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Local bond rupture of Si atoms on Si(1 1 1)-(2 × 1) induced by the surface π–π∗ excitation
Surface Science 603 (2009) L63–L65
Contents lists available at ScienceDirect
Surface Science journal homepage: www.elsevier.com/locate/susc
Surface Science Letters
Local bond rupture of Si atoms on Si(1 1 1)-(2 1) induced by the surface p–p* excitation E. Inami, K. Tanimura * The Institute of Scientific and Industrial Research, Osaka University, 8-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan
a r t i c l e
i n f o
Article history: Received 11 November 2008 Accepted for publication 3 March 2009 Available online 13 March 2009
Keywords: Desorption induced by electronic transition Laser methods Scanning tunneling microscopy Photochemistry Silicon Surface defects
a b s t r a c t A scanning tunneling microscopy study has revealed that threefold-coordinated Si atoms at intrinsic sites of reconstructed (2 1) structure on the Si(1 1 1) surface are removed to form a surface monovacancy by an electronic mechanism under surface-specific optical transitions at 0.45 eV. This result provides direct evidence for the relaxation of excited surface electronic states as the origin of excitation-induced structural instability on semiconductor surfaces. Ó 2009 Elsevier B.V. All rights reserved.
Reconstructed surfaces of covalent semiconductors show several surface-specific phenomena because of their unique electronic and structural properties [1]. Sensitive structural instability under electronic excitation is a typical example. Extensive studies on the excitation-induced structural instability of semiconductor surfaces have shown that atoms at perfect surface sites are subject to bond rupture [2–7]. Since this instability is surface-specific, the relaxation of excited surface electronic states is suggested to play a crucial role [2,6,8]. However, an un-ambiguous correlation between excited surface electronic states and structural instability induced has not yet been demonstrated, mainly because of the difficulty of generating the surface excited states selectively against strong energetic overlap of surface- and bulk-optical transition in most cases. The Si(1 1 1)-(2 1) surface is characterized by quasi onedimensional zigzag chains of Si atoms, associated with substantial buckling (see Fig. 1a and b). This buckling is accompanied by a net charge transfer from the down (Sidown) to up (Siup) atoms of the chain that induces a significant ionicity in the bonding [1,9,10]. Surface-specific transitions from the occupied Siup band (p) to the unoccupied Sidown band (p*) show a strong peak at 0.45 eV, a value far below the bulk band gap of 1.12 eV [9–11]. Therefore, surface electronic states may be selectively excited, without inducing significant bulk excitation. In this letter, we demonstrate using scanning tunneling microscopy (STM) that the optical excitation * Corresponding author. Tel.: +81 6 6879 8490; fax: +81 6 6879 8494. E-mail address: [email protected] (K. Tanimura). 0039-6028/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2009.03.003
at approximately 0.45 eV leads to bond rupture of intrinsic Siup atoms in the (2 1) reconstructed structure, establishing the first direct correlation between the surface excitation and structural instability. The samples were P-doped (3 1015 cm3) n-type Si crystals with resistivity of 3.15 X cm. Specimens with a crosssection of 0.2 mm 5 mm were cleaved in an ultra-high vacuum (UHV) chamber with a base pressure of 5 1011 Torr, and the surface structures were characterized in situ using a UHV-STM at 291 K. Laser pulses of 2000–2500 nm (80-fs width), were generated by an optical parametric generator, pumped with an 800 nm fs-laser pulse with a repetition rate of 1 kHz. The infrared (IR) fs-laser pulses excited the surface at 45° to normal at fluence between 3 and 50 lJ/cm2. Fig. 1 presents STM images acquired before, (c), and after, (d), irradiation with laser pulses of 2200 nm at a fluence of 47 lJ/ cm2. The electric vector of the IR laser light was parallel to the Si-chain direction. In the images, each white spot corresponds to Siup. Prior to irradiation, defect concentrations on single-domain terraces were less than 0.1% over a typical area 0.4 0.4 lm2. After laser excitation several newly generated dark spots are apparent. The concentration of dark spots increases with laser pulses, exhibiting the following characteristics. Isolated dark spots are predominantly formed at the beginning stage, followed by progressive formation of clusters of spots with increasing laser pulses. Under extended irradiation, dark spot islands were formed, and a periodic atomic structure could be resolved inside well-developed clusters. Quantitative analysis of height profiles of constant-current STM
SU RF A LE CE TT S ER CIE S NC E L64
E. Inami, K. Tanimura / Surface Science 603 (2009) L63–L65
Fig. 1. Top (a) and side (b) views of schematic lattice diagram of tilted chains on Si(1 1 1)-(2 1). STM images acquired with a negative sample-bias voltage of 2.5 V for Si(1 1 1)-(2 1) before, (c), and after, (d), irradiation with 60,000 laser pulses of 80-fs duration at 2200 nm and a constant fluence of 47 lJ cm2 (590 MW cm2 in intensity). The spots brighter than normal Siup sites near the dark spots in Fig. 1d are due to an experimental artifact coming from incomplete compensation of tip-surface distance in the constant-height mode of the image acquisition.
dNh ¼ r/ðtÞðN0 Nh Þ BNh Ne Nh =sh ; dt
ð1Þ
1.0
J(t) (ML)
1.5 0.2 0.1 0
0
100 200 300 TIME DELAY (ps)
(a) 0
10
12
-2
10
0
5
20
5
0
100 200 300 TIME DELAY (ps)
10
(b) 0
200 400 600 EXCITATION INTENSITY (MWcm -2)
0
INTEGRATED DENSITY (arb. units)
0.5
Nh (10 cm )
BOND RUPTURE RATE (10 -7 ML/pulse)
images revealed that the periodic structure corresponded to the second-layer Si arrangement, as in the case of bulk-valence excitation reported previously (see Ref. [12]). Therefore, the dark spots generated by laser excitation are vacancies formed by the removal of Siup atoms. An important finding is that surface vacancies are not formed at all when irradiated with laser pulses polarized perpendicularly to the Si-chain direction, even though the power density is identical. Because of the high peak power of fs-laser pulses, irradiation could induce bulk-valence excitation by a three-photon absorption process in the present case, or multi-photon ionization of surface atoms. However, the strong polarization-dependent characteristics of the bond rupture reveals definitively that the surface optical transitions from p-to-p* states is the primary origin of the bond breaking of Si atoms on this surface, since the 0.45 eV surface transition is completely polarized along the Si-chain direction [9–11]. The contributions of bulk electronic transitions via three-photon absorption can be neglected in Si-bond rupture under such IR laser excitation. These features of surface-vacancy formation are common for other excitation-wavelengths ranging from 2000 to 2500 nm, although a weak dependence of the rate of forming vacancies were detected. The dependence could be explained well in terms of the difference in the excitation densities coming from wavelengthdependent absorption coefficient of p-to-p* transition [13]. Below we discuss mainly the results obtained under 2200 nm excitation. We statistically analyze the images by surveying over 50000 sites to count the number density Nj of vacancy clusters consisting of j vacancy sites (j 6 1), which is simply as a count of sites irrespective of their size. Since any bond ruptures at sites nearest P pre-existing vacancies do not change the total N ( j N j ), N represents only the concentration of new vacancies formed at originally perfect sites [7,13]. We measured the growth of N as a function of the number of laser pulses at a given fluence, and determined the per-pulse bond rupture rate, g0, from the initial slope of the growth curve [12,14]. The magnitude of g0 thus determined is plotted in Fig. 2a; g0 depends super-linearly on laser intensity. Since multiphoton absorption processes for generating bulk-excited species do not lead to bond rupture here, this super-linear dependency indicates that the non-linear interaction of surface photoexcited species generated by one-photon p-to-p* transition plays a crucial role in intrinsic local bond rupture mechanism. A time-resolved two-photon photoelectron spectroscopy of Si(1 1 1)-(2 1) has shown that the decay of surface holes generated by p-to-p* excitation is described by the rate equation:
Fig. 2. (a) The per-pulse bond rupture rate on surfaces with vacancy concentrations below 0.001 ML as a function of excitation intensity on the n-type Si(1 1 1)-(2 1) surface. The solid curve is a fit of the theoretical results derived by the two-hole localization mechanism to the experimental results, with using an empirical value of C in Eq. (2) (see text). The inset shows the temporal changes of the calculated bond rupture rate induced by a single shot of a 2200 nm laser pulse at an intensity of 590 MW cm2. (b) The calculated time-integrated surface hole density based on the rate equation model, grey curve, and the evaluated per-pulse bond rupture rate, solid curve, as a function of excitation intensity. The inset shows the temporal changes of calculated surface hole density induced by a single shot of 2200 nm laser pulse at the intensity of 590 MW cm2. Decay constants in Eq. (3) are B = 0.004 cm2/ s, sh = 100 ps, and se = 330 ps (Ref. [15]).
where Nh and Ne are the densities of surface holes and electrons, /(t) represents the photon flux, r is the absorption crosssection, B is the coefficient of surface electron-hole recombination, and 1/sh represents the rate of scattering processes of holes from the p band [15]. A similar equation holds for the surface electrons. They have shown that the temporal changes of Nh and Ne differ significantly. Therefore, surface excited states generated by p-to-p* excitation
are free carriers rather than excitons; transition from quasi-particle states to free carriers are fast enough. Then, the non-linear interaction of the surface carriers is the issue to be considered in elucidating the bond rupture mechanism. Theoretical calculations suggest that the formation energy of a Si atom vacancy at a threefold-coordinated site on reconstructed Si surfaces is about 0.9 eV [16]. In order to induce a local bond rupture, the surface carriers must be localized at a given site to generate enough force to overcome the binding. Our previous study of this surface under bulk-valence excitation has shown that bulk-valence holes play an essential role in bond rupture via two-hole localization (THL) at intrinsic surface sites [14]. Here, under surface-specific optical excitation, two-dimensional surface holes are generated directly. Therefore, it is reasonable to examine quantitatively the possible roles of photo-injected holes in the surface p band on the bond rupture under IR laser excitation. For simplicity, we approximate the p band as a two-dimensional band with a constant density of states. Then, we can apply the original Sumi’s formalism [17]. For a hole density Nh in the p band of Si(1 1 1)-(2 1) with a band width W, a rate, J, of surface bond rupture induced by the successive two-hole localization is given by
J ¼ N0 C expðEd =kB TÞfexpðnÞ 1g2 ; 14
ð2Þ
2
where N0 (=3.9 10 cm ) represents the total density of bonds capable of holding the first localized hole on this surface, kB is the Boltzmann constant, and Ed is the energy of the first-hole localized metastable state measured from the valence band maximum (VBM). The normalized hole density n is defined as n = Nh/Z, where Z, given by (N0/W)2kBT, is the effective number of the free-hole states at a temperature T [14]. The constant C is defined as 2
C ¼ ½4p=ðh SkBT Þ1=2 2
Z
dEgðEÞ exp½E=kB T
ðEb þ U EÞ =ð4SkB T Þ;
ð3Þ
where g(E) is a spectral function of the matrix elements for the transitions from a delocalized state to the two-hole localized state, S represents the lattice relaxation energy associated with the second hole localization, U is the Coulomb repulsive energy between the two-holes localized on a single bond, and Eb is the kinetic energy lost in the process of localizing the second hole at the bond, given by half of W. With g(E) obtained in Ref. [17], the magnitude of C is evaluated by the second-order expansion of the exponent of Eq. (3), under the condition that Ed þ Eb þ U S 6 0, which makes the two-hole localized state possible [17]. A photoemission study has shown that W = 0.9 eV for the p band [18], giving Z of 2.3 1013 cm2 at room temperature. Although the energy Ed of a hole localization has not been studied, theoretical study on the exciton self-trapping showed that the lattice relaxation gives an additional binding energy of 17.5 meV for a hole (and an electron) [19]. We use this value, and set Ed = 0.018 eV, since the top of the p band is close to the VBM [18]. The energy U has been calculated to be 0.94 eV for this surface [14]. The unknown energy in Eq. (2) is S, which should be greater than 1.4 eV (P Ed þEb þ U). When we assume S = 2.5 eV as in our previous study [14], we obtain a value for C of 1.5 105 s1. The density of photogenerated surface holes can be evaluated using Eq. (1). The absorption coefficient (rN0) of the p-to-p* transition at 2200 nm has been obtained experimentally to be 0.03 [13], and /(t) is determined experimentally. Then, by combining Eqs. (1)–(3), we can calculate the bond rupture rate as a function of time and the excitation intensity Iex. The inset of Fig. 2b shows the calculated temporal changes of Nh. Because of the rather slow decay rates of surface carriers listed
CE N IE SC S R CE E A TT RF LE SU
E. Inami, K. Tanimura / Surface Science 603 (2009) L63–L65
L65
in the figure caption [15], the maximum densities of Nh reached at the end of 80-fs laser excitation are proportional to Iex. However, the time-integrated density shows sub-linear growth because of the quadratic term of surface electron-hole recombination as shown by the grey curve in Fig. 2b. On the other hand, at highintensity excitation n becomes large, enhancing the bond rupture rate significantly. An example of the evaluated J(t) is shown in the inset of Fig. 2a, where effective bond rupture terminates within 100 ps. Since our definition of per-pulse bond rupture rate g0 is reR þ1 lated to J(t) as g 0 ¼ 1 JðtÞdt, we can calculate g0 based on the results of J(t). The theoretical results of g0 is shown in Fig. 2b. The solid curve in Fig. 2a is an empirical fit of calculated g0 to experimental results with a reduced value of C by a factor of 10 Although a super-linear dependency is reproduced reasonably well by the THL mechanism, the calculated rate (solid curve in Fig. 2b) is higher than the experimental results. We presume that the discrepancy is partially due to our approximation of the surface p band as a two-dimensional band with a constant density of states. In fact, the p band on Si(1 1 1)-(2 1) is quasi one-dimensional with an effective transfer only along the chain direction, and the density of states is not constant [13]. Therefore, numerical factors in Eqs. (2 and 3) may need modification. Another source of the discrepancy may be concerned with the lattice relaxation energy S of the two-hole localized state, which is not known precisely. When S is reduced to 1.4 eV, the smallest value possible in the range, C is reduced by a factor of 10, almost consistent with the empirically determined C in Fig. 2a. When these limitations and approximations in determining absolute bond rupture rate are taken into account, we can conclude that the THL mechanism captures the essential physics, at a semi-quantitative level, of the bond rupture at intrinsic sites under surface optical excitation that prepares a two-dimensional surface hole distribution. The drawbacks of alternative models have been discussed in detail in Ref. [14]. Statistical analysis of the STM images has shown that the fractions of vacancy clusters relative to the total vacancy sites under IR laser excitation is essentially the same as that under bulk-valence excitation [14]. Therefore, we presume that bond rupture near pre-existing vacancy sites also due to the THL mechanism as in the case of bulk-valence excitation. Acknowledgement This work was supported by a Specially Promoted Research of Grant-in-Aid for Scientific Research from the MEXT, Japan. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]
W. Mönch, Semiconductor Surfaces and Interfaces, Springer, Berlin, 1995. J. Kanasaki, T. Ishida, K. Ishikawa, K. Tanimura, Phys. Rev. Lett. 80 (1998) 4080. J. Kanasaki, K. Iwata, K. Tanimura, Phys. Rev. Lett. 82 (1999) 644. H. Kwak, K.C. Chou, J. Guo, H.W.K. Tom, Phys. Rev. Lett. 83 (1999) 3745. B.Y. Han, K. Nakayama, J.H. Weaver, Phys. Rev. B 60 (1999) 13845. J. Kanasaki, M. Nakamura, K. Ishikawa, K. Tanimura, Phys. Rev. Lett. 89 (2002) 257601. T. Gotoh, S. Kotake, K. Ishikawa, J. Kanasaki, K. Tanimura, Phys. Rev. Lett. 93 (2004) 117401. K. Tanimura, J. Kanasaki, J. Phys.:Condens. Matter 18 (2006) S1479. F. Ciccacci, S. Selci, G. Chiarotti, P. Chiaradia, Phys. Rev. Lett. 56 (1986) 2411. F. Ancilotto, W. Andreoni, A. Selloni, R. Car, M. Parrinello, Phys. Rev. Lett. 65 (1990) 3148. M. Rohlfing, S.G. Louie, Phys. Rev. Lett. 83 (1999) 856. E. Inami, K. Ishikawa, K. Tanimura, Surf. Sci. 540 (2003) L587. G. Chiarotti, S. Nannarone, R. Pastore, P. Chiaradia, Phys. Rev. B 4 (1971) 3398. E. Inami, K. Tanimura, Phys. Rev. B 76 (2007) 035311. J. Bokor, R. Storz, R.R. Freeman, P.H. Bucksbaum, Phys. Rev. Lett. 57 (1986) 881. H. Lim, K. Cho, R.B. Capaz, J.D. Joannapoulos, K.D. Brommer, B.E. Larson, Phys. Rev. B 53 (1996) 15421. H. Sumi, Surf. Sci. 248 (1991) 382. P. Martensson, A. Cricenti, G.V. Hansson, Phys. Rev. B39 (1985) 6959. M. Rohlfing, J. Pollmann, Phys. Rev. Lett. 88 (2002) 176801.
Contents lists available at ScienceDirect
Surface Science journal homepage: www.elsevier.com/locate/susc
Surface Science Letters
Local bond rupture of Si atoms on Si(1 1 1)-(2 1) induced by the surface p–p* excitation E. Inami, K. Tanimura * The Institute of Scientific and Industrial Research, Osaka University, 8-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan
a r t i c l e
i n f o
Article history: Received 11 November 2008 Accepted for publication 3 March 2009 Available online 13 March 2009
Keywords: Desorption induced by electronic transition Laser methods Scanning tunneling microscopy Photochemistry Silicon Surface defects
a b s t r a c t A scanning tunneling microscopy study has revealed that threefold-coordinated Si atoms at intrinsic sites of reconstructed (2 1) structure on the Si(1 1 1) surface are removed to form a surface monovacancy by an electronic mechanism under surface-specific optical transitions at 0.45 eV. This result provides direct evidence for the relaxation of excited surface electronic states as the origin of excitation-induced structural instability on semiconductor surfaces. Ó 2009 Elsevier B.V. All rights reserved.
Reconstructed surfaces of covalent semiconductors show several surface-specific phenomena because of their unique electronic and structural properties [1]. Sensitive structural instability under electronic excitation is a typical example. Extensive studies on the excitation-induced structural instability of semiconductor surfaces have shown that atoms at perfect surface sites are subject to bond rupture [2–7]. Since this instability is surface-specific, the relaxation of excited surface electronic states is suggested to play a crucial role [2,6,8]. However, an un-ambiguous correlation between excited surface electronic states and structural instability induced has not yet been demonstrated, mainly because of the difficulty of generating the surface excited states selectively against strong energetic overlap of surface- and bulk-optical transition in most cases. The Si(1 1 1)-(2 1) surface is characterized by quasi onedimensional zigzag chains of Si atoms, associated with substantial buckling (see Fig. 1a and b). This buckling is accompanied by a net charge transfer from the down (Sidown) to up (Siup) atoms of the chain that induces a significant ionicity in the bonding [1,9,10]. Surface-specific transitions from the occupied Siup band (p) to the unoccupied Sidown band (p*) show a strong peak at 0.45 eV, a value far below the bulk band gap of 1.12 eV [9–11]. Therefore, surface electronic states may be selectively excited, without inducing significant bulk excitation. In this letter, we demonstrate using scanning tunneling microscopy (STM) that the optical excitation * Corresponding author. Tel.: +81 6 6879 8490; fax: +81 6 6879 8494. E-mail address: [email protected] (K. Tanimura). 0039-6028/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2009.03.003
at approximately 0.45 eV leads to bond rupture of intrinsic Siup atoms in the (2 1) reconstructed structure, establishing the first direct correlation between the surface excitation and structural instability. The samples were P-doped (3 1015 cm3) n-type Si crystals with resistivity of 3.15 X cm. Specimens with a crosssection of 0.2 mm 5 mm were cleaved in an ultra-high vacuum (UHV) chamber with a base pressure of 5 1011 Torr, and the surface structures were characterized in situ using a UHV-STM at 291 K. Laser pulses of 2000–2500 nm (80-fs width), were generated by an optical parametric generator, pumped with an 800 nm fs-laser pulse with a repetition rate of 1 kHz. The infrared (IR) fs-laser pulses excited the surface at 45° to normal at fluence between 3 and 50 lJ/cm2. Fig. 1 presents STM images acquired before, (c), and after, (d), irradiation with laser pulses of 2200 nm at a fluence of 47 lJ/ cm2. The electric vector of the IR laser light was parallel to the Si-chain direction. In the images, each white spot corresponds to Siup. Prior to irradiation, defect concentrations on single-domain terraces were less than 0.1% over a typical area 0.4 0.4 lm2. After laser excitation several newly generated dark spots are apparent. The concentration of dark spots increases with laser pulses, exhibiting the following characteristics. Isolated dark spots are predominantly formed at the beginning stage, followed by progressive formation of clusters of spots with increasing laser pulses. Under extended irradiation, dark spot islands were formed, and a periodic atomic structure could be resolved inside well-developed clusters. Quantitative analysis of height profiles of constant-current STM
SU RF A LE CE TT S ER CIE S NC E L64
E. Inami, K. Tanimura / Surface Science 603 (2009) L63–L65
Fig. 1. Top (a) and side (b) views of schematic lattice diagram of tilted chains on Si(1 1 1)-(2 1). STM images acquired with a negative sample-bias voltage of 2.5 V for Si(1 1 1)-(2 1) before, (c), and after, (d), irradiation with 60,000 laser pulses of 80-fs duration at 2200 nm and a constant fluence of 47 lJ cm2 (590 MW cm2 in intensity). The spots brighter than normal Siup sites near the dark spots in Fig. 1d are due to an experimental artifact coming from incomplete compensation of tip-surface distance in the constant-height mode of the image acquisition.
dNh ¼ r/ðtÞðN0 Nh Þ BNh Ne Nh =sh ; dt
ð1Þ
1.0
J(t) (ML)
1.5 0.2 0.1 0
0
100 200 300 TIME DELAY (ps)
(a) 0
10
12
-2
10
0
5
20
5
0
100 200 300 TIME DELAY (ps)
10
(b) 0
200 400 600 EXCITATION INTENSITY (MWcm -2)
0
INTEGRATED DENSITY (arb. units)
0.5
Nh (10 cm )
BOND RUPTURE RATE (10 -7 ML/pulse)
images revealed that the periodic structure corresponded to the second-layer Si arrangement, as in the case of bulk-valence excitation reported previously (see Ref. [12]). Therefore, the dark spots generated by laser excitation are vacancies formed by the removal of Siup atoms. An important finding is that surface vacancies are not formed at all when irradiated with laser pulses polarized perpendicularly to the Si-chain direction, even though the power density is identical. Because of the high peak power of fs-laser pulses, irradiation could induce bulk-valence excitation by a three-photon absorption process in the present case, or multi-photon ionization of surface atoms. However, the strong polarization-dependent characteristics of the bond rupture reveals definitively that the surface optical transitions from p-to-p* states is the primary origin of the bond breaking of Si atoms on this surface, since the 0.45 eV surface transition is completely polarized along the Si-chain direction [9–11]. The contributions of bulk electronic transitions via three-photon absorption can be neglected in Si-bond rupture under such IR laser excitation. These features of surface-vacancy formation are common for other excitation-wavelengths ranging from 2000 to 2500 nm, although a weak dependence of the rate of forming vacancies were detected. The dependence could be explained well in terms of the difference in the excitation densities coming from wavelengthdependent absorption coefficient of p-to-p* transition [13]. Below we discuss mainly the results obtained under 2200 nm excitation. We statistically analyze the images by surveying over 50000 sites to count the number density Nj of vacancy clusters consisting of j vacancy sites (j 6 1), which is simply as a count of sites irrespective of their size. Since any bond ruptures at sites nearest P pre-existing vacancies do not change the total N ( j N j ), N represents only the concentration of new vacancies formed at originally perfect sites [7,13]. We measured the growth of N as a function of the number of laser pulses at a given fluence, and determined the per-pulse bond rupture rate, g0, from the initial slope of the growth curve [12,14]. The magnitude of g0 thus determined is plotted in Fig. 2a; g0 depends super-linearly on laser intensity. Since multiphoton absorption processes for generating bulk-excited species do not lead to bond rupture here, this super-linear dependency indicates that the non-linear interaction of surface photoexcited species generated by one-photon p-to-p* transition plays a crucial role in intrinsic local bond rupture mechanism. A time-resolved two-photon photoelectron spectroscopy of Si(1 1 1)-(2 1) has shown that the decay of surface holes generated by p-to-p* excitation is described by the rate equation:
Fig. 2. (a) The per-pulse bond rupture rate on surfaces with vacancy concentrations below 0.001 ML as a function of excitation intensity on the n-type Si(1 1 1)-(2 1) surface. The solid curve is a fit of the theoretical results derived by the two-hole localization mechanism to the experimental results, with using an empirical value of C in Eq. (2) (see text). The inset shows the temporal changes of the calculated bond rupture rate induced by a single shot of a 2200 nm laser pulse at an intensity of 590 MW cm2. (b) The calculated time-integrated surface hole density based on the rate equation model, grey curve, and the evaluated per-pulse bond rupture rate, solid curve, as a function of excitation intensity. The inset shows the temporal changes of calculated surface hole density induced by a single shot of 2200 nm laser pulse at the intensity of 590 MW cm2. Decay constants in Eq. (3) are B = 0.004 cm2/ s, sh = 100 ps, and se = 330 ps (Ref. [15]).
where Nh and Ne are the densities of surface holes and electrons, /(t) represents the photon flux, r is the absorption crosssection, B is the coefficient of surface electron-hole recombination, and 1/sh represents the rate of scattering processes of holes from the p band [15]. A similar equation holds for the surface electrons. They have shown that the temporal changes of Nh and Ne differ significantly. Therefore, surface excited states generated by p-to-p* excitation
are free carriers rather than excitons; transition from quasi-particle states to free carriers are fast enough. Then, the non-linear interaction of the surface carriers is the issue to be considered in elucidating the bond rupture mechanism. Theoretical calculations suggest that the formation energy of a Si atom vacancy at a threefold-coordinated site on reconstructed Si surfaces is about 0.9 eV [16]. In order to induce a local bond rupture, the surface carriers must be localized at a given site to generate enough force to overcome the binding. Our previous study of this surface under bulk-valence excitation has shown that bulk-valence holes play an essential role in bond rupture via two-hole localization (THL) at intrinsic surface sites [14]. Here, under surface-specific optical excitation, two-dimensional surface holes are generated directly. Therefore, it is reasonable to examine quantitatively the possible roles of photo-injected holes in the surface p band on the bond rupture under IR laser excitation. For simplicity, we approximate the p band as a two-dimensional band with a constant density of states. Then, we can apply the original Sumi’s formalism [17]. For a hole density Nh in the p band of Si(1 1 1)-(2 1) with a band width W, a rate, J, of surface bond rupture induced by the successive two-hole localization is given by
J ¼ N0 C expðEd =kB TÞfexpðnÞ 1g2 ; 14
ð2Þ
2
where N0 (=3.9 10 cm ) represents the total density of bonds capable of holding the first localized hole on this surface, kB is the Boltzmann constant, and Ed is the energy of the first-hole localized metastable state measured from the valence band maximum (VBM). The normalized hole density n is defined as n = Nh/Z, where Z, given by (N0/W)2kBT, is the effective number of the free-hole states at a temperature T [14]. The constant C is defined as 2
C ¼ ½4p=ðh SkBT Þ1=2 2
Z
dEgðEÞ exp½E=kB T
ðEb þ U EÞ =ð4SkB T Þ;
ð3Þ
where g(E) is a spectral function of the matrix elements for the transitions from a delocalized state to the two-hole localized state, S represents the lattice relaxation energy associated with the second hole localization, U is the Coulomb repulsive energy between the two-holes localized on a single bond, and Eb is the kinetic energy lost in the process of localizing the second hole at the bond, given by half of W. With g(E) obtained in Ref. [17], the magnitude of C is evaluated by the second-order expansion of the exponent of Eq. (3), under the condition that Ed þ Eb þ U S 6 0, which makes the two-hole localized state possible [17]. A photoemission study has shown that W = 0.9 eV for the p band [18], giving Z of 2.3 1013 cm2 at room temperature. Although the energy Ed of a hole localization has not been studied, theoretical study on the exciton self-trapping showed that the lattice relaxation gives an additional binding energy of 17.5 meV for a hole (and an electron) [19]. We use this value, and set Ed = 0.018 eV, since the top of the p band is close to the VBM [18]. The energy U has been calculated to be 0.94 eV for this surface [14]. The unknown energy in Eq. (2) is S, which should be greater than 1.4 eV (P Ed þEb þ U). When we assume S = 2.5 eV as in our previous study [14], we obtain a value for C of 1.5 105 s1. The density of photogenerated surface holes can be evaluated using Eq. (1). The absorption coefficient (rN0) of the p-to-p* transition at 2200 nm has been obtained experimentally to be 0.03 [13], and /(t) is determined experimentally. Then, by combining Eqs. (1)–(3), we can calculate the bond rupture rate as a function of time and the excitation intensity Iex. The inset of Fig. 2b shows the calculated temporal changes of Nh. Because of the rather slow decay rates of surface carriers listed
CE N IE SC S R CE E A TT RF LE SU
E. Inami, K. Tanimura / Surface Science 603 (2009) L63–L65
L65
in the figure caption [15], the maximum densities of Nh reached at the end of 80-fs laser excitation are proportional to Iex. However, the time-integrated density shows sub-linear growth because of the quadratic term of surface electron-hole recombination as shown by the grey curve in Fig. 2b. On the other hand, at highintensity excitation n becomes large, enhancing the bond rupture rate significantly. An example of the evaluated J(t) is shown in the inset of Fig. 2a, where effective bond rupture terminates within 100 ps. Since our definition of per-pulse bond rupture rate g0 is reR þ1 lated to J(t) as g 0 ¼ 1 JðtÞdt, we can calculate g0 based on the results of J(t). The theoretical results of g0 is shown in Fig. 2b. The solid curve in Fig. 2a is an empirical fit of calculated g0 to experimental results with a reduced value of C by a factor of 10 Although a super-linear dependency is reproduced reasonably well by the THL mechanism, the calculated rate (solid curve in Fig. 2b) is higher than the experimental results. We presume that the discrepancy is partially due to our approximation of the surface p band as a two-dimensional band with a constant density of states. In fact, the p band on Si(1 1 1)-(2 1) is quasi one-dimensional with an effective transfer only along the chain direction, and the density of states is not constant [13]. Therefore, numerical factors in Eqs. (2 and 3) may need modification. Another source of the discrepancy may be concerned with the lattice relaxation energy S of the two-hole localized state, which is not known precisely. When S is reduced to 1.4 eV, the smallest value possible in the range, C is reduced by a factor of 10, almost consistent with the empirically determined C in Fig. 2a. When these limitations and approximations in determining absolute bond rupture rate are taken into account, we can conclude that the THL mechanism captures the essential physics, at a semi-quantitative level, of the bond rupture at intrinsic sites under surface optical excitation that prepares a two-dimensional surface hole distribution. The drawbacks of alternative models have been discussed in detail in Ref. [14]. Statistical analysis of the STM images has shown that the fractions of vacancy clusters relative to the total vacancy sites under IR laser excitation is essentially the same as that under bulk-valence excitation [14]. Therefore, we presume that bond rupture near pre-existing vacancy sites also due to the THL mechanism as in the case of bulk-valence excitation. Acknowledgement This work was supported by a Specially Promoted Research of Grant-in-Aid for Scientific Research from the MEXT, Japan. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]
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