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Analysis of complex thermal desorption spectra: PTCDA on copper
Surface Science 603 (2009) 482–490
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Analysis of complex thermal desorption spectra: PTCDA on copper Th. Wagner *, H. Karacuban, R. Möller Universität Duisburg-Essen, Center for Nanointegration Duisburg-Essen, Lotharstr. 1-21, 47057 Duisburg, Germany
a r t i c l e
i n f o
Article history: Received 2 September 2008 Accepted for publication 5 December 2008 Available online 16 December 2008 Keywords: Thermal desorption spectroscopy (TDS) 3,4,9,10-Perylene-tetracarboxylicdianhydride (PTCDA) Organic nanocrystals Growth
a b s t r a c t Organic molecules often show very complex thermal desorption spectra. If there is an ordered structure the activation energy for desorption Edes will decrease within the first few layers because of the decreasing van der Waals interaction between molecules and substrate. This is specially true for the system 3,4,9,10-perylene-tetracarboxylic-dianhydride (PTCDA) on Cu(1 1 1). The thermal desorption spectra for this particular system consist of three different signals which can be attributed to the second layer, the multilayer and a phase consisting of nanocrystals. We did not see any desorption from the first layer of PTCDA on Cu(1 1 1). In the first part of this paper, we will outline a numerical algorithm to evaluate the spectra with respect to the desorption energy of the second layer (Edes;secondlayer ¼ 2:35 eV) and the multilayer (Edes;multilayer ¼ 2:2 eV). In agreement with the transition state theory, we found a pre-exponential factor of 4 1019 s1 . Furthermore, we will show that nanocrystals have a contribution to the thermal desorption spectra different from the one of the multilayer. By evaluation of the third, high temperature signal it is possible to get parameters which describe the distribution of the nanocrystals and therefore gain further understanding of their growth. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction The growth of thin, ordered layers is technologically very important. Therefore, people try to gain insight into the adsorption and diffusion processes on the surface. The time reversal process of the adsorption is the desorption. Due to the reversibility one is tempted to study the desorption of particles to understand the fundamental processes taking place on the surface while 2D islands or 3D crystals are forming on the surface. Especially, thermal desorption spectroscopy (TDS, or thermal programmed desorption (TPD), see Ref. [1]) is meant to be a simple experiment to study surface kinetics: One only has to detect the particles desorbing from the surface as a function of temperature and time while the temperature of the sample is increased linearly. Despite of the intensive use of TDS to determine rate data, the interpretation of these experiments with respect to binding energies is still controversial – not only because the binding energy is not always equivalent to the activation energy for desorption. In the past, several algorithms have been discussed which are based on the Polanyi–Wigner model [2]: E dN des ¼ mðNÞ Nn e kb T dt
ð1Þ
* Corresponding author. Present Address: Institut für Experimentalphysik, Johannes Kepler Universität Linz, Altenbergerstr. 69, A-4040 Linz, Austria. E-mail address: [email protected] (Th. Wagner). URL: http://www.exp.physik.uni-due.de/moeller (R. Möller). 0039-6028/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2008.12.007
In this rate equation the number of adsorbed particles is given by N kb is the Boltzmann constant, whereas T is the temperature. The activation energy for desorption is given by Edes . In general the pre-exponential factor m is a function of the coverage. n represents the order of the process. Redhead [3] derived from Eq. (1) a relation between the maximum of the desorption trace and the activation energy. Redhead’s equation looks very handy but can only be applied to first order processes and needs the additional knowledge of the pre-exponential factor. The leading edge analysis [4] or Arrhenius plot can be used in principle to get the activation energy for desorption Edes and the pre-exponential factor m but is useless for peaks which are superimposed. The complete analysis [4] does not assume any dependency of m and Edes to the coverage but relies on a huge number of high quality data with a sufficient signal to noise ratio. Especially, if there are several contributions to the desorption spectra one is tempted to simulate the spectra by the numerical integration of Eq. (1). Although one can reproduce the spectra very well the simulation does not produce reliable values for Edes and m because they are highly correlated [5]. See Refs. [6,7] for a detailed discussion of the different approaches. Within this paper we want to evaluate our thermal desorption spectra following the ideas presented by Nieskens et al. [7] and Tait et al. [8] who rewrite the Polanyi–Wigner equation so that the activation energy of desorption Edes becomes a function of the number of adsorbed particles. We will simplify the numerical algorithm by assuming that the desorption of thick layers is not dependent on the coverage. We will confirm our experimental value for the pre-exponential factor by transition state theory.
Th. Wagner et al. / Surface Science 603 (2009) 482–490
Fig. 1. Residual gas spectrum of the PTCDA source which was held at 573 K.
Due to the relevance on catalytic processes most thermal desorption experiments focus on small molecules. Only a few quantitative studies on the desorption of organic molecules have been carried out so far, e.g. linear and cyclic n-alkenes [9,8] and oligo phenylenes [10–12]. Gonella et al. [13] have studied the effect of the inter-adsorbate repulsion of tetracene which was adsorbed on Ag(1 1 1). For samples covered by a multilayer they also found different desorption peaks which they have attributed to crystallites having different structures and morphologies. 3,4,9,10-Perylene-tetracarboxylic-dianhydride (PTCDA) (see inset of Fig. 1) is a well-known organic semiconductor for which the growth on a variety of substrates was studied intensively by direct imaging techniques (see Ref. [14] for a recent review). By means of STM [15] and nc-AFM [16] it was shown that the first two layers of PTCDA on Cu(1 1 1) both exhibit a herringbone structure but the electronic and geometric properties differ for these two layers. This can be attributed to the decreasing influence of the substrate. Schuerlein and Armstrong [17] have shown thermal desorption spectra of PTCDA on Cu(1 0 0) suggesting a third phase in addition to the desorption of the second layer and the thin film. Kilian et al. [18] presented thermal desorption data of PTCDA on Ag(1 1 1) which only exhibit two features. Although it is known for long that PTCDA grows on most surfaces in the Stranski–Kastranov mode (see Ref. [19], exception alkali halogenides [20,21]) only recent studies, e.g. Refs. [18,22–25], focus on the growth mechanism and the size distribution of these nanocrystallites. The present paper will contribute to this ongoing work by analysing the desorption traces originated from small organic nanocrystallites on the surface.
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tor was degassed for several hours slightly below the evaporation temperature of the PTCDA. Fig. 1 shows a typical mass spectrum just before the preparation of a PTCDA film. The assignment of the mass peaks corresponds to Ref. [26]. The manipulator can be rotated so that the sample is facing to the PTCDA source or to the mass spectrometer. A movable aperture is mounted in front of the single crystal to avoid the adsorption of molecules on the sample holder (Omicron type). Such a contamination may lead to artifacts in the thermal desorption spectra. While preparing the PTCDA films the aperture was in the front of the copper single crystals so that only a circular spot with a diameter of about 5 mm was exposed to the source. During the evaporation the mass spectrometer was used to monitor the particle flux (at mass 392 amu) from the evaporator. The time integral of the mass spectrometer signal was used as the initial coverage. Before the desorption experiment the aperture had been moved so that it was not in the field of view of the mass spectrometer. In addition, the aperture was connected to a liquid nitrogen tank used to cool the whole head of the manipulator. By replacing the exposed sample by a clean one, it was tested, that the mass spectrometer does not detect any PTCDA molecules coming from the manipulator or the aperture during the desorption experiment. The heating of the single crystal was done by radiative heating. Therefore a bulb filament was mounted underneath the single crystal. For the temperature measurement a calibrated thermocouple (type K) was pressed by a spring mechanism directly to the single crystal. A PID controller (Eurotherm 815S) was used to set up a temperature ramp with slope 1 K s1. Within each series the coverage was increased from below 1 monolayer to several layers. During the desorption experiment not only the intact molecules was monitored by the mass spectrometer but also some known fragments as shown in Fig. 1. During the desorption experiments the ratio between the PTCDA fragments was found to be constant. Therefore, only the mass 392 u corresponding to the intact PTCDA molecule will be plotted within this paper. 3. Results Fig. 2 shows a typical set of spectra acquired for a Cu(1 1 1) surface covered with different amounts of PTCDA. For the coverage of
2. Experimental details The experiments were carried out in an ultra high vacuum (UHV) system with a base pressure below 1 109 mbar. The vacuum system is equipped with an Argon ion source (1.5 kV, 20 lA cm2), a quadrupole mass spectrometer (Pfeiffer Vacuum, QMG422 with a cross-beam ion source) and a temperature variable manipulator. The home build PTCDA source is mounted opposite to the mass spectrometer. Cu(1 1 1) and Cu(1 0 0) single crystals (diameter 8 mm) were used as samples. The sequence of sputtering (15 min) and annealing (1 h at 820 K) was repeated until no significant traces of impurities had been found by means of XPS and STM. Between the thermal desorption cycles only one sputter and anneal cycle was required. The commercially available PTCDA was pre-purified by gradient sublimation before inserted into vacuum. Afterwards the evapora-
Fig. 2. Series of thermal desorption spectra acquired with increasing amount of PTCDA on Cu(1 1 1). The slope of the temperature ramp was 1 K s1. The plotted mass represents the intact PTCDA molecule. Although the full range of the temperature is 300-800 K only the non-zero part was plotted. For reasons of a better visibility offsets are applied to the individual spectra.
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0.4 monolayer, the spectrum is given just by noise. Only for coverages above an equivalent of one close-packed layer desorbing molecules are detected. At first – for low coverages – a signal in the temperature range between 520 and 573 K appears in the spectra. If the signal is not superimposed by others, which are discussed later on, the leading edges of these signals, which can be described by an exponential function, fall together. The maximum is followed by a sharp drop to the noise limit. It is shifting to higher temperatures with increasing coverage until it reached the limit of 573 K. This behavior is typical for the desorption process of zeroth order from a well defined, close-packed layer. In particular, the area under the saturated peak was assumed to be equivalent to 1 monolayer. The evaporator was then calibrated by taking the linear slope in Fig. 3 into account. In addition, we confirmed the calibration by means of STM. If more than an equivalent of two close-packed layers is deposited on the surface a second peak appears in the thermal desorption spectra (see Figs. 2 and 3). The leading edge of the peak is located at about 470 K and is given by an exponential slope. Again for all spectra acquired for different initial coverages the leading edges of this signal fall together. After reaching the maximum there is sharp drop to the noise level. The maximum of the peak is continuously shifting to higher temperatures if the coverage is increased. Especially, there is no saturation. The signal can be attributed to the desorption from the third and higher layers. The peak shape is also typical for a desorption process of zeroth order. As the peak appears before the low coverage peak saturates one can assume that the third layer starts growing before the second layer is closed. This is in agreement with the findings of Fendrich and Krug [27] who have shown by force field calculations that there is an Ehrlich–Schwoebel effect for PTCDA. While dosing more than an equivalent of four close-packed layers a third peak at the high temperature end of the spectra appears. The maximum for the peak is located around 580 K. In contrast to the earlier discussed peaks this one has a roundish maximum. We will discuss this peak in Section 3.4 as desorption trace of nanocrystals which had been described by STM [28,19] earlier. We want to put some attention to the spectrum with an initial coverage of seven close-packed layers (see Fig. 2). Whereas the peak which can be attributed to the second layer and the thick film behave as in the other spectra the third peak which resembles the
exposure of PTCDA / close-packed layers 0
2
4
6
8
10
12
20
14
16
desorption of PTCDA / arb. units
14 15
12 ×5
10
10 8
×25
6 5
4 2
desorption of PTCDA / close-packed layers
16
0
0 0
5
10
15
20
exposure of PTCDA / arb. units Fig. 3. The graph compares the amount of molecules which had been prepared on the surface before the TDS experiment with the area under the thermal desorption spectra shown in Fig. 2. The exposure of PTCDA was calculated as the integrated flux detected during the film preparation.
signal from the crystal phase is shifted to a higher temperature. We found the jumping of this particular desorption trace also in other experimental runs. As described in Section 2 we can ensure that this signal is due to desorption of PTCDA from the sample and not from the sample holder or similar. While repeating the experiment with the same initial coverage the maximum of this peak may shift by 10 K whereas the other peaks keep their positions. In Section 3.4 we will be able to relate this behavior to the morphology of the sample. The fact that there is no desorption from the first layer of PTCDA on Cu(1 1 1) is also supported by Fig. 3. In the diagram the integrated flux during the desorption process is plotted against the integrated flux during the preparation. Until an equivalent coverage of 1.8 close-packed layers is dosed to the surface there is nearly no desorption. Starting from this coverage one can fit the data points by a linear function. The smooth change of the slope also explains the slight shift to higher coverages for the turning point. In addition, scanning probe measurements [16,15] show that the density of at least the first two or three layers of PTCDA is dependent on the distance to the copper surface indicating a strong interaction of the first layers to the substrate. By X-ray standing wave (XSW) Gerlach et al. [29] showed that on Cu(1 1 1) the PTCDA molecules within the first layer are bended. They also found a reduced distance between substrate and first layer compared to adjacent [1 0 2] planes in the bulk. This usually indicates a very strong interaction of the first layer with the substrate. 3.1. Desorption energy of defined layers Nieskens et al. [7] and Tait et al. [30] suggested a new way to analyse thermal desorption spectra. Both authors start from the Polanyi–Wigner rate equation (see Eq. (1) and Ref. [2] for details). is proporIn the limit of a high pumping speed, the derivative dN dt tional to the partial pressure p which is itself proportional to the current I at the detector of the mass spectrometer. Assuming a desorption process of zeroth order one can rewrite Eq. (1) as follows: E
kdesT
IðTÞ ¼ I0 hðNÞ e
b
ð2Þ
For simplicity we will only describe the case of zeroth order desorption which is given for at least two of the three signals in Fig. 2. However, the algorithm can be extended to an arbitrary order of the desorption process. The heavy-side function hðNÞ considers that the number of adsorbed particles N is finite. The factor I0 takes the pre-exponential factor m of the original Polanyi–Wigner equation into account. It also includes the sensitivity of the mass spectrometer and the slope of the temperature ramp. As at least the sensitivity of the mass spectrometer is unknown, we do not want to give it a physical interpretation other than being an arbitrary but fixed value for a specific adsorbate and the experimental setup. As long as N P 0 one can rewrite Eq. (2) so that Edes becomes a function of the temperature T and the current I measured by the mass spectrometer:
Edes ¼ kb T ½lnðIÞ lnðI0 Þ
ð3Þ
This equation gives only a physical value for Edes if one uses the correct value for the pre-exponential factor m, respectively, I0 . Nieskens et al. [7] suggested to use DFT calculations to get the pre-exponential factor. Tait et al. [30] propose a self consistent fit algorithm, but they are using a calibrated QMS. In our case, none of these options is applicable. Therefore, we will assume that the pre-exponential factor and the activation energy for desorption are constant if the coverage is higher than 3 monolayers. This can be justified by the fact that the molecules in the third and higher layers do not interact any more with the substrate. In this particular case the plot of Eq. (3)
Th. Wagner et al. / Surface Science 603 (2009) 482–490
8
6
I0 overestimated
-9
3
7
current I (of QMS) / 10 A
kbT*(ln(I)-ln( 0)) / eV
4
5 Edes,2nd layer=2.32 eV 2
4
Edes,multilayer=2.20 eV 3 best fit 2
1 I0 underestimated 0 300
400
1
500
600
700
0 800
temperature / K Fig. 4. The graph shows a thermal desorption spectrum of 12.7 monolayer PTCDA on Cu(1 1 1) which had been transformed by Eq. (3) and different values for I0 . The region which is highlighted in gray indicates the part of the spectrum which was used to optimize the parameter I0 .
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had been tested. The fact that the peak of the crystal phase overlaps with the signal from the second layer limits the number of data points representing only the signal from the crystal phase. Therefore it is hard to decide for which combination of I0 and n the described procedure gives a horizontal line for the region of that peak. Maybe the best results were obtained for n ¼ 1=2 and n ¼ 2=3 which can be interpreted as the desorption from step edges and, respectively, as the desorption from nanocrystals. In general, a fractional number n indicates a desorption from a non-flat surface (3D crystal) or that the particles can desorb only from parts of the surface (e.g. defects). For example, Shimada et al. [34] used n ¼ 2=3 to fit the desorption spectra of vandyl phthalocyanine (VOPc) on KBr(0 0 1). Their interpretation is that 2 the area from which the molecules desorb scales with N3 (N the number of molecules on the surface). The problem is to find an appropriate scaling factor which has to consider the geometrical aspects of the surface. As the position of the crystal phase peak is not fixed – see Fig. 2, spectrum for 7 monolayers – also the geometry of the surface (number and size of crystals) may have changed. In Section 3.4 we will present an algorithm which also can extract the size distribution of the crystal from the thermal desorption data. 3.2. Comparison with other copper surfaces
should give a horizontal line in the region of the spectra where the signal from the multilayer dominates. For each spectra the parameter I0 was optimized so that the resulting plots fulfill this condition. The mean values of all spectra is given by I0 ¼ 9:0 1011 A. The corresponding statistical standard error is 3:6 1011 A. This value for I0 was taken to evaluate the spectra according to the activation energy for desorption. As shown in Fig. 4, there is a plateau in the part of the spectra which corresponds to the thick film. The level of the plateau is – averaged over all spectra – 2.20 eV which is the activation energy for desorption of the multilayer. The fact that the transformed spectra in the gray region is given by a horizontal line confirms that the desorption can be described by a zeroth order process. Nevertheless, we cannot exclude that the activation energy for desorption and the pre-exponential factor are related as some authors discuss [31,32,7]. At the point in Fig. 4 where the peak of the multilayer drops, there is a step up by 0.12 eV in the transformed spectrum. The level of the plateau is 2.32 eV which can be interpreted as the activation energy for a zeroth order desorption process for the second layer. The averaged value is 2.35 eV. The conclusion holds only if one assumes the same pre-exponential factor for the multilayer and the monolayer. As the peak of the second layer is superimposed by that one of the later discussed crystal phase, one can not decide if this assumption is actually justified for the particular spectrum shown in Fig. 4. But spectra with a coverage below 4 monolayers show also a plateau for the second monolayer. As predicted the activation energy for desorption is smaller for the multilayer as for the second layer and, especially, the first layer from which no desorption was observed. This confirms that the first layer of PTCDA on the copper is interacting strongly with the substrate. The influence of the substrate will decrease within three layer so that it is neglectable. At least for the first layer of PTCDA on Cu(1 1 1) the interaction between substrate and molecules is very strong as supported by XSW and photoelectron spectroscopy (UPS/XPS). Schreiber et al. [29,33] report a smaller bonding distance of PTCDA on Cu(1 1 1) (0.266 nm) than the stacking distance dð102Þ ¼ 0:321 nm. In addition, the PTCDA within the first adsorbate layer are bended and molecular orbitals are shifted. The evaluation of the third peak which is attributed to the crystal phase is in principle also possible with the outlined algorithm. Therefore we varied not only the parameter I0 but also the order n of the desorption process. Especially, values for n between 0 and 1
For comparison, we also carried out the thermal desorption experiment on Cu(1 0 0) (not shown in detail here) and Cu(1 1 1) with many structural defects. We prepared the latter one by sputtering the Cu(1 1 1) surface as usually but skipping the later annealing step. A so prepared surface should consist of a very high but somehow fixed density of step edges, small facets and so on. Fig. 5 shows a series of spectra on surface with the increased amount of structural defects. For a coverage below 3 monolayers (we used the same calibration of the source as for the well prepared Cu(1 1 1)) almost no signal is detected. Only by enlarging the y-scale a very broad peak is visible between 550 and 650 K. At an initial coverage of 3 monolayers the integral of this signal is constant. As the peak appears already for low coverages and saturates we can interpret this as the desorption from a finite number
Fig. 5. The water fall plot shows thermal desorption spectra of PTCDA on Cu(1 1 1) surface with an increased amount of structural defects. The surface actually was a Cu(1 1 1) single crystal which was sputtered but not annealed. The spectra have been acquired for different initial coverages (as indicated at the curves) and with a fixed temperature ramp of 1 K s1. The inset shows the spectra with an initial coverage of 2.7 monolayer und 3.7 monolayer with an three times enlarged ordinate.
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Th. Wagner et al. / Surface Science 603 (2009) 482–490
of adsorption sites. These might be given by defects which had been produced by the sputtering process. As there are many different kinds of possible facets, step edges and vacancies (or adatoms) with different activation energies for desorption, the peak – actually interpreted as a superposition of several peaks – appears very broad. The desorption trace from the multilayer and the one from the crystal phase behave for well prepared Cu(1 1 1) and sputtered one the same. The signal from the multilayer shows the typical behavior of a zeroth order peak as discussed before. Therefore, the same data processing as for the Cu(1 1 1)-spectra was applied to it. The analysis produces a parameter I0 in the same order of magnitude as for the annealed Cu(1 1 1). The overall analysis gives a activation energy for desorption Edes;multilayer ¼ 2:21 eV. As already concluded from the similarity of the peak position and the peak shape the desorption energy of the multilayer is (almost) equal to the one found for the annealed surface. Table 1 summarizes the findings for the different copper surfaces. It also includes the desorption energy of a second layer of PTCDA on Cu(1 0 0). One can see that the molecules of the second layer on Cu(1 0 0) have to overcome a slightly lower barrier than the ones on the annealed Cu(1 1 1). Nevertheless, the values are the same if taking the experimental error into account, so that we think that the downshift of 0.04 eV is not significant but due to experimental uncertainness. Yim et al. [35] have calculated the interaction energy of an individual PTCDA molecule moving on top of a close-packed but stepped layer of PTCDA by taking van der Waals forces into account. The value of 2.15 eV which agrees very well with our findings is given by the minima in the potential map on the terrace. This value represents the potential energy for a molecule which can move freely in two dimensions on the surface. As there would be an additional interaction with other molecules in the same layer if the molecules would desorb from a step edge or a kink the good agreement between force field calculations and our results may indicate that the desorption takes place from a 2D gas phase. We will come back to this in the following section. Schuerlein et al. [17] showed some thermal desorption spectra of PTCDA on Cu(1 0 0). They extracted from their spectra a desorption energy of 1.54 eV for the second layer and 1.48 eV for the multilayer. Unfortunately, they do not state how they have obtained the values in detail. We assume that they fitted the spectra with a fixed pre-exponential factor of m ¼ 1 1013 s1 . By doing so, the pre-exponential factor is interpreted as a typical surface phonon frequency. A couple of papers [36,9,8,37] on the desorption of cyclic and linear n-alkanes show that the pre-exponential factor strongly depends on the adsorbate and can vary several orders of magnitude. We also evaluated our data by the leading edge method. The averaged values produced by this had been systematically by about 0.2 eV lower compared to the ones in Table 1. In addition, the standard deviation for the activation energy of desorption evaluated by
Table 1 The table compares the activation energies for desorption of PTCDA on different copper surfaces. The data have been evaluated by the described algorithm with n ¼ 0 and I0 ¼ 9:0 1013 A. In addition, the last two rows represent data from the literature. The value of PTCDA on PTCDA is taken from a paper by Yim et al. [35]. The values represent the minima in the potential map while a single PTCDA molecules is moved on an close-packed PTCDA structure. Edes;second Cu(1 1 1) Sputtered Cu(1 1 1) Cu(1 0 0) Cu(1 0 0) [17] PTCDA [35]
layer
2.35 ± 0.20 2.31 ± 0.20 1.54
(eV)
Edes;multilayer (eV) 2.20 ± 0.20 2.21 1.48 2.15
the leading edge method is more than a factor of two larger than the one of the described algorithm. At a first glance, this is surprising because our algorithm and the leading edge method are correlated. On the other hand our algorithm puts less statistical weight on the data points of the noisy background as seen in Fig. 4. 3.3. Pre-exponential factor
m
In principle, the evaluation procedure described before is capable to produce a meaningful value for the pre-exponential factor m. But this is only possible if the mass spectrometer is fully calibrated. Especially, this includes the knowledge of the sensitivity for the particular molecular species. Usually, this is not the case. Therefore, we have used the current I0 instead of m. Eq. (1) describes the desorption process on the microscopic scale without the contribution of any instrumental parameter. By a simple curve sketching for the case n ¼ 0 and a saturated layer one finds the following relation between the temperature T max at which the maximum of the curve occurs and the pre-exponential factor m:
m¼b
Edes;second
layer
kb T 2max
exp
Edes;second layer kb T max
ð4Þ
b = 1 K s1 is slope of the linear temperature ramp used in the experiments. As marked in Fig. 2 the signal of the saturated second layer produces a maximum in the desorption spectra at T max ¼ 573 K. In the particular case of PTCDA on Cu(1 1 1) Eq. (4) yields m ¼ 4 1019 s1 . According to the transition state theory (TST) [38] the pre-exponential factor can be written as:
mTST ¼
kb T qz h qads
ð5Þ
where qads and qz are single-particle partition functions for the adsorbed (initial) and the transition state, respectively, calculated at the temperature T. We will neglect effects of conformational entropy and assume rigid molecules. In order to simplify the calculation of the partition functions, the transition state is given by the gas phase molecules, which can be described by a 3D rotator. Furthermore, we make the assumption that the molecules have free translation on the surface, i.e. they behave translationaly like a 2D gas, but that all rotation is prohibited. The last argument may be justified by the fact that the desorption process is described by a zeroth order process which is quite unusual for a close-packed layer. In general, this is explained by a two phase model [39–42]: The desorption itself takes place from a dilute, 2D gas-like phase which covers the whole sample. A second, condensed phase acts as an reservoir for the gas phase to maintain a constant number of particles in the dilute phase. By taking the above mentioned conditions into account, most contributions to qads and qz cancel each other so that one only has to calculate the rotational partition function of the molecule in the transition state:
qrotational ¼
3 1 p 12 ð8kb TÞ2 ðIx Iy Iz Þ2 rh3
ð6Þ
Within this equation Ix , Iy and Iz represent the moments of inertia of the molecule. The symmetry factor r can be thought of classically as the number of indistinguishable rotational configurations for the molecule, and so it prevents overcounting. Tait et al. [8] have successfully applied the described model to predict the chain length dependency of the pre-exponential factor of n-alkanes. For the particular case of PTCDA, we have calculated the moments of inertia by Hyperchem using the AMBER94 force field [43] for geometry optimization. The parameters used to evaluate
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Th. Wagner et al. / Surface Science 603 (2009) 482–490 Table 2 Parameters used to calculate the pre-exponential factor state theory.
a
mTST by means of transition
Ix (u nm2)
Iy (u nm2)
Iz (u nm2)
r
qrotational
mTST (s1)
12.20
57.01
69.21
6
7,590,000
9 1019
multilayer the Eqs. (5) and (6) are displayed in Table 2. The calculated value mTST ¼ 9 1019 s1 has the same order of magnitude as the experimental one. To confirm the model used for the transition state theory, one would need to vary the molecular species, e.g. by using naphthalene-tetracarboxylic-dianhydrid (NTCDA) and terrylenetetracarboxylic-dianhydrid (TTCDA) instead of PTCDA. The data are not available yet.
substrate
b
3.4. Signal from nanocrystals The contribution of the crystal phase to the desorption spectra is likely not described by simply applying Eq. (1) to the desorption spectra. The best fit was achieved with a fractional order which indicates that the number of desorption sites may be limited by the morphology of the sample. Earlier scanning tunneling experiments which had been carried out at room temperature (see Refs. [28,19], and the inset of Fig. 7) have proven the existence of nanocrystallites on a variety of metallic substrates after a intermediate annealing step. The temperature of the annealing step was 500– 520 K which is in the same range when the desorption starts. At this time, the sample might look like in Fig. 6a: the whole surface is covered by several layers of PTCDA – the mean coverage might be ten layers. Due to the annealing process some crystals have formed. Their height is maybe 30–100 layers, but they cover only a small fraction of the total surface area. Therefore, their contribution to the desorption signal is small. Most of the particles detected by the mass spectrometer have their origin in the multilayer. While increasing the temperature the whole multilayer desorbs (see 6b). Although the desorption from the crystal phase is described by the same parameters than the one from the multilayer (see below), there are still crystals left on the surface. The number of layers desorbed from the crystals and the multilayer are the same, but the crystals are much thicker. Even after the desorption of the second layer, which has – as shown in chapter 3.1 – a higher activation energy for desorption, there are still crystals on the surface. As sketched in Fig. 6d the crystal with the largest height will remain the longest time on the surface. The desorption signal from an individual crystal will drop abruptly to zero once all the particles from the crystal have desorbed. So the desorption traces from an individual crystal can be described by a zeroth order process as we have found for the multilayer. As every crystal contains a different amount of molecules the maxima of the individual peaks appear at different temperatures. The total signal measured by the mass spectrometer is a superposition of all desorption traces of the individual crystals. As more and more crystals have desorbed the total signal from this phase will drop smoothly. Based on Fig. 6 one can make up a simple mathematical model to describe the spectra displayed in Fig. 2. The most crucial assumption is that the second layer, the multilayer and the crystal phase behave totally independent. We will have the contribution Isecond layer from the second layer of PTCDA on Cu(1 1 1), Imulitlayer from the thick film, and Icrystal from the crystal phase. They all sum up to the total particle current Itotal measured by the mass spectrometer:
Itotal ¼ Isecond
layer
þ Imultilayer þ Icrystal
ð7Þ
Especially, we will neglect every mass transport between these three and assume that there are already nanocrystals on the surface.
2nd layer substrate
c
1st layer substrate
d
1st layer substrate
e
1st layer substrate Fig. 6. The sequence of sketches shows different states of the desorption experiment. In state (a), represents the stage with the lowest temperature, the major contribution in the desorption spectrum comes from the multilayer. Once the multilayer has desorbed (see (b)) the signal from the close-packed second layer dominates the spectrum. In the third state (c) there is only from a distribution of crystals. As not all crystals have the same height, some have desorbed already totally whereas others needs longer. (e) Represents the sample after the desorption experiment. The sample is at the final temperature. Only the first layer is left on the substrate. Within the carton the density of the crystallites and their slopes are exaggerated to focus on the main ideas.
This is in contrast to the experimental findings which have shown that the crystals (on noble metal surfaces) are grown by annealing the surface. But to include the interlayer mass transport one would
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tion. Within the STM image quite some pixels are found which are even higher than the Gaussian distribution. These additional peaks can be related to the contribution of individual crystals to the histogram. We will use the mean height h crystal and the standard deviation r to describe the height distribution. The area covered by the crystal is now calculated as:
Acrystal ¼ Acrystal t¼0
Fig. 7. The histogram represents the height distribution of the STM images shown as inset. The STM images has a size of 1400 nm 1400 nm and was acquired on a Cu(1 1 0) single crystal covered by PTCDA nanocrystals (see Ref. [19] for details). The first maximum in the histogram is given by the mean height of the multilayer, the second by the crystals. One can fit the second peak by a Gaussian distribution.
Z
1
0
Edes;second layer / exp kb T ! Acrystal t¼0 Edes;multilayer exp Imultilayer / 1 Atotal kb T Acrystal Edes;multilayer Icrystal / exp Atotal kb T
Isecond
layer
ð8Þ
The difference between Imultilayer and Icrystal in Eq. (8) is given by the area which contributes to the desorption. As only the area Acrystal is covered by crystals there is the additional weight factor
Acrystal . Atotal
Atotal is the total area of the sample covered by molecules. In addition, this is equal to the area covered by the second layer. So the weight factor for the second layer is one. At the beginning of the desorption experiment the following equation holds:
Atotal ¼ Amultilayer þ Acrystal t¼0
ð9Þ
This equation implies that the ‘active’ area for desorption from the crystals is equal to the projected area of the crystals. The actual area from which the desorption of the crystals takes place is bigger. As the angle of the facets with respect to the surface is in the range of 15–30° the actual error is less than 15% [28,18]. In Fig. 6 (and the mathematical model) the desorption from the facets is neglected. The molecules will only desorb from the top layer. At the limit of the top layer the crystals plunge down vertically. So the projected surface is equal to the area of the top layer. The weight factor for Imultilayer is a constant (for a specific sample) whereas the one for Icrystal is time dependent. In order to evaluate Acrystal ðtÞ we need to know the height distribution of the crystals. In Fig. 7 a histogram of a large area STM scan of a crystaline PTCDA film on Cu(1 1 0) is shown. The peak which can be attributed to the top layers of the nanocrystals can be fitted by a Gaussian distribu-
ð10Þ
The integral is limited to positive values of h to account only for existing crystals. Crystals with a zero or negative height have desorbed already. The molecules desorb form the crystals layer by layer, meaning the number of layers desorbing per time at a certain temperature is the same for a high and a low crystal. Therefore, the Gaussian distribution will move to negative h, so that the standard deviation r is constant whereas the mean height h crystal is a function of time and temperature. If q is the density of the molecules and N crystal the total number of molecules bound within the crystal phase, one can write the volume of the crystal phase as:
V crystal ¼ Acrystal h crystal ¼ need to perform Monte Carlo simulations [44–49] which is beyond the scope of this paper. To simplify the model (and to keep the number of parameters low) we will assume that the physical processes of the desorption from the multilayer and the crystal phase are the same. We will assume the same order of the process, the same pre-exponential factor m and the same activation energy Edes . This is satisfied by the fact that the formation of the crystals might be promoted only by a small energy gain with respect to the multilayer.
2 hh crystal exp 12 r pffiffiffiffiffiffiffi dh 2pr
Ncrystal
q
ð11Þ
This equation is formally only correct in the limit of vertical facets as shown in Fig. 6. As the area Acrystal changes much slower than the mean height h crystal one can approximate for a single time step:
@h dNcrystal =dt m Edes crystal ¼ exp @t qAcrystal qAcrystal kb T
ð12Þ
Finally, Eqs. (8)–(12) are the basis to simulate the thermal desorption spectra. We used the values for the desorption energy and the pre-exponential factor evaluated in Section 3.1. The numerical algorithm which was implemented in Microcal OriginC needs the amount of molecules in the second layer, the multilayer and the crystal phase as input. Furthermore, it requires the fraction of the sample covered by crystals and the standard deviation of the height distribution. The five variables had been optimized in order to minimize quadratic deviation. Fig. 8 shows an example for the good agreement between the data and the simulated spectrum. The area under the experimental data is equal to 11.2 close-packed layers of PTCDA. The simulation provides that the second layer is totally closed. Within the multilayer an equivalent of 6.6 close-packed layers is bound. Although only 3.6% of the surface is covered with nanocrystals, the amount of molecules in the crystal phase is equivalent to 3.0 close-packed layers which is about a quarter of the desorbing molecules. STM findings for a similar initial coverage support that crystallites at this coverage are very seldom – one within the scan range (about 100 lm2). The STM measurements carried out earlier also confirm that for an initial coverage of about 10 layers crystals can be found with a height of about 100 layers. A summary of the parameters used to fit the experimental data is given in Fig. 9. As expected the mean height of the crystals, the width of the Gaussian distribution, and the area covered by crystals increases with the total coverage. The diagram compares also two different experimental series. Whereas the data within each series are more or less consistent there is a significant difference between both: Within the first series (dataset 1) higher crystals are found which cover a smaller part of the surface compared to the second series (dataset 2). By multiplying the area covered by the crystals by their mean height one finds that for both series about 25% the material is found in the crystal phase if the initial coverage is higher than about 4 monolayer.
Th. Wagner et al. / Surface Science 603 (2009) 482–490
489
crystal phase is shifted to higher temperatures. In Fig. 9 the data points of this particular spectrum are given by an unusual high mean height h crystal of the crystals whereas the area covered by crystals seems to be lower than the expected one. The reason might be the annealing of the single crystal which had been longer than usual so that the surface roughness was decreased. 4. Summary and conclusions
Fig. 8. Simulation of an individual thermal desorption spectra of PTCDA on Cu(1 1 1). The parameters for the signal of the multilayer and the second layer had been taken from the evaluation algorithm presented in Section 3.1. The thickness of the layers was adjusted to the data: hsecond layer ¼ 1 layer, hmultilayer ¼ 6:8 layer, and h crystal ¼ 82 layer with a standard deviation of 30 layer. 3.6% of the sample area had been assumed to be covered by the crystal phase.
One can understand this by taking the number of nucleation centers into account: The density of the nucleation centers is reciprocal to the size of capture zone around nucleation center from where molecules contribute to the growth of an individual crystal [50]. For dataset 1 the number of nucleation centers, e.g. defects, step edges and adsorbates, is lower than for dataset 2. Therefore, fewer crystals grow which become higher. Actually, both series have been carried out with the same Cu(1 1 1) single crystal, but between both experiments maybe 50–100 additional cycles of sputtering and annealing have been applied to the crystal. Due to the ‘aging’ of the sample the number of steps in the second experimental run was surely increased. The explanation holds also for the spectrum representing an initial coverage of 7.0 monolayers in Fig. 2. Here, the signal of the
We have successfully analysed different features within complex thermal desorption spectra of the organic molecule PTCDA on Cu(1 1 1). Therefore, we have extended an algorithm originally proposed by Nieskens et al. and Tait et al. to the case of an completely unknown pre-exponential factor m and an uncalibrated mass spectrometer. The evaluation of the data shows that the interaction with the substrate changes the activation barrier for desorption. Whereas the first layer was bound so strongly that it was possible to desorb it, the second layer shows a higher desorption energy than the thick film. We have given an estimate for the pre-exponential factor which was also confirmed by transition state theory. The preexponential factor is six orders of magnitude higher than the one which is usually discussed in the surface phonon model. In agreement with this, the activation energy for the desorption is higher than the one found for PTCDA on Cu(1 0 0) in the literature. In addition, we have found a third feature in the spectra which can be attributed to a phase consisting of small nanocrystals. The analysis of the position and the shape of the desorption trace allows us to determine the height distribution of the nanocrystals. It was also shown, that defects on the surface have an impact on the size distribution of the nanocrystals. Although the numerical algorithm which was used to simulate the spectra does not include the interchange of particles between the second layer, the multilayer and the crystal phase it still describes the spectra very well. The fact that is was possible to use the same parameters to describe the desorption process of the multilayer and the crystal phase may indicate that there is only a small gain in energy for a single molecule by joining a crystallite.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] Fig. 9. Results of the simulation of the thermal desorption spectra. The upper diagram shows the mean height h crystal as a function of the initial coverage. The error bars indicate the width of the Gaussian distribution. In the lower panel the relative area
Acrystal Atotal
is plotted. Both diagram contain the data of two different experimental
series. The lines indicate a linear fit of the data points. The data points representing the 7.0 monolayer spectrum in Fig. 2 are highlighted by a gray background.
[17] [18] [19] [20]
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Analysis of complex thermal desorption spectra: PTCDA on copper Th. Wagner *, H. Karacuban, R. Möller Universität Duisburg-Essen, Center for Nanointegration Duisburg-Essen, Lotharstr. 1-21, 47057 Duisburg, Germany
a r t i c l e
i n f o
Article history: Received 2 September 2008 Accepted for publication 5 December 2008 Available online 16 December 2008 Keywords: Thermal desorption spectroscopy (TDS) 3,4,9,10-Perylene-tetracarboxylicdianhydride (PTCDA) Organic nanocrystals Growth
a b s t r a c t Organic molecules often show very complex thermal desorption spectra. If there is an ordered structure the activation energy for desorption Edes will decrease within the first few layers because of the decreasing van der Waals interaction between molecules and substrate. This is specially true for the system 3,4,9,10-perylene-tetracarboxylic-dianhydride (PTCDA) on Cu(1 1 1). The thermal desorption spectra for this particular system consist of three different signals which can be attributed to the second layer, the multilayer and a phase consisting of nanocrystals. We did not see any desorption from the first layer of PTCDA on Cu(1 1 1). In the first part of this paper, we will outline a numerical algorithm to evaluate the spectra with respect to the desorption energy of the second layer (Edes;secondlayer ¼ 2:35 eV) and the multilayer (Edes;multilayer ¼ 2:2 eV). In agreement with the transition state theory, we found a pre-exponential factor of 4 1019 s1 . Furthermore, we will show that nanocrystals have a contribution to the thermal desorption spectra different from the one of the multilayer. By evaluation of the third, high temperature signal it is possible to get parameters which describe the distribution of the nanocrystals and therefore gain further understanding of their growth. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction The growth of thin, ordered layers is technologically very important. Therefore, people try to gain insight into the adsorption and diffusion processes on the surface. The time reversal process of the adsorption is the desorption. Due to the reversibility one is tempted to study the desorption of particles to understand the fundamental processes taking place on the surface while 2D islands or 3D crystals are forming on the surface. Especially, thermal desorption spectroscopy (TDS, or thermal programmed desorption (TPD), see Ref. [1]) is meant to be a simple experiment to study surface kinetics: One only has to detect the particles desorbing from the surface as a function of temperature and time while the temperature of the sample is increased linearly. Despite of the intensive use of TDS to determine rate data, the interpretation of these experiments with respect to binding energies is still controversial – not only because the binding energy is not always equivalent to the activation energy for desorption. In the past, several algorithms have been discussed which are based on the Polanyi–Wigner model [2]: E dN des ¼ mðNÞ Nn e kb T dt
ð1Þ
* Corresponding author. Present Address: Institut für Experimentalphysik, Johannes Kepler Universität Linz, Altenbergerstr. 69, A-4040 Linz, Austria. E-mail address: [email protected] (Th. Wagner). URL: http://www.exp.physik.uni-due.de/moeller (R. Möller). 0039-6028/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2008.12.007
In this rate equation the number of adsorbed particles is given by N kb is the Boltzmann constant, whereas T is the temperature. The activation energy for desorption is given by Edes . In general the pre-exponential factor m is a function of the coverage. n represents the order of the process. Redhead [3] derived from Eq. (1) a relation between the maximum of the desorption trace and the activation energy. Redhead’s equation looks very handy but can only be applied to first order processes and needs the additional knowledge of the pre-exponential factor. The leading edge analysis [4] or Arrhenius plot can be used in principle to get the activation energy for desorption Edes and the pre-exponential factor m but is useless for peaks which are superimposed. The complete analysis [4] does not assume any dependency of m and Edes to the coverage but relies on a huge number of high quality data with a sufficient signal to noise ratio. Especially, if there are several contributions to the desorption spectra one is tempted to simulate the spectra by the numerical integration of Eq. (1). Although one can reproduce the spectra very well the simulation does not produce reliable values for Edes and m because they are highly correlated [5]. See Refs. [6,7] for a detailed discussion of the different approaches. Within this paper we want to evaluate our thermal desorption spectra following the ideas presented by Nieskens et al. [7] and Tait et al. [8] who rewrite the Polanyi–Wigner equation so that the activation energy of desorption Edes becomes a function of the number of adsorbed particles. We will simplify the numerical algorithm by assuming that the desorption of thick layers is not dependent on the coverage. We will confirm our experimental value for the pre-exponential factor by transition state theory.
Th. Wagner et al. / Surface Science 603 (2009) 482–490
Fig. 1. Residual gas spectrum of the PTCDA source which was held at 573 K.
Due to the relevance on catalytic processes most thermal desorption experiments focus on small molecules. Only a few quantitative studies on the desorption of organic molecules have been carried out so far, e.g. linear and cyclic n-alkenes [9,8] and oligo phenylenes [10–12]. Gonella et al. [13] have studied the effect of the inter-adsorbate repulsion of tetracene which was adsorbed on Ag(1 1 1). For samples covered by a multilayer they also found different desorption peaks which they have attributed to crystallites having different structures and morphologies. 3,4,9,10-Perylene-tetracarboxylic-dianhydride (PTCDA) (see inset of Fig. 1) is a well-known organic semiconductor for which the growth on a variety of substrates was studied intensively by direct imaging techniques (see Ref. [14] for a recent review). By means of STM [15] and nc-AFM [16] it was shown that the first two layers of PTCDA on Cu(1 1 1) both exhibit a herringbone structure but the electronic and geometric properties differ for these two layers. This can be attributed to the decreasing influence of the substrate. Schuerlein and Armstrong [17] have shown thermal desorption spectra of PTCDA on Cu(1 0 0) suggesting a third phase in addition to the desorption of the second layer and the thin film. Kilian et al. [18] presented thermal desorption data of PTCDA on Ag(1 1 1) which only exhibit two features. Although it is known for long that PTCDA grows on most surfaces in the Stranski–Kastranov mode (see Ref. [19], exception alkali halogenides [20,21]) only recent studies, e.g. Refs. [18,22–25], focus on the growth mechanism and the size distribution of these nanocrystallites. The present paper will contribute to this ongoing work by analysing the desorption traces originated from small organic nanocrystallites on the surface.
483
tor was degassed for several hours slightly below the evaporation temperature of the PTCDA. Fig. 1 shows a typical mass spectrum just before the preparation of a PTCDA film. The assignment of the mass peaks corresponds to Ref. [26]. The manipulator can be rotated so that the sample is facing to the PTCDA source or to the mass spectrometer. A movable aperture is mounted in front of the single crystal to avoid the adsorption of molecules on the sample holder (Omicron type). Such a contamination may lead to artifacts in the thermal desorption spectra. While preparing the PTCDA films the aperture was in the front of the copper single crystals so that only a circular spot with a diameter of about 5 mm was exposed to the source. During the evaporation the mass spectrometer was used to monitor the particle flux (at mass 392 amu) from the evaporator. The time integral of the mass spectrometer signal was used as the initial coverage. Before the desorption experiment the aperture had been moved so that it was not in the field of view of the mass spectrometer. In addition, the aperture was connected to a liquid nitrogen tank used to cool the whole head of the manipulator. By replacing the exposed sample by a clean one, it was tested, that the mass spectrometer does not detect any PTCDA molecules coming from the manipulator or the aperture during the desorption experiment. The heating of the single crystal was done by radiative heating. Therefore a bulb filament was mounted underneath the single crystal. For the temperature measurement a calibrated thermocouple (type K) was pressed by a spring mechanism directly to the single crystal. A PID controller (Eurotherm 815S) was used to set up a temperature ramp with slope 1 K s1. Within each series the coverage was increased from below 1 monolayer to several layers. During the desorption experiment not only the intact molecules was monitored by the mass spectrometer but also some known fragments as shown in Fig. 1. During the desorption experiments the ratio between the PTCDA fragments was found to be constant. Therefore, only the mass 392 u corresponding to the intact PTCDA molecule will be plotted within this paper. 3. Results Fig. 2 shows a typical set of spectra acquired for a Cu(1 1 1) surface covered with different amounts of PTCDA. For the coverage of
2. Experimental details The experiments were carried out in an ultra high vacuum (UHV) system with a base pressure below 1 109 mbar. The vacuum system is equipped with an Argon ion source (1.5 kV, 20 lA cm2), a quadrupole mass spectrometer (Pfeiffer Vacuum, QMG422 with a cross-beam ion source) and a temperature variable manipulator. The home build PTCDA source is mounted opposite to the mass spectrometer. Cu(1 1 1) and Cu(1 0 0) single crystals (diameter 8 mm) were used as samples. The sequence of sputtering (15 min) and annealing (1 h at 820 K) was repeated until no significant traces of impurities had been found by means of XPS and STM. Between the thermal desorption cycles only one sputter and anneal cycle was required. The commercially available PTCDA was pre-purified by gradient sublimation before inserted into vacuum. Afterwards the evapora-
Fig. 2. Series of thermal desorption spectra acquired with increasing amount of PTCDA on Cu(1 1 1). The slope of the temperature ramp was 1 K s1. The plotted mass represents the intact PTCDA molecule. Although the full range of the temperature is 300-800 K only the non-zero part was plotted. For reasons of a better visibility offsets are applied to the individual spectra.
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0.4 monolayer, the spectrum is given just by noise. Only for coverages above an equivalent of one close-packed layer desorbing molecules are detected. At first – for low coverages – a signal in the temperature range between 520 and 573 K appears in the spectra. If the signal is not superimposed by others, which are discussed later on, the leading edges of these signals, which can be described by an exponential function, fall together. The maximum is followed by a sharp drop to the noise limit. It is shifting to higher temperatures with increasing coverage until it reached the limit of 573 K. This behavior is typical for the desorption process of zeroth order from a well defined, close-packed layer. In particular, the area under the saturated peak was assumed to be equivalent to 1 monolayer. The evaporator was then calibrated by taking the linear slope in Fig. 3 into account. In addition, we confirmed the calibration by means of STM. If more than an equivalent of two close-packed layers is deposited on the surface a second peak appears in the thermal desorption spectra (see Figs. 2 and 3). The leading edge of the peak is located at about 470 K and is given by an exponential slope. Again for all spectra acquired for different initial coverages the leading edges of this signal fall together. After reaching the maximum there is sharp drop to the noise level. The maximum of the peak is continuously shifting to higher temperatures if the coverage is increased. Especially, there is no saturation. The signal can be attributed to the desorption from the third and higher layers. The peak shape is also typical for a desorption process of zeroth order. As the peak appears before the low coverage peak saturates one can assume that the third layer starts growing before the second layer is closed. This is in agreement with the findings of Fendrich and Krug [27] who have shown by force field calculations that there is an Ehrlich–Schwoebel effect for PTCDA. While dosing more than an equivalent of four close-packed layers a third peak at the high temperature end of the spectra appears. The maximum for the peak is located around 580 K. In contrast to the earlier discussed peaks this one has a roundish maximum. We will discuss this peak in Section 3.4 as desorption trace of nanocrystals which had been described by STM [28,19] earlier. We want to put some attention to the spectrum with an initial coverage of seven close-packed layers (see Fig. 2). Whereas the peak which can be attributed to the second layer and the thick film behave as in the other spectra the third peak which resembles the
exposure of PTCDA / close-packed layers 0
2
4
6
8
10
12
20
14
16
desorption of PTCDA / arb. units
14 15
12 ×5
10
10 8
×25
6 5
4 2
desorption of PTCDA / close-packed layers
16
0
0 0
5
10
15
20
exposure of PTCDA / arb. units Fig. 3. The graph compares the amount of molecules which had been prepared on the surface before the TDS experiment with the area under the thermal desorption spectra shown in Fig. 2. The exposure of PTCDA was calculated as the integrated flux detected during the film preparation.
signal from the crystal phase is shifted to a higher temperature. We found the jumping of this particular desorption trace also in other experimental runs. As described in Section 2 we can ensure that this signal is due to desorption of PTCDA from the sample and not from the sample holder or similar. While repeating the experiment with the same initial coverage the maximum of this peak may shift by 10 K whereas the other peaks keep their positions. In Section 3.4 we will be able to relate this behavior to the morphology of the sample. The fact that there is no desorption from the first layer of PTCDA on Cu(1 1 1) is also supported by Fig. 3. In the diagram the integrated flux during the desorption process is plotted against the integrated flux during the preparation. Until an equivalent coverage of 1.8 close-packed layers is dosed to the surface there is nearly no desorption. Starting from this coverage one can fit the data points by a linear function. The smooth change of the slope also explains the slight shift to higher coverages for the turning point. In addition, scanning probe measurements [16,15] show that the density of at least the first two or three layers of PTCDA is dependent on the distance to the copper surface indicating a strong interaction of the first layers to the substrate. By X-ray standing wave (XSW) Gerlach et al. [29] showed that on Cu(1 1 1) the PTCDA molecules within the first layer are bended. They also found a reduced distance between substrate and first layer compared to adjacent [1 0 2] planes in the bulk. This usually indicates a very strong interaction of the first layer with the substrate. 3.1. Desorption energy of defined layers Nieskens et al. [7] and Tait et al. [30] suggested a new way to analyse thermal desorption spectra. Both authors start from the Polanyi–Wigner rate equation (see Eq. (1) and Ref. [2] for details). is proporIn the limit of a high pumping speed, the derivative dN dt tional to the partial pressure p which is itself proportional to the current I at the detector of the mass spectrometer. Assuming a desorption process of zeroth order one can rewrite Eq. (1) as follows: E
kdesT
IðTÞ ¼ I0 hðNÞ e
b
ð2Þ
For simplicity we will only describe the case of zeroth order desorption which is given for at least two of the three signals in Fig. 2. However, the algorithm can be extended to an arbitrary order of the desorption process. The heavy-side function hðNÞ considers that the number of adsorbed particles N is finite. The factor I0 takes the pre-exponential factor m of the original Polanyi–Wigner equation into account. It also includes the sensitivity of the mass spectrometer and the slope of the temperature ramp. As at least the sensitivity of the mass spectrometer is unknown, we do not want to give it a physical interpretation other than being an arbitrary but fixed value for a specific adsorbate and the experimental setup. As long as N P 0 one can rewrite Eq. (2) so that Edes becomes a function of the temperature T and the current I measured by the mass spectrometer:
Edes ¼ kb T ½lnðIÞ lnðI0 Þ
ð3Þ
This equation gives only a physical value for Edes if one uses the correct value for the pre-exponential factor m, respectively, I0 . Nieskens et al. [7] suggested to use DFT calculations to get the pre-exponential factor. Tait et al. [30] propose a self consistent fit algorithm, but they are using a calibrated QMS. In our case, none of these options is applicable. Therefore, we will assume that the pre-exponential factor and the activation energy for desorption are constant if the coverage is higher than 3 monolayers. This can be justified by the fact that the molecules in the third and higher layers do not interact any more with the substrate. In this particular case the plot of Eq. (3)
Th. Wagner et al. / Surface Science 603 (2009) 482–490
8
6
I0 overestimated
-9
3
7
current I (of QMS) / 10 A
kbT*(ln(I)-ln( 0)) / eV
4
5 Edes,2nd layer=2.32 eV 2
4
Edes,multilayer=2.20 eV 3 best fit 2
1 I0 underestimated 0 300
400
1
500
600
700
0 800
temperature / K Fig. 4. The graph shows a thermal desorption spectrum of 12.7 monolayer PTCDA on Cu(1 1 1) which had been transformed by Eq. (3) and different values for I0 . The region which is highlighted in gray indicates the part of the spectrum which was used to optimize the parameter I0 .
485
had been tested. The fact that the peak of the crystal phase overlaps with the signal from the second layer limits the number of data points representing only the signal from the crystal phase. Therefore it is hard to decide for which combination of I0 and n the described procedure gives a horizontal line for the region of that peak. Maybe the best results were obtained for n ¼ 1=2 and n ¼ 2=3 which can be interpreted as the desorption from step edges and, respectively, as the desorption from nanocrystals. In general, a fractional number n indicates a desorption from a non-flat surface (3D crystal) or that the particles can desorb only from parts of the surface (e.g. defects). For example, Shimada et al. [34] used n ¼ 2=3 to fit the desorption spectra of vandyl phthalocyanine (VOPc) on KBr(0 0 1). Their interpretation is that 2 the area from which the molecules desorb scales with N3 (N the number of molecules on the surface). The problem is to find an appropriate scaling factor which has to consider the geometrical aspects of the surface. As the position of the crystal phase peak is not fixed – see Fig. 2, spectrum for 7 monolayers – also the geometry of the surface (number and size of crystals) may have changed. In Section 3.4 we will present an algorithm which also can extract the size distribution of the crystal from the thermal desorption data. 3.2. Comparison with other copper surfaces
should give a horizontal line in the region of the spectra where the signal from the multilayer dominates. For each spectra the parameter I0 was optimized so that the resulting plots fulfill this condition. The mean values of all spectra is given by I0 ¼ 9:0 1011 A. The corresponding statistical standard error is 3:6 1011 A. This value for I0 was taken to evaluate the spectra according to the activation energy for desorption. As shown in Fig. 4, there is a plateau in the part of the spectra which corresponds to the thick film. The level of the plateau is – averaged over all spectra – 2.20 eV which is the activation energy for desorption of the multilayer. The fact that the transformed spectra in the gray region is given by a horizontal line confirms that the desorption can be described by a zeroth order process. Nevertheless, we cannot exclude that the activation energy for desorption and the pre-exponential factor are related as some authors discuss [31,32,7]. At the point in Fig. 4 where the peak of the multilayer drops, there is a step up by 0.12 eV in the transformed spectrum. The level of the plateau is 2.32 eV which can be interpreted as the activation energy for a zeroth order desorption process for the second layer. The averaged value is 2.35 eV. The conclusion holds only if one assumes the same pre-exponential factor for the multilayer and the monolayer. As the peak of the second layer is superimposed by that one of the later discussed crystal phase, one can not decide if this assumption is actually justified for the particular spectrum shown in Fig. 4. But spectra with a coverage below 4 monolayers show also a plateau for the second monolayer. As predicted the activation energy for desorption is smaller for the multilayer as for the second layer and, especially, the first layer from which no desorption was observed. This confirms that the first layer of PTCDA on the copper is interacting strongly with the substrate. The influence of the substrate will decrease within three layer so that it is neglectable. At least for the first layer of PTCDA on Cu(1 1 1) the interaction between substrate and molecules is very strong as supported by XSW and photoelectron spectroscopy (UPS/XPS). Schreiber et al. [29,33] report a smaller bonding distance of PTCDA on Cu(1 1 1) (0.266 nm) than the stacking distance dð102Þ ¼ 0:321 nm. In addition, the PTCDA within the first adsorbate layer are bended and molecular orbitals are shifted. The evaluation of the third peak which is attributed to the crystal phase is in principle also possible with the outlined algorithm. Therefore we varied not only the parameter I0 but also the order n of the desorption process. Especially, values for n between 0 and 1
For comparison, we also carried out the thermal desorption experiment on Cu(1 0 0) (not shown in detail here) and Cu(1 1 1) with many structural defects. We prepared the latter one by sputtering the Cu(1 1 1) surface as usually but skipping the later annealing step. A so prepared surface should consist of a very high but somehow fixed density of step edges, small facets and so on. Fig. 5 shows a series of spectra on surface with the increased amount of structural defects. For a coverage below 3 monolayers (we used the same calibration of the source as for the well prepared Cu(1 1 1)) almost no signal is detected. Only by enlarging the y-scale a very broad peak is visible between 550 and 650 K. At an initial coverage of 3 monolayers the integral of this signal is constant. As the peak appears already for low coverages and saturates we can interpret this as the desorption from a finite number
Fig. 5. The water fall plot shows thermal desorption spectra of PTCDA on Cu(1 1 1) surface with an increased amount of structural defects. The surface actually was a Cu(1 1 1) single crystal which was sputtered but not annealed. The spectra have been acquired for different initial coverages (as indicated at the curves) and with a fixed temperature ramp of 1 K s1. The inset shows the spectra with an initial coverage of 2.7 monolayer und 3.7 monolayer with an three times enlarged ordinate.
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of adsorption sites. These might be given by defects which had been produced by the sputtering process. As there are many different kinds of possible facets, step edges and vacancies (or adatoms) with different activation energies for desorption, the peak – actually interpreted as a superposition of several peaks – appears very broad. The desorption trace from the multilayer and the one from the crystal phase behave for well prepared Cu(1 1 1) and sputtered one the same. The signal from the multilayer shows the typical behavior of a zeroth order peak as discussed before. Therefore, the same data processing as for the Cu(1 1 1)-spectra was applied to it. The analysis produces a parameter I0 in the same order of magnitude as for the annealed Cu(1 1 1). The overall analysis gives a activation energy for desorption Edes;multilayer ¼ 2:21 eV. As already concluded from the similarity of the peak position and the peak shape the desorption energy of the multilayer is (almost) equal to the one found for the annealed surface. Table 1 summarizes the findings for the different copper surfaces. It also includes the desorption energy of a second layer of PTCDA on Cu(1 0 0). One can see that the molecules of the second layer on Cu(1 0 0) have to overcome a slightly lower barrier than the ones on the annealed Cu(1 1 1). Nevertheless, the values are the same if taking the experimental error into account, so that we think that the downshift of 0.04 eV is not significant but due to experimental uncertainness. Yim et al. [35] have calculated the interaction energy of an individual PTCDA molecule moving on top of a close-packed but stepped layer of PTCDA by taking van der Waals forces into account. The value of 2.15 eV which agrees very well with our findings is given by the minima in the potential map on the terrace. This value represents the potential energy for a molecule which can move freely in two dimensions on the surface. As there would be an additional interaction with other molecules in the same layer if the molecules would desorb from a step edge or a kink the good agreement between force field calculations and our results may indicate that the desorption takes place from a 2D gas phase. We will come back to this in the following section. Schuerlein et al. [17] showed some thermal desorption spectra of PTCDA on Cu(1 0 0). They extracted from their spectra a desorption energy of 1.54 eV for the second layer and 1.48 eV for the multilayer. Unfortunately, they do not state how they have obtained the values in detail. We assume that they fitted the spectra with a fixed pre-exponential factor of m ¼ 1 1013 s1 . By doing so, the pre-exponential factor is interpreted as a typical surface phonon frequency. A couple of papers [36,9,8,37] on the desorption of cyclic and linear n-alkanes show that the pre-exponential factor strongly depends on the adsorbate and can vary several orders of magnitude. We also evaluated our data by the leading edge method. The averaged values produced by this had been systematically by about 0.2 eV lower compared to the ones in Table 1. In addition, the standard deviation for the activation energy of desorption evaluated by
Table 1 The table compares the activation energies for desorption of PTCDA on different copper surfaces. The data have been evaluated by the described algorithm with n ¼ 0 and I0 ¼ 9:0 1013 A. In addition, the last two rows represent data from the literature. The value of PTCDA on PTCDA is taken from a paper by Yim et al. [35]. The values represent the minima in the potential map while a single PTCDA molecules is moved on an close-packed PTCDA structure. Edes;second Cu(1 1 1) Sputtered Cu(1 1 1) Cu(1 0 0) Cu(1 0 0) [17] PTCDA [35]
layer
2.35 ± 0.20 2.31 ± 0.20 1.54
(eV)
Edes;multilayer (eV) 2.20 ± 0.20 2.21 1.48 2.15
the leading edge method is more than a factor of two larger than the one of the described algorithm. At a first glance, this is surprising because our algorithm and the leading edge method are correlated. On the other hand our algorithm puts less statistical weight on the data points of the noisy background as seen in Fig. 4. 3.3. Pre-exponential factor
m
In principle, the evaluation procedure described before is capable to produce a meaningful value for the pre-exponential factor m. But this is only possible if the mass spectrometer is fully calibrated. Especially, this includes the knowledge of the sensitivity for the particular molecular species. Usually, this is not the case. Therefore, we have used the current I0 instead of m. Eq. (1) describes the desorption process on the microscopic scale without the contribution of any instrumental parameter. By a simple curve sketching for the case n ¼ 0 and a saturated layer one finds the following relation between the temperature T max at which the maximum of the curve occurs and the pre-exponential factor m:
m¼b
Edes;second
layer
kb T 2max
exp
Edes;second layer kb T max
ð4Þ
b = 1 K s1 is slope of the linear temperature ramp used in the experiments. As marked in Fig. 2 the signal of the saturated second layer produces a maximum in the desorption spectra at T max ¼ 573 K. In the particular case of PTCDA on Cu(1 1 1) Eq. (4) yields m ¼ 4 1019 s1 . According to the transition state theory (TST) [38] the pre-exponential factor can be written as:
mTST ¼
kb T qz h qads
ð5Þ
where qads and qz are single-particle partition functions for the adsorbed (initial) and the transition state, respectively, calculated at the temperature T. We will neglect effects of conformational entropy and assume rigid molecules. In order to simplify the calculation of the partition functions, the transition state is given by the gas phase molecules, which can be described by a 3D rotator. Furthermore, we make the assumption that the molecules have free translation on the surface, i.e. they behave translationaly like a 2D gas, but that all rotation is prohibited. The last argument may be justified by the fact that the desorption process is described by a zeroth order process which is quite unusual for a close-packed layer. In general, this is explained by a two phase model [39–42]: The desorption itself takes place from a dilute, 2D gas-like phase which covers the whole sample. A second, condensed phase acts as an reservoir for the gas phase to maintain a constant number of particles in the dilute phase. By taking the above mentioned conditions into account, most contributions to qads and qz cancel each other so that one only has to calculate the rotational partition function of the molecule in the transition state:
qrotational ¼
3 1 p 12 ð8kb TÞ2 ðIx Iy Iz Þ2 rh3
ð6Þ
Within this equation Ix , Iy and Iz represent the moments of inertia of the molecule. The symmetry factor r can be thought of classically as the number of indistinguishable rotational configurations for the molecule, and so it prevents overcounting. Tait et al. [8] have successfully applied the described model to predict the chain length dependency of the pre-exponential factor of n-alkanes. For the particular case of PTCDA, we have calculated the moments of inertia by Hyperchem using the AMBER94 force field [43] for geometry optimization. The parameters used to evaluate
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Th. Wagner et al. / Surface Science 603 (2009) 482–490 Table 2 Parameters used to calculate the pre-exponential factor state theory.
a
mTST by means of transition
Ix (u nm2)
Iy (u nm2)
Iz (u nm2)
r
qrotational
mTST (s1)
12.20
57.01
69.21
6
7,590,000
9 1019
multilayer the Eqs. (5) and (6) are displayed in Table 2. The calculated value mTST ¼ 9 1019 s1 has the same order of magnitude as the experimental one. To confirm the model used for the transition state theory, one would need to vary the molecular species, e.g. by using naphthalene-tetracarboxylic-dianhydrid (NTCDA) and terrylenetetracarboxylic-dianhydrid (TTCDA) instead of PTCDA. The data are not available yet.
substrate
b
3.4. Signal from nanocrystals The contribution of the crystal phase to the desorption spectra is likely not described by simply applying Eq. (1) to the desorption spectra. The best fit was achieved with a fractional order which indicates that the number of desorption sites may be limited by the morphology of the sample. Earlier scanning tunneling experiments which had been carried out at room temperature (see Refs. [28,19], and the inset of Fig. 7) have proven the existence of nanocrystallites on a variety of metallic substrates after a intermediate annealing step. The temperature of the annealing step was 500– 520 K which is in the same range when the desorption starts. At this time, the sample might look like in Fig. 6a: the whole surface is covered by several layers of PTCDA – the mean coverage might be ten layers. Due to the annealing process some crystals have formed. Their height is maybe 30–100 layers, but they cover only a small fraction of the total surface area. Therefore, their contribution to the desorption signal is small. Most of the particles detected by the mass spectrometer have their origin in the multilayer. While increasing the temperature the whole multilayer desorbs (see 6b). Although the desorption from the crystal phase is described by the same parameters than the one from the multilayer (see below), there are still crystals left on the surface. The number of layers desorbed from the crystals and the multilayer are the same, but the crystals are much thicker. Even after the desorption of the second layer, which has – as shown in chapter 3.1 – a higher activation energy for desorption, there are still crystals on the surface. As sketched in Fig. 6d the crystal with the largest height will remain the longest time on the surface. The desorption signal from an individual crystal will drop abruptly to zero once all the particles from the crystal have desorbed. So the desorption traces from an individual crystal can be described by a zeroth order process as we have found for the multilayer. As every crystal contains a different amount of molecules the maxima of the individual peaks appear at different temperatures. The total signal measured by the mass spectrometer is a superposition of all desorption traces of the individual crystals. As more and more crystals have desorbed the total signal from this phase will drop smoothly. Based on Fig. 6 one can make up a simple mathematical model to describe the spectra displayed in Fig. 2. The most crucial assumption is that the second layer, the multilayer and the crystal phase behave totally independent. We will have the contribution Isecond layer from the second layer of PTCDA on Cu(1 1 1), Imulitlayer from the thick film, and Icrystal from the crystal phase. They all sum up to the total particle current Itotal measured by the mass spectrometer:
Itotal ¼ Isecond
layer
þ Imultilayer þ Icrystal
ð7Þ
Especially, we will neglect every mass transport between these three and assume that there are already nanocrystals on the surface.
2nd layer substrate
c
1st layer substrate
d
1st layer substrate
e
1st layer substrate Fig. 6. The sequence of sketches shows different states of the desorption experiment. In state (a), represents the stage with the lowest temperature, the major contribution in the desorption spectrum comes from the multilayer. Once the multilayer has desorbed (see (b)) the signal from the close-packed second layer dominates the spectrum. In the third state (c) there is only from a distribution of crystals. As not all crystals have the same height, some have desorbed already totally whereas others needs longer. (e) Represents the sample after the desorption experiment. The sample is at the final temperature. Only the first layer is left on the substrate. Within the carton the density of the crystallites and their slopes are exaggerated to focus on the main ideas.
This is in contrast to the experimental findings which have shown that the crystals (on noble metal surfaces) are grown by annealing the surface. But to include the interlayer mass transport one would
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tion. Within the STM image quite some pixels are found which are even higher than the Gaussian distribution. These additional peaks can be related to the contribution of individual crystals to the histogram. We will use the mean height h crystal and the standard deviation r to describe the height distribution. The area covered by the crystal is now calculated as:
Acrystal ¼ Acrystal t¼0
Fig. 7. The histogram represents the height distribution of the STM images shown as inset. The STM images has a size of 1400 nm 1400 nm and was acquired on a Cu(1 1 0) single crystal covered by PTCDA nanocrystals (see Ref. [19] for details). The first maximum in the histogram is given by the mean height of the multilayer, the second by the crystals. One can fit the second peak by a Gaussian distribution.
Z
1
0
Edes;second layer / exp kb T ! Acrystal t¼0 Edes;multilayer exp Imultilayer / 1 Atotal kb T Acrystal Edes;multilayer Icrystal / exp Atotal kb T
Isecond
layer
ð8Þ
The difference between Imultilayer and Icrystal in Eq. (8) is given by the area which contributes to the desorption. As only the area Acrystal is covered by crystals there is the additional weight factor
Acrystal . Atotal
Atotal is the total area of the sample covered by molecules. In addition, this is equal to the area covered by the second layer. So the weight factor for the second layer is one. At the beginning of the desorption experiment the following equation holds:
Atotal ¼ Amultilayer þ Acrystal t¼0
ð9Þ
This equation implies that the ‘active’ area for desorption from the crystals is equal to the projected area of the crystals. The actual area from which the desorption of the crystals takes place is bigger. As the angle of the facets with respect to the surface is in the range of 15–30° the actual error is less than 15% [28,18]. In Fig. 6 (and the mathematical model) the desorption from the facets is neglected. The molecules will only desorb from the top layer. At the limit of the top layer the crystals plunge down vertically. So the projected surface is equal to the area of the top layer. The weight factor for Imultilayer is a constant (for a specific sample) whereas the one for Icrystal is time dependent. In order to evaluate Acrystal ðtÞ we need to know the height distribution of the crystals. In Fig. 7 a histogram of a large area STM scan of a crystaline PTCDA film on Cu(1 1 0) is shown. The peak which can be attributed to the top layers of the nanocrystals can be fitted by a Gaussian distribu-
ð10Þ
The integral is limited to positive values of h to account only for existing crystals. Crystals with a zero or negative height have desorbed already. The molecules desorb form the crystals layer by layer, meaning the number of layers desorbing per time at a certain temperature is the same for a high and a low crystal. Therefore, the Gaussian distribution will move to negative h, so that the standard deviation r is constant whereas the mean height h crystal is a function of time and temperature. If q is the density of the molecules and N crystal the total number of molecules bound within the crystal phase, one can write the volume of the crystal phase as:
V crystal ¼ Acrystal h crystal ¼ need to perform Monte Carlo simulations [44–49] which is beyond the scope of this paper. To simplify the model (and to keep the number of parameters low) we will assume that the physical processes of the desorption from the multilayer and the crystal phase are the same. We will assume the same order of the process, the same pre-exponential factor m and the same activation energy Edes . This is satisfied by the fact that the formation of the crystals might be promoted only by a small energy gain with respect to the multilayer.
2 hh crystal exp 12 r pffiffiffiffiffiffiffi dh 2pr
Ncrystal
q
ð11Þ
This equation is formally only correct in the limit of vertical facets as shown in Fig. 6. As the area Acrystal changes much slower than the mean height h crystal one can approximate for a single time step:
@h dNcrystal =dt m Edes crystal ¼ exp @t qAcrystal qAcrystal kb T
ð12Þ
Finally, Eqs. (8)–(12) are the basis to simulate the thermal desorption spectra. We used the values for the desorption energy and the pre-exponential factor evaluated in Section 3.1. The numerical algorithm which was implemented in Microcal OriginC needs the amount of molecules in the second layer, the multilayer and the crystal phase as input. Furthermore, it requires the fraction of the sample covered by crystals and the standard deviation of the height distribution. The five variables had been optimized in order to minimize quadratic deviation. Fig. 8 shows an example for the good agreement between the data and the simulated spectrum. The area under the experimental data is equal to 11.2 close-packed layers of PTCDA. The simulation provides that the second layer is totally closed. Within the multilayer an equivalent of 6.6 close-packed layers is bound. Although only 3.6% of the surface is covered with nanocrystals, the amount of molecules in the crystal phase is equivalent to 3.0 close-packed layers which is about a quarter of the desorbing molecules. STM findings for a similar initial coverage support that crystallites at this coverage are very seldom – one within the scan range (about 100 lm2). The STM measurements carried out earlier also confirm that for an initial coverage of about 10 layers crystals can be found with a height of about 100 layers. A summary of the parameters used to fit the experimental data is given in Fig. 9. As expected the mean height of the crystals, the width of the Gaussian distribution, and the area covered by crystals increases with the total coverage. The diagram compares also two different experimental series. Whereas the data within each series are more or less consistent there is a significant difference between both: Within the first series (dataset 1) higher crystals are found which cover a smaller part of the surface compared to the second series (dataset 2). By multiplying the area covered by the crystals by their mean height one finds that for both series about 25% the material is found in the crystal phase if the initial coverage is higher than about 4 monolayer.
Th. Wagner et al. / Surface Science 603 (2009) 482–490
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crystal phase is shifted to higher temperatures. In Fig. 9 the data points of this particular spectrum are given by an unusual high mean height h crystal of the crystals whereas the area covered by crystals seems to be lower than the expected one. The reason might be the annealing of the single crystal which had been longer than usual so that the surface roughness was decreased. 4. Summary and conclusions
Fig. 8. Simulation of an individual thermal desorption spectra of PTCDA on Cu(1 1 1). The parameters for the signal of the multilayer and the second layer had been taken from the evaluation algorithm presented in Section 3.1. The thickness of the layers was adjusted to the data: hsecond layer ¼ 1 layer, hmultilayer ¼ 6:8 layer, and h crystal ¼ 82 layer with a standard deviation of 30 layer. 3.6% of the sample area had been assumed to be covered by the crystal phase.
One can understand this by taking the number of nucleation centers into account: The density of the nucleation centers is reciprocal to the size of capture zone around nucleation center from where molecules contribute to the growth of an individual crystal [50]. For dataset 1 the number of nucleation centers, e.g. defects, step edges and adsorbates, is lower than for dataset 2. Therefore, fewer crystals grow which become higher. Actually, both series have been carried out with the same Cu(1 1 1) single crystal, but between both experiments maybe 50–100 additional cycles of sputtering and annealing have been applied to the crystal. Due to the ‘aging’ of the sample the number of steps in the second experimental run was surely increased. The explanation holds also for the spectrum representing an initial coverage of 7.0 monolayers in Fig. 2. Here, the signal of the
We have successfully analysed different features within complex thermal desorption spectra of the organic molecule PTCDA on Cu(1 1 1). Therefore, we have extended an algorithm originally proposed by Nieskens et al. and Tait et al. to the case of an completely unknown pre-exponential factor m and an uncalibrated mass spectrometer. The evaluation of the data shows that the interaction with the substrate changes the activation barrier for desorption. Whereas the first layer was bound so strongly that it was possible to desorb it, the second layer shows a higher desorption energy than the thick film. We have given an estimate for the pre-exponential factor which was also confirmed by transition state theory. The preexponential factor is six orders of magnitude higher than the one which is usually discussed in the surface phonon model. In agreement with this, the activation energy for the desorption is higher than the one found for PTCDA on Cu(1 0 0) in the literature. In addition, we have found a third feature in the spectra which can be attributed to a phase consisting of small nanocrystals. The analysis of the position and the shape of the desorption trace allows us to determine the height distribution of the nanocrystals. It was also shown, that defects on the surface have an impact on the size distribution of the nanocrystals. Although the numerical algorithm which was used to simulate the spectra does not include the interchange of particles between the second layer, the multilayer and the crystal phase it still describes the spectra very well. The fact that is was possible to use the same parameters to describe the desorption process of the multilayer and the crystal phase may indicate that there is only a small gain in energy for a single molecule by joining a crystallite.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] Fig. 9. Results of the simulation of the thermal desorption spectra. The upper diagram shows the mean height h crystal as a function of the initial coverage. The error bars indicate the width of the Gaussian distribution. In the lower panel the relative area
Acrystal Atotal
is plotted. Both diagram contain the data of two different experimental
series. The lines indicate a linear fit of the data points. The data points representing the 7.0 monolayer spectrum in Fig. 2 are highlighted by a gray background.
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