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Anomalous high-frequency oscillations in a field emission tube and their significance in pulsed field emission
ARTICLE IN PRESS
Ultramicroscopy 107 (2007) 854–856 www.elsevier.com/locate/ultramic
Anomalous high-frequency oscillations in a field emission tube and their significance in pulsed field emission M.J. Hagmanna, D.A. Christensenb, M.S. Mousac, A. Baturind, E.P. Sheshind, a
NewPath Research, P.O. Box 3863, Salt Lake City, Utah 84110, USA Department of Bioengineering, University of Utah, Salt Lake City, Utah 84112, USA c Department of Physics, Mu’tah University, P.O. Box 7, Al-Karak, Jordan d Moscow Institute of Physics and Technology, 9 Institutski Lane, 141700 Moscow, Russia b
Abstract Relaxation oscillations occur when a capacitor is inserted in series with a field emission tube, a DC high-voltage power supply, and a ballast resistor. The waveform of these oscillations is highly reproducible with a dominant frequency of 200 MHz and a decay time of 20 ns. The peak current as high as 320 mA has been observed although the tungsten emitter is only rated for 10 mA. We have shown that these oscillations are due to a displacement current, charging of the anode-tip capacitance, and are not of a field emission origin. We conclude that the effects of displacement current should be considered in measurements of field emission with microsecond pulses, where high-current densities can be observed. r 2007 Published by Elsevier B.V. PACS: 84.30N; 79.70 Keywords: Oscillations; Field emission; Displacement current
1. Experimental observations It is commonly held that the field emission of electrons, by quantum tunnelling from an electrically conducting tip into vacuum, can produce a current density of up to 109 A/m2 in a steady state, or 1012 A/m2 when the DC supply is pulsed for microsecond operation [1]. For the case of tungsten emitters, these current densities would require an applied electric field at the surface of the metal of 4.7 and 8.6 V/nm, respectively [2]. We have studied relaxation oscillations that occur spontaneously in a field emission tube where the peak current density appears to be approximately 3 1013 A/m2. Fig. 1 shows one of three similar field emission tubes used in present studies. These tubes are rated for a maximum field emission current of 10 mA. The DC field emission current I was measured as a function of the anode-to-cathode potential difference V, and a leastCorresponding author. Tel.: +7 495 408 5944; fax: +7 495 409 9543.
E-mail address: [email protected] (E.P. Sheshin). 0304-3991/$ - see front matter r 2007 Published by Elsevier B.V. doi:10.1016/j.ultramic.2007.02.019
squares regression in a Fowler–Nordheim plot [3] was used to determine the parameters A and B, such that I ¼ AV 2 eB=V .
(1)
A potential of 6500 V gives the maximum rated current of 10 mA, and the Fowler–Nordheim analysis shows that this corresponds to an electric field of 4.8 V/nm at the tip with a current density of approximately 109 A/m2. After determining the Fowler–Nordheim parameters, the tube was tested in the following circuit: the negative terminal of a Fluke 410B high-voltage power supply was grounded, and a 100 M ballast resistor was connected to the positive terminal of this supply. However, the other lead from this resistor was accidentally connected to a pin that is adjacent to an anode pin on the header of the field emission tube instead of to an anode pin. One of the filament pins was connected to an analogous DC microammeter, and a 50 RF load connected this meter to ground in order to complete the circuit. The ballast resistor should have been connected to the anode pin, but the error in using an adjacent pin caused the relaxation oscillations.
ARTICLE IN PRESS M.J. Hagmann et al. / Ultramicroscopy 107 (2007) 854–856
855
Fig. 1. Scheme of field emission tube. The W-tip is mounted on a Wfilament loop at the right hand side. The anode is a nickel cylinder that is seen at the left hand side, and the apex of the tip is 1 mm from the center of the circular face of the anode. The anode is held in place by two wires that are connected to two of the pins on one header. Each end of the filament loop is connected to one pin of the other header, and the other pins are not used.
A Tektronix 2712 spectrum analyzer, a LeCroy 9362 oscilloscope, and an HP 54201A digitizing oscilloscope were connected across the RF load at different times to measure the time-dependent current. When the oscilloscope is set for relatively slow scans, it is seen that there is a series of regularly spaced short bursts of current. As the supply voltage is reduced, the peak current in these bursts remains constant, but these bursts are spaced further apart. For example, the time between the bursts is 260 ms with the supply set at 7900 V, 1.7 ms at 6500 V, and more than 1 min at 4600 V. Using a shorter time base, it is seen that these bursts have a reproducible waveform with a dominant frequency near 200 MHz and a decay time (1/e) of 20 ns. Fig. 2 shows the waveform with the supply set at 7200 V, but the shape and time scale of each burst are independent of that voltage. The peak current in this waveform is 154 mA, and values as high as 320 mA were seen in other measurements. The spectrum analyzer showed maxima in the power spectral density at 258, 570, and 882 MHz with nulls between these frequencies, followed by broad peaks at other frequencies up to the limit of 1.8 GHz for this instrument. Radiation that is caused by the current bursts was measured by using dipole antennas to couple the spectrum analyzer directly to the tube. 2. Mechanism of the spontaneous oscillations The oscillations occur only when the ballast resistor is connected to a pin that is adjacent to one of the two anode pins on the field emission tube, and this inadvertently inserts a capacitance of 0.2 pF in series with the field emitter. Thus, the anode has no connection to the external circuit, so it floats in potential and becomes negatively charged as it receives the electrons that are emitted by the nearby tip. This charging reduces the potential difference between the tip and the anode, which decreases the field emission current. Thus, the potential difference across the capacitance between the anode pin and the pin that is connected to the ballast resistor increases until breakdown occurs to discharge this capacitance. Shorting of the
Fig. 2. Waveform of a current burst measured at the load resistor. Applied voltage: 7200 V, peak current: 154 mA (values as high as 320 mA were observed in other measurements).
capacitance by this breakdown causes a sudden increase in the potential difference between the tip and the anode, which causes the observed current burst. These phenomena may be understood by using an equivalent circuit consisting of an ideal DC voltage source in series with a capacitor, a resistor, and an ideal field emission tube. The relatively slow charging of the capacitor during each cycle, but not the phenomena of breakdown, may then be modeled by using Eq. (1) for the current in this circuit. Thus, we obtain the following equation: i AV 2 dV h 1 þ 2RAV eB=V þ RAB eB=V þ eB=V ¼ 0. dt C (2) Let time t ¼ 0 be the beginning of a cycle, immediately following the previous breakdown, so that the voltage across the capacitance is zero. Then, Eq. (2) may be solved to give the following equation that may be used to determine the value of V during each cycle. C B=V C B=V 0 V RCB RCB e e 2RC ln ¼ t. þ AB AB V0 V V0 (3) Here, V0 is the value of the voltage V at time t ¼ 0, which may be determined by using iterations to solve the following equation, where VDC is the potential of the ideal voltage source. V 0 þ RAV 20 eB=V 0 ¼ V DC .
(4)
Fig. 3 shows the values of the anode–cathode potential difference calculated for the beginning (t ¼ 0) and the end (t ¼ T) of each cycle between two consecutive current bursts, using different values for the potential of the ideal voltage source VDC, which determines the duration of the cycle. These calculations, which were made using Eqs. (3) and (4), show that the bursts are spaced further apart as the supply voltage is reduced, which agrees with our
ARTICLE IN PRESS 856
M.J. Hagmann et al. / Ultramicroscopy 107 (2007) 854–856
3. Summary
Fig. 3. Values of the anode–cathode potential difference calculated for the beginning (t ¼ 0) and the end (t ¼ T) of each cycle between two consecutive current bursts. The ‘‘ideal voltage source’’ VDC determines the duration of the cycle.
measurements. Furthermore, these calculations show that at time t ¼ T, the potential across the capacitor is approximately 2000 V for all of the values of VDC in our experiments. We measured the potential between the anode pin and the adjacent pin that is connected to the ballast resistor, using an oscilloscope with a 100 k shunt to limit the effects of its input capacitance, and placing a 2.7 G resistor in series with the oscilloscope to limit loading of the circuit. Thus, we were able to verify that the waveform at this point is consistent with our calculations, and that breakdown across the pin-to-pin capacitor occurs when the potential reaches 2000 V. The measurements are also consistent with the calculations, showing that as the capacitor breaks down, the anode-tip potential rises by 1400 V, which causes the observed current burst. Since the dominant frequency in each current burst is approximately 200 MHz, the rise in the anode potential would cause dV/dt ¼ 1.8 1012 V/s, so the displacement current charging the anode-tip capacitance of 0.15 pF would be given by C dV/dt ¼ 270 mA. Thus, we conclude that the extremely large values for the peak current in each current burst are caused by displacement current and are not field emission.
Summarising, the displacement current could be easily confused with field emission in understanding our measurements, therefore, an enhanced attention should be paid to the possible effects of displacement current in the measurements that involve the microsecond pulses in field emission. Several papers describing measurements of current densities on the order of 1011 A/m2 with tungsten [4,5] and niobium [6] tips provide enough detail to estimate that the peak displacement current may be from 10% [4] to more than 50% [5,6] of the total measured current which is reported. A current density of up to 1014 A/m2 in pulsed field emission from tungsten [7] has been reported, the displacement current was not mentioned yet [4–7]. By contrast, two papers describing pulsed field emission from ferroelectrics mention the need to consider the displacement current, and also how this effect may be mitigated [8,9]. We conclude that the effects of displacement current should be generally considered in field emission with microsecond pulses, where high-current densities are expected. Acknowledgments The authors would like to thank Professor Richard Forbes for helpful discussions in regard to our measurements and their interpretation. A.B. and E.P.S. acknowledge the support by INTAS Ref. no. 04-78-7183. References [1] R. Gomer, Field Emission and Field Ionization, American Institute of Physics, New York, 1993. [2] M.J. Hagmann, Ultramicroscopy 79 (1999) 115. [3] R.G. Forbes, J. Vac. Sci. Technol. B 17 (1999) 534. [4] Y. Song, E. Garate, N. Rostoker, J. Appl. Phys. 76 (1994) 609. [5] W.P. Dyke, J.K. Trolan, Phys. Rev. 89 (1953) 799. [6] S.I. Shkuratov, S.A. Barengolts, E.A. Litvinov, J. Vac. Sci. Technol. B 13 (1995) 1960. [7] N. Anazawa, R. Aihara, S. Ohta, J. Phys. E: Sci. Instrum. 8 (1975) 971. [8] P. Lubicki, in: Proceedings of the 1998 IEEE Annual Conference on Electrical Insulation and Dielectric Phenomena, vol. 1, 1998, pp. 296. [9] J.-I. Asano, M. Okuyama, Y. Hamakawa, Jpn. J. Appl. Phys. 32 (1993) 396.
Ultramicroscopy 107 (2007) 854–856 www.elsevier.com/locate/ultramic
Anomalous high-frequency oscillations in a field emission tube and their significance in pulsed field emission M.J. Hagmanna, D.A. Christensenb, M.S. Mousac, A. Baturind, E.P. Sheshind, a
NewPath Research, P.O. Box 3863, Salt Lake City, Utah 84110, USA Department of Bioengineering, University of Utah, Salt Lake City, Utah 84112, USA c Department of Physics, Mu’tah University, P.O. Box 7, Al-Karak, Jordan d Moscow Institute of Physics and Technology, 9 Institutski Lane, 141700 Moscow, Russia b
Abstract Relaxation oscillations occur when a capacitor is inserted in series with a field emission tube, a DC high-voltage power supply, and a ballast resistor. The waveform of these oscillations is highly reproducible with a dominant frequency of 200 MHz and a decay time of 20 ns. The peak current as high as 320 mA has been observed although the tungsten emitter is only rated for 10 mA. We have shown that these oscillations are due to a displacement current, charging of the anode-tip capacitance, and are not of a field emission origin. We conclude that the effects of displacement current should be considered in measurements of field emission with microsecond pulses, where high-current densities can be observed. r 2007 Published by Elsevier B.V. PACS: 84.30N; 79.70 Keywords: Oscillations; Field emission; Displacement current
1. Experimental observations It is commonly held that the field emission of electrons, by quantum tunnelling from an electrically conducting tip into vacuum, can produce a current density of up to 109 A/m2 in a steady state, or 1012 A/m2 when the DC supply is pulsed for microsecond operation [1]. For the case of tungsten emitters, these current densities would require an applied electric field at the surface of the metal of 4.7 and 8.6 V/nm, respectively [2]. We have studied relaxation oscillations that occur spontaneously in a field emission tube where the peak current density appears to be approximately 3 1013 A/m2. Fig. 1 shows one of three similar field emission tubes used in present studies. These tubes are rated for a maximum field emission current of 10 mA. The DC field emission current I was measured as a function of the anode-to-cathode potential difference V, and a leastCorresponding author. Tel.: +7 495 408 5944; fax: +7 495 409 9543.
E-mail address: [email protected] (E.P. Sheshin). 0304-3991/$ - see front matter r 2007 Published by Elsevier B.V. doi:10.1016/j.ultramic.2007.02.019
squares regression in a Fowler–Nordheim plot [3] was used to determine the parameters A and B, such that I ¼ AV 2 eB=V .
(1)
A potential of 6500 V gives the maximum rated current of 10 mA, and the Fowler–Nordheim analysis shows that this corresponds to an electric field of 4.8 V/nm at the tip with a current density of approximately 109 A/m2. After determining the Fowler–Nordheim parameters, the tube was tested in the following circuit: the negative terminal of a Fluke 410B high-voltage power supply was grounded, and a 100 M ballast resistor was connected to the positive terminal of this supply. However, the other lead from this resistor was accidentally connected to a pin that is adjacent to an anode pin on the header of the field emission tube instead of to an anode pin. One of the filament pins was connected to an analogous DC microammeter, and a 50 RF load connected this meter to ground in order to complete the circuit. The ballast resistor should have been connected to the anode pin, but the error in using an adjacent pin caused the relaxation oscillations.
ARTICLE IN PRESS M.J. Hagmann et al. / Ultramicroscopy 107 (2007) 854–856
855
Fig. 1. Scheme of field emission tube. The W-tip is mounted on a Wfilament loop at the right hand side. The anode is a nickel cylinder that is seen at the left hand side, and the apex of the tip is 1 mm from the center of the circular face of the anode. The anode is held in place by two wires that are connected to two of the pins on one header. Each end of the filament loop is connected to one pin of the other header, and the other pins are not used.
A Tektronix 2712 spectrum analyzer, a LeCroy 9362 oscilloscope, and an HP 54201A digitizing oscilloscope were connected across the RF load at different times to measure the time-dependent current. When the oscilloscope is set for relatively slow scans, it is seen that there is a series of regularly spaced short bursts of current. As the supply voltage is reduced, the peak current in these bursts remains constant, but these bursts are spaced further apart. For example, the time between the bursts is 260 ms with the supply set at 7900 V, 1.7 ms at 6500 V, and more than 1 min at 4600 V. Using a shorter time base, it is seen that these bursts have a reproducible waveform with a dominant frequency near 200 MHz and a decay time (1/e) of 20 ns. Fig. 2 shows the waveform with the supply set at 7200 V, but the shape and time scale of each burst are independent of that voltage. The peak current in this waveform is 154 mA, and values as high as 320 mA were seen in other measurements. The spectrum analyzer showed maxima in the power spectral density at 258, 570, and 882 MHz with nulls between these frequencies, followed by broad peaks at other frequencies up to the limit of 1.8 GHz for this instrument. Radiation that is caused by the current bursts was measured by using dipole antennas to couple the spectrum analyzer directly to the tube. 2. Mechanism of the spontaneous oscillations The oscillations occur only when the ballast resistor is connected to a pin that is adjacent to one of the two anode pins on the field emission tube, and this inadvertently inserts a capacitance of 0.2 pF in series with the field emitter. Thus, the anode has no connection to the external circuit, so it floats in potential and becomes negatively charged as it receives the electrons that are emitted by the nearby tip. This charging reduces the potential difference between the tip and the anode, which decreases the field emission current. Thus, the potential difference across the capacitance between the anode pin and the pin that is connected to the ballast resistor increases until breakdown occurs to discharge this capacitance. Shorting of the
Fig. 2. Waveform of a current burst measured at the load resistor. Applied voltage: 7200 V, peak current: 154 mA (values as high as 320 mA were observed in other measurements).
capacitance by this breakdown causes a sudden increase in the potential difference between the tip and the anode, which causes the observed current burst. These phenomena may be understood by using an equivalent circuit consisting of an ideal DC voltage source in series with a capacitor, a resistor, and an ideal field emission tube. The relatively slow charging of the capacitor during each cycle, but not the phenomena of breakdown, may then be modeled by using Eq. (1) for the current in this circuit. Thus, we obtain the following equation: i AV 2 dV h 1 þ 2RAV eB=V þ RAB eB=V þ eB=V ¼ 0. dt C (2) Let time t ¼ 0 be the beginning of a cycle, immediately following the previous breakdown, so that the voltage across the capacitance is zero. Then, Eq. (2) may be solved to give the following equation that may be used to determine the value of V during each cycle. C B=V C B=V 0 V RCB RCB e e 2RC ln ¼ t. þ AB AB V0 V V0 (3) Here, V0 is the value of the voltage V at time t ¼ 0, which may be determined by using iterations to solve the following equation, where VDC is the potential of the ideal voltage source. V 0 þ RAV 20 eB=V 0 ¼ V DC .
(4)
Fig. 3 shows the values of the anode–cathode potential difference calculated for the beginning (t ¼ 0) and the end (t ¼ T) of each cycle between two consecutive current bursts, using different values for the potential of the ideal voltage source VDC, which determines the duration of the cycle. These calculations, which were made using Eqs. (3) and (4), show that the bursts are spaced further apart as the supply voltage is reduced, which agrees with our
ARTICLE IN PRESS 856
M.J. Hagmann et al. / Ultramicroscopy 107 (2007) 854–856
3. Summary
Fig. 3. Values of the anode–cathode potential difference calculated for the beginning (t ¼ 0) and the end (t ¼ T) of each cycle between two consecutive current bursts. The ‘‘ideal voltage source’’ VDC determines the duration of the cycle.
measurements. Furthermore, these calculations show that at time t ¼ T, the potential across the capacitor is approximately 2000 V for all of the values of VDC in our experiments. We measured the potential between the anode pin and the adjacent pin that is connected to the ballast resistor, using an oscilloscope with a 100 k shunt to limit the effects of its input capacitance, and placing a 2.7 G resistor in series with the oscilloscope to limit loading of the circuit. Thus, we were able to verify that the waveform at this point is consistent with our calculations, and that breakdown across the pin-to-pin capacitor occurs when the potential reaches 2000 V. The measurements are also consistent with the calculations, showing that as the capacitor breaks down, the anode-tip potential rises by 1400 V, which causes the observed current burst. Since the dominant frequency in each current burst is approximately 200 MHz, the rise in the anode potential would cause dV/dt ¼ 1.8 1012 V/s, so the displacement current charging the anode-tip capacitance of 0.15 pF would be given by C dV/dt ¼ 270 mA. Thus, we conclude that the extremely large values for the peak current in each current burst are caused by displacement current and are not field emission.
Summarising, the displacement current could be easily confused with field emission in understanding our measurements, therefore, an enhanced attention should be paid to the possible effects of displacement current in the measurements that involve the microsecond pulses in field emission. Several papers describing measurements of current densities on the order of 1011 A/m2 with tungsten [4,5] and niobium [6] tips provide enough detail to estimate that the peak displacement current may be from 10% [4] to more than 50% [5,6] of the total measured current which is reported. A current density of up to 1014 A/m2 in pulsed field emission from tungsten [7] has been reported, the displacement current was not mentioned yet [4–7]. By contrast, two papers describing pulsed field emission from ferroelectrics mention the need to consider the displacement current, and also how this effect may be mitigated [8,9]. We conclude that the effects of displacement current should be generally considered in field emission with microsecond pulses, where high-current densities are expected. Acknowledgments The authors would like to thank Professor Richard Forbes for helpful discussions in regard to our measurements and their interpretation. A.B. and E.P.S. acknowledge the support by INTAS Ref. no. 04-78-7183. References [1] R. Gomer, Field Emission and Field Ionization, American Institute of Physics, New York, 1993. [2] M.J. Hagmann, Ultramicroscopy 79 (1999) 115. [3] R.G. Forbes, J. Vac. Sci. Technol. B 17 (1999) 534. [4] Y. Song, E. Garate, N. Rostoker, J. Appl. Phys. 76 (1994) 609. [5] W.P. Dyke, J.K. Trolan, Phys. Rev. 89 (1953) 799. [6] S.I. Shkuratov, S.A. Barengolts, E.A. Litvinov, J. Vac. Sci. Technol. B 13 (1995) 1960. [7] N. Anazawa, R. Aihara, S. Ohta, J. Phys. E: Sci. Instrum. 8 (1975) 971. [8] P. Lubicki, in: Proceedings of the 1998 IEEE Annual Conference on Electrical Insulation and Dielectric Phenomena, vol. 1, 1998, pp. 296. [9] J.-I. Asano, M. Okuyama, Y. Hamakawa, Jpn. J. Appl. Phys. 32 (1993) 396.