Size dependence of confined acoustic phonons in CuCl nanocrystals Itoh lab Takanobu Yamazaki Itoh lab Takanobu Yamazaki J. Zhao and Y. Masumoto, Phys. Rev. B 60, 4481 (1999).

1 Contents Introduction Experiment Summary Quantum dot Quantum size effect Line broadening Persistent spectral hole burning Motivation Experimental setup Sample Result Discussion

2 Quantum dot (QD) Bulk crystal QD Energy level Acoustic phonon mode ω q ω q continuous discrete k E k E

3 Quantum size effect ( a ex ＜ R,L ) Weak confinement R : radius L : side length E bulk = eV (2 K) M = m e +m h =2.3m 0 2R L ΔE E ex : eV (CuCl) 2R E x a ex : exciton Bohr radius For spherical dot For cubic dot

4 Quantum size effect ( a ex ＜ R,L ) For spherical dot For cubic dot ΔE E ex : eV (CuCl) 2R E x Dot size little big Blue shift largesmall Weak confinement a ex : exciton Bohr radius

5 Line broadening Homogeneous broadening Inhomogeneous broadening Photon energy Intensity due to exciton lifetime and dephasing time due to size distribution Full absorption absorption line of single size QDs

6 Persistent spectral hole burning phenomena (PSHB) Absorption (a.u.) Photon energy (eV) Before laser exposureAfter laser exposure Pump laser Ionization Exciton in QD With laser exposure Absorption (a.u.) Photon energy (eV) Absorption (a.u.) Photon energy (eV) Exciton in QD Exciton in QD Exciton lifetime short long

7 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.

8 Experimental setup Dye laser Q-switched Nd 3+ :YAG laser 355 nm (THG) Pulse duration : 5 ns Pulse reputation : 30 Hz Spectral linewidth : meV Halogen lamp Sample in cryostat (2 K) Pump Probe 75cm spectrometer CCD

9 Sample (CuCl QD) Z 1,2 Z3Z3 Γ k Band structure (CuCl Bulk) E Γ6Γ6 Γ7Γ7 Γ8Γ8 Valence band Conduction band electron hole Exciton binding energy : 197 meV Exciton Bohr radius : 0.7 nm Spherical shapeCubic shape QDs in glass QDs in NaCl Shape of CuCl QD

10 Experimental result - 1 (a) Absorption spectrum (b) PSHB spectra CuCl QDs in glass (Average radius : 1.4 nm) zero phonon hole Stokes-side acoustic phonon hole anti-Stokes-side acoustic phonon hole pump energy A : B : C : D : E : F : G : H : Stokes-sidebandanti-Stokes-sideband G E Energy phonon photon

11 Experimental result - 1 (a) Absorption spectrum (b) PSHB spectra CuCl QDs in glass (Average radius : 1.4 nm) 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

12 Experimental result - 2 CuCl QDs in NaCl (inhomogeneously broadened 3.22 ～ 3.28eV) (a) Absorption spectrum (b) PSHB spectra pump energy A : B : C : D : E : F : G : H : Interval between the zero-phonon line and the Stokes-side acoustic phonon hole ex) H : 0.7 meV smaller than those in glass!!

13 Discussion - 1 (under stress-free boundary condition) Free vibration of a homogeneous elastic sphere Lowest eigenmode spheroidal( 楕円体 ) (n=0) torsional ( ねじれ ) (n=1) l : angular momentum quantum number n : brunch number (n,l)=(0.1) (n,l)=(0.2) ν : frequency of the lowest eigenmode V t : transverse sound velocity of bulk CuCl c : speed of light Free vibration of an isotropic cube Lowest eigenmode torsional ( ねじれ ) flexural ( 屈曲） shear( ずれ ) H. Lamb, Proc. London Math. Soc.13,189 (1882) H. H. Demarest, Jr., J. Acoust. Soc. Am (1971)

14 Discussion - 2 ν 10, 20 ν d1, a1, s1 in KCl in glass in NaCl 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 Square root of confinement energy Inverse of diameter and side length

15 Discussion - 2 ν 10, 20 ν d1, a1, s1 in KCl in glass in NaCl Square root of confinement energy Inverse of diameter and side length About discrepancy... Supposing ideal cube (in vacuum) Existence of deformation In glass Influence of matrix In NaCl negligible important

16 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.