Department of PHYSICS,Clarkson University

DIPANKAR ROY

Ó D.Roy (2007)

ROY-GROUP'S CURRENT RESEARCH PROJECTS:

SECOND HARMONIC GENERATION (SHG) STUDIES OF METAL-LIQUID INTERFACES

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Introduction

Due to their technological importance and their intriguing but complicated structure, metal-liquid interfaces (MLI) have secured a special place in the field of surface science. Frequent applications of MLI are found in various electrochemically controlled surface processes. However, still a large number of unresolved problems are found in this area. Here, the interface is electrically charged, populated by polar and ionic species, and alters both physically and chemically during surface reactions. The electronic details of such an interface are rather complicated. At the same time, it is these electronic features of MLI that play crucial roles in determining the rates and nature of electrode reactions. The surface second harmonic generation (SHG) work in our group focuses on these electronic features of surface reactions on metals.

Traditionally, MLI are studied with electrochemical methods, including both D.C. (such as voltammetry) and A.C. (such as impedance spectroscopy) techniques. In both cases, the electrical response of the active interface is monitored under externally applied voltage modulations. In most cases, however, these data are overwhelmed by the macroscopic properties of the surface. Most efforts of the past decade to overcome this problem have combined electrochemical methods with optical techniques. Linear reflectance (electroreflectance and differential reflectance) has become a standard surface tool in this latter category. SHG is a natural extension of this technique, and provides drastically superior surface sensitivity compared to linear reflectance (as well as, to the other traditional methods of linear optics). We are using SHG to investigate variouselectronic properties of MLI. In the following, we briefly explain how the SHG technique works, and how it allows us to probe various electronic properties of MLI.

Background: Light Induced Polarization of an Interface

Let us consider a situation where an electric field, ), at an optical frequency, w, is incident at an angle, y₁, from medium 1 (a liquid in our work) uponmedium 2 (a solid substrate in our work). The electric field transmitted in medium 2 has the form:

(1) ) = E₂(w) e^–i^w^t + complex conjugate,

where E₂(w) = E₁(w) t₁₂(w), and t₁₂(w) is the Fresnel coefficient for transmission from medium 1 to medium 2 . This term depends on the polarization (and the angle) of the incident light. The angle of refraction is y_2,and the wave vectors are k₁ for medium 1 and k₂ for medium 2. The propagation of the electric field in medium 2 is confined within a relatively short length, d (skin depth of the substrate material). The intensity, I_w,(power per unit area) of the incident light is :

(2) I_{w =}[e₁(w)]^1/2 |E₁(w) |²/(2p A),

Where A is the area of illumination, and the dielectric function of medium 1, denoted as e₁(w), is considered to be a scalar quantity. In general, the induced electronic polarization, , of the interface has the form

(3),

where the ith components (i º x,y,z in a rectangular Cartesian system) of the linear and second order surface polarization vectors are

(4) (w) = P_i⁽¹⁾⁽w)e ^–i^w^t + complex conjugate,

(5)(2w) = P_i⁽²⁾(2w)e ^–i(2^w)^t + complex conjugate,

where

(6) P_i⁽¹⁾= å_j(w) E_2;j(w),

(7) P_i⁽²⁾= å_j å_k(w,2w) E_2;j(w)E_2;k(w).

and are the first- and second-order susceptibilities of the solid surface, respectively (the second order susceptibility of the liquid is zero). The dielectric function, e_2;_ij(w), of the solid surface is related to as follows

( 8) e_2;_ij(w) = d_ij + [4 p/d],

where d_ij is the Kronecker Delta, and d is the thickness of the surface layer. For small E₁(w), (which is typical of most continuous wave lasers), E₂(w) is also small, and then according to Eqs. (6) and (7), |P⁽²⁾| <<|P⁽¹⁾|. In this case, surface properties are studied by analyzing the behavior of [that is, by analyzing e_2;_ij(w)]. This is the regime of linear reflection. For large E₁(w) (which is typical of short-pulse lasers), and depending on the magnitude of of the surface under study, |P⁽²⁾| can become measurable. This is the regime of nonlinear (second order) reflection.

Linear Reflectance of the Interface

In a large number of experiments involving MLI, the anisotropy in the first order susceptibility of the surface can be neglected. In these cases, e_2;_ij₌e₂(a scalar quantity), and

(9) e₂ = 1 + [4 pc⁽¹⁾/d].

For most systems we study, this dielectric function is a complex quantity, expressed in terms of its real (Re) and imaginary (Im) parts:

(10) e₂= Re e₂+ Im e_2.

The components of the complex wave vectors are related to e₂ as follows

(11) k_1x = k_2x = [wn₁/c] sin y₁

(12) k_1z= [wn₁/c]cos y₁

(13) k_2z = [wn₂/c]cos y₂.

The real (Re n₂) and imaginary (Im n₂) parts of the refractive index (n₂) of the solid surface are related toRe e₂ and Im e₂.

(14) Re e₂= Re n₂² – Im n₂²

(15) Im e₂= 2 Re n₂ Im n_2.

The linear reflectance signal has the form, S_w= |R₁₂(w)|²I_w, where R₁₂is the linear reflection coefficient,

(16)

By studying the variations in R₁₂ (at different frequencies and incidence angles) under different surface conditions, we can study the surface effects by appropriately analyzing the dielectric function, e₂. In this technique, however, the optical signal contains some information about the bulk material of the surface (within the optical skin depth at the experimental photon frequency).

How Does SHG Work?

The polarization expressed in Eq. (7) is usually considered with the dipole approximation. In this formulation, is non-zero only for those systems where the inversion symmetry is broken. At the interface, this condition is automatically satisfied. Thus, when an interface is probed with a high optical field, only the top-most layer of the surface generates the dipole allowed SH. The oscillating dipoles (a polarization sheet located in medium 2 immediately below the interface) radiates at the second harmonic frequency, 2w, of the incident light [Eq. (7)]. The SHG signal, S_2w,has the following form

(17) S_2w= |F_out_×P⁽²⁾|²,

where F_outis the output Fresnel factor that contains the dielectric functions of the interface at the SH frequency, 2w. P⁽²⁾ is defined in Eq. (7). F_outdepends on the polarization of the detected SH light. The nonzero elements of are determined by the symmetry of the surface. For example, for an isotropic surface, the nonzero and independent elements of are , and . The result of the dot product in Eq. (17) depends on the components of P⁽²⁾ -- which in turn, are determined by t₁₂[defined in the context of Eq. (1)] and hence, by the angle and polarization of the incident light. For instance, for a p(input)-p(output) combination of polarizations, Eq. (17) takes the following form

(18) S_2w(p-p) = C_p |(p-p)|²I_w²,

where C_p is a constant, and is the effective surface susceptibility, expressed as

(19) (p-p) = L_1p+L_2p– L_3p.

The terms, L_1p, L_2p and L_3p arise from a combination of F_out and t₁₂, and contain e₁(w), e₁(2w), e₂(w) and e₂(2w). Similarly, for the combination, s(input)-p(output), we have

(20) S_2w(s-p) = C_p |(s-p)|²I_w², where C_p is a constant, and

(21) (s-p) = Ls .

Thus by choosing different combinations of input and output polarizations, we can probe different components of . These different components of contain information about different surface features (such as adsorbate bonds parallel and perpendicular to the interface). In SHG experiments, we must confirm that the observed signal is indeed SHG, and not a fluorescence from surface impurities. This is done by verifying (1) the highly monochromatic nature, and (2) the quadratic power dependence [Eqs. (18) and (20)] of SHG. In a typical experiment, the intensity (and sometimes, the phase) of the SHG signal from the active interface is measured as the surface is modified under precise electrochemical control. Often, the experiments are repeated at different combinations of the input and output polarizations. The electronic effects on the surface are manifested in the optical parameters, e₂(w), e₂(2w), _and. These parameters control the observed variations in the phase and intensity of SHG. The SHG data are analyzed to understand these electronic effects

Some Important Features of Surface SHG

1) SHG is intrinsically surface sensitive.
2) It is a non-intrusive tool.
3) It shows fast response to changes in interfacial conditions.
4) SHG is sensitive to both linear and nonlinear optical properties of the interface.
5) SHG contains information about both structural and electronic properties of the interface.
6) Both the density and the spatial profile of the interfacial free electron density can be probed with SHG.
7) Information about crystal induced and image potential surface states can be obtained through SHG.
8) Electrochemical Stark effects can be probed with SHG.
9) The nature of surface bonds for various adsorbates can be studied with SHG.
10) Certain effects of surface plasmon resonance can be measured with SHG.
11) Interband transition in the surface layer, and its response to changes in surface conditions can be studied using SHG.

SHG Studies in Our Lab

Our SHG experiments are focused on the characterization of various metal-liquid interfaces.

Earlier SHG setup in our lab

Reports of our SHG studies

19. M. J. Walters, C. M. Pettit and D. Roy,
"Surface Kinetics of Eelectrodeposited Silver on Gold Probed with Potential Step and Optical Second Harmonic Generation Techniques", Physical Chemistry Chemical Physics 3 (2001) 570-578.

18. D. Roy, "Comment on Molecular Orientation by Second Harmonic Generation: Self Assembled Monolayers", Physical Review B 61 (2000) 13283-13286.

17. M.J. Walters, C.M Pettit, F.X. Bock, D.P. Biss and D. Roy, "Capacitance of a Metal-Liquid Interface During Anion Adsorption: Phase Selective Measurements in the Presence of D.C. Voltage Sweep and Finite Solution Resistance", Surface and Interface Analysis 27 (1999) 1027-1036.

16. M.A. Lovell, M.J. Walters and D. Roy,
"Characterization of Electrodeposited Thin Film of Cadmium on Molybdenum using Optical Second Harmonic Generation", Physical Chemistry Chemical Physics 1 (1999) 1985-1993.

15. M. J. Walters and D. Roy, "Interference of Linear and Nonlinear Optical Effects in Second Harmonic Generation from Metal-Liquid Interfaces'', Applied Spectroscopy 52 (1998) 1554-1568.

14. M. A. Lovell and D. Roy,
"Effects of Sub-Surface Oxygen on Electrodeposition of Cadmium on Copper'', Electrochimica Acta 43 (1998) 2117-2130. Addition and Correction 44 (1999) 2327.

13. M. A. Lovell, M. J. Walters and D. Roy,
"Surface Modification of Copper due to Co-Adsorbed Oxygen and Cadmium Probed with Optical Second Harmonic Generation", Electrochimica Acta 43 (1998) 2101-2110.

12. M. A. Lovell and D. Roy, "Optical Second Harmonic Generation from a Catalytically Active Molybdenum Electrode'', Applied Surface Science 135 (1998) 46-52.

11. G. Nagy and D. Roy, "Optical Second Harmonic Generation as a Probe of Selective Dissolution of Brass'', Langmuir 11 (1995) 3457-3466. Addition and Correction, 12 (1996) 1696.

10. G. Nagy and D. Roy, "Surface Charge Dependence of Second Harmonic Generation from Brass'', Langmuir 11 (1995) 711-715.

9. D. Roy, "DC Field Induced Optical Second Harmonic Generation from Metal-electrochemical Interfaces'', Electrochimica Acta 39 (1994) 2699-2703. Addition and Correction 40 (1995) 2557.

8. R. Gao and D. Roy, "Effects of Diffusion Limited Mass Transfer on Metal Underpotential Deposition Voltammograms'', Journal of Applied Electrochemistry 24 (1994) 1276-1278.

7. G. Nagy and D. Roy, "Optical Characterization of a Partially Ag-Coated Ni Electrode with Second Harmonic Generation'', Journal of Physical Chemistry 98 (1994) 6592-6600.

6. G. Nagy and D. Roy, "Second Harmonic Generation from a Charged Ni Electrode with and without Anion Adsorption'', Surface Science 320 (1994) 7-16.

5. G. Nagy and D. Roy, "Surface Charge Dependence of Second Harmonic Generation from a Ni Electrode'', Chemical Physics Letters 214 (1993) 197-202.

4. G. Nagy and D. Roy, "Oxidation of Cu in Halide Electrolytes Studied with Optical Second Harmonic Generation'', Langmuir 9 (1993) 1868-1877.

3. R. Gao, T. D. Hewitt and D. Roy, "Stark Shift of an Interband Transition in Cu Determined by Surface Charge Measurements'', Journal of Physics and Chemistry of Solids 54 (1993) 685-690.

2. T. D. Hewitt R. Gao and D. Roy,
"Effects of Surface Charge on the Second Harmonic Generation from a Cu Electrode'', Surface Science 291 (1993) 233-241.

1. T. D. Hewitt and D. Roy, "Optical Second Harmonic Generation as a Probe of Hydrogen Evolution on Copper'', Chemical Physics Letters 181 (1991) 407-412.