows. The DBR1 (DBR2) consists of 6 (5) pairs of Al 2 O 3 /TiO 2 with the central wavelength of 650 (500) nm. Another strategy to realize the multiband photodetection is to integrate dual DBRs (both with Al 2 O 3 /TiO 2 pairs) on the top Au layer as shown by the inset of Figure S4d. After examining the optical characteristics of the central wavelength and the number of pairs for each DBR, we choose the DBR1 (DBR2) of 6 (5) pairs with the central wavelength of 650 (500) nm. Figure S4d shows the normalized electric field intensity E 2 versus z and λ, where the dashed horizontal lines position the top Au, DBR1, and DBR2, respectively. It is found that TP near the Au/DBR1 interface and the 7 th -order Fabry-Perot (FP) cavity mode in the DBR1 region are excited simultaneously. The reflection and net absorption spectra of the device are plotted in Figure S4e, where the reflection of the two bare DBRs are plotted as well. It is clear that a distinct reflection dip appears in the forbidden band of DBR1, indicating that TP is excited at the wavelength, λ = 715 nm. Besides, another pronounced reflection dip occurs at λ = 546 nm in the 6

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