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THz ANTENNA-COUPLED ZERO-BIAS SCHOTTKY DIODE
DETECTORS FOR PARTICLE ACCELERATORS
R. Yadav1,∗ , S. Preu, Terahertz Devices and Systems, TU Darmstadt, Darmstadt, Germany
A. Penirschke, High Frequency Tech., Mittelhessen Univ. of Applied Sciences, Friedberg, Germany
J. Michael Klopf, M. Kuntzsch, Helmholtz-Zentrum Dresden-Rossendorf, Dresden, Germany
1
also at High Frequency Tech., Mittelhessen Univ. of Applied Sciences, Friedberg, Germany
Abstract
Semiconductor-based broadband room-temperature Terahertz (THz) detectors are well suitable for beam diagnosis
and alignment at accelerator facilities due to easy handling,
compact size, no requirement of cooling, direct detection
and robustness. Zero-Bias Schottky Diode (ZBSD) based
THz detectors are highly sensitive and extremely fast, enabling the detection of picosecond scale THz pulses. This
contribution gives an overview of direct THz detector technologies and applications. The ZBSD detector developedby our group has undergone several tests with table-top THz
sources and also characterized with the free-electron laser(FEL) at HZDR Dresden, Germany up to 5.56 THz. In orderto understand the rectification mechanism at higher THz
frequencies, detector modelling and optimization is essential for a given application. We show parametric analysis
of a antenna-coupled ZBSD detector by using 3D electromagnetic field simulation software (CST). The results will
be used for optimization and fabrication of next generation
ZBSD detectors, which are planned to be commissioned at
THz generating FEL accelerator facilities in near future.

INTRODUCTION
The electromagnetic spectrum from 0.1 to 10 THz was
commonly known as terahertz (THz) gap until recently as rigorous research and development have led to develop sources,
detectors and components which help to bridge the THz
gap [1]. Among available tabletop THz sources, accelerator based sources such as free electron lasers (FEL), synchrotrons and linear particle accelerators generate coherent
as well as non-coherent THz signals [2]. THz signals canbe used for various applications such as spectroscopy, studyof matters, medical imaging, etc. [3]. THz detectors plays acrucial role in order to harness the full power of THz signals
in various applications. These detectors can be classified
into several categories based on their working principles(such as thermal detectors, electrical detectors etc. [1]), operating ranges (frequency of coverage for example narrow or
broadband [1]) and operating conditions (room temperatureor cryogenic conditions [1, 4–8]). There has been a rigorous work for the development of Schottky diode for THz
applications [7, 9–11].
Zero-Bias Schottky Diode (ZBSD) based THz detectors
are an end product of combination of ZBSD, antenna, planar electronic components and post detection electronics.
∗ rahul.yadav@iem.thm.deTherefore, the overall performance of the ZBSD detector isdependent on all these components. In order to optimize
the ZBSD THz detectors, in this paper we focus on the investigation of planar antennas for antenna-coupled ZBSD
detector, which is planned to be primarily commissioned at
ELBE facility in Helmholtz Zentrum Dresden-Rossendorf(HZDR), Germany and other facilities too.

SIGNAL RECTIFICATION IN ZBSD
For conventional Schottky diodes, the external bias 𝑉
modifies the Schottky barrier height, which led the electrons
to cross the barrier and ultimately led to set the operating
point of Schottky diode by reducing differential resistance(𝑅𝑑𝑖𝑓 𝑓 ) [11,12]. In case of ZBSD, the material is engineeredin such a way that at 𝑉 = 0 sufficient electrons are able
to cross the barrier, yet with sufficient non-linearity of the
IV characteristics to cause rectification. The ZBSD used
for the detector development in our group are fabricated on
Indium Gallium Arsenide (InGaAs) substrate which haveelectron affinity of 4.5 eV. Due to the proprietary reason by
ACST GmbH, the in-depth information of Schottky diodeitself is out of context of this paper. The ZBSD used herefeature a quasi-vertical structure for Schottky and ohmic
contact [9], rather than either having only planar or only
vertical structure [11].
The signal rectification takes place at the Schottky contact
of ZBSD, which can be understand by using Taylor series[13] as follows: The incident (monochromatic) Terahertz
wave is transformed to a bias by the antenna as
𝑈0 (𝑡) = 𝑈0 cos(𝜔𝑡)(1)where 𝑈0 (𝑡) is the signal with amplitude 𝑈0 and angularTHz frequency 𝜔. By using the Taylor series expansion of
the exponential diode characteristic up-to second order, thediode current 𝐼0 becomes
𝐼0 (𝑡) = 𝐴1 𝑈0 cos(𝜔𝑡) + 𝐴2 𝑈02 cos2 (𝜔𝑡) + ....

(2)

1
1
= 𝐴1 𝑈0 cos(𝜔𝑡) + 𝐴2 𝑈02 + 𝐴2 𝑈0 𝑐𝑜𝑠(2𝜔𝑡) (3)22
where the second term in Eq. (3) is the DC term. The firstand second terms are derived from diode characteristics [11]:1
𝑅𝑑𝑖𝑓 𝑓(4)

1
2 ⋅ 𝑅𝑑𝑖𝑓 𝑓 ⋅ 𝜂 ⋅ 𝑈𝑇

(5)

𝐴1 =
𝐴2 =

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Table 2: Dimensions of the Structures
AbbreFull form
viationFigure 1: Sketch of the antennas investigated for ZBSD
THz detectors (inset shows the central part where ZBSD
is coupled) (a) left: antenna with substrate view, right: 1.5
turns log spiral antenna, (b) left: 2.5 turns log-spiral antenna,
right: 1.5 turns smaller-log spiral antenna, (c) H-dipole
antenna and (d) Folded dipole antenna. Note: antennas are
excited using discrete port in CST between two electrodes
in channel 𝐿𝐶ℎ × 𝑊𝐶ℎ , where practically ZBSD is located.
where in Eq. (5), 𝜂 is diode ideality factor and 𝑈𝑇 is semiconductor (InGaAs) thermal voltage. As the second orderterm contains a rectified component 𝐼𝐷 𝐶 = 𝐴2 𝑈02 , 𝐴2 isdirectly proportional to the responsivity of the ZBSD.

ANTENNA-COUPLED ZBSD DETECTOR
The antenna plays a crucial role in the performance of thedetector because it couples the incident THz radiation to the
ZBSD, where it gets rectified. Planar antennas are used inthis work to couple the ZBSD for detector development. The
selection of the antenna depends on the desired application
and required bandwidth. Table 1 shows different types ofantennas which are used for the development of ZBSD THz
detector.
Table 1: Investigated Antenna for ZBSD THz Detector
S.No

Antenna type

Abbreviation

1
2
3
4

Log-spiral
Small log-spiralH-dipole
Folded dipole

LSA
SLSA
HD
FD

The LSA and SLSA are self-complimentary, frequencyindependent antennas, which means theoretically they haveno limitation on operational bandwidth. However, practically the upper bandwidth limitation is defined by the innermost arm radius and lower frequency by outermost arm
radius [14] as shown in Fig. 1 (a) and (b).
We also investigated antenna types that are frequently applied in Terahertz photomixers, such as the H-dipole (HD)antenna (Fig. 1 (c)). In this type of antenna, either the central
bar (high frequencies) the arm structure (low frequencies)
radiates as the wave propagates along it. These type of antennas are considered as broadband antennas. In order toincrease the detector sensitivity in narrow-band operation,
investigations on performance of folded dipole (FD) anten-

Dimension[µm]

LSA𝐿 Log-spiral antenna length
1174.25
LSA𝑊 Log-spiral antenna width
557.60H
Substrate height
4.5
L𝐶ℎ
Channel length
2.4, 3, 6, 8
W𝐶ℎChannel width
2.4, 10SLSA𝐿 Small log-spiral antenna length413.14SLSA𝑊 Small log-spiral antenna width
200.90L𝐻𝐷
H-dipole antenna length700
W𝐻𝐷 H-dipole antenna width350
D𝐻𝐷
H-dipole antenna arm distance50
t𝐻𝐷
H-dipole antenna arm thickness
10
W𝐹𝐷 Folded-dipole antenna width
458
L𝐹𝐷
Folded-dipole antenna length
1020
D𝐹𝐷
Folded-dipole antenna arm distance 80
t𝐹𝐷
Folded-dipole antenna arm thickness 10
nas were also performed (Fig. 1 (d)).The dimensions of theinvestigated antennas are mentioned in Table 2.
The ZBSD will be fabricated on an Indium Gallium Arsenide (InGaAs) substrate which is equivalent to the area
mentioned by 𝐿𝐶ℎ × 𝑊𝐶ℎ in the Fig. 1. The ZBSD will
be integrated with the antenna, which will be fabricated on
the film-thin substrate of 4.5 µm thickness and dielectric
constant of |𝜀𝑟 | = 2.8.

RESULTS AND DISCUSSION
The dielectric constant of the material on which antennacoupled ZBSD is fabricated plays an important role in the performance of the detector. According to babinet’s principle[14], the radiation impedance (Z𝐴 ) of self-complimentaryantenna (LSA and SLSA) is inversely proportional to its
effective refractive index (n𝑒𝑓 𝑓 ) and thus to its dielectric constant as
𝑍𝐴 =
𝑍𝐴 =

𝑍0
2 ⋅ 𝑛𝑒𝑓 𝑓

(6)

𝑍0

(7)

√2 ⋅ (𝜀1 + 𝜀2 )where, Z0 is the wave impedance in free space (377 Ω),𝜀1 is dielectric constant of free space (1) and 𝜀2 is dielectric constant of thin-film substrate (2.8). Considering therespective values of ZBSD fabrication material, unloaded
radiation resistance is 𝑍𝐴 =137 Ω. Figure 2, shows the effect of |𝜀𝑟 | variation on the performance of LSA antenna
with 10 × 8 µm2 channel when exciting the antenna from thecenter (where ZBSD is located), which directly relates tothe ZBSD detector performance as well. The |𝑆11 | (scattering parameters in the channel 𝐿𝐶ℎ × 𝑊𝐶ℎ where practically
ZBSD is located) shows standing waves for almost all |𝜀𝑟 |until 0.6 THz due to the inductive part of the antenna being
dominant (Fig. 2(d)), while above 0.6 THz the imaginary
part of radiation impedance becomes capacitive which leads

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Figure 2: Effect of variable |𝜀𝑟 | on LSA antenna with 10 × 8 µm2 channel with ZBSD having C𝑗 = 1 fF and R𝑑𝑖𝑓 𝑓 = 5 kΩ, (a)|𝑆11 |, (b) Phase response, (c) VSWR response and (d) Impedance, solid lines represent real part and dotted lines represent
imaginary part.

Figure 3: (a) Total device impedance for constant C𝑗 = 1 fF and variable R𝑑𝑖𝑓 𝑓 , (b) Total device impedance for variable C𝑗
and constant R𝑑𝑖𝑓 𝑓 = 5 kΩ with SLSA antenna with 2.4 × 2.4 µm2 channel. Dotted lines: imaginary part, solid lines: realpart of impedance, on substrate of 4.5 µm thickness and dielectric constant of |𝜀𝑟 | = 2.8.
to sign flip of phase (Fig. 2(b)). The voltage standing wave
ratio (VSWR) is almost below 3 up to 0.8 THz and thenincreases gradually to 6 at 2 THz (Fig. 2(b)), which means
as frequency increases the capacitive part of the radiation
impedance become significantly important.
The junction capacitance (C𝑗 ) and differential resistance(R𝑑𝑖𝑓 𝑓 ) are the important parameters of ZBSD which effectthe antenna performance as a function of frequency. Fig. 3(a)shows the variation of R𝑑𝑖𝑓 𝑓 while keeping the C𝑗 = 1 fF
constant. The variation in differential resistance does notaffect the radiation impedance of the detector. As the frequency increases, the capacitive part of impedance become
inductive after 2.5 THz. This is because the wavelength isreaching towards the same dimension of the central electrodes (where the ZBSD is coupled). When in the case ofR𝑑𝑖𝑓 𝑓 is kept constant at 5 kΩ and C𝑗 is variable (Fig. 3(b)),
the radiation impedance of the antenna is changed significantly. The lower the junction capacitance C𝑗 is, the higher
is the real part of radiation impedance and longer the frequency range over which the imaginary part stays capacitive
before becoming inductive. This proves that it is importantto have lower C𝑗 to have better responsivity of the device at
higher THz frequency. Therefore, we selected to consider
C𝑗 = 1 fF and R𝑑𝑖𝑓 𝑓 = 5 kΩ for remaining studies in thiswork.
Figure 4 shows the radiation impedance versus frequency
response from 0.05 to 4 THz (except LSA 2.4 × 2.4 µm2
which is from 0.05 to 2 THz only) with variable channel

dimensions of 10 × 3 µm2 , 10 × 6 µm2 and 2.4 × 2.4 µm2 for
all the four types of antennas considered for investigationin this study. LSA with channel dimension of 10 × 3 µm2
and 10 × 6 µm2 have real Z𝐴 of 133 Ω at lower frequencies (0.05 THz), which further decreases to 50 Ω at 1 THz(Fig. 4 (a)). The smaller channel dimension of 2.4 × 2.4 µm2
have real Z𝐴 of 268 Ω at 0.069 THz and decreases to approximately 100 Ω at 1 THz. This shows the better device
response with smaller channel dimensions for LSA type devices. The smaller log-spiral devices (SLSA) are 2.84 times
smaller in length compared to LSA devices. The SLSA devices in Fig. 4 (b) shows the resonance behaviour around
0.1 THz for all the three channel dimensions, which afterwards drop of real (Z𝐴 ) to 78 Ω for 2.4 × 2.4 µm2 channel
and almost 50 Ω for both 10 × 3 µm2 and 10 × 6 µm2 channel. While the real part is almost similar for 10 × 3 µm2 and10 × 6 µm2 (as observed in Fig. 4 (a) and (b)), the imag (Z𝐴 )shows the smaller channel length have slightly prolonged
capacitive behaviour. The H-dipole antenna has resonances
at 0.16, 0.38 and 0.61 THz as shown in Fig. 4 (c) for all
studied channel dimensions. The HD with 2.4 × 2.4 µm2
have real (Z𝐴 ) of 2.3 kΩ compared to approx 1.9 kΩ for both
10 × 3 µm2 and 10 × 6 µm2 channel at 0.16 THz. The folded
dipole antenna (FD) is a narrow band resonant having theresonance peak at 0.2 THz as shown in Fig. 4 (d). This typeof antenna can be used to boost up the device responsivity atparticular frequency for a very specific frequency selective
application.
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Figure 4: Antenna radiation impedance versus frequency response for variable channel dimensions of (a) 1.5 turn log-spiralantenna, (b) 1.5 turn small log-spiral antenna, (c) H-dipole antenna and (d) folded-dipole antenna from 0.05 to 4 THz.
Dotted lines: imaginary part, solid lines: real part of radiation impedance, on substrate of 4.5 µm thickness and dielectric
constant of |𝜀𝑟 | = 2.8.

Figure 5: (a) Comparison of radiation impedance of all the four investigated antennas with channel dimension of 10 × 3 µm2
from 0.05 to 4 THz and (b) comparison of log-spiral antennas with channel dimension of 2.4 × 2.4 µm2 from 0.05 to 2 THz.
Dotted lines: imaginary part, solid lines: real part of radiation impedance, on substrate of 4.5 µm thickness and dielectric
constant of |𝜀𝑟 | = 2.8.
Figure 5 (a) compares the impedance response for all fourtypes of antennas with channel dimension of 10 × 3 µm2(this channel dimension is used for comparison because adevice with smaller channel length has comparatively better response). Clearly the HD and FD devices are the best
option for frequency selective improvement due to their resonant behaviour at specific frequencies. The LSA and SLSA
devices are the best choice for broadband applications, however with frequency their responsivity decreases [7]. As
shown in Fig. 6, the device reponsivity decreases as 𝑓 −6 towards higher THz frequencies. On comparing the LSA andSLSA antennas impedance for 2.4 × 2.4 µm2 channel dimension, it is observed that both antennas have resonant peaks
at 0.07 and 0.2 THz, respectively. The response for LSA
is higher than SLSA at lower frequencies as expected, but
above approx. 1 THz, the response of SLSA is slightly betteras shown in Fig. 5 (b). The antenna with 2.5 turns features
non-resonant behaviour and response decreases gradually
over frequency. It does not have any prominent inductive
component.

Figure 6: Responsivity of the log-spiral antenna-coupled
broadband THz detector [7].
channel dimension in antenna design in this paper. The
proper selection of C𝑗 and R𝑑𝑖𝑓 𝑓 is important for the better
device response. The selection of the antenna type is often a
trade-off between its responsivity and operational bandwidth.
Short channel dimensions (here 10×3 µm2 and 2.4×2.4 µm2 )are best choices for future device fabrication. The antennastudies presented here provide the expected performance ofthe optimized ZBSD detectors to be fabricated in the near
future under this project.

CONCLUSIONACKNOWLEDGEMENT

In this paper, we investigated the importance of antenna
selection and design based on the desired operational bandwidth. At higher THz frequency, typical antenna sizes aremuch bigger compared to the THz wavelength incident on
the detector, therefore only the central electrodes play a crucial role. We investigated and showed the importance ofThis work is supported by the German Federal Ministry of Education and Research (BMBF) under contract
no. 05K22RO1 at Mittelhessen University of Applied Sciences, Friedberg (Hesse), Germany. Parts of this researchwere carried out at ELBE at the Helmholtz-Zentrum Dresden- Rossendorf e.V.

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