Experimental investigations on miniaturized high-frequency vacuum electron devices

Abstract

We investigated the foundations for high-frequency vacuum electron devices experimentally, with emphasis on deep etch X-ray lithography: lithographie, galvanoformung, abformung (LIGA) to fabricate a miniaturized interaction circuit and a photonic crystal (PC) resonator to excite a stable high-order mode. The successful operation of a LIGA-fabricated folded-waveguide traveling-wave tube was reported. From such physical considerations as Debye length and photonic band gap, we proposed a reflex klystron adopting a cold cathode and a PC resonator.

Full text

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Above the W-band, traditional machining is not feasible
for the circuit fabrication because the dimensions of interac-
tion-circuits should become smaller as the radiation frequency
increases. Recent developments in microelectromechanical
Proof
the 2-D structure of the PC cavity improves its compatibility
with MEMS fabrication technologies. A PC reflex klystron
employing a cold cathode is under development using the
LIGA fabrication. As a preliminary study, the physical prop-
erties of the PC resonator and the coupling to the fundamental
guiding mode are analyzed theoretically and experimentally. A
X-band PC reflex klystron is examined by a three-dimensional
(3-D) particle-in-cell (PIC) code, MAGIC3D [24], for the
IEEE TRANSACTIONS ON PLASMA SCIENCE1
Experimental Investigations on Miniaturized
High-Frequency Vacuum Electron Devices
Seong-Tae Han, Student Member, IEEE, Seok-Gy Jeon, Young-Min Shin, Kyu-Ha Jang, Jin-Kyu So, Jong-Hyun Kim,
Suk-Sang Chang, and Gun-Sik Park, Member, IEEE
Abstract—We investigated the foundations for high-frequency
vacuum electron devices experimentally, with emphasis on deep
etchX-raylithography:lithographie,galvanoformung,abformung
(LIGA) to fabricate a miniaturized interaction circuit and a pho-
tonic crystal (PC) resonator to excite a stable high-order mode.
The successful operation of a LIGA-fabricated folded-waveguide
traveling-wave tube was reported. From such physical considera-
tions as Debye length and photonic band gap, we proposed a reflex
klystron adopting a cold cathode and a PC resonator.
Index Terms—Debye length, deep etch X-ray lithography:
lithographie, galvanoformung, abformung (LIGA), photonic
crystal (PC) resonator, terahertz.
I. INTRODUCTION
I
principle, has been growing [1]–[4]. There have been many
efforts to generate terahertz radiation, from quantum cascade
lasers (QCLs) using the tiny sub-bands in the semiconductor
quantum wells, to free electron lasers (FELs) and to Gyrotrons,
using the radiation caused by the periodic motion of an electron
beam in a vacuum [5]–[8]. However, the semiconductor devices
have fundamental limits, such as low-operating temperature
and low-output power, and the vacuum deviceshave restrictions
in application due to the bulk magnets. Nevertheless, a number
of outstanding legacies of vacuum electronics technology, such
as the lack of ohmic loss and high-breakdown strength, promise
to provide the access to high-frequency regimes with high
efficiency and power-density compared to solid state devices
[9], [10]. Therefore, considerable efforts have been made on
the fabrication of miniature high-frequency and high-powered
vacuum tubes [11], [12].
NTEREST in terahertz frequencies, located between the
boundaries of the electronic principle and the photonic
Manuscript received September 1, 2004; revised November 29, 2004. This
work wassupported in partby the Ministry ofScience and Technology(MOST)
of the Republic of Korea through the National Research laboratory Program.
This work was also supported by the Nano-Systems Institute (NSI-NCRC) pro-
gram sponsored by the Korea Science and Engineering Foundation (KOSEF).
Experiments at Pohang Light Source (PLS) were supported in part by MOST
and POSCO <<AUTHOR: Please define acronym>>.
S.-T. Han, S.-G. Jeon, Y.-M. Shin, K.-H. Jang, J.-K. So, and G.-S. Park are
with the School of Physics and Nano-System Institute (NSI-NCRC), Seoul Na-
tional University, Seoul 151-742, Korea (e-mail: gunsik@plaza.snu.ac.kr).
J.-H. Kim and S.-S. Chang are with the Pohang Accelerator Laboratory,
POSTECH, Pohang 790-784, Korea.
Digital Object Identifier 10.1109/TPS.2005.844529
system (MEMS) technologies have encouraged researchers to
investigate miniature high-frequency active electron devices,
as well as passive devices [13]–[15]. Among various MEMS
techniques, deep etch X-ray lithography: lithographie, gal-
vanoformung, abformung (LIGA) has advantages due to its
high aspect ratio, sidewall smoothness, and structure height
[16]–[18]. Therefore, we fabricated a Ka-band folded-wave-
guide traveling-wave tube (TWT) by the lithographic process
using the synchrotron X-ray source at the Pohang light source
(PLS). The successful operation of the LIGA-based vacuum
electron device is reported in Section II.
As the operation frequency increases up to terahertz, the
required current density for showing collective behavior
increases drastically [19]. Hence, the electron sources for
terahertz regimes must be capable of generating current density
of at least 100–1000
. Such current densities at low-op-
erating voltage may be generated by employing cold cathodes,
such as carbon nanotubes and Spindt-type tips [20], [21]. In
Section III, we discuss the current density requirement in terms
of Debye length and investigate the possibility of a cold cathode
for the electron sources of high-frequency vacuum tubes.
In a miniature vacuum electron device operating at frequen-
cies above hundreds of gigahertz, the scaled-down size of its
beam tunnel restricts the available beam current which, in turn,
reduces the maximum achievable power. This becomes more
serious in a TWT due to its long drift path of electrons for the
distributed interaction between the electron beam and the elec-
tromagnetic wave. Therefore, an array-operation of miniature
vacuum electron devices could be a natural way of overcoming
the restrictions on the power of individual miniature devices,
but it gets extremely difficult to match the phases of each device
correctly. As an alternative to the array-operation, we proposed
a reflex klystron operating at an ultrahigh order transverse mag-
netic (TM) mode by adopting a photonic crystal (PC) cavity.
Thetwo-dimensional(2-D)PCconstitutingthecavityformsthe
photonic bandgap (PBG) [22], [23], which suppresses parasitic
modes and excites a selected high-order TM dominantly. This
dominant high-order resonant mode is coupled to an external
system simply through a line defect in the 2-D PC. Moreover,
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dling at higher frequencies.
Fig. 1 shows the top and bottom halves of a waveguide TWT
circuit fabricated by the LIGA process. As depicted in Fig. 2(a),
the LIGA-fabricated single-stage Ka-band amplifier shows a
linear gain of 15 dB and a narrow bandwidth of 1.7% with a
12.4-kV, 47-mA electron beam. In Fig. 2(b), the drive curve
of the amplifier exhibits good linearity in AM–AM conversion.
Maximum power, up to 20 W, was obtained at 35 GHz with
29-dBminputpower,wheretheconversionefficiencywasabout
3.4%.The experimentalresultswere comparedwith predictions
made by MAGIC3D, and show good agreement, as depicted in
Figs. 2(a) and (b).
Proof
between the circular beam tunnel and the square beam tunnel
except for a small reduction of output power originating from
the reduction of the beam filling factor. It thus supports the fea-
sibility of employing thesquare beam tunnel for two-step LIGA
fabrication. We have now initiated the process for the develop-
ment of two-step LIGA-fabricated W-band tubes.
2 IEEE TRANSACTIONS ON PLASMA SCIENCE
Fig. 1.
which is an electric-field-plane (E-plane) bended folded waveguide with 56
periods. Lowest transverse electric (TE) mode, TE10, propagates along the
waveguide. Electron sees a transverse magnetic (TM) mode in terms of space
harmonic when it enters the beam holes.
Interaction circuit consists of LIGA-fabricated two symmetric halves,
proof-of-concept of the high-order TM mode oscillation in a
reflex klystron. Those results are given in Section IV.
II. LIGA-FABRICATED TWT
The LIGA process involves a thick X-ray resist, high-en-
ergy X-ray radiation exposure, and development to arrive at a
3-D resist structure. Subsequent metal deposition fills the resist
mold with a metal and, after resist removal, the final structure
is a freestanding metal one. The range of possible sizes in all
three dimensions covers micron and submicron ranges in the
horizontal dimensions, and millimeter and centimeter ranges
in the vertical dimensions with a high aspect ratio and abso-
lutetolerance.Therefore,wetriedfabricatingaKa-bandfolded-
waveguide traveling-wave tube to demonstrate its capability for
miniaturized high-frequency vacuum electron devices.
A. LIGA-Based Ka-Band Folded-Waveguide TWT
A folded-waveguide TWT is a promising high-frequency
miniature radiation source with relatively high average power,
because it has a simple structure compatible with lithographic
processes and its all-metal structure enables high power han-
B. Two-Step LIGA
As frequency goes up, the diameter of the electron beam
tunnel is reduced, i.e., the diameter for a W-band TWT is about
400
. Misalignment of the beam tunnel by conventional
Fig. 2.
function of driving frequency, where the input power was fixed to 20 dBm. (b)
Output power as a function of input power at 35 GHz.
(a) Gain of the LIGA-fabricated folded-waveguide TWT amplifier as a
machining, such as electrical discharge machining (EDM) and
grinding, can degrade electron beam transmission even though
other parts of circuit are built by LIGA with accurate dimen-
sions [18]. As for higher frequencies, above the W-band, it is
almost impossible to fabricate a beam tunnel by conventional
machining. Therefore, we have proposed a two-step LIGA
[25] with a square beam tunnel as a breakthrough alternative
technique.
Fig. 3 shows the results of MAGIC3D simulation for the
scaled W-band version of a Ka-band folded waveguide back-
ward wave oscillator (BWO) [26]. There is no big difference
III. COLLECTIVE BEHAVIOR CRITERION
There is a minimum current density necessary to achieve col-
lective behavior that becomes important at high frequencies.

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isotropic Maxwellian velocity distribution at temperature
we may write
Proof
vacuum electron devices. By adopting a cold cathode, the min-
imum current density can be reduced by about an order of mag-
nitude. Recent developments in field emitter arrays, such as
Spindt-type tips and carbon nanotubes, are promising for future
applications.
HAN et al.: EXPERIMENTAL INVESTIGATIONS ON MINIATURIZED HIGH-FREQUENCY VACUUM ELECTRON DEVICES3
Fig. 3.
current for W-band folded waveguideBWOs.The diameter ofthe circular beam
tunnel and the width of the square beam tunnel are same as 440 ??.
MAGIC 3-D simulation results; output power versus electron beam
Letusconsideranensembleofelectronsmovingsynchronously
with a traveling-wave field. The equation of motion of th elec-
tron in the presence of the density fluctuation by the traveling-
wave field leads to the motion of a harmonic oscillator with a
resonance frequency of
in the moving frame with the beam
velocity, where we neglected the thermal motion of electrons
which is destructive to the collective behavior. Now let us con-
sideranassemblyofelectronswithfinitetemperature.Pinesand
Bohm[27]expandedthepotentialenergyofinteractionbetween
electrons into a Fourier series, then introduced Fourier compo-
nent of the electron density fluctuations,
electron density. Since there are a very large numbers of parti-
cles at random locations, they used random-phase approxima-
tion (RPA) and obtained
, about the average
(1)
The first term on the right-hand side of (1) represents the
density fluctuations arising from the randomly moving indi-
vidual particles by thermal motion. For an electron gas with an
,
(2)
where
collective behavior is dominant only when
is the average thermal velocity. Hence, we see that
(3)
which leads (1) to the same result as the case of no thermal
motion. In the case
, each particle is surrounded by
a cloud of extent
. As a result of this screening, the cloud
may be regarded as an effective free particle (macro-particle).
In vacuum electronic devices, bunching of the macro-parti-
cles due to the modulation by electromagnetic wave is a key pa-
TABLE I
MINIMUM CURRENT DENSITIES
rameter for their operations. However, if the wavelength in the
interaction region,
the Debye length, no significant interaction occurs between the
dilutemacro-particlesandelectromagneticwave[28].Fromthis
criterion, the minimum current density for sufficient interaction
at a given frequency is derived as
, is comparable to, or less than
(4)
where
beam,
conventional vacuum electron devices, the scale factor is about
10. The minimumcurrent densities calculated for some electron
tubes are shown in Table I, where the electron temperature is
assumed to be 1500 K.
The operational current density of the helix TWT is much
higher than the minimum current density, so that the output
power reaches to hundreds of watts. However, as for the high
frequency tubes, such as Ledatron, reflex klystron, and back-
ward wave oscillator, operational current densities are compa-
rable to minimum current densities, so that the output powers
are restricted to a few or few tens of mW-level. If the Debye
length is comparable to the bunching wavelength, i.e., the op-
erational current density is less than the minimum current den-
sity, electron bunches may be dissipated by the thermal motion
of electrons. Therefore, the output power of the Smith–Purcell
emission, introduced in Table I, should be much less than the
mW scale.
As shown in (4), the minimum current density is inversely
proportional to the electron-beam voltage. However, increasing
the voltage is not appropriate for miniaturized high-frequency
vacuum electron devices. Instead, decreasing the temperature
of the electron beam is preferred in high-frequency miniature
is the angular frequency,
the voltage, and
the temperature of electron
the scale factor. For
IV. REFLEX KLYSTRON ADOPTING A PC RESONATOR
In order to increase the power capability of a miniaturized
high-frequency vacuum electron device, we are considering a

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numberoflinearelectronbeams.Byusinga2-DPCresonator,
an ultra high-order
mode can be selectively excited
without mode competition in the resonator region and coupled
to the fundamental mode in a rectangular waveguide through a
line defect embedded in the 2-D PC.
Proof
Mode
high frequency miniature vacuum electron devices. The first
successful operation of a LIGA-fabricated vacuum tube yielded
the prospect of a highly efficient high-frequency miniature
vacuum tube compatible with mass production. Also, we have
shown that a high-order mode PC resonator is a promising
scheme for the high power generation of terahertz frequencies.
Moreover, the integration of a cold cathode with the novel
ideas introduced above might break through the bottleneck
obstructing the realization of a micro-sized vacuum electron
device beyond the millimeter and submillimeter wave bands.
4IEEE TRANSACTIONS ON PLASMA SCIENCE
Fig. 4.
TM330-like mode is dominantly excited by nine electron beams in the photonic
crystal resonator and coupled to ??
Fourier transform for the excited electromagnetic field in the photonic crystal
reflex klystron. ??
mode is most dominant (the fundamental mode and
other low-order modes are excluded) due to the photonic bandgap effect.
(a) MAGIC3D simulation for photonic crystal reflex klystron.
-like mode in the line defect. (b) Fast
reflexklystron adopting a modePC resonatorand by
A. Stable Excitation of High-Order
The mode stability of a PC resonator was experimentally
checked by comparing the
with that in a conventional metal resonator. The PC resonator
consists of dielectric (alumina) rods forming a 2-D photonic
bandgap (PBG) and metal (aluminum alloy) plates, which is
similar to that shown in Fig. 4 (
constant of the PC and the filling ratio are 10 mm and 0.19,
respectively. The resonance frequency (
metal cavity was set to 10.587 GHz, which is the same as that
mode in the PC resonator
mode). The lattice
mode) of the
of a PC resonator. The line defect forming PC waveguide was
matched to a standard WR-75 metal waveguide. The 25 probes
were distributed at each predicted peak of the electric field
corresponding to the
mode. By changing the radius of
the rod located between the resonator and the line defect in the
PC, the coupling level between the resonator and the external
system was controlled. And every reflection and transmission
spectra was measured using a vector network analyzer. In the
X-band PC resonator, the maximum voltage difference between
the 25 probes was measured to be 11.4% of the average value
when
was 0.17. However, for the same measurement taken
from the conventional resonator, the maximum difference was
measured to be 76.7% when
superiority of a PC resonator in sustaining stable high-order
modes compared to a conventional resonator.
was 0.17, which shows the
B. High-Order
Klystron
Mode Radiation in a PC Reflex
The performance of the reflex klystron using a PC resonator
was predicted by MAGIC3D simulation. Its structure is iden-
tical to a traditional reflex klystron, except for the high-order
(
-like) mode PC resonator and the array of nine elec-
tron beams. For the
-like mode, an array of nine elec-
tron beams (3 by 3) was designed to interact with each peak
of electric field in the resonator. Because the total beam power
can be nine times of that in a conventional reflex klystron, the
output power in the device is about ten times of that in a con-
ventional one. The increased power can be explained by the
physical properties of the PC resonator, such as the enhance-
ment of the ohmic quality factor and the increase of available
beam current. Fig. 4(a) and (b) shows the electric contour plot
andthefastFouriertransform(FFT)resultofthegeneratedelec-
tromagnetic wave at the gap of the cavity, respectively, in which
we can see that the
-like mode is most dominant owing
to the effect of PBG. Miniaturization of the device using the
LIGA fabrication is underway along with a development of a
coldcathodefromwhichanarrayoflinearelectron-beams(3by
3)can be emittedto interactwith
The PC reflexklystron fabricated by the MEMStechnology and
excited by electron beams generated from a cold cathode can
be a promising scheme for a compact submillimeter radiation
source, of which power level is comparatively larger than other
miniature devices.
-modein thePCcavity.
V. CONCLUSION
Several innovative approaches were investigated to realize

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Proof
12, 1972. He received the B.S and M.S degrees from
Seoul National University, Seoul, Korea, in 1998
and 2001, respectively, where he is currently a Ph.D.
candidate in the School of Physics.
He had been engaged in the study of wide-band
helix traveling wave tube (TWT), and harmonic mul-
tiplyingKataperedwaveguidegyro-TWT.Currently,
his activities are focused on development of a sub-
millimeter wave vacuum tube using micro-fabrica-
tion technologies, such as LIGA, DRIE, and etc. His
main effort is dedicated to the application of photonic crystal to a vacuum de-
vice, which promises increase of output power and operation frequency ex-
tending terahertz regime.
HAN et al.: EXPERIMENTAL INVESTIGATIONS ON MINIATURIZED HIGH-FREQUENCY VACUUM ELECTRON DEVICES5
ACKNOWLEDGMENT
The authors would like to thank Prof. K. Mizuno of Tohoku
University, Sendai, Japan, for his valuable discussions.
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Seong-Tae Han (S’04) was born in Seoul, Korea, on
September 10, 1972. He received the B.S. and M.S.
degrees in physics education and physics, respec-
tively, from Seoul National University, Seoul, Korea,
in 1999 and 2001, respectively. He is currently
working toward the Ph.D. degree at the School of
Physics, Seoul National University.
His research interests cover traveling-wave tube,
microelectromechanical system (MEMS) applica-
tion, and nonlinear dynamics in vacuum electronic
devices. He is now pursuing a LIGA-compatible,
miniature, novel-concept vacuum tube combined with cold cathode such as
field emitter arrays and carbon nanotubes for millimeter and sub-millimeter
wave. He is also interested in novel vacuum electron devices adopting recent
innovations such as photonic crystal and counter-streaming electron beam.
Seok-Gy Jeon was born in Iksan, Korea, on June