# TeraHertz Desorption Emission Spectroscopy (THz DES) of space relevant ices

Olivier Auriacombe,1,2 S. Rea,2 S. Ioppolo,3 M. Oldfield,2 S. Parkes,4 B.
Ellison2 and H. Fraser1
1School of Physical Sciences, The Open University, Walton Hall, Milton Keynes,
MK7 6AA, UK
2Millimetre Wave Technology Group, STFC Rutherford Appleton Laboratory,
Didcot, OX11 0QX, UK
3School of Electronic Engineering and Computer Science, Queen Mary University
of London, London, E14NS, UK
4STAR-Dundee Ltd., Dundee, DD1 4EE, UK E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We present an experimental instrument that performs laboratory-based gas-phase
Terahertz Desorption Emission Spectroscopy (THz-DES) experiments in support of
astrochemistry. The measurement system combines a terahertz heterodyne
radiometer that uses room temperature semiconductor mixer diode technology
previously developed for the purposes of Earth observation, with a high-vacuum
desorption gas cell and high-speed digital sampling circuitry to enable high
spectral and temporal resolution spectroscopy of molecular species with
thermal discrimination. During use, molecules are condensed onto a liquid
nitrogen cooled metal finger to emulate ice structures that may be present in
space. Following deposition, thermal desorption is controlled and initiated by
means of a heater and monitored via a temperature sensor. The ‘rest frequency’
spectral signatures of molecules released into the vacuum cell environment are
detected by the heterodyne radiometer in real-time and characterised with high
spectral resolution. To demonstrate the viability of the instrument, we have
studied Nitrous Oxide ($N_{2}O$). This molecule strongly emits within the
terahertz (sub-millimetre wavelength) range and provide a suitable test gas
and we compare the results obtained with more traditional techniques such as
quadrupole mass spectrometry. The results obtained allow us to fully
characterize the measurement method and we discuss its potential use as a
laboratory tool in support of astrochemical observations of molecular species
in the interstellar medium and the Solar System.

###### keywords:

Astrochemistry, Molecular processes, Radiative transfer, Instrumentation:
detectors, Methods: laboratory: molecular, Techniques: spectroscopic

††pubyear: 2022††pagerange: TeraHertz Desorption Emission Spectroscopy (THz
DES) of space relevant ices–TeraHertz Desorption Emission Spectroscopy (THz
DES) of space relevant ices

##  1  Introduction

Enhancing our understanding of the formation and evolution of the Universe is
strongly dependent upon the observation of molecular matter that exists in the
interstellar medium (ISM) and the Solar System. The ISM harbours the materials
from which new stars are born, exoplanetary systems are formed, and the
building blocks of life are likely created. These processes occur within low-
temperature ($<100~{}K$) high-density regions of space ($10^{4}~{}cm^{-3}$)
that are mostly opaque to visible radiation (Van Dishoeck, E.F., 2017). They
are, however, observable at longer wavelengths, i.e. throughout the infrared
millimetre (mm-wave), microwave and radio wavelength portions of the
electromagnetic spectrum.

The development of related ground-based observational facilities has enabled
astronomers to access the spectral ‘fingerprints’ of a huge range of gas-phase
chemical species that are of pivotal importance to uncovering the processes in
star and planetary formation. During the past decade, for instance, a large-
scale facility, the Atacama Large Millimeter and sub-millimeter Array (ALMA).
In doing so, however, new questions have been raised associated with
understanding the origins and chemical pathways of many large molecules and
exotic species identified in star-forming regions ((Van Dishoeck, E. F. et
al., 2014; Öberg et al., 2011)). This requires increased use of already
overcommitted facilities and for which access time is limited through intense
user competition, in addition to variable atmospheric conditions. The
provision of low-cost and accessible laboratory-based measurement tools that
complement observational facilities such as ALMA can provide a very useful
alternative for the astrochemist. For instance, by using methods for molecular
detection that are akin to those deployed on telescopes, laboratory
experiments that emulate the ISM environment can support understanding origins
of molecular species and differentiate between gas-phase and solid state
chemical pathways. Simulating space environments under fully controlled
conditions is thus an attractive experimental capability that offers potential
for a step-change approach in performing laboratory astrochemistry.

Our approach towards the above is the development of an experimental technique
that is hereafter referred to as Terahertz Desorption Emission Spectroscopy
(THz-DES). In essence, the experimental method performs THz (submm-wave)
emission spectroscopy of gas-phase molecules that desorb from the solid state
in a vacuum environment. Because the molecular density of the desorbed species
in the experiment is low, narrow spectral emission features are present,
typically a few MHz full-width half-maximum (FWHM), that correspond to those
observed within the ISM. We show that by measuring spectral features as the
molecules desorb, species can be identified via their excitation states, and
kinetic and thermodynamic information such as desorption energies can be
extracted Belloche et al. (2019). Acquiring both spectroscopic and
thermodynamic data concurrently provides a novel and valuable laboratory tool
to aid in the understanding of astrochemical processes in star-forming regions

Whether deployed on a large single dish telescope (Davies et al. (1992);
Little et al. (1992)) or interferometric telescope systems Wootten & Thompson
(2009), heterodyne frequency down conversion systems provide a powerful
spectral observation tool. Through its use, more than 200 molecules have been
detected and spectroscopically resolved in the interstellar regions within our
Galaxy, and more than 60 have been observed in extragalactic molecular clouds.
Detections include neutral, radical and ionic or cationic species Müller et
al. (2005), and small unsaturated molecules, larger carbon-based molecules
dominated by long chain structures with large dipole moments, and fullerenes
and polycyclic aromatic hydrocarbons (PAHs) McGuire (2021). Predominantly
these species are formed by gas-phase chemistry, although it is well known
that a number of abundant molecules, such as $H_{2}$, $H_{2}O$ and $CH_{3}OH$
(Tielens & Hagen (1982); Walsh et al. (2016); Ioppolo et al. (2008); Fuchs et
al. (2009)) form mostly via solid state pathways involving the dust and ices
found in dense interstellar molecular clouds. Vital challenges to
astrochemistry are to refine our understanding of the chemical growth
mechanisms, and to determine the role that they play in influencing the
physical and chemical conditions present as star and planet formation
progresses.

One group of species, known as complex organic molecules (COMs) have received
significant focus over the past decade from "molecule hunting" astronomers
(Belloche et al. (2014, 2019)). COMs are some of the largest molecules
detected in space, and since they tend to be saturated organic species, are
considered as a bridge between the simpler gas-phase species that are often
used to probe or trace astrophysical conditions, and the potential
astrobiological processes that may emerge on a newly forming planet or moon.
Many of the proposed formation mechanisms for COMs in the ISM derive from
processes involving the formation and/or destruction of $CH_{3}OH$ (Bergantini
et al. (2018); Linnartz et al. (2015)). However, it remains unclear whether
COMs are formed in the gas-phase or solid state, or a combination of the two;
the chemistries may even be molecule dependent. What is clear, though, is that
we are only able to detect and identify COMs in space by their gas-phase
emission spectra, particularly in the sub-mm and radio regions of the
electromagnetic spectrum, where spectral features are species-unique, and
given the large dipole moments of many COMs, relatively intense, despite their
low abundance (Herbst & van Dishoeck (2009); Balucani et al. (2015)).
Moreover, the James Webb Space Telescope (JWST) mission will help
understanding the interplay between gas and ice across a variety of different
sources in the ISM. A primary objective of the laboratory THz-DES spectrometer
described here is, therefore, to detect COMs spectroscopically in the gas-
phase once they have desorbed from the solid state and, through a series of
experimental variants, concurrently determine the desorption energies of COMs.

To date, laboratory temperature programmed desorption (TPD) experiments
(Fraser et al. (2002); Fraser et al. (2001); Fuchs et al. (2006); Fayolle et
al. (2011); Collings et al. (2004)), using quadrupole mass spectrometry (QMS),
have been shown to be of great importance in gaining an understanding of the
evolution of ice molecules from dust surface analogues. The TPD technique has
historically facilitated the measurement of binding, desorption, and diffusion
energies, and the sticking probabilities and desorption orders, of molecules
incident upon and released surfaces, and in the context of laboratory
astrophysics, proved exceeding productive to astrochemical models and our
understanding of simple species in the ISM, e.g. $H_{2}O$, CO, and $CH_{3}OH$
(Fayolle et al. (2011); Brown et al. (2006)). In a few cases (using much
higher concentrations of COMs than anticipated in the ISM) the solid state
mid-IR spectra and desorption properties of certain COMs have also been
reported Terwisscha van Scheltinga et al. (2018) to support direct observation
of the ISM.

In the last few years, similar (though not identical) experimental
developments to our method have been reported. In 2017, Wehres et al. (2017)
described the design, construction, and operation of two laboratory broadband
emission spectrometers for gas-phase characterization of large molecules. The
first is based on a Schottky-barrier diode heterodyne receiver spectrometer
operating between 80 and 110 GHz, whilst the second uses cryo-cooled SIS
technology and operates at higher frequency between 270 and 290 GHz Wehres et
al. (2018). Gas phase pyridine and methyl cyanide features were successfully
detected and matching analytic simulations were presented for the observed
spectral transitions. In 2018, a new technique combining a Terahertz
radiometer (41 - 49) GHz and a vacuum chamber was developed to observe the
generation of cold plasma and UV photochemistry in the gas phase under low
pressure as described by Tanarro et al. (2018). However, in the context of the
experiment described here, it is important to note that the spectrometer
developments were not coupled to a system where the gas-phase molecules
originated from the solid state. More recently, Yocum et al. (2019) reported
on an experiment using a THz source and hot-electron bolometer to detect the
gas-phase absorption spectra of simple molecular species such as $H_{2}O$,
$D_{2}O$ and $CH_{3}OH$ desorbing into the gas-phase from ices grown in an
ultra-high vacuum (UHV) chamber. This experimental set-up (SubLIME), combined
with a Fourier-transform Infrared spectrometer, gave the spectroscopic insight
on the ultraviolet photolysis and warm up of methanol ice sample, for the
first time observed at those frequencies in a laboratory environment Yocum et
al. (2021). This showed the potential of the use of submillimetre/far-infrared
technique to identify molecules in complex gas mixtures. One challenge of this
technique was the sensitivity of absorption spectroscopy to the desorbing
molecules. The combination of temperature programmed desorption and microwave
spectroscopy techniques was discussed by Theulé et al. (2020). In these
experiments, desorption of water, deuterium, methanol, and ammonia was
measured using a hot electron bolometer and Si-diode technology combined with
Fourier transform spectrometers. While Theule et al. observed the desorption
through a waveguide cavity, Yocum et al. (2019) detected the desorption above
a metal substrate as seen in standard TPD studies.

The method presented here differs from other techniques in two ways; first,
molecules are detected in emission (not absorption) and second, since an
absolute power measurement is made, molecular abundances can be determined.
Our method differs notably in that the previous experiments used an
illuminating source (100 GHz - 1 THz or 24 GHz) to excite the desorbing
molecules. In our technique, we observe the emission spectra against a cold
blackbody background that is more representative of the astronomical
observation method. We thus measure the absolute intensities from the
desorbing molecules. Moreover, the THz-DES bandwidth is much more extensive at
4 GHz per sideband. This allows us to simultaneously observe a range of
spectral lines. The THz-DES is therefore able to observe across a full
bandwidth with a high acquisition speed of the desorption process without the
need for averaging scan and by observing the desorption in real time. Finally,
the radiometer used as a detector is compact and operates at room temperature
making the system easy to integrate to any UHV chamber, although it has a
lower sensitivity when compared with a cooled radiometer system. The aim of
this paper is to describe the development and operation of the THz-DES method
and to discuss its potential application in the study of COMs desorption from
the solid phase. Here we demonstrate the capabilities of the system by using
the strong THz emission lines of $N_{2}O$ as an example of typical operation,
showing that both spectra and thermodynamic data can be obtained concurrently
during these types of experiments.

##  2 THz-DES Instrument Description

The THz-DES experimental apparatus is designed to perform gas-phase emission
spectroscopy of molecules sublimating from interstellar ice analogues through
thermal mechanisms. The technique can in principle be also applied to study
molecules released from the solid state via non-thermal desorption mechanisms
such as photodesorption or ion spattering. By using a broad instantaneous
bandwidth semiconductor detector in the form of a Schottky barrier diode
mixer, combined with a high-speed digital sampling system, our experiment
provides the means of analysing desorption mechanisms whilst producing
spectral data resembling direct astrophysical observations of molecules in
star forming regions Mifsud et al. (2021). A semiconductor device offers the
additional advantages of room temperature or cryogenic operation, with the
latter offering potential for a future sensitivity enhancement.

Our instrument, shown schematically in Figure 1, comprises a total power
heterodyne radiometer (1), a desorption chamber (3) in which the desorption
process takes place, a dosing line through which a selected quantity of gas is
injected into the cell, and a cold trap that emulates cold surfaces in space
such as dust grains and icy planets and moons. The present system provides a
measurement capability within the frequency range (320-326.5) GHz and
(340-346.5) GHz with a spectral resolution and integration time that are user
selectable. Spectral images are acquired at a rate that is governed by the
integration period selected. The THz-DES system provides absolute intensity
measurements of the real line shapes of the molecular features via a
calibration module (2).

Figure 1: Schematic of the THz-DES experiment with (1) Radiometer; (2)
Calibration Module; (3) Desorption Chamber; (4) Data Acquisition. During
experiments ices are formed on the cold finger in the vacuum cell by dosing
known quantities of gas into the chamber (3). The cold finger is then heated
at a controlled rate, measured using platinum resistance thermal sensors.
Radiation "arriving" at the front end feedhorn is combined with a local
oscillator signal and processed via two fast Fourier transform wideband
spectrometers (1). The spectral data (including calibration measurements (2))
and temperature data are combined and processed to generate the final
experimental spectra as a function of time (temperature) and frequency with
absolute brightness temperature (4).

###  2.1 Desorption Chamber

The molecular chamber cell for this experiment is a high-vacuum system that
achieves an ultimate pressure in the range $10^{-6}$ mbar, as measured by
Pirani (PR10-K Edwards) and Penning (Penning CP25-K Edwards) gauges. Such a
base pressure is sufficiently low to simulate space relevant processes and to
allow for the system’s demonstration. The cell is composed of a $1~{}m$ length
of cylindrical steel tubing with an internal bore diameter of $0.13~{}m$.
Selection of the diameter is a compromise between minimising chamber volume to
limit molecule-wall interactions post desorption and minimizing the radiometer
antenna beam truncation whilst still achieving the maximum beam volume filling
and detection sensitivity. The dosing line, cold trap, and a vacuum pumping
system are connected via high vacuum ports to the main chamber. A vacuum seal
and semi-transparent THz window of $50~{}\mu m$ thick Mylar (Goodfellow) film
is located at both ends of the cell. Each window provides a signal
transmission of typically 93% Kurtz et al. (2005) with negligible absorption
within the spectral range of the instrument, but together they introduce a
Fabry-Perot interference effect within a signal path that results in a
frequency dependent variation of the spectral noise floor. This effect can be
to a large extent mitigated through the application of instrument calibration
and data post-processing techniques.

Gas species are introduced into the dosing line via small lecture bottle
sources. The line pressure is measured by a Pirani gauge (PR010 Balzers) and
thus provides a known and constant volume of gas. Molecular species introduced
to the cell are condensed on the cold trap surface, as shown in Figure 1,
which is cooled to liquid nitrogen temperatures. To avoid significant
protrusion into the interference with the receiver reception beam, the trap
internal diameter and length was restricted to $51~{}mm$ and $120~{}mm$,
respectively. A co-located heating element and platinum resistance (PRT)
thermal sensor are used to respectively vary and monitor the cold trap surface
temperature. The heater and thermal sensor are connected to a Eurotherm
control unit via a high vacuum feedthrough (LEMO) to achieve a closed loop
thermal stabilisation of the trap surface. The cold trap surface temperature
is recorded by a computer during a measurement cycle and simultaneously with
the spectral data during an experiment. A typical set-point THz-DES
temperature curve acquired during a measurement cycle is shown in Figure 2.
When the liquid nitrogen is fully evaporated (point t=0 s in Figure 2), the
temperature of the cold trap begins to increase. By changing the set point, a
thermal ramp can be applied thus allowing a degree of control of the rate of
temperature increase.

Figure 2:  Measured temperature of the cold trap over time during a desorption
experiment and with no thermal control.

###  2.2 Radiometer

At the core of the THz-DES instrument is a sensitive radiometer system
previously developed to measure molecular signatures present within the
Earth’s atmosphere (Rea et al., 2012b) and operated at room temperature. The
radiometer, which is operated in a total power mode, is divided into two main
parts: Front-End Module (FEM), which contains a heterodyne down-conversion
receiver system; and Back-End Module (BEM), which performs digital signal
processing of the FEM intermediate frequency (IF) down-converted signal. These
are outlined in Figure 3.

Figure 3: Schematic of the heterodyne spectrometer principle. The radio-
frequency signal (RF) represents THz emissions. The mixing is taking place
within the Front-end module - FEM (I) via the tuneable LO source (II). The
signal is then down converted and analysed in the back-end module - BEM (III)
with the spectrometer units.

The FEM (Figure 3, (I)) uses a sub-harmonic Schottky barrier diode image
rejection mixer in a fundamental mode waveguide structure, which has been
described in greater detail elsewhere ((Rea et al., 2009; Rea et al., 2012a)).
The sub-harmonic mixer configuration simplifies the provision of local
oscillator (LO) power and results in a compact and lower cost instrument
front-end.

Mixer sideband separation allows down-conversion of the heterodyne signal
bands located either side of the LO into two discrete IF paths that correspond
to upper sideband, USB, and lower sideband, LSB (Song, 2017) THz frequency
inputs. Signal cross-coupling between the sidebands, which is a source of
spectral contamination, is typically lower than 30 dB. The IF centre frequency
is 10 GHz with a bandwidth of 4.5 GHz per sideband. The baseband frequency of
the LO is generated by a microwave frequency synthesizer (XS-14XX, HERLEY-CTI)
at (13 to 15) GHz and combined with an external reference of 10 MHz
(OCXO-S109-LF, KVG) to provide a stable output signal. Frequency up-conversion
via an harmonic multiplier (x6) and a stage of amplification (APH631, NORTHRUP
GRUMMAN) followed by a further stage of harmonic up-conversion (x2) provides a
final LO signal of (312 - 360) GHz, which is injected into the mixer via a
waveguide LO input port. In this experiment, the LO was set at 334.5 GHz,
which provided a total spectral coverage of (322.25 to 326.75) GHz and (342.25
to 346.75) GHz corresponding to the LSB and USB, respectively (Figure 3,
(II)).

After appropriate signal conditioning, i.e. amplification and filtering, the
IF output corresponding to each sideband is sampled within the BEM by an 8-bit
high-speed analogue-to-digital converter (ADC). A dedicated 2048-point Fast-
Fourier transform (FFT) chip then produces a power spectrum of the sampled
signal, which, when divided into two 1024-point frames operating in parallel,
delivers a real-time sequential flow of spectral data. The combination of
signal sampler and processor forms a wideband digital spectrometer (WBS, STAR-
Dundee, Ltd), as shown in Figure 3, (III). Each WBS unit provides an
instantaneous spectral bandwidth of 2.5 GHz with a spectral resolution of 1.22
MHz with corresponding spectra stored in a computer for display and further
processing. Because of the limited availability of WBS units at the time of
development of our instrument, an electronically controlled switch (single-
pole double-throw: SPDT) is used to select the desired sideband prior to a
filtering stage. This configuration limits the available spectral range of the
present system and is a disadvantage that will be rectified as more WBS units
become available.

System sensitivity, as defined by the noise equivalent delta temperature
($NE\delta T$) (Hersman & Poe, 1981) depends on various parameters (equation
1) such as the system noise temperature ($T_{sys}$), the spectral resolution
(B), the integration time ($\tau$), the calibration procedure ($\tau_{c}$) and
the gain variation ($\Delta G/G$). Use of cooled Schottky ((Zimmerman et al.,
1991; Siegel et al., 1998)) or superconducting mixers (Keen et al., 1986)
would provide enhanced $NE\delta T$ but at the expense of a greater system
complexity. This improvement is an intended future instrument enhancement

$NE\delta
T=(T_{sys}+T_{scene})\times\sqrt{\frac{1}{B\times\tau_{s}}+\frac{1}{B\times\tau_{c}}+\left(\frac{\Delta
G}{G}\right)^{2}}.$ (1)

Coupling of the molecular emission signal into the mixer is achieved through
the combination of an ultra-Gaussian corrugated feed horn antenna, designed by
Airbus UK (formerly EADS Astrium), that is directly attached to the mixer, and
a subsidiary off-axis parabolic mirror with a focal length of 30.62 mm. The
latter directs the signal towards the entrance aperture of the feed horn,
which is located at the mirror focus. Viewed from the perspective of the
radiometer, the parabolic mirror quasi-collimates the radiometer antenna beam
allowing propagation through the cell with minimal truncation and with a
Gaussian defined beam waist radius of 6.318 mm as evaluated at a point 1/e
from the on-axis amplitude at 320 GHz.

To retrieve the brightness temperature of the observed desorption from
acquired data, a linear radiometer transfer function is used (Kerr et al.,
1997). The expression of a scene view (line-of-sight) brightness temperature
is retrievable depending on the noise contribution in the receiver for the
scene view and two reference targets at different temperatures (cold and hot),
as explained elsewhere (Kerr et al., 1997). A rotating plane mirror driven by
a Brushless DC-Servomotor (FAULHABER) is located between the vacuum cell and
parabolic mirror to direct the radiometer input signal path to one of three
scene views: (ii) = vacuum cell, (iii) = cold (liquid nitrogen) calibration
target and (i) = room temperature calibration target, in Figure 1. The
described instrument calibration procedure, in addition to control of the
experimental environmental temperature to within 3K, respectively minimizes
the contribution of and variation in background noise. Experimental error
arising from background noise is thus mitigated and its influence on the
accuracy of the acquired spectral data is considered negligible. The targets
provide sources of known radiometric brightness and are thus used to calibrate
the radiometric performance of the radiometer. The cold target is formed from
a small container lined at its base with a pyramidal microwave absorber (TK
RAM, Thomas Keating, Ltd) and filled with liquid nitrogen (assumed physical
temperature of 77.4 K at one atmosphere of pressure (Hardy, 1973)).

The room temperature target, which operates at typically 300 K and for
convenience we refer to here as being ‘hot’, consists of an aluminium
substrate (65 mm diameter) which is machined in the form of an array of
pyramids. A ferrite-loaded epoxy absorber (Emerson and Cuming CR114) is cast
onto the aluminium in a manner the replicates the pyramids of the array. The
THz surface reflectivity of the target has been previously determined at the
required frequency and a power reflection coefficient of less than -30 dB
measured across the observational bandwidth. A low reflection coefficient
reduces standing waves between the target, receiver and cell windows. It also
ensures that the target radiometric brightness temperature is accurately
represent by measurement of its physical temperature. The latter is monitored
to an accuracy of $\pm 0.02~{}K$ by two thermal sensors that are permanently
inserted into the aluminium substrate. In this configuration, the brightness
temperature of a molecular species can be compared to the spectral intensity
of the same species observed in a molecular cloud, depending on its optical
depth and the spectral radiance intensity (source) in accordance to radiative
transfer equations and the Rayleigh-Jeans law (Rybicki & Lightman, 1986).

###  2.3 Radiometer Sensitivity

The sensitivity of the THZ-DES instrument defines the precision to which the
desorption spectral signatures can be measured (the radiometric precision). It
is quantified by the minimum change in noise equivalent temperature that can
be detected by the radiometer system, commonly referred to as the $NE\delta
T$. The parameter is dominated by the inherent electrical noise generated by
the radiometer, signal integration time, spectral resolution selection, and
radiometer stability and variable spectral baseline artefacts, the latter
being dependent upon the environmental and system physical temperature.
Performing optimal observations via the THz-DES technique configuration of the
instrument parameters (the ‘instrument state’) in order to minimize the
$NE\delta T$.

In evaluating the radiometer $NE\delta T$, calculation of the standard
deviation of the scene brightness temperature whilst viewing a temperature-
stabilised radiometric target in the scene view was performed. From this, the
$NE\delta T$ for different integration times and spectral resolutions were
measured (Figure 4). Consistent with the equation 1, an improvement in
radiometric sensitivity is obtained by increasing the spectral resolution
(x-axis); an effect that is further enhanced when system integration times are
reduced, e.g. 0.5 s (blue curve). However, this sensitivity improvement is at
the expense of a degraded spectral resolution capability.

Figure 4: Measured noise equivalent differential temperature ($NE\delta T$) as
a function of the spectral resolution (B) at different integration time
($\tau$). The Blue curve is for 0.5 s integration time whereas the red curve
are the results for $\tau$ = 2 s and the green, $\tau$ = 7.5 s.

The output noise power of the radiometer system is proportional to the system
noise temperature ($T_{sys}$), which is the sum of noise component arising
from the antenna, mixers and IF amplifiers. The radiometer operates in
Rayleigh-Jeans area of the Black-body spectral region, where the brightness of
a Black-body is linearly proportional to the frequency. A sequential
introduction of the hot and cold signals into the radiometer input allows the
system noise to be evaluated (Hayes, 1966). When performing the above
measurement, both sidebands are evaluated and thus a double sideband (DSB)
system noise value, $Tsys_{DSB}$, is determined. In a sideband separating
instrument, an adjusted factor is required which governed by the effective
sideband gain ratio (Kerr et al., 2003). The typical sideband image rejection
factor is respectively $14.8\pm 1.1~{}dB$ for the LSB and $20.1\pm 3.4~{}dB$
for the USB with a LO at 334.5 GHz and integration time of 1 s. This provides
the single sideband (SSB) system noise temperature for each sideband, which,
in the case of the radiometric system presented here, is determined to be
$4.75\times 10^{3}\pm 4.4\times 10^{2}~{}K$.

###  2.4 System Stability

The system integration time is dependent upon the nature of the spectral
observation undertaken. Variance in the chamber is minimal as the pressure is
kept under high vacuum and no changes occurs before desorption. Therefore, it
is ultimately limited by the radiometer stability, which is dominated by the
system gain drift ($\Delta G/G$). Assessment of the system stability is
performed using the Allan Variance measurement method Schieder & Kramer (2001)
which provides a quantitative estimate for the attainable integration time
(minima on the Allan curve). This evaluation technique was applied to our THz-
DES instrument in which the radiometer viewed a constant temperature
radiometric target in the scene view. After an initial stabilization period of
15 mins, the BEM output was recorded at regular time intervals. The Allan
Variance was calculated from the raw data using an Overlapping Allan Variance
routine Leupers et al. (2013). The optimum integration can be found when the
impact of drift contribution are minimum as well as the lowest white noise
level Schieder & Kramer (2001). The THz-DES instrument stability becomes
compromised with an integration above 80 s Auriacombe et al. (2015) and any
additional integration time does not result in enhanced radiometric precision
and beyond this time a recalibration of the system is required. With improved
radiometer thermal stability, this limitation can likely be extended. However,
the rapid desorption of the ice analogue with increased temperature of the
trap limits the integration time to below 80 s.

##  3 Experimental Operation

The instrument LO frequency, digital sampling rate, and integration time can
be adjusted via software control to suit user requirements. The system
integration time, $\tau$, controls the measurement sensitivity and spectral
resolution and the sampling frequency allows the control of the IF bandwidth.
Selection of the sideband (LSB or USB) via the electrical switch and tuning of
the LO frequency defines the target spectral windows. In addition to
influencing the system sensitivity, system integration time defines the rate
at which changes in spectral features can be observed. Thus, the instrument
set-up needs to be matched to the nature of the experiment. For the current
version of the instrument configuration, thermal desorption of a molecular
species is a relatively rapid process (typically a duration of 60 s and a rate
of 0.1 K/s) and requires a relatively fast acquisition time (typically 0.5 s)
in order to capture changing spectral features. As the molecular density in
the optical path is low, a high-spectral resolution (< 3 MHz) is required in
order to fully resolve the emission line signatures.

###  3.1 Ice Deposition

During the measurement, a defined volume of gas is allowed to enter the cell
through the dosing line and with the liquid nitrogen trap cooled to
approximately 77.4 K. To minimize species cross-contamination, the dosing line
is initially evacuated to a base pressure of approximately $10^{-5}$ mbar via
a turbo pump (Leybold vacuum, Turbotronik NT-50), flushed with the selected
gas and evacuated again. This procedure is further repeated a minimum of twice
before the line is ultimately filled to a pre-determined pressure with the
species of interest (25 mbar in 3.2 L volume). If required, multiple species
can be added to the cell sequentially by using the same procedure or,
alternatively, introduced simultaneously by pre-mixing different gasses within
the dosing line. Thus, species can be condensed in pure, mixed and layered
form onto the cold trap.

In the experiments presented here, gasses condense onto the cold trap surface
to form a solid with an estimated average number of molecules per unit area of
order $2\times 10^{20}$ molecules/$cm^{2}$. This estimated value was retrieved
from the experimental data, the Ideal Gas Law and the radiative transfer model
presented in Section 3.3 (Figure 7), by approximating the number of molecules
desorbing over the duration of the data acquisition period. This allows the
simulation of interstellar and Solar System relevant ice compositions and
structures. The THz-DES instrument is particularly suited to investigate
hydrogen-deuterium exchanges between, for instance, H2O and D2O (Furuya et
al., 2016) as well as ortho-/para- transitions (Arasa et al., 2015) and
symmetry quantum transitions between A- and E- species (e.g. methanol
molecules; De Lucia et al. (1989)). Future studies will focus on such topics.

After deposition, the cold trap temperature is increased providing a source of
thermal energy that eventually results in a change of state of the molecular
material directly from solid to gas phase. The radiometer views the liberated
gas through the length of the cell and against a liquid nitrogen (77.4 K)
cooled blackbody background target that has been especially designed to
present a high emissivity (i.e. close to 1) within the THz frequency range.
Because the effective gas temperature is greater than that of the external
target, spectral features are recorded in emission against the cold background
in a similar manner to observations of an astronomical spectral source.

###  3.2 Example Spectrum Signatures

For our instrument, we have primarily studied N2O. Nitrous oxide has been
identified in the ISM (Ziurys et al., 1994), and it exhibits a bright spectral
line at 326.556 GHz corresponding to the transition 13(0,0)-12(0,0). Together
with other nitrogen oxides, it is also found in planetary environments
((Churchill & Kasting, 2000; Ioppolo, S. et al., 2020)) and cometary comae
(Saxena, 2004). Hence it has been selected as the first study target to
evaluate the suitability of our experiment for astrochemical applications.

Figure 5:  Nitrous Oxide spectra at a pressure of $8\times 10^{-1}$ mbar
before (Top) and after (Bottom) background subtraction. Two N2O spectral
features are observable at 326.56 GHz and 326.68 GHz after deleted the
standing waves coming from the experimental set-up.

As shown in Figure 4, spectral features can be detected, measured and
characterised using the THz-DES system with gas-phase molecules. For
experiments with N2O, the local oscillator was set at 334.5 GHz. A background
spectral measurement is first performed with the cell at $10^{-6}$ mbar.
Multiple reflections between the Mylar windows generate a standing wave that
in turn induces baseline artifacts in the power spectrum. The baseline
contribution is measured in the absence of the gas and subsequently subtracted
from the acquired spectra via data post processing. The background data is
then subtracted using a Matlab routine to improve the spectral baseline. A
gas-phase spectrum of 0.8 mbar of N2O before (blue curve) and after (red
curve) background subtraction is presented in Figure 5. Two N2O features are
easily detectable corresponding to the transition J = 13(0,0)-12(0,0) at
326.55 GHz with a brightness temperature of 80 K above our background
temperature and J = 13(-1,2) - 12(1,2) at 326.68 GHz with a peak at 7 K above
the background.

###  3.3 Desorption Temperature and Molecular Sensitivity

Nitrous oxide sublimation has been studied in literature as a function of
pressure and temperature ((Huebner et al., 2006; Fray & Schmitt, 2009)).
Figure 6 plots past results on the sublimation of N2O and compares them with
our instrument’s results. Starting at a temperature of 100 K, the THz-DES
desorption temperature and pressure ranges are shown above the horizontal
black line in Figure 6. Figure 2 indicates that the liquid nitrogen cooling
system used in the experimental arrangement is appropriate to study desorption
of molecules such as N2O.

Figure 6:  Desorption pressures and temperatures for N2O molecules.

Figure 7 shows the brightness temperature of N2O molecules for the transition
$13_{0,0}-12_{0,0}$ at 326.55 GHz as a function of N2O pressure. The
brightness temperature does not vary linearly as a function of the amount of
molecules emitting in the gas phase. The brightness temperature was calculated
using line-by-line radiative transfer model with a 1 m gas cell and a
blackbody source of 130 K (Dudhia, 2017). In Figure 4, the detection
sensitivity threshold is added for integration times of 0.5 s and 5 s, in blue
and red, respectively, with a spectral resolution of 1.22 MHz. The THz-DES
results presented in this manuscript were acquired with the settings
corresponding to the blue threshold, which in the case of N2O detection is
$4\times 10^{-3}$ mbar. Due to the relatively high pressure in the chamber,
the desorbed molecules are considered to be in thermodynamic equilibrium with
the chamber wall when they are detected by the radiometer.

Figure 7:  Brightness temperature of N2O molecules for the transition J =
13(0,0)-12(0,0) at 326.55 GHz as a function of N2O pressure.

Other technologies such as QMS, THz bolometer Yocum et al. (2019), and Si-
diode Theulé et al. (2020) instruments, offer a higher sensitivity when
compared with the current iteration of the THz-DES. However, our THz-DES
approach provides observational advantages through direct measurement of the
emission lines of molecules as they desorb, and in real time and over a large
instantaneous bandwidth. This allows the characterisation of each desorption
process in the chamber, independently. Additionally, it is able to detect a
wider range of species within its frequency range such as radicals, or complex
molecules and which are hard to detect via other techniques. Figures 6 and 7
show that the current configuration for our THz-DES system is fully
operational under high-vacuum conditions. The future introduction of UHV
conditions in the gas cell will require the use of a lower surface temperature
and enhanced radiometric sensitivity. The first can be achieved with a
different cryogenic system onto which deposit ices. Due to the lower pressure
conditions in an UHV chamber, the desorption temperature for $N_{2}O$ is
between 60 and 80 K, requiring the use of, for instance, a helium close-cycle
cryostat to deposit it onto a cold substrate. Moreover, to reach UHV
conditions, a better pumping system is required because the effective pumping
speed of the THz-DES gas cell is measured around 20 L/s, while standard UHV
systems are greater 100 L/s. Finally, enhanced radiometric sensitivity could
be achieved by cryo-cooling the receiver mixer low-noise IF amplifier which,
although adding instrument complexity and cost.

##  4 DESORPTION RESULTS

###  4.1 THz-DES Emission Spectra

In a first experiment, N2O was allowed to condense onto the cold trap at 77.4
K. By heating the trap, the condensed material was then thermally desorbed.
Figure 8 shows THz-DES spectra as a function of the surface cold finger
temperature (K)($T_{surface}$) and brightness temperatures (K). Changes in the
spectra profiles observed in Figure 8 are consistent with variations in
molecular density. For instance, as desorption increases, the molecular
density within the cell environment rises producing a corresponding increase
in brightness temperature and linewidth at the spectral line frequency. The
onset of N2O desorption appeared to occur at $T_{surface}$ of approximatively
100 K, as measured by Fray et al.(Fray & Schmitt, 2009). At $T_{surface}$ =
129 K, all N2O molecules have been desorbed and the maximum intensity is
observed. The molecular density within the cell then gradually decreases
towards zero as molecules exit the cell via the vacuum pump resulting in a
corresponding reduction in spectral linewidth and brightness temperature (from
$T_{surface}$ = 159 K).

Figure 8:  N2O THz-DES Result for one exposure time deposition. The contour
figure of the brightness temperature of desorbed N2O molecules is plotted as a
function of the frequency (x-axis) and the trap physical temperature (y-axis).
The A-line is a cut of the brightness temperature as a function of the
frequency at $T_{surface}$ = 124 K corresponding to the red curve in Figure 9.
The B-line is a cut of the brightness temperature as a function of the surface
temperature at 326.551 GHz corresponding to the green curve in Figure 10.

The brightness temperature for different $T_{surface}$, as a function of WBS
frequency channels (A-line in Figure 8), is shown in Figure 9. Brightness
temperatures for $T_{surface}$ of 94.8 K (blue curve), 115.3 K (red curve),
129.0 K (green curve and previous A-dashed line) and 141.5 K (black curve) are
shown from 326.545 GHz to 326.565 GHz. At $T_{surface}$ = 94.8 K, no N2O is
desorbed showing the noise floor of the experiment. Desorption commences as
the temperature further rises above 100 K. The brightness temperature
increases at the frequency of the N2O feature (326.553 GHz) as the number of
molecules emitted is higher. The value of the brightness temperature rises
from 56.74 K to 92.36 K when $T_{surface}$ increases from 115.3 K to 129 K.
When the gaseous molecules are removed from the vacuum cell, the brightness
temperature decreases (40.98 K at $T_{surface}$ = 141.5 K) and eventually
returns to the THz-DES noise floor.

Figure 9: Brightness temperature for spectral feature of N2O molecules as a
function of the frequency at different trap physical temperature, respectively
94.8 K (blue curve), 115.3 K (red curve), 129.0 K (green curve) and 141.5 K
(black curve).

The line broadening effect is observable in the frequency domain (as seen in
Figure 9). Adjacent spectrometer channels to the centre line frequency,
326.553 GHz for N2O, are tracers of this broadening effect. At first, natural
broadening occurs as the number of molecules desorbing in gas phase is low.
Then the spectral line FWHM increases due to pressure broadening (Chamberlain
& Hunten, 1987), which results in a time and temperature dependent spread
function across different spectrometer channel frequencies. The resulting
line-shape function is a Lorentzian (dashed-lines in Figure 9; Tan et al.
(2017)). The spectral line intensifies and becomes wider over the frequency
(red vs. green curves). The line intensity increases until the molecular
density in the beam path reaches a value where self-broadening is important,
leading to a higher FWHM, from 1.9 MHz to 3.0 MHz at $T_{surface}$ of 117.3 K
and 129.0 K.

Another way of analysing the measured brightness temperature of the desorbed
N2O is to plot it against $T_{surface}$ for specific frequency channels
(B-line in Figure 8) as shown in Figure 10. The four frequency channels
correspond to the central frequency line channel at 326.5535 GHz (blue curve)
and at the following spectral intervals from the central frequency: 1 channel
(red curve), 2 channels (green curve) and 5 channels (black curve). The red
and green traces represent tracers of pressure broadening, as stated above,
from which it is observed that the intensity increases until the molecular
density in the beam path reaches a value where self-broadening becomes
apparent. By analysing the central frequency, N2O desorption starts around 100
K, i.e. when the intensity from the blue curve becomes higher than the noise
floor. From $T_{surface}$ = 95 - 135 K, the brightness temperature increases
to reach a maximum value at approximately 80 K. At this point, more N2O ice is
sublimated into the desorption chamber. The newly gaseous molecules emit with
more intensity as their amount increases. The brightness temperature provides
a direct measurement of this phenomena. From $T_{surface}$ = 130 - 160 K, the
pumping rate becomes higher than the desorption rate. The number of molecules
in the chamber drops, as observed from the brightness temperature. After 160
K, no radiation is detected. All icy molecules have desorbed and are pumped
and hence removed from the cell.

Figure 10:  Brightness temperature for spectral feature of N2O molecules for
its peak frequency (blue curve) and the “wings”, which are the nearest
spectrometer channels (red, green and black curves).

###  4.2 Water Contamination Impact

Under our current experimental conditions, water molecules can co-deposit with
the nitrous oxide during gas dosing and throughout the ice experiment for a
cold trap temperature below the desorption of water ice. The THz-DES is able
to monitor the presence of any molecule which has a rotational spectral
feature within the THz-DES frequency range. Fortunately, this is the case for
water which presents a para-$H_{2}O$ $5_{1,5}-4_{2,2}$ at 325.153 GHz Pickett
et al. (1998). Water is expected to either co-desorb with $N_{2}O$ via a
volcano mechanism Smith et al. (1997) or desorb from around 200 K at a
pressure of $10~{}^{-6}$ mbar Feistel & Wagner (2007). Figure 11 shows the
desorption of the nitrous oxide (blue curve) and the brightness temperature
corresponding to the frequency of the water line at 325.153 GHz (red curve).
No water desorption is detectable for any surface temperature, either while
the nitrous oxide is desorbing or when the water desorption temperature is
reached (200 K). This shows that water contamination is negligible due to the
relatively short deposition and desorption experiment that takes place within
a period of 30 - 45 minutes.

Figure 11:  Brightness temperature of N2O molecules at 326.56 GHz (blue curve)
and brightness temperature of possible H2O molecules at 325.15 GHz (red
curve).

###  4.3 Ice Thickness Dependence

According to TPD experiments reported in literature (Fraser et al., 2002), the
thickness of a desorbing ice (in multi-layer regime) should not impact the
desorption rate because only the order of reaction would impact the desorption
slope (Thrower et al., 2009). The growth of an ice layer of an estimated solid
phase molecular density of $2\times 10^{20}$ molecules/$cm^{3}$ is referred to
as one-deposition. Ices with three times this deposited amount and 6 times
larger than the first one have been studied independently with THz-DES. Figure
12 compares the brightness temperature intensity measured for the central
feature frequency for one ’deposition’ (blue curve), three ’deposition’ (red
curve) and 6 ’deposition’(green curve). The brightness temperature maximum is
reached when an optical density saturation effect is reached. The three N2O
thick ice layers start to desorb at the same temperature (around 90 K) and
follow the same desorption trend, from $T_{surface}$ = 90 - 125 K. However,
the desorption lasts longer for the thicker ice as expected due to a larger
amount of condensed matter desorbing (red and green curves), at $T_{surface}$
of 140 K (blue curve), 155 K (red curve) and 170 K for 6 exposure times
deposition (green curve). As the pumping rates are similar in all experiments,
the gradient of the respective brightness temperatures is also similar.
Therefore, the thickness of the N2O ice does not impact the thermal desorption
rate, which is in good agreement with previous TPD experiments of similar
thermal processes.

Figure 12:  Brightness temperature versus surface temperature as a function of
the ice thickness for N2O. The blue curve is related to the brightness
temperature for an ice made via 1 exposure time deposition whereas in the case
of the red curves, 3 times more N2O has been deposited and for the green curve
6 times more.

###  4.4 Thermal Desorption Activation Energy

In a thermal desorption experiment, the activation energy corresponds to the
energy required for the pure ice to change phase from solid to gas. The
thermal desorption activation energy ($E_{des}$) can be measured with standard
TPD techniques and is usually retrieved from the Polanyi-Wigner equation and
Arrhenius equation, described in detail elsewhere (De Jong & Niemantsverdriet,
1990). The rate of desorption over temperature($R_{des}$), shown in equation 2
(King, 1975), depends on a pre-exponential factor ($\nu(\theta)$), the surface
coverage ($\theta$), the kinetic order of reaction (m), the heating rate
($\beta$), the gas constant (R), the desorption temperature (T) and desorption
activation energy ($E_{des}$)

$R_{des}(T)=\frac{\nu(\theta)\times\theta^{m}}{\beta}\times
exp\left(-\frac{E_{des}(\theta)}{R\times T}\right).$ (2)

Only the desorbing region ($T_{surface}$ = 90 - 125 K) in Figure 12 are used
to quantitatively determine the N2O thermal desorption activation energies for
the three ice thicknesses. To calculate $E_{des}$, each brightness
temperatures are fitted using the Reference Forward model (Dudhia (2017);
shown in Figure 7) in order to retrieve the amount of molecules desorbing at
their corresponding surface temperature. As stated previously, the
desorption’s slopes in Figure 12 are similar for various surface coverage.
This corresponds to a $0^{th}$ reaction kinetic order and would made the term
$\theta^{m}$ equal to 1 in equation 2. The THz-DES desorption activation
energies calculated for one, three and six deposition exposure times are
$13.4\pm 3.2$ kJ/mol, $10.9\pm 0.3$ kJ/mol and $13.9\pm 2.5$ kJ/mol,
respectively. In the literature, $E_{des}$ for N2O ices is between 18 and 29
kJ/mol with standard TPD experiments (Black et al., 1930; Bryson et al., 1974;
Cornish & Avery, 1990; Kiss et al., 1991; Sawabe & Matsumoto, 1992; Brown &
Bolina, 2006; Lian et al., 2010; Toker et al., 2013). The reference enthalpy
energy for sublimation of N2O is given between $23.6\pm 0.4$ kJ/mol (Bryson et
al., 1974). This value correspond to the sublimation of a N2O of an ice of
more than $10^{19}$ molecules with a pressure up to $10^{-4}$ mbar.

The thermal desorption activation energies measured with the THz-DES
experiment are therefore within the same order of magnitude of those presented
in the literature. Differences could be explained by limitations within the
THz-DES experimental set-up, such as low pressure (only high-vacuum), possible
re-adsorption of desorbed molecules, substrate made of stainless steel with
Kapton heaters, non-linear heating rate, etc. However, it is also possible
that the measured desorption activation energies is accurate and would simply
differ from literature values because of the existence of spectroscopic
preferential desorption mechanism, called rotational cooling. For instance,
this was measured by Lian et al. (2010), where the N2O desorption energy was
about 22.19 kJ/mol at 2236 $cm^{-1}$ and 28.95 kJ/mol at 2270 $cm^{-1}$. To
validate this hypothesis, it would be necessary to characterise the THz-DES
signal of different spectral transitions to probe the presence of rotational
cooling, which is beyond the scope of this work.

##  5 Conclusions

We have developed an experimental method that emulates thermal desorption
mechanisms that occur in star forming regions of the ISM and that can
therefore be used to support astrochemical investigations. Our initial
instrument configuration uses a heterodyne receiver operating between 320-350
GHz in a sideband separating detection mode with interfacing optics and a
calibration system that together form a sensitive radiometer operating at room
temperature. The system is combined with a vacuum desorption cell, dosing
line, and cold trap to freeze and then thermally desorb species from the solid
to the gas phase that are then spectroscopically observed against a cold
background reference. Spectral emission brightness temperatures of species are
recorded over time with high spectral resolution.

The THz-DES system exhibits the advantage of measuring the absolute emission
intensities of desorbing molecules by calibrating the measured spectra. The
acquisition is performed in real time, that is no averaging scan, with a 4
GHz, single-sideband, instantaneous bandwidth. The spectroscopic information
provided by the THz-DES experiment allows the identification of molecules
desorbing from an ice and emitting against a 77.4 K blackbody in the spectral
range covered by the instrument. This specific instrumental feature is
potentially advantageous for the study of radicals and complex organic
molecules, since their unambiguous identification in standard TPD measurements
with a QMS are not straight forward.

Our work has demonstrated the system performance and its potential future
impact in astrochemical studies of thermal and non-thermal desorption
mechanisms. We have shown, for instance, that desorption of different
thicknesses of $N_{2}O$ ice does not introduce changes in the desorbing rate
of $N_{2}O$. The thermal desorption activation energy for $N_{2}O$ was
calculated from the THz-DES results between 10 and 18 kJ/mol, which correlates
with previous results based on standard quadrupole mass spectrometry
techniques as reported in the literature (18 to 29 kJ/mol). Thermal desorption
would appear to be a rotational energy selective mechanism as the activation
energies vary depending on the spectral lines observed. By observing different
spectral lines with THz-DES for one molecular kind, it will be possible to
identify any rotational cooling during desorption Tully (1994).

Future instrumental developments will include the introduction of a wider
spectral bandwidth through the addition of more radiometer channels to
increase the spectral observation range. An improved sensitivity will be
achieved by cooling the FEM mixer and the addition of more WBS units to allow
simultaneous observation. When combined with an ultra-high vacuum gas cell,
enhanced simulation of the interstellar and Solar System environments will be
possible. This will support astronomers in the investigation of a series of
thermal and non-thermal desorption processes that include photo and chemical
desorption, and cosmic ray induced sputtering of the molecular ice.

## Acknowledgements

The authors would like to thank the support of Star Dundee, Ltd for its advice
and help regarding the WBS spectrometer software. SI acknowledges the Royal
Society for financial support.

## Data Availability

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

## References

  * Arasa et al. (2015) Arasa C., Koning J., Kroes G.-J., Walsh C., van Dishoeck E. F., 2015, Astron. Astrophys., 575, A121
  * Auriacombe et al. (2015) Auriacombe O., Fraser H., Ellison B., Rea S., 2015, in IET Colloquium on Millimetre-Wave and Terahertz Engineering Technology 2015. pp 1–4
  * Balucani et al. (2015) Balucani N., Ceccarelli C., Taquet V., 2015, Monthly Notices of the Royal Astronomical Society: Letters, 449, L16
  * Belloche et al. (2014) Belloche A., Garrod R. T., Müller H. S. P., Menten K. M., 2014, Science, 345, 1584
  * Belloche et al. (2019) Belloche A., Garrod R. T., Müller H. S. P., Menten K. M., Medvedev I., Thomas J., Kisiel Z., 2019, A&A, 628, A10
  * Bergantini et al. (2018) Bergantini A., Góbi S., Abplanalp M. J., Kaiser R. I., 2018, The Astrophysical Journal, 852, 70
  * Black et al. (1930) Black H. K., van Praagh G., Topley B., 1930, Trans. Faraday Soc., 26, 196
  * Brown & Bolina (2006) Brown W. A., Bolina A. S., 2006, Monthly Notices of the Royal Astronomical Society, 374, 1006
  * Brown et al. (2006) Brown W. A., Viti S., Wolff A. J., Bolina A. S., 2006, Faraday Discuss., 133, 113
  * Bryson et al. (1974) Bryson C. E., Cazcarra V., Levenson L. L., 1974, Journal of Chemical & Engineering Data, 19, 107
  * Chamberlain & Hunten (1987) Chamberlain J. W., Hunten D. M., 1987
  * Churchill & Kasting (2000) Churchill D. J., Kasting J. F., 2000, in Schürmann B., ed., ESA Special Publication Vol. 451, Darwin and Astronomy : the Infrared Space Interferometer. p. 183
  * Collings et al. (2004) Collings M. P., Anderson M. A., Chen R., Dever J. W., Viti S., Williams D. A., McCoustra M. R. S., 2004, Monthly Notices of the Royal Astronomical Society, 354, 1133
  * Cornish & Avery (1990) Cornish J. C., Avery N. R., 1990, Surface Science, 235, 209
  * Davies et al. (1992) Davies S. R., Cunningham C. T., Little L. T., Matheson D. N., 1992, International Journal of Infrared and Millimeter Waves, 13, 647
  * De Jong & Niemantsverdriet (1990) De Jong A., Niemantsverdriet J., 1990, Surface Science, 233, 355
  * De Lucia et al. (1989) De Lucia F. C., Herbst E., Anderson T., Helminger P., 1989, Journal of Molecular Spectroscopy, 134, 395
  * Dudhia (2017) Dudhia A., 2017, Journal of Quantitative Spectroscopy and Radiative Transfer, 186, 243
  * Fayolle et al. (2011) Fayolle E. C., Bertin M., Romanzin C., Michaut X., Oberg K. I., Linnartz H., Fillion J.-H., 2011, The Astrophysical Journal Letters, 739, L36
  * Feistel & Wagner (2007) Feistel R., Wagner W., 2007, Geochimica et Cosmochimica Acta, 71, 36
  * Fraser et al. (2001) Fraser H., Collings M., McCoustra M., Williams D., 2001, MNRAS, 327, 1165
  * Fraser et al. (2002) Fraser H. J., Collings M. P., McCoustra M. R. S., 2002, Review of Scientific Instruments, 73, 2161
  * Fray & Schmitt (2009) Fray N., Schmitt B., 2009, Planetary and Space Science, 57, 2053
  * Fuchs et al. (2006) Fuchs G. W., et al., 2006, in NASA LAW 2006. p. 73
  * Fuchs et al. (2009) Fuchs G. W., Cuppen H. M., Ioppolo S., Romanzin C., Bisschop S. E., Andersson S., van Dishoeck E. F., Linnartz H., 2009, A&A, 505, 629
  * Furuya et al. (2016) Furuya K., van Dishoeck E. F., Aikawa Y., 2016, A&A, 586, A127
  * Hardy (1973) Hardy W. N., 1973, IEEE Transactions on Microwave Theory and Techniques, 21, 149
  * Hayes (1966) Hayes D. D., 1966, High Gain antenna techniques. System gain-to-noise temeprature ratio measurements on an adaptively phased array. Technical Report No ADC-TR-66-125, Vol I
  * Herbst & van Dishoeck (2009) Herbst E., van Dishoeck E. F., 2009, Annual Review of Astronomy and Astrophysics, 47, 427
  * Hersman & Poe (1981) Hersman M. S., Poe G. A., 1981, IEEE Transactions on Microwave Theory and Techniques, 29, 32
  * Huebner et al. (2006) Huebner W., Benkhoff J., Capria M.-T., Coradini A., De Sanctis M. C., Orosei R., Prialnik D., 2006
  * Ioppolo, S. et al. (2020) Ioppolo, S. Kanuchová, Z. James, R. L. Dawes, A. Jones, N. C. Hoffmann, S. V. Mason, N. J. Strazzulla, G. 2020, A&A, 641, A154
  * Ioppolo et al. (2008) Ioppolo S., H. Cuppen M., Romanzin C., van Dishoeck E. F., Linnartz H., 2008, The Astrophysical Journal, 686, 1474
  * Keen et al. (1986) Keen N. J., Mischerikow K. D., Ediss G. A., Perchtold E., 1986, Electronics Letters, 22, 353
  * Kerr et al. (1997) Kerr A. R., Feldman M. J., Pan S.-K., 1997, in Eighth International Symposium on Space Terahertz Technology. p. 101
  * Kerr et al. (2003) Kerr A. R., Pan S. K., E. E. J., 2003, Memo 357, Sideband calibration of millimeter-wave receivers. ALMA, NRAO
  * King (1975) King D. A., 1975, Surface Science, 47, 384
  * Kiss et al. (1991) Kiss J., Lennon D., Jo S. K., White J. M., 1991, The Journal of Physical Chemistry, 95, 8054
  * Kurtz et al. (2005) Kurtz D. S., Crowe T. W., Hesier J. L., Porterfield D. W., 2005, 30th Int Conference on Infrared and Millimeter Waves, 1, 76
  * Leupers et al. (2013) Leupers R., Bhattacharyya S. S., Deprettere E. F., 2013, Handbook of Signal Processing Systems. Vol. 2, Springer Science
  * Lian et al. (2010) Lian J. C., Kieseritzky E., Gonchar A., Sterrer M., Rocker J., Gao H.-J., Risse T., 2010, The Journal of Physical Chemistry C, 114, 3148
  * Linnartz et al. (2015) Linnartz H., Ioppolo S., Fedoseev G., 2015, International Reviews in Physical Chemistry, 34, 205
  * Little et al. (1992) Little L. T., Davies S. R., Cunningham C. T., 1992, International Journal of Infrared and Millimeter Waves, 13, 659
  * McGuire (2021) McGuire B. A., 2021, arXiv e-prints, p. arXiv:2109.13848
  * Mifsud et al. (2021) Mifsud D. V., Hailey P. A., Traspas Muiña A., Auriacombe O., Mason N. J., Ioppolo S., 2021, Frontiers in Astronomy and Space Sciences, 8
  * Müller et al. (2005) Müller H. S., Schlöder F., Stutzki J., Winnewisser G., 2005, Journal of Molecular Structure, 742, 215
  * Öberg et al. (2011) Öberg K. I., Qi C., Wilner D. J., Andrews S. M., 2011, ApJ, 743, 152
  * Pickett et al. (1998) Pickett H., Poynter R., Cohen E., Deltisky M., Pearson J., Muller H., 1998, Journal of Quantitative Spectroscopy and Radiative Transfer, 60, 883
  * Rea et al. (2009) Rea S. P., Alderman B., Henry M., Matheson D. N., Munro Y., 2009, IEEE Microwave and Wireless Components Letters, pp 101–103
  * Rea et al. (2012a) Rea S., Oldfield M., Moyna B., Gerber D., Whale M., Murk A., 2012a, Infrared, Millimeter, and Terahertz Waves (IRMMW-THz)
  * Rea et al. (2012b) Rea S. P., Renker M., Moyna B. P., Gerber D., Whale M., Murk A., 2012b, in 2012 37th International Conference on Infrared, Millimeter, and Terahertz Waves. pp 1–2
  * Rybicki & Lightman (1986) Rybicki G. B., Lightman A. P., 1986, Radiative Processes in Astrophysics
  * Sawabe & Matsumoto (1992) Sawabe K., Matsumoto Y., 1992, Chemical Physics Letters, 194, 45
  * Saxena (2004) Saxena P. P., 2004, Bulletin of the Astronomical Society of India, 32, 185
  * Schieder & Kramer (2001) Schieder R., Kramer C., 2001, A&A, 373, 746
  * Siegel et al. (1998) Siegel P. H., Mehdi I., Dengler R. J., Lee T. H., Humphrey D. A., Pease A., Zimmermann R., Zimmermann P., 1998, in 1998 IEEE MTT-S International Microwave Symposium Digest (Cat. No.98CH36192). pp 407–410 vol.2
  * Smith et al. (1997) Smith R. S., Huang C., Wong E. K. L., Kay B. D., 1997, Phys. Rev. Lett., 79, 909
  * Song (2017) Song H.-J., 2017, Proceedings of the IEEE, 105
  * Tan et al. (2017) Tan S., Berceau P., Saraf S., Lipa J. A., 2017, Opt. Express, 25, 7645
  * Tanarro et al. (2018) Tanarro I., et al., 2018, A&A, 609, A15
  * Terwisscha van Scheltinga et al. (2018) Terwisscha van Scheltinga J., Ligterink N. F. W., Boogert A. C. A., van Dishoeck E. F., Linnartz H., 2018, A&A, 611, A35
  * Theulé et al. (2020) Theulé P., Endres C., Hermanns M., Bossa J.-B., Potapov A., 2020, ACS Earth and Space Chemistry, 4, 86
  * Thrower et al. (2009) Thrower J. D., Collings M. P., Rutten F. J. M., McCoustra M. R. S., 2009, The Journal of Chemical Physics, 131, 244711
  * Tielens & Hagen (1982) Tielens A. G. G. M., Hagen W., 1982, A&A, 114, 245
  * Toker et al. (2013) Toker G., Sagi R., Bar-Nachum S., Asscher M., 2013, The Journal of Chemical Physics, 138, 044710
  * Tully (1994) Tully J. C., 1994, Surface Science, 299-300, 667
  * Van Dishoeck, E. F. et al. (2014) Van Dishoeck, E. F. Bergin, E. A. Lis, D. C. Lunine, J. I. 2014, Protostars and Planets VI, p. 944
  * Van Dishoeck, E.F. (2017) Van Dishoeck, E.F. 2017, Proceedings of the International Astronomical Union, 13, 3–22
  * Walsh et al. (2016) Walsh C., et al., 2016, ApJ, 823, L10
  * Wehres et al. (2017) Wehres N., et al., 2017, in IAU Symposium.
  * Wehres et al. (2018) Wehres N., et al., 2018, Physical Chemistry Chemical Physics (Incorporating Faraday Transactions), 20, 5530
  * Wootten & Thompson (2009) Wootten A., Thompson A. R., 2009, Proceedings of the IEEE, 97, 1463
  * Yocum et al. (2019) Yocum K. M., Smith H. H., Todd E. W., Mora L., Gerakines P. A., Milam S. N., Widicus Weaver S. L., 2019, The Journal of Physical Chemistry A, 123, 8702
  * Yocum et al. (2021) Yocum K. M., Milam S. N., Gerakines P. A., Weaver S. L. W., 2021, ] 10.3847/1538-4357/abf14e, 913, 61
  * Zimmerman et al. (1991) Zimmerman R., Zimmerman R., Zimmerman P., 1991. Eur. Microw. Conf.
  * Ziurys et al. (1994) Ziurys L. M., Apponi A. J., Hollis J. M., Snyder L. E., 1994, ApJ, 436, L181