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A low-energy high-brightness electron gun for inverse photoemission
230
Nuclear Instruments and Methods in Physics Research A234 (1985) 230-234 North-Holland, Amsterdam
A LOW-ENERGY HIGH-BRIGHTNESS ELECTRON GUN FOR INVERSE PHOTOEMISSION N . G . S T O F F E L * a n d P.D. J O H N S O N Physics Department, Brookhaven National Laboratory, Upton, N Y !1973, USA
Received 9 July 1984
We describe the design and construction of an electron gun which produces a 1 mm focused beam with a 5° full width of angular convergence. The maximum achievable beam current depends on the energy, Vo, and is given as In,ax -- 0.1 (pA/V3/2)× Vo3/2. The gun is used in inverse photoelectron spectroscopy (IPES), and is operated at energies as low as 5 eV. The gun employs a BaO cathode operating at 850-1100°C. The low thermal energy spread of the beam ( k T ~ 0.1 eV) and the narrow convergence angle are ideal for momentum resolved IPES. The focused beam is well suited for use with a grating spectrograph IPES detector. The output beam parameters could easily be modified, within certain fundamental constraints, to suit purposes other than IPES. The design principles and the factors controlling beam parameters are discussed in detail.
1. Introduction The recent development of inverse photoelectron spectroscopy [1-3] (bremsstrahlung spectroscopy) has created a need for well-characterized beams of low energy electrons with currents approaching the fundamental limits imposed by space charge effects. The production of optimum low energy electron beams cannot be achieved by electron guns designed for use at higher energies. Instead, a gun with fundamentally different operating principles is required, and space charge effects must be considered from the outset. One common approach for preparing intense electron beams is the Pierce diode gun [4]. Emission from a relatively wide planar or concave cathode is radially compressed and accelerated by converging electric field lines generated by the geometry of the diode structure. A Pierce diode was used successfully by Fauster et al. [3] for IPES, but this technique presents several disadvantages which are overcome by the gun described in this paper. First, the Pierce configuration cannot produce a tightly focussed beam at any significant distance from the cathode. This is particularly true at low energies where the minimum beam size is increased due to the transverse thermal energies of the electrons [5]. Second, the thermal spread of the beam limits the momentum resolution attainable with a Pierce gun in IPES. The full width at half-maximum (fwhm) of the Maxwellian momentum distribution projected along one transverse direction is given by: A k = 2(2 m k T In 2)1/2/~,
* Present address: AT&T Bell Laboratories, 600 Mountain Avenue, Murray Hill, New Jersey 07974, USA. 0168-9002/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
which equals = 0.27 A-1 for a cathode temperature of 880°C ( k T = 0.1 eV). This momentum spread is not reduced by the Pierce geometry. Finally, while the total current of the Pierce diode can be rather high, its brightness at very low energies is limited by space charge effects due to the relatively low electric fields existing at the cathode surface. The conflicting requirements of high brightness and low energy lead us naturally to consideration of a geometry in which a small, bright source of electrons, generated at higher energy, is decelerated and refocused onto the sample. The space charge limited current density at a cathode varies as the three-halves power of the extraction voltage and inversely as the square of the linear scale [6]. Therefore, the brightness of the cathode con be greatly increased by such an approach. This general technique and specific examples have been discussed by Simpson and Kuyatt [7]. Many different implementations of this technique are possible. In practice, however, the design of our gun was essentially dictated by specific design objectives appropriate to our application, IPES, and by fundamental electron optical principles.
2. Design objectives The electron gun was designed for use with two different photon detectors. The fist, a Geiger-Mi~ller type detector [2] detects photons at a fixed energy of 9.7 + 0.4 eV and can be used with a rather poorly focused electron beam. In order to be useful for momentum-resolved IPES, however, this detector must be coupled with an electron gun which can produce beams down to ~. 5 eV with a narrow transverse
N.G. Stoffel, P.D. Johnson / Electron gun for inversephotoemission momentum spread. With this detector the beam energy must be ramped to produce a spectrum. The second detector is a grating spectrograph [8] which relies on a narrowly focused electron beam in lieu of entrance slits to provide good energy resolution. Narrow energy and angular widths are also required, but the beam energy can be fixed at a particular value in the range 5-25 eV. For both detectors we find it convenient to have the focus of the gun 2 cm past the last gun electrode so that the gun does not interfere with rotation of the sample manipulator or block the collection of photons. The focal length of our gun is electronically adjustable, but the maximum focused current is reduced by radial space charge forces if the cathode to focus distance is increased. The maximum current also depends on the square of the convergence angle. In the present case we chose a full angular width of 5 ° as a compromise between momentum resolution and current requirements. This convergence corresponds to a full width momentum broadening of 0.1 A - 1 at 5 eV or 0.2 A,- 1 at 20 eV. A beam width of 1 mm was chosen as a good match to our grating spectrometer. The gun described in this paper achieves these design objectives, but from the following discussion of the gun design procedure it will become obvious that all important beam parameters can be varied by changes in the gun dimensions and some can be controlled electronically.
3. Gun design The final gun design, illustrated in fig. 1, consists of a diode extraction source and a three-element refocusing lens. The source and the lens are matched to one another, but as electron optical devices they can be treated independently. The source produces a divergent beam at an energy equal to the anode potential Va I-
vo-:o
Vo l'l I
Boo
~ I-
t_
vF --
.I
D
ii, Vo j[ l
-
I p
i-
0'
~I
Fig. 1. The electron optical components of the electron gun are shown schematically. The output electrode is normally operated at ground potential In the text the operating voltages are" referred to the cathode potential, V~, Va, VE, and V0 then give the approximate kinetic energy of the electrons within the anode, focus and output electrodes in units of eV. In the final gun design, Va/Vo=6 and VE~ 0.1v0. L = D = 1 6 ram; Q = 2.5D and P = 1.3D. The output electrode is drawn roughly to scale, but its shape is not crucial to proper gun operation.
231
which is then decelerated to energy V0 in the lens. At the energies of interest the maximum beam current is limited by the refocusing stage, not the source. The maximum achievable perveance of an electron gun/'max is a parameter which indicates the maximum current Iraax which can be provided before space charge effects either prevent further current increases or cause undesirable effects in the beam. Perveance is given as
em~, = I m J Vo3/2. The final beam energy Vo is given in V or eV and the usual unit of perveance is the #perv: 1 #perv = 1 # A / V 3/2. In principle, Pm~ is independent of V0 and depends only on the geometry and not the scale of the electron gun. For a beam with full angular width 0 it can be shown [9] that there is an approximate upper limit:
e,,~, (~,per~) =
38 t a n 2 ( 0 / 2 ) .
For 0 = 5 ° we find a perveance of about 0.1/xperv. The BaO cathode [10] can produce emission current densities of better than 10 A / e r a 2 and is easily capable of providing the currents needed to reach this perveance. Since lends aberrations can prevent the gun from achieving its design specifications, a tubular geometry was chosen for the lens with the focusing element of the lens having a length equal to its diameter, The extensive lens calculations of Harting and Read (HR) [11] have shown that this type of lens generally has a low spherical aberration coefficient. From their calculations it was also noted that the spherical aberrations increase rapidly for decelleration ratios Va/Vo greater than about 10 : 1. We somewhat arbitrarily chose V J V o = 6 : 1 and designed the source stage with this ratio in mind. Another design parameter directly affecting spherical aberration is the fraction of the lens diameter filled by the beam at its broadest point. This fill factor should be kept below 0.25 as a rule of thumb. For our convergence and lens to focus distance a diameter of 16 mm satisfies this criterion. The object and image distances measured from the center of the focus electrode, P and Q in fig. 1, determine ihe magnification of the electron lens. The magnification, in turn, affects the angular convergence of the output beam. The angular width of the source has an intrinsic part and a thermally induced part as will be discussed below. By choosing a magnification larger than unity, both the thermal and intrinsic contributions to the angular width can be reduced when the source is imaged onto the sample. From Liouville's theorem it can be shown that the product of the square root of the beam energy, the convergence angle, and the beam diameter cannot be reduced by an electron optical system. Therefore, the lens can reduce the angular width of the beam at most by a factor of ( V J V o ) I / 2 / M , where
232
N. (7. Stoffel, P.D. Johnson / Electron gun for inverse photoemission
M is the linear magnification. This factor immediately suggests the use of a small, bright source of electrons which can be substantially magnified to produce the final image size. Using this approach we are able to reduce the effects of thermal angular spreads to negligible levels even at the lowest beam energies. The electron source is illustrated in fig. 2. A 3 m m diameter planar BaO dispenser cathode is placed a distance d = 1 ram behind a copper anode which contains an aperture of radius a = 0.2 mm. The cathode is heated by an internal filament. The perveance of this planar diode source considered by itself is given by [12] Pmax = 2.3 # p e r v • ¢raE/d 2. The aperture in the anode acts as a lens with a focal length of negative 3d [12], i.e. a diverging lens. In the absence of thermal effects there would be a virtual point image of the source at a distance 3d behind the aperture as shown in fig. 2a. The intrinsic divergence of the (o)
BoO CATHODE
~-
3d
(b)
I {
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source which is due to lens effects is 2 a / 3 d radians (full width [13] and is independent of V~. The finite transverse thermal energy of the electrons at the cathode causes the virtual point-source image to be broadened to a Maxwellian profile with a width (fwhm) of -1.66(kT/Va) 1/2. 3d as shown in fig. 2b. The thermal contribution to the divergence of the source is 1.66(kT/Va) 1/2. This thermal angular distribution is convoluted with the intrinsic divergence. For the values of a, d, and k T appropriate to this design, the intrinsic divergence is larger than the thermal divergence for V~ > 15 V. Since the gun is operated with a decellerating ratio V J V o = 6 : 1, Va is greater 30 V for final energies above 5 eV. Therefore, the intrinsic divergence, about 8 ° , is much larger than the thermal divergence contribution over the normal operating range of the gun (V0 = 5 - 5 0 eV). Thus the thermal divergence can be ignored. Since the reduction in convergence is given by ( V J V o ) I / 2 / M , it is seen that a linear magnification of at least M = 3 is required to meet our design objective of a 5 ° convergence angle in the final beam. In terms of the lens diameter, D = 16 mm, an image distance Q = 2.5D provides the required gun to sample separation. The zoom lens data of H R allow us to estimate the object distance P which produces the necessary magnification. We chose P = 1.3D yielding a value of M = 3.5. Estimates of the spherical aberration coefficients are also available from HR. The broadening of the beam at the sample due to this aberration is calculated to be less than 0.1 mm. The voltage required on the focus electrode is VF = 0.9V0. Our actual lens geometry differs slightly from the idealized lenses of H R in that the lens fields are terminated at a short distance on either end of the lens. Therefore we calculated the electric fields in our chosen lens geometry [14] and ray-traced electron trajectories through the lens. We found that the field termination did not significantly affect either the electric fields or the optical parameters of the lens. We decided against the addition of deflection plates for steering the electron beam. A short cathode to sample distance was, we felt, an important requirement for achieving high perveance, and deflection plates would have resulted in a significant fractional increase in this overall length.
I 4. Construction and testing
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Fig. 2. The electron source consists of a BaO cathode placed 1 nun behind a 0.4 nun aperture. Lens effects at the aperture produce a virtual source inaage 3 nun behind the aperture. This image is a point when thermal effects are neglected as in (a), but is broadened to a finite size by transverse thermal energy as in (b), The vertical scales of the figures have been exaggerated.
The electron gun was assembled from ultrahigh vacuum compatible materials. The gun electrodes were machined out of silicon-copper and insulated by aluminum spacers. Nonmagnetic stainless steel fasteners and supporting structures were used. The BaO cathode was supported by tungsten wires, which i s one of the few metals which does not cause poisoning of the BaO cathode emission. The gun was mounted on a ultrahigh
N.G. Stoffel, P.D. Johnson / Electron gun for inverse photoemission vacuum flange with a five-pin electrical feedthrough. A micrometer driven gimbal-bellows assembly allows adjustment of the gun's aim under vacuum. The electronics required to operate the gun are shown in fig. 3. The potentiometer in the feedback loop of the operational amplifier is used to set V a / V o. Note that V J Vo = R f / R i + 1. The focal length of the gun is controlled by VF which is automatically scaled to o0 by the potentiometer R F- Both the magnification and the convergence of the gun are affected by the fecal length and by V J V o , affording some electronic adjustment capability of these parameters. The dependence can be determined with some effort from HR. The work function offset supply compensates for the difference between the low work function of BaO and the gun electrodes. Its value can be measured by noting the threshold voltage required between the cathode and anode to initiate an emission current. This value is rather small, typically 1-2 V, so the offset supply is not strictly necessary. However, it is useful for obtaining maximum performance when ramping the gun at very low energies. Without the offset supply, the gun voltages do not truly scale, so some defocusing will occur while ramping the beam energy.
BoO Cathode ~J~
Focus
233
The beam size at the sample plane was measured in order to optimize the focus potentiometer and beam perveance. We use a small Faraday collector on an xyz manipulator to measure the beam profile. Total beam current was measured with another larger collector. As expected, the beam output current was directly proportional to the anode current as long as the gun was properly focused. When the beam current exceeds some optimal value, space charge effects cause a rapid increase in the beam width at the best focus. This is evident in fig. 4 where we show profiles of the image for 10 and 168 # A beam currents and the same V0, 19 eV. By extrapolating the inflection points of these profiles to the base line as indicated in the figure, we estimate full widths of 1.2 and 2.7 ram. The minimum measured beam size at any energy or current was 1.1 mm. The design angular convergence of 5 ° full width was verified by measuring the variation of the beam profile along the axis with the gun focused 2 cm from the last electrode. In fig. 5 we have plotted beam widths obtained in this manner as a function of perveance for three values of V0. The measured full width of the beam was constant for beams below 0.1 #perv. At perveances above 1 /tperv the beam width was more than doubled at all energies. The beam current is controlled by varying the cathode emission current via the heater current. However, residual gas poisoning of the cathode also affects
Output
\
i
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BEAM PROFILE 19 eV
I °"se'Sup°'y I - -
-l-
Cathode Heater Supply 0-1.5 A,O-7 V
input
I
.•
~168/~A 2.7mm --="
Programmabl+e J ] SupplyO-200V
Fig. 3. Schematic of circuit used to control the electron gun. A single program voltage changes the beam output energy, which is read by the digital voltmeter (DVM). The power supply ratings are sufficient for output energies up to 40 eV.
"~O~A
1.2 mm
I
q
-5
-2
l l l -l 0 I DISTANCE (mm)
l 2
Fig. 4. Beam profiles in the sample plane for perveances of 0.12 and 2 #perv. An increase in perveance above 0.1/~perv causes the beam size to increase dramatically due to space charge effects.
234
N.G. Stoffel, P.D. Johnson / Electron gun for inverse photoeraission i
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3
+
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2
+ O
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0
•
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Fig. 5. Beam full width as a function of perveance at three beam energies. The beam size is constant below 0.1 #perv.
commercial electron gun currently available provides the perveance, convergence, and beam size of this electron gun. We have described the design procedure for this gun in a manner which, we hope, makes clear the relationship between the geometrical and electrical parameters and the performance of the gun. The output beam can be tailored by a similar design procedure to provide a space charge limited beam with different properties. As designed, the gun provides a nearly ideal excitation source for momentum-resolved inverse photoelectron spectroscopy. This work is supported by the Division of Materials Sciences, U S Department of Energy under contract DE-AC02-76CH00016.
References its emission current when it is operated below 1000°C. An emission stabilization feedback loop between the anode current ammeter and the cathode supply would be necessary to hold the beam current constant to a few percent over long time periods. Such a feedback loop could also be programmed to produce constant perveance with changing beam energy. The optimum focus potentiometer setting should be constant in principle, but does vary slightly with perveance above = 0.1 #perv due to space charge effects in the lens and near the focus. Since our grating IPES spectrometer requires an optimum focus at a fixed energy, we find it useful to place a 1 m m diameter Faraday collector on our sample manipulator. This collector can be moved to the sample position and the focus and aim of the gun can be optimized by maximizing current to the collector. Approximately 99% of the cathode current strikes the anode in our gun design. As a result, the output voltage of the gun as it is currently designed is limited to V0 < 50 eV at 0.1 # p e r v by the maximum tolerable heat load into the anode. With a smaller cathode, lower V J V o, or a redesigned anode this limit would be pushed considerably higher.
5. Conclusions The electron gun described in this paper attains a high perveance and brightness at very low energies. N o
[1] V. Dose, Appl. Phys. C14 (1981) 1381. [2] D.P. Woodruff, P.D. Johnson and N.V. Smith, J. Vac. Sci. Technol. A1 (1983) 1104. [3] Th. Fauster, F.J. Himpsel, J.E. Fischer and E.W. Plummer, Phys. Rev. Lett. 51 (1983) 430. [4] LR. Pierce, J. Appl. Phys. 11 (1940) 548. [5] W. Sinz, Nucl. Instr. and Meth. 187 (1981) 259. [6] C.D. Child, Phys. Rev. 32 (1911) 492; I. Langmuir, Phys. Rev. 2 (1913) 450. [7] J.A. Simpson and C.E. Kuyatt, Rev. Sci. Instr. 34 (1963) 265. [8] A spectrograph operating on a similar principle is described by Th. Fauster, F.J. Himpsel, J.J. Donelon and A. Marx, Rev. Sci. Instr. 54 (1983) 68. [9] J.R. Pierce, Theory and design of electron beams, 2nd ed. (Van Nostrand, Princeton, New Jersey, 1954). [10] Standard BaO Cathode (Std. 134) from Spectra-Mat, Inc. [11] E. Hatting and F.H. Read, Electrostatic lenses (Elsevier, Amsterdam, 1976). [12] P.T. Kirstein, G.S. Kino and W.E. Waters, Space charge flow (McGraw-Hill, New York, 1967) p. 131. [13] The estimates of the angular and spatial source widths given herein can be derived in a simple manner by assuming constant field between the anode and cathode and a Maxwellian distribution of velocities at the cathode and by using a thin lens approximation at the anode aperture. Ray tracings of the source verified these estimated widths. [14] Lens fields were calculated using the successive approximation method; see B. Paszkowski, Electron optics (Iliffe, London, 1968) p. 77.
Nuclear Instruments and Methods in Physics Research A234 (1985) 230-234 North-Holland, Amsterdam
A LOW-ENERGY HIGH-BRIGHTNESS ELECTRON GUN FOR INVERSE PHOTOEMISSION N . G . S T O F F E L * a n d P.D. J O H N S O N Physics Department, Brookhaven National Laboratory, Upton, N Y !1973, USA
Received 9 July 1984
We describe the design and construction of an electron gun which produces a 1 mm focused beam with a 5° full width of angular convergence. The maximum achievable beam current depends on the energy, Vo, and is given as In,ax -- 0.1 (pA/V3/2)× Vo3/2. The gun is used in inverse photoelectron spectroscopy (IPES), and is operated at energies as low as 5 eV. The gun employs a BaO cathode operating at 850-1100°C. The low thermal energy spread of the beam ( k T ~ 0.1 eV) and the narrow convergence angle are ideal for momentum resolved IPES. The focused beam is well suited for use with a grating spectrograph IPES detector. The output beam parameters could easily be modified, within certain fundamental constraints, to suit purposes other than IPES. The design principles and the factors controlling beam parameters are discussed in detail.
1. Introduction The recent development of inverse photoelectron spectroscopy [1-3] (bremsstrahlung spectroscopy) has created a need for well-characterized beams of low energy electrons with currents approaching the fundamental limits imposed by space charge effects. The production of optimum low energy electron beams cannot be achieved by electron guns designed for use at higher energies. Instead, a gun with fundamentally different operating principles is required, and space charge effects must be considered from the outset. One common approach for preparing intense electron beams is the Pierce diode gun [4]. Emission from a relatively wide planar or concave cathode is radially compressed and accelerated by converging electric field lines generated by the geometry of the diode structure. A Pierce diode was used successfully by Fauster et al. [3] for IPES, but this technique presents several disadvantages which are overcome by the gun described in this paper. First, the Pierce configuration cannot produce a tightly focussed beam at any significant distance from the cathode. This is particularly true at low energies where the minimum beam size is increased due to the transverse thermal energies of the electrons [5]. Second, the thermal spread of the beam limits the momentum resolution attainable with a Pierce gun in IPES. The full width at half-maximum (fwhm) of the Maxwellian momentum distribution projected along one transverse direction is given by: A k = 2(2 m k T In 2)1/2/~,
* Present address: AT&T Bell Laboratories, 600 Mountain Avenue, Murray Hill, New Jersey 07974, USA. 0168-9002/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
which equals = 0.27 A-1 for a cathode temperature of 880°C ( k T = 0.1 eV). This momentum spread is not reduced by the Pierce geometry. Finally, while the total current of the Pierce diode can be rather high, its brightness at very low energies is limited by space charge effects due to the relatively low electric fields existing at the cathode surface. The conflicting requirements of high brightness and low energy lead us naturally to consideration of a geometry in which a small, bright source of electrons, generated at higher energy, is decelerated and refocused onto the sample. The space charge limited current density at a cathode varies as the three-halves power of the extraction voltage and inversely as the square of the linear scale [6]. Therefore, the brightness of the cathode con be greatly increased by such an approach. This general technique and specific examples have been discussed by Simpson and Kuyatt [7]. Many different implementations of this technique are possible. In practice, however, the design of our gun was essentially dictated by specific design objectives appropriate to our application, IPES, and by fundamental electron optical principles.
2. Design objectives The electron gun was designed for use with two different photon detectors. The fist, a Geiger-Mi~ller type detector [2] detects photons at a fixed energy of 9.7 + 0.4 eV and can be used with a rather poorly focused electron beam. In order to be useful for momentum-resolved IPES, however, this detector must be coupled with an electron gun which can produce beams down to ~. 5 eV with a narrow transverse
N.G. Stoffel, P.D. Johnson / Electron gun for inversephotoemission momentum spread. With this detector the beam energy must be ramped to produce a spectrum. The second detector is a grating spectrograph [8] which relies on a narrowly focused electron beam in lieu of entrance slits to provide good energy resolution. Narrow energy and angular widths are also required, but the beam energy can be fixed at a particular value in the range 5-25 eV. For both detectors we find it convenient to have the focus of the gun 2 cm past the last gun electrode so that the gun does not interfere with rotation of the sample manipulator or block the collection of photons. The focal length of our gun is electronically adjustable, but the maximum focused current is reduced by radial space charge forces if the cathode to focus distance is increased. The maximum current also depends on the square of the convergence angle. In the present case we chose a full angular width of 5 ° as a compromise between momentum resolution and current requirements. This convergence corresponds to a full width momentum broadening of 0.1 A - 1 at 5 eV or 0.2 A,- 1 at 20 eV. A beam width of 1 mm was chosen as a good match to our grating spectrometer. The gun described in this paper achieves these design objectives, but from the following discussion of the gun design procedure it will become obvious that all important beam parameters can be varied by changes in the gun dimensions and some can be controlled electronically.
3. Gun design The final gun design, illustrated in fig. 1, consists of a diode extraction source and a three-element refocusing lens. The source and the lens are matched to one another, but as electron optical devices they can be treated independently. The source produces a divergent beam at an energy equal to the anode potential Va I-
vo-:o
Vo l'l I
Boo
~ I-
t_
vF --
.I
D
ii, Vo j[ l
-
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i-
0'
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Fig. 1. The electron optical components of the electron gun are shown schematically. The output electrode is normally operated at ground potential In the text the operating voltages are" referred to the cathode potential, V~, Va, VE, and V0 then give the approximate kinetic energy of the electrons within the anode, focus and output electrodes in units of eV. In the final gun design, Va/Vo=6 and VE~ 0.1v0. L = D = 1 6 ram; Q = 2.5D and P = 1.3D. The output electrode is drawn roughly to scale, but its shape is not crucial to proper gun operation.
231
which is then decelerated to energy V0 in the lens. At the energies of interest the maximum beam current is limited by the refocusing stage, not the source. The maximum achievable perveance of an electron gun/'max is a parameter which indicates the maximum current Iraax which can be provided before space charge effects either prevent further current increases or cause undesirable effects in the beam. Perveance is given as
em~, = I m J Vo3/2. The final beam energy Vo is given in V or eV and the usual unit of perveance is the #perv: 1 #perv = 1 # A / V 3/2. In principle, Pm~ is independent of V0 and depends only on the geometry and not the scale of the electron gun. For a beam with full angular width 0 it can be shown [9] that there is an approximate upper limit:
e,,~, (~,per~) =
38 t a n 2 ( 0 / 2 ) .
For 0 = 5 ° we find a perveance of about 0.1/xperv. The BaO cathode [10] can produce emission current densities of better than 10 A / e r a 2 and is easily capable of providing the currents needed to reach this perveance. Since lends aberrations can prevent the gun from achieving its design specifications, a tubular geometry was chosen for the lens with the focusing element of the lens having a length equal to its diameter, The extensive lens calculations of Harting and Read (HR) [11] have shown that this type of lens generally has a low spherical aberration coefficient. From their calculations it was also noted that the spherical aberrations increase rapidly for decelleration ratios Va/Vo greater than about 10 : 1. We somewhat arbitrarily chose V J V o = 6 : 1 and designed the source stage with this ratio in mind. Another design parameter directly affecting spherical aberration is the fraction of the lens diameter filled by the beam at its broadest point. This fill factor should be kept below 0.25 as a rule of thumb. For our convergence and lens to focus distance a diameter of 16 mm satisfies this criterion. The object and image distances measured from the center of the focus electrode, P and Q in fig. 1, determine ihe magnification of the electron lens. The magnification, in turn, affects the angular convergence of the output beam. The angular width of the source has an intrinsic part and a thermally induced part as will be discussed below. By choosing a magnification larger than unity, both the thermal and intrinsic contributions to the angular width can be reduced when the source is imaged onto the sample. From Liouville's theorem it can be shown that the product of the square root of the beam energy, the convergence angle, and the beam diameter cannot be reduced by an electron optical system. Therefore, the lens can reduce the angular width of the beam at most by a factor of ( V J V o ) I / 2 / M , where
232
N. (7. Stoffel, P.D. Johnson / Electron gun for inverse photoemission
M is the linear magnification. This factor immediately suggests the use of a small, bright source of electrons which can be substantially magnified to produce the final image size. Using this approach we are able to reduce the effects of thermal angular spreads to negligible levels even at the lowest beam energies. The electron source is illustrated in fig. 2. A 3 m m diameter planar BaO dispenser cathode is placed a distance d = 1 ram behind a copper anode which contains an aperture of radius a = 0.2 mm. The cathode is heated by an internal filament. The perveance of this planar diode source considered by itself is given by [12] Pmax = 2.3 # p e r v • ¢raE/d 2. The aperture in the anode acts as a lens with a focal length of negative 3d [12], i.e. a diverging lens. In the absence of thermal effects there would be a virtual point image of the source at a distance 3d behind the aperture as shown in fig. 2a. The intrinsic divergence of the (o)
BoO CATHODE
~-
3d
(b)
I {
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source which is due to lens effects is 2 a / 3 d radians (full width [13] and is independent of V~. The finite transverse thermal energy of the electrons at the cathode causes the virtual point-source image to be broadened to a Maxwellian profile with a width (fwhm) of -1.66(kT/Va) 1/2. 3d as shown in fig. 2b. The thermal contribution to the divergence of the source is 1.66(kT/Va) 1/2. This thermal angular distribution is convoluted with the intrinsic divergence. For the values of a, d, and k T appropriate to this design, the intrinsic divergence is larger than the thermal divergence for V~ > 15 V. Since the gun is operated with a decellerating ratio V J V o = 6 : 1, Va is greater 30 V for final energies above 5 eV. Therefore, the intrinsic divergence, about 8 ° , is much larger than the thermal divergence contribution over the normal operating range of the gun (V0 = 5 - 5 0 eV). Thus the thermal divergence can be ignored. Since the reduction in convergence is given by ( V J V o ) I / 2 / M , it is seen that a linear magnification of at least M = 3 is required to meet our design objective of a 5 ° convergence angle in the final beam. In terms of the lens diameter, D = 16 mm, an image distance Q = 2.5D provides the required gun to sample separation. The zoom lens data of H R allow us to estimate the object distance P which produces the necessary magnification. We chose P = 1.3D yielding a value of M = 3.5. Estimates of the spherical aberration coefficients are also available from HR. The broadening of the beam at the sample due to this aberration is calculated to be less than 0.1 mm. The voltage required on the focus electrode is VF = 0.9V0. Our actual lens geometry differs slightly from the idealized lenses of H R in that the lens fields are terminated at a short distance on either end of the lens. Therefore we calculated the electric fields in our chosen lens geometry [14] and ray-traced electron trajectories through the lens. We found that the field termination did not significantly affect either the electric fields or the optical parameters of the lens. We decided against the addition of deflection plates for steering the electron beam. A short cathode to sample distance was, we felt, an important requirement for achieving high perveance, and deflection plates would have resulted in a significant fractional increase in this overall length.
I 4. Construction and testing
I I I
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Fig. 2. The electron source consists of a BaO cathode placed 1 nun behind a 0.4 nun aperture. Lens effects at the aperture produce a virtual source inaage 3 nun behind the aperture. This image is a point when thermal effects are neglected as in (a), but is broadened to a finite size by transverse thermal energy as in (b), The vertical scales of the figures have been exaggerated.
The electron gun was assembled from ultrahigh vacuum compatible materials. The gun electrodes were machined out of silicon-copper and insulated by aluminum spacers. Nonmagnetic stainless steel fasteners and supporting structures were used. The BaO cathode was supported by tungsten wires, which i s one of the few metals which does not cause poisoning of the BaO cathode emission. The gun was mounted on a ultrahigh
N.G. Stoffel, P.D. Johnson / Electron gun for inverse photoemission vacuum flange with a five-pin electrical feedthrough. A micrometer driven gimbal-bellows assembly allows adjustment of the gun's aim under vacuum. The electronics required to operate the gun are shown in fig. 3. The potentiometer in the feedback loop of the operational amplifier is used to set V a / V o. Note that V J Vo = R f / R i + 1. The focal length of the gun is controlled by VF which is automatically scaled to o0 by the potentiometer R F- Both the magnification and the convergence of the gun are affected by the fecal length and by V J V o , affording some electronic adjustment capability of these parameters. The dependence can be determined with some effort from HR. The work function offset supply compensates for the difference between the low work function of BaO and the gun electrodes. Its value can be measured by noting the threshold voltage required between the cathode and anode to initiate an emission current. This value is rather small, typically 1-2 V, so the offset supply is not strictly necessary. However, it is useful for obtaining maximum performance when ramping the gun at very low energies. Without the offset supply, the gun voltages do not truly scale, so some defocusing will occur while ramping the beam energy.
BoO Cathode ~J~
Focus
233
The beam size at the sample plane was measured in order to optimize the focus potentiometer and beam perveance. We use a small Faraday collector on an xyz manipulator to measure the beam profile. Total beam current was measured with another larger collector. As expected, the beam output current was directly proportional to the anode current as long as the gun was properly focused. When the beam current exceeds some optimal value, space charge effects cause a rapid increase in the beam width at the best focus. This is evident in fig. 4 where we show profiles of the image for 10 and 168 # A beam currents and the same V0, 19 eV. By extrapolating the inflection points of these profiles to the base line as indicated in the figure, we estimate full widths of 1.2 and 2.7 ram. The minimum measured beam size at any energy or current was 1.1 mm. The design angular convergence of 5 ° full width was verified by measuring the variation of the beam profile along the axis with the gun focused 2 cm from the last electrode. In fig. 5 we have plotted beam widths obtained in this manner as a function of perveance for three values of V0. The measured full width of the beam was constant for beams below 0.1 #perv. At perveances above 1 /tperv the beam width was more than doubled at all energies. The beam current is controlled by varying the cathode emission current via the heater current. However, residual gas poisoning of the cathode also affects
Output
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Fig. 3. Schematic of circuit used to control the electron gun. A single program voltage changes the beam output energy, which is read by the digital voltmeter (DVM). The power supply ratings are sufficient for output energies up to 40 eV.
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-5
-2
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Fig. 4. Beam profiles in the sample plane for perveances of 0.12 and 2 #perv. An increase in perveance above 0.1/~perv causes the beam size to increase dramatically due to space charge effects.
234
N.G. Stoffel, P.D. Johnson / Electron gun for inverse photoeraission i
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commercial electron gun currently available provides the perveance, convergence, and beam size of this electron gun. We have described the design procedure for this gun in a manner which, we hope, makes clear the relationship between the geometrical and electrical parameters and the performance of the gun. The output beam can be tailored by a similar design procedure to provide a space charge limited beam with different properties. As designed, the gun provides a nearly ideal excitation source for momentum-resolved inverse photoelectron spectroscopy. This work is supported by the Division of Materials Sciences, U S Department of Energy under contract DE-AC02-76CH00016.
References its emission current when it is operated below 1000°C. An emission stabilization feedback loop between the anode current ammeter and the cathode supply would be necessary to hold the beam current constant to a few percent over long time periods. Such a feedback loop could also be programmed to produce constant perveance with changing beam energy. The optimum focus potentiometer setting should be constant in principle, but does vary slightly with perveance above = 0.1 #perv due to space charge effects in the lens and near the focus. Since our grating IPES spectrometer requires an optimum focus at a fixed energy, we find it useful to place a 1 m m diameter Faraday collector on our sample manipulator. This collector can be moved to the sample position and the focus and aim of the gun can be optimized by maximizing current to the collector. Approximately 99% of the cathode current strikes the anode in our gun design. As a result, the output voltage of the gun as it is currently designed is limited to V0 < 50 eV at 0.1 # p e r v by the maximum tolerable heat load into the anode. With a smaller cathode, lower V J V o, or a redesigned anode this limit would be pushed considerably higher.
5. Conclusions The electron gun described in this paper attains a high perveance and brightness at very low energies. N o
[1] V. Dose, Appl. Phys. C14 (1981) 1381. [2] D.P. Woodruff, P.D. Johnson and N.V. Smith, J. Vac. Sci. Technol. A1 (1983) 1104. [3] Th. Fauster, F.J. Himpsel, J.E. Fischer and E.W. Plummer, Phys. Rev. Lett. 51 (1983) 430. [4] LR. Pierce, J. Appl. Phys. 11 (1940) 548. [5] W. Sinz, Nucl. Instr. and Meth. 187 (1981) 259. [6] C.D. Child, Phys. Rev. 32 (1911) 492; I. Langmuir, Phys. Rev. 2 (1913) 450. [7] J.A. Simpson and C.E. Kuyatt, Rev. Sci. Instr. 34 (1963) 265. [8] A spectrograph operating on a similar principle is described by Th. Fauster, F.J. Himpsel, J.J. Donelon and A. Marx, Rev. Sci. Instr. 54 (1983) 68. [9] J.R. Pierce, Theory and design of electron beams, 2nd ed. (Van Nostrand, Princeton, New Jersey, 1954). [10] Standard BaO Cathode (Std. 134) from Spectra-Mat, Inc. [11] E. Hatting and F.H. Read, Electrostatic lenses (Elsevier, Amsterdam, 1976). [12] P.T. Kirstein, G.S. Kino and W.E. Waters, Space charge flow (McGraw-Hill, New York, 1967) p. 131. [13] The estimates of the angular and spatial source widths given herein can be derived in a simple manner by assuming constant field between the anode and cathode and a Maxwellian distribution of velocities at the cathode and by using a thin lens approximation at the anode aperture. Ray tracings of the source verified these estimated widths. [14] Lens fields were calculated using the successive approximation method; see B. Paszkowski, Electron optics (Iliffe, London, 1968) p. 77.