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Time-of-flight ion energy and ion reaction time spectrometry, spectral line shape and mechanisms of ion formation
International
Journal
of Mass Spectrometry
Elsevier Science Publishers
TIME-OF-FLIGHT SPECTROMETRY, ION FORMATION
and Ion Processes,
B.V.. Amsterdam
- Printed
70 (1986)
l-21
in The Netherlands
ION ENERGY AND ION REACTION TIME SPECTRAL LINE SHAPE AND MECHANISMS
OF
T.T. TSONG Physics Department,
(First received
The Pennsylvania
State University, Universicv Park, PA I6802 (U, S.A.)
9 July 1985; in final form 11 December
1985)
ABSTRACT Methods are presented for achieving a better accuracy in the ion energy analysis and an excellent time resolution in the ion reaction time measurement using the time-of-flight spectrometer. Analyses are also presented to show that the mechanisms of ion formation can be derived directly from the spectral line shape. Specific examples drawn from high resoiution pulsed-laser time-of-flight atom-probe spectrometer measurements are used to illustrate these methods and analyses. The richness of information contained in a high resolution time-of-flight spectrum is demonstrated with a study of field dissociation by atomic tunneling of RhHe’+ ions. The time resolution in this dissociation time measurement is as good as 20 fs, and a feature related to half a period of the rotational motion of the ion can be observed in the time-of-flight spectrum from fully resolved peaks.
INTRODUCTION
Time-of-flight (TOF) spectrometry has gained considerable popularity recently because of its simplicity in principle and operation, and the rapid progress made in fast electronics [l-4]. Although the time-of-flight spectrometer is mainly used as a tool for mass analysis, thus it is almost always called a TOF mass spectrometer, the spectrum is in fact much richer in information. A high resolution TOF spectrum contains the energy distribution of each ion species, and also information on where, how and when these ions are formed [5]. This information can be derived quite simply and directly from the line shape of the TOF spectral lines. The method of data analysis can be very simple if the spatial zone of formation of parent ions is very narrow such as right at the surface in field desorption and in desorption stimulated by particle bombardment, or can be made very narrow by a proper focusing of the electron and laser beam in electron impact ionization and photoionization or photofragmentation. We 0168-1176/86/$03.50
0 1986 Elsevier Science Publishers
B.V
2
present here a general analysis of the line shape in time-of-flight spectrometry, and also methods for an accurate ion energy measurement and a precision ion reaction time measurement. For these purposes, a special time-of-flight spectrometer configuration will be used. Examples illustrating these basic principles and methods will be drawn from field desorption experiments made with a high resolution pulsed-laser time-of-flight atomprobe spectrometer 141. A METHOD TROMETER
FOR AN ACCURATE
CALIBRATION
OF A TIME-OF-FLIGHT
SPEC-
There are many different configurations of TOF spectrometers. We will discuss only one generally used configuration here (Fig. I). However, variations to other configurations can be worked out based on the same principle. There are two separate sections, i.e. the ion formation-acceleration section of length I and the ion free drift section of length L. To achieve the best possible resolution in ion energy and ion reaction time spectrometry one should make I c L so that the total flight time of an ion is determined essentially by the kinetic energy of the ion when it has left the ion formation-acceleration section. To simplify the data analysis, one should also make the two sections well isolated by a small hole or a grid although in principle this is not a requirement. There are two constants of the system which have to be determined very accurately first. The kinetic energy of an ion is related to its flight time by
where t is the “ measured flight time” and 6 is a time delay constant accounting for the time delay in the detection process, which is due mainly to the generation and transmission times of the triggering and the ion
Acceleration section
Free flight section
I
Detector
Fig. 1. Configuration
of a time-of-flight
spectrometer.
3
signals. In the equation, the ion mass M is usually known to better than one part in 106. L and 6 are very difficult to measure directly with great accuracy. To achieve high resolution in energy and time spectrometry, accurate values of these two constants must be known. Fortunately, there usually exists an ion formation process whose energetics are very well established. In such a case, Eq. (1) should be rewritten as (2)
t=&-s
/’
Thus by measuring very carefully the “flight time” t as a function of ion energy E, and plotting t vs. I//%!$?? using the linear regression, very accurate values of L and 6 can be obtained from the slope and the intercept of the linear plot. Note that the graphical method does not usually give sufficient precision. A real example will now be drawn from the calibration of a pulsed-laser TOF atom-probe spectrometer to illustrate this method and to show the accuracy achievable [4]. In this spectrometer the sample is a sharp needle of tip radius 200-1000 A. I = 1.2 mm and L = 4200 mm: thus L/I = 3500. In fact, because of the needle-shaped geometry of the positive electrode, the effective value of L/I is much higher as will be discussed later. The system can be calibrated by measuring the flight time of pulsed-laser field desorbed inert gas ions as a function of the tip voltage. It has been established through an excellent agreement between a theoretical analysis and an experimental measurement that in pulsed-laser stimulated field desorption of adsorbed gases, ions are produced by field ionization in the field ionization zone of thermally desorbed neutral species [5]. Thus the final kinetic energy of the most energetic ions is eV - (Z - +) where V is the tip voltage, Z is the ionization energy of the gas atoms, and cp is the work function of the final electrode. In a TOF spectrometer, the average work function of the drift tube should be used since a drifting ion sees this work function most of its flight time. (I - +) is usually referred to as the critical energy deficit, AE,, of the ions. Thus Eq. (1) can be written as l/2
‘/2
A4
v-
(Q/e)
V-
(rE,/e)
i
-’
(3)
In the calibration of the system, the onset flight times, or the flight times of the most energetic ions, of He+, Ne+ and Ar+ as a function of V are measured, and a best linear fit of t vs. [M/( V - AE,/e)]“* is obtained by linear regression. From the slope and the intercept, accurate values of C and 6 as listed in Table 1 are derived. The linearity of the plot, which reflects the validity of Eq. (3) and the entire analysis, can be seen from the value of the
TABLE 1 Flight time data for He+, Ne+ and Rh*+ (C = 0.01073628 u p”sP2 kV_‘, Ion species He+
Ionic mass a (u) 4.002054
AE, b (eV) 20.10
Tip voltage
6 = 28.3 ns)
(kV)
Measured onset flight time (ns)
3.5 4.0 4.5 5.0 5.5 6.0 7.0 8.0 9.0 9.5 10.0 10.5
10.322 9.649 9.093 8.623 8.219 7.867 7.279 6.806 6.414 6.242 6.083 5.936
M = 4.001881 & 0.000455 u, SM = - 0.000173 + 0.000445 u AE, =19.82+0.87 eV, iS(AE,) = -0.28kO.87 eV ‘ONei
19.991890
17.0X103
3.0 3.5 4.0 4.5 5.0 5.5 6.0 7.0 8.0 9.0
24.956 23.094 21.593 20.353 19.303 18.400 17.614 16.302 15.245 14.370
M = 19.992687 + 0.000950 u, 6M = 0.000797 k 0.000950 u AfTc=17.29+0.31 eV, S(AE,)=0.32&-0.31 eV 12Ne+
21.990835
17.0
3.5 4.0 4.5 5.0 5.5 6.0 1.0 8.0 9.0
51.452201
10.9x2
8.0 --.24.464 9.0 9.5 10.0 10.5
M/t? = 51.448751 f 0.002324 u. S( M/n) = - 0.003450& 0.002324 u =10.25,0.42 eV, G(AE,/n) = --0.6550.74 eV
hE,/tr
See Table notes on following page.
-24.223 22.648 21.345 20.246 19.298 18.475 17.099 15.991 IS.073 ~...~
-23.060 22.444 21.874 21.346
5
coefficient of determination Y’ obtained [4b], which differs from 1 by only 1.2 x 10-s. An accuracy of about 5 parts in lo5 can be achieved routinely in mass and energy analysis using the values of C and 6 listed in the table. The same accuracy is achieved even when an einzel lens in the drift tube section is used to focus the ions although the value of C can change by almost 1%. With these two constants, the kinetic energy (absolute value) of any field desorbed ions can be calculated directly from its measured flight time t by E=
eM c( t + 8)”
ION ENERGY
DISTRIBUTION
Primury ions The flight time distribution of an ion species is also the ion energy distribution, which is related directly to the dynamics of ion formation. We consider first primary ions, i.e. ions not formed by further ion reactions. If an ion of n + charge state is emitted from the surface with an initial kinetic energy Ei, for example in the ion bombardment of a surface, then the final kinetic energy of the ion will be Ei + neV. On the other hand, if an t? + ion is formed at a distance x away from the surface with a negligible initial kinetic energy, e.g. by field ionization or by photoionization, then the final kinetic energy of the ion is neV- tzel,‘F(x’) dx’ where F(x) is the applied field at x. Thus by measuring the ion energy distribution the energy transfer process in the ion formation, or the spatial zone of ion formation. can be investigated. Let us define a few density functions of ion formation as follows: f,(E) d E represents the fractional number of ions formed with their final kinetic energy in the range between E and E + d E, f,(x) dx represents the fractional number of ions formed in the range between x and x + dx. and fF(t) dt represents the fractional number of ions formed with their total
Notes to Table 2 ’ Ionic masses are from ref. 13. h A EC values are calculated from AE, = C:l=,I, - n& + A, energy of the atom, & = 4.5 eV is the average work function sublimation energy. Experimentally measured M and AE, for each ion species table and theoretical values are given under the experimental
where I, is the ith ionization of the flight tube, and 12 is the and their deviations from the data of each ion species.
6
Rh2:55K,95kV 50-48
V/A
Fig. 2. A histogram of ion flight times in pulsed-laser stimulated field evaporation lo-” Torr at 55 K. The onset flight time is 22444 ns and FWHM is 4 ns.
of Rh in
flight time between t and t + dt. f,(t) is measured in a TOF spectrometer. and the other density functions can be derived from ,jr( t) using the relations
(5)
where dt - -&(t+s)’ dE
(6)
and dt/dx can be calculated if the electric field distribution in the ion formation-acceleration section is known. The discussion presented above is generally known although for completeness we will illustrate with an example from a study of pulsed-laser stimulated field desorption of rhodium. A flight time distribution of Rh*+ taken at 9.5 kV and a field of about 4.9 V p\-’ is shown in Fig. 2. From the mass and the onset flight time, 22.444 ps, the critical energy deficit of Rh’+ is calculated from Eq. (3) to be 20.5 A 0.84 eV, in good agreement with that expected from A E,“+ = A + C:Z, - 2~ = 21.8 eV, where A is the sublimation energy and I, is the ith ionization energy. The measured FWHM is 4 ns. In a histogram, the true FWHM is the measured value minus 1-2 bin widths. The real FWHM is therefore 2-3 ns. From Eq. (6), this corresponds to an energy spread of 3.4-5.1 eV. The electric field at the Rh emitter surface is about 4.8 V A-‘. Thus Rh ions are formed in a spatial zone of 0.35-0.53 A in width. The width is related to the dynamics of ion formation or spatial variation of electron tunneling probability.
Ions formed
by an ion reuction: low energv tail
An ion reaction usually refers to the dissociation of a compound ion into smaller ions. This is not the most general definition, but we will confine our discussion to this aspect of ion reactions even though the principle presented here can be extended to other types of ion reactions. Recently, ion reactions such as Coulomb explosion of multiply charged cluster ions, photofragmentation of cluster and compound ions, spontaneous dissociation by electronic de-excitation induced vibrational excitation, and field dissociation by atomic tunneling, etc. have attracted considerable interest. We will discuss here the energetics and line shapes of TOF spectral lines when an ion reaction is involved in the ion formation. Let us assume that the parent ions, (M + m)“+ are formed within the formation-acceleration section with the spatial density function represented by ff(_y) as defined earlier. These ions dissociate spontaneously within the acceleration section via (M + m)“+ + M”+ + mf + eP (returned
to + electrode)
or + M”+ + m” (7)
We will define a spatial density function f,(x) for the formation of the daughter ions M”+ and mt or m”. fd(x) dx represents the fractional number of cluster ions dissociated between .Y and x + dx. The probability that a parent ion formed at x’ survives at .Y without dissociation will be represented by p(x’, x), and the dissociation rate constant is represented by k(x). p(x’, x) satisfies the difference equation
p(x’, where p(x’.
x +
dx) =p(x’,
x) + dp(x’,
u( x’, x) is the velocity
x) =p(x’
of the parent
ion (formed
at x’) at x. Since
x’) = 1, we have
forx>x’
PW
The fractional given by
number
of parent
ions dissociated
4 We therefore
(9)
k(x)
dx
u(x’,
x)
between
x and dx is then
(10)
have
k( XI’) dx”/u( D(x,, x>
x’, x”)]
1
dx’
(11)
8
This equation tells us that if we know the spatial density function of formation of parent ions fr(x), the rate constant k(x), and the field distribution and therefore the velocity of the parent ions u(x’, x), then the spatial density function of formation of daughter ions fd( X) can be derived. The flight time and energy distribution of M”+ and mt can then be derived once f,(x) is known. It can be shown, as can be understood from the field desorption experiment to be described below, that if the dissociation is spontaneous, an exponentially decaying low energy tail will appear in the mass line of M”+ and m+. The tail can extend all the way from the M”+ and m+ line positions to the line position of the (M + ,)‘I+. This can be very easily understood. For those daughter ions produced immediately after the parent ions are formed, they can gain the full energy of the acceleration voltage. Thus these ions will’appear right at the flight times of M”+ and mf as if they were formed without going through the ion reaction step. On the other hand, if daughter ions are formed after the parent ions have left the acceleration section, then they will move at the same velocity as the parent ions and will be detected at the expected flight time of the parent ions. Again, we are going to draw an example from a field desorption experiment to illustrate the conclusions drawn from this analysis. We will first try to solve the master equation of this problem, Eq. (11) for field desorption. Let us consider here a very simple case, i.e. very fast spontaneous dissociation of cluster ions near the emitter surface by say photofragmentation or by electronic de-excitation induced vibrational excitation. The field and the dissociation rate are assumed to be nearly constant. Thus exp[ - kJ[2( m + M)/neF,]
fib) = kJf,(x’) xc
(x - x’)“*]
dx, (12)
j[ZneF,/(m
+ M)] (X - _Yr)“2
where x, is the critical distance of field ionization. Our measured distributions of field desorbed ions all show that f,( x’) is a very distribution with a FWHM of only 0.2-0.5 A as exemplified by Fig. qualitative understanding of the line shape in cluster dissociation assume that f,( x’) is a rectangular function of width w and height that an analytical form of fd(x) can be derived.
energy narrow 2. For a we will l/w so
fr (x’) = $ if x, I x’ S x, + w = 0 otherwise
fdb)
=x/
(13)
n,+wexp[ -kJ[2(m
xc
/[2ne&+r
+ M)/neF,]
(X
-
x))~‘*]
+ M)] (X - xf)1’2
dx,
f-
k
s
A-‘ +
M‘
1(x, x’) dx’
_,~~p~-k~~(x_x_-~)1/2
-exp[-k,/T(x
-
xc)“2]]
forx>x,+w
(14)
and
&(x)
=tJ‘l(x, x’) I,
dx’
=$[*-exp[-~/~~112]] &(x) for this simple function of x for x > time distributions of reaction are illustrated Now let us consider reaction at x.
EM(x) =
forx,Ix(x,+vv
form of jr(x) is therefore x, + w and a constant for (M + m)“+ and M ‘+ ions in Fig. 3. the final kinetic energy of
M fneF(x)dx
( m + M ) .lL
t/‘&(x) .\-
(15)
an exponentially decaying x, I x I x, + w. The flight with and without the ion an M”+ ion formed
by ion
dx
(16)
dx
(17)
But neY-
AEc+(M)
=I-‘neF(x) .X,’
dx +/‘neF(x) I
(01
(M+ml"'
FLIGHT
TIME
Fig. 3. Flight time distribution of M”+ and (M+ m)“+ with and without dissociation (M + m)“+. (See the text for explanation.) (a) No dissociation; (b) some dissociation,
of
10
Therefore EM(x)
= neV-
AEz+(M)
+
M jlneF(x) t m + M ) S<
dx -/~‘neF(x) .Y:
= neV-
AE,“+(M)
-
m (m+M)
dx
JtneF(x) XC
dx
x: is the critical distance in direct field desorption of M atoms from the surface as Mn+ ions. In Eq. (18>, we have made the approximation that x, = XL. If the field is constant, then E,(x)
= neV-
AE,“+(M)
- &n&(x
-xc)
(19)
The last term represents the part of kinetic energy of (M + m)“+ ions lost to the daughter ions m+ or atom m” at x. It is important to notice that by direct field d EM(x)/dx is different for those M”+ ions produced evaporation and those produced by the ion reaction even though the most energetic of all these ions have the same energy of neV - AE:+(M). The conclusions drawn from the above analysis are in good qualitative agreement with many of our observations. For example, in pulsed-laser stimulated field evaporation of silicon, if the laser intensity is low and d.c. field is high, then only Si2’ 1s . observed. The ion energy distributions are very sharp without any low energy tail. If the laser intensity is increased and d.c. field is lowered, then in addition to Si2+, Si’ and many Si cluster ion species are observed as shown in Figs. 4--6. While the energy distributions of Si2+ remain sharp as in regular field evaporation, Sit and all the cluster ions show low energy tails. The reason is that Si2+ can only be produced by direct field evaporation, whereas all the other ion species can be produced
2000.
1600. z. v \1200, 9,
Sdicon, 60
I
kV
300 K, 1x10-' Torr 7000
*asa
ions
0 _ k 800 0 8
400 29SiZ' 0 14520
'1. 14720 FLIGHT
Fig. 4. A TOF spectrum
n 14920 TIME
~0Si2' 15120
15320
(ns)
of SiZt taken at 6.0 kV. Note the lack of low energy tails.
11
decaying low Fig. 5. A TOF spectrum of Si+ taken at 6.0 kV. Note the long exponentially energy tails. The lack of half mass lines clearly identifies this ion species to be Si+, not Siz+.
by direct field evaporation as well as by dissociation of cluster ions. Another example is the formation of gold hydride ions as shown in Fig. 7. Pulsed-laser stimulated slow field evaporation of an Au tip in lo-* Torr of hydrogen yields Au+, and AuHz for n = 1-4. The energy distributions of these ion
Si
-Cluster
6
kV,
Ions
Ix IO-’
Magic
numbers
Critrol
no.
Torr
:4.5.6.13(?) 2+ ion:
3
f.+ lon.l3(‘)
255. c” 0 w . E ”
I
170. -I50
84 -1000
-690
-290
25610
2Si50
56
0
565
70
Si”
0 Si2+ 6
5
32690 FLIGHT
-280
36630 TIME
(ns)
Fig. 6. A TOF spectrum of silicon cluster ions. Note the low energy tails in most ion species, and especially the pronounced high energy tail in Si:. The latter is the effect of Coulomb explosion, possibly via Si:+ -+ Si: + Si+. A correct identification of the charge states and the cluster sizes is possible through the half mass lines we have observed.
’
FLIGHT
TIME
hs)
’
Fig. 7. Pulsed-laser stimulated field evaporation of Au in 1 X 1Om8 Torr of hydrogen results in formation of Auf and AuHL for m = 1-4. The shaded part is taken at low laser power. The spectral lines are sharp. As the laser power is increased, the Au + line starts to spread to both the high and low energy sides. (See the text for explanation.)
species get wider as n goes down, again is consistent with the above analysis. The energy distribution of Au+, in addition to a low energy tail, exhibits a high energy tail which will be discussed in the next section. Ions formed by an ion reaction: high energy tail in Coulomb explosion If ions are created by particle excitation such as ion bombardment in SIMS or photoexcitation in pulsed laser desorption by collective effects of the solid, then some of these ions will have energy in excess of neV, the maximum energy of the acceleration voltage. High energy tails by particle excitations are quite obvious and are not the subject of our concern here. We will show here that an ion reaction, Coulomb explosion [6], can also produce a high energy tail. Let us consider the ion reaction
W+m)
.,+
Coulomb
-+
M++m+
(20)
explosion
For simplicity, all the compound ions, (M + m)‘+, are assumed to be formed right at the electrode surface (this assumption is not necessary, but simplifies our discussion). If the ion reaction occurs at x, then the final kinetic energy of the M+ ion is given by Ix2eF( 0
x) dx + /‘eF( x) dx x
(21)
13
but J0
‘F(x)
dx = I/
(22)
Therefore (23) Equation (23) shows that as compared to M+ ions produced directly at the surface, M+ ions produced by Coulomb explosion (C.e.) have a larger final kinetic energy if M > m, the same final kinetic energy if M = m, and a smaller final kinetic energy if 1M < m. An example illustrating this point can be found in a paper by Drachsel et al. [7] in pulsed-laser stimulated field evaporation of Au. They found that when an Au tip is field evaporated with low power pulsed-laser irradiation, a fairly sharp Au+ peak can be observed, together with a small fraction of Au’+. When the laser power is increased, high energy secondary peaks start and Au;+ to appear for the Au+ and Au 2+ lines. In addition, a few Au: ions start to appear. They cannot explain satisfactorily the actual mechanism of energy transfer since the excess energy is estimated to be as high as 300 eV for Au+ and 510 eV for Au’+. These energies are about 778% of the full energies. This observation can be easily explained by invoking ion reactions of the types Coulomb
AU;+
--j
Au;_,
+Au+forn23
explosion
(24)
Cx.
2+ AU;+ --+ Au,_,
+Au+forn23
(25)
C.e.
AuHt+
-+ Au+ + Hl
etc.
(26)
The first two reactions appear unlikely since the number of cluster ions in the spectrum appear too small to account for the high energy secondary peak. The last reaction appears more likely. However, the mass resolution of their system cannot separate AuHl from Au+, thus even though it is quite clear that Coulomb explosion is responsible for the high energy peaks observed, the exact process is uncertain. Our pulsed-laser stimulated field evaporation of Au in hydrogen partial pressure of 5 X 10e9 to 1 X lo-* Torr range shoOws little high energy tail of Au+ at low laser power and high field (- 3 V A-‘) as represented by the shaded parts of Fig. 7. As the field becomes lower by gradual field evaporation and the laser power is increased, a high energy tail with an excess energy extending beyond 30 eV starts to appear in Au+. Although it
14
is again very difficult to pinpoint an exact mechanism, Eq. (26) is a likely choice since AuHl is the most abundant species and a few Au’+ ions can be observed in the experiment, similar to the result of Drachsel et al. Spectrometry
of ion reaction times: field dissociation by atomic tunneling
A high resolution TOF spectrometer is capable of measuring fast ion reactions directly with a time resolution of 10e9 to lo-” s since electronic circuits of this resolution are now quite common. The rate measurement can achieve a much better resolution if an ion reaction amplification scheme [8] is used. Using this scheme, those ion reaction events taking place in a very short time period can have their detection stretched over a much longer time period. Details of this method may be found in the original paper [8]. They can also be understood easily from the example to be discussed. The basic idea is that with the configuration we have shown in Fig. 1, if I +z L, the flight time of an ion is determined entirely by the kinetic energy of the ion when it leaves the reaction-acceleration section. The energy, however, depends entirely on the location x where the ion is produced by an ion reaction. The location depends on the ion reaction rate or the reaction time. Since the location can be determined very precisely and the velocity of the parent ion is very high, the ion reaction time can be determined with a time resolution much better than the time resolution of the flight time measuring device of the system. This method can be easily used to study ion reaction rate in Coulomb explosion, in photodissociation and in field dissociation, etc. In general, an ion reaction which occurs at a near constant rate will give rise to a low energy tail in the spectral line of the daughter ions if the charge states of the parent and daughter ions are the same, and will give rise to a high or low energy tail or none at all in Coulomb explosion depending on the masses of the parent and daughter ion species. The rate constant can be derived by fitting a theoretical model to the energy distributions of these ion species. In principle, this procedure is quite straightforward, but, in practice, there are almost always too many ion species in a spectrum and the fitting procedure is then too complicated. There is a special case where the ion reaction time can be derived quite easily and with excellent time resolution also. The ion reaction is field dissociation of RhHe2+ which we will use here as an example for a detailed discussion of ion reaction time spectroscopy. Field dissociation of a compound ion is a quantum mechanical phenomenon which has no classical analog. It is treated theoretically by Hiskes 191. Experimental evidence [lo] is based on observation of H+ ions when Hl ions are passed through a high electric field region of a few lo5 V cm-‘. This field is predicted for Hl to cause dissociation from high vibrational
15
224“
FLIGHT
TIME
Fig. 8. Pulsed-laser stimulated secondary peak of Rh”.
(ns)
28?4
field evaporation
of Rh in lo-*
Torr of 4He. Note the
states. It is also based on observation of low energy tails in field ionization mass spectral lines of hydrocarbon ions [ll]. We will present evidence of field dissociation of RhHe*+ based on observation of a secondary low energy peak of Rh*+, a RhHe*+ mass line and the non-observation of a low energy He+ mass line when Rh is pulsed-laser field evaporated in 1 x lo-’ Torr of helium below 100 K. An example is shown in Fig. 8. The well-defined secondary Rh*+ peak and the lack of a low energy He+ mass line indicates very clearly that these Rh*+ ions are produced by the ion reaction RhHe2+ + Rh2+ + He
(27)
in a well-defined spatial zone above the emitter surface. The energy difference between Rh*+ ions in the main peak and in the secondary peak, AE, can be found from AE -~E
AE =- 2At neV t,
where n = 2, V= 9500 V, At = 30 ns and t, = 22444 ns. If one approximates the tip and cathode with a parabolic configuration, one finds that AE is related to the location x where field dissociation occurs by AE=
neV 2k(l
+M/m)
In
(29)
where r0 is the tip radius, k is a constant, A4 is the mass of Rh and m is the mass of He. From Eqs. (28) and (29), one gets (30)
16
Fig. 9. A diagram
illustrating
the formation
and dissociation
of Rh4Hezt.
Using r, = 420 A, k = 5, M = 103 u and m = 4 u, one finds x = 220 A. The flight time of RhHe*+ over this distance with the field starting from zero velocity is given by (31) t(220 A) = 7.9 x lo-l3
s
Thus this TOF spectrum shows that a significant fraction ofOfield evaporated RhHe*T is field dissociated in a spatial zone of about 150 A width centered at 220 A above the emitter surface as shown in Fig. 9. The field dissociation occurs in 8 X lo-r3 s. Once a RhHe*+ ton passes through this dissociation zone, it exhibits stability. One would expect field dissociation to produce a low energy tail in the Rh*+ line instead of a very well-defined secondary peak. An explanation based on the theory by Hiskes [9] will be discussed. The equation of relative motion of He and Rh*+ in a RhHe*+ ion is given by
where p = m/[l + (m/M)] is the reduced mass of RhHe*+, Zn is the vector along the direction of pointing from He+to Rh2+, and z, is its component the electric field, F. Atomic tunneling can occur only if z, is positive. When a RhHe*+ ion is just field evaporated, z, is negative as shown in orientation A in Fig. 9. As the ion accelerates away, it also rotates by the torque of the electric force. When it rotates by 180” to orientation B, it can field dissociate. It if fails to field dissociate while in this correct orientation, it will take another full rotation of 360”, i.e. a total of thrice the time, to be in the right orientation again. By this time it is too far away from the surface and the field is too low for field dissociation to occur. Thus the field dissociation
17
zone is the result of the interplay of acceleration, rotation, vibration and atomic tunneling. The rotational motion is coherent in the sense that all RhHe2+ ions start from orientation A. For comparison, the ionization zone in field ionization is the result of the electron tunneling rate and the Fermi level of the metal. The zone is less than 0.3 A in width and it is about 4 A above the surface. The rotational motion of RhHe2+ can be estimated as the following. If we omit considering the electric force, then the rotational energy is given by
E _- J(J+1)A2 = hw mt 0 w,2
(33)
where p = 6.39 x 1O-27 kg is the reduced mass of the ion, and r, = 2.6 A is the distance between the Rh and He nuclei. One can easily show that the time needed for rotating 180” is given by
t, =
T-4 JJ(J+~)~
I-
v-4 Jfi
for large J
If we use t, = 8 x lo-l3 s, we find the rotational quantum J = 16: this corresponds to an average temperature of - 500 K. unreasonable since the substrate temperature is probably above the laser heating. However, if we consider the forced rotation by force using classical mechanics
(34) number of This is not 200 K by the electric
2
2eFr,,
pr:$=
(35)
we find t, =
/ OT[(4eF/h4r,,)(ldT
cos) + w;]~‘~
Using numerical integration, one can easily show that 1, = 3.35 X lo-l3 s for J = 1. The calculated time is too short by a factor of 3. Of course, classical mechanical calculation may not be correct, and the changes in J due to the acceleration caused by the applied electric force may lead to longer times of rotation. At the moment, no such calculation is available. Another interesting observation supporting field dissociation of RhHe2+ as an atomic tunneling phenomenon is a dramatic change in the dissociation behaviour when 4He is replaced with 3He as shown in Fig. 10. The secondary Rh2+ peak is no longer there although a few scattered low energy ions can still be found. This observation can be qualitatively understood by considering the tunneling probability. From Eq. (32) one can see that with 3He the reduced mass of RhHe2+ will be smaller, thus the barrier penetra-
Rh, 52K.9.5 kV 1.9 - 4.6 v/h pHe=2 x IO“ torr 690
ions h3He2+
?h*’
Rh4He2+ Ivcl:.-!
:
6”s
:
:
FLIGHT
:
8 :
+
TIME ‘t,
*
Fig. 10. Pulsed-laser stimulated field evaporation of Rh in lo-’ gas. Note the secondary Rh2’ peak is no longer present.
Torr of 3He-3%
4He mixed
tion probability will increase. However, the potential barrier reducing term -2eF’z/(l + M/m) is also mass dependent. With a smaller value of m the magnitude of this term is reduced, thus the barrier penetration will decrease. Apparently, the latter effect is more significant for RhHe2+ as can be seen from a WKB estimation. For this purpose the segment of U(m) will be approximated by a straight line of slope sl. The barrier is therefore a triangle of height h and with two sides of slope s1 and - 2eF/(l + M/m). The barrier penetration probability per encounter of the potential barrier is then given by D(h,
F)=exp~-~(~j1’2i$+1-2~~jh3/2i
(37)
where h is the barrier height. The interaction between He and Rh2+ should be very short ranged, thus l/s, s (1 + M/y))/neF and the l/s, term can be omitted. Fig. 8 shows that at - 4.5 V A-‘, D( h, F) should be a few percent: w,e therefore assume that for 4HeRh2+, h = 0 and D( h, F) = 1 at F = 4.8 V A-‘. The binding energy H of HeRh2’ should be the same for 3He and 4He. I? and h are related to each other by 2 eFr, h=H-(l+M,??z)
(38)
Using Eqs. (37) and (38), the barrier penetration probability per barrier encounter for 4HeRh2+ and 3HeRh2+ at different fields are listed in Table 2. This WKB calculation gives a dissociation rate of 3HeRh2+ smaller than that of 4HeRh2+ by several orders of magnitude. The calculated values of
19
I
M=l03.m
= 4 or 3
Fig. 11. A potential energy diagram illustrating the barrier used for estimating the barrier penetration probability in fiel_d dissociation using WKB-approximation. This diagram is validonly when Z is parallel to F. 7 is the bond vector pointing from He to Rh”.
D(h, F) are consistent with the experimental results. The calculation also gives a binding energy of HeRh2’ to be H = neFr,/(l + M/m) = 2 x 3.5 x 2.6/26.75 eV = 0.68 eV, consistent with a theoretical calculation [12]. Of course the calculation given is intended only for a qualitative understanding of the isotope effect we have observed. A detailed explanation will be given later [14]. The time resolution of this measurement can be calculated by realizing that the system is equipped with a digital timer of 1 ns resolution and the desorption event can be defined to within 0.3 ns, the width of the laser pulses. The overall time resolution of the system is approximately 1112 = 1 ns. This corresponds to an energy difference of about 1.69 eV, or a difference in the location of ion formation of about 0.18 A. As the velocity of a RhHe2+ ion at x = 220 A is about 1 X lo5 cm s-l, the difference in the ion reaction time is 2 X lo-t4 s. This corresponds to an amplification factor of 1 ns/2 X lo-l4 s = 5 X 104. A detailed analysis
TABLE 2 Values of D(h, F) F(V A-‘)
4.8 4.7 4.6 4.5 4.4 4.3
D(h,
F)
HeRh2’
3HeRh2+
1 0.65 0.28 0.09 0.02 0.01
2.4~10-~ < lo-‘0 < 10’0 < 10-10 < 10-10 < lo-‘0
20 shows
that the amplification
factor in this experiment
is given by
and A (220 A) = 4.8 X 104. The time resolution of this measurement is therefore 21 fs. This high amplification factor is due in part to the L/l = 3500 of the system, and in part due to the very fast drop in the field strength near the tip surface because of the very sharp field ion emitter. CONCLUSIONS
The time-of-flight spectrometer has been used mainly as a mass analyzer, and occasionally as an ion energy analyzer. We present here some analyses of the line shape, emphasizing the energy and time aspects of the time-offlight spectrometry. All the analyses presented are intended to be very general and are applicable to most time-of-flight spectrometers. However, specific examples are drawn mostly from data taken with our high resolution pulsed-laser time-of-flight atom-probe spectrometer. We illustrate the time spectroscopy aspect with a detailed discussion of field dissociation of RhHe2+ and show the richness of information contained in a high resolution time-of-flight spectrum. In this measurement we have already achieved a time resolution of 20 fs, and further improvement can be made. The time resolution is now more than sufficient to resolve single vibrational events of compound ions. However, time resolved spectroscopy of the vibration of compound ions can be made only if all the ions vibrate coherently with respect to the desorption event. Also, we do not have sufficient data at the present time. The secondary Rh2+ peak in our data on RhHe’+ is interpreted as arising from a coherent rotational motion of the ions when they are desorbed from the surface, i.e. they all start in orientation A. We are certain that further refinement in both experimental methods and data analyses can be made to study ion reactions in much better detail with the time-of-flight spectrometry. ACKNOWLEDGEMENTS
This work was supported by NSF DMR-8217119 and DOE DE-ACOZ81 ER10857. Some of the data presented were taken with the help of Y. Liou. REFERENCES 1 E.W. Miiller, J.A. Panitz and S.B. McLane, Rev. Sci. Instrum., 39 (1968) 83. E.W. Mtiller and T.T. Tsong, Prog. Surf. Sci., 4 (1973) I and references cited therein. E.W. Miiller and S.V. Krishnaswamy, Rev. Sci. Instrum., 45 (1974) 1053.
21 2 K. Sattler, J. Miihlback, E. Recknagel and A.R. Flotte, J. Phys. E. 13 (1980) 673. P. Pfau. K. Sattler, P. Pflaum and E. Recknagel, Phys. Lett. A, 104 (1984) 262. A. Benninghoven, Int. J. Mass Spectrom. Ion Phys., 53 (1983) 85. E. Ens, R. Beavis and K.G. Standing, Phys. Rev. Lett., 50 (1984) 27. 3 W. Drachsel, S. Nishigaki and J.H. Block, Int. J. Mass Spectrom. Ion Phys., 32 (1980) 222. G.L. Kellogg and T.T. Tsong, J. Appl. Phys., 51 (1980) 1184. 4 (a) T.T. Tsong, S.B. McLane and T.J. Kinkus, Rev. Sci. Instrum., 53 (1982) 1442. (b) T.T. Tsong, Y. Liou and S.B. McLane, Rev. Sci. Instrum.. 55 (1984) 1252. 5 T.T. Tsong, Phys. Rev. B, 30 (1984) 4946. T.T. Tsong. T.J. Kinkus and S.B. McLane, J. Chem. Phys., 78 (1983) 7497. 6 K. Sattler, S. Miihlback, 0. Echt, P. Pfau and E. Recknagel, Phys. Rev. Lett.. 47 (1981) 160. 7 W. Drachsel, Th. Jentsch and J.H. Block, Proc. 29th Int. Field Emission Symp., 299 (1982) Almqvist & Wiksell International. Stockholm, Sweden 1982. p. 299. 8 T.T. Tsong, J. Appl. Phys.. 58 (1985) 2404. 9 J.R. Hiskes, Phys. Rev., 122 (1961) 1207. 10 A.C. Riviera and D.R. Sweetman, Phys. Rev. Lett.. 5 (1960) 560. 11 H.D. Beckey. Field Ionization Mass Spectrometry, Pergamon, Oxford. 1971, and references cited therein. 12 M. Hotokk, T. Kinsted. P. Pyykko and Bo Roos. Mol. Phys.. 52 (1984) 23. 13 C.M. Lederer and V.S. Shirley (Eds.). Table of Isotopes, Wiley. New York, 7th edn.. 1978. 14 T.T. Tsong and M. Cole. to be published.
Journal
of Mass Spectrometry
Elsevier Science Publishers
TIME-OF-FLIGHT SPECTROMETRY, ION FORMATION
and Ion Processes,
B.V.. Amsterdam
- Printed
70 (1986)
l-21
in The Netherlands
ION ENERGY AND ION REACTION TIME SPECTRAL LINE SHAPE AND MECHANISMS
OF
T.T. TSONG Physics Department,
(First received
The Pennsylvania
State University, Universicv Park, PA I6802 (U, S.A.)
9 July 1985; in final form 11 December
1985)
ABSTRACT Methods are presented for achieving a better accuracy in the ion energy analysis and an excellent time resolution in the ion reaction time measurement using the time-of-flight spectrometer. Analyses are also presented to show that the mechanisms of ion formation can be derived directly from the spectral line shape. Specific examples drawn from high resoiution pulsed-laser time-of-flight atom-probe spectrometer measurements are used to illustrate these methods and analyses. The richness of information contained in a high resolution time-of-flight spectrum is demonstrated with a study of field dissociation by atomic tunneling of RhHe’+ ions. The time resolution in this dissociation time measurement is as good as 20 fs, and a feature related to half a period of the rotational motion of the ion can be observed in the time-of-flight spectrum from fully resolved peaks.
INTRODUCTION
Time-of-flight (TOF) spectrometry has gained considerable popularity recently because of its simplicity in principle and operation, and the rapid progress made in fast electronics [l-4]. Although the time-of-flight spectrometer is mainly used as a tool for mass analysis, thus it is almost always called a TOF mass spectrometer, the spectrum is in fact much richer in information. A high resolution TOF spectrum contains the energy distribution of each ion species, and also information on where, how and when these ions are formed [5]. This information can be derived quite simply and directly from the line shape of the TOF spectral lines. The method of data analysis can be very simple if the spatial zone of formation of parent ions is very narrow such as right at the surface in field desorption and in desorption stimulated by particle bombardment, or can be made very narrow by a proper focusing of the electron and laser beam in electron impact ionization and photoionization or photofragmentation. We 0168-1176/86/$03.50
0 1986 Elsevier Science Publishers
B.V
2
present here a general analysis of the line shape in time-of-flight spectrometry, and also methods for an accurate ion energy measurement and a precision ion reaction time measurement. For these purposes, a special time-of-flight spectrometer configuration will be used. Examples illustrating these basic principles and methods will be drawn from field desorption experiments made with a high resolution pulsed-laser time-of-flight atomprobe spectrometer 141. A METHOD TROMETER
FOR AN ACCURATE
CALIBRATION
OF A TIME-OF-FLIGHT
SPEC-
There are many different configurations of TOF spectrometers. We will discuss only one generally used configuration here (Fig. I). However, variations to other configurations can be worked out based on the same principle. There are two separate sections, i.e. the ion formation-acceleration section of length I and the ion free drift section of length L. To achieve the best possible resolution in ion energy and ion reaction time spectrometry one should make I c L so that the total flight time of an ion is determined essentially by the kinetic energy of the ion when it has left the ion formation-acceleration section. To simplify the data analysis, one should also make the two sections well isolated by a small hole or a grid although in principle this is not a requirement. There are two constants of the system which have to be determined very accurately first. The kinetic energy of an ion is related to its flight time by
where t is the “ measured flight time” and 6 is a time delay constant accounting for the time delay in the detection process, which is due mainly to the generation and transmission times of the triggering and the ion
Acceleration section
Free flight section
I
Detector
Fig. 1. Configuration
of a time-of-flight
spectrometer.
3
signals. In the equation, the ion mass M is usually known to better than one part in 106. L and 6 are very difficult to measure directly with great accuracy. To achieve high resolution in energy and time spectrometry, accurate values of these two constants must be known. Fortunately, there usually exists an ion formation process whose energetics are very well established. In such a case, Eq. (1) should be rewritten as (2)
t=&-s
/’
Thus by measuring very carefully the “flight time” t as a function of ion energy E, and plotting t vs. I//%!$?? using the linear regression, very accurate values of L and 6 can be obtained from the slope and the intercept of the linear plot. Note that the graphical method does not usually give sufficient precision. A real example will now be drawn from the calibration of a pulsed-laser TOF atom-probe spectrometer to illustrate this method and to show the accuracy achievable [4]. In this spectrometer the sample is a sharp needle of tip radius 200-1000 A. I = 1.2 mm and L = 4200 mm: thus L/I = 3500. In fact, because of the needle-shaped geometry of the positive electrode, the effective value of L/I is much higher as will be discussed later. The system can be calibrated by measuring the flight time of pulsed-laser field desorbed inert gas ions as a function of the tip voltage. It has been established through an excellent agreement between a theoretical analysis and an experimental measurement that in pulsed-laser stimulated field desorption of adsorbed gases, ions are produced by field ionization in the field ionization zone of thermally desorbed neutral species [5]. Thus the final kinetic energy of the most energetic ions is eV - (Z - +) where V is the tip voltage, Z is the ionization energy of the gas atoms, and cp is the work function of the final electrode. In a TOF spectrometer, the average work function of the drift tube should be used since a drifting ion sees this work function most of its flight time. (I - +) is usually referred to as the critical energy deficit, AE,, of the ions. Thus Eq. (1) can be written as l/2
‘/2
A4
v-
(Q/e)
V-
(rE,/e)
i
-’
(3)
In the calibration of the system, the onset flight times, or the flight times of the most energetic ions, of He+, Ne+ and Ar+ as a function of V are measured, and a best linear fit of t vs. [M/( V - AE,/e)]“* is obtained by linear regression. From the slope and the intercept, accurate values of C and 6 as listed in Table 1 are derived. The linearity of the plot, which reflects the validity of Eq. (3) and the entire analysis, can be seen from the value of the
TABLE 1 Flight time data for He+, Ne+ and Rh*+ (C = 0.01073628 u p”sP2 kV_‘, Ion species He+
Ionic mass a (u) 4.002054
AE, b (eV) 20.10
Tip voltage
6 = 28.3 ns)
(kV)
Measured onset flight time (ns)
3.5 4.0 4.5 5.0 5.5 6.0 7.0 8.0 9.0 9.5 10.0 10.5
10.322 9.649 9.093 8.623 8.219 7.867 7.279 6.806 6.414 6.242 6.083 5.936
M = 4.001881 & 0.000455 u, SM = - 0.000173 + 0.000445 u AE, =19.82+0.87 eV, iS(AE,) = -0.28kO.87 eV ‘ONei
19.991890
17.0X103
3.0 3.5 4.0 4.5 5.0 5.5 6.0 7.0 8.0 9.0
24.956 23.094 21.593 20.353 19.303 18.400 17.614 16.302 15.245 14.370
M = 19.992687 + 0.000950 u, 6M = 0.000797 k 0.000950 u AfTc=17.29+0.31 eV, S(AE,)=0.32&-0.31 eV 12Ne+
21.990835
17.0
3.5 4.0 4.5 5.0 5.5 6.0 1.0 8.0 9.0
51.452201
10.9x2
8.0 --.24.464 9.0 9.5 10.0 10.5
M/t? = 51.448751 f 0.002324 u. S( M/n) = - 0.003450& 0.002324 u =10.25,0.42 eV, G(AE,/n) = --0.6550.74 eV
hE,/tr
See Table notes on following page.
-24.223 22.648 21.345 20.246 19.298 18.475 17.099 15.991 IS.073 ~...~
-23.060 22.444 21.874 21.346
5
coefficient of determination Y’ obtained [4b], which differs from 1 by only 1.2 x 10-s. An accuracy of about 5 parts in lo5 can be achieved routinely in mass and energy analysis using the values of C and 6 listed in the table. The same accuracy is achieved even when an einzel lens in the drift tube section is used to focus the ions although the value of C can change by almost 1%. With these two constants, the kinetic energy (absolute value) of any field desorbed ions can be calculated directly from its measured flight time t by E=
eM c( t + 8)”
ION ENERGY
DISTRIBUTION
Primury ions The flight time distribution of an ion species is also the ion energy distribution, which is related directly to the dynamics of ion formation. We consider first primary ions, i.e. ions not formed by further ion reactions. If an ion of n + charge state is emitted from the surface with an initial kinetic energy Ei, for example in the ion bombardment of a surface, then the final kinetic energy of the ion will be Ei + neV. On the other hand, if an t? + ion is formed at a distance x away from the surface with a negligible initial kinetic energy, e.g. by field ionization or by photoionization, then the final kinetic energy of the ion is neV- tzel,‘F(x’) dx’ where F(x) is the applied field at x. Thus by measuring the ion energy distribution the energy transfer process in the ion formation, or the spatial zone of ion formation. can be investigated. Let us define a few density functions of ion formation as follows: f,(E) d E represents the fractional number of ions formed with their final kinetic energy in the range between E and E + d E, f,(x) dx represents the fractional number of ions formed in the range between x and x + dx. and fF(t) dt represents the fractional number of ions formed with their total
Notes to Table 2 ’ Ionic masses are from ref. 13. h A EC values are calculated from AE, = C:l=,I, - n& + A, energy of the atom, & = 4.5 eV is the average work function sublimation energy. Experimentally measured M and AE, for each ion species table and theoretical values are given under the experimental
where I, is the ith ionization of the flight tube, and 12 is the and their deviations from the data of each ion species.
6
Rh2:55K,95kV 50-48
V/A
Fig. 2. A histogram of ion flight times in pulsed-laser stimulated field evaporation lo-” Torr at 55 K. The onset flight time is 22444 ns and FWHM is 4 ns.
of Rh in
flight time between t and t + dt. f,(t) is measured in a TOF spectrometer. and the other density functions can be derived from ,jr( t) using the relations
(5)
where dt - -&(t+s)’ dE
(6)
and dt/dx can be calculated if the electric field distribution in the ion formation-acceleration section is known. The discussion presented above is generally known although for completeness we will illustrate with an example from a study of pulsed-laser stimulated field desorption of rhodium. A flight time distribution of Rh*+ taken at 9.5 kV and a field of about 4.9 V p\-’ is shown in Fig. 2. From the mass and the onset flight time, 22.444 ps, the critical energy deficit of Rh’+ is calculated from Eq. (3) to be 20.5 A 0.84 eV, in good agreement with that expected from A E,“+ = A + C:Z, - 2~ = 21.8 eV, where A is the sublimation energy and I, is the ith ionization energy. The measured FWHM is 4 ns. In a histogram, the true FWHM is the measured value minus 1-2 bin widths. The real FWHM is therefore 2-3 ns. From Eq. (6), this corresponds to an energy spread of 3.4-5.1 eV. The electric field at the Rh emitter surface is about 4.8 V A-‘. Thus Rh ions are formed in a spatial zone of 0.35-0.53 A in width. The width is related to the dynamics of ion formation or spatial variation of electron tunneling probability.
Ions formed
by an ion reuction: low energv tail
An ion reaction usually refers to the dissociation of a compound ion into smaller ions. This is not the most general definition, but we will confine our discussion to this aspect of ion reactions even though the principle presented here can be extended to other types of ion reactions. Recently, ion reactions such as Coulomb explosion of multiply charged cluster ions, photofragmentation of cluster and compound ions, spontaneous dissociation by electronic de-excitation induced vibrational excitation, and field dissociation by atomic tunneling, etc. have attracted considerable interest. We will discuss here the energetics and line shapes of TOF spectral lines when an ion reaction is involved in the ion formation. Let us assume that the parent ions, (M + m)“+ are formed within the formation-acceleration section with the spatial density function represented by ff(_y) as defined earlier. These ions dissociate spontaneously within the acceleration section via (M + m)“+ + M”+ + mf + eP (returned
to + electrode)
or + M”+ + m” (7)
We will define a spatial density function f,(x) for the formation of the daughter ions M”+ and mt or m”. fd(x) dx represents the fractional number of cluster ions dissociated between .Y and x + dx. The probability that a parent ion formed at x’ survives at .Y without dissociation will be represented by p(x’, x), and the dissociation rate constant is represented by k(x). p(x’, x) satisfies the difference equation
p(x’, where p(x’.
x +
dx) =p(x’,
x) + dp(x’,
u( x’, x) is the velocity
x) =p(x’
of the parent
ion (formed
at x’) at x. Since
x’) = 1, we have
forx>x’
PW
The fractional given by
number
of parent
ions dissociated
4 We therefore
(9)
k(x)
dx
u(x’,
x)
between
x and dx is then
(10)
have
k( XI’) dx”/u( D(x,, x>
x’, x”)]
1
dx’
(11)
8
This equation tells us that if we know the spatial density function of formation of parent ions fr(x), the rate constant k(x), and the field distribution and therefore the velocity of the parent ions u(x’, x), then the spatial density function of formation of daughter ions fd( X) can be derived. The flight time and energy distribution of M”+ and mt can then be derived once f,(x) is known. It can be shown, as can be understood from the field desorption experiment to be described below, that if the dissociation is spontaneous, an exponentially decaying low energy tail will appear in the mass line of M”+ and m+. The tail can extend all the way from the M”+ and m+ line positions to the line position of the (M + ,)‘I+. This can be very easily understood. For those daughter ions produced immediately after the parent ions are formed, they can gain the full energy of the acceleration voltage. Thus these ions will’appear right at the flight times of M”+ and mf as if they were formed without going through the ion reaction step. On the other hand, if daughter ions are formed after the parent ions have left the acceleration section, then they will move at the same velocity as the parent ions and will be detected at the expected flight time of the parent ions. Again, we are going to draw an example from a field desorption experiment to illustrate the conclusions drawn from this analysis. We will first try to solve the master equation of this problem, Eq. (11) for field desorption. Let us consider here a very simple case, i.e. very fast spontaneous dissociation of cluster ions near the emitter surface by say photofragmentation or by electronic de-excitation induced vibrational excitation. The field and the dissociation rate are assumed to be nearly constant. Thus exp[ - kJ[2( m + M)/neF,]
fib) = kJf,(x’) xc
(x - x’)“*]
dx, (12)
j[ZneF,/(m
+ M)] (X - _Yr)“2
where x, is the critical distance of field ionization. Our measured distributions of field desorbed ions all show that f,( x’) is a very distribution with a FWHM of only 0.2-0.5 A as exemplified by Fig. qualitative understanding of the line shape in cluster dissociation assume that f,( x’) is a rectangular function of width w and height that an analytical form of fd(x) can be derived.
energy narrow 2. For a we will l/w so
fr (x’) = $ if x, I x’ S x, + w = 0 otherwise
fdb)
=x/
(13)
n,+wexp[ -kJ[2(m
xc
/[2ne&+r
+ M)/neF,]
(X
-
x))~‘*]
+ M)] (X - xf)1’2
dx,
f-
k
s
A-‘ +
M‘
1(x, x’) dx’
_,~~p~-k~~(x_x_-~)1/2
-exp[-k,/T(x
-
xc)“2]]
forx>x,+w
(14)
and
&(x)
=tJ‘l(x, x’) I,
dx’
=$[*-exp[-~/~~112]] &(x) for this simple function of x for x > time distributions of reaction are illustrated Now let us consider reaction at x.
EM(x) =
forx,Ix(x,+vv
form of jr(x) is therefore x, + w and a constant for (M + m)“+ and M ‘+ ions in Fig. 3. the final kinetic energy of
M fneF(x)dx
( m + M ) .lL
t/‘&(x) .\-
(15)
an exponentially decaying x, I x I x, + w. The flight with and without the ion an M”+ ion formed
by ion
dx
(16)
dx
(17)
But neY-
AEc+(M)
=I-‘neF(x) .X,’
dx +/‘neF(x) I
(01
(M+ml"'
FLIGHT
TIME
Fig. 3. Flight time distribution of M”+ and (M+ m)“+ with and without dissociation (M + m)“+. (See the text for explanation.) (a) No dissociation; (b) some dissociation,
of
10
Therefore EM(x)
= neV-
AEz+(M)
+
M jlneF(x) t m + M ) S<
dx -/~‘neF(x) .Y:
= neV-
AE,“+(M)
-
m (m+M)
dx
JtneF(x) XC
dx
x: is the critical distance in direct field desorption of M atoms from the surface as Mn+ ions. In Eq. (18>, we have made the approximation that x, = XL. If the field is constant, then E,(x)
= neV-
AE,“+(M)
- &n&(x
-xc)
(19)
The last term represents the part of kinetic energy of (M + m)“+ ions lost to the daughter ions m+ or atom m” at x. It is important to notice that by direct field d EM(x)/dx is different for those M”+ ions produced evaporation and those produced by the ion reaction even though the most energetic of all these ions have the same energy of neV - AE:+(M). The conclusions drawn from the above analysis are in good qualitative agreement with many of our observations. For example, in pulsed-laser stimulated field evaporation of silicon, if the laser intensity is low and d.c. field is high, then only Si2’ 1s . observed. The ion energy distributions are very sharp without any low energy tail. If the laser intensity is increased and d.c. field is lowered, then in addition to Si2+, Si’ and many Si cluster ion species are observed as shown in Figs. 4--6. While the energy distributions of Si2+ remain sharp as in regular field evaporation, Sit and all the cluster ions show low energy tails. The reason is that Si2+ can only be produced by direct field evaporation, whereas all the other ion species can be produced
2000.
1600. z. v \1200, 9,
Sdicon, 60
I
kV
300 K, 1x10-' Torr 7000
*asa
ions
0 _ k 800 0 8
400 29SiZ' 0 14520
'1. 14720 FLIGHT
Fig. 4. A TOF spectrum
n 14920 TIME
~0Si2' 15120
15320
(ns)
of SiZt taken at 6.0 kV. Note the lack of low energy tails.
11
decaying low Fig. 5. A TOF spectrum of Si+ taken at 6.0 kV. Note the long exponentially energy tails. The lack of half mass lines clearly identifies this ion species to be Si+, not Siz+.
by direct field evaporation as well as by dissociation of cluster ions. Another example is the formation of gold hydride ions as shown in Fig. 7. Pulsed-laser stimulated slow field evaporation of an Au tip in lo-* Torr of hydrogen yields Au+, and AuHz for n = 1-4. The energy distributions of these ion
Si
-Cluster
6
kV,
Ions
Ix IO-’
Magic
numbers
Critrol
no.
Torr
:4.5.6.13(?) 2+ ion:
3
f.+ lon.l3(‘)
255. c” 0 w . E ”
I
170. -I50
84 -1000
-690
-290
25610
2Si50
56
0
565
70
Si”
0 Si2+ 6
5
32690 FLIGHT
-280
36630 TIME
(ns)
Fig. 6. A TOF spectrum of silicon cluster ions. Note the low energy tails in most ion species, and especially the pronounced high energy tail in Si:. The latter is the effect of Coulomb explosion, possibly via Si:+ -+ Si: + Si+. A correct identification of the charge states and the cluster sizes is possible through the half mass lines we have observed.
’
FLIGHT
TIME
hs)
’
Fig. 7. Pulsed-laser stimulated field evaporation of Au in 1 X 1Om8 Torr of hydrogen results in formation of Auf and AuHL for m = 1-4. The shaded part is taken at low laser power. The spectral lines are sharp. As the laser power is increased, the Au + line starts to spread to both the high and low energy sides. (See the text for explanation.)
species get wider as n goes down, again is consistent with the above analysis. The energy distribution of Au+, in addition to a low energy tail, exhibits a high energy tail which will be discussed in the next section. Ions formed by an ion reaction: high energy tail in Coulomb explosion If ions are created by particle excitation such as ion bombardment in SIMS or photoexcitation in pulsed laser desorption by collective effects of the solid, then some of these ions will have energy in excess of neV, the maximum energy of the acceleration voltage. High energy tails by particle excitations are quite obvious and are not the subject of our concern here. We will show here that an ion reaction, Coulomb explosion [6], can also produce a high energy tail. Let us consider the ion reaction
W+m)
.,+
Coulomb
-+
M++m+
(20)
explosion
For simplicity, all the compound ions, (M + m)‘+, are assumed to be formed right at the electrode surface (this assumption is not necessary, but simplifies our discussion). If the ion reaction occurs at x, then the final kinetic energy of the M+ ion is given by Ix2eF( 0
x) dx + /‘eF( x) dx x
(21)
13
but J0
‘F(x)
dx = I/
(22)
Therefore (23) Equation (23) shows that as compared to M+ ions produced directly at the surface, M+ ions produced by Coulomb explosion (C.e.) have a larger final kinetic energy if M > m, the same final kinetic energy if M = m, and a smaller final kinetic energy if 1M < m. An example illustrating this point can be found in a paper by Drachsel et al. [7] in pulsed-laser stimulated field evaporation of Au. They found that when an Au tip is field evaporated with low power pulsed-laser irradiation, a fairly sharp Au+ peak can be observed, together with a small fraction of Au’+. When the laser power is increased, high energy secondary peaks start and Au;+ to appear for the Au+ and Au 2+ lines. In addition, a few Au: ions start to appear. They cannot explain satisfactorily the actual mechanism of energy transfer since the excess energy is estimated to be as high as 300 eV for Au+ and 510 eV for Au’+. These energies are about 778% of the full energies. This observation can be easily explained by invoking ion reactions of the types Coulomb
AU;+
--j
Au;_,
+Au+forn23
explosion
(24)
Cx.
2+ AU;+ --+ Au,_,
+Au+forn23
(25)
C.e.
AuHt+
-+ Au+ + Hl
etc.
(26)
The first two reactions appear unlikely since the number of cluster ions in the spectrum appear too small to account for the high energy secondary peak. The last reaction appears more likely. However, the mass resolution of their system cannot separate AuHl from Au+, thus even though it is quite clear that Coulomb explosion is responsible for the high energy peaks observed, the exact process is uncertain. Our pulsed-laser stimulated field evaporation of Au in hydrogen partial pressure of 5 X 10e9 to 1 X lo-* Torr range shoOws little high energy tail of Au+ at low laser power and high field (- 3 V A-‘) as represented by the shaded parts of Fig. 7. As the field becomes lower by gradual field evaporation and the laser power is increased, a high energy tail with an excess energy extending beyond 30 eV starts to appear in Au+. Although it
14
is again very difficult to pinpoint an exact mechanism, Eq. (26) is a likely choice since AuHl is the most abundant species and a few Au’+ ions can be observed in the experiment, similar to the result of Drachsel et al. Spectrometry
of ion reaction times: field dissociation by atomic tunneling
A high resolution TOF spectrometer is capable of measuring fast ion reactions directly with a time resolution of 10e9 to lo-” s since electronic circuits of this resolution are now quite common. The rate measurement can achieve a much better resolution if an ion reaction amplification scheme [8] is used. Using this scheme, those ion reaction events taking place in a very short time period can have their detection stretched over a much longer time period. Details of this method may be found in the original paper [8]. They can also be understood easily from the example to be discussed. The basic idea is that with the configuration we have shown in Fig. 1, if I +z L, the flight time of an ion is determined entirely by the kinetic energy of the ion when it leaves the reaction-acceleration section. The energy, however, depends entirely on the location x where the ion is produced by an ion reaction. The location depends on the ion reaction rate or the reaction time. Since the location can be determined very precisely and the velocity of the parent ion is very high, the ion reaction time can be determined with a time resolution much better than the time resolution of the flight time measuring device of the system. This method can be easily used to study ion reaction rate in Coulomb explosion, in photodissociation and in field dissociation, etc. In general, an ion reaction which occurs at a near constant rate will give rise to a low energy tail in the spectral line of the daughter ions if the charge states of the parent and daughter ions are the same, and will give rise to a high or low energy tail or none at all in Coulomb explosion depending on the masses of the parent and daughter ion species. The rate constant can be derived by fitting a theoretical model to the energy distributions of these ion species. In principle, this procedure is quite straightforward, but, in practice, there are almost always too many ion species in a spectrum and the fitting procedure is then too complicated. There is a special case where the ion reaction time can be derived quite easily and with excellent time resolution also. The ion reaction is field dissociation of RhHe2+ which we will use here as an example for a detailed discussion of ion reaction time spectroscopy. Field dissociation of a compound ion is a quantum mechanical phenomenon which has no classical analog. It is treated theoretically by Hiskes 191. Experimental evidence [lo] is based on observation of H+ ions when Hl ions are passed through a high electric field region of a few lo5 V cm-‘. This field is predicted for Hl to cause dissociation from high vibrational
15
224“
FLIGHT
TIME
Fig. 8. Pulsed-laser stimulated secondary peak of Rh”.
(ns)
28?4
field evaporation
of Rh in lo-*
Torr of 4He. Note the
states. It is also based on observation of low energy tails in field ionization mass spectral lines of hydrocarbon ions [ll]. We will present evidence of field dissociation of RhHe*+ based on observation of a secondary low energy peak of Rh*+, a RhHe*+ mass line and the non-observation of a low energy He+ mass line when Rh is pulsed-laser field evaporated in 1 x lo-’ Torr of helium below 100 K. An example is shown in Fig. 8. The well-defined secondary Rh*+ peak and the lack of a low energy He+ mass line indicates very clearly that these Rh*+ ions are produced by the ion reaction RhHe2+ + Rh2+ + He
(27)
in a well-defined spatial zone above the emitter surface. The energy difference between Rh*+ ions in the main peak and in the secondary peak, AE, can be found from AE -~E
AE =- 2At neV t,
where n = 2, V= 9500 V, At = 30 ns and t, = 22444 ns. If one approximates the tip and cathode with a parabolic configuration, one finds that AE is related to the location x where field dissociation occurs by AE=
neV 2k(l
+M/m)
In
(29)
where r0 is the tip radius, k is a constant, A4 is the mass of Rh and m is the mass of He. From Eqs. (28) and (29), one gets (30)
16
Fig. 9. A diagram
illustrating
the formation
and dissociation
of Rh4Hezt.
Using r, = 420 A, k = 5, M = 103 u and m = 4 u, one finds x = 220 A. The flight time of RhHe*+ over this distance with the field starting from zero velocity is given by (31) t(220 A) = 7.9 x lo-l3
s
Thus this TOF spectrum shows that a significant fraction ofOfield evaporated RhHe*T is field dissociated in a spatial zone of about 150 A width centered at 220 A above the emitter surface as shown in Fig. 9. The field dissociation occurs in 8 X lo-r3 s. Once a RhHe*+ ton passes through this dissociation zone, it exhibits stability. One would expect field dissociation to produce a low energy tail in the Rh*+ line instead of a very well-defined secondary peak. An explanation based on the theory by Hiskes [9] will be discussed. The equation of relative motion of He and Rh*+ in a RhHe*+ ion is given by
where p = m/[l + (m/M)] is the reduced mass of RhHe*+, Zn is the vector along the direction of pointing from He+to Rh2+, and z, is its component the electric field, F. Atomic tunneling can occur only if z, is positive. When a RhHe*+ ion is just field evaporated, z, is negative as shown in orientation A in Fig. 9. As the ion accelerates away, it also rotates by the torque of the electric force. When it rotates by 180” to orientation B, it can field dissociate. It if fails to field dissociate while in this correct orientation, it will take another full rotation of 360”, i.e. a total of thrice the time, to be in the right orientation again. By this time it is too far away from the surface and the field is too low for field dissociation to occur. Thus the field dissociation
17
zone is the result of the interplay of acceleration, rotation, vibration and atomic tunneling. The rotational motion is coherent in the sense that all RhHe2+ ions start from orientation A. For comparison, the ionization zone in field ionization is the result of the electron tunneling rate and the Fermi level of the metal. The zone is less than 0.3 A in width and it is about 4 A above the surface. The rotational motion of RhHe2+ can be estimated as the following. If we omit considering the electric force, then the rotational energy is given by
E _- J(J+1)A2 = hw mt 0 w,2
(33)
where p = 6.39 x 1O-27 kg is the reduced mass of the ion, and r, = 2.6 A is the distance between the Rh and He nuclei. One can easily show that the time needed for rotating 180” is given by
t, =
T-4 JJ(J+~)~
I-
v-4 Jfi
for large J
If we use t, = 8 x lo-l3 s, we find the rotational quantum J = 16: this corresponds to an average temperature of - 500 K. unreasonable since the substrate temperature is probably above the laser heating. However, if we consider the forced rotation by force using classical mechanics
(34) number of This is not 200 K by the electric
2
2eFr,,
pr:$=
(35)
we find t, =
/ OT[(4eF/h4r,,)(ldT
cos) + w;]~‘~
Using numerical integration, one can easily show that 1, = 3.35 X lo-l3 s for J = 1. The calculated time is too short by a factor of 3. Of course, classical mechanical calculation may not be correct, and the changes in J due to the acceleration caused by the applied electric force may lead to longer times of rotation. At the moment, no such calculation is available. Another interesting observation supporting field dissociation of RhHe2+ as an atomic tunneling phenomenon is a dramatic change in the dissociation behaviour when 4He is replaced with 3He as shown in Fig. 10. The secondary Rh2+ peak is no longer there although a few scattered low energy ions can still be found. This observation can be qualitatively understood by considering the tunneling probability. From Eq. (32) one can see that with 3He the reduced mass of RhHe2+ will be smaller, thus the barrier penetra-
Rh, 52K.9.5 kV 1.9 - 4.6 v/h pHe=2 x IO“ torr 690
ions h3He2+
?h*’
Rh4He2+ Ivcl:.-!
:
6”s
:
:
FLIGHT
:
8 :
+
TIME ‘t,
*
Fig. 10. Pulsed-laser stimulated field evaporation of Rh in lo-’ gas. Note the secondary Rh2’ peak is no longer present.
Torr of 3He-3%
4He mixed
tion probability will increase. However, the potential barrier reducing term -2eF’z/(l + M/m) is also mass dependent. With a smaller value of m the magnitude of this term is reduced, thus the barrier penetration will decrease. Apparently, the latter effect is more significant for RhHe2+ as can be seen from a WKB estimation. For this purpose the segment of U(m) will be approximated by a straight line of slope sl. The barrier is therefore a triangle of height h and with two sides of slope s1 and - 2eF/(l + M/m). The barrier penetration probability per encounter of the potential barrier is then given by D(h,
F)=exp~-~(~j1’2i$+1-2~~jh3/2i
(37)
where h is the barrier height. The interaction between He and Rh2+ should be very short ranged, thus l/s, s (1 + M/y))/neF and the l/s, term can be omitted. Fig. 8 shows that at - 4.5 V A-‘, D( h, F) should be a few percent: w,e therefore assume that for 4HeRh2+, h = 0 and D( h, F) = 1 at F = 4.8 V A-‘. The binding energy H of HeRh2’ should be the same for 3He and 4He. I? and h are related to each other by 2 eFr, h=H-(l+M,??z)
(38)
Using Eqs. (37) and (38), the barrier penetration probability per barrier encounter for 4HeRh2+ and 3HeRh2+ at different fields are listed in Table 2. This WKB calculation gives a dissociation rate of 3HeRh2+ smaller than that of 4HeRh2+ by several orders of magnitude. The calculated values of
19
I
M=l03.m
= 4 or 3
Fig. 11. A potential energy diagram illustrating the barrier used for estimating the barrier penetration probability in fiel_d dissociation using WKB-approximation. This diagram is validonly when Z is parallel to F. 7 is the bond vector pointing from He to Rh”.
D(h, F) are consistent with the experimental results. The calculation also gives a binding energy of HeRh2’ to be H = neFr,/(l + M/m) = 2 x 3.5 x 2.6/26.75 eV = 0.68 eV, consistent with a theoretical calculation [12]. Of course the calculation given is intended only for a qualitative understanding of the isotope effect we have observed. A detailed explanation will be given later [14]. The time resolution of this measurement can be calculated by realizing that the system is equipped with a digital timer of 1 ns resolution and the desorption event can be defined to within 0.3 ns, the width of the laser pulses. The overall time resolution of the system is approximately 1112 = 1 ns. This corresponds to an energy difference of about 1.69 eV, or a difference in the location of ion formation of about 0.18 A. As the velocity of a RhHe2+ ion at x = 220 A is about 1 X lo5 cm s-l, the difference in the ion reaction time is 2 X lo-t4 s. This corresponds to an amplification factor of 1 ns/2 X lo-l4 s = 5 X 104. A detailed analysis
TABLE 2 Values of D(h, F) F(V A-‘)
4.8 4.7 4.6 4.5 4.4 4.3
D(h,
F)
HeRh2’
3HeRh2+
1 0.65 0.28 0.09 0.02 0.01
2.4~10-~ < lo-‘0 < 10’0 < 10-10 < 10-10 < lo-‘0
20 shows
that the amplification
factor in this experiment
is given by
and A (220 A) = 4.8 X 104. The time resolution of this measurement is therefore 21 fs. This high amplification factor is due in part to the L/l = 3500 of the system, and in part due to the very fast drop in the field strength near the tip surface because of the very sharp field ion emitter. CONCLUSIONS
The time-of-flight spectrometer has been used mainly as a mass analyzer, and occasionally as an ion energy analyzer. We present here some analyses of the line shape, emphasizing the energy and time aspects of the time-offlight spectrometry. All the analyses presented are intended to be very general and are applicable to most time-of-flight spectrometers. However, specific examples are drawn mostly from data taken with our high resolution pulsed-laser time-of-flight atom-probe spectrometer. We illustrate the time spectroscopy aspect with a detailed discussion of field dissociation of RhHe2+ and show the richness of information contained in a high resolution time-of-flight spectrum. In this measurement we have already achieved a time resolution of 20 fs, and further improvement can be made. The time resolution is now more than sufficient to resolve single vibrational events of compound ions. However, time resolved spectroscopy of the vibration of compound ions can be made only if all the ions vibrate coherently with respect to the desorption event. Also, we do not have sufficient data at the present time. The secondary Rh2+ peak in our data on RhHe’+ is interpreted as arising from a coherent rotational motion of the ions when they are desorbed from the surface, i.e. they all start in orientation A. We are certain that further refinement in both experimental methods and data analyses can be made to study ion reactions in much better detail with the time-of-flight spectrometry. ACKNOWLEDGEMENTS
This work was supported by NSF DMR-8217119 and DOE DE-ACOZ81 ER10857. Some of the data presented were taken with the help of Y. Liou. REFERENCES 1 E.W. Miiller, J.A. Panitz and S.B. McLane, Rev. Sci. Instrum., 39 (1968) 83. E.W. Mtiller and T.T. Tsong, Prog. Surf. Sci., 4 (1973) I and references cited therein. E.W. Miiller and S.V. Krishnaswamy, Rev. Sci. Instrum., 45 (1974) 1053.
21 2 K. Sattler, J. Miihlback, E. Recknagel and A.R. Flotte, J. Phys. E. 13 (1980) 673. P. Pfau. K. Sattler, P. Pflaum and E. Recknagel, Phys. Lett. A, 104 (1984) 262. A. Benninghoven, Int. J. Mass Spectrom. Ion Phys., 53 (1983) 85. E. Ens, R. Beavis and K.G. Standing, Phys. Rev. Lett., 50 (1984) 27. 3 W. Drachsel, S. Nishigaki and J.H. Block, Int. J. Mass Spectrom. Ion Phys., 32 (1980) 222. G.L. Kellogg and T.T. Tsong, J. Appl. Phys., 51 (1980) 1184. 4 (a) T.T. Tsong, S.B. McLane and T.J. Kinkus, Rev. Sci. Instrum., 53 (1982) 1442. (b) T.T. Tsong, Y. Liou and S.B. McLane, Rev. Sci. Instrum.. 55 (1984) 1252. 5 T.T. Tsong, Phys. Rev. B, 30 (1984) 4946. T.T. Tsong. T.J. Kinkus and S.B. McLane, J. Chem. Phys., 78 (1983) 7497. 6 K. Sattler, S. Miihlback, 0. Echt, P. Pfau and E. Recknagel, Phys. Rev. Lett.. 47 (1981) 160. 7 W. Drachsel, Th. Jentsch and J.H. Block, Proc. 29th Int. Field Emission Symp., 299 (1982) Almqvist & Wiksell International. Stockholm, Sweden 1982. p. 299. 8 T.T. Tsong, J. Appl. Phys.. 58 (1985) 2404. 9 J.R. Hiskes, Phys. Rev., 122 (1961) 1207. 10 A.C. Riviera and D.R. Sweetman, Phys. Rev. Lett.. 5 (1960) 560. 11 H.D. Beckey. Field Ionization Mass Spectrometry, Pergamon, Oxford. 1971, and references cited therein. 12 M. Hotokk, T. Kinsted. P. Pyykko and Bo Roos. Mol. Phys.. 52 (1984) 23. 13 C.M. Lederer and V.S. Shirley (Eds.). Table of Isotopes, Wiley. New York, 7th edn.. 1978. 14 T.T. Tsong and M. Cole. to be published.