Excitation
of Surface Plasmons in Thin Metal Films of Gold, Silver and Aluminium
Brijesh Patel and Ravi Jariwala
4C00 Full unit Project
Physics and Astronomy Dept, UCL, www.phys.ucl.ac.uk
Surface plasmons exist at dielectric-metal interfaces and can resonate if given the correct momentum and energy. This was done by exciting the surface plasmons using a parallel polarised laser beam and metal film coated prisms (crown glass) of silver, gold and aluminium. The Kretschmann-Raether method was used where evanescent waves travel through the metal films. By changing the angle of incidence on the prism, the momentum is varied. At a particular angle, surface plasmon resonance (SPR) occurred for each metal film. Matching the graphs of SPR to the theoretical models, the dielectric constant of a thin layer of magnesium fluoride was determined to be 1.415. This was a protective layer on the silver and gold film. Also the complex dielectric constant of gold and silver were determined to be -2.4+1.5i and –9.0+3.0i respectively. Further investigation was carried out on the aluminium film with a water layer. This proved the existence of an aluminium oxide layer having a dielectric constant of 1.29.
Theory
Plasmons exist in matter and are due to longitudinal waves existing in metals through the collective motion of huge numbers of electrons. The plasmons are discrete and therefore have an associated quantum nature. The plasmon is the quantum of plasma oscillations. When electromagnetic radiation is incident on an interface between a metal and dielectric medium, evanescent waves are produced and charge density oscillations are present. These charge density oscillations occur at the interface and are known as surface plasmons. They are generated at a different frequency to the plasma oscillation. The evanescent waves tunnel to a dielectric-metal interface where the fields dissipate into both mediums. The field oscillates and induces surface plasmons in the metal, which propagates along the interface. When the energy and momentum of the incident light matches that of the surfaces plasmons, they resonate. The light is absorbed and hence minimal light is reflected off the interface.
Method
Before carryout the surface plasmon resonance experiment, small tests had were carried out to check and understand the functionality of the apparatus involved. The signal divider and the functionality of the photodiodes were the first components to be tested. Tests on the polariser was also carried out to determine angles at which complete polarisation occurred. The Brewster angle test was done to confirm the polarisation states and also to obtain the refractive index of crown glass prism where the metal films were on. The refractive index was determined to be 1.732. The equipment was then set up as shown in figures 1 and 2.
This was the set up required to detect surface plasmon resonance. The polariser was set to output parallel polarised light and measurements were made across a wide range of incident angles on the metal film. This was done for the silver, gold and aluminium films. Figure 3 shows the normalised results for the aluminium film.
The minimum of the curve for parallel polarisation represents the region of surface plasmon resonance which is at 45.3 degree. The peak of the curve represents the critical angle feature. For the silver film the SPR angle was at 46.0 degrees and for the gold film, the angle was 59.1 degrees.
Analysis
Mathematica was used to model surface plasmon resonance using reflectivity equations derived from the electromagnetic theory and boundary conditions. The dielectric constant of the metal and the outer layer were variable. Mathematica was programmed to extract the experimental data from a text file and plotted with the SPR model. the dielectric parameters were varied until suitable fits were found of silver, gold and aluminium. The silver film data and its dielectric constant of -17+0.7i was used to determine the dielectric constant of the protective outer layer, magnesium fluoride. The magnesium fluoride layer had a dielectric constant of 1.415. The gold film data was used to determine its dielectric constant, -2.4+1.5i and the same with the aluminium film, -9.0+3.0i. The analysis showed that the aluminium film had an outer layer with a dielectric constant greater than one. This could be a result of there being a natural aluminium oxide layer due to the reactivity of aluminium with air (oxygen). see figure 4 for the model and experimental data match.
Further Investigation
The experiment was investigated further by considering a liquid outer layer on the aluminium film. water was placed on a microscope slide and placed carefully over the aluminium film surface. the water filled the surface and held the slide upright by its surface tension. Measurements were made over a wide range of incident angles. surface plasmon resonance was detected at an angle of 65.8 degrees. It seems as if the water layer increases the angle at which surface plasmon resonate. With an air outer layer, the SPR angle was 45.3 degrees. This is a shift of approximately 21 degrees. Fitting the results to the model gives a small phase difference which can be explained by there being a very thin aluminium oxide layer between the metal film and water layer.
Conclusion
Silver:
Dielectric constant of the magnesium fluoride outer layer was calculated to be 1.415 compared to the real value of 1.893. The difference is large but this is due to the protective layer being very thin. At such small scales, the optical properties vary from normal values.
Gold:
The dielectric constant for gold was calculated to be -2.4+1.5i. The actual value was found to be -11+1.37i. Once again a large difference has been obtained due to a systematic error in the experimental procedure.
Aluminium:
The dielectric constant of aluminium was calculated to be -9.0+3.0i and the oxide layer was found to have a dielectric constant of 1.29. The actual value of the dielectric constant of aluminium was found to be -37.0+13.0i, which is very far from the results obtained. This again, is due to a systematic error with the experimental procedure.
Having a water layer behind aluminium shifted the SPR to higher incident angles. The higher the dielectric constant of the outer layer, the higher the angle of incidence for SPR to occur. Results also proved the existence of a thin aluminium oxide layer.
References