Monitoring Ag2S

Growth With Surface Plasmon Resonance

Jonathan McAneney

Supervisor: Dr P Dawson

Technical Assistance: Dr R J Turner

D Canchal

The Surface Plasmon Resonance (SPR) technique is used to study the growth of Ag2S on the surface of thin Ag films. A Kretschmann Attenuated Total Reflection (ATR) configuration is used to couple the parallel wave vector of an incident p-polarised EM wave to the larger wave vector of the Surface Plasmon Polariton (SPP) mode. We describe a simple theory of SPR and derive the SPP dispersion relation, and the condition of SPP excitation. We report on the method of using SPR to monitor the growth of Ag2S layers on the surface of two Ag films of 40 nm and 60 nm thicknesses. The experimental results were approximated to Fresnel reflection theory and show an increase in resonance angle θsp and an increase in FWHM of the SPR curve as the Ag2S layer grows due to exposure of the Ag film to laboratory air. The rate of Ag2S growth was found to begin in a linear fashion of ~ 1 nm per week, but began to decrease after approximately three weeks. This effect shows good agreement with other experimental findings published in physics journals. Finally the experimental value for the consumption coefficient R was determined to be R = 0.57 or R = 0.65 depending on the fit used, and correlates well with the theoretical value of R = 0.6 (assuming bulk densities of Ag and Ag2S).

1

Contents Page Introduction 2

Background Physics 2 Surface Plasmon Dispersion Relation 4 Surface Plasmon Excitation 5 Effects of Growth of Ag2S Layer on SPP 8

Experiment 9

Preparation of Ag Films 9 Monitoring Ag2S Growth 10 The Fitting Program 11

Results and Discussion 12

The Fit Penalty 12 Thermal Evaporator Calibration 14 Effects of Exposure to Air on SPR Curves 16 Discussion of Results 23 The Effects of Ag2S Growth on SPR 25 Monitoring Ag2S Growth 27 Determination of Consumption Coefficient 30

Conclusions 32 References 34

2

Introduction Silver (Ag) is an attractive lustrous metal with high electrical and thermal conductivities. It has the highest reflectance in the visible and infrared than any of the metallic elements [1]. Unfortunately, it tarnishes readily when exposed to the atmosphere, and is particularly susceptible to sulphurous compounds, producing the I2-VI binary semiconductor silver sulphide (Ag2S) [2]. The rate of Ag2S growth on a thin Ag film can be monitored using the Surface Plasmon Resonance (SPR) technique with a Kretschmann attenuated total reflection (ATR) configuration. SPR is based on the excitation and detection of surface plasmons at a metal-dielectric interface [2,3] and was previously used for the determination of dielectric constants of metallic and dielectric thin films [4,5]. The generation of SPR depends on the angle of incidence θ of a p-polarised monochromatic light beam, and appears as a sharp in the internal reflectance, just beyond the critical angle, for a metal-coated prism hypotenuse. Bussjager and Macleod [1] studied the corrosion of Ag by using SPR. Experimentally they obtained a family of curves showing shifts in resonance position and changes in the shape of the SPR curves, using Ag exposed to an unknown concentration of H2S. Bennett et al [6] studied the growth of Ag2S on Ag with ellipsometric and micrograph techniques. They showed that the growth rate of the Ag2S layer decreases with time, and observed that Ag2S grows in circular clumps. Mehan and Mansingh [7] showed that radiation damping is mainly responsible for the increase in half width and dip reflectance, indicating the Ag2S layer was rough and discontinuous. In this report we shall first give a brief account of the physics behind SPR and then derive the dispersion relation for the surface plasmon polariton SPP modes. Next we will describe the excitation of these SPP modes by the method of ATR. Emphasis is placed on absorption of the enhanced internal optical fields in the metal film for producing the observed minimum in reflectivity. Finally an overview of the experimental apparatus and procedure will be presented followed by an analysis and discussion of results. Background Physics Surface plasmon polaritons (SPP) are collective electromagnetic modes of the interface between a metal and a non-metal [1,2,8]. They arise from the coupling of photons to oscillating charge density on the metals surface. These modes exist for the frequencies ω such that the real part of the dielectric function of the metal Re{εM(ω)} is less than -εA where εA is the dielectric constant of the non-metallic medium at the interface (in this experiment air). Also, these modes are p-polarised, i.e. their electric field vectors E lie in the plane defined by n the surface normal and kx the wave vector of the SPP parallel to the surface. It is assumed that the interface is perfectly flat and infinite in extent.

3

Confinement to the interface means that the field amplitudes decay exponentially in directions perpendicular to the interface. Generally, this decay occurs over a length comparable to the wavelength of freely propagating light of the same frequency ω. The dispersion relation for a SPP is given by

2

1

ε+ε

εε=ω

AM

AMxck . (1)

This is shown schematically in Fig 1 and is based on the free electron gas model of a metal, for which the dielectric function is given by

( )2

1

ω

ω−=ωε p

M , (2)

where ωp is the plasma frequency defined by [9],

2

1

0

2

ε=ω

e

pm

ne. (3)

Fig 1: Schematic representation of the SPP dispersion curve plotted ω vs kx, as given by Eq (1). Ordinarily light propagating in air cannot couple directly to SPP since its light line always lies to the left of the SPP curve. Coupling can be achieved through a prism of high refractive index, and by increasing the angle of incidence of the beam. ωp is the bulk plasmon frequency and ωp/√2 is the asymptotic limit for the SPP.

ω

ω p

A

x

ε

ck ω ====

k //

sin θ n

ck ω

p

x ====

SPP

ω ex

k ex

p

x

n

ck ω ====

4

Since for most metals εM(ω) is less than –1 for visible light, kx is greater than the wave vector of an electromagnetic wave in air at the same frequency ω. Thus, ordinarily visible light cannot couple directly to SPP. However, a Kretschmann ATR [10,11,12] configuration can be used to enhance the parallel wave vector component of an incident light beam inside a prism of high refractive index np (see Fig (2)). This prism has one face coated with the metal film, which is thin enough to allow light transmission in the visible spectrum. When the angle of incidence increases to the critical angle required for total internal reflection, an evanescent field is created within the metallic film. This evanescent field is then capable of exciting surface plasmon polaritons, and hence by classification, SPP are non-radiative.

Surface Plasmon Dispersion Relation We now derive the dispersion relation to relate the wave vector of the SPP travelling along the surface of a metal to its angular frequency ω. Consider a space 0 < z < d to be filled with a metal (see Fig (2)) of complex dielectric function εM = ε1 + ε2i, where the real part is described by the Equation (2). The imaginary part describes the optical absorption process in the metal that we shall assume to be ε2 ≡ 0 for the discussion of an ideal dispersion relation. For z > d we have air of dielectric constant εA. If we assume the existence of only a single wave on each side of the boundary and that the electric fields are monochromatic plane waves then

( ) ( )[ ]zkxktitzx zx −−ω= exp,, EE . (4)

For surface waves, we are interested in the conditions under which there are no propagating waves in either the metal or air. We assume ω and kx have values such that in the metal the solution of the wave equation can be written as

Fig 2: The Kretschmann Attenuated Total Reflection Configuration. When the angle of incidence θi equals the critical angle of total internal reflection an evanescent field is produced in the metal. The high refractive index of the prism np and the increased θi enhances the parallel wave vector of the incident light, allowing it to couple to the SPP mode.

θi

Air εA

z = 0

z = d

Prism of Refractive Index np

Metal εM = ε1 + ε2i

5

2

1

2

22

ωε−−=

ckik M

xz , (5a)

and in the air

2

1

2

22

ωε−+=

ckik A

xz . (5b)

The signs are chosen so that the electric fields in the metal and dielectric describe exponential decay normal to the field. For metals this condition is satisfied for ω < ωp, but in air the condition is only satisfied for evanescent waves in total internal reflection. We now apply the boundary conditions at the plane z = d, i.e. continuity of the tangential component of E and H, and the normal component of D and B. We assume the magnetic permeability is equal to unity and that B = H. Two transverse modes can now be classified in terms of polarization. When Ex = Ez = 0 we have s-polarisation, and no SPP mode solution exists, but when Ey = 0 we have p-polarisation and thus a SPP mode solution can be obtained. Now using the continuity of the tangential component of E and the transversality of the fields, we have

−+ ===

dzzzdzzz kk EE . (6)

Combining this with the continuity of the normal component of D gives

−+ ==

ε=εdzz

xA

dzz

xM

k

k

k

k. (7)

Substitution from Equations (5a) & (5b) allows the above condition to be rewritten as the SPP dispersion relation given in Equation (1). Surface Plasmon Excitation We now relate the amplitude of the SPP mode to the exciting incident radiation. This is achieved by using Fresnel equations of reflection. An electromagnetic wave is incident on a thin metallic film at the hypotenuse face of the prism and at an angle of incidence greater than the critical angle for total internal reflection. The geometry of the attenuated total reflection configuration is illustrated Fig (3). If we assume that the electric field vectors are p-polarised and described by monochromatic plane waves, then we have an incident and reflected propagating wave within the glass medium of the form

( )

θ−θ

ω= 111 cossinexp zxn

ci p

i

incident EE , (8a)

and

6

( )

θ+θ

ω= 111 cossinexp zxn

ci p

r

reflected EE . (8b)

In the thin metal film we can write the total electric field as a standing wave superposition of two exponentially damped waves.

( ) ( )zxnc

izxnc

i ppmetal β−

θ

ω′+β

θ

ω= expsinexpexpsinexp 1212 EEE . (8c)

The transmitted wave in the air is assumed to be evanescent:

( )

−θ

ω

θ

ω= 2

1

122

13 1sinexpsinexp ppdtransmitte nc

xnc

iEE . (8d)

β is the absorption coefficient at non-normal incidence, which by comparison with Equations (4) & (5a) and written for the geometry of Fig (4) is

( )2

1

122 sin θ−ε

ω−=β pM n

ci , (9)

Fig 4: Attenuated total reflection geometry for a thin metal film between a glass prism and air.

1

2

3

Prism

Silver

Air

(((( )))) ω E 1 i (((( )))) ω E 1

r

(((( )))) ω E 2 (((( )))) ω E 2 ′′′′

(((( )))) ω E 3

(((( )))) ωωωω i 1 H (((( )))) ωωωω r

1 H

(((( )))) ωωωω 2 H (((( )))) ωωωω ′′′′ 2 H

(((( )))) ωωωω 3 H

θ 1 θ 1

θ 2 θ 2

θ 3 z = d

x (z = 0)

z

(((( )))) ωωωω εεεε A

(((( )))) (((( )))) (((( )))) i M ω ε ω ε ω ε 2 1 ++++ ====

(((( )))) (((( )))) ωωωω ==== p p n 2 1 ω ε

7

where ppn ε=2 is the dielectric constant of the prism, and θ1 is the angle of incidence. The x

dependence of all the waves follows from Snell’s Law.

The four unknown amplitudes 3221 and,,, EEEE ′r can be related to the incident amplitude i

1E

through boundary conditions. Continuity of the tangential components of E and H at z = 0 and z = d boundaries gives the required four equations. Thus the amplitudes of the fields in the metal at z = 0 is

( )drr

t

β+=

2exp1 2312

122

i1EE , (10a)

and

( )

( )drr

dtt

β+

β=′

2exp1

2exp

2312

23122

i1EE . (10b)

The Fresnel reflection and transmission amplitude factors [13], with 12 and 23 subscripts for the glass-metal and metal-air boundaries respectively are given by:

21

1

12coscos

cos2

21

θ+θε

θ=

pM

p

n

nt , (11a)

21

21

12coscos

coscos

21

21

θ+θε

θ−θε=

pM

pM

n

nr , (11b)

32

3223

coscos

coscos2

12

1

21

21

θε+θε

θε−θε=

MA

MAr , (11c)

where θ2 and θ3 in the metal and air respectively are defined by

2

1

12

2

2 sin1cos

θ

ε−=θ

M

pn, (12a)

and

2

1

12

2

3 sin1cos

θ

ε−=θ

A

pn. (12b)

The complex nature of these angles determines the real exponential decay of the fields in the metal and air media.

8

We can now solve for r

1E and find the ratio of the reflected optical power to the incident

optical power. This is found to be,

( )( )

2

2312

2312

2exp1

2exp

drr

drrR

β+

β+= . (13)

The critical factor in the above formula is r23, which by combining Equations (11c), (12a) & (12b), can be rewritten as

( ) ( )( ) ( ) 2

12

1

21

21

122

122

122

122

23

sinsin

sinsin

ApMMpA

ApMMpA

nn

nnr

ε−θε+ε−θε

ε−θε−ε−θε= . (14)

For an ideal free electron gas, the denominator of r23 vanishes at the resonance angle

θsp given by,

2

1

sin

ε+ε

εε=θ

AM

AMsppn , (15)

which is again the condition for a SPP given in Equation (1). From Equation (10a) we can see that if θ1 = θsp then E2 ≡ 0 and the only field in the metal has a simple exponential spatial decay from the metal-air boundary to the metal-glass boundary. This description is consistent with the SPP mode discussed previously. Effects of Growth of Ag2S Layer on SPP If a layer of Ag2S is formed on the surface of the Ag film, then the dispersion relation of the SPP changes. The details of this change can be calculated by the same method as outlined above, by including a four medium in the equations. We refer the reader to Pockrand [14] for an account of this treatment. The presence of the Ag2S layer causes a shift in the resonance angle θsp. This shift is determined by the real part of the dielectric constant of Ag2S, with the imaginary part changing the internal and radiation damping on the SPP thus changing the shape (i.e. FWHM measurement) of the SPR curve.

9

Experiment Preparation of Ag Films Ag films were prepared using a thermal evaporator as illustrated in Fig (4)

Current flows through a tungsten basket in which rests a compact ball of silver. This basket is mounted in a vacuum chamber at a pressure < 10-6 mbar. As the basket heats, the Ag ball evaporates and a Ag film is collected on the face of a prism held directly above it. The thickness of the film can be estimated via a crystal oscillator mounted within the evaporation chamber. As the Ag ball evaporates, the crystal oscillator gains in mass, thus decreasing the resonance frequency at which it vibrates. Thus the thicker the Ag film, the more the frequency of the crystal oscillator decreases. The thickness of an evaporated Ag film may be estimated by the equation

−

ρ=

startfinal ff

AT

11, (16)

where T is thickness measured in Angstroms, ρ is density of the evaporated material, f is the corresponding frequency in MHz, and A is a calibration constant. Since ρ is a constant, we

Fig 4: Schematic of the thermal evaporator. Current heats the tungsten basket causing the Ag ball to evaporate.

Crystal Oscillator

Prism Holder

Evacuated Chamber

Current Heated Tungsten Basket

Ag Ball

10

can factor this density value into the calibration constant A, since in this experiment we are only concerned with the evaporation of Ag films only. Thus, before we can prepare any Ag films, determine this calibration constant A. Monitoring of Ag2S Growth Once the thermal evaporator was calibrated, two Ag films of different thickness were prepared. One film was approximately 40 nm thick, while the other was approximately 60 nm thick. When removed from the evaporator they were mounted in an atomic force microscope (AFM) operating in tapping mode, to obtain a measurement of the root mean square roughness of the surface. They were then transferred to the ATR apparatus where they were then investigated with two different wavelength lasers (543.5 nm and 632.8 nm). A schematic of this ATR apparatus is shown in Fig (5). A laser beam is directed through a polariser to ensure that all light incident on the Ag film is p-polarised. The beam then encounters a ‘frequency chopper’ before reaching the beam splitter. This beam splitter directs 52 % of the incident light to a detector. This acts as reference intensity for later normalisation. The remainder of the beam then enters the prism and is reflected of the Ag-coated face onto a second detector. The prism is mounted on a computer controlled rotatable platform. The rotation of this platform changes the angle of incidence of the laser beam at the Ag-coated face. The two detectors are connected to a lock in amplifier, through which the computer can determine the reflectivity from the metal face, by normalising the reflected intensity with the reference intensity. The computer then plots a graph of reflectivity versus angle of incidence for the obtained data. It is necessary however, to convert this raw data to a prn data file so that it is compatible with the unix based fitting program.

Fig 5: Schematic of the ATR experimental set up.

11

The two films were then exposed to laboratory atmosphere for a 35-day period and monitored on an approximately weekly period. This required the prisms to be moved, which should ideally be avoided for reasons that shall be discussed later. The Fitting Program The Fitting program is a unix based application which use Fresnel equations to approximate experimental results with theory. Fig (6) shows what the set-up file looks like for this program. We note that the parameters we need to change to obtain fits are highlighted. 40, 50, 543.5, 2, 6, 396 | Highlighted is laser wavelength 1, 1, 0 |ifittype 1=leastsqrs 0=CHISQ, IFINDMAX max (1) or min(0),IFITMETHOD 0=simplex,1=powells 2.307, 0, 2.307, 0, 1, 0, 0 |Prism data: ErP, EiP, ErC, EiC, ISOTROP, THICKNESS, WEDGE -12.20, 0.50, -12.20, 0.50, 1, 40.0, 0 | Ag layer Guess: Eps parlaller, perpend, iso, thickness, wedge -10.00, 0.20, -10.00, 0.20, 45.0, 0 |Ag layer Upper values -20.00, 0.25, -20.00, 0.25, 35.0, 0 | Ag layer Lower values 1, 1, -1, -1, 1, -1 | -1=no variable, 0=no penalty function, 1=soft,2=hard 8.87, 1.82, 8.87, 1.82, 1, 0.05, 0.00 | Ag2S Layer Guess: Eps parallel,perpendicular,iso,thick,wedge 9.00, 2.50, 9.00, 2.50, 0.10, 0.0 | upper values for simplex search 7.82, 1.56, 7.82, 1.56, 0.00, 0.0 | lower values for simplex search 1, 1, -1, -1, 1, -1 | -1= no variable, 0 = no penalty function, 1 = soft,2 = hard 1.0, 0.0, 1.0, 0.0, 1, 0, 0 | Air: Eps parallel,perpendicular,iso,thick,wedge 'ag0401g.prn ' | Data file to be fitted 0 | Angle shift 0 = No, 1=Simplex, 2=extra, 3=both 0 -0.05 | Shift angle before fitting 0=no 1=yes, shift (degrees) 0 | Expansion 0=No, 1=Simplex, 2=extra 0,1 | Weight,Exponent 0 | 0=No, 1=normalise the fit-curve 1 | 0=No, 1=randomise start points for each setup 6000 | ISEED value for the randomisation routine 0.98 | NORMALISATION FACTOR

0 | Correct for losses in equilateral prism 0=no, 1=yes

Accurate fits can be achieved by first estimating the physical parameters of the layers of a sample. Next one imposes realistic upper and lower boundary values for these parameters. When this is done, the estimated curve is displayed along side the curve of the experimental data. The two curves must be as closely matched at this point particularly at the critical angle, and one must return to the estimation stage if this is not the case. Once a reasonable match of estimated curve and experimental curve has been achieved, the program tries to match the two curves exactly by changing parameters within the upper and lower boundary conditions. If a good match is found it displays these parameters with an associated fit penalty. This fit penalty must be < 10-2 and the quoted parameters must be physically sensible for it to be considered a good fit.

Fig 6: The set up file for the Unix based fitting program. Highlighted in yellow are the main variables that need changed to fit the experimental data.

12

Results and Discussion The Fit Penalty It is important to note that the following graphs do not contain conventional error bars, but instead an associated fit penalty function will be stated for each specific curve.

Graph 1: Comparison between two fit penalties for the same data file. The wavelength of the laser used is 543.5 nm

Graph 1a: Theoretical Fit to Experimental Data with a Fit Penalty of 1.80 x 10-2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

40 41 42 43 44 45 46 47 48 49 50

Internal Angle

Reflectivity

THEORY

EXPERIMENT

Critical Angle

Graph1b: Theoretical Fit to Experimental Data with a Fit Penalty of 2.80 x 10-2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

40 41 42 43 44 45 46 47 48 49 50

Internal Angle

Reflectivity

THEORY

EXPERIMENT

Critical Angle

13

This fit penalty is a measure of the difference between the experimental data and the theoretical model, and thus the lower the fit penalty the closer the theoretical values are to the experimental. Graphs (1a) & (1b) show a comparison between experimental data and theoretical fits for the same data file. On the scale that the graphs are plotted, there is very little difference between the two. With a visual comparison, it would appear that Graph 1a is not fitted correctly at the critical angle, and that the resonance angle θsp of the theoretical fit does not coincide with θsp of the experimental data whereas, Graph (1b) appears to be fitted more accurately at these two points, even though it has the greater value of fit penalty. However, one can show that the fit penalty for Graph (1a) is indeed lower than that of Graph (1b) by comparing the relative difference between experimental data and theoretical fit. This relative difference

(RD) is calculated using E

ETRD

−= , where T = theoretical value & E = experimental

value.

Graph (2) shows a plot of the relative difference from Graphs (1a) & (1b) (red and black respectively). The smaller the values of relative difference the better the fit at those points (i.e. a relative difference value of zero would imply a perfect fit). From Graph (2), it is observed that Graph (1a) is not fitted well at the critical angle (as observed before), and that both Graphs (1a) and (1b) are reasonably well around their minima at θsp, having approximately the same relative difference value at that point. It is clear that the descending side of the minimum is better fit in Graph (1a) than in Graph (1b), but that both have poor fits on the ascending side of their minima. The two curves may be qualitatively compared by the summing together the values for relative difference over all data points in Graph (2), shown in Table (1).

Graph 2: Relative difference between theoretical fit and experimental data for graphs 1a (red) and 1b (black). ?ote that the smaller the peak, the better the fit at that point.

Relative Difference Between Thoetical Fit & Experimental Data

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

41 41.5 42 42.5 43 43.5 44 44.5 45 45.5 46

Internal Angle

Relative Difference

Graph 1a (fit = 1.80E-02)

Graph 1b (fit = 2.80E-02)

Critical angle

14

Graph Sum of Relative Difference 1a 2.816 1b 3.710

The overall conclusion drawn from Graph (2) is that the experimental fit is better in Graph (1a) than it is in Graph (1b), thus confirming that the lower the fit penalty calculated by the Unix fitting program, the better the theoretical fit. Thermal Evaporator Calibration The calibration of the thermal evaporator was achieved by evaporating three Ag films onto a glass slide, which was then mounted onto a clean prism via an index matching resin. It was then placed in the ATR apparatus. Graph (3) shows the three SPR curves achieved for frequency differences of approximately 3000 Hz, 2000 Hz, and 1350 Hz.

The thickness of the three Ag films was found to be (a) 22.3 nm (b) 13.8 nm, and (c) 10.3 nm. Then using Equation (16) a straight-line graph was plotted, with the gradient giving the calibration constant, A (see Graph (4)). It is important to note however, that the thickness values above are subject to error, due to the fit penalties for each curve. We note that curve (a) has a low fit penalty, whereas both curves (b) and (c) have exceptional poor fit penalties associated with them. Thus we may conclude

Table 1: The Sum of Relative Difference Over All Data Points for Graphs 1a and 1b

Graph 3: SPR curves used for the calibration of the thermal evaporator. The curves are characteristic of (a) 22.3 nm (b) 13.8 nm and (c) 10.3 nm. The wavelength of light used was 632.8 nm.

SPR Curves for the Calibration of Thermal Evaporator

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

40 41 42 43 44 45 46 47 48 49 50

Internal Angle

Reflectivty

Freq Change 3000Hz

Freq Change 2000Hz

Freq Change 1350Hz

Critical Angle

Fit = 5.59 x 10-2

Fit = 1.08

Fit = 1.06

a

c

b

15

that the thickness of the Ag sample represented by curve (a) is approximately 22 nm, whereas the Ag samples represented by curves (b) and (c) could differ substantially from the quoted values. Table (2) shows a comparison of the dielectric constants of these Ag films. We note that the value for the dielectric constants for both samples (b) and (c) are not consistent with that accepted for silver, this value being closer to that of (a). Indeed both curves (b) and (c) proved significantly harder to fit than curve (a) (see H Raether [2]), which could be due to the samples loosing their bulk dielectric properties below an approximate thickness of 20 nm. This loss in bulk dielectric property could be responsible for the poor fit penalties, and hence produce an error in the quoted thickness values.

Sample Thickness (nm) Dielectric Constant Fit Penalty a 22.3 -18.5 + 0.83i 5.59 x 10-2 b 13.8 -15.7 + 3.61i 1.06 c 10.3 -15.8 + 7.71i 1.08

The calibration constant A = 2.5735 Å/sec was determined by measuring the gradient of a least squares fit line through the three points in Graph (4). Since Equation (16) does not contain an additional constant (i.e. it is of the form y = mx) the least mean square fit had to have an intercept value of zero. The dashed line in Graph 4 shows the extrapolation of this line to zero. We note that this constant A includes the value for the density of Ag, since we are only concerned with evaporating Ag films in this project.

Calibration of Thermal Evaporator

y = 2573509.17x

0

50

100

150

200

250

0.00E+00 1.00E-05 2.00E-05 3.00E-05 4.00E-05 5.00E-05 6.00E-05 7.00E-05 8.00E-05 9.00E-05

Reciprocal Frequency Difference (sec)

Thickness (Angstroms)

Graph 4: The gradient a least mean squares line through the three points determines the value of calibration constant A. The dashed line represents an extrapolation to zero.

Table 2: Comparison of dielectric constants for the three thickness values with their corresponding fit penalties.

16

The determination of this calibration constant allows the frequency difference required for the evaporation of any thickness of Ag film to be calculated. Since the calibration constant is undoubtedly subject to error due to the associated fit penalties (see Graph 3 and discussion), this calculation of frequency change will be an estimate at best and hence, the desired Ag film thickness will not be exact.

Effects of Exposure to Air on SPR Curves Having calibrated the thermal evaporator two Ag films of approximately 40 nm (sample (1)) and 60 nm (sample (2)) were prepared. Graphs (5) & (6) show the effects on SPR monitored over a 35-day period with two different wavelengths of laser light. These graphs show the reflection of the laser incident laser beam at the glass metal interface and take into account loses at the prism entrance and exit faces. We note that the maximum reflectivity in these graphs does not equal unity as one may expect in a total internal reflection regime, and is attributed to loses within the metal film. Also shown in Graphs (7a) – (7d) is a comparison of the experimental data, and the curves fitted to that data. For easier comparison, the curves have remained the same colour as those in Graphs (5) and (6). The refractive indices of the prisms were np = 1.5189 for 543.5 nm wavelength laser, and np = 41.302 for the 632.8 nm laser. Thus the critical angle occurs at θc = 41.176o and 41.302o respectively. These are marked on the graphs as a vertical blue dashed line. Comparing Graphs (5a) & (5b) visually, we see that the reflectivity at the resonance angle (θsp) decreases quite smoothly over time for Graph (5a), whereas in Graph (5b) the reflectivity decreases in a step like stages. We can also see the same thing occurring in Graph (6b) (the reflectivity at θsp increases in this case) although the lack of data makes this observation inconclusive. This would imply that data obtained with the 632.8 nm laser is harder to fit than that obtained with the 543.5 nm laser. The major difference between these graphs is that for Graphs (5a) & (5b) the value of reflectivity at θsp decreases the longer the Ag film is exposed to air, whereas in Graphs (6a) & (6b) the value of reflectivity at θsp increases the longer the Ag film is exposed to air. This would suggest that the thickness values of the two Ag films are on either side of the thickness required for optimal resonance to occur. At the optimal thickness (~ 50 nm) the EM wave couples completely with the SPP and the reflectivity at θsp is reduced to zero. Graphs (5a) & (5b) show a trend over time for the reflectivity to tend to zero at θsp and implies that sample (1) is thinner than this optimal thickness, but as the Ag2S layer grows the internal and radiation damping of the SPP match producing optimal coupling. By contrast, sample (2) is already thicker than this optimal thickness and hence any increase in Ag2S layer thickness causes a greater mismatch of internal and radiation damping causing the reflectivity at θsp to increase.

17

Graph 5a : Change of SPR Curves for ~ 40 nm Ag Film Exposed to Air for 35 Days

Monitored with l = 543.5 nm Laser

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

41 42 43 44 45 46 47 48 49 50

Internal Angle

Reflectivity

Day 0- Fit 1.80E-02

Day 7- Fit 6.54E-02

Day 15- Fit 2.12E-02

Day 22- Fit 6.55E-02

Day 28- Fit 4.96E-02

Day 35- Fit 7.79E-02

Critical Angle

Graph 5b : Change of SPR Curves for ~ 40 nm Ag Film Exposed to Air for 35 Days

Monitored with λ = 632.8 nm Laser

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

41 42 43 44 45 46 47 48 49 50

Internal Angle

Reflectivity

Day 0- Fit 8.69E-02

Day 7- Fit 1.26E-02

Day 15- Fit 5.82E-02

Day 22- Fit 3.43E-02

Day 28- Fit 3.66E-02

Critical Angle

Graph 5a & 5b: Comparison of SPR curves for the ~ 40 nm Ag film monitored with two different wavelengths of laser over a 35 day exposure period to air. As an Ag2S layer forms, the minimum reflectivity decreases, the curves become broader and the minimum occurs at larger angles. Compare with Graphs (6a) & (6b).

18

Graph 6a : Change of SPR Curves for ~ 60 nm Ag Film Exposed to Air for 35 Days

Monitored with λ = 543.5 nm Laser

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

41 42 43 44 45 46 47 48 49 50

Internal Angle

Reflectivity

Day 0- Fit 3.20E-02

Day 10- Fit 5.48E-02

Day 17- Fit 2.90E-02

Critical Angle

Graph 6b : Change of SPR Curves for ~ 60 nm Ag Film Exposed to Air for 35 Days

Monitored with λ = 632.8 nm Laser

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

41 42 43 44 45 46 47 48 49 50

Internal Angle

Reflectivity

Day 0- Fit 1.89E-01

Day 10- Fit 2.89E-02

Day 17- Fit 1.15E-02

Critical Angle

Graph 6a & 6b: Comparison of SPR curves for the ~ 60 nm Ag film monitored with two different wavelengths of laser over a 35 day exposure period to air. As an Ag2S layer forms, the minimum reflectivity increases, the curves become broader and the minimum occurs at larger angles. Compare with Graphs (5a) & (5b).

19

Graph 7a: Theoretical Fits to Experimental Data for 40 nm Sample with 543.5 nm Laser

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.91

41

42

43

44

45

46

47

Internal Angle

Reflectivity

Day 0 Fit

Day 0 Expt

Day 15 Fit

Day 15 Expt

Day 35 Fit

Day 35 Expt

Critical Angle

20

Graph 7b: Theoretical Fits to Experimental Data for 40 nm Sample with 632.8 nm Laser

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.91

41

42

43

44

45

46

47

Internal Angle

Reflectivity

Day 0 Fit

Day 0 Expt

Day 15 Fit

Day 15 Expt

Day 28 Fit

Day 28 Expt

Critical Angle

21

Graph 7c: Theoretical Fits to Experimental Data for 60 nm Sample with 543.5 nm laser

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.91

41

42

43

44

45

46

47

Internal Angle

Reflectivity

Day 0 Fit

Day 0 Expt

Day 10 Fit

Day 10 Expt

Day 17 Fit

Day 17 Expt

Critical Angle

22

Graph 7d: Theoretical Fits to Experimental Data for 60 nm Sample with 632.8 nm laser

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.91

41

41.5

42

42.5

43

43.5

44

44.5

45

Internal Angle

Reflectivity

Day 0 Fit

Day 0 Expt

Day 10 Fit

Day 10 Expt

Day 17 Fit

Day 17 Expt

Critical Angle

23

Discussion of Results The AFM analysis (Fig (7) & Fig (8)) shows that both samples are very rough having the values of root mean square roughness of approximately 1.5 nm. This roughness could play an important role in the fitting of the experimental data, since the roughness would create extra damping effects on the SPP and hence could change the width of the resonance dip.

The experimental data was fitted around the accepted values of dielectric constant ε for both Ag and Ag2S. These values were obtained from H Raether [2], and N Mehan & A Minsingh [7]. Fits were only accepted if the thickness values of the Ag film and the Ag2S layer were physically sensible, and had low fit penalty of approximately 10-2 or less. Table (3) summarises the physical parameters obtained from fitting the data represented in both Graphs (5) and (6). The exceptions to the above argument are highlighted in red in Table (3). These results have been permitted since the increase of thickness from the previous result is approximately 0.01 nm. As discussed below, these discrepancies could be occur due to errors in fitting the SPR curves, or in the positioning of the laser spot on the film.

Fig 7: AFM image of the 40 nm sample. The root mean square roughness is determined to be 1.545 nm. This large roughness value will damp the SPP mode. Also note what appears to be a loss of crystalline structure (boxed area), which could be an artefact of the evaporation process.

24

We consider the results obtained with Sample (1) using the 543.5 nm laser the best fitting of all the results. This is because the value of dielectric constant for both the Ag and Ag2S layers remain consistent over time. This is what one would expect to find since the dielectric constant is constant for a specific wavelength of light. In comparison, the results obtained with sample (1) using the 632.8 nm laser are not as well fitted, since the degree of variation of the value of dielectric constant for the Ag2S layer is greater. There is not enough measurements to draw conclusions about how well fited the experimental data is for sample (2). This is due to a certain difficulty in attempting to get physically meaningful results whilst obtaining reasonable fit penalties when theoretically fitting the experimental data. This could be due to the difficulty in determining the position of the critical angle in the experimental data. At the critical angle the reflectivity is at a maximum value, however for this sample thickness the percentage of transmitted/absorbed light (determined by the minimum before the critical angle) is quite low, being ~ 2 %. This means that there is very little difference between these two reflectivity values. Since the experimental data is subject to a certain degree of noise, an error in the positioning of the critical angle can occur, resulting in large fit penalties.

Fig 8: AFM image of the 60 nm sample. The root mean square roughness is determined to be 1.451 nm. This large roughness value will damp the SPP mode.

25

Day

Ag εεεε (Re)

Ag εεεε (Im)

Ag Thickness (nm)

Ag2S εεεε (Re)

Ag2S εεεε (Im)

Ag2S Thickness (nm)

Fit Penalty

Sample 1 543.5 nm Laser Corresponding to Graph 5a

0 -11.625 0.469 43.649 0.000 0.000 0.000 1.80E-02

7 -11.456 0.385 43.658 8.792 1.783 1.086 6.54E-02

15 -11.350 0.430 42.759 8.119 1.796 1.951 2.12E-02

22 -11.297 0.375 41.793 8.676 1.703 2.807 6.55E-02

28 -11.410 0.377 41.587 8.843 1.733 3.374 4.96E-02

35 -11.519 0.364 41.321 8.619 1.721 3.851 7.79E-02

Sample 1 632.8 nm Laser Corresponding to Graph 5b

0 -17.710 0.699 41.721 0.000 0.000 0.000 8.69E-02

7 -17.474 0.494 41.247 8.203 1.853 1.415 1.26E-02

15 -17.964 0.353 40.421 8.753 2.149 2.653 5.82E-02

22 -17.877 0.398 39.534 9.222 1.717 3.396 3.43E-02

28 -18.172 0.465 39.550 9.220 1.721 3.966 3.66E-02

Sample 2 543.5 nm Laser Corresponding to Graph 6a

0 -18.699 0.628 63.472 8.274 2.459 0.000 1.89E-01

10 -18.261 0.821 60.580 8.202 2.332 1.447 2.89E-02

17 -18.180 0.680 60.140 8.162 2.328 2.018 1.15E-02

Sample 2 632.8 nm Laser Corresponding to Graph 6b

0 -11.8638 0.4593 62.136 0.000 0.000 0.000 3.20E-02

10 -12.3924 0.66346 61.622 8.22238 2.31845 1.7237 5.48E-02

17 -12.4012 0.6806 60.777 8.64436 2.32646 2.70684 2.90E-02

It was observed that the thickness of the Ag film differed for the same sample, depending on the wavelength of laser used. Since the material’s thickness is independent of the wavelength, one must consider that this discrepancy arises due to another factor. The most obvious is error due to the fitting process, but other minor factors could be involved. One such factor could be due to the repositioning of the prism after changing samples. This would cause the laser to hit a different spot on the Ag film. Although it is assumed that the Ag film is isotropic and of uniform thickness, this may not actually be the case. The film could indeed vary in thickness, but in reality this change would not be significantly large (i.e. < 1 nm). This could also explain the discrepancies in Table (3) (highlight in red). Also, since sulphur in the air does not attack the Ag film in a uniform manner, the change of position of the laser spot could play an important role in the determination of the Ag2S layer thickness. The Effects of Ag2S Growth on SPR So far we have performed an analysis of the available data in a quantitative manner by visual comparison of Graphs (5) and (6), and values in Table (3). We now explicitly extract information from these graph related to Ag2S growth.

Table 3: Summary of the physical characteristics obtained after fitting the data represented in Graphs (5) and (6). The values highlighted in red are discrepancies where the thickness of the Ag film is greater than expected (see main text for explanation).

26

Graph 8a : The change in FWHM and θθθθsp over a 35 day period monitored with 543.5 nm laser

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 5 10 15 20 25 30 35

Time (Days)

FWHM θθ θθ

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Change in θθ θθsp

Graph 8a & 8b: Change of θθθθsp (red line) and FWHM (blue line) measurements over the maximum 35-day period with 543.5 nm and 632.8 nm lasers. ?ote how they begin to level out after Day 22.

Graph 8b : The change in FWHM and θθθθsp over a 35 day period monitored with 632.8 nm laser

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25 30 35

Time (Days)

FWHM θθ θθ

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Change in θθ θθsp

27

We shall however, only use data collected from sample 1 since there are more fitted measurements taken over the 35-day period. Graphs (8a) & (8b) compare the change of resonance angle θsp, and the degree of resonance broadening monitored with the 543.5 and 632.8 nm wavelength lasers, over the 35 days that sample 1 was exposed to air. The degree of resonance broadening was determined by measuring the full width of each curve at half its maximum height (FWHM). This maximum height is the calculated difference in reflectivity values between the critical angle and at θsp. The FWHM was measured as a function of angle θ, and is shown as the blue line in Graphs (8a) and (8b). The change in θsp is simply a measurement of the increase in resonance angle from Day 0, and is shown in Graphs (8a) and (8b) as the red line. Visual comparison of Graphs (8a) and (8b) show that the change in both FWHM and θsp are not linear in nature. One can observe that the data points appear to be almost linear in fashion up to Day 22 at which point the curvature begins to become quite pronounced. Indeed it appears that the change in both FWHM and θsp tend towards constant values as the exposure time increases, implying the rate of Ag2S formation decreases. We now compare the FWHM measurements obtained with the two lasers. This comparison is shown in Table (4), with their calculated ratios. It can be seen that the measurement of the FWHM using the 543.5 nm laser is an average 1.9 times larger than FWHM measurement using the 632.8 nm laser. Essentially this means that the FWHM is greater at short wavelengths due to the material properties of Ag (i.e. the shorter the wavelength the smaller the magnitude of Re{εM} and the greater Im{εM}).

Day Change in FWHM for 543.5 nm

Change in FWHM for 632.8 nm

FWHM Ratio

543.5 nm : 632.8 nm 0 0.85 0.45 1.88

7 0.90 0.57 1.58

15 1.30 0.67 1.94

22 1.55 0.81 1.91

28 1.80 0.88 2.04

Mean Value = 1.87

Monitoring Ag2S Growth As mentioned previously the thickness of the sample is indeed increasing due to the growth of an Ag2S layer on the surface of the Ag film. Graphs (9a) & (9b) compare the difference in thickness of the Ag film and Ag2S growth monitored with the two laser wavelengths over the 35-day period.

Table 4: The comparison of the change FWHM (in degrees) after 28 days for the 534.5 nm and 632.8 nm lasers used in the experiment. Also calculated is the ratio of the FWHM values measured with the respective lasers. The mean value of this ratio is found to be of the order of 1.9.

28

One thing we note in comparing Graphs (9a) and (9b) is that the thickness values for both the Ag film and the Ag2S layer are different. This should not be so, since it is the same sample under consideration, with the only difference in conditions being the use of a different laser wavelength. The reasons why this could be so have been discussed previously. However, if we compare the difference in thickness values for both layers (see Table (5)) then we see that these values are approximately equal, with the largest difference between these values (not

Graph 9a : The change in thickness of the Ag film and Ag2S layer

over a 35 day period monitored with 543.5 nm laser

0

0.5

1

1.5

2

2.5

3

3.5

4

0 5 10 15 20 25 30 35

Time (Days)

Ag2S Thickness (nm)

40

40.5

41

41.5

42

42.5

43

43.5

44

Ag Film Thickness (nm)

Ag2S Layer

Ag Film

Graph 9b : The change in thickness of the Ag film and Ag2S layer

over a 35 day period monitored with 632.8 nm laser

0

0.5

1

1.5

2

2.5

3

3.5

4

0 5 10 15 20 25 30 35

Time (Days)

Ag2S Thickness (nm)

38

38.5

39

39.5

40

40.5

41

41.5

42

Ag Film Thickness (nm)

Ag2S Layer

Ag Film

Graph 9a & 9b: Change of Ag2S thickness (red line) and Ag film thickness (blue line) over the maximum 35-day period with 543.5 nm and 632.8 nm lasers. ?ote how they begin to level out after Day 22. Compare with growth rate of Ag2S layer in Fig (10) below.

29

including the value of 0 nm thickness for the Ag2S difference) being of the order 0.4 nm. Such a small difference suggests that, the discrepancy in measured thickness of this film with the two laser wavelengths is due to the fitting process (and to a minor extent the repositioning of the laser spot).

Day

Ag Thickness Graph 8a

Ag Thickness Graph 8b

Difference Ag

(8a – 8b)

Ag2S Thickness Graph 8a

Ag2S Thickness Graph 8b

Difference in Ag2S

(8a – 8b) 0 43.649 41.721 1.928 0 0 0 7 43.658 41.247 2.411 1.086 1.415 -0.329

15 42.759 40.421 2.338 1.951 2.653 -0.702 22 41.793 39.543 2.259 2.807 3.396 -0.589 28 41.321 39.550 2.037 3.374 3.966 -0.592

It is interesting to note that like Graphs (8a) and (8b) the data points are not linear, and again appear to begin to level out after 22 Days, implying a decreasing rate of Ag2S formation. Thus we may conclude that as the Ag2S layer grows, there is less silver exposed to the air (or less sulphur can diffuse through the Ag2S layer). G.J. Kovacs [15] obtained the same approximate curve in a 1978 experiment (see Fig (9)). He determined the growth rate of Ag2S, to be ~ 0.5 nm per week for the first few weeks compared to our value of ~ 1 nm per week. Indeed, Kovacs required approximately seventy days to grow the same thickness of Ag2S, as we did in thirty-five days. Thus, the sulphur content of our environment was approximately twice that of the environment when he performed the experiment.

We must note that Kovacs did not fit his data but instead calculated the thickness values from the minimum of his experimental curves. Examination of these curves shows them to be poorly defined at the critical angle, whilst also appearing to badly normalised at this point (Compare Fig (10) with Graphs (5) – (7) above). This may cause some error on his calculated values of thickness of the Ag2S layer.

Table 5: The different thickness measurements for the same sample monitored with 543.5 nm (Graph 9a) and 632.8 nm (Graph 9b) lasers. The differences between the two measurements have been calculated. The differences between the two extreme values (i.e. 2.411-1.928 nm for Ag and (-) 0.329 – (-) 0.702 for Ag2S) are both of the order of 0.4 nm.

Fig 9: G. J. Kovacs’ experimental data showing the growth of Ag2S over an 80-day period. The rate of growth was determined to be approximately 0.5 nm per week for the first few weeks. The decrease in thickness of Ag film due to sulphide formation was accounted for by using a consumption coefficient of R = 0.6 (see below). Taken from G.J. Kovacs [15]

30

Mehan & Mansingh [7] also observed a saturation tendency after an initial linear increase although since they used a rapid corrosion technique using a gases solution of H2S instead of laboratory atmosphere to grow the Ag2S layer (see Fig (11)).

Determination of Consumption Coefficient It is also observed that as the Ag2S layer grows thicker, the thickness of the Ag film decreases. This is because if an Ag2S layer of uniform thickness d grows over a Ag film of the same surface area, then the film thickness must decrease by an amount Rd (where R is the consumption coefficient) due to the consumption of the Ag surface by sulphur to create the Ag2S layer. By plotting a graph of the change of Ag thickness against the increased thickness of the Ag2S layer, and calculating the gradient of the best-fit line, the consumption coefficient can be determined. Graph (10) illustrates such a plot, with the data taken from sample (1) using both the 543.5 nm and 632.8 nm lasers.

Fig 10: G. J. Kovacs’ [15] experimentally measured ATR curves taken at successive two-week intervals. ?ote the poor correlation at the critical angle.

Fig 11: Mehan and Mansingh [7] experimental fits showing the effects of different concentrations of H2S on the growth rate of Ag2S. Also shown is curve calculated from data taken from Bussjager and Macleod [1].

31

The two trendlines in Graph (10) show the least square fits of the experimental data. The red line is the true fit to the data with an equation of y = 0.6473x + 0.2354. However, if there is no growth an Ag2S layer, then there will be no change in the thickness of the Ag film, and hence, logically this trendline must intercept at the origin. The blue line in Graph (10) shows the trendline extrapolated through zero, and has an equation of y = 0.5708x. The two gradients show that the consumption coefficient can have a value of R = 0.65 or 0.57 (to 2 decimal places). We believe however that the value of this coefficient lies between these two values, since the second point from the left is undoubtedly incorrect having approximately no change in Ag thickness, when there is a non zero growth of Ag2S layer. This would imply that the decrease in Ag thickness should be less at this point changing the weighting of the lines, and thus changing the gradients of the trendlines (i.e. decrease for red, increase for blue). The theoretical value R can be calculated to be 0.6 if one assumes bulk densities of Ag and Ag2S [15]. Our experimental value shows good agreement with this result.

Detremination of the Consumption Coeffiecent R

y = 0.5708x y = 0.6473x - 0.2354

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Ag2S Thickness (nm)

Decrease in Ag Thickness (nm)

Graph 10: Determination of the consumption coefficient R by calculating the gradient of the decrease in Ag film thickness Vs increase of Ag2S thickness. The red line sows a true least squares fit to the data; the blue line shows extrapolation of this fit through zero.

32

Conclusions The calibration of the thermal evaporator was quite successful, which allowed us to obtained two Ag films close to the desired thickness values of 40 nm and 60 nm, despite the fact there was poor fit penalties associated with two of the SPR curves. These Ag films were determined to be 43.6/41.7 nm and 63.5/62.1 nm thick with the 543.5 nm and 632.8 nm lasers respectively. This difference in thickness as measured with the two lasers was attributed to errors in the fitting of the experimental data, and to a lesser extent the movement and repositioning of the sample. These films were then exposed to air for a 35-day period, and monitored at approximately weekly intervals. After fitting the experimental data, graphs of reflectivity versus internal angle were plotted (see Graphs (5) & (6)) for both samples, monitored with each laser. It was noted in each that the maximum reflectivity did not equal one, this being attributed to loses within the prism. It was observed that the SPR curves displayed in both sets of graphs, showed a tendency for the resonance angle θsp to increase with increased exposure time to the atmosphere. It also was observed that the reflectivity at θsp decreased for the thinner sample, and increased for the thicker sample. Since the samples were on either side of the thickness value associated with optimal resonance, this implies that the increasing thickness of the Ag2S layer growing on sample (1) causes the internal and radiation damping to match, and thus create an optimal resonance condition for the thinner sample. These observations led us to conclude that the total thickness of both samples was indeed increasing with time due to the growth of an Ag2S layer. This was confirmed by the experimental data for the physical parameters of the two samples (see Table (3)). It was found that the data for the thicker sample was harder to fit than its thinner counterpart, and hence only three fit curves were obtained in the time constraints of this project. We think this difficulty lies with the determination of the critical angle, since it is not as well defined as the critical angle of the thinner sample. The data obtained with the thinner sample was determined to have a better experimental fit, although it was easier to fit the data obtained with the 543.5 nm laser than that obtained with the 632.8 nm laser. We believe this difference in fitting arises from the saturation of the photodiode due the higher intensity of the 632.8 nm laser than its 543.5 nm counterpart. The FWHM for each curve was measured and found to be increasing with time. This could be interpreted as an increase in the surface roughness causing increased damping of the SPP mode and hence increasing the FWHM. It was also observed that the FWHM measurement is greater for the shorter wavelength laser, this being due to the decrease in Re |εM| and the increase in Im |εM| at this short wavelength. It was noted that the growth rate of the Ag2S layer began almost linearly at ~ 1 nm per week but decreased after approximately three weeks. This observation correlates quite well with literature [7,14] although the latter growth rates are different due to different concentrations of sulphur present in the experimental environment. We observed that as a Ag2S film grows on the surface of the Ag film, the thickness of the latter decreases. Thus, the consumption coefficient, R was determined by plotting a graph of

33

the decrease in thickness of the Ag film versus the increase in Ag2S layer thickness and calculating the gradient. This gave a value of R between 0.57 and 0.65, which is in good agreement with the theoretical value of R = 0.6 (assuming the bulk densities of Ag and Ag2S).

34

References

1. Rebecca J. Bussjager et al, Appl. Opt. 35, 5044 (1996) 2. H. Raether, “Surface Plasmons on Smooth and Rough Surfaces and on Gratings”, Vol

III of Springer Tracts in Modern Physics. (Springer-Verlay, Berlin 1988)

3. H. Raether, “Surface plasma oscillations and their applications” in Physics of Thin Films, G. Hass and M. H. Francombe, eds. (Academic, New York 1977) Vol 9

4. W. P. Chen & J. M. Chen, J Opt. Soc. America 71, 189 (1981)

5. Y. Levy et al, J. Appl. Phys 57, 2601 (1985)

6. Bennett et al, J Appl. Phys 40, 3351 (1969)

7. Navina Mehan & Abhai Mansingh, Appl. Opt. 39, 5214

8. J.D. Swalen et al, Am. J. Phys. 48, 669 (1980)

9. C. Kittel, Introduction to Solid State Physics, 7th Edition. John Wiley & Sons 1996

10. E. Kretschmann and H. Raether, Z. Naturforsch. Teil A 23, 2135 (1968)

11. E. Kretschmann, Z. Phys 241, 313 (1971)

12. E. Burstein et al J. Vac Sci Tech 11, 1004 (1974)

13. M. Born and E. Wolf, Principles of Optics 7th Edition, Cambridge University Press

(1999)

14. I Pockrand, Surf. Sci, 72, 577 (1978)

15. G. J. Kovacs, Surf. Sci 78, L245 (1978)