Size dependence of confined acoustic phonons in CuCl nanocrystals

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

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

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

4. Weak confinement E ΔE Ebulk = 3.2022 eV (2 K) M = me +mh =2.3m0 Eex : 3.2022 eV (CuCl) R : radius 2R x L : side length L 2R Quantum size effect ( aex＜ R,L ) For spherical dot For cubic dot aex : exciton Bohr radius

5. Weak confinement E ΔE Eex : 3.2022 eV (CuCl) x 2R Quantum size effect ( aex＜ R,L ) For spherical dot For cubic dot Dot size little big Blue shift large small aex : exciton Bohr radius

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

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

8. 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.

9. CCD Experimental setup Q-switched Nd3+:YAG laser 355 nm (THG) Dye laser Pulse duration : 5 ns Pulse reputation : 30 Hz Spectral linewidth : 0.014 meV Pump Probe Halogen lamp 75cm spectrometer Sample in cryostat (2 K)

10. Exciton binding energy : 197 meV Exciton Bohr radius : 0.7 nm QDs in glass QDs in NaCl Shape of CuCl QD electron hole Spherical shape Cubic shape Sample (CuCl QD) Band structure (CuCl Bulk) E Γ6 Conduction band Z3 Z1,2 Valence band Γ7 Γ8 k Γ

11. pump energy zero phonon hole A : 3.2583 B : 3.2626 C : 3.2669 D : 3.2712 E : 3.2755 F : 3.2798 G : 3.2841 H : 3.2882 Stokes-side acoustic phonon hole anti-Stokes-side acoustic phonon hole Experimental result - 1 CuCl QDs in glass (a) Absorption spectrum (b) PSHB spectra (Average radius : 1.4 nm) Stokes-sideband anti-Stokes-sideband E Energy phonon photon G

12. zero phonon hole Stokes-side acoustic phonon hole anti-Stokes-side acoustic phonon hole Experimental result - 1 CuCl QDs in glass (a) Absorption spectrum (b) PSHB spectra (Average radius : 1.4 nm) 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 Acoustic phonon energy Dot size

13. 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 Experimental result - 2 CuCl QDs in NaCl (a) Absorption spectrum (inhomogeneously broadened 3.22～3.28eV) (b) PSHB spectra Interval between the zero-phonon line and the Stokes-side acoustic phonon hole ex) H : 0.7 meV smaller than those in glass!!

14. Lowest eigenmode Lowest eigenmode torsional (ねじれ) spheroidal(楕円体) (n=0) flexural (屈曲） torsional (ねじれ) (n=1) shear(ずれ) Discussion - 1 (under stress-free boundary condition) Free vibration of a homogeneous elastic sphere Free vibration of an isotropic cube H. H. Demarest, Jr., J. Acoust. Soc. Am. 49. 768 (1971) H. Lamb, Proc. London Math. Soc.13,189 (1882) (n,l)=(0.1) (n,l)=(0.2) (n,l)=(0.1) 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

15. νd1, a1, s1 ν10, 20 in KCl in glass in NaCl 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 Inverse of diameter and side length

16. νd1, a1, s1 ν10, 20 in KCl in glass in NaCl negligible important Discussion - 2 Square root of confinement energy About discrepancy... Supposing ideal cube (in vacuum) Existence of deformation Influence of matrix In glass In NaCl Inverse of diameter and side length

17. 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.