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Computer modelling of field emission gun scanning electron microscope columns
Ultramicroscopy 21 (1987) 33-46 North-Holland, Amsterdam
33
C O M P U T E R M O D E L L I N G OF F I E L D E M I S S I O N G U N S C A N N I N G E L E C T R O N MICROSCOPE COLUMNS J.A. V E N A B L E S * and G. COX School of Mathematical and Ptlvscial Sciences, Universi(v of Sussex, Brighton BN1 9QH, UK Received 24 April 1986
Some computer programs are described which enable the performance of 2-, 3- and 4-magnetic lens (scanning) electron microscope columns to be modelled. The case of a 3-lens field emission SEM with a magnetic gun lens is explicitly considered: this case is extended to a 4-lens STEM with an objective lens working at fixed demagnification. The usefulness of these programs for optimizing the details of the column layout and for predicting performance is illustrated. The trajectory displacement (or transverse Boersch) effect is included and is predicted to affect the performance of practical columns containing one or more crossovers.
1. Introduction and background information
Over the last 15-20 years, the high brightness of the field emission source has been exploited in a new generation of high resolution scanning (SEM) and scanning transmission (STEM) electron microscopes. However, the optics of a field emission electron optical column differ considerably from that of a thermionic column, because the high brightness is achieved by a combination of small effective source size (5-10 nm diameter) with a small total emission, typically 1-10/~A for cold field emission. To obtain a sizable probe current such columns are run under conditions of relatively small total demagnification. Under these conditions all the lenses in the column are imp o r t a n t in determining the electron-optical performance. This paper describes a suite of computer programs which have been developed to aid in the design and evaluation of such electron-optical columns. The programs combine the effects of the field emission gun (FEG), the magnetic lenses and their aberrations, the apertures and their size and p o s i t i o n s , a n d the effects of statistical * Also at Department of Physics, Arizona State University, Tempe, Arizona 85287, USA.
electron-electron interactions in the neighborhood of crossovers. The present programs have been developed from previous codes for a 2-lens F E G - S E M , described in detail by Venables and Janssen [1]. These codes, and the values of constants in them, were tested against edge-resolution experiments on a VG HB50 SEM column. Good overall agreement was obtained; but at the highest resolution detailed agreement could only be achieved if an implausibly large chromatic aberration was assumed, corresponding to an energy spread A E - 3 eV F W H M . Since energy spreads of _< 0.5 eV have been measured using energy-loss spectrometers on similar F E G - S T E M machines, it seemed likely that another explanation was required. It is now fairly clear that statistical electronelectron interactions can be important in these F E G - S E M columns. The (longitudinal) Boersch effect contributes to the energy spread at crossovers; but, more importantly, the transverse Boersch effect (or trajectory displacement effect) contributes to a broadening of the spot at such crossovers. In conjunction with Dr. G.H. Jansen, we have incorporated his description of the trajectory displacement effect into our column calculations [2]. The results, shown in fig. 1, indicated that this
0304-3991/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
J.A. Venables, G. Cox / Computer modelling of FEG-SEM columns
34
Ip(A)
10-8
10-9
10-10
1rim
lOnm
lOOnm
d
Fig. 1, Ip(d) measurements for Sussex HB50 SEM column [1], compared with predictions including the trajectory displacement effect (full lines) and without it (dashed lines), for various beam voltages indicated, and a final aperture diameter, a~ ~ 150 p,m; after ref. [2].
effect was sufficient to explain the previous HB50 measurements with a more reasonable energy spread of AE < 0.5 eV FWHM. Jansen et al. [2] also obtained approximate agreement with measurements on two other FEG columns, the Philips EM420ST and a Hewlett-Packard lithography machine. These correlations with experimental results give us some confidence that we can extrapolate to new situations, using programs which incorporate all the above effects. However, we should note at the outset that typically several parameters needed in the program cannot be checked experimentally at all easily. In particular the trajectory displacement effect behaves very like chromatic aberration, and its absolute magnitude is uncertain. Detailed modelling of combined electric and magnetic fields in the gun region is awkward (see ref. [3]) and has not been attempted; also the source size and aberrations of the gun itself are variable depending on tip treatment and position. Nevertheless, we can easily explore with these programs
the variations in performance predicted for a range of parameter values, so that sensitive features of the designs can be investigated. For analytical applications requiring relatively high probe currents, aberrations in the gun-condenser region of the column can be dominant. Good performance thus requires a short-focallength gun lens with low aberration coefficients. Although several other solutions have been proposed, we have proposed [4] and implemented on the HB50 [5] a magnetic lens at earth potential, rather open-ended towards the tip. A similar design has been fitted to some VG HB501 and HB50A machines and marketed separately as the FEG 2000 series guns. With such a gun lens, a SEM requires a 3-lens column to be fully flexible. The analysis of a design for a surface analytical SEM is described in section 3. In a STEM it is often convenient to run the objective lens at fixed demagnification, with the sample conjugate to a selected area aperture. This then leads to a 4-lens design with 2 condenser lenses to vary probe size and angular divergence flexibly. The extension to this situation is discussed in section 4. But first the main features of the programs are discussed in section 2 below.
2. Column model and computer codes 2.1. The column model
The model described follows closely previous work on a 2-lens FEG-SEM (ref. [1], hereafter 1), In particular the following features are identical to I: (1) The description of the field emission gun itself, including the angular emission from the tip, electrostatic lens effects, and the (small) gun aberrations (I, section 3.1 and appendix A). The effect of the second electrostatic lens (m I in l) is uncertain and has been investigated further. (2) The use of thin lens geometrical optics, and Fert and Durandeau-type lens formulae for weak lenses, such as condensers and SEM objectives, where the focus is outside the lens field (I, section 3.2).
J.A. Venables, G. Cox / Computer modelling of FEG-SEM columns
(3) The treatment of lens aberrations by additions as sums of squares, with constants appropriate for the 20-80% edge resolution ( d ) being the measure of spot size at a given probe current Ip, as shown here in fig. 1 and subsequently (I, section 3.3 and appendix B). Extensions to the model presented previously include: (4) The addition of a (strong) gun lens with a differential pumping aperture in its bore, whose position and size can be varied. The gun lens is operated with fixed object distance with a given gun configuration; thus the gun plus gun lens acts as a fixed input element in any calculation, with data input from a (changeable) "gun file". This is described in more detail in section 2.2. (5) Various options within the column calculation to enable the user to choose: (a) either a real aperture in the objective lens (as in I), or, as in many SEM and STEM instruments, a virtual objective aperture between the gun and condenser lenses. In the first case the final aperture angle o~ is fixed and the probe current Ip is varied; in the second, Ip is fixed and a is the independent variable; (b) the presence or absence of a crossover between the condenser and objective lenses. The second case allows the condenser to be used as a minor trim on the gun lens, as discussed in section 3. The 2-lens column with this condenser lens off (i.e. gun lens and objective alone) has been modelled by a similar program. In this case both lp and c~ are fixed for a given objective aperture size. All the column options and dimensions are input from a "column file". (6) The addition, for STEM columns, of an objective lens working at fixed demagnification. In this 4-lens program the condenser and objective lens become first and second condenser lenses respectively. The objective lens properties (magnification, aberration coefficients) are input from an "objective file"; since the objective properties are fixed we are not restricted by thin lens or other assumptions, but can input the results of detailed magnetic lens calculations for the actual geometry. This is discussed further in section 4. (7) The inclusion of various models of longitudinal and transverse Boersch effects as given by Jansen and coworkers [2]. This is discussed further in section 2.3.
35
In summary, we now have several similar programs for 2-lens (either condenser + objective or gun + objective), 3-lens (gun, condenser, objective) and 4-lens (gun, 2 condensers, objective) operation. The output gives the Ip(d ) curves for a range of objective aperture sizes for a given gun lens setting, and the dominant aberration, for several values of the energy spread AE. Individual aberrations, lens magnifications and currents are also calculated. The programs are in F O R T R A N - I V and use --40 kilobytes of memory. On our PDP 11/23 they execute in - 3 0 s to 2 min, dominated by printing time.
2.2. Strong and asymmetric lenses For good performance at both high and low probe currents, a strong gun lens is needed. The focal properties of such a lens can be calculated using lens calculations of the type developed originally by Munro [6]. We have been able to use the CIELAS 1 package at Cambridge University [7] to optimize the designs of individual lenses, including a new gun lens and an objective lens for a new surface SEM, as described in section 3.2. The objective lens designed, with a sample outside the lens, behaves as a weak lens, with C~ = kf3/D 2, as assumed in the column calculations. But because of the sharp cone angle of this lens, the field is asymmetric between the polepieces. Thus the CIELAS I programs can be used not only to optimize the details of the design, but also to furnish values of k and the lens center position for detailed column calculations. The gu n lens, however, has the field emission tip immersed in the field and forms a strong lens whose objective properties (at inifinite magnification) are needed. These have been optimized in the same way, and C~ plotted against objective focal length, f0, in the form C~ = k(fo/f~,~)", where fm is the minimum projector focal length as given by the F e r t - D u r a n d e a u formula. For the lens design of fig. 4, we found k = 2 . 2 8 and n = 2 . 2 over the whole range of focal lengths needed for the column calculation. The choice of fm can be made such that the F e r t - D u r a n d e a u formulae also account for the gun lens currents needed to power
J.A. Venables, G. Cox / Computer modelling of FEG-SEM columns
36
the lens, according to the CIELAS I values. All this simply means that we can parameterize the results of a detailed lens calculation well enough to use in a column calculation, even though the lenses are either strong a n d / o r considerably asymmetric. However, for the gun lens there are two minor problems in the present calculations. The Munro-type program does not perform at its best for open lenses, as pointed out by Mulvey [8], since there is a net dipole field with a long range, which is not taken into account with the usual boundary conditions. This results in underestimating the maximum field strength for a given lens current. Also the gun lens is acting on an accelerating electron beam, so the focal length will in practice be smaller than estimated by these programs. Both these effects, therefore, act in the direction of making the actual gun lens have high probe current properties superior to those calculated, though the low current conditions may be more difficult to achieve in practice.
somewhat uncertain. Also included are several minor effects which reduce C t by up to 25% when the crossover is not in the middle of the column section [2]. The trajectory displacement effect as given by eq. (1) increases as the beam angle a decreases, but for small angles and probe currents it goes through a maximum; smaller angles correspond to the "pencil beam" regime [10], in which the electrons are effectively following each other in a line. The reduction in displacement caused by this effect, which is substantial after a (virtual) objective aperture, is included. The effects at different parts of the column are combined linearly, magnified as appropriate. There may well be additional effects in the lower voltage region near the tip which are not included, but such effects can be simulated by varying the effective source size. The longitudinal Boersch effect, which leads to an energy spread at crossovers, is less controversial [2,11]. It was calculated according to
Trajectory Boersch effects
~ E = C~lh~-lV~ 1/2,
2.3.
displacement
and
longitudinal
The trajectory displacement effects as modelled by Jansen et al. [2,9] have been included in the column calculations for each section of the column which contains a crossover. The constants used are appropriate for the low-current (Lorentzian) asymptote for the 20-80% edge resolution, as for the other aberrations calculated in I. For a section of the column length L, Jansen et al.'s expression for the trajectory displacement diameter, d t, is d t = C~(d
Ib/d~)2/3Z2/3V14/3,
(11
where the beam current at that point is lh at voltage VZ (all symbols as in I, and values in SI units). The value of the constant C~ has been controversial, and it is only recently that essential agreement has been reached about the power law dependencies. Comparison with Monte Carlo calculations [9] suggests that the theory [2] overestimated the effect by = 50%; consequently we have used C t = 5.0, which incorporates this comparison, but it is clear that the exact value is
(2)
where a is the angular divergence at the corresponding crossover. The constant Cc = 3.8 × 105 for A E = the F W H M energy spread. These energy spreads were added in quadrature with an initial energy spread in the gun assumed to be 0.22 eV at low beam currents, rising to - 0 . 5 eV at 10 /xA emission. Because of the uncertainties in the absolute value of A E, and its dependence on total tip emission current, the estimated energy spread was not used directly in the column calculation. Instead, column properties were calculated for different A E values spanning the range of interest, and the influence of A E noted. Typically, the trajectory displacement effect was larger than the chromatic aberration, and has a similar, though not identical, dependence on the beam energy V~.
3. Electron-optical design of a surface S E M
3.1. Design constraints The electron-optical column considered is a 3-lens SEM, operating up to 30 kV. The SEM is
J.A. Venables, G. Cox / Computer modelling of FEG.SEM columns
an aI1-UHV construction for use in surface science and contains a cylindrical mirror analyzer (CMA) installed concentrically around the electron-optical column, for various forms of electron spectroscopy. The construction details, spectroscopy, and uses will be reported elsewhere [12]; here we concentrate solely on the probe-forming optics as an example of computer modelling of an SEM column. A schematic diagram of the column is given in fig. 2. The objective-condenser-scan coil assem-
Condenser lens
bly has been designed to be in one closed container, inside the CMA. Between the gun lens and the condenser is a relatively large space for a gun isolation valve, beam blanking, virtual objective aperture, and C M A detectors. The gun lens is mounted on the bottom of the column on a standard 200 m m flange, and the gun is suspended from this. The main design constraint is the need to house the UHV-sealed condenser-objective unit inside the bore of the CMA. This arises because the
__ ;
VOA
37
~
Detector
__
--1
Fig. 2. Schematic diagram of a new SEM column for surface studies. It incorporates a FEG, gun lens, virtual objective aperture (VOA) and uses the condenser lens as a trim. The obJective-condenser unit is housed inside a cylindrical mirror analyser (CMA).
J.A. Venables, G. Cox / Computer modelling of FEG-SEM columns
38
distance to the exit slits from the sample is about 2.55 times the inner cylinder diameter for suitable CMA focusing. We have chosen to solve this problem by designing a rather large CMA of 101 mm inner diameter, which allowed the objective lens diameter to be 88 mm. However, because we also wanted to collect a large fraction of the emitted electrons into the CMA, the objective lens had to be rather strongly conical. The design evolved after testing on the CIELAS I programs is described in section 3.2. Given a compact condenser-objective unit inside the CMA, there is considerably more freedom in the choice of the other electron-optical elements, We have chosen to rely entirely on a virtual objective aperture (VOA) with the gun lens providing a crossover in front of the aperture. The gun is differentially pumped, so the crossover is fairly close to this differential pumping aperture (DPA). The positions of both the VOA and the DPA can be optimized using the column model. A final constraint was the lens power supplies. In our case the lenses are designed to operate from the supplies of a Cambridge Instruments S-200 SEM delivering up to 12 V or 2 A maximum for
each lens. In addition the lenses are bakeable up to 200°C. This necessitated the use of specially insulated wire at 21 SWG for the objective condenser lens and 18 SWG for the gun lens; the number of ampere turns needed in each lens is, of course, an output of the column calculation and of the CIELAS ! programs.
3.2. Objective-condenser and gun lens designs The objective-condenser unit is indicated schematically in fig. 3. Superimposed on the figure are the measured axial B-fields, and the field calculated using the CIELAS I program for the objective. The measured peak field is some 10% lower than that calculated for the given number of ampere turns, indicating that we may just be approaching saturation under 30 kV operating conditions. Stray fields in the CMA must be kept to a minimum in this application, and current efforts to reduce these may result in some design changes. However, the on-axis optical properties are unlikely to be much affected. The lens center is located some 7 mm in front
B (Gauss) - -
600
.....
Measured Calculated
/A I
500
400
300
200
100
- 20
0
20
40
-60
-40
-20
0
20
Z(mm)
Fig. 3. Cross-sectional drawing of the objective condenser lens, with measured B-fields, and that calculated using CIELAS 1 superimposed. The fields correspond to an excitation of 954 AT for the objective and 473 AT for the condenser lens.
J.A. Venables, G. Cox / Computer modelling of FEG-SEM columns
39
design has been incorporated into the column calculations in the manner described in section 2.2, assuming that all the focusing takes place at the beam voltage 1/'1. In fact, the gun lens will perform better than this implies, since the local measure of focusing power in the acceleration region is B 2 / V I *. Accordingly this is also plotted in fig. 4, on the assumption that V1 = V0 = 3 kV between the tip and the first anode, Vt varies linearly between 3 and 30 kV between first and second anodes, and is constant at 30 kV thereafter. It is clearly possible to consider adjusting anodes and gun positions to minimize the focal length, or equivalently maximize f ( B 2 / V l * ) d z. Even without these effects, the focal length can be reduced below 15 m m with the lens supplies available.
of the inner polepiece, giving a lens-sample distance, vs = 37 m m for the sample at the focus point of the CMA, 15 m m beyond the end of the lens housing.. The bores of the objective lens at Dt=6mmand D2--24mm,withthegapS=20 mm, the outer cone angle being 26 °. The calculated spherical aberration is easily parameterized a s C s = k f 3 / D 2, with D = ( D 1 + 1)2)/2 and k = 1.16. These constants are input into the column calculation. The gun lens design is indicated in fig. 4. Again the measured and calculated B-fields are superimposed on the figure. As can be seen, the curve calculated by CIELAS I is pessimistic as discussed in section 2.2. The field penetrated a long way into the tip region, falling off as - z 3 from a peak around 5 m m in front of the inner polepiece. This
B (Gauss)
1000
- -
Measured
.....
Calculated
800
600
400
200
-80
-60
-40
.~20
0
20
40
60
8 3O
Tip position
- -
Varying voltage ( 3 - 3 0 kV)
.....
Constant voltage (30 kV)
20
1o
// /
- 8 0'
- 6 'o
- 4' 0
/ /
//
- 2 0'
0'
' 20
4'0
6'0
Z(mm
)'
Fig. 4. Cross-sectional drawing of the gun lens with measured and calculated B-fields superimposed, for an excitation of 2050 AT. Also shown is B2/V for the variation V(z) in the accelerating region discussed in the text.
J.A. Venables, G. Cox / Computer modelling of FEG-SEM columns
40
3.3. Predicted perforrnance The predicted optimum performance of this SEM column is indicated in fig. 5, for a total emission current from the tip, I t = 10 /~A. The l p ( d ) curves are for 30 and 5 kV for an energy spread AE = 0.5 eV F W H M , for a range of suitable virtual objective aperture (VOA) sizes. This figure is useful to explore the optimum VOA diameter. With a suitable choice (e.g. 70-100 # m diameter for 30 kV, somewhat larger for 5 kV) the probe current can be varied simply via the gun lens while staying close to the overall optimum curve. A characteristic of the gun lens is the high total
,
'V-
current available. Essentially all the current which gets through the first anode can be focussed onto the sample. Although by comparison with fig. 1 at 30 kV the ultimate resolution is not improved, the high current performance (10 nA into 15 nm, 0.1 /,A into 60 nm and 0.5 ~*A into 0.6 /~m) is much improved. Fig. 6 shows the effect of trajectory displacement on the computed performance. It is seen that trajectory displacement effectively limits the column brightness around the knee of the I p ( d ) curve, where a F E G - S E M column is typically operating. Its importance is greater at lower beam voltage. The main effect arises from the first crossover, in front of the VOA. After this aperture the
,
r
Current limit by DPA
10- 6
400
--
200
70,1 O0
Ip(A)
10-'/
400 200
- 100
5kV
3 0 kV
70,100
10- 6
10 - 9
10-10
I /--200
Parameter: VOA Diameter: p m
-100
70,100 10 -11
] lnm
10nm
I
-
10nm
100nm
I
lO00nm
d
Fig. 5. I p ( d ) curves calculated for the new Sussex SEM, including trajectory displacement effects, at 30 and 5 kV for various VOA diameters, for I t = 10 FA.
41
J.A. Venables, G. Cox / Computer modelling of FEG-SEM columns
10-7
Ip(A)
5kV
30kV Without
T
ith T
D
Without
10-8
S/ //'//
10-9
//
/:
/////
VOA d i a m e t e r 70 gm . . . . . . . . 100 I~m 200 Hm
/ // ' / //
//
10_10~ lnm
, i
1Ohm
/ / I
lOnm
I
lOOnm
d
Fig. 6. I p ( d ) curves, illustrating the effect of trajectory displacement at 30 and 5 kV for various VOA diameters, for I t = 10 #A.
beam is typically in the pencil beam regime [10], with a much reduced effect. This is, however, a strong (additional) argument for using a virtual, rather than a real, objective aperture. These comparisons suggest that some further improvement might be obtained by eliminating the crossover between the gun and condenser lenses, where the maximum effect of trajectory displacement, and a major contribution to the Boersch effect, occurs. The crossover at this point is dictated by the presence of the DPA and by the need to control Ip and column magnification accurately. In addition, the crossover makes it easy to steer the beam through the DPA for high current applications, while the DPA acts as a splash aperture at high resolution. Of course, the major reason for the DPA is the good UHV requirement for the operation of a cold field emission gun. Alternative approaches without any crossovers using thermal field emitters for similar
applications are being pursued by others [13-15]. At present these machines use all-electrostatic focussing; the present programs could be used to explore the characteristics of the corresponding magnetic focusing designs. In figs. 5 and 6 we have assumed that there is no crossover between the condenser and objective lenses. There is a slight reduction in predicted performance if one is included. Without a crossover, the condenser is operating as a minor trim to optimize the angular divergence. The small lens currents involved will be advantageous in our application where the lens is close to the detection area of the CMA, which is sensitive to stray magnetic fields. 3.4. Choice of operating conditions The operating conditions of this particular SEM will of course be chosen after considerable practi-
42
J.A. Venahles, G. Cox / Computer modelling of FEG-SEM columns
cal experience, and with regard to any influence stray magnetic fields may have on the electron spectroscopy. But one attractive feature is to operate with the condenser lens at most as a very minor trim. With the virtual objective aperture at the point chosen, the optimum curve of fig. 5 can be approached closely for a particular VOA size, over a wide range of gun lens settings, with the condenser lens off. This may prove to be a particularly convenient mode for a range of high resolution conditions. For high current (weaker gun lens) conditions, larger size VOA's may be needed, and the condenser lens must be used to compress the beam, optimizing the final angular convergence at the sample. Nonetheless 1 or 2 aperture sizes are sufficient to span the operating range of current very close to the optimum curve. This is of course not possible with real objective apertures in the objective lens region.
restriction to a fixed setting for the objective lens. It is of course well known that the probe shape at high resolution is a function o f diffraction, spherical aberration, and defocus (A f ) , and that the combined coherent effects can be calculated using phase contrast transfer theory [16,17]. The only detailed study in the context of high resolution STEM columns is that of Mory and Colliex [17]. They show that the 20-80 edge resolution has a minimum d=0.4(~3C~) 1/4. The quadratic addition combination used here gives 0.409 for this constant; these constants therefore are essentially consistent. Both treatments [16] give the corresponding defocus value A f ~ - 0.75(~(~)1/2 which is intermediate between the conditions of minimum and maximum phase contrast (Scherzer focus) for which the resolution d=O.66(X:~C~)1/4 is typically quoted. At higher probe currents, where incoherent imaging conditions prevail, the treatment of the STEM should be identical to the SEM column discussed in section 3.
4. Extension to 4-lens S T E M designs
4.2. Ultimate resolution and analytical performance: the VG HB501 S T E M and related columns
4.1. Objective lens data A 4-lens design has many possible operating modes, since only 2 parameters, the probe current lp and the final aperture angle a, need to be varied. However, it is common practice to set the objective lens working at fixed (de-)magnification so that the sample is conjugate to a selected area aperture plane. Under these conditions the number of variables is identical to the 3-lens SEM described in the last section. We have modified the corresponding programs to accommodate this extra stage by relabeling the condenser and objective lenses as condensers C1 and C2, and inputting the required objective data from an "objective file." No restrictions are implied on the type of objective lens (strong, asymmetric, condenser-objective, etc.) used. All that is needed is the selected area aperture-to-sample distance, the objective magnification, and the C~ and Cc values at zero magnification. These quantities can be obtained from a detailed Munro-type calculation [6,7] of the objective lens. The fact that so little data is needed is a consequence of the
The optics of the VG HB5 and 501 STEMs have been referred to in several papers, but no analysis has been made of columns fitted with a gun lens. As in the SEM designs (section 3) this lens has been added to improve the high current analytical performance. We have shown, however, that unless the gun lens is strongly excited there is a danger that the new column does not have enough overall demagnification for the highest resolution applications. Under these conditions, lens C 1 has to be strongly demagnifying with an (unwanted) crossover between C 1 and C 2, which also contributes to the trajectory displacement effect. A typical set of I v ( d ) curves shown for an HB501 column is shown for 100 kV operation in fig. 7, indicating the effect of trajectory displacement on the performance, with a crossover between C1 and C2. In fig. 7a, for a total tip emission I t = 10 /~A, the trajectory displacement effect is just making an effect. However, as seen in fig. 7b for I t = 5, 10 and 20 /LA, a strong saturation sets in above 10 t~A, with not much ad-
J.A. Venables, G. Cox / Computer modelling of FEG-SEM columns
0-1
,o-7 Ip(A)
0-1
1
10
denser lens currents and angular current densities, and deduced virtual tip positions for their HB5. Their results correlate well with our calculation of the gun, provided we ignore the second electrostatic pinhole lens in the gun (m I in I) by setting mt = 1. However, in the present calculations with a gun lens, this "lens" is ineffective anyway, because it coincides with the center of the gun lens. Their work, inter alia, emphasizes that the current falling on the V O A is an important experimental quantity, which can be used to establish the angular current density. This in turn provides a useful check on the model of the gun. The present calculations have been used to suggest design improvements. These include m o v e m e n t of the D P A and V O A to more advantageous positions, moving condenser 1 and 2 further apart, and other more minor changes. One attrac-
a,_,=,o.2. ° - --
no T D
"
Expt.
//~
/~
20 / 20
//
/Lo
/
t% 1
d
J 1
43
0-1
1
10
10
(nm)
Fig. 7. l p ( d ) curves calculated for the VG HB501 column with (full lines) and without (dashed lines) trajectory displacement: (a) I t = 10 ~,A; (b) I t = 5, 10 and 20/~A, Experimental points taken from ref. [171. See text for discussion.
vantage gained in increasing I t to 20 /~A. In addition, the Boersch effect energy spread is increasing to A E > 1 eV at 20/~A, whereas it can be kept < 0.5 eV at 10 /~A and below. In the high resolution region around lp = 10 10 A, the gun lens needs to be operated at around unity magnification, with an excitation near 4000A • T. M o r y and Colliex [17] have measured 2 0 - 8 0 edge resolutions for two conditions of their HB5, without a gun lens, which are indicated in fig. 7. These points are for a nominal I t = 5 #A. These points fall in between the curves calculated for I t = 5 and 10 /~A. This indicates that the brightness actually achieved in an HB5 is close to that assumed in the present calculations, B = 4.6 × 1 0 9 A / c m 2 - sr at 100 kV. If their value of I t = 5 # A is taken literally, the curves of fig. 7 without the trajectory displacement effect indicate that B _> 4 × 10 9 A / c m 2- sr. M o r y and Colliex [17] have also measured con-
10-7
Ip(A)
--
with T.D.
~
a. optimised // --noTD //
/
~o- 8
/
/
/
?c, on,, /
// /
10
/y
10-10
//
f 0.1
~
]% 1
f
-
b. o n e V O A s i z e optimised
---
i
1
I
d
10(nm)
Fig. g. /p(d) curves calculated for the new Arizona STEM column for I t = ]0 #A: (a) "optimized" column with (full line) and without (dashed line) trajectory displacement; (b) column operated with either C 1 or C 2 only at a fixed VOA diameter (full lines) compared with the optimum curve (dashed line). See text for discussion.
44
J.A. Venables, G. Cox / Computer modelling of FEG-SEM columns
tive possibility, a d v o c a t e d by M o r y a n d Colliex [17], is to use C 2 only for high resolution a p p l i c a tions, and Ca only for high c u r r e n t applications. This is facilitated b y m o v i n g the c o n d e n s e r lenses further apart. W i t h the a d d i t i o n a l flexibility of v a r y i n g the p r o b e current using the gun lens, a n d c h o o s i n g a suitable V O A diameter, it is p o s s i b l e to stay e x t r e m e l y close to the o p t i m u m curve over a large range o f Iv. This is illustrated in fig. 8 using c o l u m n p a r a m eters for a new surface-oriented S T E M p r e s e n t l y b e i n g designed for A r i z o n a State U n i v e r s i t y [18]. T h e o p t i m u m curves with a n d without trajectory d i s p l a c e m e n t are given in fig. 8a for I t = 10 /tA, for the same a b e r r a t i o n coefficients as used for fig. 7. The curve with only C~ excited a n d a fixed V O A d i a m e t e r stays r e m a r k a b l y close to the optim u m curve for a l m o s t 3 orders of m a g n i t u d e in lp; in fact a slightly larger a p e r t u r e than that shown lies essentially on top of the o p t i m u m curve for 5 × 10 - H < Ip < 3 × 10 -~ A. T h e reason is that, for a suitable choice of V O A d i a m e t e r a n d position, a n d the lens position, the curve can be tangential to the o p t i m u m curve in the region of b o t h the u p p e r a n d lower knees of this curve. T h e C 2 lens is clearly less well p o s i t i o n e d in this sense, a n d can only be used on its own in the high resolution region.
5. Conclusions Several p r o g r a m s have been d e v e l o p e d which have allowed us to explore the p e r f o r m a n c e a n d o p t i m i z e design of F E G - S E M a n d F E G - S T E M columns. F o r c o l u m n s c o n t a i n i n g crossovers the p e r f o r m a n c e is f o u n d to be affected b y the trajectory d i s p l a c e m e n t (or transverse Boersch) effect, as well as other aberrations. E x a m p l e s of a s u r f a c e - S E M and a high resolution S T E M are given to illustrate the use of these p r o g r a m s in o p t i m i z i n g the design of such microscopes.
Acknowledgments W e are grateful to K.C.A. S m i t h a n d J. T a y l o r for use of the C I E L A S I lens analysis p a c k a g e at
C a m b r i d g e University; to G . H . Jansen for j o i n t w o r k at Sussex in 1982-83, a n d for subsequent c o r r e s p o n d e n c e ; to W . R . K n o w l e s a n d J.P. D a v e y of C a m b r i d g e I n s t r u m e n t s for advice on practical S E M lens designs; to S. y o n H a r r a c h for i n f o r m a tion a b o u t the V G HB501 S T E M ; a n d to m a n y colleagues (refs. [11] a n d [18]) for their j o i n t work on other aspects of the s u r f a c e - S E M construction at Sussex a n d the s u r f a c e - S T E M for A r i z o n a State. These i n s t r u m e n t s are being c o n s t r u c t e d with g r a n t s from the S E R C , a n d D O D a n d N S F respectively. G. C o x acknowledges s u p p o r t from the D A A D in 1984-85.
References [1] J.A. Venables and A.P. Janssen, Ultramicroscopy 5 (1980) 297. [2] G.H. Jansen, J.M.J. van Leeuwen and K.D. van der Mast, Proc. Microcircuit. Eng. (1983) 99; J.M.J. van Leeuwen and G.H. Jansen, Optik 65 (1983) 179: G.H. Jansen, personal communication. [3] J.R.A. Cleaver, Optik 52 (1978) 293. [4] J.A. Venables and G.D. Archer, in: Proc. European Regional Conf. on Electron Microscopy, Hamburg, 1980, Vol. 1, p. 54. [5] J.A. Venables, G.D.T. Spiller, D.J. Fathers, C.J. Harland and M. Hanbiicken, Ultramicroscopy 11 (1983) 149. [6] E. Munro, in: Image Processing and Computer Aided Design in Electron Optics, Ed. P.W. Hawkes (Academic Press, New York, 1983) p. 283. [7] R. Hill and K.C.A. Smith, in: Electron Microscopy and Analysis 1981, Inst. Phys. Conf. Ser. 61, Ed. M.J. Goringc (Inst. Phys., London-Bristol, 1982) p. 71. [8] T. Mulvey, in: Magnetic Electron Lenses, Springer Topics in Current Physics, Vol. 18, Ed. P.W. Hawkes (Springer, Berlin, 1982) p. 390. [9] G.H. Jansen and W. Stickel, Proc. Microcircuit Eng. (1984) 43. [10] K.D. van der Mast, G.H. Jansen and J.E. Barth, Proc. Microcircuit Eng. (1985) 169. [11] G.H. Jansen, T.R. Groves and W. Stickel, J. Vacuum Sci. Technol. B3 (1985) 190. [12] J.A. Venables, C.J. Harland, G. Cox, P.S. Flora and M. Hardiman, work in progress. [13] L.H. Veneklasen, G. Todd and H. Poppa, in: Proc. 9th Intern. Congr. on Electron Microscopy, Toronto, 1978, Ed. J.H. Sturgess (Microsc. Soc. Canada, Toronto, 1978) Vol. I, p. 12; L.H. Veneklasen, G, Todd and H. Poppa, in: Scanning Electron Microscopy/1979, Vol. I, Ed. O. Johari (SEM, AMF O'Hare, IL, 1979) p. 207.
J,A. Venables, G. Cox / Computer modelling of FEG-SEM columns [14] M.M. El-Gomati, M. Prutton and R. Browning, J. Phys. El8 (1985) 32. [15] L.W. Swanson and J. Orloff, in: Electron Optical Systems (SEM AMF O'Hare, IL, 1984) pp. 137-162: F.E. Inc., model 83 TFE Electrostatic gun (1986): P.A. Bennett, personal communication, 1986. [16] J.C.H. Spence, Experimental High Resolution Electron Microscopy (Oxford Univ. Press, London, 1981) pp. 200, 217.
45
[17] C. Mory, Th~se d'Etat, Orsay (1985); C. Colliex and C. Mory, in: Quantitative Electron Microscopy Scottish Universities Summer School in Physics, Vol. 25, Eds. J.N. Chapman and A.J. Craven (1983) p. 149; C. Mory and C. Colliex, in preparation. [18] J.A. Venables, N.J. Long, P.A. Bennett, J.M. Cowley and others, work in progress.
33
C O M P U T E R M O D E L L I N G OF F I E L D E M I S S I O N G U N S C A N N I N G E L E C T R O N MICROSCOPE COLUMNS J.A. V E N A B L E S * and G. COX School of Mathematical and Ptlvscial Sciences, Universi(v of Sussex, Brighton BN1 9QH, UK Received 24 April 1986
Some computer programs are described which enable the performance of 2-, 3- and 4-magnetic lens (scanning) electron microscope columns to be modelled. The case of a 3-lens field emission SEM with a magnetic gun lens is explicitly considered: this case is extended to a 4-lens STEM with an objective lens working at fixed demagnification. The usefulness of these programs for optimizing the details of the column layout and for predicting performance is illustrated. The trajectory displacement (or transverse Boersch) effect is included and is predicted to affect the performance of practical columns containing one or more crossovers.
1. Introduction and background information
Over the last 15-20 years, the high brightness of the field emission source has been exploited in a new generation of high resolution scanning (SEM) and scanning transmission (STEM) electron microscopes. However, the optics of a field emission electron optical column differ considerably from that of a thermionic column, because the high brightness is achieved by a combination of small effective source size (5-10 nm diameter) with a small total emission, typically 1-10/~A for cold field emission. To obtain a sizable probe current such columns are run under conditions of relatively small total demagnification. Under these conditions all the lenses in the column are imp o r t a n t in determining the electron-optical performance. This paper describes a suite of computer programs which have been developed to aid in the design and evaluation of such electron-optical columns. The programs combine the effects of the field emission gun (FEG), the magnetic lenses and their aberrations, the apertures and their size and p o s i t i o n s , a n d the effects of statistical * Also at Department of Physics, Arizona State University, Tempe, Arizona 85287, USA.
electron-electron interactions in the neighborhood of crossovers. The present programs have been developed from previous codes for a 2-lens F E G - S E M , described in detail by Venables and Janssen [1]. These codes, and the values of constants in them, were tested against edge-resolution experiments on a VG HB50 SEM column. Good overall agreement was obtained; but at the highest resolution detailed agreement could only be achieved if an implausibly large chromatic aberration was assumed, corresponding to an energy spread A E - 3 eV F W H M . Since energy spreads of _< 0.5 eV have been measured using energy-loss spectrometers on similar F E G - S T E M machines, it seemed likely that another explanation was required. It is now fairly clear that statistical electronelectron interactions can be important in these F E G - S E M columns. The (longitudinal) Boersch effect contributes to the energy spread at crossovers; but, more importantly, the transverse Boersch effect (or trajectory displacement effect) contributes to a broadening of the spot at such crossovers. In conjunction with Dr. G.H. Jansen, we have incorporated his description of the trajectory displacement effect into our column calculations [2]. The results, shown in fig. 1, indicated that this
0304-3991/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
J.A. Venables, G. Cox / Computer modelling of FEG-SEM columns
34
Ip(A)
10-8
10-9
10-10
1rim
lOnm
lOOnm
d
Fig. 1, Ip(d) measurements for Sussex HB50 SEM column [1], compared with predictions including the trajectory displacement effect (full lines) and without it (dashed lines), for various beam voltages indicated, and a final aperture diameter, a~ ~ 150 p,m; after ref. [2].
effect was sufficient to explain the previous HB50 measurements with a more reasonable energy spread of AE < 0.5 eV FWHM. Jansen et al. [2] also obtained approximate agreement with measurements on two other FEG columns, the Philips EM420ST and a Hewlett-Packard lithography machine. These correlations with experimental results give us some confidence that we can extrapolate to new situations, using programs which incorporate all the above effects. However, we should note at the outset that typically several parameters needed in the program cannot be checked experimentally at all easily. In particular the trajectory displacement effect behaves very like chromatic aberration, and its absolute magnitude is uncertain. Detailed modelling of combined electric and magnetic fields in the gun region is awkward (see ref. [3]) and has not been attempted; also the source size and aberrations of the gun itself are variable depending on tip treatment and position. Nevertheless, we can easily explore with these programs
the variations in performance predicted for a range of parameter values, so that sensitive features of the designs can be investigated. For analytical applications requiring relatively high probe currents, aberrations in the gun-condenser region of the column can be dominant. Good performance thus requires a short-focallength gun lens with low aberration coefficients. Although several other solutions have been proposed, we have proposed [4] and implemented on the HB50 [5] a magnetic lens at earth potential, rather open-ended towards the tip. A similar design has been fitted to some VG HB501 and HB50A machines and marketed separately as the FEG 2000 series guns. With such a gun lens, a SEM requires a 3-lens column to be fully flexible. The analysis of a design for a surface analytical SEM is described in section 3. In a STEM it is often convenient to run the objective lens at fixed demagnification, with the sample conjugate to a selected area aperture. This then leads to a 4-lens design with 2 condenser lenses to vary probe size and angular divergence flexibly. The extension to this situation is discussed in section 4. But first the main features of the programs are discussed in section 2 below.
2. Column model and computer codes 2.1. The column model
The model described follows closely previous work on a 2-lens FEG-SEM (ref. [1], hereafter 1), In particular the following features are identical to I: (1) The description of the field emission gun itself, including the angular emission from the tip, electrostatic lens effects, and the (small) gun aberrations (I, section 3.1 and appendix A). The effect of the second electrostatic lens (m I in l) is uncertain and has been investigated further. (2) The use of thin lens geometrical optics, and Fert and Durandeau-type lens formulae for weak lenses, such as condensers and SEM objectives, where the focus is outside the lens field (I, section 3.2).
J.A. Venables, G. Cox / Computer modelling of FEG-SEM columns
(3) The treatment of lens aberrations by additions as sums of squares, with constants appropriate for the 20-80% edge resolution ( d ) being the measure of spot size at a given probe current Ip, as shown here in fig. 1 and subsequently (I, section 3.3 and appendix B). Extensions to the model presented previously include: (4) The addition of a (strong) gun lens with a differential pumping aperture in its bore, whose position and size can be varied. The gun lens is operated with fixed object distance with a given gun configuration; thus the gun plus gun lens acts as a fixed input element in any calculation, with data input from a (changeable) "gun file". This is described in more detail in section 2.2. (5) Various options within the column calculation to enable the user to choose: (a) either a real aperture in the objective lens (as in I), or, as in many SEM and STEM instruments, a virtual objective aperture between the gun and condenser lenses. In the first case the final aperture angle o~ is fixed and the probe current Ip is varied; in the second, Ip is fixed and a is the independent variable; (b) the presence or absence of a crossover between the condenser and objective lenses. The second case allows the condenser to be used as a minor trim on the gun lens, as discussed in section 3. The 2-lens column with this condenser lens off (i.e. gun lens and objective alone) has been modelled by a similar program. In this case both lp and c~ are fixed for a given objective aperture size. All the column options and dimensions are input from a "column file". (6) The addition, for STEM columns, of an objective lens working at fixed demagnification. In this 4-lens program the condenser and objective lens become first and second condenser lenses respectively. The objective lens properties (magnification, aberration coefficients) are input from an "objective file"; since the objective properties are fixed we are not restricted by thin lens or other assumptions, but can input the results of detailed magnetic lens calculations for the actual geometry. This is discussed further in section 4. (7) The inclusion of various models of longitudinal and transverse Boersch effects as given by Jansen and coworkers [2]. This is discussed further in section 2.3.
35
In summary, we now have several similar programs for 2-lens (either condenser + objective or gun + objective), 3-lens (gun, condenser, objective) and 4-lens (gun, 2 condensers, objective) operation. The output gives the Ip(d ) curves for a range of objective aperture sizes for a given gun lens setting, and the dominant aberration, for several values of the energy spread AE. Individual aberrations, lens magnifications and currents are also calculated. The programs are in F O R T R A N - I V and use --40 kilobytes of memory. On our PDP 11/23 they execute in - 3 0 s to 2 min, dominated by printing time.
2.2. Strong and asymmetric lenses For good performance at both high and low probe currents, a strong gun lens is needed. The focal properties of such a lens can be calculated using lens calculations of the type developed originally by Munro [6]. We have been able to use the CIELAS 1 package at Cambridge University [7] to optimize the designs of individual lenses, including a new gun lens and an objective lens for a new surface SEM, as described in section 3.2. The objective lens designed, with a sample outside the lens, behaves as a weak lens, with C~ = kf3/D 2, as assumed in the column calculations. But because of the sharp cone angle of this lens, the field is asymmetric between the polepieces. Thus the CIELAS I programs can be used not only to optimize the details of the design, but also to furnish values of k and the lens center position for detailed column calculations. The gu n lens, however, has the field emission tip immersed in the field and forms a strong lens whose objective properties (at inifinite magnification) are needed. These have been optimized in the same way, and C~ plotted against objective focal length, f0, in the form C~ = k(fo/f~,~)", where fm is the minimum projector focal length as given by the F e r t - D u r a n d e a u formula. For the lens design of fig. 4, we found k = 2 . 2 8 and n = 2 . 2 over the whole range of focal lengths needed for the column calculation. The choice of fm can be made such that the F e r t - D u r a n d e a u formulae also account for the gun lens currents needed to power
J.A. Venables, G. Cox / Computer modelling of FEG-SEM columns
36
the lens, according to the CIELAS I values. All this simply means that we can parameterize the results of a detailed lens calculation well enough to use in a column calculation, even though the lenses are either strong a n d / o r considerably asymmetric. However, for the gun lens there are two minor problems in the present calculations. The Munro-type program does not perform at its best for open lenses, as pointed out by Mulvey [8], since there is a net dipole field with a long range, which is not taken into account with the usual boundary conditions. This results in underestimating the maximum field strength for a given lens current. Also the gun lens is acting on an accelerating electron beam, so the focal length will in practice be smaller than estimated by these programs. Both these effects, therefore, act in the direction of making the actual gun lens have high probe current properties superior to those calculated, though the low current conditions may be more difficult to achieve in practice.
somewhat uncertain. Also included are several minor effects which reduce C t by up to 25% when the crossover is not in the middle of the column section [2]. The trajectory displacement effect as given by eq. (1) increases as the beam angle a decreases, but for small angles and probe currents it goes through a maximum; smaller angles correspond to the "pencil beam" regime [10], in which the electrons are effectively following each other in a line. The reduction in displacement caused by this effect, which is substantial after a (virtual) objective aperture, is included. The effects at different parts of the column are combined linearly, magnified as appropriate. There may well be additional effects in the lower voltage region near the tip which are not included, but such effects can be simulated by varying the effective source size. The longitudinal Boersch effect, which leads to an energy spread at crossovers, is less controversial [2,11]. It was calculated according to
Trajectory Boersch effects
~ E = C~lh~-lV~ 1/2,
2.3.
displacement
and
longitudinal
The trajectory displacement effects as modelled by Jansen et al. [2,9] have been included in the column calculations for each section of the column which contains a crossover. The constants used are appropriate for the low-current (Lorentzian) asymptote for the 20-80% edge resolution, as for the other aberrations calculated in I. For a section of the column length L, Jansen et al.'s expression for the trajectory displacement diameter, d t, is d t = C~(d
Ib/d~)2/3Z2/3V14/3,
(11
where the beam current at that point is lh at voltage VZ (all symbols as in I, and values in SI units). The value of the constant C~ has been controversial, and it is only recently that essential agreement has been reached about the power law dependencies. Comparison with Monte Carlo calculations [9] suggests that the theory [2] overestimated the effect by = 50%; consequently we have used C t = 5.0, which incorporates this comparison, but it is clear that the exact value is
(2)
where a is the angular divergence at the corresponding crossover. The constant Cc = 3.8 × 105 for A E = the F W H M energy spread. These energy spreads were added in quadrature with an initial energy spread in the gun assumed to be 0.22 eV at low beam currents, rising to - 0 . 5 eV at 10 /xA emission. Because of the uncertainties in the absolute value of A E, and its dependence on total tip emission current, the estimated energy spread was not used directly in the column calculation. Instead, column properties were calculated for different A E values spanning the range of interest, and the influence of A E noted. Typically, the trajectory displacement effect was larger than the chromatic aberration, and has a similar, though not identical, dependence on the beam energy V~.
3. Electron-optical design of a surface S E M
3.1. Design constraints The electron-optical column considered is a 3-lens SEM, operating up to 30 kV. The SEM is
J.A. Venables, G. Cox / Computer modelling of FEG.SEM columns
an aI1-UHV construction for use in surface science and contains a cylindrical mirror analyzer (CMA) installed concentrically around the electron-optical column, for various forms of electron spectroscopy. The construction details, spectroscopy, and uses will be reported elsewhere [12]; here we concentrate solely on the probe-forming optics as an example of computer modelling of an SEM column. A schematic diagram of the column is given in fig. 2. The objective-condenser-scan coil assem-
Condenser lens
bly has been designed to be in one closed container, inside the CMA. Between the gun lens and the condenser is a relatively large space for a gun isolation valve, beam blanking, virtual objective aperture, and C M A detectors. The gun lens is mounted on the bottom of the column on a standard 200 m m flange, and the gun is suspended from this. The main design constraint is the need to house the UHV-sealed condenser-objective unit inside the bore of the CMA. This arises because the
__ ;
VOA
37
~
Detector
__
--1
Fig. 2. Schematic diagram of a new SEM column for surface studies. It incorporates a FEG, gun lens, virtual objective aperture (VOA) and uses the condenser lens as a trim. The obJective-condenser unit is housed inside a cylindrical mirror analyser (CMA).
J.A. Venables, G. Cox / Computer modelling of FEG-SEM columns
38
distance to the exit slits from the sample is about 2.55 times the inner cylinder diameter for suitable CMA focusing. We have chosen to solve this problem by designing a rather large CMA of 101 mm inner diameter, which allowed the objective lens diameter to be 88 mm. However, because we also wanted to collect a large fraction of the emitted electrons into the CMA, the objective lens had to be rather strongly conical. The design evolved after testing on the CIELAS I programs is described in section 3.2. Given a compact condenser-objective unit inside the CMA, there is considerably more freedom in the choice of the other electron-optical elements, We have chosen to rely entirely on a virtual objective aperture (VOA) with the gun lens providing a crossover in front of the aperture. The gun is differentially pumped, so the crossover is fairly close to this differential pumping aperture (DPA). The positions of both the VOA and the DPA can be optimized using the column model. A final constraint was the lens power supplies. In our case the lenses are designed to operate from the supplies of a Cambridge Instruments S-200 SEM delivering up to 12 V or 2 A maximum for
each lens. In addition the lenses are bakeable up to 200°C. This necessitated the use of specially insulated wire at 21 SWG for the objective condenser lens and 18 SWG for the gun lens; the number of ampere turns needed in each lens is, of course, an output of the column calculation and of the CIELAS ! programs.
3.2. Objective-condenser and gun lens designs The objective-condenser unit is indicated schematically in fig. 3. Superimposed on the figure are the measured axial B-fields, and the field calculated using the CIELAS I program for the objective. The measured peak field is some 10% lower than that calculated for the given number of ampere turns, indicating that we may just be approaching saturation under 30 kV operating conditions. Stray fields in the CMA must be kept to a minimum in this application, and current efforts to reduce these may result in some design changes. However, the on-axis optical properties are unlikely to be much affected. The lens center is located some 7 mm in front
B (Gauss) - -
600
.....
Measured Calculated
/A I
500
400
300
200
100
- 20
0
20
40
-60
-40
-20
0
20
Z(mm)
Fig. 3. Cross-sectional drawing of the objective condenser lens, with measured B-fields, and that calculated using CIELAS 1 superimposed. The fields correspond to an excitation of 954 AT for the objective and 473 AT for the condenser lens.
J.A. Venables, G. Cox / Computer modelling of FEG-SEM columns
39
design has been incorporated into the column calculations in the manner described in section 2.2, assuming that all the focusing takes place at the beam voltage 1/'1. In fact, the gun lens will perform better than this implies, since the local measure of focusing power in the acceleration region is B 2 / V I *. Accordingly this is also plotted in fig. 4, on the assumption that V1 = V0 = 3 kV between the tip and the first anode, Vt varies linearly between 3 and 30 kV between first and second anodes, and is constant at 30 kV thereafter. It is clearly possible to consider adjusting anodes and gun positions to minimize the focal length, or equivalently maximize f ( B 2 / V l * ) d z. Even without these effects, the focal length can be reduced below 15 m m with the lens supplies available.
of the inner polepiece, giving a lens-sample distance, vs = 37 m m for the sample at the focus point of the CMA, 15 m m beyond the end of the lens housing.. The bores of the objective lens at Dt=6mmand D2--24mm,withthegapS=20 mm, the outer cone angle being 26 °. The calculated spherical aberration is easily parameterized a s C s = k f 3 / D 2, with D = ( D 1 + 1)2)/2 and k = 1.16. These constants are input into the column calculation. The gun lens design is indicated in fig. 4. Again the measured and calculated B-fields are superimposed on the figure. As can be seen, the curve calculated by CIELAS I is pessimistic as discussed in section 2.2. The field penetrated a long way into the tip region, falling off as - z 3 from a peak around 5 m m in front of the inner polepiece. This
B (Gauss)
1000
- -
Measured
.....
Calculated
800
600
400
200
-80
-60
-40
.~20
0
20
40
60
8 3O
Tip position
- -
Varying voltage ( 3 - 3 0 kV)
.....
Constant voltage (30 kV)
20
1o
// /
- 8 0'
- 6 'o
- 4' 0
/ /
//
- 2 0'
0'
' 20
4'0
6'0
Z(mm
)'
Fig. 4. Cross-sectional drawing of the gun lens with measured and calculated B-fields superimposed, for an excitation of 2050 AT. Also shown is B2/V for the variation V(z) in the accelerating region discussed in the text.
J.A. Venables, G. Cox / Computer modelling of FEG-SEM columns
40
3.3. Predicted perforrnance The predicted optimum performance of this SEM column is indicated in fig. 5, for a total emission current from the tip, I t = 10 /~A. The l p ( d ) curves are for 30 and 5 kV for an energy spread AE = 0.5 eV F W H M , for a range of suitable virtual objective aperture (VOA) sizes. This figure is useful to explore the optimum VOA diameter. With a suitable choice (e.g. 70-100 # m diameter for 30 kV, somewhat larger for 5 kV) the probe current can be varied simply via the gun lens while staying close to the overall optimum curve. A characteristic of the gun lens is the high total
,
'V-
current available. Essentially all the current which gets through the first anode can be focussed onto the sample. Although by comparison with fig. 1 at 30 kV the ultimate resolution is not improved, the high current performance (10 nA into 15 nm, 0.1 /,A into 60 nm and 0.5 ~*A into 0.6 /~m) is much improved. Fig. 6 shows the effect of trajectory displacement on the computed performance. It is seen that trajectory displacement effectively limits the column brightness around the knee of the I p ( d ) curve, where a F E G - S E M column is typically operating. Its importance is greater at lower beam voltage. The main effect arises from the first crossover, in front of the VOA. After this aperture the
,
r
Current limit by DPA
10- 6
400
--
200
70,1 O0
Ip(A)
10-'/
400 200
- 100
5kV
3 0 kV
70,100
10- 6
10 - 9
10-10
I /--200
Parameter: VOA Diameter: p m
-100
70,100 10 -11
] lnm
10nm
I
-
10nm
100nm
I
lO00nm
d
Fig. 5. I p ( d ) curves calculated for the new Sussex SEM, including trajectory displacement effects, at 30 and 5 kV for various VOA diameters, for I t = 10 FA.
41
J.A. Venables, G. Cox / Computer modelling of FEG-SEM columns
10-7
Ip(A)
5kV
30kV Without
T
ith T
D
Without
10-8
S/ //'//
10-9
//
/:
/////
VOA d i a m e t e r 70 gm . . . . . . . . 100 I~m 200 Hm
/ // ' / //
//
10_10~ lnm
, i
1Ohm
/ / I
lOnm
I
lOOnm
d
Fig. 6. I p ( d ) curves, illustrating the effect of trajectory displacement at 30 and 5 kV for various VOA diameters, for I t = 10 #A.
beam is typically in the pencil beam regime [10], with a much reduced effect. This is, however, a strong (additional) argument for using a virtual, rather than a real, objective aperture. These comparisons suggest that some further improvement might be obtained by eliminating the crossover between the gun and condenser lenses, where the maximum effect of trajectory displacement, and a major contribution to the Boersch effect, occurs. The crossover at this point is dictated by the presence of the DPA and by the need to control Ip and column magnification accurately. In addition, the crossover makes it easy to steer the beam through the DPA for high current applications, while the DPA acts as a splash aperture at high resolution. Of course, the major reason for the DPA is the good UHV requirement for the operation of a cold field emission gun. Alternative approaches without any crossovers using thermal field emitters for similar
applications are being pursued by others [13-15]. At present these machines use all-electrostatic focussing; the present programs could be used to explore the characteristics of the corresponding magnetic focusing designs. In figs. 5 and 6 we have assumed that there is no crossover between the condenser and objective lenses. There is a slight reduction in predicted performance if one is included. Without a crossover, the condenser is operating as a minor trim to optimize the angular divergence. The small lens currents involved will be advantageous in our application where the lens is close to the detection area of the CMA, which is sensitive to stray magnetic fields. 3.4. Choice of operating conditions The operating conditions of this particular SEM will of course be chosen after considerable practi-
42
J.A. Venahles, G. Cox / Computer modelling of FEG-SEM columns
cal experience, and with regard to any influence stray magnetic fields may have on the electron spectroscopy. But one attractive feature is to operate with the condenser lens at most as a very minor trim. With the virtual objective aperture at the point chosen, the optimum curve of fig. 5 can be approached closely for a particular VOA size, over a wide range of gun lens settings, with the condenser lens off. This may prove to be a particularly convenient mode for a range of high resolution conditions. For high current (weaker gun lens) conditions, larger size VOA's may be needed, and the condenser lens must be used to compress the beam, optimizing the final angular convergence at the sample. Nonetheless 1 or 2 aperture sizes are sufficient to span the operating range of current very close to the optimum curve. This is of course not possible with real objective apertures in the objective lens region.
restriction to a fixed setting for the objective lens. It is of course well known that the probe shape at high resolution is a function o f diffraction, spherical aberration, and defocus (A f ) , and that the combined coherent effects can be calculated using phase contrast transfer theory [16,17]. The only detailed study in the context of high resolution STEM columns is that of Mory and Colliex [17]. They show that the 20-80 edge resolution has a minimum d=0.4(~3C~) 1/4. The quadratic addition combination used here gives 0.409 for this constant; these constants therefore are essentially consistent. Both treatments [16] give the corresponding defocus value A f ~ - 0.75(~(~)1/2 which is intermediate between the conditions of minimum and maximum phase contrast (Scherzer focus) for which the resolution d=O.66(X:~C~)1/4 is typically quoted. At higher probe currents, where incoherent imaging conditions prevail, the treatment of the STEM should be identical to the SEM column discussed in section 3.
4. Extension to 4-lens S T E M designs
4.2. Ultimate resolution and analytical performance: the VG HB501 S T E M and related columns
4.1. Objective lens data A 4-lens design has many possible operating modes, since only 2 parameters, the probe current lp and the final aperture angle a, need to be varied. However, it is common practice to set the objective lens working at fixed (de-)magnification so that the sample is conjugate to a selected area aperture plane. Under these conditions the number of variables is identical to the 3-lens SEM described in the last section. We have modified the corresponding programs to accommodate this extra stage by relabeling the condenser and objective lenses as condensers C1 and C2, and inputting the required objective data from an "objective file." No restrictions are implied on the type of objective lens (strong, asymmetric, condenser-objective, etc.) used. All that is needed is the selected area aperture-to-sample distance, the objective magnification, and the C~ and Cc values at zero magnification. These quantities can be obtained from a detailed Munro-type calculation [6,7] of the objective lens. The fact that so little data is needed is a consequence of the
The optics of the VG HB5 and 501 STEMs have been referred to in several papers, but no analysis has been made of columns fitted with a gun lens. As in the SEM designs (section 3) this lens has been added to improve the high current analytical performance. We have shown, however, that unless the gun lens is strongly excited there is a danger that the new column does not have enough overall demagnification for the highest resolution applications. Under these conditions, lens C 1 has to be strongly demagnifying with an (unwanted) crossover between C 1 and C 2, which also contributes to the trajectory displacement effect. A typical set of I v ( d ) curves shown for an HB501 column is shown for 100 kV operation in fig. 7, indicating the effect of trajectory displacement on the performance, with a crossover between C1 and C2. In fig. 7a, for a total tip emission I t = 10 /~A, the trajectory displacement effect is just making an effect. However, as seen in fig. 7b for I t = 5, 10 and 20 /LA, a strong saturation sets in above 10 t~A, with not much ad-
J.A. Venables, G. Cox / Computer modelling of FEG-SEM columns
0-1
,o-7 Ip(A)
0-1
1
10
denser lens currents and angular current densities, and deduced virtual tip positions for their HB5. Their results correlate well with our calculation of the gun, provided we ignore the second electrostatic pinhole lens in the gun (m I in I) by setting mt = 1. However, in the present calculations with a gun lens, this "lens" is ineffective anyway, because it coincides with the center of the gun lens. Their work, inter alia, emphasizes that the current falling on the V O A is an important experimental quantity, which can be used to establish the angular current density. This in turn provides a useful check on the model of the gun. The present calculations have been used to suggest design improvements. These include m o v e m e n t of the D P A and V O A to more advantageous positions, moving condenser 1 and 2 further apart, and other more minor changes. One attrac-
a,_,=,o.2. ° - --
no T D
"
Expt.
//~
/~
20 / 20
//
/Lo
/
t% 1
d
J 1
43
0-1
1
10
10
(nm)
Fig. 7. l p ( d ) curves calculated for the VG HB501 column with (full lines) and without (dashed lines) trajectory displacement: (a) I t = 10 ~,A; (b) I t = 5, 10 and 20/~A, Experimental points taken from ref. [171. See text for discussion.
vantage gained in increasing I t to 20 /~A. In addition, the Boersch effect energy spread is increasing to A E > 1 eV at 20/~A, whereas it can be kept < 0.5 eV at 10 /~A and below. In the high resolution region around lp = 10 10 A, the gun lens needs to be operated at around unity magnification, with an excitation near 4000A • T. M o r y and Colliex [17] have measured 2 0 - 8 0 edge resolutions for two conditions of their HB5, without a gun lens, which are indicated in fig. 7. These points are for a nominal I t = 5 #A. These points fall in between the curves calculated for I t = 5 and 10 /~A. This indicates that the brightness actually achieved in an HB5 is close to that assumed in the present calculations, B = 4.6 × 1 0 9 A / c m 2 - sr at 100 kV. If their value of I t = 5 # A is taken literally, the curves of fig. 7 without the trajectory displacement effect indicate that B _> 4 × 10 9 A / c m 2- sr. M o r y and Colliex [17] have also measured con-
10-7
Ip(A)
--
with T.D.
~
a. optimised // --noTD //
/
~o- 8
/
/
/
?c, on,, /
// /
10
/y
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//
f 0.1
~
]% 1
f
-
b. o n e V O A s i z e optimised
---
i
1
I
d
10(nm)
Fig. g. /p(d) curves calculated for the new Arizona STEM column for I t = ]0 #A: (a) "optimized" column with (full line) and without (dashed line) trajectory displacement; (b) column operated with either C 1 or C 2 only at a fixed VOA diameter (full lines) compared with the optimum curve (dashed line). See text for discussion.
44
J.A. Venables, G. Cox / Computer modelling of FEG-SEM columns
tive possibility, a d v o c a t e d by M o r y a n d Colliex [17], is to use C 2 only for high resolution a p p l i c a tions, and Ca only for high c u r r e n t applications. This is facilitated b y m o v i n g the c o n d e n s e r lenses further apart. W i t h the a d d i t i o n a l flexibility of v a r y i n g the p r o b e current using the gun lens, a n d c h o o s i n g a suitable V O A diameter, it is p o s s i b l e to stay e x t r e m e l y close to the o p t i m u m curve over a large range o f Iv. This is illustrated in fig. 8 using c o l u m n p a r a m eters for a new surface-oriented S T E M p r e s e n t l y b e i n g designed for A r i z o n a State U n i v e r s i t y [18]. T h e o p t i m u m curves with a n d without trajectory d i s p l a c e m e n t are given in fig. 8a for I t = 10 /tA, for the same a b e r r a t i o n coefficients as used for fig. 7. The curve with only C~ excited a n d a fixed V O A d i a m e t e r stays r e m a r k a b l y close to the optim u m curve for a l m o s t 3 orders of m a g n i t u d e in lp; in fact a slightly larger a p e r t u r e than that shown lies essentially on top of the o p t i m u m curve for 5 × 10 - H < Ip < 3 × 10 -~ A. T h e reason is that, for a suitable choice of V O A d i a m e t e r a n d position, a n d the lens position, the curve can be tangential to the o p t i m u m curve in the region of b o t h the u p p e r a n d lower knees of this curve. T h e C 2 lens is clearly less well p o s i t i o n e d in this sense, a n d can only be used on its own in the high resolution region.
5. Conclusions Several p r o g r a m s have been d e v e l o p e d which have allowed us to explore the p e r f o r m a n c e a n d o p t i m i z e design of F E G - S E M a n d F E G - S T E M columns. F o r c o l u m n s c o n t a i n i n g crossovers the p e r f o r m a n c e is f o u n d to be affected b y the trajectory d i s p l a c e m e n t (or transverse Boersch) effect, as well as other aberrations. E x a m p l e s of a s u r f a c e - S E M and a high resolution S T E M are given to illustrate the use of these p r o g r a m s in o p t i m i z i n g the design of such microscopes.
Acknowledgments W e are grateful to K.C.A. S m i t h a n d J. T a y l o r for use of the C I E L A S I lens analysis p a c k a g e at
C a m b r i d g e University; to G . H . Jansen for j o i n t w o r k at Sussex in 1982-83, a n d for subsequent c o r r e s p o n d e n c e ; to W . R . K n o w l e s a n d J.P. D a v e y of C a m b r i d g e I n s t r u m e n t s for advice on practical S E M lens designs; to S. y o n H a r r a c h for i n f o r m a tion a b o u t the V G HB501 S T E M ; a n d to m a n y colleagues (refs. [11] a n d [18]) for their j o i n t work on other aspects of the s u r f a c e - S E M construction at Sussex a n d the s u r f a c e - S T E M for A r i z o n a State. These i n s t r u m e n t s are being c o n s t r u c t e d with g r a n t s from the S E R C , a n d D O D a n d N S F respectively. G. C o x acknowledges s u p p o r t from the D A A D in 1984-85.
References [1] J.A. Venables and A.P. Janssen, Ultramicroscopy 5 (1980) 297. [2] G.H. Jansen, J.M.J. van Leeuwen and K.D. van der Mast, Proc. Microcircuit. Eng. (1983) 99; J.M.J. van Leeuwen and G.H. Jansen, Optik 65 (1983) 179: G.H. Jansen, personal communication. [3] J.R.A. Cleaver, Optik 52 (1978) 293. [4] J.A. Venables and G.D. Archer, in: Proc. European Regional Conf. on Electron Microscopy, Hamburg, 1980, Vol. 1, p. 54. [5] J.A. Venables, G.D.T. Spiller, D.J. Fathers, C.J. Harland and M. Hanbiicken, Ultramicroscopy 11 (1983) 149. [6] E. Munro, in: Image Processing and Computer Aided Design in Electron Optics, Ed. P.W. Hawkes (Academic Press, New York, 1983) p. 283. [7] R. Hill and K.C.A. Smith, in: Electron Microscopy and Analysis 1981, Inst. Phys. Conf. Ser. 61, Ed. M.J. Goringc (Inst. Phys., London-Bristol, 1982) p. 71. [8] T. Mulvey, in: Magnetic Electron Lenses, Springer Topics in Current Physics, Vol. 18, Ed. P.W. Hawkes (Springer, Berlin, 1982) p. 390. [9] G.H. Jansen and W. Stickel, Proc. Microcircuit Eng. (1984) 43. [10] K.D. van der Mast, G.H. Jansen and J.E. Barth, Proc. Microcircuit Eng. (1985) 169. [11] G.H. Jansen, T.R. Groves and W. Stickel, J. Vacuum Sci. Technol. B3 (1985) 190. [12] J.A. Venables, C.J. Harland, G. Cox, P.S. Flora and M. Hardiman, work in progress. [13] L.H. Veneklasen, G. Todd and H. Poppa, in: Proc. 9th Intern. Congr. on Electron Microscopy, Toronto, 1978, Ed. J.H. Sturgess (Microsc. Soc. Canada, Toronto, 1978) Vol. I, p. 12; L.H. Veneklasen, G, Todd and H. Poppa, in: Scanning Electron Microscopy/1979, Vol. I, Ed. O. Johari (SEM, AMF O'Hare, IL, 1979) p. 207.
J,A. Venables, G. Cox / Computer modelling of FEG-SEM columns [14] M.M. El-Gomati, M. Prutton and R. Browning, J. Phys. El8 (1985) 32. [15] L.W. Swanson and J. Orloff, in: Electron Optical Systems (SEM AMF O'Hare, IL, 1984) pp. 137-162: F.E. Inc., model 83 TFE Electrostatic gun (1986): P.A. Bennett, personal communication, 1986. [16] J.C.H. Spence, Experimental High Resolution Electron Microscopy (Oxford Univ. Press, London, 1981) pp. 200, 217.
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[17] C. Mory, Th~se d'Etat, Orsay (1985); C. Colliex and C. Mory, in: Quantitative Electron Microscopy Scottish Universities Summer School in Physics, Vol. 25, Eds. J.N. Chapman and A.J. Craven (1983) p. 149; C. Mory and C. Colliex, in preparation. [18] J.A. Venables, N.J. Long, P.A. Bennett, J.M. Cowley and others, work in progress.