Surface analyzer for determining the energy distribution of scattered proton beams

A surface analyzer for analyzing the atomic composition of the surface of sample. An ion source generates a proton beam. A magnet directs the proton beam through an accelerating device toward the sample for collision therewith. Protons that are scattered at an angle of 180.degree. pass through the accelerating device in the reverse direction and are decelerated. The magnet directs the protons as a parallel beam to a position detecting device that indicates the position at which the proton beam strikes and energy loss of the protons can be determined.

FIELD OF THE INVENTION 
The present invention relates to an improvement of an energy detector used 
in a surface analyzer to determine the enery distribution of scattered 
proton beams. 
BACKGROUND OF THE INVENTION 
A surface analyzer is an apparatus in which a sample to be analyzed is 
irradiated with accelerated proton beams. A scattering pattern of the 
proton beams caused by collisions with atoms in the sample which 
decelerate the protons is generated and the energy distribution of the 
decelerated proton beams is measured to identify the species of atoms on 
the surface of the sample, as well as to determine their proportions. 
The crystalline structure of the bulk of a sample can be analyzed by X-ray 
diffraction. Techniques such as electron diffraction are also available 
for examining the cyrstalline structure of a near-surface area of the 
sample. None of these methods, however, are capable of providing the 
distribution of elements on the very surface of the sample, for example on 
the topmost or within the top two atomic layers. 
The present inventors developed a technique called PELS (proton energy loss 
spectroscopy) as a method for measuring the elements on the topmost or 
within the top two atomic layers of a sample. PELS is a new technique of 
measurement and its operating principles will be briefly described. 
Suppose, as shown in FIG. 3, a proton of mass number m, moving with 
velocity U hits an atom of mass M at rest. After collision, the proton is 
scattered by the atom and glances off at velocity V along a path deflected 
from its original path by an angle .theta. while the atom moves at 
velocity W in another direction defined by angle .PHI.. Since momentum is 
conserved in both the x- and y-directions, the following two equations are 
established: 
EQU mU=mV cos .theta.+MW cos .PHI. (1) 
EQU O=mV sin .theta.+MW sin .PHI. (2) 
If the collision is completely elastic, kinetic energy is conserved so 
that; 
EQU (1/2)mU.sup.2 =(1/2)mV.sup.2 +(1/2)MW.sup.2 
Eliminating W from Eqs. (1) to (3), 
EQU (.GAMMA.+1)V.sup.2 -2U cos .theta.V-(.GAMMA.-1)U.sup.2 =0 (4) 
Then, 
##EQU1## 
where 
EQU .GAMMA.=(M/m) (6) 
The minus sign in Eq. (5) indicates scattering at angle (.pi.-.theta.). 
Only the plus sign should be taken to consider scattering at angle 
.theta.. 
The proton will lose part of its energy as a result of scattering. For the 
same scattering angle a collision with a lighter atom will cause greater 
energy loss than a collision with a heavier atom. Therefore, by measuring 
the energy loss occurring in the proton, the identity of the atom against 
which it collided can be determined. 
If the kinetic energy of the proton before a collision is written as 
E.sub.0, 
EQU E.sub.0 =(1/2)mU.sup.2 ( 7) 
and if the energy of the proton after collision is written as E.sub.1, 
E.sub.1 is always smaller than E.sub.0. The ratio of E.sub.1 /E.sub.0 is 
called the coefficient of attenuation K. The following equations will be 
established: 
EQU E.sub.1 =KE.sub.0 ( 8) 
##EQU2## 
It is not .theta. but .GAMMA. which is a variable because .theta. is 
uniquely determined by the experimental apparatus employed. 
The present inventors first developed a PELS apparatus of low scattering 
angle (.theta..congruent.0) as disclosed in Unexamined published Japanese 
application No. 180945/1984 (published Oct. 15, 1984) and 151958/1986 
(published July 10, 1986). 
The low scattering-angle apparatus has the disadvantage that it is highly 
susceptible to the surface state of a sample to be analyzed as will be 
apparent from FIG. 12. In addition to single scattering, double scattering 
might also occur on account of asperities on the surface of the sample. 
Another disadvantage of the use of a low scattering-angle is its low 
resolution since K is not highly sensitive to .GAMMA. as suggested by Eq. 
(9). 
The operating theory of PELS is basically set forth in Eq. (9) but this 
assumes attenuation by single scattering and is not valid if multiple 
scattering occurs. 
Low scattering angles were selected for the simple reason that they produce 
high proton yield. FIG. 13 shows the proton yield vs. scatterning angle 
.theta. for Au and Si. The proton yield as relative against the scattering 
angle is determined by geometric factors and will not depend upon the 
physical properties of a specific atom. As shown in FIG. 13, a maximum 
yield is also attained at .theta.=180.degree.. Eq. (9) shows that at 
.theta.=180.degree., the highest resolution can be attained with respect 
to .GAMMA.. In this case where .theta.=.pi., the coefficient of 
attenuation K can be rewritten as: 
##EQU3## 
The parameter .GAMMA. denotes the ratio of the mass, M, of the atom to the 
mass, m, of the proton. If the slight difference between the mass of the 
proton and the atomic mass unit is disregarded, .GAMMA. may safely be 
referred to as the mass number of the atom of interest. 
For various elements, the .GAMMA. values and hence K values can be 
determined. The mass numbers, as defined above, of atoms are listed below 
together with corresponding K values: 
Al: .GAMMA.=26.98, K=0.8621 
Ga: .GAMMA.=69.72, K=0.94422 
As: .GAMMA.=74.9, K=0.94799. 
In this way, the K values of all elements of atoms can be easily 
calculated. 
The foregoing discussion can be summarized as follows. If the kinetic 
energy, E.sub.1, of a proton after collision is measured, K can be 
determined by calculating the ratio of E.sub.1 to E.sub.0. This leads to 
the determination of .GAMMA. value and hence to the identification of the 
atom against which the proton collided. Then, the abundance of that 
particular atom in a sample of interest can be determined from the energy 
spectrum. In most cases, E.sub.0 is selected at about 100 keV. 
The principles of PELS are very simple as described above. In order to 
enable measurements by PELS, the proton must be scattered only once. 
Instead of direct measurement of E.sub.1, the energy loss 
.DELTA.E[=(1-K)E.sub.0 ] may be measured. The name "PELS" derives from 
this measurement of the energy loss distribution of a proton. 
As shown in FIG. 4, when protons having mass m are scattered by a heavy 
atom M, an area where no protons exist will occur in the forward direction 
and this is generally referred to as a shadow cone. Few of the protons 
travelling a far distance from the atom M are scattered and those 
travelling near the atom M are highly likely to be scattered. This is the 
mechanism behind the formation of a shadow cone. 
If an x-axis is assumed to lie in the direction in which a proton travels 
and a y-axis is assumed to lie in a direction perpendicular to that 
direction of travel, a repelling Coulomb force acting between the atom and 
the proton, will produce a shadow cone with a shape that can be expressed 
by: 
##EQU4## 
where e is the elementary quantity of a load, z is a charge on the proton, 
and Z is a charge on the atom (with e being a unit). 
By using the shadow cone, one can identify the atoms in the top monolayer 
of a sample, as is clear from the following discussion. Suppose proton 
beams are directed perpendicularly to the surface of a GaAs sample as 
shown in FIG. 5. The protons are scattered both by Ga and by As, so two 
peaks occur in the distribution of proton energy as shown in FIG. 6. 
If proton beams are impinged on the sample at an angle as shown in FIG. 7 
such that the atoms of the element in the next to the top layer are 
located within the shadow cones created by the atoms of the element in the 
topmost layer, the distribution of proton energy loss will have only the 
peak corresponding to the atoms in the topmost layer. With reference to 
FIG. 8, only the Ga peak appears. This result shows that Ga atoms are 
present in the topmost layer of the sample. 
When proton beams are launched into a sample, proton energy loss occurs as 
a result of collisions not only with atoms but also with electrons. The 
energy loss due to collisions with electrons is proportional to the 
distance the proton travels in the sample. This will be explained more 
specifically with reference to FIG. 9. 
If proton beams are launched into a sample at an angle .theta./2 with 
respect to surface layers, the proton energy loss differs between two 
cases. One case is when an incident proton is scattered at point J in the 
topmost layer and is reflected at angle .theta./2, and the other case is 
where the incident proton is scattered at point G in the next to the top 
(second) layer. The differential energy loss is expressed as: 
EQU .DELTA.E=2dS cos ec(.theta./2) (12) 
where d is the distance between two layers and S is the stopping power of 
electrons. The value of .DELTA.E increases with decreasing .theta.. Even 
if .theta.=.pi., .DELTA.E is 112 eV assuming that d=5.6 .ANG. and S=10 
eV/.ANG.. 
The above discussion shows that even in the case of normal (.theta.=.pi.) 
launching of proton beams, the energy lost by the protons scattered from 
the topmost layer differs by about 100 eV from the loss due to scattering 
in the second layer. In other words, even if the atom of mass M which is 
the principal factor of proton scattering is the same, protons will lose 
energy by different degrees in the topmost and second layers. 
By decreasing .theta., .DELTA.E can be sufficiently increased to provide 
for distinction between proton scattering by dissimilar atoms in the 
topmost and second monolayers. 
FIG. 10 shows the general layout of a prior art PELS measuring system in 
the case where the scattering angle .theta. is 180.degree.. Protonic beams 
extracted from an ion source A are subjected to mass separation in a 
magnet B. Only monovalent proton ions are selected and introduced into an 
acceleration tube C for acceleration. 
The proton beams acquiring a kinetic energy of E.sub.0, which is the sum of 
the extraction energy Eex and the acceleration energy Eacc provided by the 
acceleration tube C, will impinge on a sample .SIGMA.. The protons are 
scattered by atoms in the surface of the sample .SIGMA.. 
Only the protons scattered at angle .theta.=.pi. will travel backward 
through the accelerating tube. Those which were scattered at angle 
.theta..noteq..pi. will collide against the wall of the chamber, make 
transition from the ionic to the neutral molecule (H.sub.2) form, and be 
discharged from the chamber. The protons scattered at angle .theta.=.pi. 
and that travel backward through the accelerating tube are decelerated. In 
other words, the accelerating tube now works as a decelerating tube. 
The decelerating energy Edec is equal to the accelerating energy Eacc: 
EQU Eacc=Edec (13) 
One of the advantages of the case where .theta.=.pi. is that a common tube 
can be used both as an accelerating tube C for accelerating proton beams 
and as a decelerating tube D for decelerating proton beams. 
The decelerated proton beams are bent by 90.degree. with a magnet F. The 
protons are thereafter launched into an analyzer G at an angle. Two 
magnets E and F are necessary in order to converge the proton beams whose 
energy has a variance due to scattering loss .DELTA.E. 
The convergent proton beams are subjected to energy detection in the 
analyzer G. A voltage V.sub.o is applied between two parallel electrode 
plates. A proton launched into the analyzer through a slit will travel on 
a parabolic path and fall into either one of the channels in a 
microchannel plate H. The channel into which the proton has fallen will 
indicate the distance L from the slit to the falling position of the 
proton, and hence the kinetic energy of the proton at the time that it was 
launched into the analyzer. 
The distance L in the analyzer G increases as the kinetic energy of the 
proton increases. If the kinetic energy of the proton projecting onto the 
slit in the analyzer G is written as Ea, the angle formed between the 
incident proton beam and the electrode plate with the slit as .PSI., the 
distance between the two parallel electrode plates as h, and the 
electrostatic voltage applied between the plates as V.sub.o, then L is 
expressed as: 
##EQU5## 
The distribution of distance L indicates the distribution of proton energy 
Ea, thereby enabling the measurement of proton energy distribution. 
All the components of the system shown in FIG. 10 are placed in high 
vacuum. The sample .SIGMA. must be in an ultrahigh vacuum. If this 
requirement for vacuum is not met, protons impinging on the molecules of a 
gas will lose energy and the scattering loss .DELTA.E due to the sample 
.SIGMA. cannot be correctly determined. 
For the sake of simplicity, the vacuum chamber and the evacuation unit are 
omitted from FIG. 10. 
The change in the energy of a proton is described hereinafter with 
reference to FIG. 11 which shows the potential energy of the proton as a 
function of its position during movement (assumed to be left to right in 
FIG. 11). 
A proton ion is extracted from the ion source at an extracting volage of 
Vex. The proton has a charge q, which produces a potential energy of qVex. 
When the proton leaves the ion source, this energy changes to kinetic 
energy. 
The proton is accelerated in the acceleration tube C at an accelerating 
voltage of Vacc. The proton emerging from the acceleration tube toward the 
sample .SIGMA. has a kinetic energyof q(Vex+Vacc), which is equivalent to 
E.sub.o and is approximately 100 keV. 
The proton beam impinges on the sample and is scattered therefrom, losing 
an energy of .DELTA.E. The scattered proton beam travels backward through 
the accelerating tube and loses kinetic energy equal to qVacc. 
The proton beam, when it enters the analyzer G, has a kinetic energy Ea 
expressed as follows: 
EQU Ea=qV.sub.o -.DELTA.E (15) 
where V.sub.o is equal to the extracting voltage Vex or may be described as 
the energy of proton launching into the analyzer G when the energy loss is 
assumed to be zero. 
The value of Ea is set to be about 0.5 keV and the energy of the scattered 
proton Es, which is written as: 
EQU Es=q(Vex+Vacc)-.DELTA.E (16) 
is set to be about 100 keV. 
Theoretically, Ea should be a variable. In practice, the atom to be 
analyzed is preliminarily determined and Vacc is determined in such a way 
that Ea associated with this atom will be about 0.5 keV. 
FIG. 14 is a schematic view showing the general layout of PELS equipment. 
Proton beams issuing from an ion source are focused by an einzel lens, 
deflected by a magnet and accelerated by an accelerating/decelerating 
tube. A sample to be analyzed is set in an ultrahigh vacuum chamber and 
can be handled with a manipulator. The accelerated proton beams are 
converged with a Q lens and subsequently impinge on the sample in the 
ultrahigh vacuum chamber. Among the protons scattered from the sample 
surface, those scattered at .theta.=180.degree. emerge from the ultrahigh 
vacuum chamber and are decelerated. The decelerated proton beams are bent 
by 180.degree. by magnets 1 and 2 and enter an analyzer for measurement of 
energy loss .DELTA.E. 
The foregoing is intended to explain the principles of PELS, the 
composition of PELS equipment, and the mechanism of its action. The 
present invention relates to an improvement of a section of PELS equipment 
for measuring the energy loss, .DELTA.E, of a proton beam. 
In the prior art system, a dc voltage V.sub.o is applied between two 
parallel electrode plates in such a way that a proton will fly on a 
parabolic path and the distance it travels is used as a basis for 
measurement of proton energy Ea in the analyzer G which depends on voltage 
for energy measurement. 
The analyzer shown schematically in FIG. 10 employs two magnets. A prior 
art analyzing system using two magnets is shown schematically in FIG. 15. 
A proton beam scattered from the sample and decelerated by a decelerating 
tube D is bent by 90.degree. in magnet E and bent by another 90.degree. in 
magnet F. This can be realized by arranging the two magnets in such a way 
that the angle of intersection between the beam and the oblique side of 
each magnet is 45.degree.. 
Even if two protons have different energies, they have the same cyclotron 
angular frequency in a magnetic field. In addition, the kinetic energy of 
protons is invariable in a magnetic field. Therefore, if a proton is 
supposed to move on a circular orbit, the radius of the circle is 
proportional to its velocity, and the time required to travel a given 
portion (arc) of the circle is the same if the central angle is the same. 
The advantage of using two magnets having an oblique angle of 45.degree. is 
that protons having different energies can be converged into a single fine 
beam. This beam is launched into an electrostatic analyzer G through a 
fine slit at an angle of 45.degree.. 
The distance L in the analyzer is determined by Eq. (14). 
The energy measuring system of the type described above is adopted in the 
PELS equipment shown in co-assigned Japanese Patent Application No. 
164299/1986 (filed July 12, 1986). An analyzing system using one magnet 
(also prior art) is shown schematically in FIG. 16. This system uses one 
magnet with an oblique angle of 45.degree.. When scattered protons are 
launched into this magnet at 45.degree., those having the smaller energy 
will travel on a circular path with a small radius of curvature, and those 
having the greater energy will travel on a circular path with a large 
radius of curvature. 
In this way, proton beams can be separated spatially. The separated beams 
are launched into a wide electrostatic analyzer G through an elongated 
slit. As in the case of a two magnet analyzer, the distance L travelled by 
protonss in the analyzer is determined by Eq. (14). 
The obvious advantage of the system shown in FIG. 16 is that the number of 
magnets needed is one, rather than two. An energy measuring system of the 
single magnet type described is shown in co-assigned Japanese Patent 
Application No. 299269/1986 (filed Dec. 16, 1986). 
The prior art system for measuring the proton energy depends on an 
electrostatic voltage for changing the direction of the travel of protons 
and this has caused several problems. For example, in the electrostatic 
analyzer, the direction in which voltage is applied is not perpendicular 
to the direction of motion of the proton beams. A faster proton beam 
having a long flight will fly to a point close to the positive electrode 
plate. Since this should not happen, the distance between the two 
electrodes must be increased but then the size of the electrostatic 
analyzer is increased. Not only does this increase the cost of the 
analyzer but also the load on the evacuation unit is increased and 
additional vacuum pumps must be installed. 
Moreover, both the parameters of the magnetic field H of a magnet and the 
voltage V.sub.o of the electrostatic analyzer G must be adjusted on the 
prior art systems. The need to adjust these parameters introduces 
complexity. For instance, if the magnetic field of magnet E is increased 
in the measuring system shown in FIG. 15, the beam emerging from this 
magnet has been bent 90.degree. but at the same time, it has been 
displaced more outwardly than when the magnet is small. Unless the 
magnetic field of magnet F is increased correspondingly, the beam emerging 
from magnet F will be offset too much to pass through the slit 5. 
In the case of the one-magnet system shown in FIG. 16, a wide electrostatic 
analyzer is necessary. Furthermore, the width of the microchannel plate 
must also be increased. This leads to a very expensive and hence 
uneconomical analyzer. 
SUMMARY OF THE INVENTION 
An object of the present invention is a surface analyzer capable of 
accurately analyzing the atomic composition of the surface of a sample. 
Another object of the present invention is a surface analyzer that requires 
a single magnet to direct a proton beam from an ion source to a sample and 
to direct protons scattered at an angle of 180.degree. following collision 
with the sample as parallel proton beams to a position detector. 
A further object of the present invention is a surface analyzer that does 
not require an electrostatic energy analyzer. 
These and other objects are accomplished by a surface analyzer for 
analyzing the atomic composition of the surface of a sample, comprising an 
ion source for generating protons, accelerating/decelerating means for 
accelerating protons moving therethrough toward the sample and 
decelerating protons moving therethrough away from the sample after 
collision with the sample and scattering at an angle of 180.degree. with 
respect to the sample, a magnet for directing protons from the ion source 
to the accelerating/decelerating means for accelerating toward the sample 
and for forming parallel beams of the protons passing through the 
accelerating/decelerating means following scattering at an angle of 
180.degree. following collision with the sample, and proton detecting 
means for receiving the parallel proton beams and for indicating the 
position at which the parallel proton beams are received such that the 
kinetic and energy loss of protons that collide with the sample and are 
scattered at an angle of 180.degree. may be determined.

DETAILED DESCRIPTION OF THE INVENTION 
In order to know the proton energy Ea, proton beams must be separated 
spatially. In the prior art, an electrostatic analyzer that uses a voltage 
V.sub.o to relate energy Ea to distance L has been employed. The 
electrostatic analyzer suffers from the disadvantages already described 
sbove. 
In the present invention, a magnetic field H, not a voltage, is used to 
achieve spatial separation of proton beams having different energies. The 
prior art also uses magnets to bend proton beams but not to achieve 
spatial separation of proton beams having different kinetic energies. In 
the present invention, a magnetic field is used for the specific purpose 
of spatially separating protons having different energies. A position 
detector composed of a microchannel plate is also used in the present 
invention. 
The composition of the surface analyzer of the present invention is 
described hereinafter with reference to FIG. 1. The apparatus is entirely 
accommodated in a vacuum chamber and held in high vacuum. The evacuation 
unit is not shown in FIG. 1. 
Instead of three magnets B, E and F used in the prior art system shown in 
FIG. 10, only one magnet Q is used in the system of the present invention. 
In the absence of an electrostatic analyzer, the position of a proton beam 
emerging from the end of the magnet Q is directly measured with a position 
detector H. The other aspects of the present invention are substantially 
the same as the prior art. In the ion source A, a gas such as hydrogen gas 
is ionized to produce protons, which are accelerated by an inter-electrode 
voltage Vex and emerge from the ion source A. The emerging protons are 
bent by the magnet Q with a curvature radius of Ro. 
Bending the proton beams by magnet Q is necessary because the scattering 
angle .theta. is 180.degree.. Since the direction in which the proton 
beams are incident on the sample is the same as the direction in which 
they are scattered from the sample the magnet is necessary to separate the 
incident beam from the scattered beam. If the scattering angle is not 
180.degree., the incident beam need not be passed through the magnet. The 
present invention of course includes the case where 
.theta..noteq.180.degree.. The shape of magnet Q is a slightly deformed 
pentagon defined by points JNSTU. 
The protons from the ion source A are launched into the magnet through side 
ST and travel on a curved path parallel to side SN. The protons emerging 
from side NJ will go straight through the accelerating tube C where they 
are accelerated and directed against the sample .SIGMA.. The incident 
protons collide with atoms in the surface of the sample 93 and are 
scattered, losing energy .DELTA.E. Those protons which were scattered at 
angle (.theta.) of 180.degree. will travel backward on the same path as 
that of the incident beam and are decelerated by the decelerating tube D. 
The decelerating energy is equal to the accelerating energy because the 
scattered protons travel through the same accelerating/decelerating tube. 
The scattered proton beams have a kinetic energy of Ea which is expressed 
as: 
EQU Ea=qV.sub.o -.DELTA.E (17) 
were qV.sub.o is constant but .DELTA.E is not and varies with the atom 
against which the proton collides. Therefore, Ea is not constant and takes 
on as many values as the number of atoms with which the proton is to 
collide. 
The scattered proton beams reenter the magnet at point W on side NJ. The 
central angle of the circular orbit on which the proton beam travels 
through the magnet is determined by the angle of intersection .alpha. 
between the straight line E.SIGMA. and side NJ of the magnet. The portion 
WJ of side NJ must be a straight line. For the sake of the simplicity in 
design, NJ can also be made a straight line. However, it is not absolutely 
necessary that NJ intersects the beam line W.SIGMA. at angle (.alpha.) of 
90.degree.. 
The cyclotron angular frequency .OMEGA. of a proton which is a free 
particle with charge q and mass m is given by the following equation in a 
magnetic field with a flux density of B: 
EQU .OMEGA.=q.sup.B /mc (18) 
where c is the velocity of light in vacuum. The value of .OMEGA. is 
independent of the proton energy. 
Two protons having different energies have the same cyclotron angular 
frequency in a magnetic field. Therefore, given the same time, the central 
angle of a circular orbit travelled by protons is the same. 
It should, however, be noted that the cyclotron radius R varies with proton 
energy. If the velocity of a proton is written as v, 
EQU v=R.OMEGA. (19) 
EQU (1/2)mv.sup.2 =Ea (20) 
Therefore, the cyclotron radius R is: 
##EQU6## 
Eq. (22) is a statement using the gauss unit system, in which: 
C=3.times.10.sup.10 cm/sec 
m=1.67.times.10.sup.-24 g 
q=4.8.times.10.sup.-10 cgsesu. 
The unit of Ea in Eq. (22) is the erg which can be related to eV by the 
following equation: 
EQU 1 erg=10.sup.12 /1.6 eV (23) 
Therefore, Ea is expressed in terms of eV as follows: 
##EQU7## 
where the unit of flux density B is gauss. 
As evident from Eq. (25), a proton having a higher energy describes a 
circular path with a greater radius of curvature. The square root of 
proton energy is proportional to the radius of the circular path. 
The proton as it emerges from the ion source has an energy of eVex. If the 
radius of the circular orbit on which this proton moves is written as Ro, 
the radius for the scattered proton which is dependent on .DELTA.E is 
given by: 
##EQU8## 
Therefore, the scatttered proton will travel on a circular path having a 
small radius if it has suffered a great energy loss, and it will travel on 
a circular path having a large radius if the energy loss is small. 
In the case where .alpha.=90.degree., a scattered proton beam emerges from 
the magnet at point X on side NJ. In this case, the following equation is 
valid: 
EQU WX=2R (27) 
Point X is close to point W if the beam has suffered a great energy loss, 
and the two points are distant from each other if the energy loss is 
small. 
Since the scattered proton beam emerges from the magnet perpendicularly to 
side NJ, the position X on which the proton is launched into the 
microchannel plate (MCP) H is expressed as: 
##EQU9## 
where Ro is not included. 
Comparing Eq. (14) with Eq. (28) or (29), it can be seen that in the 
electrostatic analyzer, energy Ea is proportional to distance I, whereas 
in the present invention, the square root of Ea is proportional to flight 
2R. 
As shown in FIG. 1, proton beams pass through the magnet Q on three 
circular paths having different radii R.sub.0, R.sub.1 and R.sub.2. These 
radii are respectively expressed by Eqs. (30), (31) and (33), which are 
obtained by substituting the energies of the respective proton beams as Ea 
into Eq. (25): 
##EQU10## 
A microchannel plate (MCP) is used as a position detector in the present 
invention. This has an array of fine (micro) channels each being capable 
of multiplying one incident protonic ion by a factor of about 10.sup.9. 
This enables identification of the position where protons have fallen. 
Even a single protonic ion can be detected. The only requirement that 
should be met is that the energy of an incident proton be greater than a 
certain threshold value Et. If the energy of an incident proton is smaller 
than Et, a low amplification (multiplication) factor will result. This 
condition may be expressed as: 
EQU Ea&gt;Et (33) 
If this condition is met, the number of protonic ions is proportional to 
the amount of electric current detected by the microchannel plate. 
Suppose that a proton beam impinging on the sample has an energy of 
Eo=q(Vex+Vacc). The energy loss .DELTA.E is expressed as: 
EQU .DELTA.E=(1-K)Eo (34) 
where 
##EQU11## 
where T is the mass number. 
The value of qVex must be greater than (Et+.DELTA.E). Suppose the following 
values as Eo, Et and Ro: 
Eo=q(Vex+Vacc)=100 keV 
Et=3 keV 
Ro=250 mm 
With qVex being varied as 34.2 keV, 15.2 keV, 8.6 keV, 7.1 keV, 6.1 keV, 
5.1 keV and 4.9 keV, the value of peak position X can be determined from 
Eq. (28) for various elements having the following values of .GAMMA.. The 
term (const) in Eq. (28) is assumed to be zero: 
______________________________________ 
r = 11 B K = 0.6944 
r = 31 P K = 0.8789 
r = 70 Ga K = 0.9445 
r = 96 Mo K = 0.9592 
r = 128 Te K = 0.96923 
r = 184 W K = 0.97849 
r = 209 Bi K = 0.981043. 
______________________________________ 
Eq. (28) can be rewritten as follows: 
##EQU12## 
The results of the above determination are shown in FIG. 2. If Vex is 
high, a broad range of mass numbers (.GAMMA.=11-209) can be covered. If 
qVex=34.2 keV, the present invention is effective for almost all elements. 
However, the resolution of atoms with large mass numbers is low if Vex is 
high. This is because atoms with large mass numbers, even if protons are 
scattered, cause only a very small amount of energy loss .DELTA.E and 
hence produce only a small difference in position X. 
Atoms with larger mass numbers can be detected if Vex is reduced. However, 
Ro includes Vex, so a change in Vex will result in a corresponding change 
in Ro and Eq. (36) is not established. In this case, the magnetic field B 
is appropriately adjusted to render Ro constant. 
It is desired to selectively detect atoms even if they have mass numbers 
(M/m) close to each other. The smallest difference, .DELTA..GAMMA., in 
mass number that allows for separation of two atoms is called the mass 
resolution, which is usually expressed by .GAMMA./.DELTA..GAMMA., or 
multiplied by m into M/.DELTA.M. This expression means that a particular 
atom with mass M can be detected separately from an atom with mass 
(M+.DELTA.M). 
To achieve this separation, a collimating slit having a width of x is 
positioned in the path of a proton beam as shown in FIG. 17. If x is 
small, high mass resolution is attained. The resolution attained can be 
defined as follows: 
##EQU13## 
where R.sub.1 and R.sub.2 are the radii of curvature of the circular paths 
traveled by protons in magnet Q after they were scattered 
(.theta.=180.degree.) by atoms with mass of M.sub.1 and M.sub.2. 
The value of x is determined by the width of the slit shown in FIG. 17 or 
the cell width of an individual microchannel in the microchannel plate. 
The slit width is a predominant factor since the cell width is extremely 
small (less than 100 microns). Calculations of M/.DELTA.M from Eq. (37) 
were conducted using a slit width of 0.5 mm (500 microns) and assuming 
M.sub.2 -M.sub.1 =1. Substantially the same results are attained even if 
the value of M.sub.2 =M.sub.1 is 2 or 3, but for the sake of simplicity, 
the value 1 was selected. The results are shown in FIG. 18, from which it 
can be seen that a higher mass resolution can be attained for atoms with 
smaller mass M (i.e., small .DELTA.E). This is because the square root of 
energy Ea is proportional to R in a magnetic field. 
This can be explained mathematically as follows. 
Looking at Eqs. (31), (32), (34) and (35), the following substitution may 
be used: 
##EQU14## 
Differentiating Eq. (39) with respect to 
##EQU15## 
When substitutions .GAMMA./.DELTA..GAMMA.=M/.DELTA.M and dR=x are used, 
##EQU16## 
Eq. (41) clearly shows that M/.DELTA.M decreases with increase in .GAMMA.. 
The case where a scattered proton beam is launched into the magnet at 
90.degree. has been described with reference to FIG. 1. It should be 
noted, however, that the present invention also works effectively even if 
.alpha. is not 90.degree.. the radius R does not include .alpha.. Since 
side NJ forms angle .alpha. with respect to beam line W.SIGMA., the 
central angle of an arc described by the scattered beam before it leaves 
the magnet is 2.alpha.. The beam emerges from the magnet at the same angle 
of .alpha. with respect to side NJ. Therefore, the microchannel plate is 
tilted by (90.degree.-2.alpha.) with respect to side NJ. In this case, the 
position X to be detected is expressed not by Eq. (28) but by: 
##EQU17## 
FIG. 19 illustrates a layout of a magnetic position detector for the 
general case where .alpha..noteq.90.degree.. 
As evident from the foregoing the present invention has several advantages. 
In an electrostatic analyzer, a proton beam is launched at an angle 
between two parallel electrodes. In order to enable energy measurements 
even for rapidly moving protons, the distance between electrodes must be 
increased. This makes the electrostatic analyzer an unduly bulky 
apparatus. By eliminating the use of an electrostatic analyzer in the 
manner of the present invention, the size of the PELS appartus is reduced. 
As an attendant advantage, the load on the evacuation unit can also be 
reduced. Moreover, in the present invention, a single magnet suffices for 
energy measurements. Since the magnetic gap may be very narrow, only a 
small space is required for magnet installation. Furthermore, by 
decreasing the ion extracting voltage Vex, the spectrum for detecting of 
heavy elements (large M and small .DELTA.E) can be expanded. Moreover, if 
a collimator is inserted as shown in FIG. 17, fine spectra (i.e., high 
resolution) can be attained although low yield results. Compared with the 
one-magnet system shown in FIG. 16, the width of a microchannel plate is 
small enough to offer an economical apparatus. Also, the number of 
operating parameters that need adjustment is reduced. The voltage, 
V.sub.0, of an electrostatic analyzer is not a design parameter. The 
combination of ion extracting voltage Vex with magnetic field B leads to 
simplified manipulation of the apparatus.