Desorption of He atoms from thin films may be resolved experimentally into quantum and thermal components. We show that quantum desorption becomes the dominant part of the signal in submonolayer films. We also show that, when all effects of collisions between desorbed atoms are eliminated, quantum desorption is not focused normal to the surface of optically polished sapphire crystals

Goodstein, D. L.

Maboudian, R.

Scaramuzzi, F.

Sinvani, M.

Vidali, G.

English

Caltech Authors - Main

VOLUME 54, NUMBER 18 PHYSICAL REVIEW LETTERS 6 MAY 1985 
Experiments on Quantum and Thermal Desorption from 4 ~ e  Films 
D. L. Goodstein, R. Maboudian, F. ~caramuzzi , (~)  M. ~ i n v a n i , ' ~ )  and G.  ~ i d a l i ( ~ )  
Low Temperature Physics, California Institute of Technology, Pasadena, CaliJbrnia 91125 
(Received 24 January 1985) 
Desorption of He atoms from thin films may be resolved experimentally into quantum and ther- 
mal components. We show that quantum desorption becomes the dominant part of the signal in 
submonolayer films. We also show that, when all effects of collisions between desorbed atoms are 
eliminated, quantum desorption is not focused normal to the surface of optically polished sapphire 
crystals. 
PACS numbers: 68.45.Da. 67.70.+n 
The ability to investigate experimentally an instance 
in which a transition from condensed to gaseous states 
may be related directly to a single quantum event is of 
obvious importance. Some years ago, experiments 
were reported in which ballistic phonons in crystals1 
and ballistic phonons and rotons in liquid helium2 gave 
rise, respectively, to desorption and evaporation of He 
atoms. More recently, both techniques have been re- 
fined to the point where they yielded convincing evi- 
dence of the existence of processes in which a single 
quasiparticle gave rise to a single desorbed3 or eva- 
porated atom.4 In the context of desorption, this has 
been called the phonoatomic effect. The phonoatomic 
effect is of additional interest because it is potentially 
an effective spectrometer for high-frequency phonons, 
and can be a direct probe of microscopic processes at a 
crystal surface. 
In this paper, we report experiments in which both 
the dependence of the phonoatomic effect on film 
thickness and the angular distribution of desorbed 
atoms are studied. Previously,' the phonoatomic ef- 
fect has appeared as a distinct but small ( - 5%) con- 
tribution to the total desorption normal to the surface 
plane due to a high-temperature but low-intensity 
beam of phonons. By reducing the film thickness we 
are able, in the present work, to take advantage of 
thermal desorption kineticsS to suppress thermal 
desorption and achieve signals which are dominated by 
the phonoatomic effect. We are also able, for the first 
time, to study the angular distribution of desorption 
under conditions in which the results cannot have 
been affected by collisions among the desorbing 
atoms, and in which thermal desorption may be 
separated experimentally from phonoatomic-effect 
desorption. 
Assuming translational invariance of the surface 
leads to the expectation that at a plane surface, nonin- 
teracting atoms desorbed by single phonons with ener- 
gies high compared to kBT f  ( Tf is the temperature of 
the film) will be strongly concentrated in the direction 
perpendicular to the and also that atoms 
desorbed at wider angles will have lower mean kinetic 
energies7 (the rainbow effect). These effects are a 
consequence of the condition that the interaction con- 
serves both the phonon energy and the component of 
its momentum parallel to the surface. They are ex- 
pected for phonoatomic, but not thermal desorption. 
~ a b o r e k ~  has observed the predicted effects in atoms 
desorbed directly from the surface of a heater, but 
subsequent analysis has indicated that both the angular 
focusing and the rainbow effect observed were most 
probably consequences of collisions among desorbing 
atoms8 Thus, the question of whether there is any 
kinematic focusing of desorbed atoms remains un- 
resolved. 
As a preliminary experiment, an apparatus similar to 
the one described in Ref. 3 was used. Basically, it con- 
sists of a fast heater (10-ns response time) evaporated 
on the bottom of a 1-cm-thick, optically polished sap- 
phire crystal. The phonons travel ballistically through 
the crystal and cause He atoms to desorb from a hole 
in a mask placed on the upper surface. Three bolome- 
ters at angles O = 0°, - 22", and - 45" from the nor- 
mal measure the time-of-flight (TOF) and angular dis- 
tribution. The experimental geometry and a typical 
distribution are shown in Fig. 1. The first shoulder at 
TIME ( p s e c )  
FIG. 1. Time-of-flight spectra at angles of approximately 
O 0 ,  22" ,  and 45" with respect to the surface normal (bolome- 
ters b,, bz, and bj, respectively). The inset shows the exper- 
imental geometry. The hole in the mask was 0.8 mm in di- 
ameter. The distance between the detector plane and the 
desorbing surface is 1.2 mm. The heater temperature was 
19 K calculated according to acoustic mismatch. Ambient 
temperature was 2.4 K. A typical pulse width used was 180 
ns. The chemical potential is roughly - 30 K. 
@ 1985 The American Physical Society 
VOLUME 54, NUMBER 18 P H Y S I C A L  R E V I E W  LETTERS 6 MAY 1985 
earlier times on curve bl represents atoms arriving 
with an associated temperature of about 9 f 2 K. It is 
due to atoms desorbed by substrate phonons having an 
apparent temperature of 9 K. The second peak is due 
to the process in which phonons are thermalized, rais- 
ing the temperature of the film slightly above the am- 
bient ( - 2.4 K), and thus causing thermal desorption. 
The absence of collisions in our experiment is a 
consequence of the low rate of desorption. If AN 
atoms per unit area desorb in time T ,  the approximate 
number of collisions per atom among them in subse- 
quent time t (the TOF to the detector) is V =  u AN 
x l n ( t / ~  ), where IT is the collision cross ~ e c t i o n . ~  In
Taborek's experiments, v is of order 1 (VAN = 1 per 
monolayer desorbed, and the logarithmic factor is al- 
ways - l ) .  In the present experiments, however, the 
flux of phonons to the desorbing surface is reduced by 
more than 3 orders of magnitude because of spreading 
in the crystal. As a result, AN is roughly lo3 times 
smaller, and we thus conclude that the collisions are 
far too few to influence the signal. 
Figure 2 shows the TOF measurements at 0" as a 
function of film thickness. At very low coverage (less 
than 1 monolayer) the phonoatomic peak is the princi- 
pal feature, but as the film thickness increases, a ther- 
mal peak at longer times starts to develop. Finally, at 
roughly two monolayers, we approach the results ob- 
tained previously by Sinvani and co- worker^,',^ i.e., 
01 ' 1  I I 1 I I 4 8 i 2 16 20 
TIME ( p s e c )  
FIG. 2. Time-of-flight spectra at 0' angle for four dif- 
ferent coverages with estimated chemical potentials of 
p = - 7 0  K, - 5 5  K, - 40 K, and - 30 K, reading from 
bottom to top. 
the thermal peak dominates the signal. In other 
words, we observe that, on the time scale of our heat 
pulses, photoatomic desorption dominates in thin 
films, but thermal processes become more important 
in thicker films. We return to this issue below. 
To be able to study the behavior of these two 
processes semiquantitatively as a function of chemical 
potential and angle, we have used a rough deconvolu- 
tion technique which is basically a four-parameter fit 
to the signal. The parameters are the magnitudes 
(S,) and positions (t, ) of the maxima of the phonoa- 
tomic and thermal distributions. Based on the analyses 
of Sinvani et al., the signals are given by 
xexp [ - p f , n ~ l  1 7-7 t i ] ]  7 
where I is the distance between the desorbing surface 
and bolometer planes, and 
and where n = 5 for point source and point detector, 
and n = 3 for infinite source and point detector. The 
phonoatomic and thermal peak temperatures are then 
given, respectively, by /3h,n and pf,n with p = ( k B T )  - '. 
With this technique, the 0" signal can be decon- 
volved by trial and error. However, as a result of the 
experimental geometry at 4S0, the resolution of the 
signal's two components is reduced to the extent that 
the deconvolution leads to ambiguous results. The 
data in Fig. 1 seem to show only a thermal desorption 
signal at 45" and were at first thought to be evidence 
of focusing, but an attempted deconvolution showed 
some phonoatomic contribution at this angle. Because 
of the importance of this point, it became evident that 
the background had to be removed. A new mask was 
designed, a schematic diagram of which is presented in 
the inset of Fig. 3. It almost completely removed the 
background as the signal in Fig. 3 indicates. 
Figure 4 shows a typical signal at 0" and 4S0, but on 
a more expanded time scale. As can be seen, a pho- 
noatomic peak is present at 45". It arrives later than 
the same peak at 0" by a factor of a, attributable to 
geometry. There is no rainbow effect, and its magni- 
tude is consistent with a cosO distribution in the 
desorbed flux. All of our data have these features. 
Thus, we find neither kinematic focusing due to pho- 
non desorption, nor focusing due to collisions. 
The absence of kinematic focusing can be attributed 
to surface roughness, surface defects, a damaged layer, 
impurities, or any other mechanism that can lift the as- 
sumption of parallel momentum conservation built 
VOLUME 54, NUMBER 18 PHYSICAL REVIEW LETTERS 6 MAY 1985 
h2 \ 
h, \ crystal 
i 
I 
0 0 20 30 $0 5 0  
TIME ( p s e c )  
FIG. 3.  The new mask, in the inset, and a typical signal at 
0" and 45" are shown (from bolometers bl  and b3, respec- 
tively). The mask, made of stainless steel, covers the whole 
desorption surface. The two holes are 1 mm in diameter, 
one at 45' to the other. The bolometers were 3 mm away 
from the surface. To enhance the signal size, a typical pulse 
width used was 1 psec. b2 was used as a heater to match the 
calibrations of bl and b3. The heater hz and bolometer b4 
were used to measure the chemical potential (Ref. 10) (i.e., 
film thickness). 
into the model. Aside from using optically polished 
crystals and handling them with standard laboratory 
care, we, at this stage, have no other means to assess 
the cleanliness of these surfaces or to improve upon 
them in situ. Several methods to achieve better sur- 
faces are under investigation. 
We have also studied the evolution of the phonoa- 
tomic effect and thermal desorption as a function of 
film thickness using the new mask. The same general 
feature was observed; i.e., it appears that in thin films, 
the phonoatomic-effect contribution dominates, but as 
the film thickness increases, desorption becomes 
mainly thermal. 
The thermal component can be understood in terms 
of the thermal time constant 7 of the film, the time it 
takes for the film to reach steady state. Based on ei- 
ther kinetic theory" or quantum mechanical calcula- 
tions,'* this rate has an exponential behavior: 
7 = T,, exp(ElkgTf),  where Tf is the film temperature 
and 7 0  and E are parameters with time and energy 
units, respectively. E has been shown experimentally 
to be strongly correlated with the chemical potential.I3 
With the assumption that yo  is relatively insensitive 
to film thickness, the time constant varies by roughly 
three orders of magnitude from p1 = - 70 K (our thin- 
nest film) to pZ=  - 30 K (our thickest film), with Tf 
taken as 4 K, slightly above the ambient temperature, 
according to the temperature of the thermal com- 
ponent of the signal. 
For thick films, it is found that T is of the order of 
microseconds, leading to a thin-film time constant of 
FIG. 4. A typical signal at (a) 0" and (b) 45" is shown on 
a more expanded time scale than the signal in Fig. 3. The 
deconvolution technique is depicted, with n = 5. The circles 
represent a fit to the thermal component of the signal, and 
the solid curve is the subtracted signal (i.e., phonoatomic 
contribution). p - - 25 K. 
roughly milliseconds. The pulse widths used in these 
experiments are of the order of 1 psec during which 
very little thermal desorption can therefore occur in 
the case of thin films, causing the spectrum to be 
dominated by the phonoatomic process. But as the 
film thickness increases, even though the phonoatom- 
ic contribution also increases, the thermal desorption 
rapidly takes over. 
There is abundant evidence that desorption of He is 
a manifestation of the anomalous Kapitza resis- 
tance.', l4  However, there is no evidence as to whether 
the mechanism of the phonoatomic effect is related to 
the Kapitza anomaly since previous experiments con- 
cerned with the Kapitza effect could not have detected 
the contribution of phonoatomic d e s ~ r ~ t i o n . ' ~  
Another observation was that the temperature as- 
signed to the phonoatomic-effect peak was at most 9 
K, whereas the heater temperature was calculated to 
be 19 K on the basis of the acoustic mismatch model. 
Apparently, impurity scattering in sapphire (which 
goes as the fourth power of frequency) and an imper- 
fect interface between heater and crystal both have the 
effect of allowing only lower-frequency phonons to ar- 
rive ballistically at the desorbing surface. These ef- 
fects have been commonly observed by other investi- 
gators.16 
In summary, we have shown that it is possible, by 
VOLUME 54, NUMBER 18 PHYSICAL REVIEW LETTERS 6 MAY 1985 
taking advantage of thermal desorption kinetics, to 
suppress thermal desorption leaving the phonoatomic 
effect the principal component of the desorption sig- 
nal. We have also shown that once all experimental 
artifacts are carefully eliminated, phonoatomic desorp- 
tion is not focused normal to the surface, but is influ- 
enced by the surface condition. These results stand in 
striking contrast to previous experimental pictures and 
provide the basis for further investigation of quantum 
desorption. 
We would like to thank Milton Cole, Michael Wei- 
mer, and Robert Housley for useful discussions, Ed- 
ward Boud for his technical assistance, and Roman 
Movshovich for his help in preparing our bolometers. 
This work was supported in part by the Office of Naval 
Research, under Contract No. N0014-80-C-0447. 
(a )~resen t  a d d r ~ s s :  Dipartimento Tecnologie Intersettoriali 
ali di Base, Energia Nucleare e delle Energie Alternative, I- 
00044 Frascati, Italy. 
( b ) ~ l s o  at Solid State Physics Department, Soreq Nuclear 
Research Center, Yavne 70600, Israel, and Physics Depart- 
ment, Technion, Technion City, 32000 Haifa, Israel. 
tc)present address: 201 Physics Building, Syracuse 
University, Syracuse, N. Y. 13210. 
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Experiments on Quantum and Thermal Desorption from ^4He Films

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Experiments on Quantum and Thermal Desorption from ^4He Films

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