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Fano-like electron–phonon interference in δ-doping GaAs superlattices
Superlattices and Microstructures, Vol. 23, No. 5, 1998
Fano-like electron–phonon interference in δ -doping GaAs superlattices Yu. A. Pusep, M. T. O. Silva, J. C. Galzerani Universidade Federalde S˜ao Carlos, 13565-905 S˜ao Carlos, SP., Brasil
S. W. da Silva Instituto de F´ısica de S˜ao Carlos, Universidade de S˜ao Paulo, 13560-970, S˜ao Carlos, SP., Brasil
L. M. R. Scolfaro, R. Enderlein, A. A. Quivy, A. P. Lima, J. R. Leite Universidade de S˜ao Paulo, 05389-970, S˜ao Paulo, SP., Brasil
The interaction between electron excitations and LO phonons is studied by Raman scattering in δ-doping GaAs superlattices. The Raman spectra measured close to the E0 + 10 resonance of GaAs present Fano-like coupling of the LO phonons with the quasicontinuum single-particle electron excitations. Due to the self-consistent origin of the electron-energy spectrum in δ-doping superlattices the resonance of the Fano interference was found to be strongly dependent on the electron density as well as the excitation energy. c 1998 Academic Press Limited
Key words: superlattices, Raman scattering, Fano-interference.
As discussed in [1] a new type of interaction between the continuum electron single-particle excitations (SPE) and the discrete LO one-photon state takes place when the excitation energy of electrons in this continuum overlaps with the energy of the LO phonon. It was proposed that the discrete-continuum interference occurred due to the Fr¨olich electric potential and may be interpreted as a result of a discrete-continuum Fanotype interference [2]. In this paper we describe a systematic study of δ-doping GaAs superlattices with different electron densities. It was shown that the same conditions (the excitation energy and the electron density) cause both the resonance of Raman scattering by the charge-density excitations (CDE) and the Raman resonance of the resulting line produced by the Fano interference. Thus the importance of the Fr¨olich type electron–phonon interaction in the Fano coupling was confirmed. Following [2] the Raman cross-section can be represented by the formula: σ (ω) = σb (ω) + σe
q 2 − 1 + 2q 1 + 2
(1)
where σb (ω) and σe , respectively, a background Raman cross-section and the amplitude, = 2(ω − ω L O − 1)/ 0 is the reduced energy where ω L O is the LO phonon frequency, 1 and 0 are, respectively, a line shift (with respect to the unperturbed bulk LO phonon) and a linewidth parameter, and q is the line profile parameter. The samples studied were periodically δ-doped GaAs structures grown by molecular beam epitaxy on (100) 0749–6036/98/051033 + 03 $25.00/0
sm960220
c 1998 Academic Press Limited
1034
Superlattices and Microstructures, Vol. 23, No. 5, 1998 N = 1.0 × 1012 cm–2 Z(X', X')Z LOF T = 10 K
q = –9.9
250
300
350
300
350
Raman intensity
CDE
EL = 1.92 eV
q = –0.35
LOF
250
CDE
EL = 1.83 eV 200
300 400 Wavenumber (cm–1)
500
Fig. 1. The Raman spectra measured close to the E0 +10 resonance of GaAs for the δ-doping GaAs superlattice with N = 5×1012 cm−2 . The insert shows the Fano line profile as obtained by the fitting.
˚ and repeated 50 times. The oriented GaAs substrates. The Si δ-doped layers were separated by d = 300 A 12 −2 12 nominal sheet electron densities (N ) varied from 1 × 10 cm to 11 × 10 cm−2 as determined during the growth. The parallel polarized Raman spectrum of one of the samples measured close to the E0 + 10 resonance of GaAs (Fig. 1) reveals a broad line attributed to the intersubband charge-density electron excitations. The position of this line is in good agreement with the calculated excitation energy of the CDE found in the samples under investigation. The spin-density excitations (SDE) contribute to the cross-polarized spectrum where a line located at a slightly lower frequency was detected. The difference between the CDE and SDE peak positions shows that the depolarization fields, which accompany the intersubband electron excitations, are important even in δ-doping superlattices. An additional asymmetrical line denoted as LO F with the frequency slightly above the LO phonon frequency of GaAs was found in the parallel polarized resonant Raman spectrum. This line was not observed either in the off-resonant Raman spectra or in the resonant cross-polarized ones. Therefore, this provides unambiguous evidence that the origin of this line is the Fr¨ohlich electron–phonon interaction. This line can be attributed to the Fano effect. The broken line in Fig. 1 is the spectra calculated with (1.1) where σb (ω) includes a broad Raman line caused by the CDE which was fitted by a Gaussian profile. By fitting of the calculated Raman spectra to the experimental ones we are able to obtain the intensities of the Fano peaks (σe ) and the line profile parameters (q) in all samples. The dependence of the Fano line profile parameter q on the excitation energy, measured for one of the samples (depicted in Fig. 2, where the dashed lines were calculated by the expression given in [1]), shows a clear resonant behaviour with the resonance position close to that of the Raman resonances for the CDE line and also the Fano resonances. This result again confirms that the Fr¨olich electron–phonon interaction is the origin of the Fano effect.
Superlattices and Microstructures, Vol. 23, No. 5, 1998
1.7
Energy (eV) 1.9
1.8
1035
2.0
2.1 A
1 0 –1 q
N = 5 × 1012 cm–2
0.4
B
0.0 –0.4 EL = 1.92 eV 2
4
6 8 N (× 1012 cm–2)
10
12
Fig. 2. A, The dependencies of the Fano line parameter q on the excitation energy measured for the δ-doping GaAs superlattice with N = 5 × 1012 cm−2 ; B, on the electron density measured with the excitation energy E L = 1.92 eV.
A similar resonant behaviour was observed for the q(N ) dependence plotted in Fig 2B; again a resonance position was found close to the values of the electron densities at which the Raman resonances of the CDE and of the Fano occur. Acknowledgements—The financial support from CNPq, FAPESP and CAPES is gratefully acknowledged.
References [1] }L. Ioriatti, Phys. Rev. B43, 14742 (1991). [2] }U. Fano, Phys. Rev. 124, 1866 (1961).
Fano-like electron–phonon interference in δ -doping GaAs superlattices Yu. A. Pusep, M. T. O. Silva, J. C. Galzerani Universidade Federalde S˜ao Carlos, 13565-905 S˜ao Carlos, SP., Brasil
S. W. da Silva Instituto de F´ısica de S˜ao Carlos, Universidade de S˜ao Paulo, 13560-970, S˜ao Carlos, SP., Brasil
L. M. R. Scolfaro, R. Enderlein, A. A. Quivy, A. P. Lima, J. R. Leite Universidade de S˜ao Paulo, 05389-970, S˜ao Paulo, SP., Brasil
The interaction between electron excitations and LO phonons is studied by Raman scattering in δ-doping GaAs superlattices. The Raman spectra measured close to the E0 + 10 resonance of GaAs present Fano-like coupling of the LO phonons with the quasicontinuum single-particle electron excitations. Due to the self-consistent origin of the electron-energy spectrum in δ-doping superlattices the resonance of the Fano interference was found to be strongly dependent on the electron density as well as the excitation energy. c 1998 Academic Press Limited
Key words: superlattices, Raman scattering, Fano-interference.
As discussed in [1] a new type of interaction between the continuum electron single-particle excitations (SPE) and the discrete LO one-photon state takes place when the excitation energy of electrons in this continuum overlaps with the energy of the LO phonon. It was proposed that the discrete-continuum interference occurred due to the Fr¨olich electric potential and may be interpreted as a result of a discrete-continuum Fanotype interference [2]. In this paper we describe a systematic study of δ-doping GaAs superlattices with different electron densities. It was shown that the same conditions (the excitation energy and the electron density) cause both the resonance of Raman scattering by the charge-density excitations (CDE) and the Raman resonance of the resulting line produced by the Fano interference. Thus the importance of the Fr¨olich type electron–phonon interaction in the Fano coupling was confirmed. Following [2] the Raman cross-section can be represented by the formula: σ (ω) = σb (ω) + σe
q 2 − 1 + 2q 1 + 2
(1)
where σb (ω) and σe , respectively, a background Raman cross-section and the amplitude, = 2(ω − ω L O − 1)/ 0 is the reduced energy where ω L O is the LO phonon frequency, 1 and 0 are, respectively, a line shift (with respect to the unperturbed bulk LO phonon) and a linewidth parameter, and q is the line profile parameter. The samples studied were periodically δ-doped GaAs structures grown by molecular beam epitaxy on (100) 0749–6036/98/051033 + 03 $25.00/0
sm960220
c 1998 Academic Press Limited
1034
Superlattices and Microstructures, Vol. 23, No. 5, 1998 N = 1.0 × 1012 cm–2 Z(X', X')Z LOF T = 10 K
q = –9.9
250
300
350
300
350
Raman intensity
CDE
EL = 1.92 eV
q = –0.35
LOF
250
CDE
EL = 1.83 eV 200
300 400 Wavenumber (cm–1)
500
Fig. 1. The Raman spectra measured close to the E0 +10 resonance of GaAs for the δ-doping GaAs superlattice with N = 5×1012 cm−2 . The insert shows the Fano line profile as obtained by the fitting.
˚ and repeated 50 times. The oriented GaAs substrates. The Si δ-doped layers were separated by d = 300 A 12 −2 12 nominal sheet electron densities (N ) varied from 1 × 10 cm to 11 × 10 cm−2 as determined during the growth. The parallel polarized Raman spectrum of one of the samples measured close to the E0 + 10 resonance of GaAs (Fig. 1) reveals a broad line attributed to the intersubband charge-density electron excitations. The position of this line is in good agreement with the calculated excitation energy of the CDE found in the samples under investigation. The spin-density excitations (SDE) contribute to the cross-polarized spectrum where a line located at a slightly lower frequency was detected. The difference between the CDE and SDE peak positions shows that the depolarization fields, which accompany the intersubband electron excitations, are important even in δ-doping superlattices. An additional asymmetrical line denoted as LO F with the frequency slightly above the LO phonon frequency of GaAs was found in the parallel polarized resonant Raman spectrum. This line was not observed either in the off-resonant Raman spectra or in the resonant cross-polarized ones. Therefore, this provides unambiguous evidence that the origin of this line is the Fr¨ohlich electron–phonon interaction. This line can be attributed to the Fano effect. The broken line in Fig. 1 is the spectra calculated with (1.1) where σb (ω) includes a broad Raman line caused by the CDE which was fitted by a Gaussian profile. By fitting of the calculated Raman spectra to the experimental ones we are able to obtain the intensities of the Fano peaks (σe ) and the line profile parameters (q) in all samples. The dependence of the Fano line profile parameter q on the excitation energy, measured for one of the samples (depicted in Fig. 2, where the dashed lines were calculated by the expression given in [1]), shows a clear resonant behaviour with the resonance position close to that of the Raman resonances for the CDE line and also the Fano resonances. This result again confirms that the Fr¨olich electron–phonon interaction is the origin of the Fano effect.
Superlattices and Microstructures, Vol. 23, No. 5, 1998
1.7
Energy (eV) 1.9
1.8
1035
2.0
2.1 A
1 0 –1 q
N = 5 × 1012 cm–2
0.4
B
0.0 –0.4 EL = 1.92 eV 2
4
6 8 N (× 1012 cm–2)
10
12
Fig. 2. A, The dependencies of the Fano line parameter q on the excitation energy measured for the δ-doping GaAs superlattice with N = 5 × 1012 cm−2 ; B, on the electron density measured with the excitation energy E L = 1.92 eV.
A similar resonant behaviour was observed for the q(N ) dependence plotted in Fig 2B; again a resonance position was found close to the values of the electron densities at which the Raman resonances of the CDE and of the Fano occur. Acknowledgements—The financial support from CNPq, FAPESP and CAPES is gratefully acknowledged.
References [1] }L. Ioriatti, Phys. Rev. B43, 14742 (1991). [2] }U. Fano, Phys. Rev. 124, 1866 (1961).