Recent improvement of silicon absorption in opto‐electric devices
1 Introduction
Si is an integral part of all electronic devices. It plays an important role in opto-electronic devices such as photodetectors and photovoltaic devices1, 2. However, since it is an indirect band-gap material, phonon assistance is required in the photo-excitation process to compensate the wave-vector difference between the valence band maximum and the conduction band minimum of holes (Γ point) and electrons (X point), respectively (
Fig. 1. Comparison of far- and near-field excitations.
(a ) Far-field (FF) excitation of Si. Here k photon, k c, k v, and k phonon are the wave vectors of photon, conduction band, valence band, and phonon, respectively. (b ) Optical near-field (ONF) excitation of Si. Figure is reproduced from ref.3 under the terms of the Creative Commons Attribution 4.0 International license.
2 Theoretical advances
Optical near-field (ONF) effect can potentially improve the carrier excitation in indirect band-gap materials. This is attributed to the fact that ONF is expected to have large wave vector components (Δk), which implies very small Δx, due to the field localization. This was validated in a study which demonstrated that ONFs, as a dipole-mode plasmon, generate carriers directly8. It was shown that in small particles, the plasmons induce an electric field that exhibits Fourier components with large wave numbers. Furthermore, it was demonstrated that such an electric field generates carriers without phonon assistance. Further investigation of the ONF excitation was performed in a system comprising of metallic nanospheres embedded in crystalline Si9. Here, the excitation was evaluated under the framework of linear perturbation theory, and it was found that the ONF effect is too weak to be measured in a real system. However, these calculations were based on analytical model systems, and not on the real carrier excitations.
To this end, Yamaguchi et al.10 evaluated the carrier dynamics using first-principles calculations, where they calculated the electron excitation by considering the indirect interband transition between states with different Bloch wave numbers. Instead of using the Bloch condition, which cannot describe the indirect interband transitions, they implemented the Born-von Kármán boundary condition11, 12. Further, they also performed a time-dependent calculation of the ONF excitation using one-dimensional Kronig-Penny (1D-KP) model (
Fig. 2. ONF excitation in indirect band-gap structure.
(a ) Potential, (b ) a schematic of the 1D-KP model, and (c ) dispersion relation. Here, E g: band-gap energy and E d: direct band-gap energy. Frames (d ) and (e ) show the normalized absorption spectra of the 1D-KP model due to the far- and near-field excitations, respectively. (f ) Absorption spectra due to the electric field components from the dipole radiation, which are r -3 (red solid line), r -2 (blue dashed line), and r -1 (green dotted line). Figure is reprinted with permission from ref.10, Copyright © 2016 American Physical Society.
A more detailed investigation of the ONF excitation in realistic three dimensional Si systems (
Fig. 3. ONF excitation in a realistic Si system.
(a ) The theoretical model consisting of a Si bilayer and the electric dipole measured at a distance of 5 Å above Si surface. (b ) Potential of the ONF induced by the electric dipole shown in (a). (c ) The Fourier transform of (b). (d ) Comparison of the absorption intensity for far-field (blue) and near-field (red) excitations. (e ) Absorption intensity as a function of the variation in the wave vector (∆k ) for the excitation at 1.6 eV. Figure is reproduced from ref.14 under the terms of the Creative Commons Attribution 4.0 International license.
where ω is the frequency of the oscillating dipole, C is a constant, and T = 30 fs is the pulse duration. The electric field distribution induced by the oscillating dipole, as described by Eq. (1) is non-uniform in spatial domain (see
3 Experimental advances
3.1 Scattering effect: Black Si
A simple yet effective way to improve the optical absorption in the solar cells is to increase the optical path length through the depletion layer between the p-n junction. To improve the light scattering efficiency, the scatterers have been fabricated at the surface of the detector, such as pyramidal Si hillocks made by the anisotropic etching18, vertically aligned single crystalline Si nanowire array19, or needles made by the laser irradiation with the ultra-short pulse width20. In particular, the latter (Si surface with needles) works as an extremely good scatterer because of its small sharp tip with no reflection from the surface. Consequently, it appears black, and is therefore called a black Si. This black Si has been used to develop highly efficient Si solar cells with 22.1% efficiency21, 22.
3.2 Plasmonic effect
To improve the scattering efficiency, many researchers utilized the field enhancement using the plasmon resonance23, 24. The scattering and absorption cross-sections are given by point dipole model25:
where α is the polarizability, a is the radius of the particle, ε is the dielectric function of the particle, εm is the dielectric function of the surrounding media, and λ is the wavelength. It is evident from Eq. (2) that ε should be negative (-2εm), i.e., the scatterer should be a metal, to utilize the plasmon resonance for the light scattering. Further from Eq. (3), it is clear that the plasmon induced light scattering is indispensable for a strong optical absorption. For a more effective trapping of the scattered light at the metallic nanoparticles on the surface, the scattered light excites the waveguide mode using a thin Si substrate of Si-on-insulator (SOI)26, 27 wafer. Furthermore, a higher coupling efficiency can be realized by controlling the size and the shape of the metallic nanoparticle28, 29. In particular, it was observed that smaller size, as well as cylindrical and hemispherical shapes of spheres lead to a longer path length in the substrate. Further improvement of the carrier-excitation was realized by introducing a photonic design to induce light trapping with three-dimensional structures consisting of nanowires and nanoparticles30, 31. Since the plasmon resonance for the Au sphere occurs at ~520 nm, ellipsoid shape32, chains of nanoparticles33, or elongated shapes such as nanorod34 with longer resonance wavelength have been implemented to obtain larger absorbance in this wavelength range. In addition, the periodic structure of the metal, i.e., metamaterial-plasmonic absorbers35, 36, has been investigated to enhance the optical absorption. The periodic structure works as a grating coupler of light with a normal incident angle. Consequently, it results in a strong absorption exceeding 80%. We investigated the self-assembly method37 to improve the efficiency of nanoparticles deposition. Using the laser-assisted deposition of the electrode metal with a reverse biased p-n junction, we realized a selective photocurrent generation in the transparent wavelength range38. We observed a drastic change in the surface morphology of the metal, and confirmed the increase in the photocurrent at the wavelength that is close to that used during the electrode deposition. Since Au has high absorption coefficient, alternative materials, such as transparent conducting oxides were considered to achieve the resonance at longer wavelengths39, 40.
3.3 Hot electrons
The internal photoemission on a Schottky barrier (
Fig. 4. Schematic of the hot electron driven photocurrent over a Schottky barrier.
(a ) The Schottky barrier (ϕ B) is lower than the band-gap energy. Therefore, a longer wavelength (λ 2) can be utilized instead of the band-gap wavelength (λ 1). Here, EC: conduction band energy, E V: valence band energy, and E F: Fermi level energy. (b ) Three dimensional plasmonic photocapacitor structure. Figure (b) is reprinted with permission from ref.44, Copyright © 2016 American Chemical Society.
3.4 Near-field effect
As discussed in the previous section, the ONF effect can improve the absorption efficiency at the band-gap wavelength. This implies that the localized field can induce large wave vector components, which in turn leads to direct excitation in indirect band-gap semiconductors (
Fig. 5. Sensitivity of the lateral p–n junction with Au nanoparticles.
(a ) Schematic of the device using a Si-on-insulator (SOI). As described in ref.3, a solution containing Au nanoparticles was dispersed on the device and the solvent was evaporated with a hot plate. We counted this procedure of the dispersion number N as one. (b ) Scanning electron micrographic (SEM) image of the device. (c ) Magnified SEM image of (b). (d ) Wavelength dependence of sensitivity of the devices. The solid blue circles show the device with the 100-nm Au nanoparticles (N = 5). The open black circles correspond to the device before the Au nanoparticle dispersion. (e ) Increased photosensitivity rate as a function of the excitation wavelength with different dispersion number N . Increased rate were obtained as the ratio between the photosensitivity of the device with and without Au nanoparticles. The solid curves show the calculated increased rate using Eq. (7). We used the Au nanoparticle coverage determined by SEM images as the ratios of the direct transition A : A =1.82% (N =10), 0.82% (N =5), and 0.48% (N =1). Figure is reproduced from ref.3 under the terms of the Creative Commons Attribution 4.0 International license.
where h is Planck constant and ν is frequency of light. Since the bias voltage was 0, the photo-current becomes the short circuit current described as46
where Q is the collection efficiency, R is the reflection coefficient, l is the absorbing layer thickness, e is the electron charge, and n is the number of photons per second per unit of the p-n junction. The ONF can induce a direct transition by the inclusion of Au nanoparticles. Thus, the photocurrent for this device is the same as that of the direct transition (ISC_D). However, since the coverage of the Au nanoparticles A is not 100 %, the photocurrent shows an increase in the regions where Au nanoparticles existed (the ratio was A), while it remained the same (the ratio was (1-A)) in other regions. Thus, the increased rate in the device can be expressed as follows:
where C is the proportional constant. As shown in
Fig. 6. Increased rate as a function of the size of Au nanoparticles.
(a ) Increased photosensitivity rate at a wavelength of 1100 nm versus diameter of the Au nanoparticles. (b ) Electric-field intensity distribution E 2 at the interface of Au nanoparticle (diameter D =100 nm). (c ) Averaged (0 ≤y ≤D /2) Fourier spectra along x-axis of the electric-field. The wave number difference between the Γ and X points: k x _ΓX=4.92 nm-1. (d ) Red solid circles: the diameter dependence of the power spectra at k x _ΓX= 4.92 (nm-1), |F (E )ΓX|2. Blue open circles: the normalized value of the |F (E )ΓX|2 by the square of the volume, |F (E )ΓX|2 r -6. Figure is reproduced from ref.3 under the terms of the Creative Commons Attribution 4.0 International license.
Although the theoretical results of the large Δk generated using the first-principle calculation14 supported the experimental results3 qualitatively, the enhancement value was not explained quantitatively. The disagreement might be due to the disagreement of the materials and the size. For example, in the first-principle calculation, the point dipole was used as a source of the ONF. More detailed calculations using the real material in a real system will be required to discuss quantitatively. In addition, the limitation of the material size in the first-principle calculation results in the disagreement of the system size. To resolve this disagreement, a smaller size of the source for ONF generation should be used, such as porous Si with several nanometer scale50-52.
4 Summary and future directions
Si is an indirect band-gap semiconductor and therefore exhibits poor optical absorption efficiency. This review presents an overview of various theoretical and experimental efforts to improve the performance of Si-based photodetectors and photovoltaic devices. The theoretical framework based on first principle calculations along with experiments including scattering effect, plasmon effect, hot electrons, and near-field effect were discussed. The ONF effect permits the generation of a large Δk by field localization, which in turn can improve the absorption efficiency of these devices. The ONF effect can intrinsically induce a direct transition due to nonuniformity of the optical field. In addition to the reviewed topics, we confirmed that near-field could enhance the optical absorption by the field enhancement effect53, which does not utilize plasmon resonance. The field enhancement by ONF was confirmed both in the first-principle calculation and in the experimental absorption spectra of the metal complex for CO2 reduction. Therefore, if the near-field source is placed with appropriate position, further enhancement of absorption is expected. Further, since the ONF has nonuniform optical field distribution in nanoscale, the ONF can generate even harmonics in materials with inversion symmetry54. Yamaguchi et al. have showed that the ONF inherently realizes strong second harmonic generation (SHG) and suggested ways to improve the efficiency of this process16, 55-57. Further improvements of Si-based opto-electronic devices may be achieved by combining and optimizing these effects. Recently, the band engineering method was proposed to enhance the absorption in another indirect band-gap material (Ge)58. Similar investigations have been made in other indirect band-gap materials including InSe59-61 and MoS262, 63. The enhancement was achieved by introducing a strain in the crystal, which changed the band diagram to the direct band-gap structure. Overall, indirect bandgap materials open new avenues for various applications, which are not limited to photodetectors64, 65, 66 and photovoltaic devices1, 2, but also include other realms such as light-emitting devices67, 68, water-splitting62, 69, etc.
5 Acknowledgements
The author wishes to express special thanks to Drs. Kenji Iida (Institute for Molecular Science), Masashi Noda (University of Tsukuba), Maiku Yamaguchi (University of Tokyo), Prof. Katsuyuki Nobusada (Institute for Molecular Science) and Kazuhiro Yabana (University of Tsukuba) for their active support and discussions. This work was partially supported by JSPS KAKENHI (Nos. JP18H01470, JP18H05157), a MEXT as a social and scientific priority issue (Creation of new functional devices and high-performance materials to support next-generation industries: CDMSI) to be tackled by using post-K computer (ID: hp170250), Asahi Glass Foundation, and Research Foundation for Opto-Science and Technology.
6 Competing interests
The author declares no competing financial interests.
[5] M Asghari, A V Krishnamoorthy. Energy-efficient communication. Nat Photonics, 2011, 5: 268-270.
[11] Martin R M.
[12] Ashcroft N W, Mermin N D.
[13] Jackson J D.
[25] Bohren C F, Huffman D R.
[29] K R Catchpole, A Polman. Plasmonic solar cells. Opt Express, 2008, 16: 21793-21800.
[45] Pankove J I.
[47] Taflove A, Hagness S C. Computational Electrodynamics: The Finite-Difference Time-Domain Method 3rd ed (Artech House, London, 2005).
[49] Maier S A.
[61] M J Hamer, J Zultak, A V Tyurnina, V Zólyomi, D Terry, et al.. Indirect to direct gap crossover in two-dimensional InSe revealed by angle-resolved photoemission spectroscopy. ACS Nano, 2019, 13: 2136-2142.
Article Outline
Takashi Yatsui. Recent improvement of silicon absorption in opto‐electric devices[J]. Opto-Electronic Advances, 2019, 2(10): 190023.