Facilities at Bath

We possess a wide range of excitation sources, giving wavelengths from 244nm to 900nm. Our main Raman systems are a Jobin-Yvon triple spectrometer for highest resolution, and a Renishaw UV Raman microscope, highly suited to resonant excitation of wide bandgap semiconductors. More details of our equipment are here.

If you have a potential application you would like to discuss with us, please contact Daniel Wolverson.

Introduction to Raman spectroscopy

Introduction.
Elementary theory of vibrational Raman scattering.
Selection rules.
Examples of what can be learnt.
Examples of experimental techniques.
References and further reading.
Example of Bath results: the new semiconductor MgS

1. Introduction

Raman spectroscopy is a large field, with many variations on the basic technique and with many new applications being found each year. It is not possible here to review all the areas of industrial and academic research in which Raman spectroscopy plays a role, so that, after a brief introduction to the topic, some illustrative examples of the applications of Raman spectroscopy will be discussed.

2. Elementary theory of Raman scattering

The purpose of this section is to give an insight into how Raman scattering arises and how the selection rules that govern it can be understood. Strictly speaking, the theory of Raman scattering is not elementary, since both group theory and perturbation theory in at least second order are required for a proper discussion of the phenomenon.

The classical theory

The interaction of light with a material can be thought of in a classical picture as being due to the action of the electric field of the light wave on the charges in the material. For simplicity, the following consider the interaction of light with a single molecule, though the results will be quite general. This discussion is based on that given by Demtröder [1]; similar treatments are found in many other books (see also [2]).

If Pi represents the dipole moment of a molecule (a vector) and Ei is the electric field vector of the light, then a general expression for the dipole moment is given by (1.1), in which the subscripts i, j, k, l... each run over the three spatial directions x, y, z:

(1.1)

This expression includes the possibility of a permanent dipole moment pi as well as several components induced by the electric field of the light. Of these, the most important here is the second term, which is linear in E; aij is referred to as the polarisability and is, in general, a tensor. The terms in higher powers of the incident electric field give rise to non-linear processes such as hyper-Raman scattering; these will not be discussed further here. Both the permanent dipole of the molecule (if any) and the polarisability may change if the molecule vibrates. One can expand pi and aij as Taylor series in terms of generalised co-ordinates qn which describes the n vibration normal modes:

(1.2)

If the atomic displacements are assumed to be small, one can approximate the time-dependence of the atomic displacements qn, with frequency wn and of the electric field of the light, frequency wL in the following way:

(1.3)

Then, these expressions can be substituted into a version of (1.1) which has been simplified by neglecting the non-linear terms (b, g, etc.) and the result can be expanded (with the use of one trigonometric identity):

(1.4)

The physical meaning of each term in this last equation can now be clarified:

(1.5)

The molecular vibration is related to the oscillation of the dipole moment at the vibrational frequency; thus, as long as is non-zero, the molecule can exchange energy with light whose frequency is equal to the frequency of vibration and infra-red (IR) absorption is possible (hence, this vibration would be called an "IR-active" mode).

(1.6)

The light induces a dipole moment which oscillates at the same frequency as the light, so that light of that frequency is re-radiated: this is elastic or Rayleigh scattering.

(1.7)

The dipole moment is modulated by the light through the polarisability, which is itself modulated by the molecular vibration. Thus, if is non-zero, two "beat" terms arise corresponding to light re-radiated at the sum and difference frequencies; this is Raman scattering (and the mode would be termed "Raman-active"). Conventionally, the scattering of light with a decrease in frequency is referred to as Stokes scattering; the converse is called anti-Stokes scattering.

Figure 1: Schematic diagram of the absorption and emission transitions predicted by the classical theory outlined in the text; the vertical scale is arbitrary.

Figure 1 illustrates the different processes discussed above for a hypothetical system with two vibrational modes (which are assumed to be both Raman-active and IR-active). The absorption bands appear at light frequencies equal to the vibrational frequencies (at the left of the figure), the Rayleigh scattering appears at the frequency of the incident light and the Stokes and anti-Stokes Raman bands appear near the energy of the incident light on the right of the figure.

The quantum mechanical theory

The Stokes scattering, which involves loss of energy from the light to the molecule, generally is observed to give a stronger signal than anti-Stokes scattering. This is in disagreement with equation (1.7) (which predicts equal intensities for both processes) and is the most obvious indication of the breakdown of the classical picture.

The quantum-mechanical theory of Raman scattering solves this problem. In the quantum picture, the molecular vibrations are quantised. The scattering process is viewed as the creation and annihilation of vibrational excitations (or "phonons") by photons. This interpretation leads naturally to the fact that photons can always create more vibrational quanta in a system, so that the probability of Stokes scattering is not temperature-dependent. However, the probability of annihilation of a vibrational quantum depends on the probability of finding the system in an excited vibrational state. The ratio of the intensities of Stokes and anti-Stokes bands thus reflects the Boltzmann factor exp(- hn/kTT) (but not only this factor [3]). The following diagram illustrates the transitions involved in Raman scattering; here, hn is the vibrational quantum energy and n is the number of vibrational quanta present in the system. There are assumed to be several vibrational levels within the electronic ground state.

Figure 2: Schematic diagram (not to scale) of the Raman scattering process (the vertical direction represents energy).

Excitation by the incoming light raises the system to an excited electronic state (this may be a virtual state or, in the case of resonant Raman scattering, a real electronic state) from which return to a different vibrational level of the electronic ground state may be possible. Stokes scattering involves the loss of energy from the incident photon to the material and thus the return of the system to a state with a higher vibrational quantum number. A full discussion of resonant Raman scattering would occupy too much space here and good texts are available; it is sufficient to say that when the excited electronic state of figure 2 is a real electronic state of the system (as opposed to a virtual state), the cross-section for Raman scattering can become many times larger than normal. This effect is often exploited experimentally to obtain stronger signals or even to investigate the electronic energy levels of the system.

3. Selection rules.

The selection rules that govern Raman scattering constitute one of the main features distinguishing it from IR spectroscopy where vibrational spectroscopy of simple molecular systems is concerned. The selection rules can be understood by reference to equation (1.7), which is re-written below in a simplified form; Esi is the electric field vector of the scattered light.

(3.1)

This equation shows that the incoming and outgoing electric fields (E0j and Esi) are related, for a given vibrational mode n, by the Raman tensor an which is defined in (3.2); if the element with subscripts i, j is non-zero, then Raman scattering is possible between E0j and Esi. We shall consider this important point in more detail. First, it is helpful to write out explicitly the tensor equation relating the incoming and outgoing light waves:

(3.2)

Group theory (beyond the scope of this discussion) allows one to determine the symmetry species of the vibrational modes and also which elements of the Raman tensor an are non-zero. Raman tensors are tabulated in many books (eg, [4]).

In order that this discussion is not too abstract, we shall now consider in elementary terms how different vibrational modes of simple molecules may be IR-active or Raman-active.

To see how Raman spectra can vary in different experimental geometries, we follow Kuzmany [4] in considering the example of calcite (from a classic early work in the field of Raman spectroscopy, [5]). The calcite unit cell, which contains two Ca2+ ions and two ions. The arrangement of these ions is such that there is a high-symmetry axis which is conventionally labelled z. The direction in which x and y axes are defined is arbitrary. Without detailed group theoretical analysis, we will simply state that the vibrations of the unit cell can in this case be classified into various symmetry types including two with conventional labels A1g and Eg. The Raman tensors for these are as follows:

(3.3)

By referring to equation (3.2), then, we expect Raman scattering from light polarised the x axis to yield light polarised along the x axis for A1g vibrational modes and along x (relative intensity c2) or z (relative intensity d2) for Eg vibrational modes. On the other hand, if the incident light is polarised parallel to the high-symmetry z axis, Raman scattering from an Eg mode will be polarised only along the x axis whilst Raman scattering from an A1g mode will be polarised only along the z axis. This is borne out by experiment.

The Porto notation is a useful convention for representing experimental scattering geometries. The symbol x(zx)y indicates that the excitation light was incident on the sample along the x axis and was polarised along the z direction, whilst the light that was detected was travelling along y and was polarised along x. This notation is most useful if the axes are defined with respect to the crystal axes of symmetry (as here) so that x...z relate directly to components of the Raman tensor, rather than using arbitrary "laboratory" axes.

4. What can be learnt.

As has been described, Raman spectroscopy can be used to obtain information about the vibrational spectrum of a material. This can lead to a better understanding of the chemical composition of the sample, as in many organic compounds, where different chemical bonds have very characteristic vibrational frequencies. It may also be possible to deduce the structure of a material; for example, in molecular systems, the juxtaposition of different chemical species leads to small modifications of the usual vibrational frequencies, so that longer-scale structure may be investigated. In crystalline solids, the selection rules for scattering from the lattice vibrations (phonons) indicate the symmetry of the crystal unit cell and can thus reveal (for example) phase changes. Finally, via resonance Raman spectra, one can sometimes correlate a particular vibrational mode with a particular electronic transition energy and thus learn more about the electronic structure of the material.

5. Examples of experimental techniques.

Only a brief discussion of techniques is possible here as the field has become immense; one useful book containing a great deal of practical information is that by Gardiner and Graves [3], where the traditional (and still widely used) experimental set-up for Raman spectroscopy is discussed along with many new developments.

Spontaneous emission from the laser

One comment on the use of lasers in Raman spectroscopy is that although lasers are often regarded as ideal monochromatic light sources, this is far from the case in practice. In the case of tunable lasers, there is always broad-band spontaneous emission over the whole tuning range of the gain medium, whilst in the case of ion lasers, there are many atomic transitions which give rise to sharp spectral lines; both of these can easily be comparable in intensity to the required signals. There are two common solutions; the most effective is to use a small monochromator (often a double-pass prism spectrometer, which is capable of handling large powers) which acts as a filter for the laser beam before it reaches the sample. About 50% of the laser power is generally lost in this process. Another solution is to pass the beam through an aperture (or spatial filter). Since the spontaneous emission is radiated isotropically, much of it can be blocked before it is focused onto the sample along with the laser beam.

Choice of laser wavelength

The massive enhancement of Raman scattering when the excitation is resonant with some electronic transition of the material has already been mentioned. To exploit this effect, one may require a range of laser lines or even a tunable laser. However, other factors influence the choice of excitation wavelength. Many materials show strong photoluminescence (fluorescence) when the excitation lies close in energy to an absorption band. This may mean that it is advantageous to avoid resonance conditions. One instrument which is popular for avoiding fluorescence problems is the Fourier Transform spectrometer, which uses very low energy excitation (wavelength 1064 nm), usually insufficient to stimulate fluorescence.

Spectrometers

Many developments have been made recently in the area of spectrometers. This is in part due to the advent of charge-coupled devices (CCDs) and other forms of array detector, which have different requirements to single-channel detectors such as photomultipliers [8]. Essentially, a single spectrometer can have a high enough resolution for Raman spectroscopy but generally will not have good enough stray light rejection. The use of a double spectrometer improves the stray light rejection at the expense of efficiency (more mirrors and gratings lead to increased losses). In both these instruments, the exit slit is necessary to obtain the best stray light rejection, so that they are not ideal for use with array detectors (though if holographic filters are available to restore the stray light rejection to an acceptable level, the exit slit can be removed).

The triple instrument is specifically designed for array detectors. The light is passed through a wide central slit between the first and second stages and the gratings are set so that the entire spectral range of interest passes through this slit, but most of the Rayleigh-scattered light is blocked. The first and second stages are arranged so the dispersions of the two gratings are opposed; thus, the light entering the final stage is not dispersed. The final stage disperses this light once more, with as high a resolution as is required and now no longer requires an exit slit, so that an array detector can be fitted. The characteristics of typical instruments of these types are summarised in the following table (adapted from [8]):

Two other recent developments are worth mentioning; the first involves the use of echelle gratings and the second, holographic filters.

Echelle gratingsare a special type of grating which have high dispersions but which suffer from the problem that the different diffraction orders overlap significantly. This problem is overcome if an array detector is used with a second, low-resolution grating oriented at right-angles to the echelle grating, so that the different orders are displaced from one another. The echelle grating disperses the light vertically and the cross-disperser disperses the different orders horizontally. With this system, the entire frequency range of vibrational modes can be covered at high resolution in one acquisition; a complete spectrum of cyclohexane, for example, could be acquired in just 1 second [8].

Raman imaging

One exciting recent development in Raman spectroscopy is the use of CCDs to form images of samples using the light emitted in a specific Raman band, so that regions composed of different materials can be distinguished. The key to this technique is the use of holographic filters to provide adequate stray laser light rejection. These filters operate at specific wavelengths and have very narrow band passes of down to 100 cm-1 (depending on the type of filter); their advantage over diffraction gratings is that two-dimensional spatial information is preserved. A particularly successful instrument (manufactured by Renishaw Transducer Systems) uses a combination of holographic filters and a Fabry-Perot etalon to achieve a spectral resolution of about 20 cm-1 in a true two-dimensional imaging mode. The instrument can also be used with a single diffraction grating to provide conventional spectra at higher resolution. The instrument is combined with a microscope, as is discussed below. One potential disadvantage of this instrument is the difficulty of using tunable lasers as excitation sources (since a continuous range of filters is then required).

Raman microscopy

Raman spectroscopy can be combined with optical microscopy to investigate microscopic samples present as, for example, inclusions within other materials. This technique has found many industrial applications, for instance, in the diagnosis of problems in the production of plastics, where catalyst particles embedded in the polymer can be identified.

A microscope may be used in conjunction with a Raman spectrometer in two basic ways. Firstly, one may select a region of a sample by inspecting its white-light image; the Raman spectrum of that region may then be recorded. Alternatively, one may record a two-dimensional "map" of the intensity of some Raman band of the material as a function of position

Reference [3] contains a very useful introductory chapter on this subject. The laser beam is generally introduced into the microscope via a side-arm with a spatial filter to improve the beam profile; a beam splitter then reflects some of the laser beam down to the sample through the objective lens. The scattered light is collected through the same objective lens and some of it passes through the beam splitter. A movable prism or mirror can be inserted into the microscope column to reflect the beam out to a spectrometer; the prism can also be withdrawn so that the light passes up to a video camera in order to allow one to identify the desired region of the sample. Spatial resolutions of around 10-6 m can be achieved, depending on the particular optical system used. Note that by use of a confocal system with appropriate spatial filtering, it is possible to obtain a very restricted depth of field, so that spectra may even be obtained from different depths in transparent samples.

Optical fibres

A common difficulty in industrial applications of Raman spectroscopy is that it may not be convenient to examine samples in the laboratory, either because frequent sampling is required or because the material of interest must be examined under extreme conditions of temperature, pressure, or chemical environment. Optical fibres provide a means of delivering the laser light to the sample and of collecting the scattered light. A single fibre may be used to transmit the excitation light, whereas the scattered light is collected by several fibres formed into a "bundle". A lens is used to image the light emitted from the bundle into a conventional Raman spectrometer; often, the bundle is shaped into a line of fibres which match the size of the spectrometer slit. A disadvantage is that the glass of the fibre carrying the laser light will itself give rise to some Raman scattering. Background subtraction procedures can solve this, but another approach uses a bandpass filter before the sample to block the Raman-scattered light from the input fibre, whilst a holographic filter after the sample prevents excitation light from entering the collection fibre.

Surface-enhanced Raman scattering

Finally, surface-enhanced Raman scattering (SERS) deserves a mention here. The effect was a subject of much research activity when it was first discovered; a good review is given in [6] and there are several textbooks on the subject. Essentially, a large enhancement of Raman-scattering cross-sections is sometimes observed for samples supported on roughened or corrugated metallic surfaces (frequently silver is used). The explanation lies in the increased electric field of the excitation light near the surface; a full discussion cannot be given here. However, the effect is becoming a standard technique for increasing sensitivity, especially where only small quantities of samples are available. A comparison can be made between the spectra of approximately a monolayer of pyridine on an "activated" silver surface and a thick layer of pyridine on an inactive surface; it is then seen that the signals arising from the monolayer and different to, and more intense than, the signals from the thick layer. Similar intensities are obtained from very different quantities of material. The interaction with the surface can also modify the form of the spectrum. The nature of the spectrum may also be influenced by the electrical potential of the silver surface; the interaction between adsorbate and metal surface is a complex one so that this is not necessarily a simple technique to apply. Recently, SERS has been combined with microscopy to use extremely fine silver wires as probes which can selectively enhance signals from the very small region of the sample surrounding the tip of the wire; this has found application in biological systems.

6. References

"Laser Spectroscopy", W. Demtröder (Springer Series in Chemical Physics 5, Springer Verlag 1988)

"The quantum theory of light", R. Loudon (Oxford University Press 1978)

"Practical Raman Spectroscopy", D. J. Gardiner and P. R. Graves (eds.) (Springer-Verlag 1989)

"Festkörperspektroskopie: Eine Einführung", H. Kuzmany, (Springer-Verlag, 1989)

S. P. S. Porto, J. A. Giordmain and T. C. Damen, Phys. Rev. 147, 608 (1966).

"Light Scattering in Solids I - VI", M. Cardona and G. Güntherodt (eds.) (Springer-Verlag, 1983 onwards; Topics in Applied Physics vols. 8, 50, 51, 54, 66 and 68)

"The vibrational spectroscopy of polymers", D. I. Bower and W. F. Maddams, Cambridge Solid State Science Series (CUP 1989)

"Charge-transfer devices in spectroscopy", J. V. Sweedler, K. L. Ratzlaff and M. B. Denton (VCH Publishers UK, 1994)

M. J. Pelletier, Appl. Spectroscopy, 44, 1699 (1990)

J. P. Alarie, D. L. Stokes, W. S. Sutherland, A.C. Edwards and T. Vo-Dinh, Appl. Spectroscopy, 46, 1608 (1992)

7. Magnesium sulphide

For an example of all of this in action, take a look at our poster on a new semiconductor (zinc blende MgS) and how its Raman modes were measured and calculated.