Surface sum frequency generation spectroscopy on non-centrosymmetric crystal GaAs (001)

Surface Science 664 (2017) 21–28

Contents lists available at ScienceDirect

Surface Science journal homepage: www.elsevier.com/locate/susc

Surface sum frequency generation spectroscopy on non-centrosymmetric crystal GaAs (001) Zhenyu Zhang a,b, Jisun Kim a, Rami Khoury b, Mohammad Saghayezhian a, Louis H. Haber b, E.W. Plummer a,∗ a b

Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803, USA Department of Chemistry, Louisiana State University, Baton Rouge, LA 70803, USA

a r t i c l e

i n f o

Keywords: Sum frequency generation spectroscopy Non-centrosymmetric crystals Heterodyne amplification Electric quadrupole Nonlinear optics

a b s t r a c t Femtosecond broadband sum frequency generation (SFG) spectroscopy is applied to surface studies of the archetypical non-centrosymmetric semiconductor GaAs (001). Azimuthal angular dependence studies in reflection geometry under eight possible polarization configurations reveal strong surface-bulk interference owing to heterodyne amplification. The crystal symmetry and the surface quadrupole contributions need to be considered to properly interpret the resulting nonlinear spectroscopic signals. In addition, over bandgap excitation by one of the incident beams brings the semiconductor surface to a transient excited state, enabling enhanced sensitivity of broadband SFG to probe the surface electronic properties of non-centrosymmetric semiconductors. These findings suggest that this technique can be generally applied to surface studies of other non-centrosymmetric crystals. © 2017 Elsevier B.V. All rights reserved.

1. Introduction Second-order nonlinear optical spectroscopies, such as second harmonic generation (SHG) and sum frequency generation (SFG), are wellestablished and versatile techniques for surface and interface studies [1–4]. Under the electric-dipole approximation, a second order nonlinear optical process is forbidden in media with inversion symmetry, but such symmetry is broken at a surface and interface, thus allowing the nonlinear processes. This enables SHG and SFG to be successfully applied as a surface sensitive probe as shown in numerous studies over the past decades. For example, SHG has been used to study adsorption at metal, semiconductor, and insulator surfaces [5]. SHG has also been used for the determination of crystal surface symmetry, surface state, charge density, and to probe time-resolved phenomena at interfaces [6–9]. Additionally, broadband vibrational SFG has had widespread applications, especially for surface molecular adsorption and time-resolved studies [10–13]. The application of SHG and SFG for the study of surfaces and interfaces has been mainly limited to centrosymmetric materials. Previous work to extend surface SHG studies to non-centrosymmetric crystals has mainly focused on GaAs (001) surfaces [14–19]. The reflected SHG signal from GaAs (001) was explained as the interference of signals from the bulk and its reconstructed surface [18], including the interference caused by a tilt angle of a vicinal GaAs (001) [19]. The surface SHG resonant enhancement at ∼ 1.45 eV from (001) N+ -doped ∗

Corresponding author. E-mail address: [email protected] (E.W. Plummer).

http://dx.doi.org/10.1016/j.susc.2017.05.011 Received 18 November 2016; Received in revised form 19 May 2017; Accepted 20 May 2017 Available online 22 May 2017 0039-6028/© 2017 Elsevier B.V. All rights reserved.

GaAs-oxide interface was studied in two independent investigations, one using nanosecond pulses (∼ 5 ns) [20] and the other using femtosecond pulses (∼ 150 fs) [21]. In both studies, the azimuthal angular dependent SFG pattern shows a two-fold symmetry due to the surface and bulk interference, instead of a bulk-only four-fold symmetry. On the other hand, the amplitude ratio of the two non-equal lobes probed by femtosecond pulses is much larger than the one by nanosecond pulses, indicating increased surface signal sensitivity. In recent years, a few studies [22–24] have reported investigations of non-centrosymmetric crystal surfaces (Z-cut 𝛼-quartz (0001)) using SFG spectroscopy with arrangements to extract surface SFG signals by orienting the crystal azimuthally to minimize bulk contributions. In these investigations, since the quartz surface has C6v symmetry due to the unavoidable atomic steps and terraces, the SFG signal from the quartz surface is not angular dependent (isotropic), whereas SFG signal from the quartz bulk is angular dependent. Using the bulk signal at different angles as a phase reference and a local oscillator, the SFG signal from the interfacial water molecules was studied along with their wavelength dependent phase information. In this paper, we report the first application of broadband SFG to investigate a non-centrosymmetric semiconductor crystal surface. In the broadband femtosecond SFG scheme (Fig. 1), the visible input is spectrally narrowed with a pulse length in the picosecond range while both the broadband IR input and SFG output are in the femtosecond regime. Broadband SFG provides an entire SFG spectrum over the corresponding IR photon energy range with the added benefit of ultrafast temporal

Z. Zhang et al.

Surface Science 664 (2017) 21–28

the visible 800 nm light penetrates into the bulk approximately 760 nm, while it is transparent at the IR wavelength. The collected SFG signal originates roughly from the top 350 nm of bulk, corresponding to the absorption depth of the light at the SFG wavelength of 685 nm [29]. At the GaAs surface, the overlapped beam size of the IR beam is more than 16 times larger than that of the 800 nm beam. The beam overlapping region in the GaAs is much larger than the layer SFG photons can penetrate, preventing possible artifacts in the detected SFG signal. A CaF2 focusing lens is used for the IR beam. Inside the vacuum chamber, the spacing from the bottom of laser access window to the top of the crystal surface is approximately 1.5 mm. A half-wave plate for 800 nm wavelength is used to adjust the polarization of the visible beam. A mechanical polarization switch is used for the broadband IR beam, consisting of magnetic base plates with either a 90° twisted periscope [30] and a normal periscope or a retroreflector and mirror with the same optical path length. This polarization switch allows the IR incident beam to be conveniently switched between P- and S- polarizations while maintaining the beam intensity, direction, and path length. The reflected SFG signal is collimated and transmitted through a polarizer for the polarizationselected measurements. SFG spectra are recorded with a high-sensitivity charge-coupled device (CCD) connected to a spectrometer. Then the SFG intensity is obtained by integrating the area under the SFG spectrum at each azimuthal angle (see Supplemental Materials).

Fig. 1. (Color online) Schematic representation of the broadband SFG setup. Pulse-shaped visible light (∼ 2 ps, 800 nm ± 10 nm) overlaps with a mid-infrared pulse (∼ 150 fs, 4762 nm ± 500 nm) on the surface of a crystal to produce the SFG signal. The reflected SFG is measured as a function of the azimuthal angle of the crystal under different incident and SFG polarizations.

resolution. Reflected SFG on GaAs (001) surface is measured and analyzed as a function of the azimuthal angular dependence under eight different polarization configurations. We show that interference between the surface and bulk SFG contributions significantly amplifies the nonlinear optical signal at the crystal surface. Our work adds a new understanding that SFG can be an effective tool to probe microscopic surface structure and electronic properties of non-centrosymmetric semiconductors [25].

3. Theoretical background We will first discuss the general theoretical background of SFG from a crystal surface and later point out problems with this treatment for interpreting our experimental results. SFG is a nonlinear optical response to ⃖⃖⃗(𝜔1 ) and 𝐸 ⃖⃖⃗(𝜔2 ) at frequencies 𝜔1 and 𝜔2 that two incident optical fields 𝐸 combine to generate an optical field at frequency 𝜔3, with 𝜔3 = 𝜔1 + 𝜔2 as shown schematically in Fig. 1. Under the electric-dipole approximation, the nonlinear response can be written [31–33] as a field-induced polarization Pi at frequency 𝜔3 , ( ) ( ) ( ) 𝑃𝑖 (𝜔3 ) = 𝜒ef(2)f 𝜔3 , 𝜔1 , 𝜔2 𝐸𝑗 𝜔1 𝐸𝑘 𝜔2 , ( (↔ ) )( ↔ ) ( ) ) ↔ (2) ( 𝜔3 , 𝜔1 , 𝜔2 𝐿𝑗 ⋅ 𝑒̂𝑗 𝜒ef(2)f 𝜔3 , 𝜔1 , 𝜔2 = 𝐿𝑖 ⋅ 𝑒̂𝑖 𝜒𝑖𝑗𝑘 𝐿𝑘 ⋅ 𝑒̂𝑘 (1)

2. Materials and methods GaAs is chosen as an archetype crystal for demonstration in this work. GaAs has a zinc blende structure (43𝑚(Td )) (Fig. 2(a)) whose bulk has no inversion symmetry and no birefringence. The refractive index for light propagation in the bulk does not change under varying incident beam polarizations or sample rotation orientations. The bulkterminated surface structure is shown in Fig. 2(b). To exclude the SFG contribution due to the depletion field present near the surface [15,26], undoped semi-insulating (𝜌 ∼ 108 Ω⋅cm) GaAs grown with the vertical gradient freeze technique is used. The polished sample surface is chemically etched [27] (see Fig. 1S) before loading into a vacuum chamber at a base pressure of 2 × 10−6 Torr. Figs. 2(c and d) show the experimental arrangement. The incident beams and the SFG signal define the XZ plane of the lab coordinate, where the Z-axis is normal to the GaAs (001) surface, 𝜙 is the azimuthal rotational angle of the X-axis away from the crystal [100] axis, 𝛼 i is the incident angle, and 𝛽 i is a refracted angle. The GaAs sample is mounted on an XYZ manipulator with a piezo motor-driven rotation stage that is rotated in the clockwise direction with respect to the incident beams (Fig. 2(c)). The incident angles on the sample are 𝛼 1 = 19.6° and 𝛼 2 = 32.0° for the visible and IR beams, respectively (Fig. 2(d)). The experimental setup is shown in Fig. 3. An amplified Titanium: sapphire laser system produces 75 fs, 3 mJ pulses at 800 nm with a repetition rate of 1 kHz coupled to an optical parametric amplifier (OPA) after a beam splitter for the tunable wavelength IR pulse generation. The bandwidth of the 800 nm beam is spectrally narrowed to a full width half maximum (FWHM) of 1.8 nm with a corresponding pulse length of approximately 2 ps using a pulse shaper consisting of a grating, a cylindrical focusing lens, an adjustable slit, and a mirror [28]. With the 800 nm beam output energy set as 3 μJ at the sample position, its wavelength is measured as 800 nm ± 3 nm. The broadband IR beam is centered at 4762 nm and has a FWHM of 200 cm−1 and a pulse length of approximately 150 fs. With a knife-edge measurement, 10/90 beam sizes on the crystal surface are 250 μm by 300 μm for the visible beam and 1.0 mm by 1.2 mm for the IR beam. During the experiments, the pulse energies of visible and IR beams are 3 μJ (40 J/m2 ) and 7.5 μJ (6.25 J/m2 ), respectively, which are far below the damage threshold. In the GaAs sample,

where, i, j, and k run through the spatial coordinates x, y, and z. The (2) 𝜒𝑖𝑗𝑘 is the second-order nonlinear susceptibility of the material. 𝑒̂𝑖 is a polarization unit vector of the optical field at 𝜔i and ⃖⃖𝐿⃗ is the Fresnel transmission tensor. For GaAs bulk, the asymmetry in the bond between adjacent Ga and As atoms causes the non-centrosymmetric structure which mainly contributes to the bulk SFG signal. The second-order nonlinear susceptibility of bulk GaAs has six non-vanishing tensor elements with the (2) (2) (2) (2) (2) (2) same unique value, 𝜒𝑎𝑏𝑐 = 𝜒𝑏𝑐𝑎 = 𝜒𝑐𝑎𝑏 = 𝜒𝑏𝑎𝑐 = 𝜒𝑎𝑐𝑏 = 𝜒𝑐𝑏𝑎 where a, b, and c correspond to the principal axes of the crystal (Fig. 2(a)). The GaAs (001) surface, shown in Fig. 2(b), has four-fold symmetry if only the topmost layer is considered and surface reconstruction is neglected. However, due to the asymmetry in the bond between adjacent Ga and As atoms, the second layer also needs to be considered so the surface symmetry belongs to the mm2 (C2𝜈 ). Under such symmetry, the surface second-order susceptibility tensor has seven independent elements, (2) (2) (2) (2) (2) (2) 𝜒𝜉𝜉𝑍 , 𝜒𝜉𝑍𝜉 , 𝜒𝑍𝜉𝜉 , 𝜒𝜂𝜂𝑍 , 𝜒𝜂𝑍𝜂 , 𝜒𝑍𝜂𝜂 , and 𝜒𝑍(2)𝑍 𝑍 [34], where 𝜉, 𝜂, and Z correspond to the principal axes of the surface. Here, 𝜉 and 𝜂 are along the [110] and [1̄ 10] directions, respectively, and Z is along the [001] direction, which is same as the c-axis in the bulk (Fig. 2(b)). The 𝜒 (2) elements which are described in the laboratory coordinates (X, Y, Z) are related to those in the crystal coordinates (a, b, c) for the bulk and (𝜉, 𝜂, Z) for the surface by ∑ (2) (2) 𝜒𝑖𝑗𝑘 = 𝜒𝑙𝑚𝑛 (𝑖̂ ⋅ 𝑙̂)(𝑗̂ ⋅ 𝑚̂ )(𝑘̂ ⋅ 𝑛̂ ) (2) 𝑙𝑚𝑛

From our experimental arrangement (Fig. 2c and d), we have 𝑎̂ = cos 𝜙𝑋̂ − sin 𝜙𝑌̂ , 𝑏̂ = sin 𝜙𝑋̂ + cos 𝜙𝑌̂ for the bulk, and 22

Z. Zhang et al.

Surface Science 664 (2017) 21–28

Fig. 2. (Color online) (a) Zinc-blende crystal structure of GaAs. (b) Top view of the atomic arrangement for the surface unit cell. The topmost surface has C4v symmetry. If sublayers are considered, the surface symmetry is lowered to C2v. Mirror planes of the surface are along the crystalline [1̄ 10] and [110] axes. (c) Schematic of the SFG experiment under PSP polarization configuration with GaAs (001) surface rotated clockwise about the crystalline [001] direction, which is in the plane of incidence. (d) SFG experimental schematic plotted on the XZ plane. The refractive index of the interface (n’) is generally different from the refractive indexes of the bulk (n1 and n2 ).

For the surface,

𝜉̂ = cos(𝜙 − 45◦ )𝑋̂ − sin(𝜙 − 45◦ )𝑌̂ , 𝜂̂ = sin(𝜙 − 45◦ )𝑋̂ + cos(𝜙 − 45◦ )𝑌̂ for the surface. Then in the laboratory coordinates the non-vanishing elements for the bulk are

2

=

( ) ( ) ( ) 𝜒XZX = 𝜒ZXX = 𝜒abc sin 2𝜙,

2

=

( ) ( ) ( ) ( ) ( ) ( ) 𝜒XZY = 𝜒YXZ = 𝜒YZX = 𝜒ZXY = 𝜒ZYX = 𝜒abc cos 2𝜙,

=

( ) 𝜒XYZ (2) 𝜒YYZ

2

2

2

2

2

2

(2) 𝜒YZY

(2) 𝜒ZYY

(2) −𝜒abc

=

=

2

2

2

2

=

( ) 𝜒XZX

2

=

(2) 𝜒YYZ

=

(2) 𝜒YZY

=

(2) 𝜒ZXX

=

(2) 𝜒ZYY

=

( ) 𝜒ZXY

2

=

(2) 𝜒XYZ

=

(2) 𝜒XZY

=

{( ) ( )} 1 (2) (2) (2) (2) − 𝜒𝜂𝜂𝑍 + 𝜒𝜂𝜂𝑍 , 𝜒𝜉𝜉𝑍 sin 2𝜙 + 𝜒𝜉𝜉𝑍 2 {( ) ( )} 1 2 (2) (2) (2) + 𝜒𝜂𝑍𝜂 , 𝜒 ( ) − 𝜒𝜂𝑍𝜂 sin 2𝜙 + 𝜒𝜉𝑍𝜉 2 {( 𝜉𝑍𝜉 ) ( )} 1 (2) (2) (2) (2) 𝜒 − 𝜒𝜉𝜉𝑍 sin 2𝜙 + 𝜒𝜂𝜂𝑍 + 𝜒𝜉𝜉𝑍 , 2 {( 𝜂𝜂𝑍 ) ( )} 1 (2) (2) (2) (2) + 𝜒𝜉𝑍𝜉 , 𝜒𝜂𝑍𝜂 − 𝜒𝜉𝑍𝜉 sin 2𝜙 + 𝜒𝜂𝑍𝜂 2 {( ) ( )} 1 (2) (2) (2) 𝜒 (2) − 𝜒𝑍𝜂𝜂 sin 2𝜙 + 𝜒𝑍𝜉𝜉 + 𝜒𝑍𝜂𝜂 , 2 {( 𝑍𝜉𝜉 ) ( )} 1 (2) (2) (2) (2) 𝜒𝑍𝜂𝜂 − 𝜒𝑍𝜉𝜉 sin 2𝜙 + 𝜒𝑍𝜂𝜂 + 𝜒𝑍𝜉𝜉 , 2 ( ) 1 (2) (2) (2) 𝜒ZYX = 𝜒𝑍𝜉𝜉 − 𝜒𝑍𝜂𝜂 cos 2𝜙, 2( ) 1 (2) (2) (2) 𝜒 cos 2𝜙, 𝜒YXZ = − 𝜒𝜂𝜂𝑍 2 ( 𝜉𝜉𝑍 ) 1 (2) (2) (2) 𝜒YZX = − 𝜒𝜂𝑍𝜂 cos 2𝜙, 𝜒 2 𝜉𝑍𝜉 (2) 𝜒ZZZ .

(4)

From Eqs. (1)–(4) the expected azimuthal angular pattern of SFG signal from bulk and surface can be calculated as shown in Table 1. The expected second order susceptibility tensor components under laboratory coordinates can be derived for other space groups based on the same considerations [35]. The polarization notations used here refer to the configurations of the beams within the laboratory frame, in order of decreasing frequencies. For example, SPP refers to an S-polarized SFG output (𝜔3 ), a Ppolarized visible input (𝜔1 ) and a P-polarized infrared input (𝜔2 ). When only the bulk contribution is considered, from Eq. (1), the SFG intensity generated from the bulk has a four-fold symmetry corresponding to (sin 2𝜙)2 for PSS and PPP, and (cos 2𝜙)2 for SPP, where 𝜙 is the azimuthal angle from the crystal axis [100] to X-axis of the laboratory coordinates. The bulk and surface contributions from all polarization

Fig. 3. (Color online) Layout of the femtosecond broadband SFG experiment setup.

( ) 𝜒XXZ

( ) 𝜒XXZ

(3)

sin 2𝜙.

23

Z. Zhang et al.

Surface Science 664 (2017) 21–28 Table 1 Azimuthal angular dependences of the nonlinear SFG polarization under the electric dipole approximation. For the zinc-blende bulk, induced polarizations only have anisotropic terms. For the surface C2v symmetry, both the isotropic and anisotropic terms exist. Bulk [4̄ 3𝑚(𝑇𝑑 )] →

→

PPP

𝑷 𝒙 + 𝑷 𝒛 = 2𝜀0 𝐸1 𝐸2 ⋅

Anisotropic terms

(2) sin 2𝜙𝜒𝑎𝑏𝑐 {sin(𝛽1

+ 𝛽2 )𝒙̂ + cos 𝛽1 cos 𝛽2 𝒛̂ }

Surface [mm2(C2v )] 𝑷⃗ 𝒙 + 𝑷⃗ 𝒛 = 𝜀0 𝐸1 𝐸2 ⋅ [ {{(𝜒 (2) − 𝜒 (2) ) cos 𝛼 sin 𝛼 + (𝜒 (2) − 𝜒 (2) ) sin 𝛼 cos 𝛼 }𝒙̂ } 1 2 1 2 𝜉𝜉𝑍 𝜂𝜂𝑍 { 𝜉𝑍𝜉 𝜂𝑍𝜂} sin 2𝜙 (2) (2) − 𝜒𝑍𝜂𝜂 ) cos 𝛼1 cos 𝛼2 𝒛̂ + (𝜒𝑍𝜉𝜉 {

Isotropic terms

+

}] (2) (2) (2) (2) [(𝜒𝜉𝜉𝑍 + 𝜒𝜂𝑍𝜂 ) sin 𝛼1 cos 𝛼2 ]𝒙̂ + 𝜒𝜂𝜂𝑍 ) cos 𝛼1 sin 𝛼2 + (𝜒𝜉𝑍𝜉 (2) (2) (2) +[(𝜒𝑍𝜉𝜉 + 𝜒𝑍𝜂𝜂 ) cos 𝛼1 cos 𝛼2 + 2𝜒𝑍 𝑍 𝑍 sin 𝛼1 sin 𝛼2 ]𝒛̂

SSS

0

0

SPP

𝑷⃗ 𝒚 = 2𝜀0 𝐸1 𝐸2 ⋅

𝑷⃗ 𝒚 = 𝜀0 𝐸1 𝐸2 ⋅

Anisotropic terms

(2) ̂ sin(𝛽1 + 𝛽2 )𝒚 cos 2𝜙𝜒abc

(2) (2) (2) (2) − 𝜒𝜂𝑍𝜂 )]𝒚̂ cos 2𝜙[cos 𝛼1 sin 𝛼2 (𝜒𝜉𝜉𝑍 − 𝜒𝜂𝜂𝑍 ) + sin 𝛼1 cos 𝛼2 (𝜒𝜉𝑍𝜉

→

PSS

𝑷 𝒛 = −2𝜀0 𝐸1 𝐸2 ⋅

𝑷⃗ 𝒛 = 𝜀0 𝐸1 𝐸2 ⋅

Anisotropic terms

(2) 𝒛̂ sin 2𝜙𝜒𝑎𝑏𝑐

(2) (2) [sin 2𝜙(𝜒𝑍𝜂𝜂 − 𝜒𝑍𝜉𝜉 ) (2) (2) +(𝜒𝑍𝜉𝜉 + 𝜒𝑍𝜂𝜂 )]𝒛̂

Isotropic terms →

SSP

𝑷 𝒚 = −2𝜀0 𝐸1 𝐸2 ⋅

𝑷⃗ 𝒚 = 𝜀0 𝐸1 𝐸2 sin 𝛼2 ⋅

Anisotropic terms

(2) sin 2𝜙𝜒𝑎𝑏𝑐 sin 𝛽2 𝒚̂

(2) (2) [sin 2𝜙(𝜒𝜂𝜂𝑍 − 𝜒𝜉𝜉𝑍 ) (2) (2) +(𝜒𝜉𝜉𝑍 + 𝜒𝜂𝜂𝑍 )]𝒚̂

Isotropic terms →

SPS

𝑷 𝒚 = −2𝜀0 𝐸1 𝐸2 ⋅

𝑷⃗ 𝒚 = 𝜀0 𝐸1 𝐸2 sin 𝛼1 ⋅

Anisotropic terms

(2) sin 2𝜙𝜒𝑎𝑏𝑐 sin 𝛽1 𝒚̂

(2) (2) [sin 2𝜙(𝜒𝜂𝑍𝜂 − 𝜒𝜉𝑍𝜉 ) (2) (2) +(𝜒𝜉𝑍𝜉 + 𝜒𝜂𝑍𝜂 )]𝒚̂

Isotropic terms PSP

𝑷⃗ 𝒙 + 𝑷⃗ 𝒛 = 2𝜀0 𝐸1 𝐸2 ⋅

𝑷⃗ 𝒙 + 𝑷⃗ 𝒛 = 𝜀0 𝐸1 𝐸2 ⋅

Anisotropic terms

(2) cos 2𝜙𝜒𝑎𝑏𝑐 (sin 𝛽2 𝒙̂ + cos 𝛽2 𝒛̂ )

(2) (2) (2) (2) cos 2𝜙[(𝜒𝜉𝜉𝑍 − 𝜒𝑍𝜂𝜂 ) cos 𝛼2 𝒛̂ } − 𝜒𝜂𝜂𝑍 ) sin 𝛼2 𝒙̂ + (𝜒𝑍𝜉𝜉

PPS

𝑷⃗ 𝒙 + 𝑷⃗ 𝒛 = 2𝜀0 𝐸1 𝐸2 ⋅

𝑷⃗ 𝒙 + 𝑷⃗ 𝒛 = 𝜀0 𝐸1 𝐸2 ⋅

Anisotropic terms

(2) cos 2𝜙𝜒𝑎𝑏𝑐 (sin 𝛽1 𝒙̂ + cos 𝛽1 𝒛̂ )

(2) (2) (2) (2) cos 2𝜙[(𝜒𝜉𝑍𝜉 − 𝜒𝜂𝑍𝜂 ) sin 𝛼1 𝒙̂ + (𝜒𝑍𝜉𝜉 − 𝜒𝑍𝜂𝜂 ) cos 𝛼1 𝒛̂ }

Table 2 Calculated Fresnel tensor values for vacuum/GaAs(001) interface based on the experimental configuration (Fig. 2(c)).

𝜆 n2 𝛼 𝛽 Lxx Lyy Lzz ex Lxx (P-polarized) ey Lyy (S-polarized) ez Lzz (P-polarized)

face layer is unknown. From Eq. (1) for the bulk, 𝐼𝑃 𝑆𝑆 ∝ |0.096∕(𝑛′ (𝜔3 ))2 × 𝜒𝑍𝑌 𝑌 |2 ,

𝜔3

𝜔1

𝜔2

𝐼𝑆𝑃 𝑃 ∝ |0.130∕(𝑛′ (𝜔2 ))2 × 𝜒𝑌 𝑋𝑍 + 0.091∕(𝑛′ (𝜔1 ))2 × 𝜒𝑌 𝑍𝑋 |2 ,

685 nm 3.79 21.4° 5.52° 0.440 0.396 1.56/(n’(𝜔3 ))2 −0.410 0.396 0.569/(n’(𝜔3 ))2

800 nm 3.68 19.6° 5.23° 0.446 0.409 1.55/(n’(𝜔1 ))2 0.420 0.409 0.521/(n’(𝜔1 ))2

4762 nm 3.3 32° 9.24° 0.521 0.413 1.48/(n’(𝜔2 ))2 0.442 0.413 0.784/(n’(𝜔2 ))2

𝐼𝑆 𝑆 𝑃 ∝ |0.127∕(𝑛′ (𝜔2 ))2 × 𝜒𝑌 𝑌 𝑍 |2 , 𝐼𝑃 𝑆𝑃 ∝ | − 0.131∕(𝑛′ (𝜔2 ))2 × 𝜒𝑋𝑌 𝑍 + 0.102∕(𝑛′ (𝜔3 ))2 × 𝜒𝑍𝑌 𝑋 |2 , 𝐼𝑆𝑃 𝑆 ∝ |0.085∕(𝑛′ (𝜔1 ))2 × 𝜒𝑌 𝑍𝑌 |2 , 𝐼𝑃 𝑃 𝑆 ∝ | − 0.088∕(𝑛′ (𝜔1 ))2 × 𝜒𝑋𝑍𝑌 + 0.099∕(𝑛′ (𝜔3 ))2 × 𝜒𝑍𝑋𝑌 |2 , 𝐼𝑃 𝑃 𝑃 ∝ | − 0.135∕(𝑛′ (𝜔2 ))2 × 𝜒𝑋 𝑋 𝑍 − 0.094∕(𝑛′ (𝜔1 ))2 × 𝜒𝑋𝑍𝑋 +0.106∕(𝑛′ (𝜔3 ))2 × 𝜒𝑍𝑋𝑋 |2

For the surface, under all polarization configurations, SFG intensities have the same terms as in Eq. (6) except for the PPP case, where it has an additional term, 0.232/(n′(𝜔3 )n′(𝜔1 )n′(𝜔2 ))2 × 𝜒 ZZZ . Here, the 𝜒 (2) elements in the laboratory coordinates (X, Y, Z) are related to those in the crystal coordinates (a, b, c) for the bulk and (𝜉, 𝜂, Z) for the surface as shown in Eq. (3) (bulk) and in Eq. (4) (surface). If the refractive index n’ (𝜔) at the interface layer is known, from Eqs. (3), (4) and (6) one can calculate the relative SFG intensity for each polarization.

configurations are shown in Table 1. The surface dipole contributions can be separated into two components described by the anisotropic and isotropic terms. However, the bulk and surface contributions can interfere, and therefore the resultant SFG patterns can deviate from the bulk-only four-fold symmetry. The Fresnel transmission tensor ⃖⃖𝐿⃗ is given by [2]: 𝜔

4. Results and discussion

2𝑛1 (𝜔𝑖 ) cos 𝛽𝑖 𝑛1 (𝜔𝑖 ) cos 𝛽𝑖 + 𝑛2 (𝜔𝑖 ) cos 𝛼𝑖 2𝑛1 (𝜔𝑖 ) cos 𝛼𝑖 = 𝑛1 (𝜔𝑖 ) cos 𝛼𝑖 + 𝑛2 (𝜔𝑖 ) cos 𝛽𝑖

𝐿𝑥𝑥𝑖 = 𝜔

𝐿𝑦𝑦𝑖 𝜔

𝐿𝑧𝑧𝑖 =

[ ] 2𝑛2 (𝜔𝑖 ) cos 𝛼𝑖 𝑛1 (𝜔𝑖 ) 2 𝑛1 (𝜔𝑖 ) cos 𝛽𝑖 + 𝑛2 (𝜔𝑖 ) cos 𝛼𝑖 𝑛′ (𝜔𝑖 )

(6)

Fig. 4 shows the measured variation of the SFG intensities (black dots) as a function of the azimuthal angle 𝜙 plotted in polar and Cartesian coordinates. All data in Figs. 4 and 5 are normalized to the peak PPP intensity of SFG signal at 315°. A significant deviation between the measured signal (black dots) and the signal expected from the bulk only (red lines, and Table 1) is observed. SSS is a special case for both the bulk (2) and surface as shown in Fig. 4(a). For bulk GaAs, 𝜒𝑖𝑗𝑘 ≠ 0 in Eq. (1) if and only if i, j, and k are different indices corresponding to the principal axes of the crystal. In SSS geometry, the incident electric fields are both perpendicular to the XZ plane so the in-plane SFG polarization is always

(5)

where n1 , n2 , and n’ are the refractive indexes (Fig. 2(d)) of two bulk media and the interface layer, which depend on the wavelength. The calculated values of the Fresnel tensors based on the experimental conditions are listed in Table 2. However, the refractive index of the inter24

Z. Zhang et al.

Surface Science 664 (2017) 21–28

Fig. 4. (Color online) Azimuthal angular dependences of reflected SFG intensity from GaAs (001) crystal surface. The black points with error bars are normalized SFG intensities at different polarization configurations. Measurements are shown in polar coordinates for (a) SSS, (b) PSS, (c) SPP, and (d) PPP. The solid red lines are the azimuthal patterns when only the bulk contributions are considered. The measurements (e – h) are plotted in Cartesian coordinates and fit using the phenomenological model for comparison.

Fig. 4(e) shows that there is very small signal (10−3 ) for SSS at certain angles which can be attributed to multiple surface reconstructions. For the PSS, SPP, and PPP configurations, the measured SFG signal (black dots) is shown with expected bulk-only signal (red lines) in Fig. 4(b – d) and with the fit based on surface-bulk interference (blue lines) in Fig. 4(f – h), as described later using the phenomenological model. At a specific angle 𝜙, the measured SFG signal arises from the coherent interference from the bulk electric dipole field EB and the surface electric dipole field ESD [12], 2 𝐼𝑆𝐹 𝐺 ∝ ||𝐸𝐵 (𝜔3 ) + 𝐸𝑆𝐷 (𝜔3 )|| 2 2 = ||𝐸𝐵 (𝜔3 )|| + ||𝐸𝑆𝐷 (𝜔3 )|| + 2Re𝐸𝐵∗ (𝜔3 )𝐸𝑆𝐷 (𝜔3 )

(7)

The cross terms due to interference are proportional to EB ESD cos[𝜑B (𝜔3 )-𝜑SD (𝜔3 )] where 𝜑B (𝜔3 )-𝜑SD (𝜔3 ) is the phase difference between bulk and surface signals. Often, the bulk contribution is much larger than the surface contributions, but the interference can cause amplification of the surface contributions, improving the sensitivity [18]. This enhancement relies on the coherence and phase-matching between the surface and bulk contributions. The output reading from the detector is the integration of SFG signal over the macroscopic overlapped region of two incident beams and over the pulse duration time of the outgoing SFG. The uniformity of phase difference [𝜑B (𝜔3 ) – 𝜑SD (𝜔3 )] is much better with femtosecond pulses than with nanosecond pulses. Thus, the heterodyne effect can be stronger with femtosecond pulses if the phase difference meets the constructive interference condition [20,21]. As shown in Eq. (6), if the refractive index n’ (𝜔) at the interface layer is known, the measured variation of the SFG intensities shown in Fig. 4 can be fitted based on Eqs. (3), (4) and (6) for each polarization, assuming the surface symmetry is also known. In the present experiment, however, the refractive index n’ (𝜔) at the interface can be significantly different from that of bulk material. The visible beam used in our experiment is pulse-shaped to ∼ 2 ps. GaAs has a bandgap of 1.42 eV at room temperature, so incident 800 nm (1.55 eV) photons excite electrons from the valence band to the conduction band. Since the electron-hole recombination happens in the nanosecond timescale, the active region where the SFG photons are generated is in a transient ex-

Fig. 5. (Color online) Azimuthal angular dependences of reflected SFG intensity from GaAs (001) crystal surface. The black points with error bars are normalized SHG intensities at different polarization configurations for (a) SSP, (b) SPS, (c) PSP, and (d) PPS. The blue solid lines are the azimuthal interference fittings based on the phenomenological model.

zero. Under SSS configuration, both 4̄ 3𝑚 and mm2 crystal structures produce no SFG signal in the electric-dipole approximation. If the bulk is not a perfect zinc-blende structure, extra second-order susceptibility tensor components may induce an in-plane SFG response, which would generate SFG contribution in the SSS configuration. The lack of significant SFG signal in SSS geometry indicates that the bulk symmetry and crystal cut meet experimental requirements, which is also verified with X-ray diffraction (XRD) measurements before and after the SFG experiments. 25

Z. Zhang et al.

Surface Science 664 (2017) 21–28

continuous. The intensity of the electric quadruple is roughly (a/𝜆)2 times smaller than that of the electric dipole. Here a is the typical atom scale and 𝜆 is the typical spatial variation of the field (e.g. wavelength of light) [3]; thus the bulk quadruple contribution can be ignored. However, at the surface, the incident optical electromagnetic fields can generate large spatial gradients across the interface boundary [40], and the interaction between the electric field gradient and the induced quadruple can result in significant second-order polarizations across the surface. This second- order polarization can be also amplified by interfering with bulk SFG signals. In the PSS configuration, the two incident electric fields only have in-plane continuous components across the boundary, so the contributions associated with the electric field gradient in Eq. (9) can be disregarded resulting in a good agreement between the experimental measurements and the phenomenological fit. In the SPP configuration, the incident electric fields have vertical components resulting in a large electric field gradient at the surface. At rotation angles of 45°, 135°, 225° and 315°, both bulk and surface dipole contributions to the SFG signal are zero (see Table 1). However, while negligible at 45° and 225°, signals are observed at angles of 135° and 315°, indicating that the surface quadrupole-field gradient interaction has anisotropic contribution to the SFG signals. The quadrupole susceptibility tensors Γijkl for both GaAs bulk and surface have 21 non-zero elements, of which 4 groups are independent for the bulk and all elements are independent for the surface. Extra considerations are needed to include electric quadrupole symmetries which require further development of the phenomenological model. On the GaAs surface, high-order SFG contributions can arise from two different sources [15]: (1) the non-local electric quadrupole responses across the surface boundary as shown in our experiment; (2) the third-order electric dipole effect under an external field. The high order nonlinear susceptibility tensors of these two effects have exactly the same non-vanishing elements. Therefore, one possible optical measurement to investigate the quadrupole symmetry is to observe SFG signal with an external electric field applied perpendicular to the GaAs surface. It is also possible that one can identify contributions from electric dipole and quadrupole symmetries by tuning the visible beam energy above and below the bandgap of GaAs. In the PPP configuration, the P-polarized electric fields generate gradients along Z-axis. In addition, 𝜒𝑍(2)𝑍 𝑍 only contributes in the PPP geometry (see Table 1). In this case, it is suggested that on GaAs (001) surface, the dominant contribution comes from the 𝜒𝑍(2)𝑍 𝑍 term [17]. This term contributes to the SFG signals through the first electric dipole term in Eq. (9). Taken together, the surface contribution causes the largest deviation from the bulk SFG signal in the PPP case. At azimuthal angles 𝜙 = 90° and 270°, there is no contribution from the bulk whereas there exists the surface dipole contribution. The observed SFG signal at 𝜙 = 90° and 270° is close to zero, suggesting that the electric dipole and quadrupolefield gradient interaction contributions almost cancel each other. On the other hand, at the azimuthal angle 𝜙 = 0° and 180°, there is also no bulk contribution, but constructive interference exists between the surface electric dipole and quadrupole-field gradient interaction. These results suggest that in the PPP case, the surface electric quadrupole contribution is approximately of the same order of magnitude as the surface dipole contribution in this experimental condition. Fig. 5 shows the azimuthal angular dependence of the SSP, SPS, PSP, and PPS configurations. Here, the polarizations of both the incident 800 nm beam, which causes over bandgap excitation, and the incident IR, which does not cause excitations, can be independently controlled, which is not accessible by a double-beam SHG experiment. For polarization configurations SSP (Fig. 5(a)) and PSP (Fig. 5(c)), the incident beams have orthogonal polarizations where the visible beam (𝜔1 ) has no electric field gradient across the surface and the IR beam (𝜔2 ) passes through the GaAs crystal without loss. The angular-dependent SFG signal from the SSP configuration is fit using A, B, P, and Q values of 0.139 ± 0.005, 0.454 ± 0.005, 0.005 ± 0.007, and 0, respectively. The PSP signal is fit using A, B, P, and Q values of − 0.031 ± 0.004,

cited state prior to the femtosecond IR pulse (∼ 150 fs) arrival for generating the femtosecond SFG signal. The refractive index n’ (𝜔) at the surface would be affected by the excited electron distribution, which makes accurate mathematical modeling very difficult based on Eqs. (3), (4) and (6). Previous investigations on pump-probe reflectivity on GaAs demonstrate the ultrafast time-dependent changes to the electron-hole distributions in similar experimental conditions [36]. It is important to note that the spectral line shape does not change when the GaAs sample is rotated for SFG measurements, as shown in Fig. S2, indicating that possible changes in the wavelength-dependent Fresnel coefficients are not responsible for the observed deviations between our experimental results and the predictions based on the electric dipole approximation model. Additionally, the measured SFG spectra from GaAs are very broad with no discernible resonant peaks. Although insight into these phase differences (𝜑B (𝜔3 )−𝜑SD (𝜔3 )) and the interface refractive index n’ (𝜔) from our measurement is limited, the azimuthal angular dependence of the SFG signals can be analyzed using the phenomenological model based on the macroscopic symmetry of crystal structure. The phenomenological theory of SHG was first developed for cubic centrosymmetric crystal [33], with an attempt to link phenomenological parameters to components of the second order susceptibility tensor of the cubic crystals. Later, it was extended to non(2) centrosymmetric zinc-blende structure by adding the bulk term, 𝜒𝑎𝑏𝑐 , into the analysis [18]. A bulk-truncated surface is first used for simplicity in order to calculate the surface dipole contributions shown in Table 1. The phenomenological model can be written as, 𝐼(𝜙) = |𝐴 + 𝐵 sin(2𝜙) + 𝑃 sin(𝜙 − 𝜋∕4) + 𝑄 cos(𝜙 − 𝜋∕4)|2

(8)

where A relates to the isotropic surface contribution and B represents the contributions from bulk dipole and surface anisotropic term in Table 1, similar to ref. [18]. The second term of Eq. (8) changes to Bcos (2𝜙)for certain polarization configurations (Table 1). However, it is well known that GaAs(001) can have multiple surface reconstructions depending on sample preparation procedures [37]. In order to represent the symmetry lowering at the surface due to coexistence of multiple surface reconstructions, the phenomenological model is extended to have P and Q terms as suggested in ref. [38]. A 𝜋/4 phase shift results from the rotation of the surface mirror planes by 45° with respect to the primary axes of the bulk crystal, as shown in Fig. 2(b). The experimental data are fit using the phenomenological model (blue lines) as shown in Fig. 4(e – h) for the polarization configurations of SSS, PSS, SPP, and PPP, respectively. The measured SFG signal in the PSS configuration is fit using Eq. (8) with A, B, P, and Q values of − 0.021 ± 0.001, 0.332 ± 0.001, 0.004 ± 0.002, and 0, respectively. The SPP signal is fit with A, B, P, and Q values of − 0.020 ± 0.006, 0.658 ± 0.007, 0, and − 0.003 ± 0.008, respectively, with cos (2𝜙) for a second term. The PPP signal is fit with A, B, P, and Q values of − 0.223 ± 0.008, 0.674 ± 0.010, 0.069 ± 0.007, and 0, respectively. The fits based on Eq. (8) are in a good agreement with PSS configuration, but deviations are observed for the SPP and PPP cases, which suggest there are additional factors playing an important role in the measured SFG signals. Initially, only dipole contributions are considered. However, the Eq. (1) can be extended to include higher-order terms with (2) 𝑃𝑖 (𝜔3 ) = 𝜒𝑖𝑗𝑘 (𝜔3 , 𝜔1 , 𝜔2 )𝐸𝑗 (𝜔1 )𝐸𝑘 (𝜔2 ) 1 +Γ𝑄 (𝜔 , 𝜔2 , 𝜔1 )𝐸𝑗 (𝜔2 ) × ∇𝑙 𝐸𝑘 (𝜔1 ) 𝑖𝑗𝑘𝑙 3 2 +Γ𝑄 (𝜔 , 𝜔1 , 𝜔2 )𝐸𝑗 (𝜔1 ) × ∇𝑙 𝐸𝑘 (𝜔2 ) 𝑖𝑗𝑘𝑙 3 3 −∇𝑙 (Γ𝑄 (𝜔 , 𝜔1 , 𝜔2 )𝐸𝑗 (𝜔1 ) × 𝐸𝑘 (𝜔2 )) 𝑖𝑗𝑘𝑙 3

(9)

1 2 where Γ𝑄 and Γ𝑄 are the susceptibilities at the surface layer for the 𝑖𝑗𝑘𝑙 𝑖𝑗𝑘𝑙

3 different optical processes and Γ𝑄 is the susceptibility from the bulk 𝑖𝑗𝑘𝑙 that contributes to the surface nonlinear optical processes [39]. In the bulk, all the coordinate components of the incident electric fields are

26

Z. Zhang et al.

Surface Science 664 (2017) 21–28

0.274 ± 0.008, 0, and 0.019 ± 0.006, respectively, with cos(2𝜙) for the B term and with an additional isotropic offset of 0.037 ± 0.003. For polarization configurations of SPS (Fig. 5(b)) and PPS (Fig. 5(d)), the observed SFG signals are very weak, likely from less bulk contribution or conditions where the Fresnel factors under these two cases are dramatically decreased. The SPS signal is fit using A, B, P, and Q values of 0.006 ± 0.001, 0.216 ± 0.001, 0.005 ± 0.001 and 0, respectively. The SFG signal from the PPS configuration is fit using A, B, P, and Q values of 0.007 ± 0.002, 0.0886 ± 0.004, 0.002 ± 0.003 and 0, respectively, with an additional offset of 0.007 ± 0.001. In PPS configuration, the observed SFG pattern is totally out of phase from both bulk and surface electric dipole contributions, where the bulk and surface are expected to have cos(2𝜙) dependence, but the observed pattern shows sin(2𝜙) dependence. When the polarizations of the incident beams are switched, according to Eq. (6), the transient refractive index n’ (𝜔) only affects the Fresnel coefficient Lzz, component (P polarization related), not Lxx and Lyy components. The two incident beams, one (800 nm) over bandgap and the other (∼4762 nm) below bandgap, have different n’ (𝜔) and Lzz components when the incident beams cross the boundary. Because Ppolarized light is affected by the wavelength-dependent Lzz term, when the polarizations of the incident beams are switched, the detected angular dependence of SSP compared to SPS, and PSP compared to PPS differs significantly with respect to each other. For example, when the P-polarized incident beam energy is above the bandgap energy, its zcomponent field will decrease after crossing the semiconductor surface due to a higher interfacial refractive index, leading to decreased bulk SFG signal compared to the corresponding orthogonal polarization configuration with an S-polarized over bandgap incident beam. A complex interplay is observed between surface and bulk signals reflected from the GaAs(001) surface using broadband SFG spectroscopy. Multiple contributors to observed SFG signals are considered: (1) electric dipole contributions from the surface and bulk “crystal” structures; (2) electric quadrupole responses across the surface boundary; (3) the transient n’ (𝜔) affected by the over bandgap excitation, indicating the “electronic” structure contribution. The role of over bandgap excitation combined with the surface quadrupole and coherent surface-bulk interference can significantly increase the surface sensitivity of polarizationdependent broadband SFG spectroscopy of non-centrosymmetric crystals. Thus, thorough theoretical investigation including these aspects would be greatly beneficial for this SFG technique in the future.

Foundation (NSF) EPSCoR CIMM project under award OIA-1541079. J.K. and E.W.P. acknowledge financial support from NSF DMR-1504226. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.susc.2017.05.011. References [1] Y.R. Shen, Surface properties probed by second-harmonic and sum-frequency generation, Nature 337 (1989) 519–525. [2] Y.R. Shen, Optical Second Harmonic Generation at Interfaces, Annu. Rev. Phys. Chem. 40 (1989) 327–350. [3] J.F. McGilp, Optical second-harmonic generation for studying surfaces and interfaces, J. Phys. Condens. Matter 1 (1989) SB85. [4] V. Franck, T. Abderrahmane, Sum-frequency generation spectroscopy of interfaces, Rep. Prog. Phys. 68 (2005) 1095. [5] R.M. Corn, D.A. Higgins, Optical second harmonic generation as a probe of surface chemistry, Chem. Rev. 94 (1994) 107–125. [6] G. Lüpke, Characterization of semiconductor interfaces by second-harmonic generation, Surf. Sci. Rep. 35 (1999) 75–161. [7] H.A. Wierenga, M.W.J. Prins, T. Rasing, Magnetization-induced optical second-harmonic generation from magnetic multilayers, Physica B 204 (1995) 281–286. [8] R. Murphy, M. Yeganeh, K.J. Song, E.W. Plummer, Second-harmonic generation from the surface of a simple metal, Al, Phys. Rev. Lett. 63 (1989) 318–321. [9] L.E. Urbach, K.L. Percival, J.M. Hicks, E.W. Plummer, H.L. Dai, Resonant surface second-harmonic generation: surface states on Ag(110), Phys. Rev. B 45 (1992) 3769–3772. [10] H. Arnolds, M. Bonn, Ultrafast surface vibrational dynamics, Surf. Sci. Rep. 65 (2010) 45–66. [11] K.B. Eisenthal, Liquid interfaces probed by second-harmonic and sum-frequency spectroscopy, Chem. Rev. 96 (1996) 1343–1360. [12] I.V. Stiopkin, H.D. Jayathilake, A.N. Bordenyuk, A.V. Benderskii, Heterodyne-detected vibrational sum frequency generation spectroscopy, J. Am. Chem. Soc. 130 (2008) 2271–2275. [13] S. Nihonyanagi, S. Yamaguchi, T. Tahara, Direct evidence for orientational flip-flop of water molecules at charged interfaces: a heterodyne-detected vibrational sum frequency generation study, J. Chem. Phys. 130 (2009) 204704. [14] S.R. Armstrong, R.D. Hoare, M.E. Pemble, I.M. Povey, A. Stafford, A.G. Taylor, B.A. Joyce, J.H. Neave, J. Zhang, Optical second harmonic generation studies of the nature of the oxide-covered and clean c(4 × 4) and (2 × 4) reconstructed GaAs(001) surfaces, Surf. Sci. Lett. 291 (1993) L751–L755. [15] T.A. Germer, K.W. Kołasin-acuteski, J.C. Stephenson, L.J. Richter, Depletion-electric-field-induced second-harmonic generation near oxidized GaAs(001) surfaces, Phys. Rev. B 55 (1997) 10694–10706. [16] R.W.J. Hollering, Bulk and surface 2nd-harmonic generation in noncentrosymmetric semiconductors, Optics Commun. 90 (1992) 147–150. [17] T. Stehlin, M. Feller, P. Guyotsionnest, Y.R. Shen, Optical 2nd-harmonic generation as a surfaceprobe for noncentrosymmetric media, Opt. Lett. 13 (1988) 389–391. [18] C. Yamada, T. Kimura, Anisotropy in 2nd-harmonic generation from reconstructed surfaces of GaAs, Phys. Rev. Lett. 70 (1993) 2344–2347. [19] M. Takebayashi, G. Mizutani, S. Ushioda, Azimuthal angle dependence of optical second harmonic intensity from a vicinal GaAs(001) wafer, Opt. Commun. 133 (1997) 116–122. [20] H. Tanaka, G. Mizutani, S. Ushioda, A new resonance of the surface SHG from GaAs(001) in air, Surf. Sci. 402–404 (1998) 533–536. [21] S. Janz, Z.H. Lu, Interband resonances in the optical second-harmonic response of the (001) GaAs-oxide interface, J. Opt. Soc. Am. B 14 (1997) 1647–1650. [22] W.T. Liu, Y.R. Shen, Surface vibrational modes of alpha-quartz(0001) probed by sum-frequency spectroscopy, Phys. Rev. Lett. 101 (2008) 016101. [23] V. Ostroverkhov, G.A. Waychunas, Y.R. Shen, Vibrational spectra of water at water/𝛼-quartz (0001) interface, Chem. Phys. Lett. 386 (2004) 144–148. [24] V. Ostroverkhov, G.A. Waychunas, Y.R. Shen, New information on water interfacial structure revealed by phase-sensitive surface spectroscopy, Phys. Rev. Lett. 94 (2005) 046102. [25] G. Lupke, Characterization of semiconductor interfaces by second-harmonic generation, Surf. Sci. Rep. 35 (1999) 77–161. [26] J. Qi, M.S. Yeganeh, I. Koltover, A.G. Yodh, W.M. Theis, Depletion-electric-field-induced changes in second-harmonic generation from GaAs, Phys. Rev. Lett. 71 (1993) 633–636. [27] R.P. Vasquez, B.F. Lewis, F.J. Grunthaner, Cleaning chemistry of GaAs(100) and InSb(100) substrates for molecular-beam epitaxy, J. Vac. Sci. Technol. B 1 (1983) 791–794. [28] H. Arnolds, J.P.R. Symonds, V.L. Zhang, D.A. King, In situ characterization of ultrafast laser pulses for sum frequency surface studies, Rev. Sci. Instrum. 74 (2003) 3943–3946. [29] E.N. Glezer, Y. Siegal, L. Huang, E. Mazur, Behavior of 𝜒(2) during a laser-induced phase transition in GaAs, Phys. Rev. B 51 (1995) 9589–9596. [30] A. Arora, S. Ghosh, A twisted periscope arrangement for transporting elliptically polarized light without change in its polarization state, Rev. Sci. Instrum. 81 (2010) 123102. [31] Y.R. Shen, Surface contribution versus bulk contribution in surface nonlinear optical spectroscopy, Appl. Phys. B 68 (1999) 295–300.

5. Conclusions Broadband SFG spectroscopy is used to study the surface of the noncentrosymmetric crystal GaAs. Azimuthal angular-dependent SFG studies of GaAs (001) under eight possible polarization configurations reveal strong surface-bulk interference due to temporal coherence of the incident visible and infrared pulses. Our results indicate significant surface quadrupole contributions due to large electric field gradients at the surface from P-polarized incident light. The effect of over bandgap excitation is also shown to be an important factor, where large differences in signal are observed when switching polarizations of nonidentical photon pairs. Since broadband vibrational SFG spectroscopy delivers resonant spectral information, its surface sensitivity to a noncentrosymmetric material can be used to investigate molecules adsorbed on the surface of non-centrosymmetric media with the molecular vibrational resonant spectrum (Fig. S3). These experimental results demonstrate that broadband SFG spectroscopy can be extended to surface studies of crystals that lack inversion symmetry, which are ubiquitous and are extensively used in many applications. Acknowledgements This project was partially funded by research support from the Office of Research and Economic Development at Louisiana State University. Z.Z. and L.H.H acknowledge financial support from the National Science 27

Z. Zhang et al.

Surface Science 664 (2017) 21–28

[32] X. Wei, S.-C. Hong, A.I. Lvovsky, H. Held, Y.R. Shen, Evaluation of surface vs bulk contributions in sum-frequency vibrational spectroscopy using reflection and transmission geometries†, J. Phys. Chem. B 104 (2000) 3349–3354. [33] J.E. Sipe, D.J. Moss, H.M. Vandriel, Phenomenological theory of optical 2nd-harmonic and 3rd-harmonic generation from cubic centrosymmetric crystals, Phys. Rev. B 35 (1987) 1129–1141. [34] R.W. Boyd, Nonlinear Optics, third ed., Academic Press, 2008. [35] C. Hirose, N. Akamatsu, K. Domen, Formulas for the analysis of the surface SFG spectrum and transformation coefficients of cartesian SFG tensor components, Appl. Spectrosc. 46 (1992) 1051–1072. [36] K. Ishioka, A.K. Basak, H. Petek, Allowed and forbidden Raman scattering mechanisms for detection of coherent LO phonon and plasmon-coupled modes in GaAs, Phys. Rev. B 84 (2011) 235202.

[37] D.K. Biegelsen, R.D. Bringans, J.E. Northrup, L.E. Swartz, Surface reconstructions of GaAs(100) observed by scanning tunneling microscopy, Phys. Rev. B 41 (1990) 5701–5706. [38] C. Yamada, T. Kimura, Comments on “optical second harmonic generation studies of the nature of the GaAs(100) surface in air, J. Crystal Growth 130 (1993) 321–322. [39] S. Yamaguchi, K. Shiratori, A. Morita, T. Tahara, Electric quadrupole contribution to the nonresonant background of sum frequency generation at air/liquid interfaces, J. Chem. Phys. 134 (2011) 184705. [40] N. Bloember, R.K. Chang, S.S. Jha, C.H. Lee, Optical second-harmonic generation in reflection from media with inversion symmetry, Phys. Rev. 174 (1968) 813.

28