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Complement to theory of Raman scattering from adsorbed molecule on semiconductor
Surface Science 133 (1983) L432-L436 North-Holland publishing Company
L432
SURFACE
SCIENCE
LETTERS
COMI’LEMFNT TO THEORY OF RAMAN SCATTERING ADSORBED MOLECULE ON SEMICONDUCTOR
FROM
H. UEBA Department
of Electronics,
Toyama University,
Takaoka, Toyama, Japan
Received 15 June 1983
The Raman polarizability of a molecule adsorbed on a semiconductor is calculated when it couples to excitonic and interband excitations in the substrate. It is found that a difference in the electronic properties of each excitation manifests itself in the excitation profile of the Raman intensity of the adsorbed molecule, i.e., the former produces a sharp peak below the onset of interband excitation, whereas the latter gives rise to weaker but more broadened structure over a wide range of the spectrum.
Surface enhanced Raman scattering (SERS) [l] from molecules adsorbed on metal substrates has attracted considerable experimental and theoretical interests. Although there still remains some controversy about its trigger, the use of the SERS effect has provided a wide variety of information on chemical properties of adsorbates, which would have never been delivered without the discovery of SERS. So far the studies have been directed to molecules on metal substrates; it is very interesting to explore whether SERS is restricted on metals or not. Recently, Brazdil and Yeager [2] have reported that the Raman bands of p-NDMA and p-DMAAB adsorbed on ZnO and TiOz surfaces undergo enhancement due to a coupling to the electronic states in these substrates. Being stimulated by their experimental results, we have calculated the Raman polarizability of an adsorbed molecule on a semiconductor surface, in which the electronic excitation in the molecule couples to the excitonic or the interband excitation in the semiconductor through non-radiative energy transfer [3]. The Raman polarizability thus calculated has been found to exhibit a peak at the energy of a resonant excitation of excitons, thereby demonstrating the possibility of SERS on semiconductors. After our previous work was completed, we have become aware of another report, by Potts et al. [4], who also observed enhanced Raman scattering from adsorbed amorphous carbon on PbTe. Interestingly enough, the wavelength dependence of the enhancement was found to exhibit a correlation with the band structure of PbTe. Namely, the spectral range where they observed the 0039-6028/83/0000-00/$03.00
0 1983 North-Holland
H. Ueba / Complement
to theoty of Raman scattering
L433
large enhancement correlates with the position of the critical points in the joint density of states of PbTe, thereby suggesting a scattering mechanism which involves the electronic interaction between the molecule and the interband transition in the semiconductor. It should be noted here that they interpreted their result due to roughness-induced coupling of the photons to the interband transition in the relevant intermediate states of the Raman scattering process. Our previous theory, however, clearly demonstrates that the electronic excitation in the semiconductor can be brought through the non-radiative energy dissipation from the excited molecular state, even in the absence of any surface roughness. In fact, the energy transfer from a molecular excited state to a semiconductor substrate has recently been studied by Whitmore et al. [5], whose measurements of the distance dependent life time of pyrazine on GaAs were well explained in terms of a hypothesis that the molecular electronic excitation is dissipated into the excitation of electron-hole pairs in the substrate. Since excitonic or interband excitations are possible candidates which accept the energy dissipation from a excited molecule, it is of interest to study the structure of the Raman polarizability of an adsorbed molecule interacting with excitonic or interband transitions in a semiconductor. The difference in the electronic properties of these excitations will then manifest itself in the excitation profile of the Raman scattering intensity. In this letter, results are presented in order to demonstrate such a characteristic difference in the Raman polarizability. The Raman polar&ability of an adsorbed molecule, in the absence of the direct electronic excitation in the semiconductor through the photon field with frequency w, is expressed as:
(1) where w = w - 3, aL&4= (~-ce.,;~:ce,-p,’
is the polarizability of a free molecule and A4 is the matrix element of the dipole transition in the molecule with energy e,s; A and Q denote the coupling strength of electron-vibrational mode and vibrational frequency, respectively. The quantity R(w)
2
1
=
1-
v2 d4
&(4
I describes a change in the polarizability of the molecule upon adsorption at the semiconductor surface. Here V measures the strength of the non-radiative energy transfer between molecule and semiconductor and
IA34
H. Ueba / Complement
&lb)=(-%,)-‘,
to theory of Raman scattering
gs(4=C(~-~k)-*, k
where ek is the energy of the electronic excitation in the semiconductor. it is needless to say that a key issue of the theory is contained in R(w), which reveals an induced resonant character at an energy satisfying Re[l - I/’ g,(w)
g,(w)] = 0.
(4)
The structure of R(w) and also the enhancement factor IR(w)l’ of the Raman scattering intensity is, therefore, determined by the properties of the electronic excitations in the semiconductor through g,(w) given by
/dr &)&T =P/dr p(r)--&+ilrp(w),
gb>=
(f-5)
where P means the principal value and p(z) represents the density of states for relevant excitations in the semiconductor. Let us now study a characteristic difference in R(w) between the excitonic and the interband coupling of the molecule. We here assume, for an exciton:
where z,,, and r are the energy and the broadening of the exciton state, and Pint(')
=
3
2D-3j2
(c -
csapy2
for the interband excitation of electron-hole pairs, where cgap and D are the band gap energy and the width of the joint density of states for the interband excitation. In what follows, numerical calculations are carried out for ceg = 3.0 eV, ceXC= cgap = 2.0 eV, y = 0.05 eV and D = 3.0 eV. Strictly speaking, cexc is smaller than cgap by the binding energy of the exciton. However, we neglect such difference without losing any interest, since the localized structure of the exciton and the continuum structure of interband excitation are well described by eqs. (7) and (8), respectively. Figs. la and lb depict la[na,,,lcalculated by eq. (1) when eqs. (7) and (8) are used respectively. In fig. la, ((~~~~1exhibits a peak whose position shifts to the lower energy side of E,,~ and the intensity increases with an increase of I’. The appearance of such a peak is caused by a virtual excitation of an exciton through the non-radiative energy transfer from the molecular excited state. On the other hand in fig. lb, a shoulder starts to appear, which is followed by a broad peak just below cgap. It is also mentioned here that at sufficiently large V there appears a sharp peak associated with an admolecule split-off state in the band gap. The different features of ((Y Raml shown in figs. la and lb then
H. Ueba /
a
L435
v=1.2
I ooU
1c
a Ram
Complement to theoty of Raman scattering
a Ram
0.8
5
I!
1
2
W(eV) Fig. 1. Raman polarizability transitions in semiconductor,
of adsorbed molecule coupled to (a) excitonic, see the text for parameters used herein.
and (b) interband
lead to those in the enhancement factor /RI* shown in figs. 2a and 2b. For the excitor% coupling shown in fig. 2a, the enhancement is sharply localized around an induced resonance, above which it undergoes a sudden quenching. On the contrary, the continuum structure of the interband coupling gives rise to the weaker but more broadened spectrum of the enhancement as plotted in fig. 2b. Such a characteristic difference in ]R]* is, therefore, expected to be observed through a careful measurement of the excitation profile of the Raman scattering intensity. According to a verbal description of the excitation profile of carbon on PbTe [4], the Raman intensity for the green-blue line excitations is larger than in the red by a factor of 200. (The maximum enhancement was estimated to be about 103.) Such a trend seems to be consistent with the present result shown in the uppermost curve of fig. 2b, where the degree of the enhancement takes its maximum of an order of lo3 just below the onset of the interband transition at 2.0 eV, which falls in the region of the strong interband transition of PbTe [6]. As one decreases the energy of the incident photon, the
Fig. 2. Enhancement
factor in the log ,c unit, (a) and (b) correspond
to those in fig. 1, respectively.
L436
H. Ueba / Complement
to theory of Raman scattering
enhancement undergoes a gradual decrease, which is a characteristic phenomenon associated with the continuum interband coupling of the molecule in its Raman scattering process. In the case of excitonic coupling, one may observe a sharper structure in the excitation profile of the Raman intensity. Although the energy between an excitonic and an onset of interband transitions is only separated by a small binding energy of the exciton (which is usually several tens of mev), the characteristic difference described above will nevertheless manifest itself in careful observation of the excitation profile. Moreover, another desirable experiment includes the temperature dependence of the Raman intensity. Namely, the band gap of a semiconductor is more or less temperature dependent, thereby causing a shift of the maximum of enhancement in accordance with that of the band gap energy. It is also mentioned that the excitonic coupling with an adsorbed molecule will not be present at rather high temperatures where excitons are short lived and decay quickly into interband excitation. One might therefore be able to observe that the sharp excitation profile at low temperatures is replaced by a broad one as the temperature is raised. In summary, we have shown that a molecule adsorbed on a semiconductor exhibits SERS when the relevant intermediate states in the Raman process involve excitor& or interband transitions in the semiconductor, and that the excitation profile of the Raman intensity enables us to determine which type of electronic excitation is coupled to the electronic excited states of the adsorbed molecule.
References [I] R.K. Chang and T.E. Furtak, Eds., Surface Enhanced Raman Scattering (Plenum, New York, 1982). For a more updated review, see: A. Otto, in: Light Scattering in Solids, Vol. 4, Eds. M. Cardona and G. Gtintherodt (Springer, Berlin, in press). [2] J.F. Brazdil and E.B. Yeager, J. Chem. Phys. 85 (1981) 2194. [3] H. Ueba, Surface Sci. 131 (1983) 347. [4] J.E. Potts, R. Merlin and D.L. Partin, Phys. Rev. B27 (1983) 3905. [5] P.M. Whitmore, A.P. Alivisatos and C.B. Harris, Phys. Rev. Letters 50 (1983) 1092. [6] S.E. Kohn, P.Y. Yu, Y. Petroff, Y.R. Shen, Y. Tsang and ML. Cohen, Phys. Rev. B8 (1973) 1477.
L432
SURFACE
SCIENCE
LETTERS
COMI’LEMFNT TO THEORY OF RAMAN SCATTERING ADSORBED MOLECULE ON SEMICONDUCTOR
FROM
H. UEBA Department
of Electronics,
Toyama University,
Takaoka, Toyama, Japan
Received 15 June 1983
The Raman polarizability of a molecule adsorbed on a semiconductor is calculated when it couples to excitonic and interband excitations in the substrate. It is found that a difference in the electronic properties of each excitation manifests itself in the excitation profile of the Raman intensity of the adsorbed molecule, i.e., the former produces a sharp peak below the onset of interband excitation, whereas the latter gives rise to weaker but more broadened structure over a wide range of the spectrum.
Surface enhanced Raman scattering (SERS) [l] from molecules adsorbed on metal substrates has attracted considerable experimental and theoretical interests. Although there still remains some controversy about its trigger, the use of the SERS effect has provided a wide variety of information on chemical properties of adsorbates, which would have never been delivered without the discovery of SERS. So far the studies have been directed to molecules on metal substrates; it is very interesting to explore whether SERS is restricted on metals or not. Recently, Brazdil and Yeager [2] have reported that the Raman bands of p-NDMA and p-DMAAB adsorbed on ZnO and TiOz surfaces undergo enhancement due to a coupling to the electronic states in these substrates. Being stimulated by their experimental results, we have calculated the Raman polarizability of an adsorbed molecule on a semiconductor surface, in which the electronic excitation in the molecule couples to the excitonic or the interband excitation in the semiconductor through non-radiative energy transfer [3]. The Raman polarizability thus calculated has been found to exhibit a peak at the energy of a resonant excitation of excitons, thereby demonstrating the possibility of SERS on semiconductors. After our previous work was completed, we have become aware of another report, by Potts et al. [4], who also observed enhanced Raman scattering from adsorbed amorphous carbon on PbTe. Interestingly enough, the wavelength dependence of the enhancement was found to exhibit a correlation with the band structure of PbTe. Namely, the spectral range where they observed the 0039-6028/83/0000-00/$03.00
0 1983 North-Holland
H. Ueba / Complement
to theoty of Raman scattering
L433
large enhancement correlates with the position of the critical points in the joint density of states of PbTe, thereby suggesting a scattering mechanism which involves the electronic interaction between the molecule and the interband transition in the semiconductor. It should be noted here that they interpreted their result due to roughness-induced coupling of the photons to the interband transition in the relevant intermediate states of the Raman scattering process. Our previous theory, however, clearly demonstrates that the electronic excitation in the semiconductor can be brought through the non-radiative energy dissipation from the excited molecular state, even in the absence of any surface roughness. In fact, the energy transfer from a molecular excited state to a semiconductor substrate has recently been studied by Whitmore et al. [5], whose measurements of the distance dependent life time of pyrazine on GaAs were well explained in terms of a hypothesis that the molecular electronic excitation is dissipated into the excitation of electron-hole pairs in the substrate. Since excitonic or interband excitations are possible candidates which accept the energy dissipation from a excited molecule, it is of interest to study the structure of the Raman polarizability of an adsorbed molecule interacting with excitonic or interband transitions in a semiconductor. The difference in the electronic properties of these excitations will then manifest itself in the excitation profile of the Raman scattering intensity. In this letter, results are presented in order to demonstrate such a characteristic difference in the Raman polarizability. The Raman polar&ability of an adsorbed molecule, in the absence of the direct electronic excitation in the semiconductor through the photon field with frequency w, is expressed as:
(1) where w = w - 3, aL&4= (~-ce.,;~:ce,-p,’
is the polarizability of a free molecule and A4 is the matrix element of the dipole transition in the molecule with energy e,s; A and Q denote the coupling strength of electron-vibrational mode and vibrational frequency, respectively. The quantity R(w)
2
1
=
1-
v2 d4
&(4
I describes a change in the polarizability of the molecule upon adsorption at the semiconductor surface. Here V measures the strength of the non-radiative energy transfer between molecule and semiconductor and
IA34
H. Ueba / Complement
&lb)=(-%,)-‘,
to theory of Raman scattering
gs(4=C(~-~k)-*, k
where ek is the energy of the electronic excitation in the semiconductor. it is needless to say that a key issue of the theory is contained in R(w), which reveals an induced resonant character at an energy satisfying Re[l - I/’ g,(w)
g,(w)] = 0.
(4)
The structure of R(w) and also the enhancement factor IR(w)l’ of the Raman scattering intensity is, therefore, determined by the properties of the electronic excitations in the semiconductor through g,(w) given by
/dr &)&T =P/dr p(r)--&+ilrp(w),
gb>=
(f-5)
where P means the principal value and p(z) represents the density of states for relevant excitations in the semiconductor. Let us now study a characteristic difference in R(w) between the excitonic and the interband coupling of the molecule. We here assume, for an exciton:
where z,,, and r are the energy and the broadening of the exciton state, and Pint(')
=
3
2D-3j2
(c -
csapy2
for the interband excitation of electron-hole pairs, where cgap and D are the band gap energy and the width of the joint density of states for the interband excitation. In what follows, numerical calculations are carried out for ceg = 3.0 eV, ceXC= cgap = 2.0 eV, y = 0.05 eV and D = 3.0 eV. Strictly speaking, cexc is smaller than cgap by the binding energy of the exciton. However, we neglect such difference without losing any interest, since the localized structure of the exciton and the continuum structure of interband excitation are well described by eqs. (7) and (8), respectively. Figs. la and lb depict la[na,,,lcalculated by eq. (1) when eqs. (7) and (8) are used respectively. In fig. la, ((~~~~1exhibits a peak whose position shifts to the lower energy side of E,,~ and the intensity increases with an increase of I’. The appearance of such a peak is caused by a virtual excitation of an exciton through the non-radiative energy transfer from the molecular excited state. On the other hand in fig. lb, a shoulder starts to appear, which is followed by a broad peak just below cgap. It is also mentioned here that at sufficiently large V there appears a sharp peak associated with an admolecule split-off state in the band gap. The different features of ((Y Raml shown in figs. la and lb then
H. Ueba /
a
L435
v=1.2
I ooU
1c
a Ram
Complement to theoty of Raman scattering
a Ram
0.8
5
I!
1
2
W(eV) Fig. 1. Raman polarizability transitions in semiconductor,
of adsorbed molecule coupled to (a) excitonic, see the text for parameters used herein.
and (b) interband
lead to those in the enhancement factor /RI* shown in figs. 2a and 2b. For the excitor% coupling shown in fig. 2a, the enhancement is sharply localized around an induced resonance, above which it undergoes a sudden quenching. On the contrary, the continuum structure of the interband coupling gives rise to the weaker but more broadened spectrum of the enhancement as plotted in fig. 2b. Such a characteristic difference in ]R]* is, therefore, expected to be observed through a careful measurement of the excitation profile of the Raman scattering intensity. According to a verbal description of the excitation profile of carbon on PbTe [4], the Raman intensity for the green-blue line excitations is larger than in the red by a factor of 200. (The maximum enhancement was estimated to be about 103.) Such a trend seems to be consistent with the present result shown in the uppermost curve of fig. 2b, where the degree of the enhancement takes its maximum of an order of lo3 just below the onset of the interband transition at 2.0 eV, which falls in the region of the strong interband transition of PbTe [6]. As one decreases the energy of the incident photon, the
Fig. 2. Enhancement
factor in the log ,c unit, (a) and (b) correspond
to those in fig. 1, respectively.
L436
H. Ueba / Complement
to theory of Raman scattering
enhancement undergoes a gradual decrease, which is a characteristic phenomenon associated with the continuum interband coupling of the molecule in its Raman scattering process. In the case of excitonic coupling, one may observe a sharper structure in the excitation profile of the Raman intensity. Although the energy between an excitonic and an onset of interband transitions is only separated by a small binding energy of the exciton (which is usually several tens of mev), the characteristic difference described above will nevertheless manifest itself in careful observation of the excitation profile. Moreover, another desirable experiment includes the temperature dependence of the Raman intensity. Namely, the band gap of a semiconductor is more or less temperature dependent, thereby causing a shift of the maximum of enhancement in accordance with that of the band gap energy. It is also mentioned that the excitonic coupling with an adsorbed molecule will not be present at rather high temperatures where excitons are short lived and decay quickly into interband excitation. One might therefore be able to observe that the sharp excitation profile at low temperatures is replaced by a broad one as the temperature is raised. In summary, we have shown that a molecule adsorbed on a semiconductor exhibits SERS when the relevant intermediate states in the Raman process involve excitor& or interband transitions in the semiconductor, and that the excitation profile of the Raman intensity enables us to determine which type of electronic excitation is coupled to the electronic excited states of the adsorbed molecule.
References [I] R.K. Chang and T.E. Furtak, Eds., Surface Enhanced Raman Scattering (Plenum, New York, 1982). For a more updated review, see: A. Otto, in: Light Scattering in Solids, Vol. 4, Eds. M. Cardona and G. Gtintherodt (Springer, Berlin, in press). [2] J.F. Brazdil and E.B. Yeager, J. Chem. Phys. 85 (1981) 2194. [3] H. Ueba, Surface Sci. 131 (1983) 347. [4] J.E. Potts, R. Merlin and D.L. Partin, Phys. Rev. B27 (1983) 3905. [5] P.M. Whitmore, A.P. Alivisatos and C.B. Harris, Phys. Rev. Letters 50 (1983) 1092. [6] S.E. Kohn, P.Y. Yu, Y. Petroff, Y.R. Shen, Y. Tsang and ML. Cohen, Phys. Rev. B8 (1973) 1477.