WO2015011029A2

WO2015011029A2 - Apparatuses and methods for analysing charged species

Info

Publication number: WO2015011029A2
Application number: PCT/EP2014/065457
Authority: WO
Inventors: Michael Hopkins; David Gahan
Original assignee: Impedans Ltd
Priority date: 2013-07-22
Filing date: 2014-07-17
Publication date: 2015-01-29
Also published as: GB2516456A; GB2516456B; GB201313068D0; WO2015011029A3

Abstract

Charged species are analysed using a system including a gate having entrance and exit positions separated by a distance S, the gate being switchable between open and closed states allowing or preventing charged particles from passing through. The gate is periodically switched at a frequency F, and a duty cycle x expressed as a ratio. The average kinetic energy, U(α), of a particle within the gate can be controlled by varying a parameter α of the system. A time-averaged collection current I from charged particles exiting the gate is measured as α is varied, and a discontinuity in the derivative of the current I at a given value of α indicates the onset of a current component attributable to a charged species of mass m entering the gate. The mass m is determined from the relationship: (I) where U_m(α) is the value of U(α) at which said discontinuity in the derivative of the current is determined.

Description

Apparatuses and methods for analysing charged species

Technical Field

This invention relates to the analysis of charged species, and has particular application in calculating the mass of charged particles such as ions. Background Art

Mass spectrometry is a very important means to detect species in the gas phase. Different chemical species are ionised and the ions are separated based on their mass to charge ratio. In some applications such as monitoring plasma processes ions are already present in the gas phase and mass spectrometry can be used to separate ions into d ifferent chemical species based on their charge to mass ratio.

Mass spectrometers generally rely on a mass analyser to separate ions in space or time. Early mass spectrometers used magnetic and electrical fields to separate ions and measure mass, but since the 1950's most modern mass analysers use electrical fields only. They measure gas phase ions with respect to their mass-to-charge ratio (m/z), the addition of charge allows the atom/molecule to be affected by electric fields thus allowing its mass measurement.

One of the ea rliest RF-only mass spectrometers was developed in 1953 by W.H. Bennett (US 2,721,271). In that apparatus ions were accelerated in a planar RF electrical field between three grids. The RF field was placed on the middle grid. The ions were accelerated (decelerated) between the first and second grids and decelerated (accelerated ) between the second and third grids depending on the phase of the potential on the middle grid. As the time averaged potential between the first and third grid is zero the net energy gain was zero except when the ion's transit time across the first gap was similar to the RF period or its harmonics (resonant ions). If the ion gained energy passing between grid 1 and grid 2 and exited grid 2 just as the field was reversing it would not lose this energy passing between grid 2 and grid 3 and indeed could gain further energy. The ions exiting the third grid had a non-zero net energy at specific frequencies.

Bennett showed that by using u p to three blocks of grids a reasona ble resolution mass

spectrometer could be built. Such spectrometers were built and used in space exploration.

However a key drawback was the likelihood of ions appearing at a harmonic of the RF frequency, so called ghost peaks. Also the multiple grid systems (up to 13 grids were needed) was d ifficult to implement in practice. The symmetry between grids was important and the RF potential had to be maintained as a small fraction of the DC potential accelerating the ions in order to maintain the expected dependence of ion energy on RF frequency and gap. This type of mass spectrometer is no longer widely used.

In US 2,939,952, Wolfgang Paul described an ion trap where a combination of RF and DC fields could be used to trap ions in a field described by a quadratic function. This quadruple mass spectrometer and its derivatives became the workhorse of basic mass analysis over the subsequent five decades. A quadrupole mass analyser consists of four parallel rods that have fixed DC and alternating RF potentials applied to them. Ions produced in the source of the instrument are then focussed and passed along the middle of the quadrupoles. Their motion will depend on the electric fields so that only ions of a particular m/z will have a stable trajectory and thus pass through to the detector. The RF is varied to bring ions of different m/z into focus on the detector and thus build up a mass spectrum.

More recently a novel synchronous ion shield mass analyzer has been proposed by J. -P. Hauschild et al in J. Mass. Spectrom. 2009, 44, 1330-1337 (see also US2010009103 Al). In this apparatus ions transit through a series of gaps with potentials applied so that only a selected mass is able to pass through without gaining or losing energy or being lost to an electrode. An energy analyser selects ions of a specific energy before the detector.

There are a number of major limitations of the current art in the creation of miniature mass spectrometers for a wide range of applications to reduce cost and make systems more portable. The first is that ion mass separation occurs at very low background pressure due to the long paths that the ions need to travel without collisions. This is particularly true for time of flight mass spectrometers where ions need to travel up to a meter to be resolved. Even ion traps such as quadrupoles still need several centimetre travel distances to separate ions. The pressure and travel limits make these technologies not ideal to meet the need to produce miniature ion mass separators. A second issue with the current art linked to miniaturisation is the need to produce complex three dimensional (3D) structures to implement ion traps. Producing complex 3D structures at micron dimensions is expensive and difficult to achieve. A third problem is that the small 3D structures limit the signal level achieved and may require an array of many devices to achieve reasonable ion throughput.

It is known that ion mass separation is possible using energy dispersion, see the review article, E Kawamura et al in Plasma Sources Sci. Technol. 8 (1999) R45-R64. In a plasma with a biased RF electrode ions are accelerated towards the surface with a dc potential V_P and an RF potential V_RF * sin(oot). A sheath forms in front of the electrode and this sheath has a scale length defined by the Debye length and Vp. Typical sheath widths are of the order of a few hundred micron. Ions entering the sheath are assumed to have low energy and are accelerated by the DC and RF potential. When the period of the RF frequency is long compared to the transit time of the ion across the sheath the ion sees the instantaneous RF field and the ions are spread out in energy depending on the phase a of the RF when they arrive at the sheath edge. At high frequency, when the period of the RF, T_RF, is short compared to the ion transit time, T_!0N, the ions sample many different RF field values as they cross the sheath. The ions see an average potential V_Av = A * V_RF, where A < 1. The Kawamura review article shows that A can be approximated by

A * TioN / T_RF (when T_RF > T|_0N); and A=l (when T_RF < T|_0N). Because the sinusoidal voltage spends more time at the max and min values and assuming ions arrive at the sheath edge with equal probably as a function of time, then the ion energy distribution will show a peak in ions at V_P ± A* V_RF.

In a plasma with a range of ions of different masses when the RF frequency and sheath width is such that the different species have different values of A, and the V_RF value is high enough to separate out the peaks at V_P ± A* V_RF, it is possible to use this energy dispersion as a crude mass separation and analysis technique.

However in this application the complete RFEA is biased by a DC and RF potential relative to the source of ions. The gap is defined by the sheath width which depends on the plasma parameters. So a reliable mass analysis is not possible using this technique, nor is it feasible to design a robust analyzer because of these constraints.

In general, a major limitation of the quadrupoles is the 3D nature of the design. This is hard to replicate in a miniature scale. While some effort has been made to create a miniature quadupole there is considerable development required to reduce the scale of the device and maintain performance. In this work we are interested in producing a simple 1-D mass analyser based on a retarding field energy analyser structure of 3 or 4 grids. Such a simple mass analyser would have many advantages over the existing art.

Disclosure of the Invention

There is provided a method of analysing charged species within a system, comprising the steps of: providing a system including a gate having an entrance position and an exit position separated by a distance S, the gate being switchable between open and closed states, wherein in the open state charged particles can pass through the gate entrance, wherein in the closed state charged particles cannot pass through the gate exit; providing a supply of charged particles to the entrance of the gate; switching said gate periodically between open and closed states wherein the switching cycle measured from one gate opening to the next gate opening has a frequency F, and wherein the ratio between the duration of the open state and the duration of the closed state over each cycle is x; varying a parameter a of the system, said parameter a being a controllable, variable system parameter which has a predictable effect on the average kinetic energy, U(a), of a particle within the gate; measuring a time-averaged collection current I as a is varied, wherein the collection current I is attributable to the collection of charged particles exiting the gate; determining a discontinuity in the derivative of the current I at a given value of a arising from the onset of a current component attributable to a charged species of mass m entering the gate from said supply of charged particles; and calculating the mass m of said charged species from the relationship:

where U_m(a) is the value of U(a) at which said discontinuity in the derivative of the current is determined.

This method differs from conventional mass analysis methods. In a classic ion trap the idea is to construct an F field that traps ions of a specific mass, this trapping requires complex field geometries. The basic idea behind ion traps is that an ion of a specific mass can respond to the RF field at low frequencies, but at higher frequencies the ion inertia means that the ion does not fully respond to the field and sees an effective potential that is lower than the peak RF potential.

In essence an ion trap, traps ions of a certain mass into a specific location in space, releasing the ion to be detected after an elapsed time or trajectory. It is not easy to trap ions in a planar geometry as the trajectories quickly exit the RF region. Bennett noted that the energy of ions transiting an RF region will be increased when ions are resonant, but resolving the ion energy and avoiding resonant ions has limited his approach. In the current invention we note that even in geometries where ions may not be trapped, they can still be gated. By gating ions but allowing a window or period when they can cross, it is possible to discriminate between ions of different energies. Thus if the ion velocity is high enough the ions will have time to cross when the gate is open. All ions that make it across the gap are collected with a suitably biased collector and we see an onset of current, as the ion velocity in the gap is increased the current continues to increase as more of the higher energy ions make it across. By analysing the onset current we can determine the discontinuity in the slope of the current at the onset and determine the ion transit time and therefore it's mass for a known velocity. By varying the ion velocity in the gap in a known way we can determine the mass of ions. Preferably, the gate is configured such that particles which are within the gate when the gate switches to a closed state cannot subsequently exit the gate in a subsequent open cycle.

The parameter a is a controllable, variable system parameter which has a predictable effect on the average kinetic energy of a particle within the gate, such that for a given value of a, the time- averaged kinetic energy of said particles when inside the gate, U(a) is known. Examples of such a variable parameter would include an accelerating voltage which accelerates charged species towards the gate, the frequency of the switching cycle, the duty cycle of the open to close period on the gate, and the size of the gate structure.

This approach makes it possible to embody a mass spectrometer in a planar device with a small gap. This allows for easy miniaturization, small size and medium vacuum operation. The planar structure also allows for single large area devices allowing high ion throughput.

Preferably, the system is provided as a planar device wherein the distance S is in the range 1 mm to 1 micron, more preferably 500 micron to 50 micron, and most preferably 300 to 200 micron.

In one embodiment, said step of determining a discontinuity in the derivative of the current I at a given value of a comprises determining said discontinuity from an analysis of l(y), where y is proportional or equal to the inverse square root of U(a).

Alternatively, said step of determining a discontinuity in the derivative of the current I at a given value of a comprises determining said discontinuity from an analysis of l(y), where y is proportional or equal to the inverse square root of a, and where a is an accelerating voltage Va applied to the particles which accelerates them towards the gate. It will be appreciated however that many graphical and analytical methods could be used to identify discontinuities in current derivative relative to y or to some other metric which is related to a.

In one embodiment, said determining step comprises identifying a peak in a difference in slope Δ²Ι/Δγ , i.e. the second difference of I with respect to y. (where Δ²Ι/Δγ = ΔΙ_η+ι/Δγ_η+ι- Δϊ_η/Δγ_η and represents the change in slope at the discontinuity).

Further, preferably, the method further comprises the step of: deriving the magnitude of a current of said charged species of mass m entering the gate, l₀(m), by calculating the magnitude of a peak in the function Δ²Ι/Δγ, wherein l₀(m) and Δ²Ι/Δγ are related according to the relationship:

The above relationship holds both where y is proportional or equal to l/V(U(a)) and to l/V(Va).

In one embodiment, said parameter a is an accelerating voltage Va applied to the particles which accelerates them towards the gate.

In this scenario, a determines the energy with which the ions enter the gate.

Preferably, the gate retards the ions so they exit the gate with net energy close to zero but the energy with which they enter determines the transit time. We assume the RF field does not change the average energy as the instantaneous RF energies average to zero and the RF is typically chosen to be small relative to the accelerating energy.

Alternatively, said step of determining a discontinuity in the derivative of the current I at a given value of a comprises analysing the current as a sum of basis functions at each voltage and determining the magnitude of each basis function.

Preferably in the case of a sinewave, said basis functions take the form l(Va) =∑_n βη (Va/Vn -1)^{1 2} where Vn is the onset voltage for mass mn, with (Va/Vn -1)^{1 2} =0 for Va<Vn .

Preferably, determining the magnitude of each basis function comprises using a least squares fitting techniques to determine the magnitude βη of each basis function.

There is also provided an apparatus for analysing charged species, comprising: a gate having an entrance position and an exit position separated by a distance S, and configured to receive a supply of charged particles to the entrance of the gate means for switching the gate between open and closed states, wherein in the open state charged particles can pass through the gate entrance, wherein in the closed state charged particles cannot pass through the gate exit; a switching control operable to switch said gate periodically between open and closed states wherein the switching cycle measured from one gate opening to the next gate opening has a frequency F, and wherein the ratio between the duration of the open state and the duration of the closed state over each cycle is x; means for varying a parameter a of the system, said parameter a being a controllable, variable system parameter which has a predictable effect on the average kinetic energy, U(a), of a particle within the gate; a current collector configured to collect a time-averaged collection current I as a is varied, wherein the collection current I is attributable to the collection of charged particles exiting the gate; and a processor programmed to: determine a discontinuity in the derivative of the current I at a given value of a arising from the onset of a current component attributable to a charged species of mass m entering the gate from said supply of charged particles; and calculate the mass m of said charged species from the relationship:

Brief Description of Drawings

The invention will now be further illustrated with the following description of embodiments thereof, given by way of example only with reference to the accompanying drawings, in which:

Fig. 1 is a schematic diagram of a first apparatus for analysing charged species; Fig. 2 is a plot showing the relationship between the F voltage V_RF and collector current la for the apparatus of Fig. 1;

Fig. 3 is a graph of collector current against the inverse square root of the accelerating voltage Va for the apparatus of Fig. 1;

Fig. 4 is a schematic diagram of a second apparatus for analysing charged species;

Fig. 5 is a schematic diagram of a third apparatus for analysing charged species;

Fig. 6 is a plot of particle energy versus distance across the apparatus of Fig. 5, at different times in the switching cycle;

Fig. 7 is a plot of current against accelerating voltage modelled for the apparatus of Fig. 5, analysing a plasma containing argon and oxygen ions;

Fig. 8 is a plot of the second difference of current with respect to acceleration voltage Va, against acceleration voltage Va, for the data from Fig. 7;

Fig. 9 is a schematic diagram of a fourth apparatus for analysing charged species;

Fig. 10 is a plot of current against accelerating voltage experimentally determined for the apparatus of Fig. 9, analysing a plasma containing argon only;

Fig. 11 is a plot of the second difference of current with respect to acceleration voltage Va, against acceleration voltage Va shown in units of equivalent ion mass in amu, for the data from Fig. 10;

Fig. 12 is a plot of the second difference of current with respect to acceleration voltage Va, against acceleration voltage Va shown in units of equivalent ion mass in amu, for the apparatus of Fig. 9, analysing a plasma containing argon and oxygen ions; and

Fig. 13 is a schematic diagram of a fifth apparatus for analysing charged species.

Detailed Description of Preferred Embodiments

Fig. 1 shows a charged particle beam 10 of current I, entering an acceleration region 12 between a first grid 14 and a second grid 16, between which the particles are accelerated through a potential Va, which is negative for positive particles. The particles then enter a retarding region 18. Assume that Va » than the original kinetic energy of the beam.

A discriminator region combining the accelerating and retarding regions, 12 and 18 is defined between first grid 14 and a third grid 20 and has length S. The beam is gated at the entrance and exit of the discriminator by a pulse of frequency F applied to the first and third grids. The pulse amplitude is +/- Vb relative to ground where Va » Vb > than the original kinetic energy of the beam so that when F is low for a positive beam, the beam passes into the accelerator region 12, and when F is high the beam is stopped at both the entrance to 12 and the exit from 18.

The charged particles that enter region 12 pass through region 18 and provided F is still low when they reach grid 20 they enter a collector 22 and are recorded as a current, la.

When F is high both gates close and no current enters or leaves the discriminator during the high period of F.

Provided the high period is long enough to ensure that no particles remain in the discriminator region, at the instant both gates open the current, la is zero and remains zero until particles pass through the length S. Then the current rises to equal the average current entering the device, I. It remains at a value I until the gates closes when it returns to zero.

The average current <la> over many periods of the frequency F is calculated as follows:

j ί time ions flowing

Eq.l. < Ia >

' V total time J

Eq.2. < Ia >

Eq.3. < Ia > /. F. (f - td)

Fig. 2 is a plot showing the relationship between the F voltage V_RF and collector current la for the apparatus of Fig. 1. The delay time td is the time it takes a charged particle to travel from grid 14 to grid 20. The ratio of time the gate is open to the total period is x. The particle velocity at grid 16 is determined by the acceleration voltage Va and the particle mass. The average velocity in the discriminator is half the peak velocity,

Eq.4.

Eq.5. td = (2SVm)/V2eFa )

Eq.6. Eq.7. < la > = Ix— {2lFS^Jrn)/^2eVa ) when ^==≤ xF Eq.8. < la > = 0 when ^2S^™ > _xp

We can see from the above that a plot of the average collector current <la> versus inverse square root of the accelerator voltage l/V(Va) is linear with slope There is a discontinuity

in the slope at zero current.

As seen in Fig. 3, where the collector current arises from the contributions of two species, each of a different mass, then the average current has two discontinuities 30, 32 and the slopes add, as indicated by the region M1+M2 (where two species contribute, the region M l, where only one species has sufficient energy to make it to the collector, and the zero current region Z, where the accelerating voltage is too low to impart either species with enough energy to make it through the gate.

By taking the difference of the derivative of d(la)/da, where a = l/V(Va) it is possible to obtain a peak at the discontinuity whose height is related to the current of a specific mass and the peak will occur at a value of a corresponding to a particular mass value. The discontinuity in d(la)/da occurs just when <la> = 0 so

Eq.9. Ix = 2 S I m/ 2 e Va

Eq.10. m = ^'(2 e Va) / 2SF

Eq.ll. M = 2x²Va . e/ 2SF)²

The mass is a linear function of the acceleration voltage Va and depends on the square of the ratio of on time of the gate, and the inverse square of the gap between gates, S and the switching frequency of the gates F.

A drawback of this embodiment is that x must be small to ensure that no particles remain in the discriminator before the next on gate. There are many ways to construct an ion gate known in the literature; Here we will give two further examples where ions which have entered the discriminator region on the previous gate signal cannot exit, allowing x to increase to 50%.

Fig. 4 shows an example of a positive, negative ion, or electron gate where charged particles 38 of known energy enter a box 40 through a slit 42. A plate 44 above the trajectory is switchable between a LO or zero bias and a HI or positive bias. When the bias is zero, the particles do not make it out of the box and hit the end wall as indicated by trajectory Vb = LO. If the plate is biased positive throughout the flight of the particle assuming a positive particle, as indicated by the trajectory Vb = HI, the plate repels the positive charged particles so that they exit a second slit 46 and can be collected and a current measured. If a particle is inside the box when the voltage Vb changes, its new trajectory 48 hits the wall. Only those particles just entering the box at or after the switching instant will be able to exit, so that no current reaches the exit until a delay equal to the time td it takes a particle to cross the discriminator. The ion gate switches off at both the entry and the exit at the same time, so that any particles within the box 40 at the moment the bias is removed, will not exit the second slit 46 as they will not have experienced the biasing potential throughout their entire flight through the discriminator. Again in this system assuming the average velocity is in this case determined from the potential Va and x=0.5, then

Eq.12. M = 2Va . e/ 2SF)²

Where eVa is the energy of particles entering the first slit, S is the horizontal distance between both slits, and F is the frequency of Vb applied to the gate. The previous example used two dimensions to prevent particles already in the discriminator from exiting. Of most interest in the present work is a gate that is planar, therefore we would like to achieve the same with one spatial dimension. This is possible if we look at a gate made using potential energy and a single spatial dimension we can construct a gate that rejects particles already in the gate when it is opened. In Fig. 5, two grids 50, 52 are spaced a distance S apart. The first grid 50 is at a potential of Va and accelerates particles from zero energy to a kinetic energy (K.E.) = Va. The particles then enter a retarding region which forms a discriminator region (across distance S) and this is gated with a potential Vb applied to a second grid 52. As Vb < Va the region is generally a retarding field region, irrespective of the polarity of Vb. The retarding force on a positive particle of charge e in the discriminator region is

Eq.13. F = mx = e E = (e/S) (-Va ± Vb) = -d (V(x))/dx where x is the distance across the discriminator gap from x=0 at grid 50 to x=S at grid 52

We can determine the energy of a particle of charge e arriving at grid 52 as its starting kinetic energy minus the retarding potential.

Eq.14. E(S) = Va- V(S) = Va - f_Q (e/S) (-Va ± Vb)dx When the transit time of the particle is short so that it crosses the d iscriminator in less than half a period t < 1/2F then when Vb does not change we have the trivial solution that E(S) equals = +eVb or -eVb. As negative energies are not allowed, the charged particle is collected or not depending on which phase it enters the d iscriminator. In Fig. 6 there is a plot of particle kinetic energy versus distance across the apparatus of Fig. 5, at different times in the switching cycle. The solid line 54 shows that when Vb is high throughout the transit of an ion, the ion runs out of energy before getting to the second grid 52 (equivalent to a notional negative energy solution E(S)). In contrast, when Vb is low throughout the transit of an ion, indicated by solid line 56, the ion reaches grid 52 with surplus energy eVb, and emerges to be collected.

If Vb changes once during the particle transit, when the particle has reached a point x = Xi, indicated at 60 in Fig. 6, a nd where 0 < Xi < S, then its energy profile is a hybrid of two lines with slopes identical to lines 54 and 56. So between grid 50 and point 60 (x = Xi) the energy profile follows line 54. Then between point 60 and grid 52, the energy profile follows broken line 58. In Fig. 6, the point 60 reached by the ion when the switch occurs is precisely the point at which the particle just reaches the grid 52 a nd can emerge to be collected. If the switch occurs later for a given ion, i.e. it has passed point 60, then it cannot retain enough energy following the slope of line 56 to reach the second grid 52.

Conversely, for any particle for which the switch occurs at an earlier point in its transit, i.e. when the particle is between grid 50 and point 60, the particle will ma ke it across the distance X a nd will emerge with an energy between 0 and eVb, depending on where the particle in question was between x=0 and x= Xi when the switch happened. The equation for the particle energy at distance S is:

Eq.15. E S = eVa- V S) = Va -

Vb)dx

Eq.16. E S = eVa- (e/5) (-Vo ± Vb)X₁ - (e/5) (-Vo ± Vb) (S -

This has two cases: (i) when Vb starts positive at x = 0 and switches negative at x = X_x and (ii) when Vb starts negative and then switches positive when the particle has travelled a distance x = X_x. In case (i) when Vb starts negative the charged particle will be trying to get past grid 52 when that grid is positive, a nd this is not possible because E(S) cannot reach Vb (and thus the particle does not have sufficient energy to pass a grid biased at +Vb, except in the trivial case where Vb does not change. So taking the case that Vb starts positive and switches negative we see that:

Thus only charged particles where Xi < ½ S can reach grid 52. So if Vb switches from positive to negative, ions which are in the region Xi > ½ S at the moment when the switch occurs will not have enough energy to reach grid 52. We therefore have the conditions for an ion gate with an entrance and exit even though we only bias a single grid. The entrance to the gate is at X=S/2 and the exit is at X=S.

The situation is more complex for charged particles that take more than 1/(2F) to cross the discriminator as they experience more than one switch of Vb. We can ensure that these ions are never collected by adding a dc bias of Vc = ½ Vb. This means that charged particles need to arrive at grid 52 with at least ½ eVb of energy. It can be shown and is somewhat intuitive that ions that take longer than 1/(2F) to cross the discriminator cannot reach grid 52 with ½ eVb in energy. It is also seen that for times less than t = 1/(2F) only ions that are in the space X₁ < ¼ S can reach grid 52 with E(S)= ½ eVb in energy. The entrance to the gate is now at X=l/4 S and the exit is at X=S, but ions already in the gate region when the gate opens cannot exit.

So with a retarding voltage Va and alternative +/- Vb (50% duty cycle at frequency, F) and additional dc bias = ½ Vb ions must exit the discriminator when Vb is negative, and must cross the gap ¾ S so that there is a delay and the average charged particle current is

Eq.20.

If we assume linear deceleration in the retarding region then the velocity at x = S/4 will be ¾ U where U is the starting velocity and the average velocity between x= ¼ S and S will be 3/8 U so the delay will be approximately

This is linear against l/V(Va) where Va is the acceleration voltage on grid 50, with a discontinuity in slope at zero current where

Eq.25. ⁸ ^/₆₅ = fq.26. m = 16eVa/(3SF)² So far we have assumed that the gate is operated with a pulse or square wave voltage. In practice it is possible to use an arbitrary waveform including sinusoidal voltages to open and close the gate. However, it is not possible to produce a simple analytical analysis in the case of a sinusoidal voltage on grid 52. Particles are accelerated to Va and then decelerated in a potential of the form

Eq.27. V = Va + Vbsin(a)t + a) Where Va is the potential on grid 50 and Vb is the amplitude of the potential on grid 52. The potential on grid two oscillates with frequency F = ω/2π. If a particle passes grid 50 when the voltage on grid 52 is at a phase a, we can represent the equation of motion as

Eq.28. ^{d 2 x}/_{d t}2 = - [{Va + Vbsin(a>t + a)}/5] (e/m) where e is the electronic charge and m is the mass of a particle and S is the gap between grid 50 and grid 52.

We can consider a dc component with acceleration

Eq.29. a = -{Vo/5}(e/m) and an ac component with amplitude A = Vb/Soo² (e/m)

Eq.30. d²*/ ' _{d t}2 = a + Ao)²sin(a)t + a) Integrating once:

Eq.31. dx/dt = at— Ao)COs (a)t + a) + k using boundary conditions to establish k = u , the velocity at grid 50

Eq.32. k = Aa)COs(a) + u and integrating a second time

Eq.33. x = ½at² + ut— Asin(a>t + a) + Aa>cos(a)t + c and using x=0 at grid 1 as the boundary condition Eq.34. c = Asin a) so that

Eq.35. x = ½at² + ut + Aa>cos(a)t + A{sin(a)— sin(a>t + a)}

We want to avoid ions that take more than one period of the F to pass through the discriminator region. To do this we note that any ion remaining more than a full period will exit at a reduced energy as they see an effective RF potential. So we bias the second grid at a dc bias of Vb/2 so that only ions with more than half Vb energy exit the gate at this grid.

Numerically, we can find the starting phases where a particle will reach a minimum path length of S. These particles will pass through grid 52 and be collected. Assuming that the ion flux is constant at grid 50 we can integrate the number of path lengths over a to get the collected current for a given mass. Fig. 7 shows the calculated current passing grid 52 for two ions, mass =32 and mass =40.

The current in Fig. 7 is modelled using the arrangement of Fig. 5, with a sinusoidal alternating voltage Vb of magnitude 10V offset at a DC bias of 5V, at a frequency of 38 MHz. The discriminator gap S is 200 micron, and the accelerating voltage Va is varied to provide the current indicated. The mass and flux of each ion species is clearly visibly separated in the 200μιη discriminator, and is visible in each case as an onset of current. The first onset (attributable to the 32 a.m.u. ion) arises at around 60 V, and the second (attributable to the 40 a.m.u. ion) is seen as a discontinuity at around 76 V. A second difference or higher order difference will separate the mass signals (we cannot strictly speaking use second or higher derivatives because they go to infinity at the discontinuity, in practice this is not a serious issue as differences are normally used to determine derivatives in experimental practice).

Fig. 8 is a plot of the second difference of current with respect to acceleration voltage Va. It can be seen that there are two distinct peaks, which arise from the two onset currents as discussed above. From Fig. 8 it can be seen that the second derivative peaks are at 60 and 76 V.

The resolution of the current and thus of the mass discrimination can be increased by reducing the uncertainty in the energy of the ions entering the gate, rearranging the ion current so that slopes for each mass are linear with respect to the independent variable, in which case the second difference (change in slope) is only due to the onset of that mass species. An alternative and perhaps more accurate method of current analysis is to assume that the current is a sum of basis functions at each voltage and using least squares fitting to determine the magnitude of each basis function. This is particularly useful where the slope of the current is linear for a specific mass but a variable cannot be found where the slope of all masses are linear with the same independent variable, this is the case for a sinusoidal voltage gate, where we find empirically that the current for a specific mass Im = βη (Va/Vn -1) ^½ . This is linear for a given mass but not all masses. So we can construct a set of basis function for each mass and the current for each mass is a linear function, Im = βη (Va/Vn -1)^{1 2} where Vn is the onset voltage for mass mn. To determine each mass we assume that the total current is a sum of n basis functions starting at each voltage Vn:

Eq.36. I Vn) = ∑_ηβη (^Va/_Vn - l) '² and using least squares fitting techniques to determine the magnitude βη of each basis function. Note that (Va/Vn -1) ^{1 2} is undefined for Va<Vn, and therefore l(Vn) is taken to be zero for such values.

Fig. 9 shows a diagram of one of the preferred embodiments of the invention. The physical structure used is that of a standard FEA structure 60 having an entrance aperture and grid 62, which is normally grounded, an electron retarding grid 64 to which an ion accelerating voltage Va is applied as a scanning voltage of 0 to -400V, both to accelerate ions as well as to retard electrons, and an ion discriminator grid 66 to which we apply a 38MHz RF voltage in additional to the normal +/-400V scanning voltage. There is also a collector 72 to collect ions which emerge from ion discriminator grid 66 and means 74 for measuring this current connected to a computer (not shown) for analysing the current.

When the ion discriminator grid 66 is biased positive it will start to repel ions with low energies and let a reduced current 70 reach the collector 72. The derivative of current 70 at the collector 72 as a function of ion discriminator bias on grid 66 gives the ion energy distribution function of ions entering perpendicular to the entrance grid 62. The ion current at energy ε then Ι(ε) ~ (dl/dVe). As thus far described, this is a standard retarding field energy analyser and is well known in the art. It is used to measure the flux and energy of ions in a plasma or beam application.

In the preferred embodiment of the current invention we extend this device to measure both ion energy and mass by adding a small RF bias to the energy discriminator grid 66. Let us assume initially without the RF bias that where Va on grid 64 is set to -400 Volts, the ions of mass mn are accelerated and travel between grids 62 and 66 in a short time which is much less than the period of the RF (38MHz). The ions enter the apparatus at grid 62 with a single energy of lOeV. They are then accelerated by 400 V at grid 64. If the discriminator grid 66 is set to +12.5V then the ions are decelerated by 412.5V on the way between 64 and 66. The potential difference between 62 and 64 is -400 and between 64 and 66 is +412.5V. The net potential difference is 12.5V which is greater than their net energy of lOeV. Therefore all the ions will be repelled and the current at the collector will be zero.

Now we add the F bias with an amplitude of 5V to the discriminator grid. The total bias on grid 66 varies from 7.5V to 17.5V due to the combination of the RF and DC. When the bias is at 7.5V ions pass through grid 66 and are collected provided their transit time between grid 64 and 66 is short compared to the RF period. When the RF is high the grid bias is 17.5V and no ions can pass through. There is however an average ion current flowing over the full cycle arising from the ions that pass through when the RF is low. Now we reduce the accelerating voltage Va on grid 64 and slow down the transit time of the ions. At some point the ions now take one RF period to transit between grid 64 and grid 66. The average current collected will go to zero just at the point where the transit time equals the rf period. Now we introduce an equal current of ions at exactly lOeV that have a lower mass. These ions take less than an RF period to transit between grid 64 and grid 66 and a current will flow. Reducing Va further will slow these ions down and again a point will be reached where the average current goes to zero.

In a more general way, for a mono energetic beam the current of ions with a specific mass l(m) oc Δ² l/AVa . In a multi-energetic beam of ions we can first separate the ions into energies by getting the derivative of the current as a function of the bias on grid 66, Ve and then into mass by getting the difference with respect to bias on grid 64, Va. The current at mass m, and energy ε, then Ι(ιη,ε) oc Δ² (dl/dVe)/AVa. More accurate results can be obtained by finding an independent variable f(Va) so that the slope dl/d f(Va) is linear for all masses, or constructing linear basis functions and solving the least squares problem, or by a number of other mathematical approaches but the principle described above still applies.

Fig. 10 shows data from a test experiment. The apparatus used was an RFEA adapted as described above in relation to Fig. 9. To construct the device we used an RFEA 70mm in diameter and 5mm thick and made of aluminium as described in detail by Gahan et al 2008 rev. Sci. Instrum. 79

033502. The gap between the ion accelerator 64 (electron repeller) and the discriminator grid 66 was 300um. The RF at 38MHz was applied to the discriminator grid and had an amplitude of Vrf = 50V. The voltage on the electron repeller was varied between -20V and -200V. For the conditions shown -Va = -m/2e ( 2 S F)² = -110 Volts for a mass of 40 amu and -86V for a mass of 32 amu. We ran the FEA in a pure argon plasma. The extracted ions had an IEDF with a mean energy of 10 eV and an energy spread of approximately 2eV. The discriminator grid was biased to +35 volts so that ions that made a single pass were collected when their velocity was high enough. It is seen from Fig. 10 that the ion current at the collector has an onset value of -110V.

Fig. 11 shows the numerical second derivative of current (a second difference) with respect to the retarding voltage on grid 64 for the current of Fig. 10. We see the numerical second derivative has a peak at a mass corresponding to 40amu. This is the dominant peak in the mass spectrum.

Fig. 12 shows the second derivative of ion current with respect to the accelerating voltage Va in a similar experiment but using a mixture of argon and oxygen. The two dominant ions detected are Ar⁺ at 40amu and 0₂ ⁺ at 32 amu.

It is seen in Fig. 12 that the mass resolution is better than +/- 4 amu (10%) and probably close to 5% . It is expected that better than 1 amu (1%) can be achieved with the current apparatus by improving the derivative technique and achieving a better energy resolution of the ions. It is also possible in another embodiment of the experiment to add an additional discriminator grid before the RF biased discriminator and electron repeller grids. This first discriminator grid energy selects the ions by means of a variable voltage AV, such that they can be resolved at the collector as a varying current ΔΙ. The mass analysis now occurs for the modulated ions ΔΙ in the specified energy range. This allows the RF biased RFEA to analyse energy and mass independently. In a further refinement shown in Fig. 13 it is possible to use the discriminator grid 66 to

discriminate mass and energy simultaneously by adding a modulating voltage to the discriminator grid 66 voltage with reference to ground and adding a separate modulation voltage to the discriminator grid relative to the ion acceleration grid 64. The modulation frequencies are at two separate frequencies, ωΐ and ω2. Typical modulation frequencies in the range of a few kilohertz can be used.

In Fig. 13 the physical components of entrance 62, acceleration grid 64, discriminator grid 66 and collector 68 are shown in solid lines, with the electrical signals indicated using dashed lines. Vm is the acceleration voltage used to determine the ion mass and Ve is the energy discrimination voltage. As the derivative of a sinewave is proportional to the amplitude of the phase shifted fundamental times the angular frequency and a second harmonic will appear only when there is change in slope then given that Ι(ιη,ε) oc Δ² (dl/dVe)/AVm. The amplitude of the current at ωΐ is proportional to the derivative of collector current at Ve and is proportional to the ion energy distribution at a specific energy defined by Ve, and the amplitude of the second harmonic at ω2 for a given Vm is proportional to the second derivative of ion current at the energy determined by Ve and is proportional to the mass, Vm at the specific energy Ve. Higher harmonics of ω2 can also be used to measure the mass. The energy and mass resolution of the instrument is determined by the amplitude of the respective modulation voltages.

It should be noted that although F voltages are applied to the discriminator grid, the collector current is measured as a time averaged current and that a preferred feature of the current invention is that no time resolved electronics are required except where modulation is used. In the case of modulation, low frequencies can be used and the current needs to be time resolved to resolve at least the second derivative of the mass modulation frequency.

Another feature is that all ions can be collected at the collector and a faraday cup is adequate to measure this current.

The system is easily constructed from planar grids and is also easy to miniaturise and use for process monitoring in situ. The collector and electron repeller grid should preferably be grounded at RF frequencies so that they do not have a significant RF voltage.

Claims

A method of analysing charged species within a system, comprising the steps of: providing a system including a gate having an entrance position and an exit position separated by a distance S, the gate being switchable between open and closed states, wherein in the open state charged particles can pass through the gate entrance, wherein in the closed state charged particles cannot pass through the gate exit; providing a supply of charged particles to the entrance of the gate; switching said gate periodically between open and closed states wherein the switching cycle measured from one gate opening to the next gate opening has a frequency F, and wherein the ratio between the duration of the open state and the duration of the closed state over each cycle is x; varying a parameter a of the system, said parameter a being a controllable, variable system parameter which has a predictable effect on the average kinetic energy, U(a), of a particle within the gate; measuring a time-averaged collection current I as a is varied, wherein the collection current I is attributable to the collection of charged particles exiting the gate; determining a discontinuity in the derivative of the current I at a given value of a arising from the onset of a current component attributable to a charged species of mass m entering the gate from said supply of charged particles; and calculating the mass m of said charged species from the relationship:

The method of claim 1, wherein the gate is configured such that particles which are within the gate when the gate switches to a closed state cannot subsequently exit the gate in a subsequent open cycle.

The method of claim lor 2, wherein the variable parameter a is a function of one or more of (i) an accelerating voltage which accelerates charged species towards the gate, (ii) the frequency F of the switching cycle, (iii) the duty cycle or ration x between the duration of the open state and the duration of the closed state over each, and (iv) the size of the gate structure.

4. The method of any preceding claim, wherein the system is provided as a planar device wherein the distance S is in the range 1 mm to 1 micron, more preferably 500 micron to 50 micron, and most preferably 300 to 200 micron.

5. The method of any preceding claim, wherein said step of determining a discontinuity in the derivative of the current I at a given value of a comprises determining said discontinuity from an analysis of l(y), where y is proportional or equal to the inverse square root of U(a).

6. The method of any of claims 1-4, wherein said step of determining a discontinuity in the

derivative of the current I at a given value of a comprises determining said discontinuity from an analysis of l(y), where y is proportional or equal to the inverse square root of a, and where a is an accelerating voltage Va applied to the particles which accelerates them towards the gate.

7. The method of any preceding claim, wherein said determining step comprises identifying a peak in Δ²Ι/Δγ , i.e. the second difference of I with respect to y.

8. The method of any preceding claim, wherein the method further comprises the step of: deriving the magnitude of a current of said charged species of mass m entering the gate, l₀(m), by calculating the magnitude of a peak in the function Δ²Ι/Δγ, wherein l₀(m) and Δ²Ι/Δγ are related according to the relationship:

9. The method of any of claims 1-4, wherein said step of determining a discontinuity in the

derivative of the current I at a given value of a comprises analysing the current as a sum of basis functions at each voltage and determining the magnitude of each basis function.

10. The method of claim 9, wherein the gate is switched according to a sinusoidal potential, and wherein said basis functions take the form l(Va) =∑_n βη (Va/Vn -1)^{1 2} where Vn is the onset voltage for mass mn, with (Va/Vn -1)^{1 2} =0 for Va<Vn .

11. The method of claim 9 or 10, wherein determining the magnitude of each basis function

comprises using a least squares fitting techniques to determine the magnitude βη of each ba function. apparatus for analysing charged species, comprising: a gate having an entrance position and an exit position separated by a distance S, and configured to receive a supply of charged particles to the entrance of the gate means for switching the gate between open and closed states, wherein in the open state charged particles can pass through the gate entrance, wherein in the closed state charged particles cannot pass through the gate exit; a switching control operable to switch said gate periodically between open and closed states wherein the switching cycle measured from one gate opening to the next gate opening has a frequency F, and wherein the ratio between the duration of the open state and the duration of the closed state over each cycle is x; means for varying a parameter a of the system, said parameter a being a controllable, variable system parameter which has a predictable effect on the average kinetic energy, U(a), of a particle within the gate; a current collector configured to collect a time-averaged collection current I as a is varied, wherein the collection current I is attributable to the collection of charged particles exiting the gate; and a processor programmed to: determine a discontinuity in the derivative of the current I at a given value of a from the onset of a current component attributable to a charged species of mass m entering the gate from said supply of charged particles; and calculate the mass m of said charged species from the relationship: