- Email: [email protected]
Characterization of ultrasharp field emitters by projection microscopy
surface science ELSEVIER
Applied Surface Science 94/95 (1996) 107-112
Characterization of ultrasharp field emitters by projection microscopy M.J. Fransen a,* ,1 E.P.N. Damen a, C. Schiller a, T.L. van Rooy a, H.B. Groen a,2 P. Kruit b a Philips Research Laboratories - Building WY41, Prof. Holstlaan 4, 5656 AA Eindhoven, The Netherlands b Delft University of Technology, The Netherlands
Received 7 August 1995; accepted 26 September 1995
Abstract
The electron optical brightness and the virtual source size of an ultrasharp field electron emitter were determined by an analysis of Fresnel fringes occurring in point projection microscopy images. Simulating the Fresnel diffraction pattern by taking into account the influence of the source size, the source diameter was determined as 5.2 ___1 nm. From additional current density measurements, using the same model, the reduced brightness was calculated. The brightness values obtained ranged from 1 × 107 to 3 × 109 A / m 2 • sr. V for currents between 1 pA and 5 nA. A comparison of our results with the work of other authors is given.
1. I n t r o d u c t i o n The sharp field electron emitters introduced by Fink [1] are considered the brightest electron sources presently available. For possible application in electron microscopy and lithography, the value for the brightness should be known accurately, since it is an important parameter in electron optical column design. We use point projection microscopy [2] for the determination of the brighmess and the virtual source size of these "ultrasharp" emitters, where we define
* Corresponding author. Tel.: +31 40 2743235; fax: +31 40 2743478; e-mail: [email protected]. Also at Delft University of Technology, The Netherlands. 2 Also at University of Groningen, The Netherlands.
an "ultrasharp" emitter as one with only a few emission sites, ultimately a single atom. A point projection micrograph, an example of which is shown in Fig. 1, is obtained by placing an object close to an ultrasharp field emitter. The enlarged image is projected on a multi-channel plate at a large distance. Imaging is restricted to partly opaque, partly transparent specimens, as the penetration depth of the electrons is only a few ,~ at typical beam energies of 3 0 - 5 0 eV. With this lensless microscope, magnifications of 105 can be obtained. Owing to this large magnification and the large wavelength of the electrons, Fresnel diffraction at thin wires [3] and edges [4] in the film are dominant in the image. We will use the Fresnel diffraction at edges to estimate the virtual source size and brightness.
0169-4332/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSD1 0 1 6 9 - 4 3 3 2 ( 9 5 ) 0 0 3 5 8 - 4
108
M.J. Fransen et al. / Applied Surface Science 9 4 / 9 5 (1996) 107-112
2. T h e o r y ds
tip
In order to determine the influence of the size of the source on the image as shown in Fig. 1, we calculate the Fresnel diffraction at an edge due to a point source. We assume that the film is perfectly opaque. We evaluate the diffraction integral in one dimension by modelling the edge shown in Fig. 2 as a half-infinite plane. The figure also gives a sketch of the experimental set-up with the relevant parameters for the determination of the source size. The intensity distribution of the electrons at the screen from diffraction at a half-infinite plane is given by [5]
edge
b
+ c(x/,o]2 +
+ s(x/L)]2),
,-, ~
1.25-
~
,',
.oo-
(1) 0.50-
'~ ~
':
I , x position on screen
screen
Fig, 2. Schematic set-up of the experiment and definition of the parameters for virtual source size and brightness determination.
where x is the coordinate at the screen, C(x) and S(x) are the Fresnel integrals [6]. The length scale L is given by
Aab L=M
Fig. 1. Shadow projection micrograph of a holey carbon foil taken at 40 V extraction voltage and an emission current of 0.5 nA.
2(a+b)
'
(2)
where a and b are the distances between tip and foil, and foil and screen respectively. M is the point projection magnification and equals ( a + b ) / a and A is the electron wavelength given by A = h/2Vr~--~; as usual, m and e are the electron mass and charge and V is the extraction potential. In Fig. 3 the intensity distribution for a point source is depicted as the uppermost curve. The curves are shifted in the vertical direction with respect to each other. In reality the ultrasharp field emitter is not an ideal point source. The electron rays appear to emerge
M.J. Fransen et al. / Applied Surface Science 94/95 (1996) 107-112 2.0
. . . . . . . . .
t . . . . . . . . .
1.5-
~,
.......
i . . . . . . . . .
i,,,
109
the axis of an electron optical system, we define this quantity as the current density j at the screen, the half opening angle a under which d s is seen from the screen (see Fig. 2) and the extraction voltage V
......
~
J
/2)2v'
B, "~
(3)
where the angle a is given by
1.0
a
ds --,
(4)
a+b
leading to
/ [
0.5
=
8,=
4j( a + b) 2
(5)
/ 0.0 . . . . . . , ~ 4 /. . . . . . ..~ . . . . . . . . . t . . . . . . . . . p. . . . . . . . -1 0 1 2 3 x position on screen (ram)
4
Fig. 3. Simulated graphs of the Fresnel diffraction pattern at an edge for a point source, a calculated intensity pattern for a source size of 6 nm and an experimentally obtained line scan. The three graphs are shifted vertically with respect to each other.
It is possible to simplify this expression by defining a relation between the width of the fringes on the screen and the F W H M of the Gaussian dg. The fringe width can be found from the position x, on the screen of the nth fringe from the edge [5]
Ox/an
x. = M from a virtual source of non-zero size, which in general has no direct relation to the physical emitting area of the emitter. The size of the virtual source is influenced by the shape of the emitter, the spread in transverse velocity of the emitted electrons, and the limitations in the experimental method, which will be discussed later. In the direction perpendicular to the optical axis we assume the virtual source to have a Gaussian intensity profile with a full width at half maximum (FWHM) diameter ds, which is magnified on the screen to a diameter dg. The value of d s is taken to be equal to the virtual source size. The pattern on the screen is thus a convolution of the intensity profile of a point source with the Gaussian. The middle curve in Fig. 3 shows the effect of the convolution with a Gaussian with a F W H M of 6 nm. In the ideal situation one would deconvolute the measured intensity profile with the point source pattern in order to find the emission profile of the source directly, so that the assumption of a Gaussian emission distribution can be checked. From the virtual source size d s we derive an expression for the reduced brightness of the tip. Since the reduced brightness B r is conserved along
~n
1 ¢ Aab
- 2
2( a + b)
(6)
Differentiation by the fringe order n yields
OX,_MA(a+b) On
(7)
xn
As the width of the fringes decreases with increasing fringe number, it is possible to find a fringe with a width that equals the F W H M of the G a u s s i a n dg, corresponding to a fringe position x r As previously stated by Spence [4], the fringe with position x~ is roughly equal to the last visible fringe on the detector. We will use this assumption for a preliminary experiment in which we determine the virtual source size and the reduced brightness of an ultrasharp field emitter approximately from the visibility of the fringes on the screen. This leads to a source size A ds = b--
(8)
Xl
and a reduced brightness 8 me ejx 2
Br
7rh2
8.5 X 1017jx 2
[Br]
A m 2 srW"
(9)
ll0
M.J. Fransen et al. / Applied Surface Science 94 / 95 (1996) 107-112
All the quantities in this expression can be determined experimentally.
3. Experiments All experiments were carried out in an ultra-high vacuum (UHV) system with a base pressure of 2 × 1 0 - 9 Pa. Foils as well as tips can be changed without venting the system. The foil can be moved in three directions with piezoelectric actuators (inchworms). A multi-channel plate with a diameter of 40 mm is used as image intensifier. The foil-to-screen distance b is 17.3 cm. Movement of the tip with respect to the foil enlarges the effective source size since the image on the screen will move with an amplitude multiplied by the magnification. To prevent this, the whole vacuum system is supported by air springs and the projection microscope itself is mounted on an O-ring stack. During experiments the turbomolecular pump is switched off and all cable connections that are not necessary are disconnected. Oscillating magnetic fields may also cause a blurring of the fringe pattern. The amplitude of these fluctuations in our laboratory is typically below 2 mG. For slow 30 eV electrons, this field would cause a blurring of the fringe pattern on the screen of at most 0.16 mm. We therefore mounted a /x-metal shielding cone between foil and multi-channel plate. Tungsten (111) oriented wires are the base material for our electron sources. They are subsequently etched, brought in the vacuum system, flashed, neon sputtered and annealed [7]. We chose for tungsten as emitter fabrication procedures are described extensively in the literature. We used thin carbon films containing holes ("holey carbon") as specimen in our projection microscope. These films are commercially available on 400 mesh TEM grid. With these specimens projection images like Fig. 1 were obtained. The micrograph shown is one of a series in which the extraction voltage was varied from 31 to 46 V, resulting in emission currents from 1 pA to 5 nA. We repeated the experiment with the same tip on a different part of the specimen, resulting in a second series. In the example of Fig. 1 the emission current was 0.5 nA at 40 V extraction voltage. The bottom curve in Fig. 3 represents a line
scan through the edge fringes of Fig. 1. From these line scans we determine the magnification and the virtual source size. In this first experiment we used the approximation stated in Eq. (8) instead of the correct procedure of deconvoluting the experimental pattern with the point source intensity profile. This was due to experimental difficulties in the deconvolution procedure. We were not able to measure the current density directly in the projection image, because we could not calibrate the amplification of the channel plate accurately enough. We therefore measured the current density with the aid of a platinum aperture with a diameter of 30 p~m. With the channel plate turned on, the imaged area could be measured, and with the channel plate turned off the corresponding current on the front of the detector was recorded.
4. Results Fig. 4 shows the calculated virtual source size as a function of the emission current. The closed circles represent the first series, while the diamonds are the second series. To determine the source size d S the
10
6
4 >
• First
series
,z, Second series
0
0.1
........
I
1.0
........
I
........
I
........
r
. . . . . .
10.0 100.0 1000.0 Emission current (pA)
10000.0
Fig. 4. Virtual source size as a function of the emission current. In both experiments the same tip was used, but on different parts of the film.
M.J. Fransen et al. / Applied Surface Science 9 4 / 9 5 (1996) 107-112 1000
approximately by taking the width of the last visible fringe equal to the F W H M of the G a u s s i a n dg, as described previously. The position of the last visible fringe x t is obtained from the micrographs directly. For the current range of 1 pA to 5 nA we found source sizes between 9 _+ 2 nm and 5.2 + 1 nm. We estimate the reduced brightness B r as determined according to Eq. (9). We measured the current density on the channelplate as a function of the emission current with the aid of an aperture, as plotted in Fig. 5. The estimated reduced brightness as a function of the emission current is plotted in Fig. 6. As an example, the value obtained from the micrograph in Fig. 1 is (5 + 1) × 10 8 A / m 2 • sr. V, for an emission current of 0.5 nA.
E 0
100
E 10
1.0
0.1
10.0 100.0 1000.0 Emission current (pA)
10000.0
Fig. 5. Current density j at the detector as a function of the emission current.
obtained line scans, an example of which is presented in Fig. 3, are compared with calculated intensity profiles to match the magnification M of the image. This yields the value of the tip-foil distance a, which in the first series was 2.28 p,m; in the second series, taken at a different position of the foil, a = 2.8 /xm. We estimated the virtual source size
10000.0 -- '
I
t
I
'
~
I
1000.0 k O
<
A 100.0
v
•o • <~
10.0 ~>• re
111
1.0
[]
First series
•
Second series
o!
Spence /
1
•
Qian
A
0
Philips FEG TEM 0 ~.
L 0. l . . . .
10-2
L . _ _ ~
100
I ,_ i ! 104 106 102 Emission current (pA)
I
!
108
101°
Fig. 6. Reduced brightness as a function of the emission current and comparison with results of other authors.
5. Discussion The apparent reduction of the source size with increasing emission current as shown in Fig. 4 is surprising. We are confident that mechanical vibrations and magnetic stray fields are not the cause for these changes; we expect the trend to be a consequence of the limitations of our detection system. The large amplification of the multi-channel plate that is necessary at low emission currents yields a noisy image, which enlarges the error at low extraction voltages. As a final result for the source size, we therefore take the smallest of the values found in our measurements, i.e. 5.2 + 1 nm. The brightness increases linearly with the current, as expected. In Fig. 6 we compare our results with those of other authors. Spence et al. [4] and Qian et al. [8] measured brightness and virtual source size for ultrasharp emitters. The brightness of the commercially available Z r / O thermal-field emitter [9] is also included in the graph. Some recalculations of experimental data taken from literature were necessary, since not every author presents the results in the same parameters and units. Spence et al. [4] used the same experimental procedure as we do. However, a different model is used, leading to another expression for the source size (5) and the current density j for the brightness estimation is determined in another way. The emitter fabrication method also differs, as can be seen from the data accompanying Spence's experiment: with a
112
M.J. Fransen et al. / Applied Surface Science 9 4 / 9 5 (1996) 107-112
shorter tip-sample distance than ours (0.95 versus 2.55 /zm), an extraction voltage twice as high as in our experiment is necessary to achieve the same emission current. This suggests that the tip geometries differ considerably. Using the experimental data in Spence's article we calculate a virtual source size of 3 nm with our own method, and a value for the brightness B r = 5.1 X 107 A / m 2 • sr. V, compared with our value of (5___l) X 108 A / m 2 . s r . V . A reason for the discrepancy might be that Spence et al. mention only that the tip current was smaller than 1 nA; our result was obtained at 0.5 nA. Another reason for this difference may be the way the current densities were determined. Spence reports 0.2 / z A / m 2 current density, whereas we find 2 / z A / m 2 at 0.5 nA. Qian et al. calculated the virtual source size of an ultrasharp field emitter from angular current density measurements obtained with a field emission microscope, using currents ranging from 10 nA to 10/zA, leading to a virtual source size of 1.2 nm. From the voltage-brightness graph and the Fowler-Nordheim plot in his article we calculated the reduced brightness values denoted by the triangles in Fig. 6. The currents used by Qian et al. are too large for our experimental method. As a final comparison the reduced brightness of a commercial W / Z r thermal-field emitter observed in a Philips transmission electron microscope (TEM) is shown in Fig. 6.
6. Conclusions The virtual source size and reduced brightness of an ultrasharp field emitter have been determined. We found a virtual source size of 5.2 _+ 1 nm; the re-
duced brightness ranged from 1 × 10 7 to 3 × 10 9 A / m 2 - sr- V for currents from 1 pA to 5 nA. The results are comparable with those in the literature. The experiments confirm that ultrasharp field emitters are the brightest electron emitters currently available. They would be ideal electron sources for application in electron microscopes if the total emission current, the emission stability and the lifetime (presented in Ref. [10]) can be improved.
Acknowledgements This work is part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie (FOM) which is financially supported by NWO. The authors would like to thank Arjan Buist and the late Herman Elswijk for inspiring discussions.
References [1] H.-W. Fink, IBM J. Res. Devel. 30 (1986) 460. [2] G.A. Morton and E.G. Ramberg, Phys. Rev. 56 (1939) 705. [3] J.C.H. Spence, X. Zhang and W. Qian, in: Electron Holography, Eds. A. Tonomura, L.F. Allard, G. Pozzi, D.C. Joy and Y.A. Ono (Elsevier, Amsterdam, 1995) p. 267. [4] J.C.H. Spence, W. Qian and M.P. Silverman, J. Vac. Sci. Technol. A 12 (1994) 542. [5] P.W. Hawkes and E. Kasper, Principles of Electron Optics III: Wave Optics (Academic Press, London, 1994) p. 1273. [6] M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions, 9th ed. (Dover, New York, 1972). [7] C. Schiller, A.A. Koomans, T.L. van Rooy, C. Sch~Snenberger and H.B. Elswijk, Surf. Sci. 339 (1995) L925. [8] W. Qian, M.R. Scheinfein and J.C.H. Spence, J. Appl. Phys. 73 (1993) 7041. [9] M.T. Otten, Proc. ICEM 13 (1994) 235. [I0] E.P.N. Damen, M.J. Fransen, C. Schiller, T.L. van Rooy and H.B. Groen, presented at 1FES 95.
Applied Surface Science 94/95 (1996) 107-112
Characterization of ultrasharp field emitters by projection microscopy M.J. Fransen a,* ,1 E.P.N. Damen a, C. Schiller a, T.L. van Rooy a, H.B. Groen a,2 P. Kruit b a Philips Research Laboratories - Building WY41, Prof. Holstlaan 4, 5656 AA Eindhoven, The Netherlands b Delft University of Technology, The Netherlands
Received 7 August 1995; accepted 26 September 1995
Abstract
The electron optical brightness and the virtual source size of an ultrasharp field electron emitter were determined by an analysis of Fresnel fringes occurring in point projection microscopy images. Simulating the Fresnel diffraction pattern by taking into account the influence of the source size, the source diameter was determined as 5.2 ___1 nm. From additional current density measurements, using the same model, the reduced brightness was calculated. The brightness values obtained ranged from 1 × 107 to 3 × 109 A / m 2 • sr. V for currents between 1 pA and 5 nA. A comparison of our results with the work of other authors is given.
1. I n t r o d u c t i o n The sharp field electron emitters introduced by Fink [1] are considered the brightest electron sources presently available. For possible application in electron microscopy and lithography, the value for the brightness should be known accurately, since it is an important parameter in electron optical column design. We use point projection microscopy [2] for the determination of the brighmess and the virtual source size of these "ultrasharp" emitters, where we define
* Corresponding author. Tel.: +31 40 2743235; fax: +31 40 2743478; e-mail: [email protected]. Also at Delft University of Technology, The Netherlands. 2 Also at University of Groningen, The Netherlands.
an "ultrasharp" emitter as one with only a few emission sites, ultimately a single atom. A point projection micrograph, an example of which is shown in Fig. 1, is obtained by placing an object close to an ultrasharp field emitter. The enlarged image is projected on a multi-channel plate at a large distance. Imaging is restricted to partly opaque, partly transparent specimens, as the penetration depth of the electrons is only a few ,~ at typical beam energies of 3 0 - 5 0 eV. With this lensless microscope, magnifications of 105 can be obtained. Owing to this large magnification and the large wavelength of the electrons, Fresnel diffraction at thin wires [3] and edges [4] in the film are dominant in the image. We will use the Fresnel diffraction at edges to estimate the virtual source size and brightness.
0169-4332/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSD1 0 1 6 9 - 4 3 3 2 ( 9 5 ) 0 0 3 5 8 - 4
108
M.J. Fransen et al. / Applied Surface Science 9 4 / 9 5 (1996) 107-112
2. T h e o r y ds
tip
In order to determine the influence of the size of the source on the image as shown in Fig. 1, we calculate the Fresnel diffraction at an edge due to a point source. We assume that the film is perfectly opaque. We evaluate the diffraction integral in one dimension by modelling the edge shown in Fig. 2 as a half-infinite plane. The figure also gives a sketch of the experimental set-up with the relevant parameters for the determination of the source size. The intensity distribution of the electrons at the screen from diffraction at a half-infinite plane is given by [5]
edge
b
+ c(x/,o]2 +
+ s(x/L)]2),
,-, ~
1.25-
~
,',
.oo-
(1) 0.50-
'~ ~
':
I , x position on screen
screen
Fig, 2. Schematic set-up of the experiment and definition of the parameters for virtual source size and brightness determination.
where x is the coordinate at the screen, C(x) and S(x) are the Fresnel integrals [6]. The length scale L is given by
Aab L=M
Fig. 1. Shadow projection micrograph of a holey carbon foil taken at 40 V extraction voltage and an emission current of 0.5 nA.
2(a+b)
'
(2)
where a and b are the distances between tip and foil, and foil and screen respectively. M is the point projection magnification and equals ( a + b ) / a and A is the electron wavelength given by A = h/2Vr~--~; as usual, m and e are the electron mass and charge and V is the extraction potential. In Fig. 3 the intensity distribution for a point source is depicted as the uppermost curve. The curves are shifted in the vertical direction with respect to each other. In reality the ultrasharp field emitter is not an ideal point source. The electron rays appear to emerge
M.J. Fransen et al. / Applied Surface Science 94/95 (1996) 107-112 2.0
. . . . . . . . .
t . . . . . . . . .
1.5-
~,
.......
i . . . . . . . . .
i,,,
109
the axis of an electron optical system, we define this quantity as the current density j at the screen, the half opening angle a under which d s is seen from the screen (see Fig. 2) and the extraction voltage V
......
~
J
/2)2v'
B, "~
(3)
where the angle a is given by
1.0
a
ds --,
(4)
a+b
leading to
/ [
0.5
=
8,=
4j( a + b) 2
(5)
/ 0.0 . . . . . . , ~ 4 /. . . . . . ..~ . . . . . . . . . t . . . . . . . . . p. . . . . . . . -1 0 1 2 3 x position on screen (ram)
4
Fig. 3. Simulated graphs of the Fresnel diffraction pattern at an edge for a point source, a calculated intensity pattern for a source size of 6 nm and an experimentally obtained line scan. The three graphs are shifted vertically with respect to each other.
It is possible to simplify this expression by defining a relation between the width of the fringes on the screen and the F W H M of the Gaussian dg. The fringe width can be found from the position x, on the screen of the nth fringe from the edge [5]
Ox/an
x. = M from a virtual source of non-zero size, which in general has no direct relation to the physical emitting area of the emitter. The size of the virtual source is influenced by the shape of the emitter, the spread in transverse velocity of the emitted electrons, and the limitations in the experimental method, which will be discussed later. In the direction perpendicular to the optical axis we assume the virtual source to have a Gaussian intensity profile with a full width at half maximum (FWHM) diameter ds, which is magnified on the screen to a diameter dg. The value of d s is taken to be equal to the virtual source size. The pattern on the screen is thus a convolution of the intensity profile of a point source with the Gaussian. The middle curve in Fig. 3 shows the effect of the convolution with a Gaussian with a F W H M of 6 nm. In the ideal situation one would deconvolute the measured intensity profile with the point source pattern in order to find the emission profile of the source directly, so that the assumption of a Gaussian emission distribution can be checked. From the virtual source size d s we derive an expression for the reduced brightness of the tip. Since the reduced brightness B r is conserved along
~n
1 ¢ Aab
- 2
2( a + b)
(6)
Differentiation by the fringe order n yields
OX,_MA(a+b) On
(7)
xn
As the width of the fringes decreases with increasing fringe number, it is possible to find a fringe with a width that equals the F W H M of the G a u s s i a n dg, corresponding to a fringe position x r As previously stated by Spence [4], the fringe with position x~ is roughly equal to the last visible fringe on the detector. We will use this assumption for a preliminary experiment in which we determine the virtual source size and the reduced brightness of an ultrasharp field emitter approximately from the visibility of the fringes on the screen. This leads to a source size A ds = b--
(8)
Xl
and a reduced brightness 8 me ejx 2
Br
7rh2
8.5 X 1017jx 2
[Br]
A m 2 srW"
(9)
ll0
M.J. Fransen et al. / Applied Surface Science 94 / 95 (1996) 107-112
All the quantities in this expression can be determined experimentally.
3. Experiments All experiments were carried out in an ultra-high vacuum (UHV) system with a base pressure of 2 × 1 0 - 9 Pa. Foils as well as tips can be changed without venting the system. The foil can be moved in three directions with piezoelectric actuators (inchworms). A multi-channel plate with a diameter of 40 mm is used as image intensifier. The foil-to-screen distance b is 17.3 cm. Movement of the tip with respect to the foil enlarges the effective source size since the image on the screen will move with an amplitude multiplied by the magnification. To prevent this, the whole vacuum system is supported by air springs and the projection microscope itself is mounted on an O-ring stack. During experiments the turbomolecular pump is switched off and all cable connections that are not necessary are disconnected. Oscillating magnetic fields may also cause a blurring of the fringe pattern. The amplitude of these fluctuations in our laboratory is typically below 2 mG. For slow 30 eV electrons, this field would cause a blurring of the fringe pattern on the screen of at most 0.16 mm. We therefore mounted a /x-metal shielding cone between foil and multi-channel plate. Tungsten (111) oriented wires are the base material for our electron sources. They are subsequently etched, brought in the vacuum system, flashed, neon sputtered and annealed [7]. We chose for tungsten as emitter fabrication procedures are described extensively in the literature. We used thin carbon films containing holes ("holey carbon") as specimen in our projection microscope. These films are commercially available on 400 mesh TEM grid. With these specimens projection images like Fig. 1 were obtained. The micrograph shown is one of a series in which the extraction voltage was varied from 31 to 46 V, resulting in emission currents from 1 pA to 5 nA. We repeated the experiment with the same tip on a different part of the specimen, resulting in a second series. In the example of Fig. 1 the emission current was 0.5 nA at 40 V extraction voltage. The bottom curve in Fig. 3 represents a line
scan through the edge fringes of Fig. 1. From these line scans we determine the magnification and the virtual source size. In this first experiment we used the approximation stated in Eq. (8) instead of the correct procedure of deconvoluting the experimental pattern with the point source intensity profile. This was due to experimental difficulties in the deconvolution procedure. We were not able to measure the current density directly in the projection image, because we could not calibrate the amplification of the channel plate accurately enough. We therefore measured the current density with the aid of a platinum aperture with a diameter of 30 p~m. With the channel plate turned on, the imaged area could be measured, and with the channel plate turned off the corresponding current on the front of the detector was recorded.
4. Results Fig. 4 shows the calculated virtual source size as a function of the emission current. The closed circles represent the first series, while the diamonds are the second series. To determine the source size d S the
10
6
4 >
• First
series
,z, Second series
0
0.1
........
I
1.0
........
I
........
I
........
r
. . . . . .
10.0 100.0 1000.0 Emission current (pA)
10000.0
Fig. 4. Virtual source size as a function of the emission current. In both experiments the same tip was used, but on different parts of the film.
M.J. Fransen et al. / Applied Surface Science 9 4 / 9 5 (1996) 107-112 1000
approximately by taking the width of the last visible fringe equal to the F W H M of the G a u s s i a n dg, as described previously. The position of the last visible fringe x t is obtained from the micrographs directly. For the current range of 1 pA to 5 nA we found source sizes between 9 _+ 2 nm and 5.2 + 1 nm. We estimate the reduced brightness B r as determined according to Eq. (9). We measured the current density on the channelplate as a function of the emission current with the aid of an aperture, as plotted in Fig. 5. The estimated reduced brightness as a function of the emission current is plotted in Fig. 6. As an example, the value obtained from the micrograph in Fig. 1 is (5 + 1) × 10 8 A / m 2 • sr. V, for an emission current of 0.5 nA.
E 0
100
E 10
1.0
0.1
10.0 100.0 1000.0 Emission current (pA)
10000.0
Fig. 5. Current density j at the detector as a function of the emission current.
obtained line scans, an example of which is presented in Fig. 3, are compared with calculated intensity profiles to match the magnification M of the image. This yields the value of the tip-foil distance a, which in the first series was 2.28 p,m; in the second series, taken at a different position of the foil, a = 2.8 /xm. We estimated the virtual source size
10000.0 -- '
I
t
I
'
~
I
1000.0 k O
<
A 100.0
v
•o • <~
10.0 ~>• re
111
1.0
[]
First series
•
Second series
o!
Spence /
1
•
Qian
A
0
Philips FEG TEM 0 ~.
L 0. l . . . .
10-2
L . _ _ ~
100
I ,_ i ! 104 106 102 Emission current (pA)
I
!
108
101°
Fig. 6. Reduced brightness as a function of the emission current and comparison with results of other authors.
5. Discussion The apparent reduction of the source size with increasing emission current as shown in Fig. 4 is surprising. We are confident that mechanical vibrations and magnetic stray fields are not the cause for these changes; we expect the trend to be a consequence of the limitations of our detection system. The large amplification of the multi-channel plate that is necessary at low emission currents yields a noisy image, which enlarges the error at low extraction voltages. As a final result for the source size, we therefore take the smallest of the values found in our measurements, i.e. 5.2 + 1 nm. The brightness increases linearly with the current, as expected. In Fig. 6 we compare our results with those of other authors. Spence et al. [4] and Qian et al. [8] measured brightness and virtual source size for ultrasharp emitters. The brightness of the commercially available Z r / O thermal-field emitter [9] is also included in the graph. Some recalculations of experimental data taken from literature were necessary, since not every author presents the results in the same parameters and units. Spence et al. [4] used the same experimental procedure as we do. However, a different model is used, leading to another expression for the source size (5) and the current density j for the brightness estimation is determined in another way. The emitter fabrication method also differs, as can be seen from the data accompanying Spence's experiment: with a
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shorter tip-sample distance than ours (0.95 versus 2.55 /zm), an extraction voltage twice as high as in our experiment is necessary to achieve the same emission current. This suggests that the tip geometries differ considerably. Using the experimental data in Spence's article we calculate a virtual source size of 3 nm with our own method, and a value for the brightness B r = 5.1 X 107 A / m 2 • sr. V, compared with our value of (5___l) X 108 A / m 2 . s r . V . A reason for the discrepancy might be that Spence et al. mention only that the tip current was smaller than 1 nA; our result was obtained at 0.5 nA. Another reason for this difference may be the way the current densities were determined. Spence reports 0.2 / z A / m 2 current density, whereas we find 2 / z A / m 2 at 0.5 nA. Qian et al. calculated the virtual source size of an ultrasharp field emitter from angular current density measurements obtained with a field emission microscope, using currents ranging from 10 nA to 10/zA, leading to a virtual source size of 1.2 nm. From the voltage-brightness graph and the Fowler-Nordheim plot in his article we calculated the reduced brightness values denoted by the triangles in Fig. 6. The currents used by Qian et al. are too large for our experimental method. As a final comparison the reduced brightness of a commercial W / Z r thermal-field emitter observed in a Philips transmission electron microscope (TEM) is shown in Fig. 6.
6. Conclusions The virtual source size and reduced brightness of an ultrasharp field emitter have been determined. We found a virtual source size of 5.2 _+ 1 nm; the re-
duced brightness ranged from 1 × 10 7 to 3 × 10 9 A / m 2 - sr- V for currents from 1 pA to 5 nA. The results are comparable with those in the literature. The experiments confirm that ultrasharp field emitters are the brightest electron emitters currently available. They would be ideal electron sources for application in electron microscopes if the total emission current, the emission stability and the lifetime (presented in Ref. [10]) can be improved.
Acknowledgements This work is part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie (FOM) which is financially supported by NWO. The authors would like to thank Arjan Buist and the late Herman Elswijk for inspiring discussions.
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