# Fileset

[Supplemental_Material_R1.pdf](https://mdr.nims.go.jp/filesets/832e4a5e-f8e9-415d-b58c-a5c4802cb20c/download)

## Creator

Takumi Oshima, Daiki Yoshikawa, Yoshihiro Ishitani

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Emission control of longitudinal optical phonon resonant thermal terahertz radiation from two-dimensional surface metal micro-structures on GaAs](https://mdr.nims.go.jp/datasets/a98bf4f0-73fe-4a7b-8124-4d45b792e261)

## Fulltext

1    Supplemental material  Emission control of longitudinal optical phonon resonant thermal  terahertz radiation from two-dimensional surface metal micro- structures on GaAs    Takumi Ohshima, Daiki Yoshikawa, and \*Yoshihiro Ishitani  Graduate School of Science and Engineering, Chiba University  1-33 Yayoicho, Inage-ku, Chiba, 263-8522, Japan  \*e-mail) ishitani@faculty.chiba-u.jp    A. Background emission spectra of the C-type (1.6, 8.3) structure  Figure S1 shows the peak fitting of the radiation emission spectrum of the A-type (1.6,  8\.4) sample and the background emission spectra of the C-type (1.6, 8.3) structure. Open  circles in Figure S1a show the experimental spectrum of Ex – Ey. The fitting was conducted  in the range of 250–290 cm-1. The background spectra of the type-C (1.6, 8.3) sample were  obtained by subtracting the LORE intensity from the Ex-component of radiation. Two  functions of quasi-Voigt and the Lorentzian were adopted. Adjusted parameters for the A-type  (1.6, 8.4) samples are peak: 284.6(±0.2) cm-1, FWHM: 12.8(±0.8) cm-1, rL: 0.58(±0.3),  intensity: 3.82 (±0.18) for quasi-Voigt function and 284.8(±0.1) cm-1, FWHM: 12.2(±0.4) cm- 1, intensity: 4.46 (±0.12) for Lorentzian. The background spectra show oscillations in the  Reststrahlen band. The peak intensity ratio of the Lorentzian against the quasi-Voigt function  is 1.17. The peak at 310 cm-1 is attributed to the over-purging of the optical path in the sample  measurement.   In the analysis of the C-type (1.6, 8.3) structure, the peak energy was adjusted to the  experimental data of 290.5 cm-1. Figure S1c shows the background analysis for the Lorentzian 2    LORE: 95%, 107 %, and 115% of the LORE of the A-type sample. Invalid double-peak feature  is observed for 95% LORE, and invalid spectrum dip is observed for 115% LORE.     B. Emission probability  The LO-phonon resonant radiation emission rate K is expressed using the Bose-Einstein  occupation factor of the LO phonon in Equation (S1).  K =  �  �ħ �ħω�  �  ����   � �   ε�  �  �  ����− �  �����  δ�ħω − ħω��  �  �  ����ħ��/�� �!�  " d� ,                     (S1)   where Vω and VL are the volumes covered by a photon and an LO phonon, respectively. dν is  the associated number of states, respectively. W is the effective window width. S is the area  (a)   (b)      (c)   Figure S1  Background emission spectra for various LORE peaks, (a) ambiguity of quasi- Voigt-type LORE intensity, (b) spectrum separation of LORE and the background emissions  for type-A (1.6, 8.4) structure, and (c) ambiguity of the Lorentzian LORE intensity for sample  C (1.6, 8.3) structure.   q-V. : quasi-Voigt function, L.: Lorentz function.  3    with the polarization charges. C is the factor representing the generation efficiency of the  polarization charge, and S is the effective area covered by the polarization charges. By using  Equation (S1), we obtain the radiative lifetime K-1 ≈50⋅Vω VL /(Wd)2 in the unit of fs. In  addition, VL is estimated to be equal to (SW). Thus, the radiative emission efficiency depends  on the ratio of the volume of the photon coherence and that of the phonon in the formula of  K-1 ≈50⋅Vω /VL (fs). The present lifetime values estimated from the FWHM values of LORE,  11-13 cm-1 give the lifetime of 470-410 fs. When considering the LO phonon coherence of  one window width, 2 µm, and radiation coherence as the wavelength, giving Vω /VL as  approximately 18, the radiative lifetime is estimated to be 450 fs.    Our previous analysis by comparing the LORE intensity with the thermal emission  intensity of a pure graphite sample at 630 K gives a radiative lifetime of 1 ps.  When  considering an estimated LO phonon lifetime of 1 ps, which is obtained by extrapolating a  reference data \[S1\], the radiative lifetime is estimated to be 1 ps, which is interpreted as a  nonradiative LO phonon lifetime. By considering radiative and nonradiative lifetimes, the LO  phonon lifetime in the present structures is obtained as 0.5 ps, which satisfactorily agrees with  the lifetime obtained from the FWHM of 11-13 cm-1. Thus, the LORE intensity estimation for  2-D structures is considered valid.    C. Dependence of emission intensity on the LO-phonon related volume  Figure S2 shows the dependence of the LORE intensity on the volume occupied by the electric  flux connecting pairs of Au plates (VC). VC is expressed as (WW+WM)×D. D is the penetration  depth of the electric flux starting from a metal plate, obtained using the results of the FDTD  simulation. D of 3 µm is considered appropriate \[18, 19\]. Here, this volume is for 1µm depth  perpendicular to the plane of this figure. Figure S2a shows the geometrical image of VC. LORE  intensity is plotted as a function of for various samples, including mesa structures. For mesa 4    structures, the mesa volume is added to VC. The emission intensity is plotted in Figure S2b.  The plots without notation are for mesa structures. Emission intensity depends on VC, as well  as on both WW and WM. For the B-type sample, the stripe structure (WW, WM) = (1.8, 10.2) has  a VC of 36 µm3. At this volume, the emission intensity of no-mesa structures saturates and  remains nearly constant. In analyzing the B-type sample, given the wide metal width of 10.8  µm and a narrow window width of 1.8 µm, the emission intensity of the A-type (2.0, 8.0) is  suitable for use.    D. Variation of peak energy of LORE   Figure S3 shows the emission spectra for A-type  (4.0, 4.0), (4.0, 8.0), and (4.0, 10.0) structures. As the  metal width decreases, the peak energy increases:  283\.4 cm-1 for (4.0, 10), 285.4 cm-1 for (4.0, 8.0), and  286\.3 cm-1 for (4.0, 4.0). The spectra show broadening  toward higher energy. Figure 1a suggests that the  positive and negative polarization charges can cancel    Figure S2 Dependence of thermal  emission spectra at 630 K on metal  width. The emission window width is  constant as 4.0 µm.  (a)  (b)   Figure S2   LORE intensity as a function of the volume occupied by the electric flux related  to the LO-phonon resonant electric dipole, (a) cross-sectional image of the sample  structure with the definition of volume of electric flux connecting pairs of metal plates, VC,  and (b) LORE intensity per line as a function of VC.   5    when the metal width is not large enough to separate them, leaving an incomplete electric  dipole. When the dipole formation is incomplete, the emission peak shifts to higher energy  side for the structures of GaN 20.  The increase in emission intensity at higher energies than  the peak suggests a transition to the bare GaAs wafer spectrum as the metal width decreases.       (S1) Vallee F. Time-resolved investigation of coherent LO-phonon relaxation in III-V  semiconductors. Phys. Rev. B 1994; 49, 2460-2468