^{1}, Qin Wang

^{1,a)}and Hang Zheng

^{1}

### Abstract

Optical absorptionspectrum of semiconductorquantum dot is investigated by means of an analytical approach based on the Green's function for different forms of coupling strength in an unified method by using the standard model with valence and conduction band levels coupled to dispersive quantum phonons of infinite modes. The analytical expression of the optical absorption coefficient in semiconductorquantum dots is obtained and by this expression the line shape and the peak position of the absorptionspectrum are procured. The relation between the properties of absorptionspectrum and the forms of coupling strength is clarified, which can be referenced for choosing the proper form of the coupling strength or spectral density to control the features of absorptionspectrum of quantum dot. The coupling and confinement induced energy shift and intensity decrease in the absorptionspectrum are determined precisely for a wide range of parameters. The results show that the activation energy of the optical absorption is reduced by the effect of exciton-phonon coupling and photons with lower frequencies could also be absorbed in absorption process. With increase of the coupling constant, the line shape of optical absorptionspectrum broadens and the peak position moves to lower photon energy with a rapid decrease in intensity at the same time. Both the coupling induced red shift and the confinement induced blue shift conduce to decrease in the intensity of absorptionspectrum. Furthermore, this method may have application potential to other confined quantum systems.

This work was supported by the SNSF of Shanghai (10ZR1415100) and NSFC.

I. INTRODUCTION

II. THE MODEL

III. OPTICAL ABSORPTION

IV. EVALUATION AND RESULTS

A. Exciton-phonon interaction

B. Solid state phonon

V. CONCLUSION

### Key Topics

- Absorption spectra
- 91.0
- Quantum dots
- 75.0
- Optical absorption
- 66.0
- Phonons
- 23.0
- Semiconductors
- 21.0

## Figures

The calculated optical absorption coefficients as function of photon frequency in the case of *g* = 0.02 and for the spectral densities and . The peak positions of the optical absorption spectrum are 0.00449 for and 0.00498 for . The linewidth from Lorentzian fitting are for and 0.00032 for .

The calculated optical absorption coefficients as function of photon frequency in the case of *g* = 0.02 and for the spectral densities and . The peak positions of the optical absorption spectrum are 0.00449 for and 0.00498 for . The linewidth from Lorentzian fitting are for and 0.00032 for .

The line shape of optical absorption spectrum as function of photon frequency with input parameters *g* = 0.1 and for the spectral density . The solid circles denote the results of measurement in an interface fluctuation quantum dot (Ref. 30, Fig. 2), and the insets show the results of theoretical studies for (a) from Ref. 21 (Fig. 4(a)), and (b) from Ref. 28 (Fig. 1, line A for *R* = 1.9 nm). The absorption peak position is set to the zero detuning position, the same as in Ref. 30 and the photon frequency is scaled by , the half-width for the low photon frequency side of the peak. Note we claim only that the subgap () optical absorption coefficients scale.

The line shape of optical absorption spectrum as function of photon frequency with input parameters *g* = 0.1 and for the spectral density . The solid circles denote the results of measurement in an interface fluctuation quantum dot (Ref. 30, Fig. 2), and the insets show the results of theoretical studies for (a) from Ref. 21 (Fig. 4(a)), and (b) from Ref. 28 (Fig. 1, line A for *R* = 1.9 nm). The absorption peak position is set to the zero detuning position, the same as in Ref. 30 and the photon frequency is scaled by , the half-width for the low photon frequency side of the peak. Note we claim only that the subgap () optical absorption coefficients scale.

The optical absorption coefficients as function of photon frequency for the spectral densities and in the case of for different values of coupling constant *g* = 0.01, 0.03, and 0.05. As the coupling constant increases, the line shape of optical absorption spectrum broadens and the peak position moves to lower photon energy with rapid decrease in intensity at the same time.

The optical absorption coefficients as function of photon frequency for the spectral densities and in the case of for different values of coupling constant *g* = 0.01, 0.03, and 0.05. As the coupling constant increases, the line shape of optical absorption spectrum broadens and the peak position moves to lower photon energy with rapid decrease in intensity at the same time.

The optical absorption coefficient as function of photon frequency for the spectral densities and in the case of fixed coupling constant *g* = 0.01 for different values of , 0.08, and 0.1. The intensity of optical absorption spectrum is reduced by more than 60% as the energy difference increases from 0.06 to 0.1.

The optical absorption coefficient as function of photon frequency for the spectral densities and in the case of fixed coupling constant *g* = 0.01 for different values of , 0.08, and 0.1. The intensity of optical absorption spectrum is reduced by more than 60% as the energy difference increases from 0.06 to 0.1.

The calculated optical absorption coefficients as function of photon frequency in the cases of with *g* = 0.05, and 0.1 for the spectral densities and . The red shift for the spectral density is much larger than that for .

The calculated optical absorption coefficients as function of photon frequency in the cases of with *g* = 0.05, and 0.1 for the spectral densities and . The red shift for the spectral density is much larger than that for .

The optical absorption coefficients as function of photon frequency with definite values of *g* = 0.05 and for (a) the spectral densities and and (b) the spectral densities and . Insets: their corresponding spectral densities as function of excited frequency in the case of *g* = 0.05. Note the abscissae scales of (a) and (b) are different.

The optical absorption coefficients as function of photon frequency with definite values of *g* = 0.05 and for (a) the spectral densities and and (b) the spectral densities and . Insets: their corresponding spectral densities as function of excited frequency in the case of *g* = 0.05. Note the abscissae scales of (a) and (b) are different.

The red shift as function of coupling constant *g* in the case of for all four kinds of spectral densities. Inset: the red shift for spectral density as function of coupling constant *g* in the cases of , 0.05, and 0.1.

The red shift as function of coupling constant *g* in the case of for all four kinds of spectral densities. Inset: the red shift for spectral density as function of coupling constant *g* in the cases of , 0.05, and 0.1.

The red shift as function of in the case of *g* = 0.01 for all four kinds of spectral densities. Inset: the red shift for spectral density as function of in the cases of *g* = 0.05, 0.1, and 0.15.

The red shift as function of in the case of *g* = 0.01 for all four kinds of spectral densities. Inset: the red shift for spectral density as function of in the cases of *g* = 0.05, 0.1, and 0.15.

The peak height (spectral intensity) of the calculated optical absorption spectrum for spectral density as function of the coupling constant *g* with , and as function of with the coupling constant *g* = 0.1, respectively. Inset: the peak height of the optical absorption spectrum for all four kinds of spectral densities as function of the coupling constant *g* in the case of . Note the lines for and are scaled by.

The peak height (spectral intensity) of the calculated optical absorption spectrum for spectral density as function of the coupling constant *g* with , and as function of with the coupling constant *g* = 0.1, respectively. Inset: the peak height of the optical absorption spectrum for all four kinds of spectral densities as function of the coupling constant *g* in the case of . Note the lines for and are scaled by.

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