7. Experimental Results and Discussion
In the previous chapter the theoretical calculations of the optical multilayer sys- tems used in the experiments were given. This chapter will describe the experi- ments which have been performed with these systems. The results obtained will be discussed.
7.1. Preliminary Experiments
As already introduced in Section 5.5 silver films are used both to adsorb 4He on them and as substrates on which a cesium film will be deposited by thermal evapo- ration at low temperatures. For both purposes, besides the quality and the surface roughness, the cleanliness and the structure of the films play an important role for the wetting properties. We first investigated the topography of the silver substrates and then the wetting properties of silver, performing adsorption experiments.
7.1.1. Silver Substrates
The silver films are prepared, as detailed described in Section 5.5, in a commercial vacuum coating system at end pressure values below 10−6 mbar. Some of those substrates were investigated and their topography was studied by means of an Atomic Force Microscope (AFM).
Figure 7.1.: AFM pictures of a silver substrate (i) 5 min. after vacuum deposition, (ii) after 60 min. and (iii) after90 min exposure in atmosphere. All dimensions are in nm,
`a dimension on pictures is40 nm. See text for details.
As described in Section 4.1.2 the silver films are sensitive to atmospheric moisture and tarnishing agents. The purpose of this preliminary experiment is to find out how long it would take to contaminate a freshly deposited silver film such that it would become unappropriate to be used in wetting experiments1.
After the deposition was finished the sample was taken out from the vacuum coating system and mounted in the AFM working in air. The pictures taken within 5 minutes after the sample was mounted in the AFM shows a relatively smooth structure of areas of up to50nm in diameter and few nm high separated by marked boundaries (see (i) in Fig. 7.1). The sample was investigated at different sites on the surface to assure reproducibility and was scanned until changes in the structure were noticed.
The first noticeable change takes place after about 1 hour when the spatial di- mension of the areas decreases and transforms to a noticeable finer structure(see (ii)). It looks like a new layer starts to nucleate homogeneously on top of the silver. These nucleation centers develop independently and the grown structures do not coalesce when they come close to one another.
After about30minutes from their appearance, these structures are about half the spatial dimension of the initial structures observed on freshly deposited silver (see (iii)). The striking difference to the initial silver surface is that the length scale of roughness drastically changes. Obviously, the actual structure has also moisture adsorbed on the surface, but this could not be visualized. The only explanation is that, on the silver surface, an additional layer of oxide and/or sulphide forms and grows at the expense of the pure silver layer. Besides the fact that this newly formed layer changes the roughness, it also has a dielectric constant different from the one of pure silver. These two parameters have a strong influence on the measurements which use the SPR technique, as it is described in detail in Section 4.1.2.
Finally, it has to be noted that the silver substrates which have been investigated using AFM have not been mounted in the experimental cell and not used to perform adsorption experiments. All the silver samples which have been used in experiments have been in atmosphere up to 40minutes maximum in order to avoid -as much as possible- the formation of additional layers of silver compounds.
7.1.2. System Behaviour during Adsorption
As it was mentioned in Section 5.2 the experimental cell was not leak tight against superfluid 4He. Consequently, we used this superleak to let 4He fill the cell con- tinuously and we monitored the pressure in the cell and the thickness of the film
1After deposition the substrates are transported and mounted under ambient atmosphere. This will give a hint of the maximum period available for mounting ("ptm"). Consequently, the substrates which require longer than "ptm" are rejected, a new deposition procedure is then necessary.
7.1. Preliminary Experiments
growing on the substrate. A typical behaviour of these parameters as a function of time is shown in Fig. 7.2.
Figure 7.2.: Temporal dependence of the pres- sure in the cell and of the helium thickness ad- sorbed onto a Ag sub- strate during the continu- ous condensing of helium gas atT = 1.45K.
Before starting the adsorption, the cell was pumped out and an end pressure2, P1, was reached. Then, the valve to the pump was closed and the adsorption was started. The pressure in the cell first increased linearly in time and then the rate changed at some value, P2. The pressure increased further until approaching a constant value, P0, which is the saturated vapor pressure corresponding to the temperature of the adsorption performed.
If more and more 4He is allowed to be adsorbed, the pressure value P0 remains constant because at this point bulk liquid 4He is present in the cell. However, the film thickness increases further but very slowly3. The subsequent increase of the film thickness as a function of the uprising bulk liquid level and the related effects are described in Section 7.2.2. The pressure which is measured at the top end of the insert and not in the cell is subject to further corrections (see Appendix C).
7.1.3. Cell Level Meter Calibration
After the system has reached the saturated vapor pressure which corresponds to the temperature the adsorption isotherm was taken (i. e. bulk liquid is present at the cell bottom), we noted the value of the capacitance corresponding to the empty cell, CE and started condensing helium gas in known amounts. Condensation continued
2In the range10−3mbar, or less.
3This is understood by the fact that from now on the bulk level is rising too and the distance from the bulk level to the the substrate surface (heighthin Fig.??) is decreasing.
until the level no longer changed, indicating that the liquid helium has reached the top of the capacitor which gives the value, CF, of the filled cell. The results of the calibration are shown in Fig. 7.3, where the capacitance variation, CCell with the height of the rising liquid level is fitted using Eq. 5.2.
Figure 7.3.: Calibration of the capacitance level meter. CE and CF rep- resents the capacitance of the empty and filled cell, respectively. The ex- perimental points in be- tween represents cross- checks done while rising the helium liquid level.
The straight line repre- sents the fit using Eq. 5.2.
To estimate the uncertainty in the height measurement, the data were fitted to a straight line. The standard deviation of the straight line from the data as calculated from the fit was 0.5mm. Taking the fit as a measure of the accuracy of the measurement, the liquid level could be estimated with an accuracy of 1mm.
7.2.
4He on Silver Substrates
In this section the results which have been obtained on silver substrates will be presented. These measurements are necessary both to calibrate the system and to check the calculations which were done in the previous chapter.
7.2.1. Thin 4He on Silver; Adsorption Isotherms
Silver belongs to materials which interact strongly with 4He via van der Waals potential and hence it will always be wetted by liquid 4He. By adsorbing 4He gas into a cell containing a silver substrate, one expects that the equilibrium film thickness should diverge as the pressure reaches the saturated vapor pressure, P0.
A typical adsorption isotherm of 4He on silver is shown in Fig. 7.4. The film thickness, d, is calculated by converting the measured shift of the stepping motor
7.2. 4He on Silver Substrates
which tracks the plasmon resonance minimum as described in 4.1.2. It is clearly seen that the film thickness starts to diverge when approaching P0.
Figure 7.4.: Experimen- tal data (open circles) of an adsorption isotherm of liquid4He on a 38nm Ag substrate taken at T = 1.45K. Close to the satu- rated vapor pressure, P0, the film thickness rapidly diverges. The dashed curve represents the fit- ting of the measured data using Eq. 1.9.
As long as the system is below the saturated vapor pressure,P0, the film thick- ness is described by Eq. 1.9 which is shown in Fig. 7.4 by the dashed line. The experimental data are in good agreement with the fitted curve for pressure ranges very close to saturation and for P/P0 < 0.55. For relative pressures higher than 0.55 the experimental data deviates from the fitting curve which could be under- stood as the effect of thermal fluctuations. When the system reaches the saturated vapor pressure, then the behaviour will be described by Eq. 1.8. If one plots 1/d3 vs. −ln(P/P0), then -according to the Eq. 1.9- one should get a straight line (see Fig. 7.5). From the slope of that linear fit one can calculate the value of the van der Waals constant (∆C3). The best fit for the experimental data plotted in Fig. 7.4 using the Eq. 1.9 provides a value of Hamaker constant, ∆C3 = 2900 KÅ3.
7.2.2. Thick Adsorbed 4He on Silver; Retardation Effects
After the system has reached the saturated vapor pressure which corresponds to the temperature at which the adsorption isotherm was taken, we continued to condense in helium gas in known amounts while simultaneously monitoring the helium film thickness. The experimental data are shown in Fig. 7.6.
There are few remarks to be made before discussing the experimental data. As the bulk liquid helium level increases it will reach the height of the incident laser beam used to measure the film thickness (see also Fig. ??) at the point,hM, where the beam hits the cell mirror. This causes a temporary loss of the SPR resonance
Figure 7.5.: The same experimental data as in Fig. 7.4 but in a 1/d3 vs. −ln(P/P0) plot. The straight lines represent linear fits for different val- ues of Hamaker constant,
∆C3.
minimum and disturbs the feed-back loop which tracks the minimum and hence there are no experimental data in the range close to hM. With the liquid level rising further, the second range,hP, where the laser beam is perturbed, takes place, namely when the laser beam is incident on the prism. Although the refractive index
Figure 7.6.: The film thickness,d, of liquid4He adsorbed onto a silver substrate as a function of the height, h, from the bulk liquid to the substrate (as defined in Fig. ??). The cross-over from the non-retarded (dotted line) to the retardedregime (dashed line) takes place at around32 nm.
of liquid helium,nHe, is very close to1, one has to make the correction of the optical path due to the propagation of the beam through an optically dense medium.
When the liquid level was close to the substrate level (i.e., h→0), it turned out
7.2. 4He on Silver Substrates
that the plane of the substrate was not parallel to the horizontal plane4. As we repeatedly condensed in and pumped out helium in order to determine the value at h= 0 where the substrate is flooded, we observed that this flooding starts from the side where the laser beam emerged from the prism. It has to be noticed that the tilting angle broadens the ranges athM andhP, namely the bigger the tilting angle, the broader these ranges are. The corrections due both to the refractive index and to the tilting angle are described in Appendix D.
Under the conditions stated above, the film thickness,d0=d(h = 0), reaches about 51nm. The dotted line in Fig.??represents a fit of the experimental data using the FHH theory (Eq. 1.8) with, for our experiment, the parameters ∆C3 = 2900KÅ3 and h = 6.2 cm. The film thickness according to this fit describes the measured data well for h >2 cm, which represents the non-retarded (i.e. thin film) regime . Forh <2cm, the film thickness is described by a function proportional toh−1/4. The regime described by this proportionality is called retarded. It should be noted that for values h < 0.25 cm the data exhibit deviations from the fit. This is not surprising since the theory does not describe the limit when h → 0. On a double logarithmic scale the cross over between the non-retarded and the retarded regimes is much easier to see and takes place at a film thickness of about 32nm.
Figure 7.7.: The same experimental data as in Fig. 7.6 but in a log-log scale. The solid line is a fit to Eq. 1.13, with A = 8∗10−5,B = 10−5, and c= 102, see text.
The best fit to the experimental data using the empirical expression given by Eq. 1.13 with the parameters A = 8∗10−5, B = 10−5, and c = 102 is plotted in Fig. 7.7 (solid line). This fit describes the experimental data on a broader range
4A tilting angle of less than1◦ between the vertical axis and the normal to the substrate plane was measured, see Appendix D.
of film thicknesses, but it is not appropriate for heights h < 0.4 cm. This could be understood by the fact that our Ag substrate is rough compared to the cleaved surface of the fluoride crystals.
7.3.
4He on Cesium Substrates
This section presents the results obtained on different cesium substrates which have been prepared by quench-condensing at low temperatures onto a thin silver film.
The preparation procedure was described in Section 5.5. A general behaviour of the system during the deposition is shown in Fig. 7.8. The temperature in the cell increases with the evaporation current and reaches values up to 90 K5 which causes problems in monitoring the thickness of the cesium film under deposition.
Once the cesium deposition was completed, the substrate was first tested for the existence of a cesium film and then adsorption experiments were performed. To
Figure 7.8.: Temporal variation of the temperature in the cellTcell (right axis) and of the input cur- rent (left axis) flowing through the cesium dispenser during deposi- tion.
accomplish this, wavelength scans on bare silver (before evaporation) and on the freshly deposited cesium substrate (after evaporation) were done. In Fig. 7.9 the contribution of the photoelectrons to the photocurrent before and after evaporation as a function of the incident wavelength is plotted. There are no photoelectrons expelled from the bare silver substrate and hence the photocurrent values are close to the dark current. In contrast, a photocurrent could be measured from the cesium substrate which reaches its maximum by about 470 nm. This was a confirmation of the fact that the silver substrate is covered with cesium and will be used in Section 7.3.2 to find out the energy available for the electrons to penetrate the
5This causes a rapid shift of the plasmon resonance which is not essentially due to the film deposition as long as the shutter is closed.
7.3. 4He on Cesium Substrates
Figure 7.9.: Wavelength scan before (open circles) and after (solid squares) deposition of a quench- condensed cesium film onto a silver substrate.
potential barrier in tunnelling experiments. In Section 7.3.3 we report the results of local measurements of the work function of these cesium substrates.
7.3.1. Thin 4He on Cesium; Adsorption Isotherms
The procedure which has been used for performing the adsorption isotherms on cesium substrates was described previously in Section 5.5. Several adsorption
Figure 7.10.: Experi- mental data of an ad- sorption isotherm of liq- uid 4He on a quench- condensed Cs substrate taken at T = 1.39 K.
Close to the saturated va- por pressure, P0, the film thickness diverges. The dashed curve represents the fitting of the mea- sured data using Eq. 1.9 with∆C3= 700KÅ3.
isotherms were taken at different temperatures ranging from1.3to2K. The typical
behaviour of the surface plasmon resonance shift during a 4He adsorption is shown in Fig. 7.10.
The 4He film grows in a step-like fashion and close to the saturated vapor pres- sure, P0, reaches a thickness of about 120 Å . The reason that the4He film thick- ness adsorbed on the cesium substrate is much thinner than the one on the sil- ver substrate resides in the fact that the interaction potential changes due to the deposition of the cesium substrate. The dashed curve represents the best fit to the experimental data using the Eq. 1.9 which provides a value of Hamaker con- stant,∆C3 = 700KÅ3. This value is in agreement with the theoretical calculation [Zar77], which gives ∆C3 = 672.8 KÅ3.
7.3.2. Thin 4He on Cesium; Photocurrent tunnelling measurements
We first address the question what is the available energy of the photoelectrons in order to tunnel through the potential barrier. The measurements done on ce- sium substrates before adsorbing helium revealed the energy spectrum as shown in Fig. 7.11. In the low energy part of the spectrum (below 2 eV) one sees that
Figure 7.11.: Intensity of the photoelectrons coming from the bare cesium substrate. In the ad- sorption experiments a photon en- ergy where the photoelectron yield has its maximum (i. e. 2.8eV) has been used.
photons can hardly generate photoelectrons, since these energies are very close to the work function of the bare cesium (see Section 7.3.3). The photoelectron yield reaches its maximum around2.8eV and this energy is used further in the adsorption experiments.
Before the gas adsorption was started we pumped out the cell in each run until the photocurrent increased to a final maximal value, indicating that most of the helium was removed from the cell and in this case the cesium substrate should be dry. Just before starting the adsorption (i.e. at P/P0 = 0), the initial value of the photocurrent, Imax, was measured.
7.3. 4He on Cesium Substrates
Figure 7.12.: A typi- cal behaviour of the pho- tocurrent as a function of the reduced pressure P/P0, taken at T = 1.70 K. Three different ranges are observed: 1- steep photocurrent decay for low values of P/P0, a level off region -2- for a broad range in P/P0 val- ues, and a sudden drop in photocurrent -range 3- close to P/P0 → 1. In- set: A log plot shows the drop in range3.
The higher the temperature, the bigger the initial photocurrent. This could be understood by the fact that the last helium layer adsorbed on the surface has been better removed by pumping at higher temperatures6.
Figure 7.13.: Normal- ized photocurrent, I/I0
vs. the reduced pressure, P/P0 curves for different temperatures. The inset shows an exponential fit for the range1.
The curves have the same qualitative behaviour, namely as helium gas is con- densed into the cell the photocurrent is decreasing. For all the measurements done
6IfT increases, thenP0 increases andP/P0 decreases.
at different temperatures we discern 3 particular ranges which depend on P/P0 values. The first range (at low values of P/P0) shows a steep decay of the pho- tocurrent, then the photocurrent levels-off for a broad range of relative pressure values P/P0 (Range2in Fig. 7.12). Before the system reaches the saturated vapor pressure (i.e. P/P0 →1), a sudden drop in photocurrent takes place (Range 3).
In order to compare the photocurrent behavior at different temperatures we nor- malized each plot to the corresponding photocurrent maximum,Imax(see Fig. 7.13).
We observe that the photocurrent decreases nearly one order of magnitude (as the system went from range 1to2) and drops by another order of magnitude (from the end of range 2 to3), see Fig. 7.14.
In some runs we stop the adsorption in the middle of the range 2 to check for the stability of the photocurrent. As long as any helium gas was adsorbed, the photocurrent was constant. Moreover, at the end of the adsorption, when slowly pumping out the cell, the current increases back to its initial value without showing any noticeable hysteresis.
Figure 7.14.: Log- arithmic plot of the normalized photocurrent, I/Imax vs. the reduced pressure, P/P0 for sev- eral temperatures. As temperature increases the range 2 (as defined in Fig. 7.12) broadens and shifts towards lower values ofI/Imax.
The decay of data in range 1 could be fitted with an exponential function (see inset in Fig. 7.13). As the temperature increases the range 2 broadens at the expense of the neighboring ranges and shifts towards lower values of the normalized photocurrent, I/Imax, see Fig. 7.14.
7.3.3. Measurements of Work function on Cesium
To perform Photoelectron Spectroscopy experiments the setup sketched in Fig. 5.6 was used. One can use the setup to measure either the integral work function over
7.3. 4He on Cesium Substrates
the whole substrate area, or to measure the local work function by focussing the beam on different positions on the substrate and scan this focal point over the substrate. The experiments done so far measured only the local work function. In this case, the lateral resolution is limited by the spatial dimension of the focus7, which in our experiments was about 0.25 mm2. The work function resolution is limited only by the wavelength resolution of the light source (monochromator). In our experiments a work function resolution of ±0.025 eV was achieved.
The work function measurements are very sensitive to the properties of the sub- strate under investigation and provide a valuable information about the quality and the chemical state of the surface. An important issue is that only the photoelec- trons located close to the surface have the possibility to leave the surface and hence these measurements characterize the surface properties and not the bulk.
A deviation of the measured work function value from that of the bulk cesium may have different causes. Impurities lying on the surface may cause a higher value of the work function. On the other hand, due to the fact that cesium is highly reactive to oxygen, the work function for an oxygen contaminated cesium substrate could be altered in both direction (see Fig. 4.7 and [Bot91]).
Figure 7.15.: Variation of the work function with the position on a ce- sium substrate; the in- set shows the position on the surface as described in Fig. 5.6.
The photocurrent measured as a function of the incident wavelength at different positions on the cesium surface is shown in Fig. 7.15. The photocurrent was nor- malized to its maximum value, Imax, obtained at λ = 425 nm. The work function was calculated using the formula Φ = hc/λc, where λc represents the cutoff wave-
7In principle, the focus is limited by the aperture of the optical windows of the cryostat and the cell.
length. The cutoff wavelength could be deduced from the I/Imax vs. λ plots as it is shown in Fig. 7.16.
Figure 7.16.: Calculation of the work function on various places of a cesium substrate. A blow-up of Fig. 7.15 at large wavelengths is shown.
The work function averaged over the whole surface is 1.88± 0.02 eV, and in the middle of the sample (position 2) a value of 1.91±0.02 eV is found, which is in agreement with those on pure Cs determined in [Rei98]. The work function distribution over the surface is relatively homogeneous. If one compares this value with those from the plot in Fig. 4.7, one concludes that the cesium film has a very good quality on the length scale given by the resolution of the measuring method.
This shows that the cesium surface is oxide free [Gre75]. On a smaller length scale the surface may show local roughness or even chemical inhomogeneities.
7.4. Discussion
The experimental results previously presented were obtained using two different types of measuring techniques which were applied simultaneously on cesium sub- strates produced by quench-condensation on silver substrates at low temperatures.
Firstly, we determine the 4He film thickness from one monolayer up to a thick saturated film by means of SPR. This technique allows us to determine the local thickness of the adsorbate averaged over regions on the length scale of the wave- length of light. The thickness of the helium film measured by this method grows typically up to 120 Å independent of the temperature.
Secondly, we measure the photocurrentI which is emitted from the cesium surface upon irradiation with an external monochromatic light source using the photoelec- tron tunnelling. From the observed reduction of I as more and more helium is adsorbed on the cesium surface, we get information about the helium coverage. We will show that Photoelectron Tunnelling is a complimentary method which allows
7.4. Discussion
us to very sensitively resolve the thickness of an adsorbed helium film on Cs from a submonolayer up to about three layers.
The typical behaviour of the photocurrent and the SPR change during adsorption of helium is shown in Fig. 7.17. The two measurements seems to provide contradic-
Figure 7.17.: Compar- ison between the helium film thickness on Cs mea- sured via SPR method (open diamonds) and the photocurrent measured via photoelectron tun- nelling (solid stars) as a function of the reduced pressure, at T = 1.36 K.
tory results. The adsorption isotherms on cesium looks similar to those on silver, which indicates that at those temperatures the Cs is wetted. However, this is only the case for certain areas of the cesium as will be shown below.
The quench condensation method used to prepare the cesium substrate produces cesium films which are rough on a micro scale. This could be understood, taking into account several aspects. On one hand, the underlaying silver substrate is not ideally flat and provides itself a degree of disorder. Secondly, during the cesium deposition process the surface diffusion of the cesium atoms is very low (being a temperature activated process) and the atoms which are landing onto the cold substrate (Tsubstrate ' 4.2 K) rather pile up into a columnar structure instead of spreading uniformly. This means that the deposited Cs film not only has an inhomogeneous thickness but also presents columnar growth as well (see Fig. 7.18).
In this context, the helium condensed into the cell will adsorb and hence wet those areas of the cesiated Ag-surface where the cesium film is too thin to show non-wetting and this is the reason the SPR measurements show that the substrate is wetted. In contrast, the cesium columns which are thick enough are non-wetted by helium and these patches are the only remaining regions for electrons to leave the surface and to give a contribution to the photocurrent signal. The photoelectron current could be assumed to have an exponential decay dependence as a function of growing adsorbed helium thickness, as shown in Fig. 7.13.
In the coverage range above one monolayer (i.e. the ranges2and3 in Fig. 7.12), a simple picture appears to be adequate, which has been applied to analyze the adsorption behaviour of H2 on Ag [Con96]: one can consider the adsorbed layer as an additional potential barrier on the metal surface (i.e. in our case cesium), which the photoelectrons can only pass via a tunnelling process. For liquid 4He Figure 7.18.: Model of the sur- face topography for a quench- condensed Cs onto a Ag substrate.
The areas of Cs which are too thin are wetted by liquid helium (as revealed by SPR measurements), whereas the columnar structure is not. The latter areas gives a con- tribution in the photocurrent sig- nal (measured via Photoelectron Tunnelling), see text for details.
the potential barrier provided by the helium atoms to the electrons is known to be E0 = 1 eV [Col74]. According to the Eq. 4.13, the transmission coefficient through such a one-dimensional barrier of width b could be rewritten in the form T ∝ exp(−b/b0). Since the thickness of one monolayer of 4He is b0 ' 3.5 Å , one obtains a drop in the transmission coefficient of one order of magnitude per monolayer [Con96].
Figure 7.19.: Photocur- rent vs. the chemical po- tential, ∆µ, for different temperatures. Far from coexistence the adsorbed helium layer behaves like a 2D-gas, see [Kli98b].
7.4. Discussion
In the coverage range below one monolayer (Range 1 in Fig. 7.12), this picture, which assumes an effective potential barrier which is distributed homogeneously across the Cs surface, is most likely not appropriate. Still the presence of helium atoms tends to reduce the photocurrent. In this range, the knowledge about the photoelectron mechanism is sparse, and moreover a change in the effective work function of the Cs due to the presence of helium might occur.
However, in the submonolayer regime (note that range1in Fig. 7.12 corresponds to low values of the reduced pressure P/P0), the adsorbed helium atoms are ex- pected to behave like a 2D-gas. The surface coverage, n2D−gas, in this regime is given by [Kli98a]
n2D−gas∝T exp
µ−ε1 kBT
, (7.1)
where ε1 represents the binding energy of a single 4He atom to the Cs .
Figure 7.20.: Logarithmic plot of the normalized photocurrent vs.
the chemical potential ∆µ. The dotted line represents the 2D-gas regime whereas the dashed line corresponds to a monolayer com- pletion. The steep increase which occurs close to coexistence is the transition from one monolayer to up to 3layers of 4He on cesium in the non wetted state.
In order to present the results more clearly we will plot, from now on, the pho- tocurrent as a function of the chemical potential offset from coexistence,∆µ, which is related to the reduced pressure by ∆µ=kBT ln(P/P0).
In Fig. 7.19 the exponential decay of the photocurrent in the range 1 is shown.
If one sets the chemical potential within this range to a constant value (say ∆µ1), this will produce different values in the photocurrent at different temperatures.
The higher the temperature, the smaller the magnitude of the photocurrent. This means (according to Eq. 7.1) that, at the same chemical potential, the surface coverage increases as the temperature increases (i.e. more helium atoms will cover the surface as the temperature increases).
As the system moves towards coexistence (i.e. ∆µ → 0), the surface coverage increases as well and gets very close to a monolayer completion which is associated
with the levelling off in the photocurrent signal. The levelling off could be better recognized in Fig. 7.20 (the horizontal dashed line), where the data for the 2D-gas regime (dotted line) have also been plotted.
Figure 7.21.: Logarith- mic plot of the photocur- rent vs. the chemical potential ∆µ for differ- ent temperatures. The growth of up to3layers of
4He on cesium takes place close to coexistence, but the film still shows non- wetting. For clarity, the curves are shifted with re- spect to one another.
Close to saturated vapor pressure, the surface coverage exhibits a steep increase, which can be interpreted as the transition from one layer to the 2−3layer regime.
According to the usual convention the system is still in the non-wetted state. A complete picture of the photocurrent measurements is shown in Fig. 7.21 where we plot the data of the experiments which were carried out at different temperatures.
Figure 7.22.: Regimes in the chemical potential vs. Tempera- ture plane with coverage less than 1 layer (hatched area) and greater than 1 layer of helium, respec- tively, on a quench-condensed ce- sium surface.
7.4. Discussion
The maximum helium thickness in this regime is hardly temperature dependent.
However, the value of the chemical potential where the drop in the photocurrent occurs depends strongly on the temperature, as shown in Fig. 7.22. As the temper- ature increases, this transition takes place closer to coexistence. The photocurrent data exhibit an increasing spread when approaching the transition from below in- dicating that the system becomes less and less stable close to the transition, which reflects the temporal oscillations in the photocurrent. Hence, the higher the tem- perature, the bigger the surface coverage oscillations (the error bars in Fig. 7.22 are bigger as the temperature increases). Consequently the precise estimation of the chemical potential value at higher temperatures is difficult.
8. Conclusions and Outlook
The work presented here was supported by the German Science Foundation (DFG) under the Priority Program "Wetting and Structure Formation at Interfaces". The purpose of this project was to study the wetting properties of liquid 4He on ce- sium substrates by means of optical (Surface Plasmon Spectroscopy) and electrical methods (Photoelectron Spectroscopy and Tunnelling).
These experiments have been performed in a Helium-4 cryostat which fulfills the requirements for a good temperature stability (∆T ≤ 1 mK) over long runs (≥ 10 h) around the base temperature of T ≈ 1.35 K. Another important fea- ture of the cryostat is that it provides optical access to the sample in three spatial directions which makes it possible to use simultaneously different methods to char- acterize the system. The experimental cell was designed [Rei99] to facilitate the study of physisorbed helium films on horizontal substrates. The methods employed provide additional information about the substrate coverage and deliver compli- mentary results to better understand the wetting properties on both macroscopic and microscopic scales.
The optical method of Surface Plasmon Spectroscopy was employed to measure the thickness of an adsorbed film on various substrates. This technique allows one to locally resolve the thickness of the adsorbed films with a high resolution ('0.3 nm). It is successfully used to measure the film thickness of the helium adsorbed on Cs and on the underlying substrate of Ag. For the latter substrate, the dependence of the film thickness as a function of the distance from the bulk liquid level to the substrate is measured. In this way, the crossover between the non-retarded and retarded regime is determined to take place around 32 nm. Although the method has a high thickness resolution, the spatial resolution is limited to the length scale of the propagation length of the surface plasmons over which the thickness is averaged.
The Ag substrates produced by vacuum deposition at room temperature and inspected immediately with an AFM , show rather smooth surfaces with structures up to 50 nm in diameter and few nm in height, distributed homogeneously on large areas. When the freshly deposited Ag exposed to laboratory environment, it develops fine surface structures which are associated with oxide/sulphide formation within1hour. The growth of this overlayer on the surface takes place at the expense of Ag and changes noticeably the surface roughness. To reduce the probability that this overlayer forms, only Ag surfaces with short exposure time have been used in the experiments.
The Cs films produced by vacuum deposition on very cold substrates (on previ- ously prepared Ag) by quench-condensing method result in a rough, inhomogeneous
Cs surfaces which show columnar growth1. The main cause of such a surface topog- raphy is the suppressed surface diffusion of Cs atoms due to the low temperatures at which these Cs substrates are produced. However, the roughness of the underlying Ag surface may also have an influence on the columnar growth.
We employed the Photoelectron Spectroscopy method to determine the chemical state and the quality of the deposited Cs films. The measured value of the work function measured locally on these substrates (Φ = 1.88 eV) proves that Cs is in metallic form and any contaminating oxides -which influence the wetting behaviour- are present.
The thickness of the helium film adsorbed on a quench-condensed cesium surface measured via Surface Plasmon Resonance technique grows typically up to 120Å . However, this method allows to determine the local thickness of the helium film averaged over the length scale of the propagation length of the surface plasmons.
The method of Photoelectron Tunnelling [Con96] is successfully employed as a complimentary technique to the SPR and reveals interesting results. It allows to very sensitively resolve the thickness of an adsorbed helium film on the non-wetted columnar patches of Cs from a submonolayer up to about three layers. At low values of the reduced pressure (i.e., in the submonolayer regime) the photocurrent decay obeys an exponential law and the adsorbed helium atoms behave like a 2D- gas. As the system moves towards coexistence, the photocurrent levels off and the surface coverage gets close to the layer completion. Close to saturated vapor pressure, surface coverage increases suddenly, which is interpreted as the transition from one layer to the 2−3 layer regime, but the system is still in the non-wetted state.
Combining these two methods allows us to understand the topography of the cesium substrate which is responsible for this adsorption behaviour. The regions where the deposited cesium is too thin, will show wetting, as revealed by the SPR technique. In contrast, the cesium columns which are thick enough are non-wetted by helium and these patches are the only remaining regions for electrons to leave the surface and contribute to the photocurrent.
The experiments carried out in this work points to the importance of the substrate roughness and how this can alter the wetting properties. There are some aspects regarding the cesium substrates produced by quench-condensation and their wetting properties which would be interesting to investigate in future experiments in order to improve the substrate homogeneity.
• Control of the Deposition Parameters. The cesium evaporation setup used in the experiments described above consists of a stabilized current power supply and a Cs dispenser and does not provide any control of the evapora- tion parameters. Although the final thickness of the deposited film could be
1Recent STM experiments of Cs deposited on HOPG [Fub04] confirms a columnar structure of up to10nm height, with a correlation length of 30nm.
measured via SPR, a very sensitive parameter which influences the roughness of the deposited films, i.e. the evaporation rate, could not be monitored. In order to obtain a homogeneous thickness for the cesium it is desirable to keep the value of the evaporation rate as low as possible.
For this purpose, a good alternative would be to use a quartz microbalance (QMB) to monitor and control the evaporation rate during the deposition process. The QMB could be used to cross check the final thickness of the deposited cesium film with the value provided via SPR. One has to choose very good quality quartz oscillators and precautions have to be taken regarding the surface roughness of those commercially available quartz oscillators.
• Wetting Studies andIn Situ Imaging of the Cesium Substrate. After the deposition of the cesium substrate the surface could be inspected in situ by means of the Low Temperature-STM and the influence of the evaporation rates on the surface roughness and wetting properties could be investigated.
The design [Och97, Rei99] and the previous work [Mug98] proved that the LT-STM is a reliable tool to characterize substrates prepared at low temper- atures. It can be used either to visualize the topography of the substrate, or to measure the work function. In this context, the simultaneous use of the LT-STM to visualize the cesium substrate in combination with optical methods (SPS and/or SPM) to measure the adsorbed helium films on these substrates would provide a complete picture of the substrate properties from the point of view of both adsorption behaviour and surface roughness.
The investigations and results obtained in this study shows that the substrate roughness plays a crucial role on the wetting properties and should be taken into consideration for future studies.
Zusammenfassung
Die hier vorliegende Arbeit beschäftigt sich mit den Benetzungseigenschaften von Helium Filmen im Rahmen eines DFG-Projektes, das in den Forschungsschwer- punkt ’Benetzung und Strukturbildung an Grenzflächen’ eingegliedert wurde. Ziel dieser Arbeit war das Benetzungsverhalten von Helium auf Cäsiumsubstraten mit- tels optischer (Oberflächenplasmonen-Resonanz) und elektrischer (Photoelektronen Tunnel) Methoden zu untersuchen.
Die Experimente wurden in einem 4He Badkryostatensystem durchgeführt, der eine hohe Temperaturstabilität (∆T ≤ 1 mK für T ≤ 2.16 K), hohe Standzeit (≥ 10 h bei T ≈ 1.35 K) und optischen Zugang bietet. Die eingesetzte Messzelle wurde entwickelt, um das Benetzungsverhalten von physisorbierten Filmen auf einer horizontalen Geometrie des Substrates zu untersuchen. Die Messmethoden liefern zusätzliche Informationen über die Bedeckung des Substrates mit einem Adsorbat, um das Benetzungsverhalten auf der makroskopischen und mikroskopischen Skala zu charakterisieren.
Die Oberflächenplasmonen-Resonanz (OPR) Methode wurde verwendet, um die Adsorbatschichtdicke an einem festgelegten Ort des Substrates mit sehr hoher Auf- lösung (' 0.3 nm) zu bestimmen. Die Messmethode wurde erfolgreich eingesetzt, um adsorbierte 4He Filme entweder auf Cäsium oder auf Silber Substraten zu be- stimmen. Der Zusammenhang zwischen der wachsenden Helium Filmschichtdicke auf einem Silbersubstrat und der Höhe des Substrates über dem Heliumspiegel wurde untersucht. Der Retardierungsübergang zwischen nicht-retardiertem und retardiertem Verhalten findet bei 32nm statt.
Die AFM-Aufnahmen von Ag Substraten die in einer kommerziellen Aufdampf- anlage bei Raumtemperatur erzeugt werden, zeigen eine relativ glatte und homo- gene Oberfläche mit Strukturen bis50nm Durchmesser und einigen nm Höhe. Die Oberfläche des frisch aufgedampften Ag Substrates entwickelt sich unter Luftlabor- bedingungen zu einer feinen Oxyd/Schwefel-Struktur, die die Substrat-Rauigkeit drastisch ändert.
Die Cäsiumfilme, die auf den unterliegenden Silbersubstraten bei tiefen Tempera- turen unter UHV-Bedingungen aufgedampft sind, haben eine raue, nicht homogene Säulenstruktur2. Die Erklärung dafür ist, dass die Oberflächendiffusion von Cäsiu- matomen, die stark von Substrattemperatur abhängt, sehr niedrig ist.
Die Photoelektronen-Spektroskopie Messmethode wurde eingesetzt, um die Qua-
2Die vor kurzem durchgeführten Experimente [Fub04] bestätigen eine Säulenstruktur mit einer mittleren Höhe von etwa10nm und einer Periodizität von30nm.
lität und chemische Beschaffenheit des frisch aufgedampften Cäsiumfilms zu über- prüfen. Der lokale Wert der Austrittsarbeit beträgt Φ = 1.88 eV und zeigt, dass die Cäsiumoberfläche rein metallisch und oxydfrei ist.
Die adsorbierte Heliumfilmdicke auf einem abschreckend-kondensiertem Cäsium- substrat, mit der OPR Messmethode gemessen, beträgt etwa 120Å bei 1.36 K.
Jedoch ist die Heliumfilmdicke über der Lateralskala der OP Lauflänge gemittelt.
Zusätzlich zur OPR Messmethode wurde die Photoelektron Tunnel (PT) Messme- thode erfolgreich eingesetzt und diese hat Informationen geliefert, die bisher nicht zugänglich waren. Sie ermöglicht, das auf die nicht benetzte Säulenstruktur adsor- bierte Helium in einem Bereich von Submonolage bis zu 3 Monolagen aufzulösen.
Für niedrige Werte vom reduzierten Druck (bzw. im Submonolage Bereich) nimmt der Photostrom mit zunehmenden Druck ab und die auf dem Substrat adsorbierten Heliumatome haben ein zweidimensionales Gas-Verhalten. Bei mittleren Werten von reduziertem Druck, bleibt der Photostrom unverändert und die Bedeckung wird bis zu einer Helium Monolage wachsen. In der Nähe des Sättigungsdampfdrucks steigt die Oberflächenbedeckung plötzlich, die als Übergang von einer Monolage bis zu 2−3 Monolagen im unvollständig benetzten Zustand zu interpretieren ist.
Die Kombination dieser Messmethoden ermöglicht das Verständnis für die Topo- graphie, die solche Benetzungseigenschaften verursachen. Die OPR zeigt, dass die Bereiche zwischen die Säulenstruktur des Cäsiumfilmes zu dünn sind und benetzt wurden. Die Cäsiumsäulenstruktur wird in Gegensatz dazu von Helium nicht be- netzt, und diese Bereiche sind die einzigen durch welche die Elektronen tunneln, und so zum Photostrom beitragen können. Bei Koexsistenz sind diese Cäsiumsäu- len immer noch nicht benetzt.
Diese Experimente haben gezeigt, dass die Substrateigenschaften –hauptsächlich deren Oberflächenrauigkeit– einen entscheidenden Einfluss auf das Benetzungsver- halten hat, und somit in zukünftigen Untersuchungen mit berücksichtigt werden sollte.
A. Dielectric Constants of Some Metals
In the following figures,the dielectric constants, , of the metals used to couple Sur- face Plasmons (Ag, Au [Joh72]) and/or used in wetting experiments (Cs [Ive37]) are shown. The variation of the real part (1), and imaginary part (2) as a function of wavelength is given.
(a) Dielectric constant for silver (b) Dielectric constant for gold Figure A.1.: Dielectric constant for silver and gold as a function of wavelength.
Figure A.2.: Dielectric constant for cesium as a function of wavelength.
B. Angle Calibration of Step Motor
In the following we give the details the angle calibration necessary to evaluate the measurements done using the Surface Plasmon Resonance. As described in Section 5.3.1, the stepping motor controls the angle of incidence and the resonance angle ΘR is tracked such that it is always at the minimum while adsorption takes place.
(a) (b)
Figure B.1.: Calibration curves for the stepping motors used in measurements via Sur- face Plasmon Resonance. The variation of the angle of incidence in the prism as a function of Stepping Motor Position for1/4 steps width(a) and for1/8 steps width(b), respec- tively.
In Fig. B.1 the variation of the angle of incidence in the prism (∆Θ) as a function of the position of the stepping motor is shown. We used in the experiments step widths of1/4thand1/8thfrom a SMP unit. The latter gives a better angle resolution and has been used in most of the experiments performed.
C. Pressure Corrections
The pressure is measured using a vacuum gauge (Baratron) with a high sensitivity which delivers PBara(V). This value is then converted in PBara(mbar) using the calibration given below.
• For (0−10) mbar we have: pBara(mbar) = pBara(V)·1.3405
• For (10−100) mbar we have: pBara(mbar) =pBara(V)·13.354
In the following we will calculate the hydrostatic pressure drop, as described in Section 1.1.2. The pressures at height h, andh+ ∆H respectively are given by
p(h) =p0·e−%gh/p0 (C.1)
p(h+ ∆H) =p0·e−%g(h+∆H)/p0 (C.2)
Figure C.1.: The experimental cell is located at a height ∆H below the vacuum gauge. There is a pressure difference,∆P, between the pressure at the level of the vacuum gauge,pBara, and the pressure at the level of the substrate,pcell0 . For our experiment,
∆H = 1.50 m and h = 400 m, it turns out that
∆P = 37.91·10−3 mbar, hence pcell0 =pBara+ ∆P.
Dividing the two equations we obtain p(h+ ∆H)
p(h) =e−%g∆H/p0, (C.3)
where p0 =p(h= 0) = 1013 mbar.
The pressure variation is given by
∆P ≡p(h+ ∆H)−p(h) =p(h)·[e−%g∆H/p0 −1]. (C.4) In our experiment h = 400 m and ∆H = 1.50 m. Using the values p0 = 1013 mbar, % = 205kg/m3 (for He) and g = 9.81 m/s2, we obtain a pressure difference
∆P = 37.91· 10−3 mbar.
Then the pressure in the cell, pcell0 , is given by
pcell0 =pBara+ ∆P. (C.5)
D. Resonance Angle Corrections due to Rising Liquid Level and Prism Tilting Angle
As described in Section 7.2.2, there are two contributions to the shift in the reso- nance angle, θR, while the liquid helium level is rising (see Fig. D.1).
The first contribution is due to the fact that the optical path of the laser beam is modified (when the liquid level is higher than the incidence point of the laser beam, M, on the mirror1) by the refractive index of the liquid,nLiqHe. This has to be corrected until the liquid level reaches the level where the laser beam is incident on the glass prism, P. At this two particular points of incidence (i. e. Mi and Pi) the laser beam is strongly scattered due to the meniscus of the liquid helium climbing on the mirror and on the prism, respectively.
The second contribution is due to the tilting angle of the prism (the upper surface of the prism is not parallel to the liquid level). In this case, the points Mi and Pi on the incidence side of the prism will not be at the same level with Pe and Me where the laser beam emerge from the prism and is reflected by the exit mirror.
This means that, if the prism is not parallel to the liquid level, the range where the beam is disturbed by the raising liquid becomes broader. In the following we will treat these contributions separately.
At the end the way we measured the tilting angle will be described and we will es- timate the critical angle of total reflection in the case of liquid/gas helium interface.
• Rising Liquid Level. A sketch of the setup is given in Fig. D.1.
We will calculate the angular displacement, ∆θLG, of the laser beam as the difference between the angle when crossing the liquid, θL, and the angle in gas, θG,2 ∆θGL=θG−θL.
At point P, when only He gas is present we have
nHeGassinγ2 =nP rsinγ3, (D.1)
and θG+γ3 =αP r.
When the liquid reaches the Level 2, at point N, we have
nHeLiqsinγ22=nHeGassinβ2, (D.2)
1The indicesiandedenotesincidentandemerging, respectively.
2In this case,θG=θR.
and at point O,
nHeGassinβ1 =nP rsinγ32, (D.3)
with θL+γ32=αP r and β2+γ22 =αP r.
Figure D.1.: The rising helium level disturbs the measurement in an SPR setup used to measure thick helium films adsorbed on Ag (see Section 7.2.2). When the liquid level rises above the laser beam level (i. e. from Level 0 to Level 2), the resonance angle, θR, jumps to θL.
The inset at the upper right side shows a zoom in at the interface liquid-gas, and the important angles, see text for details.
The inset at the top left side shows the influence of tilting. The prism is inclined with a tilting angle ,τ, towards the side of the laser beam incidence. The vertical axis,AV, and the prism axis, AG, are shown.
The values of the following parameters are given or could be measured: nP r = 1.515, nHeGas = 1.000066,nHeLiq = 1.028, αP r = 75◦, α= 35.13◦
After a simple calculation one gets θG =αP r+ arcsin
nHeGas
nP r cos(αP r+α+αm)
, (D.4)
and,
θL =αP r+ arcsin
"
nHeGas nP r
sin arcsin
"
nHeLiq
nHeGascos(α+αm)
#
−αP r
!#
, (D.5)
whereαm is the angle of the laser beam with the mirror, which can be varied from outside3.
Thus, the angular displacement is a function of the angleαm,∆θLG =f(αm).
• Tilting of the Prism. If the prism axis, AG, is inclined with an angle towards the side where the laser beam is incident, then the angle between the AG and the vertical axis AV is the tilting angle, τ (see the left upper inset in Fig. D.1)
The procedure to determine the shift in the resonance angle is the same as in the case without tilting. The contribution to the resonance shift due to the tilting angle is given by:
θeL =αP r−arcsin nHeGas
nP r sin (αP r+ τ−arcsin
"
nHeLiq
nHeGascos(α+αm−τ)
#
−αP r,
(D.6)
which in the case of no tilting, τ = 0 will give the same solution as Eq. D.5.
• Measuring the Tilting Angle. We measured the tilting angle,τ = 0 using the simple setup sketched in Fig. D.2. The beam coming from a laser which was carefully horizontally levelled goes through a pinholeL made in a screen (placed in a plane perpendicular to the laser beam), is deflected by a 45◦
Figure D.2.: Setup for measuring the tilting angle of the prism. Sc-Screen,M-Mirror.
mirrorM (mounted outside the cryostat) and enters the glass prism from the bottom.
3The connection with the incidence angle,αi is simplyαm= 90◦−αi.
The beam is retroreflected by the Ag film deposited onto the prism and re- flected by the same mirror on the screen. The displacement, LB, between the pinhole and the place where the laser beam hits the screen after reflection is measured . The distance, LA, from the screen to the prism surface could be measured. From the simple triangle geometry, we get
tan 2τ = LB
LA, (D.7)
hence τ = 1
2arctan LB
LA
. (D.8)
In the case of our experiment we find τ = 0.76◦.
• Critical Angle of Total Reflection. The critical angle of total reflection, θc, for the interface between liquid helium and helium gas is given by
θc = arcsin nHeGas nHeLiq
!
, (D.9)
which has a value of θc = 76.62◦.
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