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Surface plasmon resonances showing reflectivity maxima
-
1 August 1994
OPTICS COMMUNICATIONS Optics Communications
110 ( 1994) 80-86
Surface plasmon resonances showing reflectivity maxima K.A. Home, M. Printz, W.L. Barnes, J.R. Sambles Thin Films and Interface Research
Group, Department
ofPhysics,
Umversity ofExeter,
Devon EX4 4QL. UK
Received 18 January 1994; revised manuscript received 7 April 1994
Abstract Reported is on the observation of surface plasmon resonances showing sharp maxima in the reflectivity of transverse magnetic visible radiation. Two systems of thin layers are examined, a bilayer of vanadium/gold, and a trilayer of iron/magnesiumfluoride/silver. Theoretical reflectivity data derived from Fresnel equations have been fitted to our experimental data in order to find the optical constants and layer thicknesses of the two systems. These parameters have then been used to model the optical field profiles, thus illustrating the nature of the surface plasmon resonances associated with the observed reflectivity maxima. Further, the potential of this type of surface plasmon resonance for sensing applications is investigated.
1. Introduction The optical excitation of surface plasmons (SP) using the prism coupling geometries of Kretschmann [ 1] and Otto [ 21 has been extensively used to study and characterise thin films made from many different materials. Typically the intensity of reflected linearly polarised (TM) radiation is recorded as a function of the angle, Fig. la shows a typical example. A minimum in the reflectivity occurs when the momentum of the incident light in the plane of the surface matches that of the SP mode, energy from the incident radiation then couples to the SP mode and is thus not reflected. This reflectivity data is then used to fit theoretical predictions of the reflectivity produced from Fresnel’s equations, the optical permittivity, (E = E,+ iei), and thicknesses of each layer may thus be obtained. In sensor applications shifts in angular position of the reflectivity minimum are used to monitor the changing conditions at the surface supporting the plasmon, providing a powerful optical technique for examining surfaces. Tracking a minimum signal against a noisy background can
prove problematic, so if a sharp maximum reflectivity could be obtained, such as that shown in Fig. lb, which is responsive to changes at the surface supporting the SP mode, then the design of practical sensing devices may be more readily facilitated. Printz and Sambles [ 3 ] have recently reported the observation of a maximum in reflectivity coinciding with the excitation of a SP. This was termed an inverted surface plasmon (ISP). They deposited a chromium: gold bi-layer onto a high index prism and recorded a broad reflectivity peak of 40% against a background reflectivity of approximately 15%. The aim of our study was to investigate alternative layered systems with a view to improving the sharpness and contrast of the reflectivity maximum associated with the ISP. It is the presence of the absorbing layer, in this case chromium, a strong absorber at the wavelength of study, between the prism and the surface plasmon supporting gold layer that gives rise to this reflectivity maximum. The nature of this reflectivity maximum is more clearly seen in Fig. 2 where we have plotted the theoretical reflectivity curves for three
0030-4018/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved XSDI0030-4018(94)00233-K
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K.A. Home et al. /Optics Communications 110 (1994) 80-86
Reflectivity
(a) Reflectivity
(b) Reflectivity
minimum
maximum
Angle of incidence
Fig. 1. Comparison of typical reflectivity curves from (a) surface plasmon showing a reflectivity minimum, and (b) “inverted” surface plasmon showing a reflectivity maximum.
thicknesses of absorber. The reflectivity curve for the case of no absorber is just the usual reflectivity curve for gold on a high index prism, the dip corresponding to excitation of the surface plasmon. The other two curves are for an absorbing chromium layer between the gold and the prism, the thickness of the absorber being chosen as indicated in the figure and the gold thickness adjusted to give maximum contrast in the reflectivity signal. As the thickness of the absorber is increased the reflectivity dip broadens and becomes weaker, eventually being replaced by a reflectivity maximum rather than a minimum. We also notice that for the thickest absorber the slope of the reflectivity curve before the critical angle has changed - the shape of the reflectivity curve in this case looks to be inverted with respect to the original reflectivity curve. The optical permittivity of the absorbing chromium layer had a large imaginary component [ 31 and our theoretical modelling of such bilayer systems led us to the conclusion that in order to observe ISPs the underlayer should be strongly absorbent, i.e. 1E,1c+zci. Reference to Johnson and Christy [ 4 1, and Palik [ 5 ] indicated several metals with suitable properties, Tadifferent
ble 1. With evaporation constraints in mind this lead to the selection of vanadium overlaid with gold as one suitable system for further investigation, and iron overlaid with silver as a second choice.
2. Experimental procedure and fitting of data The metal films were deposited by thermal evaporation at a pressure of 10V4 Pa, film thickness was monitored with a quartz crystal oscillator. For the optical measurements, linearly polarised (TM) light of wavelength 632.8 nm from a HeNe laser was mechanically chopped at 1.7 kHz, thus allowing phase sensitive detection of the reflected light. A computer controlled rotation stage was used to control the angle of incidence with a resolution of 0.01”. A weak reference signal was also taken from the input beam, and division of the recorded data by the reference allowed us to compensate for source intensity fluctuations. Internal reflectivity data from the prism/metal boundary were then recorded as a function of the incident angle on the front face of the prism. These data were converted to incident angle at the prism/metal
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K.A.
Home et al. / OpticsCommunications 110 (I 994) 80-86 2. I. Experiment
0.6
Reflectivity 0.4
34
35
36
37
38
Angle of Incidence Fig. 2. Theoretical reflectivity curves for the chrome/gold system. The three curves show how the presence of the absorbing chrome layer alters the reflectivity curve from one showing a minimum to one showing a maximum.
Table 1 Optical permittivity nm
of various
metals at a wavelength
of 632.8
Material
Real part of optical permittivity
Imaginary part of optical permittivity
Ref.
Chromium Iron Vanadium Molybdenum Tungsten Gold Silver
-0.84 - 1.01 3.41 1.15 4.61 - 8.25 - 15.0
20.92 17.57 21.38 25.91 20.81 l.lli 1.02i
[41 [41 141
I51 [51 [51 [51
film interface and the measured intensity corrected for reflection losses at the prism faces. Theoretical values of optical constants and thicknesses of each layer were then least square fitted to this data, by comparing the experimental data with theoretical reflectivity data derived from Fresnel reflection equations.
I (vanadium :gold)
The vanadium: gold bi-layer on a high index (n = 1.8 ) prism was theoretically modelled using the optical constants of Table 1, to find the optimum thicknesses of each film to produce a sharp ISP maximum reflectivity. Our modelling demonstrated the need to balance the sharpness of the plasmon feature - dictated by the gold film - against the broadening of the peak due to attenuating properties of the vanadium. Having chosen the approximate thicknesses required - 12 nm vanadium, 25 nm gold - one face of a prism was suitably masked and films deposited to give three distinct areas for study: e vanadium only, vanadium : gold and gold only (Fig. 3a). The fitting of theory to the data, shown in Fig. 4, is clearly excellent. Firstly, the gold film data gave the optical permittivity value ( eAu= - 12.09 + i 1.65 ) and thickness of the gold film (d,,=29.3 nm). Next the vanadium only data was fitted. This layer was treated as a two component system of vanadium with an oxidised overlayer (ox). We fixed the thickness of the oxide arbitrarily at d,, = 3 nm. We would expect there to be a gradual transition from the oxidised surface to a pure metal region, however, we treated this as a distinct, very thin separate layer as a first approximation and were thus able to obtain a good fit to the experimental data. The values obtained for the vanadium were, (ev=2.49+i24.95, dv=21.4 nm) and fortheoxide (~,,=-1.80+i1.12,d,,=3.0nm). Finally, fitting to the data for the inverted plasmon from the metallic bi-layer required a consideration of the composition of each layer and the effects of mixing at the boundaries. The intermediate layer now becomes a mixture of vanadium oxide and gold. The gold layer parameters will be slightly different due to changes in nucleation kinetics during deposition, and some mixing with the vanadium. Therefore, for the fitting of this tri-layer the parameters of the vanadium were fixed, which is reasonable as it is the same layer characterised before and should not have been significantly influenced by the gold overlay. Also, the thickness of the intermediate layer d,,, was held at 3 nm. The theoretical lit then gives the values shown in Table 2. The difference in the optical permittivity of the gold layer from that for the gold only region is approximately 1% for the real part and 30% of the imaginary.
K.A. Home et al. /Optics Communications I10 (1994) 80-86 Prism a)
83
Prism b)
Vanadium
Gold
Silver Fig. 3. Schematic of sample geometry for the two film systems considered, (a) vanadium/gold and (b) iron/magnesium fluoride/silver.
Table 2 Fitted parameters for the vanadium :gold system Layer
Fitted optical permittivity
Fitted thickness
Vanadium Oxide Gold
2.49+24.95i (fixed) -0.64+ 0.77i - 12.79+ 1.23i
21.4 nm (fixed) 3.0 nm (fixed) 26.2 nm
The change in thickness may indicate some loss of gold to the mixed layer. Further, the slightly metallic nature of the intermediate layer is plausible owing to the introduction of the gold. We considered possible alloying of vanadium and gold and reference to metallurgical tables [ 6 ] indicated that they form a homogeneous alloy at elevated temperatures. The lack of substantial changes of the gold parameters when deposited on the vanadium suggest this was not a problem here.
1.2
2 (iron : silver)
Information on alloying properties also helped in the selection of the iron:silver system, as these two metals are virtually immiscible under the conditions needed for deposition by thermal evaporation. Since silver gives a sharper surface plasmon reflectivity minimum in the visible than gold it was anticipated that a sharp ISP would be recorded for the iron : silver system. The required thicknesses derived from our theoretical modelling were 25 nm of each metal. The rapid oxidation and/or sulphidisation of iron on ex-
I
I
I
1
I
1.0
0.8
Reflectivity 0.6
0.4
0.2
0.0
2.2. Experiment
1
32
I
I
I
I
I
33
34
35
36
37
1
38
39
Angle of incidence (degrees) Fig. 4. Reflectivity data for the vanadium/gold system. Squares are from the gold only region, circles from the Vanadium only region and crosses are from the bilayer region. For each set of experimental data the relevant fitted theoretical curve is shown as a continuous line. Only one in five data points are shown for clarity.
posure to air had to be avoided and two methods of overcoming this were followed. (i) One face of a high index prism was coated with a layer of iron and then overlaid with silver, without breaking the vacuum of the evaporation chamber. The
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K.A. Home et al. / Optics Communications I1 0 (1994) SO-86
Table 3 Fitted parameters Iron a Silver b
for the iron, magnesium
3.61+ - 16.76+
15.751 0.7Oi
fluoride,
23.8 nm 24.4 nm
shown in Fig. 5. In fitting to this data the optical permittivity of MgF, was fixed at e = 1.9044 [ 7 ] (a zero absorption coefficient was assumed). The fitted values for the iron : MgFz layer are given in Table 3. The values for the various optical permittivities are comparable to those expected from Refs. [ 41 and [ 5 1, and the thicknesses of the metal layers are approximately those expected from monitoring with the quartz crystal oscillator. The apparent loss of 9 nm of MgFz following the overlaying by silver needs further consideration, possible causes are: (a) Degeneracy of the fitting routine. The least squares lit of theory to experimental data for both curves in Fig. 5 is very good. If we try fixing the thickness LgFZ then it is not possible to obtain a good fit to the ISP. Degeneracy in fit parameters is thus ruled out as causing the change in fitted thickness. (b) Mixing of the layers. Kovacs and Scott [ 81 used a silver: MgF, : silver coated prism, and found that to obtain a lit to their data they had to allow for an intermediate cermet layer, formed as the silver infilled the rough, porous surface of the MgF2. Electron micrographs of their MgFz films showed that as the thickness of the MgF, film increased the surface became rougher, and to obtain good fits to their data they had to increase the thickness of the cermet, but
silver system 58.3 nm 49.3 nm
’ For the iron+magnesium fluoride system. b For the silver layer, assuming the iron to be the same as fitted above.
reflectivity data for this structure is shown in Fig. lb. The sharp maximum in the reflectivity data would appear to be an ISP. Attempts to obtain the optical permittivity and thickness for both layers simultaneously by fitting to this data gave results which were degenerate and therefore could not be considered reliable. (ii) A further experiment was then conducted in which, as in the vanadium : gold case, the layers could be independently measured. A thin layer of magnesium fluoride was introduced as a protective overlayer for the iron. Again a high index prism was coated with iron, followed by a MgF, layer, without breaking the vacuum of the evaporation chamber. Half of the prism face was masked and a silver film deposited on top of the MgF,, Fig. 3b. The recording of reflectivity data was carried out as before for both sections of this prism, data and fitted theory are
0.8
0.6
Reflectivity 0.4
32
33
34
35
Angle of incidence
36
37
38
39
(degrees)
Fig. 5. Reflectivity data for iron:silver coated prism. Circles are from the iron/magnesium region, squares from the complete system. For each set of experimental data the relevant fitted theory is also shown as a continuous line. Only one in five data points are shown for clarity. Also shown as a dotted line is the theoretical reflectivity data for a simple silver film, to allow comparison between the positions of reflectivity maxima for the first system, and reflectivity minima for the latter.
K.A. Home et al. /Optics Communications 110 (1994) 80-86
0.0
0.3
0.6
0.9
1.2
0
2
4
6
Air
Ag MgF,
Z-axis
Fe
Prism
, 1.0 H, (a.u)
1.5
3.0
4.5
6.0
Energy loss density
Fig. 6. The profile of the time averaged H,, field component as a function of distance through the layered system for the two structures is shown in the left hand two diagrams of this figure, the field is seen to be strongest at the surface supporting the surface plasmon, i.e. noble metal/air interface. The right hand two diagrams show the energy loss density profiles, indicating that most of the energy is dissipated in the absorbing underlayer as expected.
this was only about 1% of the total MgF, thickness. Such a thickness change would not account for the 9 nm of MgF2 in the our case, however, our sample may well have had a different surface roughness since this aspect is strongly dependent on fabrication conditions. At any event, the purpose of this part of the study was to demonstrate the reflectivity maximum and the parameters of the individual layers are of rather secondary importance so that further effort was not expended in this direction.
3. Discussion If the phenomena reported above are to prove as useful as the much studied reflectivity minima, then the observed reflectivity maxima need to be confirmed as arising from the excitation of a surface
plasmon at the noble metal : air interface. Printz and Sambles [ 31 have shown the convergence of the position of this maximum with modelled minima, in both Kretschman and Otto configurations, as a function of gold thickness. In Fig. 5 a modelled SP reflectivity minimum for a 50 nm silver film ( eAg= - 16.76 + iO.70) is shown for comparison. The difference in the angular position of the modelled minimum and the observed maximum is approximately 0.04”, indicating a good correlation between the inverted and normal SP. Modelling of field profiles using Maxwell’s equations allows further examination of each of the systems studied. The prism/metal interface is taken as the xy-plane for z= 0, and the plane of incidence the xz-plane. Using parameters derived from fitting the above data, the time averaged envelope of H,,, and the energy density loss profile dS,/dz (S= Poynting
K.A. Home et al. /Optics Communications 1 IO (1994) 80-86
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I
I
37.5
Surface Plasmon Angle (deg 37.0
36.5
36.0
+
2.4
I
2.6
I
2.6
maximum to changes in the real part of the optical permittivity of an overlayer on the plasmon supporting surface, as might be found in sensing applications [ 9, lo]. The E values and film thicknesses of the iron/ MgF,/silver coated prism derived from the fitted data of Fig. 5b were modelled with the addition of an overlayer of 20 nm thickness, and an optical permittivity (t) typical of an organic compound, e.g. cobalt phthalocyanine [ 91. The adsorption of a gas by such a layer leads not only to changes in E, but also to an increase in d. However, in our modelling d and were fixed and movement of the maximum eimaginary is due to changes in treal of the overlayer. The same modelling procedure was also followed for a simple 50 nm film of silver to compare the sensitivity of the two types of system, we see that they have a similar sensitivity.
I
3.0
Acknowledgements
qea, of overlayer Fig. 7. Angular position of reflectivity minima (circles) and minima (diamonds) as a function of optical permittivity of a 20 nm overlayer.
vector), for TM radiation at the reflectivity peak angle are plotted in Fig. 6; the units for the profiles are arbitrary. The energy loss density plots show where the energy is being dissipated in the system. The similarities between the profiles in the gold and silver layers of each system are very clear, showing the excitation of the surface plasmon leads to an enhancement of the H,, fields at the noble metal/air interface. The plots of energy density loss also show little difference in the noble metals, only changes of scale due to the strength of the field reaching the film. Most of the energy is lost in the absorbent layers, ie vanadium and iron, the loss peaking at the interface with the prism. These plots show clearly the absorbing nature of the vanadium/iron layer needed to produce the inverted surface plasmon. Fig. 7 illustrates the sensitivity of the inverted SP
K.A. Horne wishes to thank the Nuffreld Foundation for support under the Undergraduate Research Bursaries Scheme. We also wish to thank D. Jarvis for the preparation of the metal films.
References [ 1] E. Kretschmann
and H. Raether, Z. Naturforsch. a 23 (1968) 2135. [2] A. Otto, Z. Physik 216 (1968) 398. [ 31 M. Printz and J.R. Sambles, J. Mod. Optics 40 (1993) 2095. [4] P.B. Johnson and R.W. Christy, Phys. Rev. B 6 (1972) 4370. [ 5] E.D. Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985). [6] R.P. Elliot, ed., Constitution of Binary Alloys, First Supplement (McGraw-Hill, 1965 ). [7] G.W.C. Kaye and T.H. Laby, eds., Handbook of Physical Constants and Tables (Longman, 1986). [8] G.J. Kovacs and G.D. Scott, Phys. Rev. B 16 (1977) 1297. [ 91 P.S. Vukusic and J.R. Sambles, Thin Solid Films 221 ( 1992) 311. [ lo] C. Nylander, B. Liedberg and T. Lind, Sensors and Actuators 3 (1982/83) 79.
1 August 1994
OPTICS COMMUNICATIONS Optics Communications
110 ( 1994) 80-86
Surface plasmon resonances showing reflectivity maxima K.A. Home, M. Printz, W.L. Barnes, J.R. Sambles Thin Films and Interface Research
Group, Department
ofPhysics,
Umversity ofExeter,
Devon EX4 4QL. UK
Received 18 January 1994; revised manuscript received 7 April 1994
Abstract Reported is on the observation of surface plasmon resonances showing sharp maxima in the reflectivity of transverse magnetic visible radiation. Two systems of thin layers are examined, a bilayer of vanadium/gold, and a trilayer of iron/magnesiumfluoride/silver. Theoretical reflectivity data derived from Fresnel equations have been fitted to our experimental data in order to find the optical constants and layer thicknesses of the two systems. These parameters have then been used to model the optical field profiles, thus illustrating the nature of the surface plasmon resonances associated with the observed reflectivity maxima. Further, the potential of this type of surface plasmon resonance for sensing applications is investigated.
1. Introduction The optical excitation of surface plasmons (SP) using the prism coupling geometries of Kretschmann [ 1] and Otto [ 21 has been extensively used to study and characterise thin films made from many different materials. Typically the intensity of reflected linearly polarised (TM) radiation is recorded as a function of the angle, Fig. la shows a typical example. A minimum in the reflectivity occurs when the momentum of the incident light in the plane of the surface matches that of the SP mode, energy from the incident radiation then couples to the SP mode and is thus not reflected. This reflectivity data is then used to fit theoretical predictions of the reflectivity produced from Fresnel’s equations, the optical permittivity, (E = E,+ iei), and thicknesses of each layer may thus be obtained. In sensor applications shifts in angular position of the reflectivity minimum are used to monitor the changing conditions at the surface supporting the plasmon, providing a powerful optical technique for examining surfaces. Tracking a minimum signal against a noisy background can
prove problematic, so if a sharp maximum reflectivity could be obtained, such as that shown in Fig. lb, which is responsive to changes at the surface supporting the SP mode, then the design of practical sensing devices may be more readily facilitated. Printz and Sambles [ 3 ] have recently reported the observation of a maximum in reflectivity coinciding with the excitation of a SP. This was termed an inverted surface plasmon (ISP). They deposited a chromium: gold bi-layer onto a high index prism and recorded a broad reflectivity peak of 40% against a background reflectivity of approximately 15%. The aim of our study was to investigate alternative layered systems with a view to improving the sharpness and contrast of the reflectivity maximum associated with the ISP. It is the presence of the absorbing layer, in this case chromium, a strong absorber at the wavelength of study, between the prism and the surface plasmon supporting gold layer that gives rise to this reflectivity maximum. The nature of this reflectivity maximum is more clearly seen in Fig. 2 where we have plotted the theoretical reflectivity curves for three
0030-4018/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved XSDI0030-4018(94)00233-K
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K.A. Home et al. /Optics Communications 110 (1994) 80-86
Reflectivity
(a) Reflectivity
(b) Reflectivity
minimum
maximum
Angle of incidence
Fig. 1. Comparison of typical reflectivity curves from (a) surface plasmon showing a reflectivity minimum, and (b) “inverted” surface plasmon showing a reflectivity maximum.
thicknesses of absorber. The reflectivity curve for the case of no absorber is just the usual reflectivity curve for gold on a high index prism, the dip corresponding to excitation of the surface plasmon. The other two curves are for an absorbing chromium layer between the gold and the prism, the thickness of the absorber being chosen as indicated in the figure and the gold thickness adjusted to give maximum contrast in the reflectivity signal. As the thickness of the absorber is increased the reflectivity dip broadens and becomes weaker, eventually being replaced by a reflectivity maximum rather than a minimum. We also notice that for the thickest absorber the slope of the reflectivity curve before the critical angle has changed - the shape of the reflectivity curve in this case looks to be inverted with respect to the original reflectivity curve. The optical permittivity of the absorbing chromium layer had a large imaginary component [ 31 and our theoretical modelling of such bilayer systems led us to the conclusion that in order to observe ISPs the underlayer should be strongly absorbent, i.e. 1E,1c+zci. Reference to Johnson and Christy [ 4 1, and Palik [ 5 ] indicated several metals with suitable properties, Tadifferent
ble 1. With evaporation constraints in mind this lead to the selection of vanadium overlaid with gold as one suitable system for further investigation, and iron overlaid with silver as a second choice.
2. Experimental procedure and fitting of data The metal films were deposited by thermal evaporation at a pressure of 10V4 Pa, film thickness was monitored with a quartz crystal oscillator. For the optical measurements, linearly polarised (TM) light of wavelength 632.8 nm from a HeNe laser was mechanically chopped at 1.7 kHz, thus allowing phase sensitive detection of the reflected light. A computer controlled rotation stage was used to control the angle of incidence with a resolution of 0.01”. A weak reference signal was also taken from the input beam, and division of the recorded data by the reference allowed us to compensate for source intensity fluctuations. Internal reflectivity data from the prism/metal boundary were then recorded as a function of the incident angle on the front face of the prism. These data were converted to incident angle at the prism/metal
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Home et al. / OpticsCommunications 110 (I 994) 80-86 2. I. Experiment
0.6
Reflectivity 0.4
34
35
36
37
38
Angle of Incidence Fig. 2. Theoretical reflectivity curves for the chrome/gold system. The three curves show how the presence of the absorbing chrome layer alters the reflectivity curve from one showing a minimum to one showing a maximum.
Table 1 Optical permittivity nm
of various
metals at a wavelength
of 632.8
Material
Real part of optical permittivity
Imaginary part of optical permittivity
Ref.
Chromium Iron Vanadium Molybdenum Tungsten Gold Silver
-0.84 - 1.01 3.41 1.15 4.61 - 8.25 - 15.0
20.92 17.57 21.38 25.91 20.81 l.lli 1.02i
[41 [41 141
I51 [51 [51 [51
film interface and the measured intensity corrected for reflection losses at the prism faces. Theoretical values of optical constants and thicknesses of each layer were then least square fitted to this data, by comparing the experimental data with theoretical reflectivity data derived from Fresnel reflection equations.
I (vanadium :gold)
The vanadium: gold bi-layer on a high index (n = 1.8 ) prism was theoretically modelled using the optical constants of Table 1, to find the optimum thicknesses of each film to produce a sharp ISP maximum reflectivity. Our modelling demonstrated the need to balance the sharpness of the plasmon feature - dictated by the gold film - against the broadening of the peak due to attenuating properties of the vanadium. Having chosen the approximate thicknesses required - 12 nm vanadium, 25 nm gold - one face of a prism was suitably masked and films deposited to give three distinct areas for study: e vanadium only, vanadium : gold and gold only (Fig. 3a). The fitting of theory to the data, shown in Fig. 4, is clearly excellent. Firstly, the gold film data gave the optical permittivity value ( eAu= - 12.09 + i 1.65 ) and thickness of the gold film (d,,=29.3 nm). Next the vanadium only data was fitted. This layer was treated as a two component system of vanadium with an oxidised overlayer (ox). We fixed the thickness of the oxide arbitrarily at d,, = 3 nm. We would expect there to be a gradual transition from the oxidised surface to a pure metal region, however, we treated this as a distinct, very thin separate layer as a first approximation and were thus able to obtain a good fit to the experimental data. The values obtained for the vanadium were, (ev=2.49+i24.95, dv=21.4 nm) and fortheoxide (~,,=-1.80+i1.12,d,,=3.0nm). Finally, fitting to the data for the inverted plasmon from the metallic bi-layer required a consideration of the composition of each layer and the effects of mixing at the boundaries. The intermediate layer now becomes a mixture of vanadium oxide and gold. The gold layer parameters will be slightly different due to changes in nucleation kinetics during deposition, and some mixing with the vanadium. Therefore, for the fitting of this tri-layer the parameters of the vanadium were fixed, which is reasonable as it is the same layer characterised before and should not have been significantly influenced by the gold overlay. Also, the thickness of the intermediate layer d,,, was held at 3 nm. The theoretical lit then gives the values shown in Table 2. The difference in the optical permittivity of the gold layer from that for the gold only region is approximately 1% for the real part and 30% of the imaginary.
K.A. Home et al. /Optics Communications I10 (1994) 80-86 Prism a)
83
Prism b)
Vanadium
Gold
Silver Fig. 3. Schematic of sample geometry for the two film systems considered, (a) vanadium/gold and (b) iron/magnesium fluoride/silver.
Table 2 Fitted parameters for the vanadium :gold system Layer
Fitted optical permittivity
Fitted thickness
Vanadium Oxide Gold
2.49+24.95i (fixed) -0.64+ 0.77i - 12.79+ 1.23i
21.4 nm (fixed) 3.0 nm (fixed) 26.2 nm
The change in thickness may indicate some loss of gold to the mixed layer. Further, the slightly metallic nature of the intermediate layer is plausible owing to the introduction of the gold. We considered possible alloying of vanadium and gold and reference to metallurgical tables [ 6 ] indicated that they form a homogeneous alloy at elevated temperatures. The lack of substantial changes of the gold parameters when deposited on the vanadium suggest this was not a problem here.
1.2
2 (iron : silver)
Information on alloying properties also helped in the selection of the iron:silver system, as these two metals are virtually immiscible under the conditions needed for deposition by thermal evaporation. Since silver gives a sharper surface plasmon reflectivity minimum in the visible than gold it was anticipated that a sharp ISP would be recorded for the iron : silver system. The required thicknesses derived from our theoretical modelling were 25 nm of each metal. The rapid oxidation and/or sulphidisation of iron on ex-
I
I
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1
I
1.0
0.8
Reflectivity 0.6
0.4
0.2
0.0
2.2. Experiment
1
32
I
I
I
I
I
33
34
35
36
37
1
38
39
Angle of incidence (degrees) Fig. 4. Reflectivity data for the vanadium/gold system. Squares are from the gold only region, circles from the Vanadium only region and crosses are from the bilayer region. For each set of experimental data the relevant fitted theoretical curve is shown as a continuous line. Only one in five data points are shown for clarity.
posure to air had to be avoided and two methods of overcoming this were followed. (i) One face of a high index prism was coated with a layer of iron and then overlaid with silver, without breaking the vacuum of the evaporation chamber. The
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K.A. Home et al. / Optics Communications I1 0 (1994) SO-86
Table 3 Fitted parameters Iron a Silver b
for the iron, magnesium
3.61+ - 16.76+
15.751 0.7Oi
fluoride,
23.8 nm 24.4 nm
shown in Fig. 5. In fitting to this data the optical permittivity of MgF, was fixed at e = 1.9044 [ 7 ] (a zero absorption coefficient was assumed). The fitted values for the iron : MgFz layer are given in Table 3. The values for the various optical permittivities are comparable to those expected from Refs. [ 41 and [ 5 1, and the thicknesses of the metal layers are approximately those expected from monitoring with the quartz crystal oscillator. The apparent loss of 9 nm of MgFz following the overlaying by silver needs further consideration, possible causes are: (a) Degeneracy of the fitting routine. The least squares lit of theory to experimental data for both curves in Fig. 5 is very good. If we try fixing the thickness LgFZ then it is not possible to obtain a good fit to the ISP. Degeneracy in fit parameters is thus ruled out as causing the change in fitted thickness. (b) Mixing of the layers. Kovacs and Scott [ 81 used a silver: MgF, : silver coated prism, and found that to obtain a lit to their data they had to allow for an intermediate cermet layer, formed as the silver infilled the rough, porous surface of the MgF2. Electron micrographs of their MgFz films showed that as the thickness of the MgF, film increased the surface became rougher, and to obtain good fits to their data they had to increase the thickness of the cermet, but
silver system 58.3 nm 49.3 nm
’ For the iron+magnesium fluoride system. b For the silver layer, assuming the iron to be the same as fitted above.
reflectivity data for this structure is shown in Fig. lb. The sharp maximum in the reflectivity data would appear to be an ISP. Attempts to obtain the optical permittivity and thickness for both layers simultaneously by fitting to this data gave results which were degenerate and therefore could not be considered reliable. (ii) A further experiment was then conducted in which, as in the vanadium : gold case, the layers could be independently measured. A thin layer of magnesium fluoride was introduced as a protective overlayer for the iron. Again a high index prism was coated with iron, followed by a MgF, layer, without breaking the vacuum of the evaporation chamber. Half of the prism face was masked and a silver film deposited on top of the MgF,, Fig. 3b. The recording of reflectivity data was carried out as before for both sections of this prism, data and fitted theory are
0.8
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Reflectivity 0.4
32
33
34
35
Angle of incidence
36
37
38
39
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Fig. 5. Reflectivity data for iron:silver coated prism. Circles are from the iron/magnesium region, squares from the complete system. For each set of experimental data the relevant fitted theory is also shown as a continuous line. Only one in five data points are shown for clarity. Also shown as a dotted line is the theoretical reflectivity data for a simple silver film, to allow comparison between the positions of reflectivity maxima for the first system, and reflectivity minima for the latter.
K.A. Home et al. /Optics Communications 110 (1994) 80-86
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, 1.0 H, (a.u)
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Fig. 6. The profile of the time averaged H,, field component as a function of distance through the layered system for the two structures is shown in the left hand two diagrams of this figure, the field is seen to be strongest at the surface supporting the surface plasmon, i.e. noble metal/air interface. The right hand two diagrams show the energy loss density profiles, indicating that most of the energy is dissipated in the absorbing underlayer as expected.
this was only about 1% of the total MgF, thickness. Such a thickness change would not account for the 9 nm of MgF2 in the our case, however, our sample may well have had a different surface roughness since this aspect is strongly dependent on fabrication conditions. At any event, the purpose of this part of the study was to demonstrate the reflectivity maximum and the parameters of the individual layers are of rather secondary importance so that further effort was not expended in this direction.
3. Discussion If the phenomena reported above are to prove as useful as the much studied reflectivity minima, then the observed reflectivity maxima need to be confirmed as arising from the excitation of a surface
plasmon at the noble metal : air interface. Printz and Sambles [ 31 have shown the convergence of the position of this maximum with modelled minima, in both Kretschman and Otto configurations, as a function of gold thickness. In Fig. 5 a modelled SP reflectivity minimum for a 50 nm silver film ( eAg= - 16.76 + iO.70) is shown for comparison. The difference in the angular position of the modelled minimum and the observed maximum is approximately 0.04”, indicating a good correlation between the inverted and normal SP. Modelling of field profiles using Maxwell’s equations allows further examination of each of the systems studied. The prism/metal interface is taken as the xy-plane for z= 0, and the plane of incidence the xz-plane. Using parameters derived from fitting the above data, the time averaged envelope of H,,, and the energy density loss profile dS,/dz (S= Poynting
K.A. Home et al. /Optics Communications 1 IO (1994) 80-86
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Surface Plasmon Angle (deg 37.0
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maximum to changes in the real part of the optical permittivity of an overlayer on the plasmon supporting surface, as might be found in sensing applications [ 9, lo]. The E values and film thicknesses of the iron/ MgF,/silver coated prism derived from the fitted data of Fig. 5b were modelled with the addition of an overlayer of 20 nm thickness, and an optical permittivity (t) typical of an organic compound, e.g. cobalt phthalocyanine [ 91. The adsorption of a gas by such a layer leads not only to changes in E, but also to an increase in d. However, in our modelling d and were fixed and movement of the maximum eimaginary is due to changes in treal of the overlayer. The same modelling procedure was also followed for a simple 50 nm film of silver to compare the sensitivity of the two types of system, we see that they have a similar sensitivity.
I
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Acknowledgements
qea, of overlayer Fig. 7. Angular position of reflectivity minima (circles) and minima (diamonds) as a function of optical permittivity of a 20 nm overlayer.
vector), for TM radiation at the reflectivity peak angle are plotted in Fig. 6; the units for the profiles are arbitrary. The energy loss density plots show where the energy is being dissipated in the system. The similarities between the profiles in the gold and silver layers of each system are very clear, showing the excitation of the surface plasmon leads to an enhancement of the H,, fields at the noble metal/air interface. The plots of energy density loss also show little difference in the noble metals, only changes of scale due to the strength of the field reaching the film. Most of the energy is lost in the absorbent layers, ie vanadium and iron, the loss peaking at the interface with the prism. These plots show clearly the absorbing nature of the vanadium/iron layer needed to produce the inverted surface plasmon. Fig. 7 illustrates the sensitivity of the inverted SP
K.A. Horne wishes to thank the Nuffreld Foundation for support under the Undergraduate Research Bursaries Scheme. We also wish to thank D. Jarvis for the preparation of the metal films.
References [ 1] E. Kretschmann
and H. Raether, Z. Naturforsch. a 23 (1968) 2135. [2] A. Otto, Z. Physik 216 (1968) 398. [ 31 M. Printz and J.R. Sambles, J. Mod. Optics 40 (1993) 2095. [4] P.B. Johnson and R.W. Christy, Phys. Rev. B 6 (1972) 4370. [ 5] E.D. Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985). [6] R.P. Elliot, ed., Constitution of Binary Alloys, First Supplement (McGraw-Hill, 1965 ). [7] G.W.C. Kaye and T.H. Laby, eds., Handbook of Physical Constants and Tables (Longman, 1986). [8] G.J. Kovacs and G.D. Scott, Phys. Rev. B 16 (1977) 1297. [ 91 P.S. Vukusic and J.R. Sambles, Thin Solid Films 221 ( 1992) 311. [ lo] C. Nylander, B. Liedberg and T. Lind, Sensors and Actuators 3 (1982/83) 79.