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Research on the Enhancement of Absorption Properties of Silicon via Localized Surface Plasmons Resonance in Blue Light

WANG Hao-bing TAO Jin LV Jin-guang MENG De-jia LI Yang ZHAO Yong-zhou WANG Jia-xian ZHANG Jun QIN Yu-xin WANG Wei-biao LIANG Jing-qiu

王浩冰, 陶金, 吕金光, 孟德佳, 李阳, 赵永周, 王家先, 张军, 秦余欣, 王惟彪, 梁静秋. 局域表面等离激元共振增强硅蓝光波段吸收特性研究[J]. 中国光学. doi: 10.37188/CO.2020-0056
引用本文: 王浩冰, 陶金, 吕金光, 孟德佳, 李阳, 赵永周, 王家先, 张军, 秦余欣, 王惟彪, 梁静秋. 局域表面等离激元共振增强硅蓝光波段吸收特性研究[J]. 中国光学. doi: 10.37188/CO.2020-0056
WANG Hao-bing, TAO Jin, LV Jin-guang, MENG De-jia, LI Yang, ZHAO Yong-zhou, WANG Jia-xian, ZHANG Jun, QIN Yu-xin, WANG Wei-biao, LIANG Jing-qiu. Research on the Enhancement of Absorption Properties of Silicon via Localized Surface Plasmons Resonance in Blue Light[J]. Chinese Optics. doi: 10.37188/CO.2020-0056
Citation: WANG Hao-bing, TAO Jin, LV Jin-guang, MENG De-jia, LI Yang, ZHAO Yong-zhou, WANG Jia-xian, ZHANG Jun, QIN Yu-xin, WANG Wei-biao, LIANG Jing-qiu. Research on the Enhancement of Absorption Properties of Silicon via Localized Surface Plasmons Resonance in Blue Light[J]. Chinese Optics. doi: 10.37188/CO.2020-0056

局域表面等离激元共振增强硅蓝光波段吸收特性研究

doi: 10.37188/CO.2020-0056
详细信息
  • 中图分类号: O431.1; O436.2; O471.5

Research on the Enhancement of Absorption Properties of Silicon via Localized Surface Plasmons Resonance in Blue Light

Funds: Supported by the National Key Research and Development Program of China (Grant No.2018YFB1801900), Science and Technology Plan of Guangdong Province, China (Grant No.2016B010111003) and Development of Science and Technology Plan of Jilin Province, China (Grant No.20180801024GX and No.20190302062GX), the Youth Innovation Promotion Association Foundation (NO. 2018254), the State Key Laboratory of Applied Optics 2019 Open Foundation (SKLAO: 201908)
More Information
    Author Bio:

    Wang Haobing (1994—), male, born in Songyuan City, Jilin province, Master Degree Candidate. In 2017, he graduated from Changchun University of Science and Technology with a Bachelor of Science degree. He is now a graduate student of Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences. He is mainly engaged in the research of nanophotonics and semiconductor photodetectors. E-mail: 996490955@qq.com

    Wang Weibiao (1962—), male, born in Yangzhou City, Jiangsu province. He is a doctor, researcher and doctoral supervisor. He received his doctor’s degree from Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences in 1999. Now he is a researcher of this institute. He is mainly engaged in the research of photonic crystal and micro-nano photonics, LED array chip integration and application, field emission materials and electron emission characteristics. E-mail: wangwb@ciomp.ac.cn

    Liang Jingqiu (1962—), female, born in Changchun City, Jilin Province. She is a doctor, researcher and doctoral supervisor. In 2003, she received her doctor's degree from Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences. Now she is a researcher of this institute. She is mainly engaged in the research of micro/nano optical structures, devices and systems, infrared spectrum/imaging spectrum and infrared optical instruments, micro LED microdisplay chip and its application, and visible light communication devices and systems. E-mail: liangjq@ciomp.ac.cn

    Corresponding author: wangwb@ciomp.ac.cnliangjq@ciomp.ac.cn
  • 摘要: 为增强硅的蓝光吸收,在硅表面设计银纳米颗粒阵列,基于局域表面等离激元共振效应对增强的硅蓝光吸收特性进行了分析研究。采用有限时域差分法计算银纳米颗粒阵列/硅复合结构中硅的蓝光吸收特性。结果表明:金属颗粒的消光能力与其几何参数相关,改变银纳米颗粒阵列的半径r、高度H与周期P可调控局域表面等离激元共振强度与共振频率,当银纳米颗粒阵列参数:半径为r = 18.5 nm、高度为H = 45 nm、周期为P = 49 nm时,共振吸收波长为465 nm,硅的蓝光吸收率由59%增加至94%,光吸收增益为0.57,光生载流子数目增益为0.53,分析认为局域表面等离激元共振增强硅在蓝光波段的光吸收。本文的研究结果对了解局域表面等离激元效应改善硅的蓝光吸收特性的机理、设计和制备高蓝光响应度硅基可见光光电探测器,具有重要的参考价值。
  • 图  1  金属球状结构的局域表面等离激元示意图

    Figure  1.  Schematic of localized surface plasmons with a metallic spherical structure

    图  2  Ag-NPs/Si模型结构

    Figure  2.  Ag-NPs/Si model structure

    图  3  Ag-NPs几何参数对硅的光学行为影响:(a)半径r变化对硅在蓝光波段的吸收影响;(b)光吸收率与共振波长随半径r的变化;(c)半径r变化对硅在蓝光波段的吸收增益影响

    Figure  3.  Influence of geometric parameters of Ag-NPs on the optical properties of silicon: (a) absorptance versus radius r in blue band; (b) absorptance and resonant wavelength versus radius r; (c) absorptive gain versus radius r in blue band

    图  4  Ag-NPs几何参数对硅的光学性质影响:(a)高度H对硅在蓝光波段的吸收影响;(b)光吸收率与共振波长随高度H的变化;(c)高度H对硅在蓝光波段的吸收增益影响

    Figure  4.  Influence of geometric parameters of Ag-NPs on the optical properties of silicon: (a) absorptance versus height H in blue band; (b) absorptance and resonant wavelength versus height H; (c) absorptive gain versus height H in blue band

    图  5  Ag-NPs几何参数对硅的光学性质影响:(a)周期P对硅在蓝光波段的吸收影响;(b)光吸收率与共振波长随周期P的变化;(c)周期P对硅在蓝光波段的吸收增益影响

    Figure  5.  Influence of geometric parameters of Ag-NPs on the optical properties of silicon: (a) absorptance versus period P in blue band; (b) absorptance and resonant wavelength versus period P; (c) absorptive gain versus period P in blue band

    图  6  可见光波段硅的光吸收:(a)硅与基于Ag-NPs阵列硅的吸收率曲线;(b)硅的光吸收增益

    Figure  6.  Si-absorptance in visible bands from 380 nm to 760 nm: (a) absorptance of silicon versus absorptance of silicon in Ag-NP array; (b) absorptive gain of silicon

    图  7  蓝光波段结构表面反射率R与Ag-NPs光吸收损耗Ametal曲线

    Figure  7.  Reflectivity R of structure surface in blue band versus absorption loss Ametal of Ag-NPs

    图  8  蓝光波段Ag-NPs光吸收损耗Ametal曲线

    Figure  8.  Absorption loss Ametal of Ag-NPs in blue band

    图  9  入射波长465 nm载流子数量曲线:(a)载流子数量曲线;(b)载流子增益比

    Figure  9.  Generation rate of carriers at λin = 465 nm: (a) carrier generation rates of Si/Ag-NPs and Si; (b) gain ratio

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出版历程

Research on the Enhancement of Absorption Properties of Silicon via Localized Surface Plasmons Resonance in Blue Light

doi: 10.37188/CO.2020-0056
    通讯作者: wangwb@ciomp.ac.cnliangjq@ciomp.ac.cn
  • 中图分类号: O431.1; O436.2; O471.5

摘要: 为增强硅的蓝光吸收,在硅表面设计银纳米颗粒阵列,基于局域表面等离激元共振效应对增强的硅蓝光吸收特性进行了分析研究。采用有限时域差分法计算银纳米颗粒阵列/硅复合结构中硅的蓝光吸收特性。结果表明:金属颗粒的消光能力与其几何参数相关,改变银纳米颗粒阵列的半径r、高度H与周期P可调控局域表面等离激元共振强度与共振频率,当银纳米颗粒阵列参数:半径为r = 18.5 nm、高度为H = 45 nm、周期为P = 49 nm时,共振吸收波长为465 nm,硅的蓝光吸收率由59%增加至94%,光吸收增益为0.57,光生载流子数目增益为0.53,分析认为局域表面等离激元共振增强硅在蓝光波段的光吸收。本文的研究结果对了解局域表面等离激元效应改善硅的蓝光吸收特性的机理、设计和制备高蓝光响应度硅基可见光光电探测器,具有重要的参考价值。

English Abstract

王浩冰, 陶金, 吕金光, 孟德佳, 李阳, 赵永周, 王家先, 张军, 秦余欣, 王惟彪, 梁静秋. 局域表面等离激元共振增强硅蓝光波段吸收特性研究[J]. 中国光学. doi: 10.37188/CO.2020-0056
引用本文: 王浩冰, 陶金, 吕金光, 孟德佳, 李阳, 赵永周, 王家先, 张军, 秦余欣, 王惟彪, 梁静秋. 局域表面等离激元共振增强硅蓝光波段吸收特性研究[J]. 中国光学. doi: 10.37188/CO.2020-0056
WANG Hao-bing, TAO Jin, LV Jin-guang, MENG De-jia, LI Yang, ZHAO Yong-zhou, WANG Jia-xian, ZHANG Jun, QIN Yu-xin, WANG Wei-biao, LIANG Jing-qiu. Research on the Enhancement of Absorption Properties of Silicon via Localized Surface Plasmons Resonance in Blue Light[J]. Chinese Optics. doi: 10.37188/CO.2020-0056
Citation: WANG Hao-bing, TAO Jin, LV Jin-guang, MENG De-jia, LI Yang, ZHAO Yong-zhou, WANG Jia-xian, ZHANG Jun, QIN Yu-xin, WANG Wei-biao, LIANG Jing-qiu. Research on the Enhancement of Absorption Properties of Silicon via Localized Surface Plasmons Resonance in Blue Light[J]. Chinese Optics. doi: 10.37188/CO.2020-0056
    • In recent years, with the continuous development of Surface Plasmon (SP) theory and the continuous improvement of micro-nano processing technique, the sensitization of photoelectric detectors based on SPs[1] has aroused great interest among researchers. The SPs can increase the intensity of local electromagnetic field, enhance the interaction between light and matter[2], and achieve selective light absorption at an ultra-high absorption rate[3]. Thus their application in solar cells[4], LED[5, 6], surface-enhanced Raman spectrum[7], photoelectric detection[8] and other fields has attracted extensive attention.

      The material properties, geometric shape, structural parameters, medium background and other factors of micro-nano array will have an impact on the physical phenomena of SPs[9]. The nature of the material itself determines the main attenuation path of SPs so that the SPs will sensitize the photodetectors in different ways[10]. For example, in the event of SPR attenuation, the Au-Nanoparticles (Au-NPs) transfer the absorbed light energy to free electrons in the metal through Landau damping. Then the free electrons are converted into hot electrons, which jump over the Schottky barrier into the semiconductor to improve the optical response in the incident band. The attenuation pattern of SPR in the Ag-Nanoparticles (Ag-NPs) and Aluminum-Nanoparticles (Al-NPs) is to scatter the incident light energy to the medium through optical radiation[11], thus improving the light absorptivity of metal particle substrates and enhancing the photoelectric performance of photodetectors.

      In 2011, Naomi Halas’s research group[12] demonstrated that Au-nanorods could realize thermoelectron detection with incident photon energy lower than silicon bandgap width Eg, and increase the photocurrent by a factor of 20 (λin = 1.4 μm). In 2012, Li's research group[13] studied the photoelectric response performance of surface plasmon effect coupled with GaN-based detector. By preparing the Ag nanoparticles in non-uniform sizes on the GaN surface, the device responsiveness was improved by a factor of 30 (λin = 0.36 μm). In 2013, Sobhani et al.[14] prepared the Au grating on Si surface. The silica-based thermoelectron detector based on EOT effect had an optical response of 0.6 mA/W (λin = 1.46 μm) with an internal quantum efficiency of 0.2%. In 2014, Bao et al.[15] studied the photoelectric performance gain of AlGaN-based solar blinded UV detector based on the Al-NPs with a non-uniform density, enhanced the performance of AlGaN detector by exciting the surface plasmons, and increased its optical response from 0.144 A/W to 0.288 A/W (λin = 0.288 μm). The above research shows that on the one hand, the excited SP effect of metal micro-nano structure can increase the probability that the incident photons are captured by detector to generate the hole-electron pair and photocurrent. On the other hand, based on the thermoelectronic effect, the efficiency of photocurrent generation can be significantly improved by crossing the Schottky barrier, thus effectively enhancing the working performance of a photodetector in the response band.

      In silicon (Si), the excited carriers have a wide spectral response in the incident band of 380 nm - 1100 nm. However, due to the relatively large absorption coefficient and small penetration depth of Si in the blue band, the photo-generated carriers can diffuse to the interface or surface state easily[16]. As a result, fewer photo-generated carriers diffuse and drift to the depletion region, leading to low quantum efficiency and optical response of silicon photodetector (Si-PD) in this band. However, efficient Si-based blue light detectors have a great potential application market in visible light communication[17], underwater communication[18], local intelligent positioning[19] and other fields.

      So far, few reports have been made on the use of SPs to enhance the photoelectric performance of Si-PD in the blue band. In this paper, an array of metal nanoparticles was designed on the silicon surface. The Finite-Difference-Time-Domain (FDTD)[20] method was used to study the influence of metal nanoparticles with different geometric parameters on the light absorption characteristic of Si. The results were analyzed according to the physical properties of Localized Surface Plasmons (LSPs)[9]. The research on the influence of SPs on the blue light absorption of Si is expected to improve the blue light absorption of Si, so as to provide reference for the design and preparation of a Si-PD with high blue light detection efficiency based on SP enhancement.

    • If the size of metal particles is much smaller than the penetration depth of incident field, free electrons will oscillate relative to the metal lattice under the joint action of coulomb field and external electromagnetic field, and the generated non-propagating mixed excited state will be LSP[9], as shown in Fig. 1.

      图  1  金属球状结构的局域表面等离激元示意图

      Figure 1.  Schematic of localized surface plasmons with a metallic spherical structure

      Take metal spherical nanoparticles with a diameter of ˂100 nm as an example. Under the quasi-static approximation, the polarizability α can be used to describe the interaction between incident light and particles and represent the LSP intensity. Its expression is

      $$\alpha = 4{\text{π}} {a^3}\left({\frac{{\varepsilon - {\varepsilon _m}}}{{\varepsilon + 2{\varepsilon _m}}}} \right),$$ (1)

      where a is the particle radius; εm is the relative dielectric constant of the background environment; and ε is the relative complex dielectric constant of a metal particle, which is affected by the frequency of incident electromagnetic field, the characteristics and size of material, and other factors. According to the Eq. (1), when Re[ε] = −2εm, the polarizability α is the maximum and the Localized Surface Plasmons Resonance (LSPR) is excited. Re[ε] = −2εm is also called Fröhlich condition[9]. When the metal nanoparticles are in the LSPR state, the polarizability and the efficiency of incident light absorption and scattering are the maximum. Generally, the extinction cross section σext represents its total optical response with a numerical relationship of σext = σabs + σscat, where σabs and σscat are the optical absorption cross section and scattering cross section of particles respectively[21]:

      $${\sigma _{abs}} = k{\rm{Im}} \left[ \alpha \right] = 4{\text{π}} k{a^3}{\rm{Im}} \left[ {\frac{{\varepsilon - {\varepsilon _m}}}{{\varepsilon + 2{\varepsilon _m}}}} \right],$$ (2)
      $${\sigma _{scat}} = \frac{{{k^4}}}{{6{\text{π}}}}{\left| \alpha \right|^2} = \frac{8}{3}{\text{π}} {k^4}{a^6}{\left| {\frac{{\varepsilon - {\varepsilon _m}}}{{\varepsilon + 2{\varepsilon _m}}}} \right|^2},$$ (3)

      where k is the wave vector of incident light. According to Eq. (2) and Eq. (3), σscat and σabs will be affected by the dielectric constant ε of metal material if the dimensionally stable metal particles are in a medium environment with constant εm. When the dipole LSPR is excited by Re[ε] = −2εm, the extinction cross section σext of spherical particles is the largest.

      According to the Drude-Lorentz dielectric model, the incident light frequency ωF[21] satisfying the Fröhlich condition is:

      $${\omega _{\rm{F}}} = \sqrt {\frac{{\omega _p^2}}{{1 + \varOmega + 2{\varepsilon _d}}} - {\tau ^2}} ,$$ (4)

      where ωp is metal plasma frequency; Ω is the factor of the influence of electronic interband transition on metal dielectric constant[22]; ωp and Ω are both dependent on metal material; τ is the electron collision frequency mainly from electron-electron scattering, phonon-electron scattering and surface-electron scattering, which is influenced by the size of metal structure, the array distribution and the intensity of electron scattering within the material and on the structure

      surface[21]. As seen from Eq. (4), ωp, Ω and τ are fixed. ωF will decrease as the dielectric constant εm of background environment increases. The corresponding wavelength will register a redshift.

      Due to the different complex dielectric constants of various metal materials, the loss responses of incident light in various metals are different. Among them, silver (Ag) and gold (Au) are regarded as ideal materials to enhance the interaction between light and matter based on LSPR effect, due to their small absorption loss[23]. Especially in the visible light bands, compared with the LSP damping frequency of Au (ГAu), Ag has a lower damping frequency ГAg and can produce a smaller light absorption loss[24] (particularly obvious in the blue and green bands). According to the physical properties of the above materials, this paper designed an array of Ag nanoparticles (Ag-NPs) to improve the blue light absorption of Si, and calculated the influence of Ag-NP array on the light absorption of Si based on the FDTD algorithm of Maxwell equations.

    • To simulate the modulation effect of LSPs on the light absorption of silicon, a simplified model of the interaction between metal nanostructure and incident light has been established, as shown in Fig. 2. An Ag-NP array (in silvery white) is arranged on the surface of Si (in red) to form an Ag-NP/Si composite structure.

      图  2  Ag-NPs/Si模型结构

      Figure 2.  Ag-NPs/Si model structure

      The calculation settings are as follows:

      (1) Establish the geometric structure: Si is set as a 20.0 μm-thick cubic structure with smooth surface, while each Ag-NP is set as a cylindrical structure. The dielectric constant of Si is from the data in [25], while that of Ag-NPs is from the data in [26] and is corrected and approximated against the Drude-Lortenz model;

      (2) Set the simulation and calculation area: the simulation time is 5000 fs. Since Ag-NP is a periodic structure on the XY plane, the boundary condition is set as follows: the Z-axis is the absorption boundary of perfectly matched Layer (PML), and the X-axis and Y-axis are set as anti-symmetry and symmetry respectively.

      (3) Select the light source (λin): the Plane Wave with a wavelength range of 380-760 nm and a polarization direction parallel to the XY Plane is set 1.0 μm away from the upper surface of Si and is incident directly down the Z-axis;

      (4) Set the Mesh precision: It is applied to calculate the electromagnetic field distribution of a complex curved surface model structure. A 3D structure is adopted, namely dx=dy=dz=0.3 nm. The geometric area is equal to the size of a single Ag nanoparticle.

      The physical model of light absorption of Ag-NPs/Si is simply expressed by the following formula derived from the law of conservation of energy:

      $$ {A_{metal}} + {A_{Si}} + R + T = 1 $$ (5)

      where ASi is the light absorptivity of Si; R is the surface reflectivity; T is the transmittance of Si substrate (according to the dispersion properties of silicon[25], the transmission depth for λ = 760 nm is about 8.52 μm, while the designed thickness of Si is 20 μm; the incident light can be almost completely absorbed by Si, so the transmittance is considered as T = 0); Ametal represents the light absorption loss of Ag-NP array[27]. In this case, the reflectivity R in the incident band and the light absorption loss Ametal of metal particles can be accurately calculated by using the FDTD algorithm combined with the material characteristics of Si and Ag[25, 26]. Then they are substituted into the Eq. (5) to obtain the light absorptivity of Si, namely ASi (=1 − RAmetal), and its gain.

    • Under the action of incident light, metal nanoparticles can scatter and absorb the light, as described by Mie theory[28]. According to Mie theory, the optical response of metal particles to incident electromagnetic field is shown as follows[28]:

      $$E(\textit{λ}) = \frac{{24{\text{π} ^2}N{a^3}{\varepsilon _m}^{3/2}}}{{{\textit{λ}} \ln (10)}}\left[\frac{{{\varepsilon _i}}}{{{{({\varepsilon _r} + \chi {\varepsilon _m})}^2} + {\varepsilon _i}^2}}\right],$$ (6)

      where E(λ) is the extinction spectrum of a metal nanoparticle; λ is the incident wavelength; N is the concentration of free electrons in the nanoparticle; a is the particle radius, representing the influence of particle size on extinction properties; εm is the dielectric constant of background environment; εr is the real part of metal dielectric constant; εi is the imaginary part of metal dielectric constant; χ is the shape factor, usually χ = 2 for a spherical particle, χ > 2[28] for an ellipsoidal particle, showing the correlation between particle geometry and extinction ability. According to Eq. (6), the size and shape of Ag-NPs can influence their extinction spectrum in an environment with constant εm. Theoretically, by adjusting the particle size, the LSPR effect can be stimulated in the blue band to improve the blue light absorption of silicon. In addition, given the same incident wavelength, the light absorption gain of Si will also be affected by the modulation effect of geometrical factors on the extinction ability of Ag-NPs. If Gabs is the light absorption gain of Si, then:

      $$ {G_{abs}} = \frac{{{A_{Ag - NPs/S{\rm{i}}}} - {A_{Si}}}}{{{A_{Si}}}} \times 100{\rm{\% }}, $$ (7)

      where AAg-NPs/Si is the optical absorptance of Si in the Ag-NP array structure, and ASi is the optical absorptance of single medium Si.

      To realize the high blue-light absorption of Si, the Ag-NP array design is optimized by adjusting the radius r, height H and period P of Ag-NPs. In the following calculation process, the optical absorptance of Si in the Ag-NP array with different geometric parameters in the air will be obtained by using the FDTD algorithm. The material properties of Ag and Si[25, 26], the boundary conditions and other settings are the same as those in Section 2.2.

    • According to the dipole approximation theory, when the size of metal particles is much smaller than that of the LSPs excited by incident wavelength[28], the particle size L and the resonance wavelength λpeak are in the numerical empirical relationship L ~ 0.1λpeak. As the resonance wavelength should be located in the blue band, the radius r of Ag-NP cylinder is preliminarily determined to be within 12.5-22.5 nm according to the above size relation. The step size is set as 2.5 nm, and the height is H = 50.0 nm. is the coupling intensity of incident light contributed by the interaction polarization of dipolar electromagnetic field within the fixed adjacent Ag-NPs. In Fig. 2, the minimum distance D between metal particles is unchanged, i.e. D = 20.0 nm. The optical absorptance of Si (ASi) calculated with the FDTD method and its variation are shown in Fig. 3.

      The Fig. 3 (a) shows the optical absorptance of Si in the Ag-NP cylinder array with different radii (r). For r = 12.5 nm, 15.0 nm, 17.5 nm, 20.0 nm or 22.5 nm, the maximum optical absorptance of Si is ASi ≈ 74% (λ = 451 nm), ASi ≈ 76% (λ = 460 nm), ASi ≈ 77% (λ = 470 nm), ASi ≈ 78% (λ = 479 nm) or ASi ≈ 79% (λ = 486 nm) respectively. As seen from the curve, there are two absorption peaks with different intensities in the absorption spectrum of Si. This is similar to the absorption or scattering spectrum of Ag-NPs calculated in [29-35]. According to the ASi defined in Eq. (5), when Ag has a low blue-light absorption loss and the transmittance is ignored, the occurrence of double absorption peaks is mainly related to the change of Ag-NP extinction ability caused by the shape and structure of metal particles and the dielectric constant of array substrate. As known from the parametric shape factor χ in Eq. (6), the extinction spectrum of a metal particle depends on its own structure. If the surface structure of a particle is complex with several different symmetry axes, the free electrons in the LSPR state will oscillate inside the particle in different ways. The extinction spectrum reflects multiple resonance peaks. For example, an ellipsoidal metal nanoparticle has three resonance frequencies because it has three different axes of symmetry[29]. Secondly, according to the Ag-NP extinction spectrum calculated in [35] (Fig. 8), the single formant in the extinction spectrum will gradually split into two with the increase of the substrate refractivity n if n > 2. The analysis result shows that, compared with the common oxide substrates with low refractive index (such as SiO2, n < 2), silicon (Si), the substrate material used in this paper, has a higher refractive index and a higher dielectric constant. During the excitation of LSPs, the charges accumulated on the surface of Ag- NPs generate an electric field nearby, causing obvious polarization on Ag-NPs/Si interface that induces the electric field to react upon the metal nanoparticles. This may affect the internal resonance mode and generate double absorption peaks, because LSP is the quantum state of collective electron motion inside the matter in terms of quantum mechanics[9]. Under the polarized electric field at the interface, the wave functions of the quantum states of LSPs inside particles may overlap and cause the quantum interaction, which will affect the extinction performance of Ag-NPs and lead to the phenomenon of double absorption peaks. It is concluded from the above analysis that the geometrical structure of Ag-NPs and the high dielectric constant of the substrate are the main reasons for the occurrence of double peaks on the absorption spectrum of Si.

      图  3  Ag-NPs几何参数对硅的光学行为影响:(a)半径r变化对硅在蓝光波段的吸收影响;(b)光吸收率与共振波长随半径r的变化;(c)半径r变化对硅在蓝光波段的吸收增益影响

      Figure 3.  Influence of geometric parameters of Ag-NPs on the optical properties of silicon: (a) absorptance versus radius r in blue band; (b) absorptance and resonant wavelength versus radius r; (c) absorptive gain versus radius r in blue band

      The Fig. 3(b) shows the relationship between the resonance wavelength λpeak and the radius r. The curve shows that λpeak is redshifted with the increase of r, which means that λpeak increases from λpeak = 451 nm (r = 12.5 nm) to λpeak = 486 nm (r = 22.5 nm). The analysis shows that the increase of radius r will cause a longer interaction distance of dipoles in Ag-NPs, a smaller recovery coefficient and a lower resonance frequency of oscillating electrons, and the redshift of LSP formant position[36].

      The Fig. 3(c) is obtained after substituting the calculation results of Fig. 3(a) into Eq. (7). The absorption spectrum lines in the figure indicate that the change of radius r affects the light absorption gain Gabs of Si at the same incident wavelength. The analysis of this change shows that, according to Gans theory[37], the extinction coefficient σext(λ) of ellipsoidal metal nanoparticles can be expressed as:

      $${\sigma _{ext}}(\textit{λ}) = \frac{{2\text{π} V\varepsilon _{med}^{3/2}}}{{3\textit{λ} }}\sum\limits_j {\frac{{\left({1/P_j^2} \right){\varepsilon ^{''}}}}{{{{\left({{\varepsilon ^{'}} + \dfrac{{1 - {P_j}}}{{{P_j}}}{\varepsilon _{med}}} \right)}^2} + {{\left({{\varepsilon ^{'}}} \right)}^2}}}} ,$$ (8)

      where V is the particle volume; εmed is the dielectric constant of space environment; ε is the real part of dielectric constant of metal particle; ε’’ is the imaginary part of dielectric constant of metal particle; Pj represents the polarization factor and is related to the aspect ratio of the particle. According to the extinction coefficient σext(λ) defined by Eq. (8), not only the volume V but also the aspect ratio (or polarization factor Pj) of a particle will change during the adjustment of the radius r (the height H is unchanged). As a result, under the joint modulation of the parameters V and Pj, the light absorption gain Gabs of Si in the Ag-NPs with different radii is different.

      According to the above analysis, Si has a higher absorption rate (ASi ≈ 79%) in the blue band (λ=486 nm) when the radius of Ag-NPs is r = 22.5 nm (height H = 50.0 nm, period P = 65.0 nm).

    • To further optimize the light absorption gain of Ag-NP array on Si and analyze the change of blue light absorption of Si with the height H of Ag-NP cylinder, we set the radius and period as r = 22.5 nm and P = 65.0 nm respectively according to the data results in Section 3.1.1. In the range of 30.0-70.0 nm, the height H was adjusted with the step size of 10.0 nm. The absorption spectra of Si based on the Ag-NP arrays of different heights were calculated with the FDTD algorithm, as shown in Fig. 4.

      图  4  Ag-NPs几何参数对硅的光学性质影响:(a)高度H对硅在蓝光波段的吸收影响;(b)光吸收率与共振波长随高度H的变化;(c)高度H对硅在蓝光波段的吸收增益影响

      Figure 4.  Influence of geometric parameters of Ag-NPs on the optical properties of silicon: (a) absorptance versus height H in blue band; (b) absorptance and resonant wavelength versus height H; (c) absorptive gain versus height H in blue band

      The Fig. 4(a) shows the change of Si-absorptance ASi with the particle height H. For H = 30.0 nm, 40.0 nm, 50.0 nm, 60.0 nm or 70.0 nm, the maximum optical absorptance of Si is ASi ≈ 64% (λ = 452 nm), ASi ≈ 72% (λ = 466 nm), ASi ≈ 79% (λ = 486 nm), ASi ≈ 83% (λ = 498 nm) or ASi ≈ 82% (λ = 544 nm) respectively. The Fig. 4(b) shows the relationship between the resonance wavelength λpeak and the height H. The curve shows that with the increase of Ag-NP height H, λpeak is redshifted from λpeak = 452 nm (H = 30.0 nm) to λpeak = 544 nm (H = 70.0 nm). Because a cylindrical metal nanoparticle has a vertical axis and a horizontal axis, its surface plasma will resonate in two modes in different directions. That is, the vertical surface plasma will resonate in the y-direction, while the horizontal surface plasma will resonate in the x-direction. The resonance wavelength of surface plasma will shift with the change of aspect ratio[34]. Therefore, the increase of height H will lead to the decrease of electron oscillation frequency and the redshift of formant position.

      The light absorption gain in Fig. 4(c) is obtained after substituting the calculation results of Fig. 4(a) into Eq. (7). The curve in Fig. 4(c) shows the influence of height (H) change on the light absorption gain Gabs at the same incident wavelength. If H = 50.0 nm, the maximum Gabs will be 30% at λ = 475 nm. If H < 50.0 nm, Gabs will increase with the height H. If H > 50.0 nm, Gabs will decrease with the increasing height H. In other words, with the increase of Ag-NP height H, Gabs will increase first and then decrease. The analysis of this phenomenon based on the Gan theory[37] shows that, the height H (fixed radius r) determines the metal nanoparticle volume V and the polarization factor Pj, as seen from the extinction coefficient σext(λ) defined by Eq. (8). Both factors jointly modulate the intensity of coupling between incident light and Ag-NPs and affect the extinction ability of Ag-NPs, so that the Ag-NPs with different heights produce different light absorption gains for Si.

      According to the above analysis, Si has a higher absorption rate (ASi ≈ 83%) in the blue band (λ=498 nm) when the height of Ag-NPs is H = 60.0 nm (radius r = 22.5 nm, period P = 65.0 nm).

    • In fact, the optical response of a metal nanoparticle array to incident wave depends not only on the material, size, shape and ambient medium of the mono-metal nanoparticles, but also on the distribution of the array particles[40]. To further optimize the light absorption gain effect of Ag-NP array on Si, the influence of Ag-NP period P on the blue light absorption of Si was investigated. The period P contains the Ag-NP diameter 2r and the minimum spacing D between adjacent particles. If the size of Ag-NPS is fixed and D is changed in the optimization process, the coupling intensity of incident light contributed by the interaction between the dipolar fields of adjacent Ag-NPs can be changed to affect the light absorption of Si. According to the calculation results in sections 3.1.1 and 3.1.2, the radius and height were set as r = 22.5 nm and H = 60.0 nm respectively. In the range of 60.0-80.0 nm, the period P was adjusted by a step size of 5.0 nm. The optical absorption spectrum of Si was calculated with the FDTD algorithm. For the results, see Fig. 5.

      图  5  Ag-NPs几何参数对硅的光学性质影响:(a)周期P对硅在蓝光波段的吸收影响;(b)光吸收率与共振波长随周期P的变化;(c)周期P对硅在蓝光波段的吸收增益影响

      Figure 5.  Influence of geometric parameters of Ag-NPs on the optical properties of silicon: (a) absorptance versus period P in blue band; (b) absorptance and resonant wavelength versus period P; (c) absorptive gain versus period P in blue band

      The Fig. 5(a) shows the effect of metal particle period P on the optical absorption spectrum of Si. For P = 60.0 nm, 65.0 nm, 70.0 nm, 75.0 nm or 80.0 nm, the maximum optical absorptance of Si is ASi ≈ 82% (λ = 539 nm), ASi ≈ 83% (λ = 498 nm), ASi ≈ 80% (λ = 486 nm), ASi ≈ 78% (λ = 477 nm) or ASi ≈ 75.5% (λ = 462 nm). The Fig. 5(b) shows the relationship between the resonance wavelength λpeak and the period P. The curve shows that λpeak is blue-shifted from 539 nm (P = 60.0 nm) to 462 nm (P = 80.0 nm). According to the CD-Method theory[41], the dipole polarizability in Ag-NPs has the following relationship with the period:

      $$\prod = \frac{{ - A{E_0}}}{{\omega - \{ {\omega _o} - {\rm{Re}} (AS)\} + i\{ \gamma + {\rm{Im}} (AS)\} }},$$ (9)

      where П is the dipolar polarizability of metal nano array; A is the dipole action matrix related to the array period, whose modulus is a normal number; E0 is the intensity of external field; ω is the frequency of incident field; ω0 is the LSPR frequency of mono-metal nanoparticle, which is influenced by the material, size and geometry of the particle and the dielectric constant of ambient environment[9]; γ is the half width of its extinction spectrum; S is the hysteresis dipole [42]. The AS in Eq. (9) changes with the period P. According to the CD-Method theory[41], if the period is P < 100 nm, ω0 and γ will remain unchanged and λpeak will be blue-shifted with the increase of P.

      The light absorption gain of Si in Fig. 4(c), namely Gabs, is obtained after substituting the calculation results of Fig. 5(a) into Eq. (7). The curve in Fig. 4(c) shows the influence of period (P) change on the light absorption gain Gabs at the same incident wavelength. If P = 65.0 nm, then Gabs will be 34% at the incident wavelength λ = 498 nm. If P < 65.0 nm, Gabs will increase with P. If P > 65.0 nm, Gabs will decrease with the increasing P. Gabs shows a general trend of increasing first and then decreasing. According to the analysis result, the increase of the period P will affect the polarization effect of adjacent particle dipoles[43] and change the intensity of local electromagnetic field in the particle gap. If P = 65.0 nm, the interaction of local electromagnetic fields will maximize the polarizability α of metal particles and the light absorption gain Gabs of Si. If P < 65.0 nm, the too strong coupling between dipoles in adjacent Ag-NPs will increase the light absorption loss Ametal of Ag-NPs[44] and decrease the light absorption of Si and the light absorption gain Gabs. If P > 65.0 nm, the interaction between dipoles in adjacent Ag-NPs will decline with the increase of the period P. Although the non-radiation loss effect of Ag-NPs is inhibited[40], the effect of coupling between incident field and Ag-NPs is weakened. The LSP intensity decreases with the increase of the period P[44]. As a result, the reflectance R increases and the light absorption gain Gabs of Si decreases with the increase of the array period P.

      According to the above calculation, when the radius, height and period of Ag-NP array are r = 22.5 nm, H = 60.0 nm and P = 65.0 nm respectively, the maximum light absorption rate ASi of Si will be 83% and the absorption peak position will be λpeak = 498 nm with the peak wavelength at the edge of the blue band. In order to meet the current requirements for efficient blue LED detection, it is necessary to continue to adjust and optimize the design scheme so that the maximum blue light absorption of Si can happen in the range of 440-480 nm.

    • Based on the above calculation of the influence of Ag-NP geometry parameters on Si absorptance, we repeatedly optimized and calculated the radius r, height H and period P of Ag-NPs and the distance D between adjacent particles and finally obtained the following results. If r =18.5 nm, H = 45.0 nm and P = 49.0 nm, the highest light absorption rate of Si in the Ag-NPs/Si composite structure will be approximately 94% and the resonant wavelength will be λpeak = 465 nm. The light absorption spectrum of the single medium Si in Fig. 6(a) is derived from the calculation results of FDTD algorithm for the interaction between incident light field and Si[25]. It is found from the illustrated calculation results that, in the AG-NPs/Si structure, Si fails to achieve perfect blue light absorption. According to the analysis, the numerical function of Si-absorptance ASi based on Eq. (5) is expressed as: ASi = 1 − AmetalR. Due to the light absorption loss Ametal and reflectivity R of Ag-NPs, the incident light at the wavelength λ = 465 nm is not fully absorbed by Si (ASi < 100%), and double absorption peaks also appear in the absorption spectrum of Si (according to the dispersion characteristics of Si, the design thickness of Si in the Ag-NPs/Si model is much larger than the penetration depth of blue light, so blue light is almost completely absorbed by Si and the transmittance T can be ignored). This phenomenon has been explained previously and will not be explained again. After substituting the calculation results of Fig. 6(a) into Eq. (7), the light absorption gain of Si in Fig. 6(b) is obtained. At λ = 465 nm, the maximum absorptive gain is obtained, that is, Gabs = 57%.

      图  6  可见光波段硅的光吸收:(a)硅与基于Ag-NPs阵列硅的吸收率曲线;(b)硅的光吸收增益

      Figure 6.  Si-absorptance in visible bands from 380 nm to 760 nm: (a) absorptance of silicon versus absorptance of silicon in Ag-NP array; (b) absorptive gain of silicon

      We explored the influence of LSPR effect on the light absorption of Si in blue band. The analysis results show that, the absorption loss Ametal of Ag material in the blue-green band is extremely low[26], and the transmittance can be considered as T = 0 according to the dispersion relation of Si. Therefore, it can be concluded from Eq. (5) that the enhanced blue light absorption of Si results from the decrease of the surface reflectance R of Si in this band. After the incident light frequency ωin matches the ISPR frequency ωLSPR and the equation Re[ε] = −2εm is met, the generated LSPR effect provides Ag-NPs with a maximal extinction cross section (or absorption cross section mainly for small particles)[22]. The energy of incident field is converted into the oscillating kinetic energy of dipoles inside the particle to effectively reduce the reflectance R of Si surface. However, according to the polarizability α of metal particles defined in Eq. (1) and the dispersion relation of complex dielectric constant of Ag material[28], the condition ωinωLSPR in the incident band of other frequencies will cause Re[ε] ≠ −2εm, leading to a small polarizability α, a lower effect of coupling between incident light and Ag-NPs, a non-resonant state of Ag-NPs and another increase of reflectance R in theory. We detected the reflected light energy 1 μm above the Si surface, and calculated the reflectivity R with the FDTD algorithm under the same calculation conditions, as shown in Fig. 7. It is known from Fig. 6 and Fig. 7 that, when the light at λin = 465 nm is incident on the Si surface, its reflectance will be R1 ≈ 0.41. According to the Eq. (5), the optical absorptance of Si is A1 ≈ 0.59 (Ametal = 0 if no Ag-NPs exist). When the light is incident on the Ag-NPs/Si structure, the reflectance will drop to R2 ≈ 0.01. According to the FDTD numerical method, the light absorption loss of Ag-NPs is calculated to be Ametal ≈ 0.05, as shown in Fig. 8. The curve shows that, the theoretical blue-light absorption loss of Ag-NPs is similar to the light absorption loss of 40 nm Ag-NPs calculated by M.A García[34] (see the Fig. 8 in [34]). After substituting the light absorption loss Ametal of Ag-NPs into Eq. (5), the optical absorptance of Si in the Ag-NP array is determined as A2 ≈ 0.94, higher than A1 (A1 ≈ 0.59). From the curve in Fig. 8, we also find that although the light absorption loss Ametal at λ > 465 nm is ˂ 0.05, the reflectance R is still increasing, as shown in the reflectance curve of Fig. 7. As a result, the optical absorptance of Si calculated by Eq. (5) is ASi < 0.94. For example, if λ = 475 nm, R = 0.04 and Ametal = 0.03, the optical absorptance calculated by the above equation will be ASi ≈ 0.93.

      图  7  蓝光波段结构表面反射率R与Ag-NPs光吸收损耗Ametal曲线

      Figure 7.  Reflectivity R of structure surface in blue band versus absorption loss Ametal of Ag-NPs

      It can be seen from the above data that the LSPR effect reduces the reflectivity of Si surface, and that most of the incident light energy is coupled by Ag-NPs into the interior of Si and then absorbed by Si.

      图  8  蓝光波段Ag-NPs光吸收损耗Ametal曲线

      Figure 8.  Absorption loss Ametal of Ag-NPs in blue band

    • The number of generated carriers has a certain effect on the quantum efficiency of semiconductor photodetectors. If the production rate of electron-hole pairs, namely Ge(x), is used to represent the number of photo-generated carriers[38], then:

      $$ {G_e}(x) = {\varPhi _0}\alpha \exp (- \alpha x) = \frac{{(1 - R){P_{{\rm{opt}}}}}}{{S \cdot h\upsilon }}\alpha \exp (- \alpha x), $$ (10)

      where Φ0 is incident photon flux, R is reflectivity, Popt is incident light power (W/m2), S is incident area (m2), is single-photon energy (eV), and α is the absorption coefficient of a medium (m−1). The power density of incident light is 1 W/m2. Depending on the optical absorption energy (internal energy loss of undirected air propagation) of silicon, the incident photons are all converted into hole-electron pairs. The calculation conditions are the same as those in Section 2.2. By using the FDTD algorithm and Eq. (10), we calculated the number of initial photo-generated carriers of Si in the Ag-NP array under the conditions λin = 465 nm, r = 18.5 nm, H = 45.0 nm and P = 49.0 nm. The results are shown in Fig. 9(a), where the horizontal axis represents the propagation distance of incident light within Si. The comparison of carrier generation rates in Fig. 9(a) shows that the LSPR effect can increase the number of photo-generated carriers in Si, and indirectly indicates that a certain number of photo-generated carriers can be generated in the depths of silicon.

      图  9  入射波长465 nm载流子数量曲线:(a)载流子数量曲线;(b)载流子增益比

      Figure 9.  Generation rate of carriers at λin = 465 nm: (a) carrier generation rates of Si/Ag-NPs and Si; (b) gain ratio

      If G is the number of photo-generated carriers (m−3) and M is the gain ratio of G, then:

      $$M = \frac{{{G_{Ag - NPs/Si}} - {G_{{\rm{Si}}}}}}{{{G_{Si}}}},$$ (11)

      where GAg-NPs/Si and GSi are the concentrations of photo-generated carriers in Ag-NPs/Si structure and single medium Si respectively. After substituting the number of photo-generated carriers (G) calculated in Fig. 9(a) into Eq. (11), the gain of G in the Ag-NPs/Si structure is determined as M ≈ 0.53, as shown in Fig. 9(b). According to the analysis of Ge(x) defined in Eq. (10), M is caused by the decrease of the reflectivity R of Ag-NPs/Si structure. The physical mechanism of this change has been explained in the previous section, so it will not be repeated here. Therefore, the following conclusion is drawn: theoretically, the LSPR effect can increase the number of photo-generated carriers and the probability of carrier collection by electrodes, and enhance the quantum efficiency of Si-based photodetectors.

      The above research results have important theoretical reference value for the design of silicon-based visible light photodetectors with high blue-light response and for the solution to other issues.

    • The effect of Ag-NPs/Si composite structure on visible light absorption was studied in this paper. In the blue band, the relations between the geometrical parameters (radius r, height H and period P) of Ag-NPS and the light absorption of Si were calculated separately. When the radius r is increased, the optical absorptance of Si will increase and the formant position will register a redshift. When the height H is increased, the optical absorptance of Si will increase first and then decrease and the formant position will register a redshift. When the period P is increased, the optical absorptance of Si will increase first and then decrease and the formant position will register a blueshift. The optimization results of Ag-NPs/Si composite structure show that when the parameters of Ag-NP structure are r = 18.5 nm, H = 45.0 nm and period P = 49.0 nm, the maximum absorption rate of Si will be 94%, the maximum absorption peak wavelength will be λ = 465 nm, and the light absorption gain will be 0.57. The calculated gain of the number of photo-generated carriers of Ag-NPs/Si at λ = 465 nm is approximately 0.53. The enhancement of optical absorptance of Si and the increase of the number of photo-generated carriers are related to the decrease of surface reflectivity of Si caused by LSPR effect. The research results have high reference value for the design of silicon-based visible light photodetectors using Ag-NPs to enhance the blue light response.

    • 近年来,随着表面等离激元(Surface Plasmons, SPs)理论不断发展和微纳加工技术的不断提高,基于SPs对光电探测器的增敏研究[1]引起研究人员的极大兴趣。SPs具有提高局域电磁场强度、增强光与物质相互作用[2]、选择光吸收、超高的吸收率[3]等特点,使其在太阳电池[4]、LED[5, 6]、表面增强拉曼光谱[7]、光电探测[8]等领域的应用受到广泛关注。

      微纳阵列的材料性质、几何形状、结构参数、介质背景等因素会对SPs的物理现象产生影响[9],材料自身性质会决定SPs的主要衰减途径,导致SPs对光电探测器的增敏方式不同[10],例如金纳米颗粒(Au-Nanoparticles, Au-NPs)在发生SPR衰减时通过朗道阻尼将吸收的光能量传递金属内的自由电子,转换为热电子并跃过肖特基势垒注入半导体,提高入射波段光响应度;SPR在银纳米颗粒(Ag-Nanoparticles, Ag-NPs)、铝纳米颗粒(Aluminum-Nanoparticles, Al-NPs)的衰减模式是将入射光能量以光辐射的形式向介质散射[11],提高金属颗粒基底的光吸收率,增强光电探测器的光电性能。

      2011年,Naomi Halas课题组[12]证实基于Au-nanorods实现入射光子能量低于硅带隙宽度Eg的热电子探测,光电流增加20倍(入射光λin = 1.4 μm);2012年,Li课题组[13]研究表面等离激元效应与GaN基探测器耦合的光电响应性能,通过在GaN表面制备尺寸不均匀Ag纳米颗粒,使器件响应度提高30倍(入射光λin = 0.36 μm);2013年,Sobhani等人[14]在Si表面制备Au光栅,基于EOT效应的硅基热电子探测器的光响应度为0.6 mA/W(入射光λin = 1.46 μm),内量子效率为0.2%;2014年,Bao等[15]研究基于不均匀密度Al-NPs的AlGaN基日盲紫外探测器光电性能增益,通过激发表面等离激元增强AlGaN探测器的性能,光响应度从0.144 A/W增至0.288 A/W(入射光λin = 0.288 μm)。上述研究工作表明金属微纳结构激发的SPs效应,一方面增加了探测器对入射光子的捕获并产生空穴—电子对与光电流的概率,另一方面基于热电子效应,通过穿越肖特基势垒显著提高光电流产生的效率,有效增强光电探测器在响应波段内的工作性能。

      硅(Si)在380 ~ 1100 nm入射波段具有被激发载流子的宽光谱响应能力,然而由于蓝光波段Si的吸收系数相对较大、透入深度小,导致光生载流子易扩散至界面或表面态[16],使扩散和漂移至耗尽区光生载流子数目少,造成硅基光电探测器(Silicon Photodetector, Si-PD)在该波段量子效率和光响应度较低的现象。而Si基高效蓝光探测器在可见光通信[17]、水下通信[18]、局域智能定位[19]等领域拥有极大的潜在应用市场。

      目前有关基于SPs增强Si-PD蓝光波段光电性能的研究报道很少,本文在硅表面设计金属纳米颗粒阵列,基于有限时域差分法(Finite-Difference-Time-Domain, FDTD)[20],研究不同几何参数的金属纳米粒子对Si的光吸收特性的影响,根据局域表面等离激元(Localized Surface Plasmons, LSPs)的物理性质[9]对结果进行分析,希望通过研究SPs对Si在蓝光波段的光吸收影响,提高硅的蓝光吸收,为设计制备基于SPs增强的高蓝光探测效率的Si基光探测器提供参考。

    • 若金属颗粒的尺寸远小于入射场的穿透深度,自由电子在库伦场与外电磁场的共同作用下相对金属晶格振荡,产生的非传播混合激发态为局域表面等离激元[9],如图1所示。

      以直径小于100 nm的金属纳米球形颗粒为例,在准静态近似下,极化率α可描述入射光与粒子相互作用,表征局域表面等离激元强度,表达式为

      $$\tag{1} \alpha = 4\text{π} {a^3}\left({\frac{{\varepsilon - {\varepsilon _m}}}{{\varepsilon + 2{\varepsilon _m}}}} \right),$$ (1)

      式中,a为颗粒半径,εm为背景环境的相对介电常数,ε为金属粒子的相对复介电常数,受入射电磁场频率、材料特性、尺寸等因素影响。根据公式(1)表明当Re[ε] = −2εm时,极化率α极大,激发局域表面等离激元共振(Localized Surface Plasmons Resonance, LSPR)现象,Re[ε] = −2εm也称为Fröhlich条件[9]。金属纳米粒子处于LSPR状态时的极化率、吸收及散射入射光效率最大,通常消光截面σext表征其光学总响应,数值关系为σext = σabs + σscatσabsσscat分别为颗粒的光学吸收截面和散射截面[21]

      $$\tag{2} {\sigma _{abs}} = k{\rm{Im}} \left[ \alpha \right] = 4\text{π} k{a^3}{\rm{Im}} \left[ {\frac{{\varepsilon - {\varepsilon _m}}}{{\varepsilon + 2{\varepsilon _m}}}} \right],$$ (2)
      $$\tag{3} {\sigma _{scat}} = \frac{{{k^4}}}{{6\text{π} }}{\left| \alpha \right|^2} = \frac{8}{3}\text{π} {k^4}{a^6}{\left| {\frac{{\varepsilon - {\varepsilon _m}}}{{\varepsilon + 2{\varepsilon _m}}}} \right|^2},$$ (3)

      式中,k为入射光波矢。根据公式(2)与(3)可知,若尺寸不变的金属粒子在εm恒定的介质环境中,σscatσabs受金属材料介电常数ε的影响,当Re[ε] = −2εm激发偶极LSPR现象时,球形颗粒的消光截面σext最大。

      根据Drude-Lorentz介电模型,满足Fröhlich条件的入射光频率ωF[21]为:

      $$\tag{4} {\omega _{\rm{F}}} = \sqrt {\frac{{\omega _p^2}}{{1 + \varOmega + 2{\varepsilon _d}}} - {\tau ^2}} $$ (4)

      式中,ωp为金属等离子体频率, Ω为电子带间跃迁对金属介电常数的影响因子[22]ωpΩ均于金属材料相关,τ为电子碰撞频率,其碰撞主要源于电子—电子散射、声子—电子散射和表面—电子散射,频率大小受金属结构尺寸、阵列分布和材料内部及结构表面对电子的散射强度影响[21]。通过公式(4)看出,ωpΩτ固定,ωF随背景环境介电常数εm的增加而降低,对应的波长红移。

      由于各金属材料的复介电常数等特性的不同,入射光在金属内的损耗响应具有差异性,其中银材料(Ag)、金材料(Au)因较小的吸收损耗被视为基于LSPR效应增强光与物质相互作用的理想材料[23],特别是在可见光波段,与Au材料的LSPs阻尼频率ГAu相比,Ag材料具有低阻尼频率ГAg,可产生更小的光吸收损耗[24](蓝绿波段尤为明显)。根据上述材料的物理性质,本文通过设计银纳米颗粒(Ag-NPs)阵列结构,提高Si的蓝光吸收,并基于Maxwell方程组的FDTD数值算法计算Ag-NPs阵列对Si的光吸收影响。

    • 为模拟LSPs对硅光吸收的调制作用,建立了金属纳米结构与入射光相互作用的简化模型,如图2。在Si(红色部分)表面设置Ag-NPs阵列(银白色部分),形成Ag-NPs/Si复合结构。

      计算设置如下:

      (1)建立几何结构:Si设置为表面光滑的立方体结构,Ag-NPs设置为圆柱体结构,Si厚度为20.0 μm,Si的介电常数源自文献[25]数据,Ag-NPs的介电常数源于文献[26]数据,并根据Drude-Lortenz模型修正近似;

      (2)设置仿真计算区域:仿真时间5000 fs。由于Ag-NPs在XY面是周期性结构,边界条件设置为:z轴方向为完美匹配层(Perfectly matched layer, PML)吸收边界,x轴和y轴分别设置为反对称(Anti-symmetry)和对称(Symmetry);

      (3)选取光源(λin):波长范围380~760 nm、偏振方向平行于XY面的平面波(Plane Wave),设置于距Si上表面1.0 μm处、沿z轴向下正入射;

      (4)Mesh精度设置:应用于计算复杂曲面模型结构的电磁场分布,采用3D结构,dx=dy=dz=0.3 nm,几何区域设置等于单Ag纳米颗粒尺寸。

      Ag-NPs/Si的光吸收物理模型用能量守恒定律的衍生公式简化表达:

      $$\tag{5} {A_{metal}} + {A_{Si}} + R + T = 1 $$ (5)

      式中,ASi为Si的光吸收率,R为表面反射率,T为Si衬底的透射率(根据硅的色散特性[25]λ = 760 nm的透射深度约8.52 μm,而Si的设计厚度为20 μm,入射光可被Si几乎全部吸收,认为透射率T = 0),Ametal表示Ag-NPs阵列的光吸收损耗[27]。在此情况下,根据FDTD算法,结合Si及Ag的材料特性[25, 26],准确计算入射波段内反射率R与金属颗粒的光吸收损耗Ametal,代入(5)式得出Si的光吸收率ASi (=1 − RAmetal)及其增益。

    • 金属纳米颗粒在入射光的作用下,存在光的散射与吸收现象,Mie理论已对其光学响应过程做出描述[28]。根据Mie理论,金属颗粒对入射电磁场的光响应关系式如下[28]

      $$\tag{6} E(\textit{λ}) = \frac{{24{\text{π} ^2}N{a^3}{\varepsilon _m}^{3/2}}}{{\textit{λ} \ln (10)}}\left[\frac{{{\varepsilon _i}}}{{{{({\varepsilon _r} + \chi {\varepsilon _m})}^2} + {\varepsilon _i}^2}}\right]$$ (6)

      式中,E(λ)表示金属纳米粒子的消光光谱,λ为入射波长,N为纳米颗粒的自由电子浓度,a为颗粒尺寸半径,表征颗粒尺寸对消光性质的影响,εm为背景环境介电常数,εr为金属介电常数实部,εi为金属介电常数虚部,χ为形状因子,通常球形颗粒χ = 2,椭圆球体χ > 2[28],表征颗粒几何形状与消光能力的关联性。根据公式(6)表明Ag纳米颗粒在εm恒定的环境内,其尺寸与形状会影响Ag-NPs的消光光谱,理论上通过调节粒子大小可在蓝光波段激发LSPR效应,提高硅的蓝光吸收率,并且在同一入射波长下,由于几何因素对Ag-NPs消光能力的调制作用,使Si的光吸收增益效果也受到影响,设Gabs为Si的光吸收增益:

      $$\tag{7} {G_{abs}} = \frac{{{A_{Ag - NPs/S{\rm{i}}}} - {A_{Si}}}}{{{A_{Si}}}} \times 100{\rm{\% }} $$ (7)

      式中,AAg-NPs/Si为基于Ag-NPs阵列结构Si的光吸收率,ASi为单一介质Si的光吸收率。

      为实现Si的高蓝光吸收,通过分别调节Ag纳米颗粒的半径r、高度H与周期P,对Ag纳米颗粒阵列设计优化。在下列计算过程中,基于FDTD算法得到在空气中不同几何参数的Ag-NPs阵列对Si的光吸收率,其中Ag与Si的材料性质[25, 26]、边界条件等设置与2.2节相同。

    • 根据偶极子近似理论,当金属颗粒尺寸远小于入射光波长激发LSPs时[28],可认为粒子大小L与共振波长λpeak具有L ~ 0.1λpeak的数值经验关系。由于共振波长需位于蓝光波段,根据上述尺寸关系,初步确定Ag纳米圆柱半径r的范围在12.5 ~ 22.5 nm并以2.5 nm步长调节,设高度H = 50.0 nm,并且为固定相邻Ag纳米颗粒内偶极电磁场的相互极化作用对入射光的耦合强度,图2中金属颗粒最小间距D不变,设D = 20.0 nm。基于FDTD数值方法计算得到Si的光吸收率ASi及其变化情况,如图3所示。

      图3(a)给出了基于不同半径r的Ag纳米圆柱阵列Si的光吸收率,当r = 12.5 nm、15.0 nm、17.5 nm、20.0 nm与22.5 nm时,Si的最高光吸收率分别为ASi ≈ 74% (λ = 451 nm)、ASi ≈ 76% (λ = 460 nm)、ASi ≈ 77% (λ = 470 nm)、ASi ≈ 78% (λ = 479 nm)与ASi ≈ 79% (λ = 486 nm)。通过图中曲线发现,Si的光吸收谱存在两个强度不同的吸收峰,与文献[29-35]计算得到Ag-NPs的吸收或散射光谱相比具有类似情况。根据公式(5)定义的ASi,在Ag具有较低的蓝光吸收损耗并忽略透射率的情况下,分析认为Si的双吸收峰现象主要是与金属粒子的形状结构、阵列衬底的介电常数大小引起的Ag-NPs消光特性变化相关。根据公式(6)的参数形状因子χ可知,金属颗粒的消光光谱依赖于自身结构,若粒子的曲面结构较为复杂、具有多个不同的对称轴时,处于LSPR状态的自由电子在其内部会产生不同的振荡模式,消光谱反映出多个共振峰,例如:椭球型金属纳米颗粒因具有三个不同的对称轴而会产生三个共振频率[29];其次,根据文献[35]计算的Ag-NPs消光谱(图8),我们发现当衬底折射率n > 2时,随着n的增加,消光谱的单共振峰逐渐分裂为双共振峰,分析认为,与常见低折射率氧化物(例如:SiO2n < 2)衬底相比,本文使用的衬底材料—Si的折射率较高、介电常数较大,在激发LSPs的过程中,Ag纳米颗粒表面积累的电荷在附近产生电场,使Ag-NPs/Si的界面出现较明显的极化现象,诱导电荷形成的电场反作用金属纳米粒子,可能会影响内部的共振模式而产生双吸收峰现象,因为从量子力学的角度看,LSPs是物质内部电子集体运动的量子态[9],在界面处极化电场作用下,颗粒内LSPs量子态的波函数可能会发生重叠而引起量子相互作用,使Ag-NPs的消光特性受到影响而产生双吸收峰现象。结合上述分析认为,Ag纳米颗粒的几何结构与衬底较高的介电常数是Si的光吸收谱出现双峰现象的主要原因。

      图3(b)展示了共振波长λpeak与半径r的变化关系,通过图中曲线看出λpeakr的增加而红移的物理现象,即λpeak = 451 nm (r = 12.5 nm)增加至λpeak = 486 nm (r = 22.5 nm)。分析认为,半径r的增加使Ag-NPs内偶极子的相互作用距离延长,导致振荡电子回复系数减小、共振频率降低,引起LSPs共振峰位红移[36]

      图3(a)计算结果代入公式(7)得到图3(c),图中的吸收谱线表明半径r的变化使同一入射波长下Si的光吸收增益Gabs受到影响。对于该变化关系,分析认为:根据Gans理论[37],金属纳米椭球颗粒的消光系数σext(λ)表示为:

      $$\tag{8} {\sigma _{ext}}(\textit{λ}) = \frac{{2\text{π} V\varepsilon _{med}^{3/2}}}{{3\textit{λ} }}\sum\limits_j {\frac{{\left({1/P_j^2} \right){\varepsilon ^{''}}}}{{{{\left({{\varepsilon ^{'}} + \dfrac{{1 - {P_j}}}{{{P_j}}}{\varepsilon _{med}}} \right)}^2} + {{\left({{\varepsilon ^{'}}} \right)}^2}}}} $$ (8)

      式中,V表示颗粒体积,εmed表示空间环境介电常数,${\varepsilon ^{'}} $表示金属颗粒介电常数实部,${\varepsilon ^{''}} $表示金属颗粒介电常数虚部,Pj表示极化因子,与颗粒的横纵轴比有关。根据(8)式定义的消光系数σext(λ)表明,在调节半径r(高度H不变)的过程中,不仅颗粒体积V发生变化,也造成颗粒纵横比即极化因子Pj的改变,导致消光系数σext(λ)在参数VPj共同调制作用下,使不同半径r的Ag纳米颗粒对Si的光吸收增益Gabs具有差异性。

      根据上述计算数据分析认为,当Ag-NPs半径r = 22.5 nm(高度H = 50.0 nm,周期P = 65.0 nm)时,Si在蓝光λ=486 nm具有较高的光吸收率ASi ≈ 79%。

    • 为进一步优化Ag-NPs阵列对Si的光吸收增益效果,探究Si的蓝光吸收随Ag纳米圆柱高度H的变化情况,根据3.1.1节的数据结果,半径与周期分别固定为r = 22.5 nm与P = 65.0 nm,在30.0 ~ 70.0 nm范围内以10.0 nm为步长调节高度H,根据FDTD算法计算得到基于不同高度Ag纳米颗粒阵列Si的光吸收谱,如图4所示。

      图4(a)展示了Si的光吸收率ASi随调节颗粒高度H的变化情况,当H = 30.0 nm、40.0 nm、50.0 nm、60.0 nm与70.0 nm时,Si的最高光吸收率分别为ASi ≈ 64% (λ = 452 nm)、ASi ≈ 72% (λ = 466 nm)、ASi ≈ 79% (λ = 486 nm)、ASi ≈ 83% (λ = 498 nm)与ASi ≈ 82% (λ = 544 nm)。图4(b)给出了共振波长λpeak与高度H的变化关系,图中曲线表明λpeak随Ag-NPs高度H的增加而红移,λpeak = 452 nm (H = 30.0 nm)红移至λpeak = 544 nm (H = 70.0 nm)。由于金属圆柱状纳米颗粒存在纵轴和横轴,其结构决定了两种不同方向的表面等离激元共振模式:沿纵轴方向的纵向表面等离激元与沿横轴方向的横向表面等离激元模式,表面等离激元模式的共振波长会随着横纵宽度比的变化而偏移[34],因此高度H的增加导致电子振荡振荡频率降低,共振峰位发生红移。

      图4(a)计算结果代入公式(7)得到图4(c)的光吸收增益,图中曲线展示了在同一入射波长下,高度H的变化对Si的光吸收增益Gabs的影响。在λ = 475 nm处,当H = 50.0 nm时,Gabs最高为30%;当H < 50.0 nm时,Gabs随高度H的增加而提高;当H > 50.0 nm时,Gabs随高度H的增加而降低,即Ag-NPs高度H的增加使Gabs表现出先增大后减小的变化趋势。对于此现象,结合Gan理论[37]分析认为:由公式(8)定义的消光系数σext(λ)表明,高度H(固定半径r)决定了金属纳米颗粒体积V与极化因子Pj的大小,二者共同调制入射光与Ag-NPs的耦合强度,影响Ag-NPs的消光能力,使不同高度H的Ag纳米颗粒对Si的光吸收增益具有差异性。

      根据上述计算数据分析认为,当Ag-NPs高度H = 60.0 nm(半径r = 22.5 nm,周期P = 65.0 nm)时,Si在蓝光λ=498 nm具有较高的光吸收率ASi ≈ 83%。

    • 实际上,金属纳米颗粒阵列对入射波的光响应不仅取决于单金属纳米颗粒的材质、尺寸、形状与周围的环境介质,阵列颗粒的分布状况也会影响入射光场的变化[40],为更进一步优化Ag-NPs阵列对Si的光吸收增益效果,探究Ag纳米颗粒周期P对Si的蓝光吸收影响。由于P包含Ag纳米颗粒直径2r和相邻粒子最小间距D,若固定Ag-NPs尺寸,在优化过程中使D发生变化,改变相邻Ag纳米颗粒偶极场之间的相互作用对入射光的耦合强度,影响Si的光吸收。根据前文3.1.1与3.1.2节的计算结果,半径与高度分别固定为r = 22.5 nm和H = 60.0 nm,在60.0 ~80.0 nm范围内以5.0 nm步长调节周期P,根据FDTD算法计算Si的光吸收谱,结果如图5所示。

      图5(a)展示了金属颗粒周期P对Si的光吸收谱的影响,当P = 60.0 nm、65.0 nm、70.0 nm、75.0 nm与80.0 nm时,Si的最高光吸收率分别为ASi ≈ 82% (λ = 539 nm)、ASi ≈ 83% (λ = 498 nm)、ASi ≈ 80% (λ = 486 nm)、ASi ≈ 78% (λ = 477 nm)与ASi ≈ 75.5% (λ = 462 nm)。图5(b)给出了共振波长λpeak与周期P的变化关系,图中曲线展示了λpeak由539 nm (P = 60.0 nm)蓝移至462 nm (P = 80.0 nm)。根据CD-Method理论[41],Ag纳米颗粒内偶极子极化率与周期具有如下的关系:

      $$\tag{9} \prod = \frac{{ - A{E_0}}}{{\omega - \{ {\omega _o} - {\rm{Re}} (AS)\} + i\{ \gamma + {\rm{Im}} (AS)\} }}$$ (9)

      式中,П表示金属纳米阵列的偶极子极化率,A是与阵列周期相关的偶极子作用矩阵,模为正常数,E0是外场强度,ω表示入射场频率,ω0表示单金属纳米颗粒的局域表面等离激元共振频率,受颗粒的材料、尺寸与几何形状及其位于周围环境的介电常数影响[9]γ为其消光光谱半宽度,S表示迟滞偶极子[42]。周期P的变化使公式(9)式中AS发生改变,根据CD-Method理论[41],在周期P < 100 nm范围内,ω0γ固定不变,λpeak会随周期P的增加而蓝移。

      图5(a)计算结果代入(7)式得到图5(c)Si的光吸收增益Gabs,图中曲线展示了周期P的变化对Si在同一入射波长下的光吸收增益Gabs产生的影响。在入射光λ = 498 nm处,若P = 65.0 nm则Gabs为34%;当P < 65.0 nm时,Gabs随周期P的增加而提高;当P > 65.0 nm时,Gabs随高度P的增加而降低,Gabs总体表现出先增大后减小的变化趋势。分析认为:周期P的增加会影响相邻颗粒偶极子的极化效果[43],使颗粒间隙的局域电磁场强度发生变化,当周期P = 65.0 nm时,局域电磁场的相互作用使金属颗粒极化率α最大,Si的光吸收增益Gabs最高;当P < 65.0 nm时相邻Ag-NPs内偶极子之间过强的耦合,增加了Ag-NPs的光吸收损耗Ametal[44],导致Si的光吸收减少、光吸收增益Gabs降低;当P > 65.0 nm时,相邻Ag纳米颗粒内偶极子间的相互作用随周期P的增加而降低,尽管Ag-NPs的非辐射损耗效应得到抑制[40],但入射场与Ag-NPs的耦合效应减弱,LSPs强度因周期P的增加而降低[44],使反射率R有所提高,导致Si的光吸收增益Gabs随阵列周期P的增加而降低。

      根据上述计算数据,当Ag纳米颗粒阵列的半径r = 22.5 nm、高度H = 60.0 nm与周期P = 65.0 nm时,Si的光吸收率ASi最高为83%,吸收峰位为λpeak = 498 nm,该峰值波长处于蓝光波段边缘。为了适应目前对蓝光LED的高效光探测需求,有必要继续调整优化,使Si对蓝光最大吸收发生在440~480 nm区域。

    • 在前面计算Ag-NPs各几何参数对Si吸收光的影响的基础上,经对Ag纳米颗粒的半径r、高度H、周期P与相邻粒子间距D的多次优化计算,最终得出:当r =18.5 nm,H = 45.0 nm,P = 49.0 nm时,Ag-NPs/Si复合结构Si的光吸收率最高约为94%,共振波长λpeak = 465 nm,如图6(a)所示,图中单一介质Si的光吸收谱源于FDTD算法对入射光场与Si[25]相互作用的计算结果。通过图中的计算结果发现,在Ag-NPs/Si结构中,Si未能实现完美的蓝光吸收,分析认为:根据公式(5)表达Si的光吸收率ASi的数值关系:ASi = 1 − AmetalR,由于存在Ag-NPs的光能量吸收损耗Ametal与反射率R(根据Si的色散特性,Ag-NPs/Si模型中Si的设计厚度远大于蓝光的透入深度,蓝光被Si几乎全部吸收,透射率T可忽略),使得波长λ = 465 nm的入射光未能被Si全部吸收(ASi < 100%),并且在Si的光吸收谱中也存在双吸收峰,对该现象前文已做出解释,不再赘述。图6(a)计算结果代入(7)式得到图6(b)Si的光吸收增益,在λ = 465 nm处具有最高的光吸收增益Gabs = 57%。

      探究LSPR效应对Si在蓝光波段的光吸收影响,分析认为,Ag材料在蓝绿波段极低的吸收损耗[26]Ametal,并根据Si的色散关系可认为透射率T = 0,因此通过公式(5)可得出:Si的蓝光吸收增强现象源于该波段其表面反射率R的降低。入射光频率ωin与局域表面等离激元共振频率ωLSPR相匹配,满足Re[ε] = −2εm而产生的LSPR效应使Ag-NPs具有极大的消光截面(小尺寸颗粒,以吸收截面为主)[22],入射场能量转换为颗粒内部偶极子的振荡动能,有效降低了Si表面的光反射率R。然而,根据公式(1)定义的金属颗粒极化率α,通过Ag材料复介电常数的色散关系[28]可知,若其它频率的入射波段即ωinωLSPR作用Ag-NPs,会引起金属介电常数Re[ε] ≠ −2εm,导致极化率α较小,入射光与Ag-NPs的耦合效应降低,使颗粒处于非共振状态,导致反射率R在理论上再次提高。在Si表面上方1 μm处检测光反射能量,在相同计算条件下基于FDTD算法求得反射率R,如图7所示。通过图6图7知:当λin = 465 nm入射Si表面时,光的反射率R1 ≈ 0.41,根据公式(5)可得Si的光吸收率A1 ≈ 0.59(无Ag-NPs,Ametal = 0);入射Ag-NPs/Si结构时,光反射率R2 ≈ 0.01,反射率降低,根据FDTD数值方法计算Ag-NPs的光吸收损耗Ametal ≈ 0.05,如图8所示,图中曲线展示了Ag-NPs的理论蓝光吸收损耗,与M.A García[34]计算的直径40 nm的Ag-NPs的光吸收损耗类似(文献[34]中图8所示),将本文的Ag-NPs的光吸收损耗Ametal代入(5)式得基于Ag-NPs阵列Si的光吸收率A2 ≈ 0.94,与A1 ≈ 0.59相比,Si的光吸收增强。通过本文图8的曲线,我们还发现尽管入射波长λ > 465 nm时Ag-NPs的光吸收损耗Ametal小于0.05,但根据图7展示的反射曲线,反射率R在逐渐提高,使基于公式(5)计算得到Si的光吸收ASi < 0.94,例如在λ = 475 nm处,R = 0.04,Ametal = 0.03,代入上式得ASi ≈ 0.93。

      由上述数据可知,LSPR效应使Si表面的反射率降低,绝大多数入射光能量被Ag-NPs耦合至Si内部被吸收。

    • 载流子生成数量对半导体光电探测器的量子效率有一定影响。若用电子—空穴对生成率Ge(x)表征光生载流子数量[38]

      $$\tag{10} {G_e}(x) = {\varPhi _0}\alpha \exp (- \alpha x) = \frac{{(1 - R){P_{{\rm{opt}}}}}}{{S \cdot h\upsilon }}\alpha \exp (- \alpha x) $$ (10)

      式中,Φ0表示入射光子通量,R为反射率,Popt为入射光功率(W/m2),S为入射面积(m2),为单光子能量(eV),α为介质的吸收系数(m−1)。入射光功率密度为1 W/m2,视硅的光吸收能量(无向空气传播的内能损耗)全部换为空穴-电子对,计算条件与2.2节相同。根据FDTD算法与(10)式计算在λin = 465 nm时,半径r = 18.5 nm、高度H = 45.0 nm、周期P = 49.0 nm的Ag-NPs阵列下Si的初始光生载流子数量,结果如图9(a)所示,曲线横轴表示入射光在Si内部的传播距离。图中载流子数量对比曲线说明LSPR效应可提高Si的光生载流子数量,并间接表明在硅内部更深处会产生一定数量的光生载流子。

      G为光生载流子数量(m−3),M为光生载流子数量增益比:

      $$\tag{11} M = \frac{{{G_{Ag - NPs/Si}} - {G_{{\rm{Si}}}}}}{{{G_{Si}}}}$$ (11)

      式中,GAg-NPs/SiGSi分别为基于Ag-NPs阵列Si与单一介质Si的光生载流子浓度,将图9(a)中计算的载流子数量代入(11)式得到基于Ag-NPs阵列Si的光生载流子数量增益M ≈ 0.53,如图9(b)。由(10)式定义的Ge(x)分析认为:光生载流子数量的增益与Ag-NPs/Si结构的反射率R降低有关。变化物理机制在前文已做说明,在此不做赘述。因此得出结论:在理论上LSPR效应可提高光生载流子数量,增加载流子被电极收集的概率,增强Si基光电探测器的量子效率。

      上述研究结果对设计高蓝光响应度硅基可见光光电探测器等问题具有重要的理论参考价值。

    • 本文研究了Ag-NPs/Si复合结构对可见光吸收的影响。在蓝光波段下,分别计算Ag-NPs几何参数半径r、高度H与周期P与Si的光吸收的关系,当增加半径r时,Si的光吸收率增大,共振峰位红移;当增加高度H时,Si的光吸收率先增大后减小,共振峰位红移;当增加周期P时,Si的光吸收率先增大后减小,共振峰位蓝移。对Ag-NPs/Si复合结构优化结果表明,当Ag-NPs结构为r = 18.5 nm,H = 45.0 nm,周期P = 49.0 nm,Si的最高吸收率94%,最大吸收峰值波长λ = 465 nm,光吸收增益0.57;计算Ag-NPs/Si在λ = 465 nm处的光生载流子数量增益约为0.53。硅的光吸收增强及光生载流子数量提高与由LSPR效应引起Si表面反射率降低相关。研究结果对设计基于Ag-NPs增强蓝光探测响应度的硅基可见光光电探测器具有良好的参考价值。

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