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1.46 THz RTD oscillators with strong back injection from collector
Michael Feiginov, Hidetoshi Kanaya, Safumi Suzuki, and Masahiro Asada
Tokyo Institute of Technology, Meguro, Tokyo 152-8552, Japan
R
ESONANT-tunneling diodes (RTDs) are the highestfrequency active semiconductor electronic devices, which
exist nowadays. The output power of RTD oscillators is
already close to the level required for practical THz
applications. RTD oscillators can facilitate sub-THz data
transmission, they are also the most compact roomtemperature THz sources and they require low input dc power.
All these factors make RTD oscillators unique technology of
choice for real-world THz applications.
Nevertheless, the parameters of RTD oscillators still need to
be improved and understanding of their limitations stays as
unresolved problem. It has been shown in the past [1] that the
rate of the transient process inside RTDs are fundamentally
not limited by the tunnel electron lifetime () in the quantum
well (QW) between the RTD barriers, the rate is determined
by a certain relaxation time (rel) instead. However, it has been
also demonstrated that the RTDs with heavily doped collector,
where the depletion region on the collector side is reduced or
eliminated, should allow one to achieve negative differential
conductance (NDC) at frequencies >>1 and rel>>1 [2]. In
the present work we study an ultimate limit of this concept,
when the collector is heavily doped and the collector depletion
region is fully eliminated.
Emitter
QW
3.0
1.39 THz,
0.75 W
(a)
3.0
2.5
1.46 THz,
0.36 W
(b)
2.5
2.0
1.5
1.0
Spectral density, a.u.
I. INTRODUCTION
even dominant) role in our RTDs. The ratio of the
collectorQW and emitterQW injection currents is
between 2 (in the positive differential-conductance region)
and 0.3-0.7 (in the NDC region). Our RTDs exhibit well
pronounced region with NDC, where the peak-to-valley
current ratio is close to 2. The RTDs also demonstrate
excellent high-frequency performance.
Our theoretical analysis shows that rel and  in our RTDs is
around 30 fs. That indicates that our RTDs still operate in the
quasi-static regime (<<1 and rel<<1) even at THz
frequencies. Additionally, the transit time through the
collector depletion region is fully eliminated in our structures
and that also improves their performance at THz frequencies.
We integrate our RTDs with slot-antenna resonators, see
details in [3]. Depending on the RTD area and antenna
dimensions, such oscillators operate at different frequencies.
The highest frequency we have achieved is 1.46 THz, see
Fig.2. This is the highest published frequency for RTD
oscillators nowadays.
The 1.46 THz oscillator was operating close to the onset of
Spectral density, a.u.
Abstract—We are studying resonant-tunneling diodes (RTDs)
with strong back injection of electrons from collector into
quantum well. Such RTDs exhibit large negative differential
conductance and they operate up to 1.46 THz in oscillators.
2.0
1.5
~10 GHz
1.0
~25 GHz
0.5
Collector
0.5
0.0
1.35
1.40
1.45
Frequency, THz
1.0
0.0
0.0
j, eV
E2
0.5
Quasi-Fermi levels
E1
0.0
-10
-5
0
5
10
15
0.4
0.6
0.8
1.0
1.55
1.2
1.4
1.6
Frequency, THz
Fig. 2. (a) The emission spectra of two highest-frequency RTD oscillators
with the slot antenna length of 12 µm (green) and 16 µm (blue). (b) The inset
shows the emission spectra in more details.
Quasi-Fermi level
-15
0.2
1.50
20
z, nm
Fig. 1. Band diagram of our RTDs in the NDC region at 0.2 V.
II. RESULTS AND DISCUSSION
Heavy collector doping brings our RTDs to operation in a
very unusual regime, when the bottom of the ground QW
subband is close to and even bellow collector quasi-Fermi
level in the whole range of the RTD operating voltages. The
band diagram of our RTD in the NDC region of the I-V curve
is illustrated in Fig.1. The electron back injection from
collector plays essential (and in a wide range of applied biases
the oscillations, therefore its emission line was relatively
broad (~25 GHz, see Fig.2(b)). The spectra of all our lowerfrequency oscillators had the line width around ~10 GHz,
which is close to the resolution limit of our measurement
instrumentation. Fig.3 shows the output power of RTD
oscillators with different areas of the diodes. We have
fabricated two types of oscillators with the slot-antenna length
of 12 µm and 16 µm.
Fig.4 shows the oscillation frequencies of oscillators with
different RTD areas. We also show the corresponding
theoretical curves in the figure. We can see that for the same
RTD area, the oscillation frequencies of 16 µm antennas are
lower than those of 12 µm ones. This is due to the higher
100
1.4
12 m antenna
Oscillation frequency, THz
Output power, W
16 m antennas
10
12 m antennas
1
1.2
1.0
0.8
16 m antenna
0.6
0.4
0.1
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Frequency, THz
Fig. 3. An estimate for the emitted output power of our oscillators with
different RTD areas (the measured output power is corrected for the reflection
at the lens interfaces and for the spillover of the emitted power).
inductance of longer antennas (because of the high capacitive
load of RTDs, the oscillators are similar to LC resonant
circuits). However, the higher operation frequency has been
achieved with longer antenna due to better balance between
RTD capacitance and antenna inductance, which leads to
higher resonator Q factor at the specific oscillation frequency.
We can notice in Fig.3 that the 16 µm antennas provide higher
output power. This is due to higher emission efficiency of the
longer antennas and larger RTD area at a given oscillation
frequency.
One can notice in Fig.4 that the theoretical curves deviate
from the measured data in two ways. First, the theoretical
curves predict oscillation up to lower frequencies than what
we measure in experiment. This is probably due to the
theoretical model [1,2], which we use for calculation of the
RTD capacitance. The RTD capacitance is strongly affected
by the space-charge effects, which are responsible for
significant increase of capacitance in the NDC region at the
frequencies in the range rel<<1 or rel~1. Presently, our
model does not take the back injection from collector into
account. Therefore, the model is probably overestimates RTD
capacitance and, as a consequence, underestimates RTD
oscillation frequencies. Second, theoretical curves predict
lower (than experimentally observed) oscillation frequencies
for the RTDs with larger areas. This is probably due to linear
nature of our model [1,2]. When the RTD area is small, the
oscillation amplitude (and the output power) is also small. The
linear RTD model describes ac RTD characteristics and the
oscillation frequencies of oscillators reasonably well in this
regime. However, for the RTDs with larger areas, the
oscillation amplitude (and the output power) becomes large
and the linear ac RTD model gives a more rough
approximation for the RTD characteristics. That probably
leads to underestimation of the oscillation frequencies of our
oscillators with larger-area RTDs.
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
2
RTD area, m
Fig. 4. Measured (points) and calculated (lines) oscillation frequencies of
12 µm (green) and 16 µm (blue) slot antennas.
III. SUMMARY
Our RTDs with heavily doped collector and strong back
injection from collector into QW demonstrated a record
frequency for RTD oscillators. We show that back injection
does not degrade THz performance of RTD oscillators and
offers an additional degree of freedom for optimization of the
performance of THz RTD oscillators.
REFERENCES
[1]. M. Feiginov, ”Effect of the Coulomb Interaction on the Response Time
and Impedance of the Resonant-Tunneling Diodes,” Appl. Phys. Lett., vol. 76,
pp. 2904-2906, 2000.
[2] M. Feiginov, ”Displacement currents and the real part of high-frequency
conductance of the resonant-tunneling diode”, Appl. Phys. Lett., vol.78, pp.
3301-3303, 2001.
[3] M. Feiginov, H. Kanaya, S. Suzuki, and M. Asada, ”Operation of resonanttunneling diodes with strong back injection from the collector at frequencies
up to 1.46 THz”, Appl. Phys. Lett., vol.104, pp. 243509, 2014.

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