## Local field-induced optical properties of Ag-coated CdS quantum dots

Optics Express, Vol. 14, Issue 17, pp. 7994-8000 (2006)

http://dx.doi.org/10.1364/OE.14.007994

Acrobat PDF (212 KB)

### Abstract

Local field-induced optical properties of Ag-coated CdS quantum dot structures are investigated. We experimentally observe a clear exciton peak due to the quantum confinement effect in uncoated CdS quantum dots, and surface plasmon resonance and red-shifted exciton peak in Ag-coated CdS composite quantum dot structures. We have calculated the Stark shift of the exciton peak as a function of the local field for different silver thicknesses and various sizes of quantum dots based on the effective-mass Hamiltonian using the numerical-matrix-diagonalization method. Our theoretical calculations strongly indicate that the exciton peak is red-shifted in the metal-semiconductor composite quantum dots due to a strong local field, *i*.*e*., the quantum confined Stark effect.

© 2006 Optical Society of America

## 1. Introduction

1. H.S. Zhou, I. Honma, H. Komiyama, and J.W. Haus, “Controlled synthesis and quantum-size effect in gold-coared nanoparticles,” Phys. Rev. B **50**, 12052–12056 (1994). [CrossRef]

2. R.D. Averitt, D. Sarkar, and N.J. Halas, “Plasmon resonance shifts of Au-coated *Au*_{2}S nanoshells: Insight into multicomponent nanoparticle growth,” Phys. Rev. Lett. **78**, 4217–4220 (1997). [CrossRef]

3. R.D. Averitt, S.L. Westcott, and N.J. Halas, “Linear optical properties of gold nanoshells,” J. Opt. Am. B **16**, 1824–1832 (1999). [CrossRef]

3. R.D. Averitt, S.L. Westcott, and N.J. Halas, “Linear optical properties of gold nanoshells,” J. Opt. Am. B **16**, 1824–1832 (1999). [CrossRef]

4. M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. **57**, 783–826 (1985). [CrossRef]

3. R.D. Averitt, S.L. Westcott, and N.J. Halas, “Linear optical properties of gold nanoshells,” J. Opt. Am. B **16**, 1824–1832 (1999). [CrossRef]

4. M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. **57**, 783–826 (1985). [CrossRef]

5. F. Rocco, A. K. Jain, M. Treguer, T. Cardinal, S. Yotte, P.Le Coustumer, C. Y. Lee, S. H. Park, and J. G. Choi, “Optical response of silver coating on CdS colloids,” Chem. Phys. Lett. , **394**, 324–328 (2004). [CrossRef]

6. M.J. Ko, J. Plawsky, and M. Birnboim, “Fabrication of CdS/Ag hybrid quantum dot composites using a melt/quench method,” J. Non-Cryst. Solids **203**, 211–216 (1996). [CrossRef]

7. L. Pang, Y. Shen, K. Tetz, and Y. Fainman, “PMMA quantum dots composites fabricated via use of pre-polymerization,” Opt. Express **13**, 44–49 (2004). [CrossRef]

5. F. Rocco, A. K. Jain, M. Treguer, T. Cardinal, S. Yotte, P.Le Coustumer, C. Y. Lee, S. H. Park, and J. G. Choi, “Optical response of silver coating on CdS colloids,” Chem. Phys. Lett. , **394**, 324–328 (2004). [CrossRef]

9. G.W. Wen, J.Y. Lin, H.X. Jiang, and Z. Chen, “Quantum-confined Stark effects in semiconductor quantum dots,” Phys. Rev. B **52**, 5913–5922 (1995). [CrossRef]

10. G.H. Wannier, “Wave functions and effective Hamiltonian for Bloch electrons in an electric field”, Phys. Rev. **117**, 432–439 (1960). [CrossRef]

## 2. Matrix elements in exciton-Hamiltonian

9. G.W. Wen, J.Y. Lin, H.X. Jiang, and Z. Chen, “Quantum-confined Stark effects in semiconductor quantum dots,” Phys. Rev. B **52**, 5913–5922 (1995). [CrossRef]

*H*

_{e(h)}is the kinetic energy of the electron(hole),

*V*is the Coulomb interaction between the electron and hole, and

_{eh}*H*is the additional interaction of the electron and the hole in the Wannier equation [10

_{F}10. G.H. Wannier, “Wave functions and effective Hamiltonian for Bloch electrons in an electric field”, Phys. Rev. **117**, 432–439 (1960). [CrossRef]

*r*,

_{e}*r*) is determined by the following Schrödinger equation under the external field

_{h}*ε*is the dielectric constant of the QD, E is the energy of the confined exciton, and

_{d}*F*is the electric field inside the QD. This equation cannot be solved analytically without solving the Wannier equations.

9. G.W. Wen, J.Y. Lin, H.X. Jiang, and Z. Chen, “Quantum-confined Stark effects in semiconductor quantum dots,” Phys. Rev. B **52**, 5913–5922 (1995). [CrossRef]

*l*> is the Clebsch-Gordan coefficient in the Condon-Shortley convention where L and M are the quantum number of the total angular momentum and its z component, respectively, and

_{e}l_{f}m_{e}m_{h},|LM*N*

_{i=e,h}) is a quantum number set {

*n*,

_{i}*l*,

_{i}*m*}.

_{i}*ϕN*(

_{i}*r*) is a single particle wave function in the absence of an electric field and neglects the Coulomb interaction.

_{i}*C*(

*n*) is determined by diagonalization of the Hamiltonian with the basis vectors.

_{e}n_{h}l_{e}l_{h}LM*is the nth root of the eigenvalue equation*

_{nl}*j*(

_{l}*x*) = 0.

## 3. Optical properties of QDs in the presence of local field

*ε*and

_{q}*ε*, of the CdS core and Ag shell, respectively. For noble metals at optical frequencies, the dielectric function can be expressed as

_{sh}*ε*(

_{q}*ω*), of CdS QDs is written as

*γ*is the excitonic broadening constant and

_{e}*ω*is the one-pair ground state energy.

_{e}*d*

_{0e}is the dipole moment between the ground state and the one-pair state and is given by

*p*=

_{cv}*e*<

*v*|

*r*|

*c*> comes from the overlap integral of the conduction and valence Bloch wavefunctions, and σ(

*s*, -

*s*) is the spin part.

*ε*(

_{sh}*ω*), of the nanoshell, which are contributed by Drude-like electrons and interband transitions

*ε*(

*ω*)

_{inter}, is given by [3

**16**, 1824–1832 (1999). [CrossRef]

## 4. Results and discussion

*m*(

_{e}*CdS*) = 0.18/

*m*

_{0},

*m*(

_{h}*CdS*) = 0.7

*m*

_{0}with

*m*

_{0}being the electron mass in free space and the dielectric constants

*ε*(CdS) = 8.5.The CdS/Ag QD is embedded in an aqueous medium of dielectric constant

_{d}*ε*= 1.78. We used the nine lowest single particle states of electrons and holes for the numerical calculation.

_{a}*R*= 1.3

*nm*with silver thickness of 0.35 nm. The real Ag-CdS composite core-shell structure is presented in the reference [8]. The dashed line is the measured linear absorption of the pure QD and shows the lowest exciton absorption peak at 4.01 eV. The dotted line is the measured spectrum of the CdS/Ag QD. Absorption peaks are apparent between 3.0 eV and 4.5 eV, and a new peak appears at 3.36 eV from the plasmon resonance, originating from the coated silver on the CdS semiconductor QD. This plasmon resonance corresponds to a silver thickness of 0.35 nm. The pre-existent absorption peak at 4.01 eV has shifted by 0.09 eV to a lower energy 3.92 eV as well as broadened due to the surface plasmon. We propose that the red-shift of the absorption peak is attributed to local-field enhancement by the metal surrounding the semiconductor core. The local field is estimated to be approximately 1 × 10

^{6}

*V*/

*cm*for the observed red-shift of 0.09 eV. The solid line in Figure 1 shows the calculated absorption spectrum in the presence of the electric field. From the measured and calculated curves, we conclude that the shift of the lowest exciton peaks in the QD occurs due to surface plasmon oscillations in the metal coating.

*s*(

*p*)

_{e}and 1

*s*(

*p*)

_{h}single states while SD and DS states are composed of 1

*s*(

*d*)

_{e}and 1

*d*(

*s*)

_{h}single states. Thus, SS denotes the lowest exciton state with total angular quantum number L=0, PP is the lowest exciton state with total angular quantum number L=1 and SD and DS are exciton states with total angular quantum number L=2. The quantum confined Stark effect(QCSE) is clearly demonstrated as exciton energy levels shift towards the low energies as applied electric field increases. The shift of the exciton peaks is proportional to the strength of the electric field, consistent with the Wannier Stark ladder of quantum wells. However, in the strongly confined 3-dimensional system, the Stark shift is not linear, but rather squarely proportional to the strength of the electric field. The amount of shifting of the SS exciton is more than those of PP, DS, and SD excitons. The Stark shift is larger in the lower total angular quantum number in the symmetry charge distribution system. Comparing the Stark shifts of (1

*d*1

_{e}*s*) and (1

_{h}*s*1

_{e}*d*), the Stark effect is dominant in lower angular momentum and lower effective mass.

_{h}13. U. Kreibig and L. Genzel, “Optical Absorption of small metallic particles,” Surf. Sci. **156**, 678–700 (1985). [CrossRef]

## 5. Conclusion

*i*.

*e*., the quantum confined Stark effect.

## Acknowledgements

## References and links

1. | H.S. Zhou, I. Honma, H. Komiyama, and J.W. Haus, “Controlled synthesis and quantum-size effect in gold-coared nanoparticles,” Phys. Rev. B |

2. | R.D. Averitt, D. Sarkar, and N.J. Halas, “Plasmon resonance shifts of Au-coated |

3. | R.D. Averitt, S.L. Westcott, and N.J. Halas, “Linear optical properties of gold nanoshells,” J. Opt. Am. B |

4. | M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. |

5. | F. Rocco, A. K. Jain, M. Treguer, T. Cardinal, S. Yotte, P.Le Coustumer, C. Y. Lee, S. H. Park, and J. G. Choi, “Optical response of silver coating on CdS colloids,” Chem. Phys. Lett. , |

6. | M.J. Ko, J. Plawsky, and M. Birnboim, “Fabrication of CdS/Ag hybrid quantum dot composites using a melt/quench method,” J. Non-Cryst. Solids |

7. | L. Pang, Y. Shen, K. Tetz, and Y. Fainman, “PMMA quantum dots composites fabricated via use of pre-polymerization,” Opt. Express |

8. | E.-H. Jeang, J.-H Lee, K.-C. Je, S.-Y. Yim, S.-H. Park, Y.-S. Choi, J.-G. Choi, M. Treguer, and T. Cardinal, “Fabrication and optical characteritics of CdS/Ag metal-semiconductor composite quantum dots,” Bull. Korea Chem. Soc. |

9. | G.W. Wen, J.Y. Lin, H.X. Jiang, and Z. Chen, “Quantum-confined Stark effects in semiconductor quantum dots,” Phys. Rev. B |

10. | G.H. Wannier, “Wave functions and effective Hamiltonian for Bloch electrons in an electric field”, Phys. Rev. |

11. | J.C.Maxwell Garnett, “Colours in Metal Glasses, in Metallic, and in Metallic Solutions”, Philos. Trans. R. Soc. London,203, 385–420 (1904); 205, 237–288 (1906). [CrossRef] |

12. | O. Madelung, M. Schultz, H. Weiss, and Landolt-Börnstein, |

13. | U. Kreibig and L. Genzel, “Optical Absorption of small metallic particles,” Surf. Sci. |

14. | K.-C. Je, S.-Y. Yim, J.-H. Lee, E.-H. Jeung, and S.-H. Park, “Field-induced Stark effects in Ag-coated CdS quantum dots”, in |

**OCIS Codes**

(260.6580) Physical optics : Stark effect

(300.1030) Spectroscopy : Absorption

(300.6470) Spectroscopy : Spectroscopy, semiconductors

**ToC Category:**

Spectroscopy

**History**

Original Manuscript: April 20, 2006

Revised Manuscript: July 25, 2006

Manuscript Accepted: July 30, 2006

Published: August 21, 2006

**Citation**

Koo-Chul Je, Honglyoul Ju, Mona Treguer, Thierry Cardinal, and Seung-Han Park, "Local field-induced optical properties of Ag-coated CdS quantum dots," Opt. Express **14**, 7994-8000 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-17-7994

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### References

- H. S. Zhou, I. Honma, H. Komiyama, and J. W. Haus, "Controlled synthesis and quantum-size effect in goldcoared nanoparticles," Phys. Rev. B 50, 12052-12056 (1994). [CrossRef]
- R. D. Averitt, D. Sarkar, and N. J. Halas, "Plasmon resonance shifts of Au-coated Au2S nanoshells: Insight into multicomponent nanoparticle growth," Phys. Rev. Lett. 78, 4217-4220 (1997). [CrossRef]
- R. D. Averitt, S. L. Westcott, and N. J. Halas, "Linear optical properties of gold nanoshells," J. Opt. Am. B 16, 1824-1832 (1999). [CrossRef]
- M. Moskovits, "Surface-enhanced spectroscopy," Rev. Mod. Phys. 57, 783-826 (1985). [CrossRef]
- F. Rocco, A. K. Jain, M. Treguer, T. Cardinal, S. Yotte, P. Le Coustumer, C. Y. Lee, S. H. Park, J. G. Choi, "Optical response of silver coating on CdS colloids," Chem. Phys. Lett. 394, 324-328 (2004). [CrossRef]
- M. J. Ko, J. Plawsky and M. Birnboim, "Fabrication of CdS/Ag hybrid quantum dot composites using a melt/quench method," J. Non-Cryst. Solids 203, 211-216 (1996). [CrossRef]
- L. Pang, Y. Shen, K. Tetz and Y. Fainman, "PMMA quantum dots composites fabricated via use of prepolymerization," Opt. Express 13, 44-49 (2004). [CrossRef]
- E.-H. Jeang, J.-H, Lee, K.-C. Je, S.-Y. Yim, S.-H. Park, Y.-S. Choi, J.-G. Choi, M. Treguer and T. Cardinal, "Fabrication and optical characteritics of CdS/Ag metal-semiconductor composite quantum dots," Bull. Korea Chem. Soc. 25, 967-969 (2004).
- G. W. Wen, J. Y. Lin, H. X. Jiang, and Z. Chen, "Quantum-confined Stark effects in semiconductor quantum dots," Phys. Rev. B 52, 5913-5922 (1995). [CrossRef]
- G. H. Wannier, "Wave functions and effective Hamiltonian for Bloch electrons in an electric field," Phys. Rev. 117, 432-439 (1960). [CrossRef]
- J. C. Maxwell Garnett, "Colours in metal glasses, in metallic, and in metallic solutions," Philos. Trans. R. Soc. London 203, 385-420 (1904); 205, 237-288 (1906). [CrossRef]
- O. Madelung, M. Schultz, and H. Weiss, Landolt-Börnstein, Semiconductors. Physics of Group IV Elements and III-V Compounds, (Springer, Berlin 1982).
- U. Kreibig and L. Genzel, "Optical Absorption of small metallic particles," Surf. Sci. 156, 678-700 (1985). [CrossRef]
- K.-C. Je, S.-Y. Yim, J.-H. Lee, E.-H. Jeung, and S.-H. Park, "Field-induced Stark effects in Ag-coated CdS quantum dots," in Quantum Dots, Nanoparticles, and Nanoclusters II, D. L. Huffaker and P. K. Bhattacharya, eds., Proc. SPIE 5734, 146-151 (2005). [CrossRef]

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