Some designs electron and ion optics

SOME DESIGNS

ELECTRON AND ION OPTICS

PROEFSCHRIFT

TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAP AAN DE TECHNISCHE HOGESCHOOL TE DELFT, OP GEZAG VAN DE RECTOR MAGNIFICUS DR O. BOTTEMA, HOOGLERAAR IN DE AF-DELING DER ALGEMENE WETENSCHAPPEN, VOOR EEN

COMMISSIE UIT DE SENAAT TE VERDEDIGEN OP WOENSDAG 6 OCTOBER 1954

DES NAMIDDAGS TE 4 UUR

DOOR

JAN BART LE POOLE

NATUURKUNDIG INGEÏNIEUR

GEBOREN TE AMERSFOORT

<^Wti<«p]J^

Oo*' ,\eo»W ^o^

S^

l

o^«» I

> , ₉ 1954

p

DIT PROEFSCHRIFT IS GOEDGEKEURD DOOR DE PROMOTOR PROF. DR H. B. DORGELO.

Aan de nagedachtenis van mijn Vader.

C O N T E N T S .

page C H A P T E R I. Achromatic electron diffraction . . . . 9

§ I. Introduction 9 § 2. Correction of chromatic error 10

§ 3. Application of the correction 13 § 4. Further improvements 15 § 5. Hysteresis of the iron shield 17

§ 6. Distortion 17 § 7. Rotation of the pattern 20

§ 8. Achromatic two-lens systems 20 § 9. Construction of diffractographs . . . . 26

C H A P T E R II. A simplified electron microscope . . . . 39

§ 1. Introduction 39 § 2. The most efficient field 39

§ 3. T h e paraxial differential equation . . . 40

§ 4. Design of the polepieces 41 § 5. Chromatic errors 46 § 6. Position and size of the objective aperture 49

§ 7. Discussion 51 § 8. Design of the lens 52

§ 9. Application of the lens in a simplified

microscope 55 § 10. The projector lens 56

§ 11. Alignment of the microscope 59 § 12. Extension of the magnification range . . 61

C H A P T E R III. Focussing aids 63 § 1. Introduction 63 § 2. Optical magnification of the image . . . 64

§ 3. The condensor as focussing aid . . . . 66

§ 4. The beam wobbler 66 § 5. Illumination in the electron microscope. . 67

§ 6. Discussion of the wobbler method . . . 71 § 7. Objective method of focussing . . . . 73

§ 8. Errors of the wobbler method 74 § 9. Measurement of astigmatism 78 § 10. The Metrovick focussing aid 79 C H A P T E R IV. A new type of mass spectroscope . . . 81

§ 1. Introduction. 81 § 2. Principle of the method 82

§ 3. Required frequency 82

§ 4. Dispersion 83 § 5. Design of the instrument 85

§ 6. Variations in the method 92

Samenvatting 95 Summary 96

C H A P T E R I.

A C H R O M A T I C E L E C T R O N D I F F R A C T I O N .

§ 1. Introduction.

In a conventional electron diffraction apparatus the angle at which the electron beam is deflected by the crystal depends on the wavelength of the radiation. I.e. u^ k ), in which k is a. factor de-pend.ing on the crystal only. This means that X should be known with the same accuracy with which the lattice constants of the crystal are to be measured.

Since the wavelength depends on the accelerating voltage V following X = 1/ —^- A, the accelerating voltage should be known accurately.

Now high voltage measurement is not easy because all known methods have grave inaccuracies.

1. T h e spark-gap method usually is not sufficiently accurate. 2. Electrostatic methods up till now have not been developed far

enough to obtain the required accuracy.

3. T h e only simple method left is the measurement of current through a high voltage resistor.

There are two types of these: a. Semiconductors.

b. Wirewound resistors.

Type 3. can be made reasonably accurate, but unfortunately it does not strictly follow Ohms' law. Over short periods the usual resistors of good quality will keep constant within one part in 2000 — 10000, but to compare two diffraction patterns, taken with seme months in between, higher stability is required.

Type b. is very accurate, if properly constructed. It requires a huge amount of wire however, to obtain a sufficiently high resistance. •

At 100 kV, this resistance should be of the order of 100 megohm in order to keep the load of the H.T. supply within reasonable limits. Larger current than 1 mA would require large smoothing condensers. Moreover, the heat dissipation would cause difficul-ties. At 1 mA this is already 100 W a t t s !

W i t h manganine, having a specific resistivity of 4 X 10~^£? m, about 20 km are required if the wire diameter is 10 fi. Corrosion can easily cause a layer of 0.1 u to become non conductive, cor-responding to a 4 % change in value. This means that special pre-cautions have to be taken to prevent corrosion and just illustrates that, though high accuracy H.T. resistors can be made, they will be extremely expensive.

§ 2. Correction of chromatic error.

It is possible to get rid of the chromatic variation in a very simple way.

If a magnetic lens is introduced between specimen and screen (or film) the variations in ring diameter, as caused by variations of the accelerating voltage, can be eliminated in first approxima-tion ' ) . This follows from the calculaapproxima-tions below. Lattice constants

d can then be found by dividing a constant of the apparatus by

the ring diameter. This constant depends on the dimensions of the diffractograph and the lenscurrent only, as will be shown.

Spec

Fig. 1. Principle of achromatic diffraction.

T h e angle jS over which the beam is bent by the lens is (see fig. 1):

j3 = hi A = aaA, (1)

Since we find Now ftg = fta — /? 6 hs = a{a -\- b) — a a b A nX a = c/2

A = ~ = cr^x^

and for weak lenses

in which I is the number of A.T. So (3) becomes

hi = — (a -f è) J— a fe P

Fig,. 2 gives hi plotted against X.

(2) (3) (4) (5)

(6)

Fig. 2. Radius hs of diffraction rings as a function of wavelength X-Achromatism in marked region.

Now put: then:

X~ Xo + AX,

ft3 + z l / . 3 = = ^ ( a - f & ) - " ^ ^ abX,^+ ' ^ ^ ( a +

fo)^-- ^ C / ^ a M „ 3 fo)^-- 3 ( 4 ^ r ^ i ' a 6 V (7)

Xad \ Ao / d

For very small values of —-- , the term with (^-j—) can be Xo \ XQ 1 neglected. So if a + 6 = 3 a è C / - ' / l . 2 (8) we find A h-i^Q and / . , = " i ^ ( a + f c ) - | ^ ° ( a + è ) = | - ^ ( a + è) (9)

The ring diameter has to be reduced by 1/3 to obtain achroma-tism!, in first approximation.

T h e equation (9) may also be written:

d= -^ - r ^ (a + fc), or using (8)

3 Ala

2 n{B + b) i / a + fe

"^^^ —h-.J^^'JJbc ^'"^^

Here /„ is the number of A.T. used for achromatism and obviously a, b and C are constants in a given apparatus, So:

J = ^ (11)

The conditions for achromatism are valid as long as the term con-taining —— is negligible compared to the other terms. Now according to eq. ( 7 ) , eq. (8) and eq. ( 9 ) :

^nCP-ah ,

^.+.,(^)=-A..(r

So the remaining variation in h.\ is:

J/i-, 3 lAX-^^

« 3 2 \ Xo I

If the lattice constant has to be known with 1/1000 accuracy, hj, must have the same accuracy. So:

Since X =^ 1/ T/ '^•

A V

V = ± 5.2 %

These voltage fluctuations may be either up or down, so the total admissible variation is more than 10 'y'c for 0.1 % accuracy.

§ 3. Application of the correction.

The very large variation in voltage allowing accurate diagrams suggests that the diffraction apparatus may be run on alternating voltage. It is difficult however to design the acceleration tube for that purpose, since the latter will usually be less stable if the voltage is reversed. Also, since dielectric losses in the insulation increase with the square of the alternating voltage, the requirements for these parts will be far more difficult to fulfil.

Fig. 3a. Villard circuit.

Fig. 3b. Villard voltage.

It is better therefore to run the tube on so called ,.Villard vol-tage". Since the peak voltage of this circuit is twice the transformer

voltage, it gives twice the voltage with the same components at the expense of only one condensor extra. This condensor needs only have insulation for half the peak working voltage. See fig. 3a and fig. 3b.

Of course emission should only run as long as the voltage is sufficiently high.

W e will now compute the time during which this is the case. See fig. 3b. Since

V = E{1 +s.incot) (13) A V = E(l — cos Ü) A t) '^'^ h (cüAt)2E

A V

2E = i(coAt)2

or: ^ A t ^ i y ^ (14)

A V

Supposing -^-p =^; 5 % is admissible, we find: co A t '^ 0.45. As w T = 2 Ji:

^ = 0.07.

Per period current may flow during 2 A t, i.e. 0.14 of the total period. This reasonably large ratio means that the intensity of the beam, is sufficiently large for practically all purposes.

Running the diffractoigiraph on alternating current may have still another advantage: since the beam is chopped and synchronised with the main power line, deflections by stray magnetic fields, caused by transformers or other apparatus in the vicinity, will appear to be more or less constant in time, owing to stroboscopic effect. Consequently, less magnetic screening is required.

Furthermore, the high voltage valve can be eliminated. T o this end a filament F has to be provided in the acceleration tube near the Wehnelt shield. This filament then replaces the filament

(,,cathode") of the H.T. valve, the other electrode (,,anode") being the Wehnelt shield.

Beam chopping can be accomplished very simply with the circuit given in fig. 4. T h e condensor C will be charged by the emission from filament F. Current will only flow as long as the negative voltage on the gun exceeds a certain treshold value. Since the vol-tage on condensor C is proportional to the mean charging current

from filament F, the mean emission from the gun stabilises itself. By varying R, C and the depth of the cathode in the Wehnelt cylinder, emission and duration of the pulses may be varied at will.

Fig. 4. Beam chopping circuit.

§ 4. Further improvements.

Since the choice of the position of the lens is still free, a second requirement may be fulfilled at the same time: either the lens may play the part of a condensor at the same time (in that case the source has to be imaged on the screen), or it may be required that the ring diameter be independent of the position of the object. In that case the screen has to be in the focal plane of the lens. So

f=b.

Since -^—p- = -~Y (e^q- 5 and eq. 8), we find:

Ó ao f

f^2a = b (15)

So the lens must be at 1/3 of the distance specimen-screen. This requirement is easily fulfilled and is of particular importance where reflection patterns are to be made.

(Only if the electron source is at infinity, it is possible to fulfil both requirements at the same time).

Reflection patterns have become very important since they allow simple and reliable preparation methods to be used. Diffraction is obtained by putting the specimen at grazing angle with the incident beam. T h e specimen may consist of a polished metal plane on which the specimen may be smeared or dusted, or as the case may be, the surface of the metal may be the specimen itself. It is relatively simple to heat treat the specimen during observation in the vacuum.

Fig. 5. Focussing of reflection patterns.

T h e accuracy of measurement however is impeded by the fact that the point of incidence of the primary beam is not known and that, in actual fact, it is not a point but a streak. See fig. 5. So the distance object-screen is somewhat indeterminate. If requirement 2 is fulfilled however, all rays, diffracted at the same angle will be focussed in a sharp ring.

Another case involving specimens with an indefinite distance to the screen is gas-diffraction. Since the gases never give sharp rings, the apparent quality of the pattern will hardly improve at all when the type of focussing as mentioned above is used. In the processing

of the results obtained however, it is the intensity distribution of the pattern which is important and this would be changed by blurring.

§ 5. Hysteresis of the iron shield.

A rather serious drawback of the lens is the possibility of hyste-resis causing different fields at the same lens current, depending on the history of the iron shield. Clearly, this drawback does not exist when a permanent magnet is used, since then the field remains constant all the time, provided the magnet is properly aged.

The effect of hysteresis can easily be eliminated however by reversing, the current several times after every change in current. Superimposition of a decreasing alternating current will be a simpler and even better remedy still. The hysteresis-effect depends on the size and the shape of the lens and on the iron used. Proper heat treatment will reduce it appreciably. In experiments with a non heat treated steel lensshield, hysteresis caused differences in focal distances of about 2 % , corresponding to 1 % ringdiameter. T h e surest way, of course, is to use a lens without iron. This can easily be done, since only a weak lens is required. In that case the influence of magnetic stray fields is greater however.

§ 6. Distortion.

Another difficulty is the fact that electron lenses have spherical aberration. This means that the outer rings of the pattern will be reduced too much; in other words the pattern is distorted. It is impossible to eliminate this distortion completely, but its effect may be reduced to less than about h % for a^^ 0.1. Since the original ring diameter without lenses is given by /!2 = (a -(- ^) t^n a, where

sin a = —- (c? = lattice constant), we find that:

.. = i i + i » ' = i i + i l i | l + l ( 4 n (16,

dcosa d ( 2 \d I )

For a = 0.1:

The ring diameter is no longer inversely proportional to the lattice constant. The error could be called ,,distortion" in analogy

with optics, since it depends on the angle. It could therefore be eliminated by the lens distortion, by proper choice of its dimensions.

According to van Ments and Le Poole - ) :

f = 2.4(^f „7)

where Z is the diagonal of the pole pieces and /ii is the height of incidence. (See fig. 1).

For freedom of distortion it must be required that

A^(hi-h) =^a^hs (18)

t

2

Af _ 3

I ~

2

Since hi = a a, we find: (19) Spec. = 0.78 or Z = 1.26 a (20)

t =^H"f=f^

2 X 2 . 4 30

Fig. 6. Correction of distortion.

This can best be realised by a long coil as given in fig. 6. In this construction the ring diameter will be exactly inversely pro-portional to the lattice constant. (In actual fact, the distortion

factor does not strictly apply to a case where the lens forms no imaige).

This lens will no longer be ,,weak", so the power is no longer inversely proportional to V.

The derivation of the ,,V,3 condition" must therefore be revised. ƒ2

Since the dispersion of a magnetic lens depends on .j , the problem

P

Let us therefore investigate the set-up as given in fig. 6 somewhat closer. The focal distance required is 2a. According to van Ments and Le Poole - ) :

ƒ = 36Z ( 1 + 0.004) (21) W i t h Z = 1.26 a and / ^ 2 a follows: K = 25. The dispersion of

the lens at this K value is somewhat decreased:

df _ 36 Z I.e. Or

Af

FOTK = AA A = 25: = -AA AK AK (1 — 0.004/:) /^^^ ( ^ + 0.004) ^ • (22) , . 0 . 9 0 - . - 0 . 9 0 - . So that in this region:

A = Ci* V-«-»o = Ci ii-80 (23)

Accordirig to eq. (3):

hi = a{a -(- b) — a ab A

This can be transformed with a = —— (4) and (23) into:

d hi = ^ (a + b) ~ "^ C, a b A^so (24) ^ ' ' » " ( a + 6) — 2.80 4 C i a è A i . 8 o (25) So dX ~ d' ^ ' d dhi

Again for achromatism it is required that ^—i^ = 0. This is true if:

o X

4 (a + t ) := 2.80 4 Ci a 6 X^-^ (26) a d

O r

^ = 1 = ^ 8 ^ <^')

With this correction, if / — b, we find a + & = 2.80 a.

So: Z> = 1.80 a and hi = (l - y ^ ] ^^ = 0.643 hz

This process could, of course, be repeated until sufficiently accu-rate values for b/a and /13 are found.

Since the distortion was small anyway however, a diffractograph with b ^=.2 a as calculated first will yield equally good results in practice, provided the power of the lens is adjusted to have achro-matism.

§ 7. Rotation of the pattern.

It has been established now, that the diameter of Debye-Scherrer rings can be achromatised. For the study of polycrystalline speci-mens this will be sufficient. If single crystals or other specispeci-mens with definite texture are to be examined however, the angle of rotation has to be achromatised too. To do this it is necessary to use two lenses with opposed fields and since the angle of rotation

0.186/ , , , , ,. . m = — ^ - , the two lenses must have the same, or about the same number of A.T.

§ 8. Achromiatic two-lens systems.

W i t h the two lenses, the ,,2/3 condition" will have to be cor-rected. Similar to eq. (3) it can now be shown that:

hi = a{a + b + c) — ua{b -\- c)Ai —

— (x{a + b)c A-2 + aa b c AiA., (28)

Again we want hi to be independent of X. Since a = ' ^ (4) and A, = CJiV.^ (5) A, = 02/22/2 (5):

hi = " j (a + Z> + c) " 1 CJMb + c)

-- -- ^ Q/22(a + Z>)c + ^ CiC2/i2/o2a be (29) a d So: ^ = ^ (a + è + c ) — 3^X^CJi^a(b + c ) -- -- ^ X^CsLzHa + fc)c + 5 4 i ' Q C i l i ^ ^ a be (30) a d

The condition for achromatism thus becomes: (a + Z>+ c ) — 3 a ( 6 + c ) A i — '

— 3{a + b)cA2 + 5abcAiA2 = 0 (31)

Inserting this in (28), it is found that:

hi = i u(a + b + c ~ abc AiAi) (32)

Since the new condition for achromatism yields a quadratic equation, there are two solutions. One solution corresponds to

abc A1A9 <C a -\- b -]- c and is of the same type as that described

hitherto (fig. 7a).

Fig. 7a. Spec a B ^

-( 1 — ~ ~ ~ ~ ~ - = A —

tt, x^

b - ' - ' ' ' \ c 1

Fig. 7b. The two types of two-lens diffractographs.

The other solution corresponds to abc A1A2 > a -|- & -f- c, so /13 is negative (see fig. 7b). Its possibilities will be discussed later,

It may seem, that with two lenses, there are so many degrees of freedom in the choice of the positions and strengths of the lenses, that it would be possible to require:

Unfortunately this is not true, as will be proved now. 1st order achromatism requires (31):

(a + fc + c ) — 3 a{b + c)Ai — 3{a + b)c A2 + S a t c A i A o — 0 2"d order achromatism requires:

3 a{b + c)Ai + 3(a + b)cA., — 10 abc A1A2 = 0 (33) It is useful to introduce a third equation which means no limita-tion, but facilitates the calculations;

a J^ b + c — a{b + c)Ai —{a + b)c A. + abc AiAo = Z (34)

It is logical to call / the ,,effective length" of the diffractograph, since it represents the distance between specimen and screen of a diffraction apparatus without lenses, giving the same ring diameters at equal accelerating voltage.

It will be proved that these three equations have no real solutions for Ai and A<. First the equations will be simplified as follows:

Be: a + b + c = s (35)

a{b + c)Ai + ( a + b)c A2 = v (36)

abcA,A-, = p (37)

W i t h these equations (31), (33) and (34) become:

s — 3 y + 5 p = 0 (31') 3 „ _ lOp = 0 (33')

s - v ^ p = l (34')

These equations yield:

p = —-1, s = --1 and y = —- Z.

'^ 8 8 4

0

be positive, i.e. the electron beam must hit the screen at the same side of the axis where it leaves the specimen. This excludes solu-tions of the form as given in fig. 7b.

Now eqs. (35), (36) and (37) become:

a + 6 + c =

a(Z^ + c)Ai -f (a + b)c As^

abc A1A2 =

Equation (36') may be written thus:

abc AiAa ^j+. + (a + b)c Ag -bcA2

Ï'

4'

i'

4 -

= 0 (35') (36') (37') (38) and with (37') Or: (a + fc)cA22-AzA2+-g-Z : ^ = 0 (40) In order that A2 be real:

| , 2 _ | , (a + bHb + c)^^ ^^^^ It has already been found that I is positive, so

25 3 (a + fc)(fc + c)

4 ' > T b

^^^'

O r Since eq. (35')

'>g(- + ' + ' + f

aJ^b - | - c = ^ Z

which is obviously impossible.

This result also follows much more directly from the behaviour of the two lens system, when the accelerating voltage is varied.

In fig. 8a a particular diffracted ray is shown at ten different accelerating voltages:

Fig. 8a. Electron trajectories at different velocities.

At low voltage the diffraction angle is large as a result of the large wavelength of the electron radiation. This case is shown in trajectory 1. The ray is bent sharply in the first lens which, at low voltage, is very strong. It crosses the axis between the two lenses and consequently enters the second lens at the other side of the axis. The second lens is very strong too and bends the ray back above the axis, where it finally hits the screen at a great distance from the axis.

As the voltage increases, both points of intersection with the axis (images of the specimen) move towards the screen as the lenses grow weaker. The height of incidence on the screen therefore decreases rapidly.

Ray no 3 hits the screen very near the axis.

After that the rays no longer cross the axis between the lenses and the second im,aige of the specimen has disappeared just before that.

T h e height of incidence at the screen increases below the axis (negative effective length), until it reaches a maximum as the image of the specimen moves further to the screen. This maximum lies at

the voltage for which the system is achromatic (2'"' solution of eq. (31)).

Ray no 6 again hits the screen very near the axis. As, with increasing voltage, the lenses grow weaker still, there is no longer an image of the specimen and the height of incidence again increases to a maximum. (1^' solution of eq. (31)).

Finally, the height of incidence decreases steadily until it is zero at infinite voltage.

This succession of events is plotted in fig. 8b.

Fig. 8b. Radius of diffraction rings plotted against accelerating voltage.

For simplicities sake the lenses are considered as ,,thin", though at sufficiently low voltages no magnetic lens can remain so. In actual fact therefore, the curve shown in fig. 8b should oscillate towards the h-axis.

Although the position and height of the maxima vary with the dimensions of the two lenses, the general character of the curve must remain the same. It must start at -f infinity, go to a negative minimum, rise to a positive maximum and then drop asymptotically to the V-axis.

It is unconceivable to have such a curve, with either one of the inflection points coinciding with the maximum or the minimum.

Consequently, it is impossible to have achromatism in second approximation.

T h e solution where abc A1A2 > a -\- b -\- c contains other possi-bilities however.

1. Since a, b and c can be chosen freely, /13 can be chosen to suit the purpose, keeping a + Z? -|- c constant. I.e. the diffraction patterns can be enlarged to a predetermined value. This is useful for the study of large lattice constants.

2. The distortion caused by lens 1 can be corrected by lens 2. This can easily be shown by an extreme case.

If lens 2 is very strong, equation (31) becomes: 3(a + b)c At = 5 abc A^Ai

A, = ' ( ^ + / > (44) 5 ab

Lens 1 will reduce the outer rings too much. Lens 2 however will magnify the outer rings too much and the result is free of distortion provided the aberration coefficients of the two lenses are given the proper value as determined by shape and size of the polepieces.

T h e complete problem of designing a diffractograph with 2 lenses is best solved by a trial and error method, since the equations are too complicated to give'a complete and clear picture.

3. Since the diffracted rays cross the axis, the field of image will not be limited, if a lens with small bore is put there. This lens

/ / 2 \

will have a small focal distance at the same excitation \K!=- ^r I as the other lenses and can be used either as a projector for an electron microscope or to obtain magnified electron diffraction pat-terns. Both possibilities have been realised by Corbet of Royal Dutch Shell in cooperation with the author.

§ 9. Construction of diffractographs.

The types of diffraction apparatus corresponding to the two solutions of eq. (31) (fig. 7a and b) have both been carried out in the electronmicroscopy department.

The simplest of the two, not provided with microscope facilities will be described first.

In the whole design, priority was given to utmost simplicity. It was therefore decided to make a preliminary test, running an acce-lerating tube on Villard voltage with a separate valve. N o extra difficulties whatsoever being encountered, the next step was to run the actual diffraction apparatus on Villard voltage with the valve built in the accelerating tube itself, as described before. This expe-riment did show some difficulties which had to be overcome.

In the first experiments the automatic bias was obtained by a resistor between the high voltage condensor and the filament trans-former. It was found that the alternating voltage on the Wehnelt cylinder, caused by the capacitive current in the filament trans-former, caused the beam chopping system to be very ineffective. By putting the R.C. circuit for automatic bias between H.T. supply and Wehnelt cylinder, the phase of the disturbing alternating, voltage was reversed. It now became very beneficial, since the negative bias has a minimum when the H.T. is maximum. (See fig. 9 ) .

Fig. 9. Beam chopping left: conventional circuit right: R—C circuit in Wehnelt lead V^j. = accelerating voltage, V^ = cut-off voltage

V = Wehnelt voltage.

Great difficulties arose from leakage currents (brush discharges), since the preliminary experiments had to be made with an air insu-lated H.T. supply. It showed possible however, to suppress the leakages sufficiently by suitable arrangement of the components and rounding off sharp edges.

An effect, which had not been anticipated, resulted from the necessity of having the bias resistor in the Wehnelt cylinder cur-rent. This means, that the bias is no longer determined by the beam current itself, but by the charging current of the H.T. condensor. Now it is self evident that these curnents are equal in the stationary condition. T h e unanticipated effect was, that operation conditions were not stationary at all. Variations in the mains voltage resulted in variations of the condensor charge and hence in fluctuations of

the charging current. This in turn gave rise to serious bias fluctua-tions. In fact, even a fairly slow rise in primary voltage (1—2 Volts/sec.) completely suppressed the electron beam in the diffrac-tion apparatus. Very disturbing variadiffrac-tions in the intensity of the diffraction pattern resulted even on the fairly stable main voltage in this laboratory. Moreover intentional changes in the accelerating voltage could only be carried out very slowly.

The remedy was simple. The capacity of the H.T. condensor was reduced to the very minimum necessary for maintaining the voltage duriijg the short beam pulses. At a mean beam current of 50/( A the charge per pulse is 1 // coulomb. A condensor of 2500 pF, as used now, loses only 400 Volts, not disturbing for stationary operation, yet large enough for quickly following fluctuations of the mains. Of course the compulsory use of such a small condensor only makes the set-up even more attractive, because of its lower cost and small-er space required.

The correct filament current setting of the cathode which charges the H.T. condensor proved a difficulty in the preliminary experi-ments. The only way of finding out whether sufficient electrons were emitted, was to raise the temperature very slightly and see if the accelerating voltage changed. This was concluded from variation in diameter of diffraction rings, with achrcmatisation lens switched off. It therefore practically required the instrument to be in normal operation conditions, which, in turn, could only be expected if both filaments have the correct or too high temperature. Moreover, the specimen had to give clear diffraction rings very reliably and had to be in the electron beam with certainty. The reliable specimen used was ZnO smoke on a grid. N o wonder a number of filaments burned out long before the instrument was adjusted. It was necessary therefore to adjust filament temperature independently from other conditions of the apparatus. Measuring the filament current would not do, because a partly evaporated filament requires far less current than a new one. Moreover its emissivity (work function) depends very much on its surface condition; it is particularly sensi-tive to the presence of oxygen. The only reliable way of adjusting the filament current is therefore to measure the emissivity itself. This was accomplished by applying an a.c. voltage of some 300 Volts on the filament. Instead of an actual meter, an inexpensive neon indicator tube is used for measuring the emission to the surrounding grounded screen.

This method having established itself as very satisfactory, efforts were made to measure the beam current with a neon indicator tube too. Now the total beam current is of the order of only 30 micro-amps. The current required for „full glow" of the neon indicator tube being some 1.5 mA, this seems very unpromising. Here, the fact that the beam is chopped comes in very handy however, as a result of the quick response of the neon indicator. Instead of measuring the mean value of the current, it indicates the maximum current. The emission „shots" can be assumed to be represented by parabolae. Their mean value is therefore 2 / 3 of the maximum value. Since, moreover, current is only flowing during 1/7 to 1/9 of the total time, the maximum current is about 10 times the mean current. See fig. 10.

M

meon current

indicated current

Fig. 10. Emission measurement by neon indicator.

T h e greater part of the total beam current is caught in a catcher electrode (usually wrongly called Faraday cage) simultaneously serving as a preliminary aperture. T h e current runs through a neon indicator tube and is read very satisfactorily.

The fluorescent screen received a great deal of care. The use of a transparent screen was considered essential in this case for two reasons. In the first place the tube was wanted to be of the inclined type, like the Philips electron microscope. The possible disadvantage of a less efficient screen is of no importance here, since in practi-cally all cases the intensity of the diffraction pattern is largely sufficient. So the advantage of closer view can hz fully used here, without that drawback. By choosing this arrangement, the

accelera-ting tube can be very close to the high voltage supply. So close indeed that one single insulator can run from the oil into the vacuum. This in turn does away with the high voltage cable. The latter would be difficult to realise for the desired Villard voltage of 100 kV.

Secondly, the use of a transparant screen does away with the 29

necessity of peepholes, to look at the pattern. This is important since the type of correcting lens used shows less distortion the nearer the field reaches to the film.

The desirability of the transparent screen thus being established, one problem remains to be solved: A fluorescent layer on glass gives rise to very troublesome spurious rings and considerable loss of contrast. This results from the fact that some of the fluorescent grains are in direct contact with the glass •'). This enables light rays going into the glass at angles beyond the critical one. These rays are then totally reflected back to the screen.

The solution is to have the fluorescent material free from the glass. This can be done, as had already been found in the electron microscope, by coating commercial aluminium foil, some 10 in in thickness, with a fluorescent layer. The electrons will penetrate the foil and no noticeable loss in sensitivity occurs, if the accelerating voltage is more than 60 kV. A screen of that type was put in the diffractograph. It was very satisfactory as far as contrast and resolving power went, but had a very serious drawback: The central beam very soon pierced the screen, owing to poor heat con-duction of the thin aluminium foil.

The final solution was copied from the way Leica films are made. The fluorescent material is deposited on a glass window, which instead of being completely transparent, has a considerable absorp-tion. Light emitted by the fluorescent layer in order to reach the eyes, only has to cross the glass once. T o reach the fluorescent layer again after total reflection, it has to cross the glass twice, Moreover, since total reflection occurs for oblique rays only, the intensity of spurious rings will be decreased by a layer of absorbing glass roughly three times the thickness of the glass itself. So, if the glass absorbs the light to 1/3, the intensity of the spurious rings will be reduced to some 4 % .

Similar to the screens in cathoderay oscillographs, the glass can be made in the colour of fluorescence, so that very little of the light in the room is reflected by the screen. A screen made this way had excellent qualities and was used as the final solution. T o avoid charging up, to increase the light emission on the other side and to make the screen non transparent to light, the fluorescent layer was coated with an aluminium layer of some 1—2microns.

with only a small number of seals, it could be expected to be pumped very easily. This was more than confirmed by experiments. It was found that only 75 seconds were required to pump the ap-paratus down sufficiently for operation at 100 kV, from atmo-spheric pressure. The pumps used are the same as in the Philips electron microscope: a 50 1/s oil diffusion pump backed by a mercury vapour jet pump ^).

Probably the Villard voltage makes it possible to operate the instrument at higher pressure.

Since the current generating the magnetic field of the condensor has to be adjusted for different accelerating voltages in the same way as the current of the corrector lens, both coils are connected in series. This means that the diffractograph is focussed as long as the voltage is adjusted to the corrector current.

One more difficulty had to be overcome. A number of pictures taken, showed blurred rings. Their sharpness was nowhere near that of many pictures obtained in preliminary experiments. The striking part was, that the inner rings showed as much blurring or even more than the outer ones. At first the electronic stabiliser was suspected not to stabilise to the required degree. This was most likely, since it had shown a strong tendency to oscillate. However, no traces of oscillations were found, though pictures taken with another supply of lens current were noticeably better.

Finally it was found that the blurring increased with the expo-sure. This proved to be the key to the solution. Evidently the blur-ring was due to electric charge on the film. Now there are several ways to avoid the effects of charge on the film.

1. A suitable film can be selected, which has a slightly conduc-tive base. Indeed some films seem to exist, which have that property. The author has no experience with them however. 2. A conductive mesh screen may be put very close to the film. 3. A conductive plate may be put at the back of the film. T h e conductive plate seemed the most attractive solution. It is common in most optical cameras, where the film should be per-fectly flat, owing to small depth of focus. In this diffraction appa-ratus however, where the electrons hit the film after moving practi-cally parallel to the axis, there are no such requirements. Conse-quently, in order to prevent scratches on the film, this plate was not incorporated in the camera.

Fig. 12. Pulse-operated diffraction apparatus. Manufactured by Techn. Phys. Dept. Delft.

T h e action of the plate to prevent deviation of the electron beams by film charges is as follows. The charge on the film induces an equal but contrary charge in the plate. This induced charge is symmetrical to the film charge with the plate surface as a symmetry plane. The closer the charge on the film is to the metal plate, the more the induced contrary charge counteracts the effects of the first.

This means that it is essential to have a metal plate supporting the film. T o ensure a close contact with only a slight pressure, the supporting surface of this plate is bent slightly. As mentioned above, this introduces no noticeable distortion, since the electrons run nearly parallel to the axis.

It was found that in this way the effects of electric charge were completely overcome, even with strong overexposure of the film.

The apparatus just described is shown in figs. 11 and 12. The other type of diffractograph, based on the second solution of eq. (31) fig. 7b will be described now.

The apparatus is provided with microscope facilities for a mag-nification of 2500 diam. Microscopy in this case is not meant for high resolution work; it just serves the purpose of obtaining infor-mation about the distribution of particles in the specimen. It has proved very useful to be able to select the area from which the diffraction pattern is taken for two reasons:

a. Different areas of a specimen, consisting of one component. do not always give equally clear diffraction patterns.

b. A specimen may contain several components.

The second reason makes it desirable to be able to limit the area which is subjected to electron diffraction.

The components of the apparatus will be described in the order in which the electrons pass them on their way from the source to the screen.

T o be able to vary the intensity of illumination without distur-bing the focussing, there are two condensors. It may be remem-bered that, for having the size of the diffraction pattern indepen-dent of the axial position of the specimen, parallel illumination is required (see § 4 ) . T h e condensors make it possible to vary the magnification of the image of the source, keeping this image at infinity.

1st condensor 2nd condensor aperture specimen objective 1st diffr. lens 2nd diffr. lens projector viewing chamber

Fig. 13. Lens system of diffraction apparatus with microscopy facilities.

A variable aperture, between the second condensor and the spe-cimen permits limitation of the illuminated area.

Specimens can be changed by means of an airlock, accommoda-ting specimens of some 3 mm in diameter.

The objective is of special design, to have a large free space for the object. For this purpose both magnetic polepieces are prac-tically in the upper surface of the objective. Consequently nearly all of the magnetic field is external, and both principal planes of the objective lie in front of the polepieces. Only by such measures it was possible to obtain a sufficiently high magnification with no more than some 2000 A.T. excitation at 100 kV. In a more recent design the objective and the specimen airlock together can be re-placed by a large specimen chamber, more suitable for reflection work.

The first diffraction lens has a wide bore, to keep distortion low. It can be aligned so as to have both diffraction lenses exactly coaxial. Alignment can be judged by altering the lenscurrent. The central spot of the diffraction pattern remains in the same position if the position of the lens is properly adjusted.

The second diffraction lens has its magnetic field in the direc-tion opposite to that of the first. Its bore is much smaller than that of the first diffraction lens, and is chosen so, that no distortion occurs in the final pattern. It was subsequently found that, although the distortion is perfectly corrected at the proper accelerating vol-tage, this correction is upset by small variations in high voltage

(2 % ) . This is due to too great distortion in the separate diffrac-tion lenses. Consequently in the more recent design the partial distortions are greatly reduced by using lenses with wider bores and more A.T.

The microscope projectorlens is one piece with the second dif-fraction lens. Its polepieces are removable for cleaning.

For microscopy at the very small magnification of some 250 diam. the second diffraction lens can be used as projector.

The screen is viewed through a lead glass cone. T o prevent the inner wall from being charged by the electrons, it is made conductive by a very thin, evaporated layer of manganine. This was preferred to a semiconductive layer of tinoxide simply because evaporation of manganine is a standard technique in the electron microscope department. Coating was only done after the experiment had shown

grave asymmetric distortion of the diffraction patterns, obviously due to wall charges.

The camera is designed for 70 mm non perforated film. The fact that the crossover is very close to the film (some 30 cm) makes it necessary to keep the film perfectly flat. This is done by a spring loaded metal plate. W h e n the film is moved on for the next expo-sure, the pressure is released automatically. The design of the camera is due to Kramer.

Lenscurrents are electronically stabilised. Stabilisers and pumping unit are mounted in the desk. The apparatus is shown in figure 13 and on page 8.

L I T T E R A T U R E : 1. M. van Ments and ]. B. Le Poole.

Proceedings of the conference on Electron Microscopy Delft 1949, p. 35. 2. M. van Ments and J. B. Le Poole.

Appl. Sci. Res, Vol. B 1, p. 3, 1947.

3. E. Brüchc and A. Recfenagel, Elektronen Gerate, p. 140. Julius Springer, Berlin 1941.

4. A. C. van Dorsten, H. Nieuwdorp and A. Verhoeff, Philips Techn. Review Vol. 12, p. 33, 1950.

Simplified 75 kV electron microscope.

C H A P T E R II.

A S I M P L I F I E D E L E C T R O N M I C R O S C O P E .

§ 1. Introduction.

By using objective lenses of very small focal distance the chro-matic aberration may be reduced considerably. Moreover the effects of wall charges, magnetic stray fields and mechanical instability are also decreased appreciably, owing to the large magnification at a small distance from the objective. It will be shown that a resolution of 60^—70 A is attainable even with voltage fluctuations of 1%, so that the main advantage of electrostatic lenses over the magnetic type no longer exists. Only special electrostatic objectives, like Le Riitte's double lens ' ) , also giving high magnification at short distance may yield the same overall stability. Since the object is to reduce chromatic aberration, a magnetic double objective. which could easily be made to have extremely small focal distance, would not give any improvement, if the first lens were not very strong. On the contrary, since chromatic error depends on the

mag-r , mag-r , / , , M -f 2 -f 1/M

nitication or the first lens (oc = dc „ ^ i at constant aperture angle), this type of lens would not solve the problem.

§ 2. The most effic/ent field.

The problem of designing an objective with a focal distance of 0.75 mm at 75 k V seems very simple. All that has to be done is to increase the magnetic field, so the lens would simply have to be scaled down to the desired size.

First of all however, it must be remembered that a specimen must be introduced at the focal plane. It is essential therefore, either to use a bore, which is big enough for the specimen, or to bring the specimen in from aside. The construction first mentioned will yield focal distances of about 2 mm at the very best, so it is clear that for extreme lens power the second construction is the only pos-sible one.

A second factor to be taken into account is saturation of the polepieces. It will be shown that the best results are obtained when the polepieces are just about saturated. Since the maximum field always occurs at the surface of the iron, the maximum focussing effect will be obtained with a homogeneous field of this maximum field intensity all over. So called ,,focussing" of lines of force is a confusing name; it does not exist.

§ 3. The paraxial differential equation.

In the case of a homogeneous magnetic field the paraxial equa-tion becomes extremely simple. It is possible to find simple expres-sions for the position of the focal plane, focal distance, chromatic aberrations etc.

Let r be the distance to the axis of the lens, x the distance along the axis, B the flux density, and e/m the specific charge of the electron.

The paraxial equation takes the form:

d^r e dx"'^ &mV

A particular solution is:

B^ (1)

'"'°'^Vl^v'' <^^

dr

^"^ dx=- '"^ ]' 8 ^ "•" ^ |/ ^ "• Hence, the focus being where r = 0:

(3) or or

^/s^v'-f

p_/g)/'*'"^ = „/?=>°/xio-.VV

dx (4) (5) (6)

In these eqs. ZF is the distance of the focal plane to the face of the polepiece, f the focal distance and R the radius of curvature of an electron trajectory perpendicular to the homogeneous magnetic

At V* = 75 kV or V = 8.1 X 10"* Volt and iron polepieces with

B = 2.4 V sec/m2, we find:

ZF := 1.25 X lO-'' m and / = 0.78 X 10-3 m.

With cobaltiron polepieces between which B =r 2.7 V sec/m'^. we find:

ZF = 1.10 X 10-^ m and f = 0.70 X lO-^ m.

These focal distances are smaller than obtained with other field distributions as described by von Ardenne, Ruska and others ~).

§ 4. Design of the polepieces.

T h e magnet will be very similar to those built in some labora-tories for obtaining very strong magnetic fields, though on a much smaller scale. Of course the polepieces have to be provided with a bore to allow the electrons to pass. Since the field in the gap penetrates into the holes, the diameter should be as small as possi-ble to obtain a concentrated magnetic field. This is the more essen-tial when the polepieces are already saturated, since the lines of force will concentrate on the edges. The result of this is an appa-rent larger diameter of the bore •')• Finally a large bore would mean taking away ferromagnetic material from the place where it is most needed. The necessity of a small bore being established, it is clear that, by definition, the flux density in this bore will equal it„H in the iron. It is essential to round off the edges of the bore. Sharp edges will rarely be rotational symmetric and even if they are, the local concentration of the field will cause the edges to be highly saturated. The apparent increase of the radius of curvature of the edges will depend on the magnetic properties of the polepiece material. This means that slight inhomogeneities will cause asym-metry of the field. In high permeability material only the shape of the polepieces is important.

It is practically impossible to compute the field inside the iron. since the permeability varies from point to point. Valuable infor-mation was obtained from the work of Dreyfus on the design of the big Bellevue magnet **).

Although it is possible to obtain a flux density in the gap, which is several times the saturation flux density of the polepieces, this would not yield a smaller focal length of the lens. According to Dreyfus, saturation penetrates deeply into the polepieces as soon 41

as the flux density in the gap exceeds the saturation of the jx>le tips. This means that a field of appreciable length would exist in the bores of the polepieces in this case.

It will be shown, that the minimum focal distance of a lens is only some 30 % less than that of a lens without saturation. This small gain makes the use of these optimum conditions very doubtful. For a simplified microscope, w^here, as will be explained later, good alignment is of primary importance, it is decidedly undesirable to have the flux density in the polepieces more than a few percent above saturation.

Fig. 1. Field distribution in saturated short focus lens.

In the considerations following now, the B—H curve of the pole-pieces will be simplified. It will be assumed that fi„ H is negligible as lonigi as the saturation magnetisation has not been reached and that from there on B = «„ H -\- Ö,,. Since for reasonably soft iron Ö = 2.1 V sec/m- for M„ H := 0.1 V sec/m^, this assumption is not far from the truth. For further simplification the field strength in the bore will be represented by:

Hi represents the field strength in the iron at the polefaces, and

Z the depth of penetration of the saturation.

See fig. 1. The paraxial diff. equation for — Z < x < 0 becomes:

% = - ^ r ,«,; / / , 2 COS.3 ^ ( 8 )

dx^ 8 m V 2 /

If the focussing effect of this part of the field is small, the ,,weak lens" solution of this equation may be used. For minimum focal length this condition is fulfilled and even essential, as will become clear later on. It is convenient to introduce z ^ l — x.

71 Z

Eq. (7) then becomes: H = f/, sin

^r-j-r„ fi„- Hr { 1 — cos -j— cos -j—] dz =: — and eq. This dr dz ~ (8): yielc 16 dz^ s: e mV r,, e \6mV U r = rA\ e 3 „ ^ / I . nu 16 mV \ 71 I

S'-T6^-^W("-^-^)^"!=

Electrons therefore enter the homogeneous part of the field with:

© , = - T 6 ^ ^ " ^ " ' ^ ^ ' ^ ' <^) and at

T h e combined power of the complete lens is smaller than that of the homogeneous part alone. This follows from evaluation of the complete solution of the paraxial diff. equation for the homogeneous field (1):

cPr

dx^ "^ 8 mV fi2

W i t h ^ ^ B - = i (5) this yields: o mV [o-r = Pcos^+ Qsin— ( 1 1 ) to to J dr P . X Q X and —— = — . 5m - — \ - -.— cos -^— (12) dx f„ f„ f„ fo

The focal plane is where r = 0,

so P cos r = Q sin -i:^

!•• to

tanj- = - ^ (13) dr

Our object is to find -,— at this point.

dr r„ P . IF , Q h -j— ^ r ^ ^ sm — ^- ^ ^ cos -f-dx f fo to fo to In the focus . ZF P , ZF Q and to ^ P 2 ^ Q 2 f„ ^/piJ^Qi as derived from (13), while ^ ^ ^ i ± Q = = . V ^ ^ + Q^ (14) Returning to the solutions (9) and (10) of the paraxial equation

for the first part of the field, we find at x ^ 0: r , ^ P = r „ ( l - ° l l l 5 «;2H,2Z2

\ am.V

r„ u„- HiH

\dx]i fo 16 mV

Inserting P and Q in equation (14) we find:

0.15 e

Since ~—fy u,r H,- Z- < < 1, we may write:

omV '

4 = 7 - 1 / 1 — c " ^ /'"- ti? f = - M l — l^-r^ ^"- Hi^ P _{8 m V ' " ' fo I 8 m V} In this expression //,Z is proportional to the number of extra ampèreturns Ie needed for the saturated poilepieces.

I.e.

JHdx = [Hi

cos .-r dx = = i h. 71X , 2 Hi I , , 2 1 ji So /

T^'

0 . 1 5 e 2 ^' j2 8 mV ""^ '^16 ' (15) T o find the number of A . T . n e e d e d for the field in the gap, the width s of the igap must be k n o w n . T o be able to insert a specimen, s, must be greater t h a n Zp. So suppose s ^ 1.2 ZF.

A b o v e w e found ( 4 ) :

u

~ 71 i / 8 f f l V

_~

_YB\

_{e •}

so t h e number of A . T . used for the gap is:

1.2 71 1 ' 8 m \ / . B„ 1.2 71 n ,

Uo 2 Uo \

0 . 3 6 77^ ^&mV

/<o-Inserting this in eq. (15) we find:

1 _J^

T~7o

= — 1 — 0.34 (16)

A l t h o u g h - . - is not k n o w n , it may be found with reasonable accu-racy from D r e y f u s ' w o r k by extrapolation. If the polepieces are not s a t u r a t e d , no extra A . T . will be needed. T h e curve m u s t therefore go t h r o u g h the origin. See fig. 2.

J + 4

;

Fig. 2. Extrapolated excitation curve.

W^e •will assume:

4—(^r

This fits very well with Dreyfus' curve ^) for the points

B := L5 fi« and B = 2 B,,. Inserting (17) in the equation (16), we

find:

or with (6)

|=iJ—-'(V^)!

1 - l / ^ X Ö ^ - 3 1 f ^ - ^ ' V ^

rf

For maximum power: 1

dB ''- f &mV(' -"'H B, J '^-^y B„ j B. ^

So maximum power of the lens is obtained 38 % above the satu-ration of the polepieces.

In this case—^ = 1.30 -^^-(if ƒ* is the focal distance when B =^ B.

t I

as follows from (18).

Since the maximum power of the lens is only a little more than that obtained with polepieces ijust above saturation, it will be pre-ferable in most cases to use the objective in the latter condition.

All further calculations will be carried out for this case. § 5. Chromatic errors.

Chromatic error too, can be computed easily. The longitudinal chromatic aberration follows from eq. (4)

Ah _^ A V

ZF ~ " V

A, i ; ^ ^

o r zl ZF = 2 'F — T ^ ^

A V

The depth of focus and resolution being related as:

do= \.5^XAh

at 75 kV: X = 0.042 A yielding J„ = 70 A.

(19)

Now even without any stabiliser at all, the voltage stability is usually better than 1 % over a short period and in any case a good saturated core stabiliser will keep variations to within § %. This corresponds to 50 A resolution.

Since focussing remains sufficiently accurate with voltage fluctu-ations, it remains, to study the variation of magnification as a result of chromatic aberration.

If the accelerating voltage decreases, the focal distance decreases too. In the new situation the objective forms an image of a plane just under the object. On this plane a sharp sha^dow of the specimen is projected by the illuminating beam. (It is assumed that the illumination is coherent and that the blurring is caused by Fresnel fringes only).

^A Y/

Fig. 3. Influence of convergence of illumination on magnification error.

Owing to the concentrating action of the first part of the field, the illumination is convergent. The resulting shadow on the siharply imaged plane is therefore smaller than the object itself. The varia-tion of the magnificavaria-tion by the decrease in focal distance is coun-teracted by this convergence. W e will compute the total effect, assuming the incident beam is parallel. See fig. 3.

Clearly, if the object plane (=s5 focal plane) of the lens shifts by

an amount A f:

P-P' = AIF^ (20)

T h e ray equation for a ray passing the objectplane at a distance p from the axis of the field is derived from solution (2) of the paraxial diff. eq. combined with (5) and r equaling p for x := a,

- - P cos 4 - (21) cos —p

t

Consequently for x = a; dr p . a , -j- = sin— 2 2 ) dx a f f cos j

-t

Inserting eq. (22) in (20) we find;

p — p ' = J ZF J tan

-p' = p [ \ - ^ t a n ^ ) (23)

In the new situation p ' is magnified by

M + J M = M (' 1 +

Aj-^

So after the shift of the focal plane Mp becomes: M p ( l + i l ^ ) ( l - ^ ^ . a n ^

|In order to have no change in final magnification it is required that:

' + f ) ( ' T ^ 7 )

-or

^l Ah a , - . .

-y = -^tan^ (24)

From (4) and (5) we find - - = — . So eq. (24) yields:

a 2 tan —- = —

2 2 2

or a ^ f arctan = r — ly arctan — (25)

71 71 71

a = 0.36ZF (26) For achromatisation of the magnification, the distance between

specimen and upper polepiece must be 0.4 — 0.5 mm. This distance is approximately that required to insert the specimenholder, especi-ally if stereopictures are to be taken.

§ 6. Position and size of the objective aperture.

By computing the intensity distribution arising from diffraction and spherical aberration, Glaser '') found for the ,,optimum" aperture angle of a miscroscope objective:

='''H,

(27) in which Cs is the spherical aberration constant and a the aperture angle.

Inserting Cs = 1.5 mm and X = 0.04 A, we find: a = 0.81 X 10-2 radians. So the approximate radius of the aperture:

r„ = af = 0.81 X lO"-^ X 0.75 ^ 6 /n.

For extra contrast it may be desirable to reduce the apeiture still further. The anticipated resolution being some 60 A, it is possible to reduce the aperture without seriously affecting resolution until — = 6 0 A or a— 2.4 X lO"-' radians.

a

This would require an aperture about 4/< in diameter. It is ex-tremely doubtful if an aperture of this size would not foul up quickly, thus causing serious astigmatism. Therefore 10/< would seem a suitable limit for the size of the aperture. In order to avoid limitation of the field, it is necessary to put the diaphragm in the vicinity of the back focal plane.

The required accuracy of its position will now be computed. Clearly, for symmetry reasons, the aperture should be as far from the lower polepiece as the object is from the upper one. See fig. 4.

In earlier computations we found as the equation for a: ray pas-sing the specimen in a point P at a distance p to the axis:

e q . ( 2 1 ) :

r =:

cos

p X

-— cos —f-/

Now suppose the error in the position of the aperture is t, and the radius of the aperture is r„.

Fig. 4. Position tolerance of objective aperture.

The illuminating ray passing P will just pass the aperture if

t

dx

(28)

Now in the back focal plane:

dx f cos

J

So: t = — r cos —f-P t (29) (30) In this equation p represents the radius of the field.

Assuming the minimum magnification to be 1500 diam. and the diameter of the final image 13 cms, the required objective field diameter is some 90// or p = 45/t.

From eq. (25) we find:

a 2 cos —=- = cos arctan — = 0.85

So t = 0.85 - ^ f.

P

Inserting r„ = 5 u, p := 45 fi and f = 0.75 mm, we find

t z= 7 X 10-- mm.

Van Dorsten suggests the aperture and the specimen to be mova-ble in axial direction to meet this rather (high requirement.

§ 7. Discussion.

Apart from its good features, the type of lens just described. has some drawbacks.

It is difficult for instance to keep the small bores clean. Fortu-nately the most sensitive lower polepiece is very well protected by the objective aperture and similar measures could be taken for the upper polepiece.

Secondly, it may be expected at first sight, that the lens shows bad astigmatism, since it will be difficult to drill the small holes in the polepieces round enough. T h e small focal distance however. will reduce the longitudinal astigmatism. Moreover, since most of the focussing action is due to the homogeneous part of the lens, astigmatism may not be too bad. Of course the faces of the pole-pieces should be as symmetric as possible.

As to spherical aberration: O'wing to the steepness of the field-curve at the ends, it may be expected that this is large.

It is simple to compute this:

0

So for the homogeneous part of the field where

Ip

0

with r = fcos ~ and r' = sin ^ ( ( 2 ) . (3), (4) and ( 5 ) ) / /

C s i = ^ 5 . i n 2 ^ + cos2 ^ ) cos3 ^ < f x = ^ / ^ 0 . 5 m m . (32)

0

This very small value of Csi corresponds to the homogeneous part of the field only and could be expected to be small. As the electrons leave the field however, they pass a region where H' is very large. It is necessary therefore to compute the contribution of this part of the field to the constant of spherical aberration. Suppose the field falls off according to S , =^ Be '^. W h e r e the electrons leave the field r' := 0, so according to (31)

0

Cs.^T^'r»/ />''^' + -Av ^A f'dx (33)

_{16 m V . ' \ ' 4 m V}

— OO

c2

Inserting Bi := B e ^-2 this yields:

0 4*2' C s 2 = j | - ^ - ^ - fi-^+e-^) dx (34) — OO W i t h c ^ 0.3 mm, and f =: 0.73 mm, Cs2 =r 0.71 mm, so Csi -j- Cs2 = Cs = 1-25 mm.

This is unexpectedly small. § 8. Design of the lens.

According to the principles just described, an experimental lens was designed.

Since it would be complicated to design an airlock, the specimen was to be inserted with the microscope under atmospheric pressure. T o avoid the necessity of frequently changing the specimens, their useful area was designed to be 1 cm", instead of the 0.05 cm- of the usual small grids.

The distance between specimen and upper polepiece was suppo-sed to be 0.2 mm and the lens was to be usuppo-sed at 90 kV.

T o be sure that saturation would occur, the distance between the polepieces was made 1.4 mm. The bore was 0.3 mm so, taking into account the drop of the field just in front of the polepiece,

ZF = 1.1 mm.

Since ZF = 10.5 X 10^° ^ and V = 90(1 + 9.10-2J = 98 kV.

the magnetic field required was B 10.5 X 10-0 y v

ZF = 3.0Vsec/m2

Uo

The required number of A.T. was / = — = 3350 A.T. Since llo

the saturated polepieces would need extra A.T., the coils were de-signed for 3600 A.T.

The complete design is given in fig. 5.

y// ^•'y fzi^^^^TT.^——^

Fig. 5. Experimental short focus objective.

The first experiment showed the necessity to align the polepieces during operation and adjusting screws were provided for that purpose. This was not unexpected since the small bores were likely to require a very high degree of alignment.

After this was done, the lens proved to work up to an acceleration voltage of 63 kV, corresponding to a field of

B=z 10.5 X 10-«\/63000 = 2.4 V sec/m2 1.1 X 10-3

So apparently 2,4 V sec/m'- is the fieldintensity giving the best results, as predicted in § 4.

The distance between the polepieces was subsequently increased to 1.6 mm., corresponding to ZF = 1.3 mm and 85 kV maximum voltage. From magnification measurements, which admittedly were

not better than about 5 % in accuracy, a focal distance of 0.8 mm was derived.

lOcm

I (

Fig. 6. Short focus lens for 450 kV microscope.

iSince the main difficulties in machining this type of lens lie in its small dimensions, it is clear that this gets easier for higher working voltages. In view of the small chromatic error, it seems therefore specially suited for ultra high voltage microscopy. Accordingly it was decided to construct a similar lens for the 450 kV microscope. '')

In this case the corrected voltage amounts to 450 (1 + 0,44) = 650 kV. W i t h a field of 2.2 V sec/m^ this means:

ZF = ^ VÓS'X 10' X 10-« = 3.8 X lO^'^ m and / = 2.5 mm. It was decided not to use the very maximum field in this case, in order to have some more room avsilable for the stereo-airlock, since stereo pictures can be expected to be very important for thick specimens. The distance between the polepieces is 4.8 mm, requiring

/ = ^:^XJ0^X22 ^ 35^^ ^^

Excitation is done by 4 coils, which can be switched off at will to keep power consumption as small as possible at all voltages. The coils have cooling plates in between as shown in the cross section drawing (fig. 6 ) .

§ 9. Application of the lens in a simplified microscope. As a result of iets properties the lens seems ideally suited for a simplified electron microscope.

T h e idea of simpler and less expensive microscopes is not new.

The first one was marketed by R.C.A. in '42 **), but owinig, to the

fact that at that time too little was known about the future develop-ment of electron microscopy and also because the general design of the ..desk model" was not altogether sound, it has never become very popular.

Recently however, the demand for simpler instruments has greatly increased, the electron microscope having become so much more established as a tool of research.

T h e old dream of using permanent magnets, was put into practice by R.C.A. ") as well as by von Borries '") and caused considerable interest. Very soon other firms showed prototypes of simplified microscopes.

T h e author feels that the use of permanent magnets is not the way to simplification. Of all probems involved in the design of electron microscopes, the design of a lenscurrent stabiliser is about the easiest. T h e much more difficult problem of high voltage stabilisation, however beautifully and reliably solved in some cases 1'), is still present in microscopes using permanent magnet lenses. In fact, H.T. stabilisation must be even better since the use of permanent magnets is more attractive the smaller the required magnetomotive force. This means greater focal length of the objec-tive and hence more chromatic aberration.

T h e very strong objective as just described however, renders H.T. stabilisation unnecessary, or at least very simple. Moreover, since the lenscurrents need not be stabilised, it is possible to use

low voltage energising with selenium rectifiers. Apart from greater

reliability it allows the use of thicker wire for the coils, resulting in a more favourable ratio between the space occupied by copper and that by insulation. The required power was thus cut by about 15 — 2 0 % .

The number of A.T. no longer being limited, the accelerating voltage can be chosen to the price of the H.T. supply. This was determined at 75 kV, higher than that of any other of the simpli-fied microscopes.

§ 10. The projector lens.

Variable maignification having become very popular '^^), it was clear that even a simplified microscope should be provided with it. Here a new problem arose. Since the microscope was to be operated on non-stabilised high voltage and lenscurrents, not only its focussing, but its magnification and rotation of the image had to be sufficiently independent of its working conditions.

It has already been shown, that the magnification of the objec-tive could be made independent of H.T. and lenscurrent.

Using the intermediate lens system for variation of magnification however, it is extremely difficult if not impossible to make the same apply to the overall magnification of the instrument.

The original system, as designed by the author, where the pro-jector lens is kept at its achromatic and distortion-free operating condition, can not be used in this case. Variation of magnification in that system was obtained by changing the current in the inter-mediate lens. It was essential therefore that the magnification depended on this current, which was just what we do not want. The system of R.C.A., where projector and intermediate lens are varied simultaneously i'') would be much better, but there is doubt wether this system would be sufficiently achromatic in all necessary set-tings. Moreover it would be difficult to keep the sum of the currents constant, while changing the distribution of currents.

A look at the graphs, applying to projector lenses ^^) reveals a very useful feature however. See fig. 7.

It has been shown that all projectors can be operated under a condition where they are achromatic and that then they are also free of distortion. This condition is therefore very desirable for our case.

The projector is achromatic where the focal length has a mini-mum. The important feature is that the minima of all curves lie at very nearly the same value of -.. This means that the power of a