totally erroneous at still lower powers as demonstrated in the next set of data.
Assembled in Fig. 4.4 is a similar series of signals for Ts = 2.88 K (or -24 db).
The spectra in the main figure, in common with those of 4.3, share the same qualitative shape and any differences between the two sets are quantitative issues. For example, the steep initial rise and common shoulder originating from the first particles to reach the detector occurs at slightly later times because of the effect the lower substrate temperature has on their velocity dis- tribution. Moreover, the waveforms here crest distinctly later and are somewhat broader than their counterparts in Fig. 4.3, reflecting changes in the velocity distribution as well as differences in the time evolution of desorption. In fact, full scale in this figure is about one-seventh of what it is in 4.3 on account of the slower desorption rate, and the pulse widths necessary to generate this series are significantly longer than what they are at -17 db, though still all less than the time of flight.
The inset tells a different story. For pulse widths greater than the time of flight the peak height saturates as before but the tails do not. They continue to grow and constitute a substantial portion of the total area under each waveform.
This behavior is easily interpreted in terms of the convolution of a time varying desorption rate with a fixed Green's function. If the scale of this variation is long (but not too long) compared with the width of the propagator then by the time tp becomes comparable to this width all the fast, easily desorbed particles have already contributed to the signal. The broad fall-off in the tails is the result of a much slower (perhaps nearly constant) evaporation rate from a film that has not quite yet reached steady state. If the desorption time scale were to increase further, then the ratio of peak amplitude to tail amplitude would turn in favor of the latter until, in the limit of a truly constant desorption rate, the signal would
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spectra presented in the inset to Fig. 4.4 which require further explanation. The first of these points is purely technical and concerns the sharp spike and accom- panying offset prominent at 35 and 50 µsec and also just barely noticeable at 20 µsec. There is a small but direct electromagnetic coupling between heater and bolometer in the absence of any gas in the cell that manifests itself as a pedestal of duration tp whose rise and fall is coincident with the beginning and end of the pulse. This explains the jump in the signal at t=tp as well as the initial offset of all of the spectra at t=O despite their return to the prepulse baseline at long times. The effect is presumably due to the perturbation produced by the extra
"static" magnetic field arising at the bolometer from the nearby sheet of current flowing through the heater, and is masked at higher powers by the strength of the desorption signal. A second question is why the fall-off in the signal after t=tp has such a peculiar shape and why it is not more similar to the shape exhibited by the waveforms in the main figure. The reason is that there is a finite delay between the time at which the pulse is terminated and the time when this effect is felt at the bolometer. The length of this delay reflects the velocity distribution of the fastest particles and is equal to the duration between t=O and the first onset of signal but, unlike the case of the initial shoulder, it is the slowest particles which govern the form of the subsequent decay.
An appropriate integration time emerges naturally for each of the waveforms in Fig. 4.4 (e.g., t1=35 µsec would be fine for all of the shorter pulses;
t1=70 µsec for the longer ones) and the signal area versus pulse width, with any pedestal contribution subtracted out, is plotted as the lower set of points in Fig.
4.5. Shown on the same scale for comparison are the results from an identical tp sequence - excepting the extra point at 100 nsec - at a slightly elevated sub- strate temperature, Ts
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accurately reflect differences between the two sets of data in the amount desorbed as a function of time. For example, the desorption rate, which is given by the slope of D.n(tp) vs. tp, is obviously greater at the higher substrate tempera- ture; at tp = 500 nsec about six times as much has been desorbed by the film at 3.46 K compared with what happens when it is at 2.88 K. By the time tp has increased to 50 µsec, however, this ratio has narrowed to 2:1 and the higher power area has pretty well saturated. As we saw in Fig. 4.4 though, this is not true of the -24 db data and its area continues to grow out to pulse widths of over 100 µsec. So despite large variations in the initial desorption rate, the net change in surface coverage at steady state, D.n55 , is less sensitive to substrate temperature.
Practically speaking, it is not an entirely unambiguous matter to decide, at these low power levels, whether or not the film actually has reached a steady state. This is partly due to nuisance concerns associated with long pulses, such as the possibility some energy reaches the detector via direct thermal conduction rather than through desorption, and that the signal never therefore saturates.
More to the point is the fact that, in principle, some signal must always originate from the film even when there is no net desorption. This is because atoms leav- ing the pulsed source are hotter than they would be in equilibrium, contributing an excess energy flux of 2k (T5-T 0)neq in the absence of any excess number flux.
Were we to draw a smooth curve through either set of points in Fig. 4.4, we would immediately notice something interesting, namely that neither curve intercepts the tp axis at tp=O, but that each crosses it somewhere between 50 and 100 nsec later! It's not as if we wouldn't see any signal at all for shorter pulses - we in fact do, though it's very small - rather, the extension to short times of a function whose second derivative remains of one sign (the curve we would natur- ally be lead to draw through the data) is misleading. The true D.n(tp) curve does
zero'th-order boundary layer approximation as illustrated, for example, in Fig.
3.7. If we simply imagine displacing the approximation for the film thickness as a function of time there forward until it overlaps the correct solution then we get something resembling the curve we would use to represent our data. What is missing from our plot in Fig. 4.4 is the behavior of desorption "inside the boun - dary layer" where the film temperature is still changing rapidly with time. That the 50-100 nsec "lag" we see agrees with our estimate of the combined time it takes for substrate and film to warm lends support to this conjecture.
The logarithm of the rate of change of surface coverage with time (the net desorption rate) is illustrated in Fig. 4.6 for the -20 db example of the previous figure. The values shown are actually averages of the finite difference quotients computed between each pair of points in 4.5, interpolated to the appropriate time with due regard for the unequal spacing in tp (this is done to facilitate a comparison with the second difference quotients needed to calculate T1c1(t )). An exponential with a time constant of 508 nsec gives a good fit to first five points but quickly falls below the rest of the data. The upward deflection of the desorp- tion rate from this initial extrapolation means that we have a local time constant increasing with time. As our discussion in Chapter 3 concluded, such a behavior reveals the nonlinearity of the underlying adsorption isotherm, and in particular its positive curvature, when the sticking coefficient is independent of coverage.
Our intuition about T1c1(t) is confirmed in the inset to Fig. 4.6 by direct cal- culation using the finite-difference approximation to (3.65). At short times, T 1c1
is indeed very close to the value given by the exponential fit in the main figure but it increases severalfold thereafter. As the scatter in this plot suggests, it is not easy to reliably compute ratios of first and second derivatives from
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