Development of a High-Precision Power Supply and Current Measuring Device for Field Emission Spectroscopy∗

Considerable attention is currently being given to nanotip electron sources. These have a number of desirable emission characteristics, including high current density at low voltage, a small source size leading to high coherency, and narrow confinement of the electron beam. To date, we have developed a high-precision energy analyzer capable of obtaining the emission spectrum of the electrons emitted from a nanotip electron source. To improve the resolution of the analyzer, we design an optimum energy analyzer electrode and a more stable power supply. Moreover, the beam current measurement circuit is needed to facilitate the adjustment of the optical axis. Therefore, we have also developed a computer-controlled power supply with low noise, low ripple, and stable output voltage, together with a current measurement circuit and its associated software. [DOI: 10.1380/ejssnt.2016.97]


I. INTRODUCTION
Nanotip electron sources are very sharp electron emitters that are used to improve the performance of electron optical apparatus.Single-atom electron sources (SAESs) [1,2] emit electrons from the terminal atom of a nanopyramid-shaped tip.SAESs have characteristics superior to those of conventional electron sources, including high brightness and high coherence, and are expected to become the preferred stable electron source in future electron optical systems.Therefore, this work aims to determine the physical characteristics and the energy spectrum of an electron beam emitted from an SAES.
We have proceeded in the preparation of a field emission spectroscopy (FES) to acquire SAES energy spectra.To further improve the resolution of the energy analyzer, we must design an optimum energy analyzer electrode and a more stable power supply.Furthermore, an electrode current measurement circuit is needed to facilitate the adjustment of the optical axis.In our FES apparatus, 17 power supplies, 17 voltmeters, and 8 ammeters are used.Connecting these instruments to a computer and controlling them simultaneously are difficult using a commercial instrument.The power supply must output a constant voltage within a narrow range.The voltage range of commercial power supplies is too wide, and the voltage supplied has a large ripple.An onboard-type power supply has the same drawback.Although a battery can supply a stable constant voltage, the voltage unavoidably drops as the charge becomes exhausted, and frequent exchange of batteries is inefficient.The current flowing through an electrode in the FES apparatus is less than one nanoampere, and the ammeter must be capable of measuring this small current while a constant voltage is applied to the electrode.This is difficult to achieve using a commercial ammeter.We therefore develop a computer-controlled power supply with low noise, low rippling, and a stable output voltage for use with the current measurement circuit and its software.

II. FIELD EMISSION SPECTROSCOPY
FES is a technique that acquires an energy spectrum of the electrons emitted from a field emitter.Figure 1 shows a schematic diagram of the FES apparatus we developed.The field emitter is grounded to earth, whereas the extractor is kept floating at a positive potential of approximately 1 kV to extract electrons from the field emitter and the screen at 2 kV to display the emission pattern.A 5-mm diameter pinhole at the center of the fluorescent screen is used to introduce the electrons into the two-stage cylindrical deflector analyzer (CDA).In the two-stage CDA, the electrons are dispersed and the electrons that pass through the final slit are counted by the channeltron.The two CDAs have an inner radius of R 1 = 37.5 mm, an outer radius of R 2 = 67.5 mm, a central path radius of r c = 50.3mm, and a deflection angle of 107.5 • .The width of all the slits is 0.45 mm.

III. PRINCIPLES OF THE CDA
Figure 2 shows the principles of the CDA, where R 1 and R 2 represent the inner and outer radius of the CDA, respectively.In Fig. 2, the ideal rotational symmetry (r, θ, z) is treated as a coordinate system.
In Fig. 2, E 0 represents the energy of an electron that enters the CDA from the initial position O with an initial incident angle of 0, and then travels along the central path.E 0 is the pass energy.Each electron enters the CDA from an arbitrary initial position P 0 with an arbitrary initial energy E and an arbitrary initial incident angle α 0 .At a pass energy of E 0 , the initial energy E is expressed as where ∆E is the deviation from the pass energy E 0 .The position of the electron in the CDA is defined as P(r, θ).At a central path radius of r c , r can also be expressed as where ρ is the deviation from the central path r c and is equal to ∆r 1 at the initial position (see Fig. 2).The equation of motion of a circulating electron of radius r is where m is the mass, v is the rotational speed, e is the electron charge, and F r is the radial component of the electric field.In a cylindrical field, the electric field F r can also be expressed as where ∆V is the potential difference between the inner and outer electrodes.The pass energy E 0 can be obtained from Eqs. ( 3) and (4) without considering the radius r: Assuming that the electric field in the CDA is an ideal cylindrical field and that the z-axis component of the electric field is 0, we can obtain the equation of motion of an electron in the CDA as follows: Due to space limitations, the calculation process is not shown here, but using the Taylor expansion around r c [3][4][5], Eq. ( 6) can be solved as Equation (7) gives the trajectory equation up to the second order in α 0 .In Eq. ( 7), the first and second terms on the right-hand side represent the deviations with respect to ∆r 1 and ∆E, respectively.The third and subsequent terms represent the deviations with respect to α 0 .The condition under which the third term on the right-hand side becomes 0 is given by Substituting Eq. ( 8) into Eq.( 7), we can express the energy deviation ∆E as We now consider the case that the exit slits with the slit width s is placed at a position θ = 127 • .The maximum and minimum energy deviations ∆E ± , under which electrons can pass through the exit slit of the CDA, are expressed as where s is the width of the entrance or exit slit of the CDA (see Fig. 3), and α max is the maximum value of α 0 .The base width ∆E B of the transmitted energy distribution is Electrons whose energy falls within ∆E B can pass though the exit slit.The energy resolution of the CDA can be approximated by ∆E B /2 because the energy resolution is determined by the full width at half maximum (FWHM) of the transmitted energy distribution [3].
In our FES, taking careful account of the fringing field at the vicinity of slits [6,7], the deflection angle θ and the ratio in the CDA radii R 2 /R 1 are determined to be 107.5 • and 1.8, respectively.

IV. COMPUTER-CONTROLLED POWER SUPPLY
Under the following conditions: the maximum value of the initial incident angle α max = 0, the slit width s = 0.45 mm, the central path radius r c = 50.3mm, and the pass energy E 0 = 0.3 eV, we substitute these values into Eq.( 11 Considering the FWHM, we can calculate the energy resolution of the single CDA as 2.7 meV.Since our FES uses a two-stage CDA, the energy resolution is estimated to be 1.4 meV.However, in practice, other factors such as the signal-to-noise ratio (S/N) and the effect of the fringing field at the vicinity of the slits must be taken into account.
We therefore set the target value of the energy resolution of our FES apparatus at 3 meV.The potential difference ∆V between the CDA electrodes is calculated by Figure 4 shows the computer-controlled power supply that we developed.To obtain an energy resolution of 3 meV, we limit the constant voltage noise to within 1 mVpp.
The FES apparatus has 17 electrodes.Each electrode has a different voltage, and these have to be set simultaneously.Currents can be measured at eight of the electrodes (three slit electrodes and five electrostatic lens electrodes).The output voltage is generated by a 16-bit D/A converter.However, the D/A converter usually has noise greater than 30 mVpp.To suppress this noise, the output voltage is supplied by a specially designed buffer amplifier A hi-mode circuit capable of supplying the high voltage required (13-50 V) is used for the deceleration of the electrostatic lens.

V. DEVELOPMENT OF THE BUFFER AMPLIFIER CIRCUIT
The noise in the voltage output from the D/A converter mainly comprises ripple noise and common-mode noise.To obtain an energy resolution of 3 meV, the ripple and common-mode noise must be limited to within a maximum of 1 mVpp.In our FES apparatus, a voltage in the range −5 to 15 V must be supplied to each electrode, but the D/A converter cannot achieve more than ±10 V. We therefore develop a buffer amplifier circuit in which the ripple and common-mode noise can be limited within 1 mVpp and the output voltage has an arbitrary range.In practice, 17 buffer amplifier circuits are needed, as each electrode has a unique voltage.
Figure 5 shows a schematic diagram of the buffer amplifier circuit, where V DA , V RS , and V BA represent the output voltages from the D/A converter, the reference voltage unit, and the buffer amplifier circuit, respectively.First, the common-mode noise is canceled and removed by the differential amplifier, and the ripple noise is reduced by the low-pass filter (LPF).Next, an arbitrary voltage V RS is generated in the reference voltage unit, and the ripple noise in V RS is reduced by the LPF.The filtered reference V RS is added to the filtered D/A output V DA by the adder unit, and the residual ripple noise is further reduced by the final LPF.Finally, the V BA is outputted from the buffer amplifier circuit.
Figures 6 (a that our buffer amplifier circuit successfully reduced ripple noise.

VI. DEVELOPMENT OF THE CURRENT MEASUREMENT CIRCUIT
Adjusting the optical axis of the analyzer can be a complex task because of the curved optical axis, such as a plane mirror analyzer (PMA), a cylindrical mirror analyzer (CMA), a spherical deflector analyzer (SDA) [8,9].If the electrons fail to reach the channeltron of an analyzer, it is difficult to identify their final position.If the current at the electrode or slit reached by the electrons can be measured, their final location can be found, making it easy to adjust the optical axis.The current at the electrode or slit, i.e., the electrode current, is less than one nanoampere (typically, 10 −9 to 10 −13 A), because most of the electron beam current flows to earth via the fluorescent screen, and the electron beam which passes through the screen pinhole is reduced by collisions at the inner or outer electrode of the CDA.The electrode current must be measured while a constant voltage is applied to the electrode.
Figure 7 shows a schematic diagram of the current measurement circuit.The potential difference between the two input terminals is automatically adjusted to zero (imaginary short) using the feedback loop of an operational amplifier (op-amp).The input impedance of the op-amp is very high, and the electron current injected into the electrode flows via the shunt resistor into the output terminal of the op-amp in the current measurement circuit.Note that the direction of flow of the current is opposite to that of the electron current.The voltage generated between the ends of the shunt resistor is outputted via two buffer circuits and a differential amplifier circuit to the A/D converter.Therefore, the electrode current must be measured while a constant voltage is being applied to the electrode.

VII. TESTING THE CURRENT MEASUREMENT CIRCUIT
We then test the current measurement circuit that we developed.In principle, the current measurement circuit should be tested by irradiating it with an electron beam from the field emitter in the FES apparatus.However, our FES apparatus has not been fully completed.Instead, we test the current measurement circuit by replacing the electron beam irradiation system with a 10 GΩ resistor.Then, we describe the result that the current measurement circuit is used to measure the beam current from the electron gun, from a point of a practical view.

A. Test of the operating principle
Figure 8 shows a schematic diagram of the circuit used to test our current measurement circuit.In Fig. 8, V in is the input voltage to the current measurement circuit, and V moni and I moni represent the measured output voltage and the electrode current of the electrode, respectively.A pico-ammeter is connected between the equivalent resistor and the earth to measure the actual electrode current I p .

Output voltage
We first check that the measured output voltage V moni is always identical to the input voltage V in .Figure 9 shows the measured output voltage V moni versus the input voltage V in .From the figure, it can be seen that the slope of the graph is substantially 1, suggesting that the two voltages are indeed always identical.

Electrode current
Next, we check that the measured electrode current I moni is identical to the electrode current I p measured by the pico-ammeter.Figure 10 shows the measured and actual electrode currents as a function of the input voltage V in .The results show good agreement between the measured electrode current I moni and the actual electrode current I p at every input voltage.This confirmed that the electrode current could be precisely measured using our current measurement circuit.
These results suggest that we have, in principle, succeeded in developing a current measurement circuit.

B. Electron beam current measurement
The current measurement circuit is then used to measure the screen current in a conventional field emission microscopy (FEM) system.Figure 11 shows the FEM system, which comprises an emitter, an extractor, and a screen.The emitter is a conventional tungsten tip with  a curvature radius at the emitter apex of the order of 0.1 µm.Electrons are emitted from the apex to the screen by an extractor voltage V ext .The experimental procedure is as follows.To accurately measure the screen current I p (the beam current), a pico-ammeter is connected between the screen and the earth (a).The pico-ammeter is then replaced by our current measurement circuit (b) and the screen current I moni is measured again.The value recorded by the measurement circuit is compared with that measured by the pico-ammeter.Figure 12 shows the I-V characteristics of the screen current using our measurement circuit and the pico-ammeter.As can be seen, the measured screen current I moni agrees well with the actual screen current I p .This confirmed that our current measurement circuit could precisely measure the electrode current in an actual electron beam irradiation system.Next, we test whether the screen current can precisely be measured using our current measurement circuit (c) when an arbitrary input voltage V in is applied to the screen.Figure 13 shows the screen current I ′ moni as a function of the input voltage V in .As shown in Fig. 13, we can see that the graph has a slight slope.As this reason, the following process is considered.Secondary electrons are generated by the irradiation of the electron beam on the screen.The generated secondary electrons are easily trapped with the screen as a positive voltage is applied to the screen.Therefore, as shown in Fig. 13, it is found that the graph has a slight slope.As above mentioned, this result demonstrates that the electrode current can precisely be measured with our current measurement circuit despite the application of voltage to the electrode.

VIII. CONCLUSIONS
We developed 17 buffer amplifier circuits that were able to suppress the noise from a D/A converter.
We developed eight current measurement circuits that allowed the electrode current to precisely be measured while a constant voltage was being applied to the electrode.Our current measurement circuit was tested by replacing the electron beam irradiation system with an equivalent resistor with a resistance of 10 GΩ.These results demonstrated, in principle, that an electrode current could precisely be measured by our current measurement circuit.We then used the circuit to measure the screen current in a conventional FEM system.The re-sults demonstrated that the electrode current could precisely be measured using our current measurement circuit, even when a voltage was being applied to the electrode of the FEM system.As a result, we have succeeded in developing the current measurement circuit.
A future challenge is to measure the energy spectrum of an electron beam emitted from an SAES using our FES apparatus.

FIG. 1 .
FIG. 1. Schematic diagram of the FES.The 2nd CDA has the same dimensions as the 1st CDA.All the silts have the same width.
), and calculate ∆E B as