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Multilayer thermal desorption
Multilayer received
1 December
D Edwards,
thermal
desorption’
1979
Jr, Brookhaven
National
Laboratory.
Upton.
NY
11973,
USA
The detection and identification of condensable impurities in a high pressure helium stream as applicable to the lsabelle liquid helium refrigeration system has motivated a study of multilayer desorption of condensed layers from a metal substrate. In this paper, the multilayer desorption analysis which is necessary for such a technique is developed. The result is that from a measurement of the peak temperature T, and peak temperature width AW of a single desorption transient the heat of vaporization E of the substance can be determined from the relation: E/UT, = In 2/( NV/T,). Hence an identification of the condensed material can be made. In addition, the peak temperature of the desorption transient of a known substance is calculated for a multilayer film and for a particular layer thickness ( 100 layers) is plotted for a number of common substances.
1. Introduction
Recent investigationshave involved the thermal desorption of adsorbedor condensedmaterial from metal substrates.‘*’The immediateusein our laboratory for this technique is to both detect and identify the impurities in the Isabelle34 K helium refrigeration system. The identification of the impurity is essentialif the source of the contaminant is to be located, whereas the quantitative detection is necessaryto insure operation of the Isabelle helium refrigerator since it is well known that impuritieswithin the cold circuit helium systemcan limit the refrigerator performance. Figure 1 showsan examplefrom ref 2 in which the desorption spectraof -100 layers of NH3 condensedon a stainlesssteel substrateis recordedasa function of sampletemperature.Seen is the characteristic profile of a multilayer zeroth order desorption transient-an approximate exponential rise of the desorptionrate to the maximum followed by a very rapid fall of the desorption rate after maximum. Also observed in this figure is that the full temperature width at half maximum is -4-S% of the peak temperature (T,) which is considerably narrower than either a simplefirst (8 % T,,,)or second(12% T,,,) order desorptiontransient4. It is the purposeof the presentstudy (i) to evaluatethe heat of vaporization from the peak width and peak temperatureof a single multilayer desorption transient; (ii) to determine the temperatureof the maximum of the desorptiontransient given both the rate constantsof the process(heat of vaporization, preexponential factor) and the systemparameters(number of adsorbedlayers, systemvolume, pumping speed,temperature sweeprate). The above analysisis presentedfor the two possiblemeasurement modes-external pumping speed = 0, dp/dr recorded; external pumping speed# 0. p recorded.The analysisfor each
l Work performedunder the auspices of the US Departmentof Energy.
Vacuum/volume @ Pergamon
30/number Press LtdlPrinted
4/5.
0042-207X/80/0501 in Great Britain
-0189SO2.00/0
-IO
TIN
in the Figure 1. The desorptionof -50 layersof NH, measured dp/drmode.Threeseparatesweeps areshown.
mode does allow for the possibility of significant samplereadsorption during the desorptioninterval. The implicationsof the analysiswill be that either the heat of vaporization (and hencesubstanceidentification) of a condensable substancecan be determined using a small samplesize (-25 layers on a -1 cm2 substrate,3 x lOI total adsorbed molecules)or the temperatureof the maximumof the desorption transientcan be estimatedusingthe systemparameterstogether with the tabulated rate constants of the adsorbant. Thus it becomespossibleto either identify an unknown adsorbant,in, for example, the higher pressurehelium streamof the Isabelle refrigeration systemor estimatethe desorptiontemperatureof a known adsorbant from the characteristicsof the multilayer desorptiontransient. 189
D Edwards, Jr: Multilayer thermal desorption 2. Model and analysis
n,w = fw)
The thermal desorption of many layers of a condensable substance adsorbed onto a solid surface can be thought of qualitatively in the following piecewise manner (i) until the desorption process removes the next to last layer of the condensed film, the rate of desorption is proportional to the number of molecules in the uppermost layer-a constant equal to n,; (ii) during the desorption of the final layer the desorption rate falls quite quickly to zero since the rate is now proportional to the number of molecules in the last layer which decreases to zero during the final layer desorption. The fractional width of the falling portion of the transient is in fact of order l/number of layers, being of order of a few per cent for h-355100 initially adsorbed layers. Since the desorption rate with the exception of the last layer, is independent of the total amount on the surface the transient profile is determined by a zeroth order desorption equation and is developed below for the two separate measurement modes.
and conserving
2.1. Measurement modes. At present there are two experimentally distinct methods used in making thermal desorption measurements. The first” requires the desorption into an essentially pumpless system. In this mode-mode I-the peak structure of the desorption process is recovered by displaying dp/dr vs substrate temperature where p is the system pressure. Due to some experimental difficulties resulting from wall pumping of chemically active gases this mode has been restricted to the study of the desorption of implanted inert gases. It has occurred, however, in the present context of multilayer desorption that this mode has been found to be particularly suited to this measurement situation. The second measurement mode-mode II-involves the desorption into a system with a finite real pump present6 and the peak structure of the desorption process is exhibited by the pressure itself. Due to the various experimental circumstances characteristic of multilayer adsorption-desorption processes both of these measurement modes are particularly applicable, complementary, and are developed below. 2.2. Analysis. The analysis section will be divided into two sections. In the first part the heat of vaporization will be determined from the peak width and peak temperature of the multilayer desorption transient for the two measurement modes. In the second part the peak temperature of a given desorption transient will be determined for a particular set of molecular and system parameters.
(2) the molecular
Vdp = {number
flux at the sample surface:
into gas phase/s-number out of
dr
gas phase/s}
or
where f is the number/s strictly leaving or desorbing from the sample and S, is the pumping speed of the sample itself. Iterating the above equations it is found that for t < t,
-Vdp = TSf- T,'f+ TS"f + dr
+(Ts4f)
where TV = V/S,, f = df/dt and I,,, is the time at which only 1 layer of the multilayer remains on the sample. Thus for t > 1, p is constant and dp/dr = 0. The number desorbing per second from the multilayer adsorbate may be parametrized by an Arrhenius type of equation: / = -p,e-EI”T
(5)
where E is the heat of vaporization of the condensed substance, T is the sample temperature, K is Boltzmann’s constant, y is the pre-exponential factor and n, has been previously defined. In addition a linear temperature sweep is assumed --T = T + fir. Using the above relations, equation (4) becomes:
(6) where Y = E/KT. Consider that the peak of the desorption transient (the desorption transient in this mode is taken to be a plot of dp/dc vs I) occurs at temperature T,,, and that T,, is the temperature on the rising portion of the transient for which dp/dr is half of its value at T,,,-note that the location of T,,, itself is arbitrary since a cut can be made at any one location of the rising position of the transient. Using these definitions A W, the full temperature width at half maximum, may be formed by AW=
T,,, - Th.
Using w = A W/T,,,, a = EIKT,,,, OLmay be found as a series in w 2.2.1. Heat of vaporization: no real pump. Consider initially that the adsorbed multilayer contains /lo adsorbed molecules whereas in each layer there are 11, molecules. Also assume that the sample with the adsorbed multilayer is in a system of volume V with no real pump present and that the system pressure p is measured from which dp/dt is formed’. Conserving the total number of molecules within the system at any time t: n,(r) + n,(t) = 110
(1)
where n,(l) is the number of adsorbed molecules remaining on the sample at time I, and )1,(t) is the number of molecules in the gas phase again at time 1. Using the relation: 190
%=;{I + O2
+do+w(&-l
+d,)
-’ + s, + $(w3)‘7 ( In2 > 1
where 5, = -28,~~
- 12602~02
In 2 + +(So3)
(7)
D Edwards,
Multilayer thermal desorption
Jr:
2.2.4. Peak temperature: S # 0, the following allow
,2=..,,(-*+~)+fi,‘E,‘(*73-~-36in2)
where a0 is determined
with
ao2exp(ao)
Eg = 0.05.
2.2.2. Heat of vaporization: a real pump. Consider now that there is a real pump S present in addition to the readsorption pump .S,. The pressure p as discussed previously will now display the peak structure of the desorption process provided that S is sufficiently large-/3( V/S)/A W ( 0.05 is adequate for most purposes. The analysis proceeds in essentially the same manner as before with the result that: (1 - 26, + ~(clf?,‘)} y
2 {I - 36, + r#J(as,2)}
(
a0 =
In 6, - 2 In (In b,) + a,c + a2c2 + a3c3 + a4c4 + &c’).
where a, =
2,
a2 = I - 4/d,,
I 22 24 16 a4 = - - + - -, do2 do3 2 3do
V/(S
+
the terms of order 8,, a is found as a series in w
which again allows E to be calculated from a measurement of A W and T,,, alone independent of any other parameters. Said somewhat differently the correct choice of the hidden parameters is essential for the validity of the measurement technique but once this choice is made the end result is independent of that choice. 2.2.3. Peak temperature of the transient: S = 0. Consider now that both the rate constants of the multilayer adsorbant and the system parameters are known including the number of initially adsorbed layers. Then proceeding in a similar manner as previously described T, may be found from: a =
a,
-
82
+
b22 2
+
dJ(g23)
(10)
where , E = r,PK/E, The desorption
rs = V/S,, transient
do = 2 In (In b,),
As an example consider the following multilayer desorption measurement : mole-‘,
y = lOI ?I, = I layer,
s-l,
parameters
for a
S, = 100 I s-‘, 17~ = 100 layers,
K = 1.986 cal mol-’ K-‘,
I’= 1 1.
Using the above, T, may be found for the two measurement modes :
S,).
’
Neglecting
+ 4 do
c = do/In bo.
/I = 0.1 K s-l, T, =
a3 = ? - f o
S = (0 or 1) I s-‘,
+ r#J(‘/a3)
where
T’
(12)
Although equation (12) is able to be solved in an iterative fashion, a series solution may also be used and is given by:
)
8 1 2!!
by:
= b,
E = lO”ca1 -
(11)
with
Thus equation (7) allows the heat of vaporization, E, of a substance to be determined by the measurement of the peak width and peak temperature of a single multilayer desorption transient. It is remarked that although the adsorption of a multilayer is essential for the technique and corresponding analysis, the number of layers does not have to be known for E to be determined. In addition, E determined via equation (7) is effectively independent of y, /I’, n,, S,.
w = y
in which
a = ao( 1 - 2/a; + 8/ao3 + r#~(I /zo4>)
+ d@o’)
B,=fg, 0 m
S # 0. For the situation to be found:
T,,,
8, = ao2E
S = 0. in this case is a plot of dp/dt vs t.
T,,,(S = 0 1 s-l,
mode I) = 242.9 K, equation
(10)
T,,,(S = 1 I s-l,
mode II) = 201.1 K, equation
(I I).
In addition the small correction terms can be found for the above situation (E, = 5 Y 10e6 and ~8, = 4 / 10e6) and thus are seen to be quite small for the above analysis. Although the temperature 7, of the desorption transient is clearly logarithmic in a number of parameters including the temperature sweep rate j?, the wall pumping speed S, and the number of initially adsorbed layers rzO,a plot of T, for adsorbed water vapor (c - IO kcal mole-‘) as a function of the number of initially adsorbed layers (not presented) shows a rather weak dependence of T,,, on the number of initially adsorbed layers. The temperature increment found from the above study is -20 K for every order of magnitude increase in initial layer thickness. The scaling of this plot will, of course, be the same for both j3 and S,. In other words, increasing the wall readsorption pumping speed (or temperature sweep rate) by an order of magnitude would increment the desorption temperature by -20 K. 3. Discussion Apart from the ability to determine the heat of vaporization from a single multilayer desorption transient, one of the interesting features of the present study is the possibility of 191
D Edwards,
Jr: Multilayer
100
thermal
LAYER
s: I KlS
I.
desorption
having that particular heat of vaporization. An empirical the calculated relation between T,,, and E is given by:
DESORPTION IO’? S/SW.
fit to
01
T,,, N 20E
J4oc Tm(K1
Figure 2. The heat of vaporization is plotted as a function of the maximum desorption temperature for an initial 100 layer film.
with T, in K, E in kcal mole-‘. In addition an estimate of the temperature below which -I00 layers of a substance is vacuum stable can also be made from Figures 2 and 3. For vacuum stability of reasonable duration, the operating temperatures should be below T,,, by several peak widths (AWN 0.05 T,); i.e. T ( T,,, - 0.2 T,,,. With sub-monolayer amounts of adsorbed material the desorption rate is typically found to follow a first or second order desorption equation. As was also found here the desorption energy for the first or second order desorption process may be determined from a measurement of the peak temperature or peak width of a single desorption transient. A comparison of these results with the present shows:
0.69/a 0th order .AW = 2.44/a
1st order
(13)
3.24/a 2nd order illustrating that for a given a, T,,, the zeroth order desorption transient is considerably narrower than the first order transient which in turn is narrower than the second order transient.
References T,,,(OKI Figure 3. The heat of vaporization plotted vs r,. Also included are some common substances. predicting T,,, for a given quantity of a particular substance condensed on a surface. Seen in Figures 2 and 3 is the temperature T, of the peak of the desorption transient plotted as a function of E. On these plots are listed some substances
192
’ T E Madey and J T Yates, SurjSci (in press). * D Edwards, Jr, J Vat Sri Techt~ol, 16, 1979, 695. 3 W J Schneider and D Edwards, Jr, IEEE Trrons NM/ Sci, NS-26, 1979, 4091. D Edwards, Jr and W J Schneider, patent pend. ’ D Edwards, Jr, SurfSci. 54, 1976, I. 5 E V Kornelsen, Radar Ef, 13, 1972, 227 and contained references to earlier work. 6 P A Redhead, Vactrrrtn, 12, 1962, 203. ’ An example of such a system is described in reference 2. a D Edwards, Jr, Vucurrm, 26, 1976, 91.
1 December
D Edwards,
thermal
desorption’
1979
Jr, Brookhaven
National
Laboratory.
Upton.
NY
11973,
USA
The detection and identification of condensable impurities in a high pressure helium stream as applicable to the lsabelle liquid helium refrigeration system has motivated a study of multilayer desorption of condensed layers from a metal substrate. In this paper, the multilayer desorption analysis which is necessary for such a technique is developed. The result is that from a measurement of the peak temperature T, and peak temperature width AW of a single desorption transient the heat of vaporization E of the substance can be determined from the relation: E/UT, = In 2/( NV/T,). Hence an identification of the condensed material can be made. In addition, the peak temperature of the desorption transient of a known substance is calculated for a multilayer film and for a particular layer thickness ( 100 layers) is plotted for a number of common substances.
1. Introduction
Recent investigationshave involved the thermal desorption of adsorbedor condensedmaterial from metal substrates.‘*’The immediateusein our laboratory for this technique is to both detect and identify the impurities in the Isabelle34 K helium refrigeration system. The identification of the impurity is essentialif the source of the contaminant is to be located, whereas the quantitative detection is necessaryto insure operation of the Isabelle helium refrigerator since it is well known that impuritieswithin the cold circuit helium systemcan limit the refrigerator performance. Figure 1 showsan examplefrom ref 2 in which the desorption spectraof -100 layers of NH3 condensedon a stainlesssteel substrateis recordedasa function of sampletemperature.Seen is the characteristic profile of a multilayer zeroth order desorption transient-an approximate exponential rise of the desorptionrate to the maximum followed by a very rapid fall of the desorption rate after maximum. Also observed in this figure is that the full temperature width at half maximum is -4-S% of the peak temperature (T,) which is considerably narrower than either a simplefirst (8 % T,,,)or second(12% T,,,) order desorptiontransient4. It is the purposeof the presentstudy (i) to evaluatethe heat of vaporization from the peak width and peak temperatureof a single multilayer desorption transient; (ii) to determine the temperatureof the maximum of the desorptiontransient given both the rate constantsof the process(heat of vaporization, preexponential factor) and the systemparameters(number of adsorbedlayers, systemvolume, pumping speed,temperature sweeprate). The above analysisis presentedfor the two possiblemeasurement modes-external pumping speed = 0, dp/dr recorded; external pumping speed# 0. p recorded.The analysisfor each
l Work performedunder the auspices of the US Departmentof Energy.
Vacuum/volume @ Pergamon
30/number Press LtdlPrinted
4/5.
0042-207X/80/0501 in Great Britain
-0189SO2.00/0
-IO
TIN
in the Figure 1. The desorptionof -50 layersof NH, measured dp/drmode.Threeseparatesweeps areshown.
mode does allow for the possibility of significant samplereadsorption during the desorptioninterval. The implicationsof the analysiswill be that either the heat of vaporization (and hencesubstanceidentification) of a condensable substancecan be determined using a small samplesize (-25 layers on a -1 cm2 substrate,3 x lOI total adsorbed molecules)or the temperatureof the maximumof the desorption transientcan be estimatedusingthe systemparameterstogether with the tabulated rate constants of the adsorbant. Thus it becomespossibleto either identify an unknown adsorbant,in, for example, the higher pressurehelium streamof the Isabelle refrigeration systemor estimatethe desorptiontemperatureof a known adsorbant from the characteristicsof the multilayer desorptiontransient. 189
D Edwards, Jr: Multilayer thermal desorption 2. Model and analysis
n,w = fw)
The thermal desorption of many layers of a condensable substance adsorbed onto a solid surface can be thought of qualitatively in the following piecewise manner (i) until the desorption process removes the next to last layer of the condensed film, the rate of desorption is proportional to the number of molecules in the uppermost layer-a constant equal to n,; (ii) during the desorption of the final layer the desorption rate falls quite quickly to zero since the rate is now proportional to the number of molecules in the last layer which decreases to zero during the final layer desorption. The fractional width of the falling portion of the transient is in fact of order l/number of layers, being of order of a few per cent for h-355100 initially adsorbed layers. Since the desorption rate with the exception of the last layer, is independent of the total amount on the surface the transient profile is determined by a zeroth order desorption equation and is developed below for the two separate measurement modes.
and conserving
2.1. Measurement modes. At present there are two experimentally distinct methods used in making thermal desorption measurements. The first” requires the desorption into an essentially pumpless system. In this mode-mode I-the peak structure of the desorption process is recovered by displaying dp/dr vs substrate temperature where p is the system pressure. Due to some experimental difficulties resulting from wall pumping of chemically active gases this mode has been restricted to the study of the desorption of implanted inert gases. It has occurred, however, in the present context of multilayer desorption that this mode has been found to be particularly suited to this measurement situation. The second measurement mode-mode II-involves the desorption into a system with a finite real pump present6 and the peak structure of the desorption process is exhibited by the pressure itself. Due to the various experimental circumstances characteristic of multilayer adsorption-desorption processes both of these measurement modes are particularly applicable, complementary, and are developed below. 2.2. Analysis. The analysis section will be divided into two sections. In the first part the heat of vaporization will be determined from the peak width and peak temperature of the multilayer desorption transient for the two measurement modes. In the second part the peak temperature of a given desorption transient will be determined for a particular set of molecular and system parameters.
(2) the molecular
Vdp = {number
flux at the sample surface:
into gas phase/s-number out of
dr
gas phase/s}
or
where f is the number/s strictly leaving or desorbing from the sample and S, is the pumping speed of the sample itself. Iterating the above equations it is found that for t < t,
-Vdp = TSf- T,'f+ TS"f + dr
+(Ts4f)
where TV = V/S,, f = df/dt and I,,, is the time at which only 1 layer of the multilayer remains on the sample. Thus for t > 1, p is constant and dp/dr = 0. The number desorbing per second from the multilayer adsorbate may be parametrized by an Arrhenius type of equation: / = -p,e-EI”T
(5)
where E is the heat of vaporization of the condensed substance, T is the sample temperature, K is Boltzmann’s constant, y is the pre-exponential factor and n, has been previously defined. In addition a linear temperature sweep is assumed --T = T + fir. Using the above relations, equation (4) becomes:
(6) where Y = E/KT. Consider that the peak of the desorption transient (the desorption transient in this mode is taken to be a plot of dp/dc vs I) occurs at temperature T,,, and that T,, is the temperature on the rising portion of the transient for which dp/dr is half of its value at T,,,-note that the location of T,,, itself is arbitrary since a cut can be made at any one location of the rising position of the transient. Using these definitions A W, the full temperature width at half maximum, may be formed by AW=
T,,, - Th.
Using w = A W/T,,,, a = EIKT,,,, OLmay be found as a series in w 2.2.1. Heat of vaporization: no real pump. Consider initially that the adsorbed multilayer contains /lo adsorbed molecules whereas in each layer there are 11, molecules. Also assume that the sample with the adsorbed multilayer is in a system of volume V with no real pump present and that the system pressure p is measured from which dp/dt is formed’. Conserving the total number of molecules within the system at any time t: n,(r) + n,(t) = 110
(1)
where n,(l) is the number of adsorbed molecules remaining on the sample at time I, and )1,(t) is the number of molecules in the gas phase again at time 1. Using the relation: 190
%=;{I + O2
+do+w(&-l
+d,)
-’ + s, + $(w3)‘7 ( In2 > 1
where 5, = -28,~~
- 12602~02
In 2 + +(So3)
(7)
D Edwards,
Multilayer thermal desorption
Jr:
2.2.4. Peak temperature: S # 0, the following allow
,2=..,,(-*+~)+fi,‘E,‘(*73-~-36in2)
where a0 is determined
with
ao2exp(ao)
Eg = 0.05.
2.2.2. Heat of vaporization: a real pump. Consider now that there is a real pump S present in addition to the readsorption pump .S,. The pressure p as discussed previously will now display the peak structure of the desorption process provided that S is sufficiently large-/3( V/S)/A W ( 0.05 is adequate for most purposes. The analysis proceeds in essentially the same manner as before with the result that: (1 - 26, + ~(clf?,‘)} y
2 {I - 36, + r#J(as,2)}
(
a0 =
In 6, - 2 In (In b,) + a,c + a2c2 + a3c3 + a4c4 + &c’).
where a, =
2,
a2 = I - 4/d,,
I 22 24 16 a4 = - - + - -, do2 do3 2 3do
V/(S
+
the terms of order 8,, a is found as a series in w
which again allows E to be calculated from a measurement of A W and T,,, alone independent of any other parameters. Said somewhat differently the correct choice of the hidden parameters is essential for the validity of the measurement technique but once this choice is made the end result is independent of that choice. 2.2.3. Peak temperature of the transient: S = 0. Consider now that both the rate constants of the multilayer adsorbant and the system parameters are known including the number of initially adsorbed layers. Then proceeding in a similar manner as previously described T, may be found from: a =
a,
-
82
+
b22 2
+
dJ(g23)
(10)
where , E = r,PK/E, The desorption
rs = V/S,, transient
do = 2 In (In b,),
As an example consider the following multilayer desorption measurement : mole-‘,
y = lOI ?I, = I layer,
s-l,
parameters
for a
S, = 100 I s-‘, 17~ = 100 layers,
K = 1.986 cal mol-’ K-‘,
I’= 1 1.
Using the above, T, may be found for the two measurement modes :
S,).
’
Neglecting
+ 4 do
c = do/In bo.
/I = 0.1 K s-l, T, =
a3 = ? - f o
S = (0 or 1) I s-‘,
+ r#J(‘/a3)
where
T’
(12)
Although equation (12) is able to be solved in an iterative fashion, a series solution may also be used and is given by:
)
8 1 2!!
by:
= b,
E = lO”ca1 -
(11)
with
Thus equation (7) allows the heat of vaporization, E, of a substance to be determined by the measurement of the peak width and peak temperature of a single multilayer desorption transient. It is remarked that although the adsorption of a multilayer is essential for the technique and corresponding analysis, the number of layers does not have to be known for E to be determined. In addition, E determined via equation (7) is effectively independent of y, /I’, n,, S,.
w = y
in which
a = ao( 1 - 2/a; + 8/ao3 + r#~(I /zo4>)
+ d@o’)
B,=fg, 0 m
S # 0. For the situation to be found:
T,,,
8, = ao2E
S = 0. in this case is a plot of dp/dt vs t.
T,,,(S = 0 1 s-l,
mode I) = 242.9 K, equation
(10)
T,,,(S = 1 I s-l,
mode II) = 201.1 K, equation
(I I).
In addition the small correction terms can be found for the above situation (E, = 5 Y 10e6 and ~8, = 4 / 10e6) and thus are seen to be quite small for the above analysis. Although the temperature 7, of the desorption transient is clearly logarithmic in a number of parameters including the temperature sweep rate j?, the wall pumping speed S, and the number of initially adsorbed layers rzO,a plot of T, for adsorbed water vapor (c - IO kcal mole-‘) as a function of the number of initially adsorbed layers (not presented) shows a rather weak dependence of T,,, on the number of initially adsorbed layers. The temperature increment found from the above study is -20 K for every order of magnitude increase in initial layer thickness. The scaling of this plot will, of course, be the same for both j3 and S,. In other words, increasing the wall readsorption pumping speed (or temperature sweep rate) by an order of magnitude would increment the desorption temperature by -20 K. 3. Discussion Apart from the ability to determine the heat of vaporization from a single multilayer desorption transient, one of the interesting features of the present study is the possibility of 191
D Edwards,
Jr: Multilayer
100
thermal
LAYER
s: I KlS
I.
desorption
having that particular heat of vaporization. An empirical the calculated relation between T,,, and E is given by:
DESORPTION IO’? S/SW.
fit to
01
T,,, N 20E
J4oc Tm(K1
Figure 2. The heat of vaporization is plotted as a function of the maximum desorption temperature for an initial 100 layer film.
with T, in K, E in kcal mole-‘. In addition an estimate of the temperature below which -I00 layers of a substance is vacuum stable can also be made from Figures 2 and 3. For vacuum stability of reasonable duration, the operating temperatures should be below T,,, by several peak widths (AWN 0.05 T,); i.e. T ( T,,, - 0.2 T,,,. With sub-monolayer amounts of adsorbed material the desorption rate is typically found to follow a first or second order desorption equation. As was also found here the desorption energy for the first or second order desorption process may be determined from a measurement of the peak temperature or peak width of a single desorption transient. A comparison of these results with the present shows:
0.69/a 0th order .AW = 2.44/a
1st order
(13)
3.24/a 2nd order illustrating that for a given a, T,,, the zeroth order desorption transient is considerably narrower than the first order transient which in turn is narrower than the second order transient.
References T,,,(OKI Figure 3. The heat of vaporization plotted vs r,. Also included are some common substances. predicting T,,, for a given quantity of a particular substance condensed on a surface. Seen in Figures 2 and 3 is the temperature T, of the peak of the desorption transient plotted as a function of E. On these plots are listed some substances
192
’ T E Madey and J T Yates, SurjSci (in press). * D Edwards, Jr, J Vat Sri Techt~ol, 16, 1979, 695. 3 W J Schneider and D Edwards, Jr, IEEE Trrons NM/ Sci, NS-26, 1979, 4091. D Edwards, Jr and W J Schneider, patent pend. ’ D Edwards, Jr, SurfSci. 54, 1976, I. 5 E V Kornelsen, Radar Ef, 13, 1972, 227 and contained references to earlier work. 6 P A Redhead, Vactrrrtn, 12, 1962, 203. ’ An example of such a system is described in reference 2. a D Edwards, Jr, Vucurrm, 26, 1976, 91.