Size dependence of confined acoustic phonons in CuCl nanocrystals J. Zhao and Y. Masumoto, Phys. Rev. B 60, 4481 (1999). Itoh lab Takanobu Yamazaki Contents • Introduction Quantum dot Quantum size effect Line broadening Persistent spectral hole burning Motivation • Experiment Experimental setup Sample Result Discussion • Summary 1 Quantum dot (QD) Energy level Acoustic phonon mode Bulk crystal ω E continuous k QD q ω E discrete k q 2 Quantum size effect Weak confinement ( aex ＜ R,L ) For spherical dot Esphere Ebulk E For cubic dot Ecube Ebulk 2 2 2MR2 3 2 2 2ML2 ΔE Eex : 3.2022 eV (CuCl) x 2R Ebulk = 3.2022 eV (2 K) M = me +mh =2.3m0 R : radius L : side length 2R L aex : exciton Bohr radius 3 Quantum size effect Weak confinement ( aex ＜ R,L ) For spherical dot Esphere Ebulk E For cubic dot Ecube Ebulk 2 2 2MR2 3 2 2 2ML2 ΔE Dot size Eex : 3.2022 eV (CuCl) x 2R aex : exciton Bohr radius little big Blue shift large small 4 Line broadening Homogeneous broadening due to exciton lifetime and dephasing time Inhomogeneous broadening due to size distribution Intensity Full absorption absorption line of single size QDs Photon energy 5 Persistent spectral hole burning phenomena (PSHB) Pump laser Photon energy (eV) Absorption (a.u.) With laser exposure After laser exposure Exciton in QD Photon energy (eV) Exciton in QD Exciton lifetime short Photon energy (eV) Exciton in QD Absorption (a.u.) Absorption (a.u.) Before laser exposure Ionization long 6 Motivation Raman scattering Ordinal method to obtain information of the lattice vibrational modes PSHB spectra Ordinal method to study the size-dependent confined exciton energy The authors observe the dot size dependence of the confined acoustic phonons in nanocrystals by using PSHB. 7 Experimental setup Q-switched Nd3+:YAG laser 355 nm (THG) Dye laser Pump 75cm spectrometer CCD Pulse duration : 5 ns Pulse reputation : 30 Hz Spectral linewidth : 0.014 meV Probe Halogen lamp Sample in cryostat (2 K) 8 Sample (CuCl QD) Band structure (CuCl Bulk) E Exciton binding energy : 197 meV Exciton Bohr radius : 0.7 nm Γ6 Conduction band Z3 Z1,2 Valence band Shape of CuCl QD Γ7 QDs in glass QDs in NaCl Spherical shape Cubic shape Γ8 Γ k electron hole 9 Experimental result - 1 (Average radius : 1.4 nm) (a) Absorption spectrum (b) PSHB spectra pump energy A : 3.2583 B : 3.2626 C : 3.2669 D : 3.2712 E : 3.2755 F : 3.2798 G : 3.2841 H : 3.2882 zero phonon hole Stokes-side acoustic phonon hole anti-Stokes-side acoustic phonon hole Stokes-sideband Energy CuCl QDs in glass anti-Stokes-sideband E phonon photon G 10 Experimental result - 1 CuCl QDs in glass (Average radius : 1.4 nm) (a) Absorption spectrum (b) PSHB spectra zero phonon hole Stokes-side acoustic phonon hole anti-Stokes-side acoustic phonon hole Interval between the zero-phonon hole and the Stokes-side acoustic phonon hole The energy of the confined acoustic phonon in the nanocrystal ex) C : 2.2 meV Dot size Acoustic phonon energy 11 Experimental result - 2 CuCl QDs in NaCl (inhomogeneously broadened 3.22～3.28eV) (a) Absorption spectrum (b) PSHB spectra pump energy A : 3.2336 B : 3.2368 C : 3.2410 D : 3.2452 E : 3.2494 F : 3.2535 G : 3.2578 H : 3.2621 Interval between the zero-phonon line and the Stokes-side acoustic phonon hole ex) H : 0.7 meV smaller than those in glass!! 12 Discussion - 1 (under stress-free boundary condition) Free vibration of a homogeneous elastic sphere H. Lamb, Proc. London Math. Soc.13,189 (1882) Lowest eigenmode Free vibration of an isotropic cube H. H. Demarest, Jr., J. Acoust. Soc. Am. 49. 768 (1971) Lowest eigenmode spheroidal(楕円体) (n=0) 10 1.17vt / 2Rc 20 0.85vt / 2Rc (n,l)=(0.1) (n,l)=(0.2) torsional (ねじれ) (n=1) 20 0.82vt / 2Rc (n,l)=(0.1) torsional (ねじれ) d1 0.45vt / Lc flexural (屈曲） a1 0.59vt / Lc shear(ずれ) s1 0.61vt / Lc c : speed of light Vt : transverse sound velocity of bulk CuCl ν : frequency of the lowest eigenmode l : angular momentum quantum number n : brunch number 13 Discussion - 2 Square root of confinement energy In glass Good agreement with vibration mode of sphere In NaCl Nearer to the frequency of cube than sphere Confined acoustic phonon energy is associated with the shape of QD νd1, a1, s1 ν10, 20 Inverse of diameter and side length in KCl in glass in NaCl 14 Discussion - 2 Square root of confinement energy About discrepancy... Supposing ideal cube (in vacuum) Existence of deformation Influence of matrix In glass negligible In NaCl important νd1, a1, s1 ν10, 20 Inverse of diameter and side length in KCl in glass in NaCl 15 Summary • They studied the size dependence of the confined acoustic phonons in CuCl QDs embedded in glass and NaCl matrix by PSHB spectroscopy. • For CuCl QDs in glass matrix, the confined acoustic phonon mode is explained as the lowest-frequency vibration of the sphere with the free boundary condition. • That in NaCl matrix is explained as the softened lowest-frequency vibration of the cube with the strained boundary condition. 16
© Copyright 2024 ExpyDoc
