EXPERIMENTAL COMPARISON BETWEEN PSBD PHYSICAL MODELS 

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The Submillimeter Wave Instrument (SWI)

JUICE-SWI is a submillimeter heterodyne spectrometer with a frequency resolution of ~107 covering two spectral ranges around 600 GHz and 1200 GHz [JUICE-SWI-Payload (2016)] proposed by an European international consortium headed by the Max Planck Institute für Sonnensystemforschung (MPS) of Gottingen, Germany [Hart13]. The science objectives of SWI are the investigation of the middle atmosphere of Jupiter and the atmospheres and exospheres of the Galilean satellites [Hart13]. SWI consist of three primary units: the Telescope and Receiver Unit (TRU), the Radiator Unit (RAU) and the Electronic Unit (EU). Fig. 1.2. JUICE-SWI RTU block diagram of the different parts of the instrument, as 21th June 2016. The Receiver Unit (RU) in light blue is the only cooled part of the SWI instrument.  The RTU consists of the Telescope Unit (TU) with a 30 cm antenna effective diameter with tracking mechanisms and a receiver optical bench, and the microelectronic modules of the sub-millimeter Receiver Unit (RU). Two independent double sideband receivers were initially proposed in the SWI baseline to obtain simultaneous observing capability for two different frequencies within the 530-625 GHz frequency range [Jaco15].
However, an alternative configuration was open in the baseline of the submillimeter instrument shown in Fig. 1.2. It consists of two independent double sideband receivers, around 600 GHz and 1200 GHz. This optional second channel was never developed based on PSBDs in Europe and the only precedent was developed by JPL in the USA [Schl14]. The 1.2 THz channel was motivated by methane transition at 1256 GHz but a wide richness of compounds can be found in this frequency range [Encr04]. However, this channel had to be demonstrated and developed by the European SWI consortium in order to be included in the fly RTU module. LERMA got involved in the development and demonstration of the 1.2 THz channel for SWI which is the motivation of this PhD.
work.
 The RAU consists of a radiator used to passively cool down the Sub-millimeter detectors between 120-150 K to improve their sensitivity and their signal-to-noise ratio.
 The EU consists of several electronic devices dedicated to determine the spectral line shapes and the lines surveys. A detailed study of the SWI structural and tracking systems of the RTU is carried out in [Jaya14].
The different contributions of European institutions in the consortium were distributed as follows. LERMA represents the French contribution distributed between the RU and the EU. MPS represents the German contribution to the structure design and manufacture of the RTU and RAU as well as the project management led by Dr. P. Hartogh. Omnisys represents Sweden’s contribution divided between the RU and the EU. The Laboratorium Satelitarnych Aplikacli Ukladow FPGA (CBK) represents Polish’s contribution to the EU. RPG represents the second German’s contribution focused on the amplification stage of the RU. The National Institute of Information and Communications Technology (NICT) represents Japan’s contribution focused on the primary mirror manufacture of the TU and some components of the EU. The Institut of Applied Physics (IAP) University of Bern represents Switzerland’s contribution focused on the optical test bench design to match the signal obtained by the TU into the RU.
All-solid-state Planar Schottky Diode technology has been chosen for the microelectronic MMIC chips that conform the LO multiplication chains and the frequency mixers for SWI. A passive cooling system is proposed to control temperature conditions of the SWI instrumentation between 120-150 K. It requires a bandwidth of a 20 % around the center frequency of each receiver with 100 MHz spectral resolution. The sensibility specifications proposed less than 1500 K of DSB noise temperature at 120-150 K for the 600 GHz channel and less than 4000 K for the 1200 GHz channel. LERMA got involved in SWI project in summer 2013 and it was in charge of the industrial delivery of two USO at 100 MHz and two K-band synthesizer of the SWI-EU to generate the initial LO chain bandwidth for each receiver between 22-26 GHz. LERMA was also in charge of the development and delivery of a frequency multiplier of the SWI-RU between 270-320 GHz to complete the LO multiplication chain of each receiver. Omnisys was in charge of the frequency mixers development and delivery for the 600 GHz channels. A contract between LERMA and Omnisys was closed within the framework of the SWI project. In summer 2014, LERMA got involved in the development of a 1.2 THz frequency mixer in the framework of the European SWI consortium. LERMA of the Observatoire de Paris in close collaboration with the Laboratoire de Photonique et de Nanostructures (LPN) of the Centre National de la Recherche Scientifique (CNRS) represent the French contribution to the SWI project. LERMA was in charge of the design, optimization and test of the developed modules while LPN-CNRS was in charge of manufacturing the modules. LERMA’s contribution in the development of a 1.2 THz mixer prototype was initially supported by a contract between Centre National d’Études Spatiales CNES and LERMA-LPN, and this was complemented by this PhD work, fully supported by Labex Exploration Spatiale des Invironnements Planétaires (Labex-ESEP) and granted to this author, Diego Moro Melgar. The CNES financial support and LERMAs commitment culminated with an ESA official contract that allowed LERMA to get involved in the 1.2 THz channel for SWI. LERMAs commitment in the CNES and ESA contracts was the demonstration of a PSBD-based 1.2 THz sub-harmonic frequency mixer able to fulfill the SWI specifications (less than 4000 K DSB noise temperature at 120 K). The challenge was proposed to both LERMA and Omnisys. The demonstration of the 1.2 THz channel feasibility was successfully accomplished by both groups at the beginning of 2016.
The satisfactory results obtained by LERMA in the development of a 1.2 THz receiver culminated in summer 2016 with a full financial support by CNES of LERMA’s contribution to the 1.2 THz channel delivery. However, the French contribution was not completely finished when this doctoral work was accomplish and further work on the final fly version of the 1.2 THz channel was required.

Design and Optimization of PSBD-based MMIC modules

The methodology followed in the design and optimization of PSBD-based MMIC modules for multiplication and mixing applications is briefly described in this section. Further details are referenced to previous works and documentation where it is detailed and discussed. The flowchart of the design and optimization process is illustrated in Fig. 1.3. It mainly consist on a three dimensional Computer-Aided Design (CAD) software with an Electromagnetic Field Simulator implemented to solve the Maxwell equations in a defined mesh of the 3D structure.
These kinds of software are focused on the solution of the S-parameters of a structure that allow characterizing the losses associated to a specific geometry, materials and impedance matching. However, these kinds of software are not sufficient to carry out the optimizations of MMIC modules since the electrical behavior of active (oscillators) or passive (PSBDs, HBVs, SIS, HEB, etc) devices are not accounted for in HFSS simulations. The complementary software used in this work to develop the virtual design of each MMIC module is the socalled Advance Design System (ADS) software. It is an electronic design automation software system developed by Keysight Techonologies which is dedicated to RF, microwave and high speed digital applications. ADS software allows us to carrying out harmonic balance simulations of non-linear electronic circuits to obtain their frequency and time domain response. The CAD software that has been mainly used in this work is the High Frequency Simulation/Structure Software (Ansys-HFSS) [Ansys-HFSS 2016].

Analytical Model of Planar Schottky Barrier Diodes

This chapter is dedicated to the presentation of the physical model for the PSBDs used in this work. SBDs are well-known SC devices and the Bethe theory is a well-established analytical model to describe their electrical behavior. Important work has been developed during decades related with SBDs small-signal equivalent circuit models [Gonz97]. However, experimental devices are much more complex to describe, starting with two and three dimensional phenomena that can modify the ideal behavior described by Bethe’s theory.
Additionally, the PSBDs used in the THz modules developed in this work, function under large-signal conditions in which the validity of the small-signal equivalent circuit model is questionable. Theoretical research has been motivated by these phenomena, theoretical studies are available in the bibliography related with geometric phenomena [Dick67], [Cope70], [Geld91], [Louh94], [Moro16], fabrication process and defects [Call87], [Pére05], [Tung14] low temperature phenomena [Pad65], [Koll86], [Louh93], [Sieg91], [Hübe98], cyclostationary conditions [Shik04], [Pére04], [Graf10], saturation carrier phenomena [Graj00b], [Pard12], hot electron phenomena [Hjel90], etc. As a consequence, there is no consensus concerning the most suitable model of PSBDs for these experimental high frequency applications. This is mainly due to the high complexity of real phenomena, especially dynamic phenomena, that cannot be easily differentiated in experimental devices and they often interact with each to other. An additional complexity is associated with the commercial non-linear simulators, like ADS, that have not been specifically developed to take into account frequency dependent phenomena in the Schottky diode model. This results in a widespread use of a simple analytical model for SBDs simulations which is well described in this section since it is integrated into the ADS software.
The most common technique to simulate the SBD dynamic response in large-signal conditions is based on the so-called harmonic balance (HB) method [Gilm91a], [Gilm91b], [Rizz94]. The description of the electrical behavior of the device in terms of an analytical model is usually required by HB simulators, which provide the time and frequency domain response of the electrical device within a given circuit. Although HB simulations are able to provide the dynamic response of an electronic device under time-dependent excitations, static analytical models of the device are usually required by commercial HB simulators. This is the case of the HB simulations carried out with the ADS simulator within this work, where the electrical behavior of SBDs is given by the static current-voltage (I-V) and capacitancevoltage (C-V) characteristics of the diode, which are incorporated by means of analytical equations that require to comply with continuity conditions at least up to their first derivate.
These analytical functions are then applied to simulate the electric response in the circuit elements of the so-called Lumped Elements Circuit (LEC) model [Gonz97], [Pard14], that will be used to simulate the SBDs. The limitations imposed by commercial simulators has motivated important research work during last decades in the development of “in-house tools” for PSBDs modeling. The existence of frequency-dependent phenomena in Schottky diodes is well-known, especially at very high frequencies, where the transit time of the electrons can be in the same order of the signal period. Important advancements have been carried out by theoretical researchers specialized in Drift-Diffusion (DD) [Graj00a], [Graj04], [Sile05], Hydro Dynamic (HD) and Monte Carlo [Gonz97], [Pard12], [Pard15], [Pard16] models to simulate SBDs and shed light on non-equilibrium conditions. Further implementations of these theoretical models in HB simulators have notably contributed to improve the knowledge about the operation of circuits based on SBDs under dynamic conditions. The MC simulator has demonstrated to be the most suitable method to study electronic SC devices since it is the only physical model that uses a microscopic approach to study the electrons’ behavior. Very sophisticated MC simulators have been developed to account for all kind of dynamic phenomena associated to the electrons transport in SC devices. The most important challenge of MC simulators is the strong computational requirements to simulate these devices. However, extraordinary advancements have been carried out in this direction by Dr. J. Siles in [Sile05], [Sile09a] using an improved DD model for PSBDs and Dr. D. Pardo in [Pard15], [Pard16] with a MC simulator coupled with HB simulations. The main challenge of these advanced PSBDs models is their strong computational requirements and the difficulty to match them with the techniques used in experimental applications. The coupling of a onedimensional MC simulator with HB simulations carried out by Dr. D. Pardo would not have been affordable for the practical development of this work due to the extremely demanding computational capacity required to perform such coupled MC-HB simulations of PSBDs in RF conditions. Additionally, one-dimensional simulations do not correctly describe the operation of real PSBDs in which 2D models can more accurately describe them, as discussed in this work. Based on the analysis carried out by Dr. J. Grajal in [Graj00a], [Graj00b] and Dr. J. Siles in [Sile08a], [Sile09a], we will try to optimize the properties of the PSBDs for the different modules developed by LERMA-LPN for specific multiplication and mixing applications.

The Two-Dimensional Monte Carlo Simulator

The ensemble MC simulators self-consistently coupled with a one/two-dimensional Poisson solver have demonstrated to be the most suitable tool in the study of modern ultra-scaled SCbased electronic devices [Mate15]. This is due to the microscopic approach to the Boltzmann’s transport equation solution in SC materials together with a precise consideration of the topology of the devices. This simulator was provided by the Research Group on High- Frequency Nanoelectronic Devices of the University of Salamanca (http://nanoelec.usal.es/) and has been previously used for the simulation of several types of semiconductor devices. A one-dimensional version of this MC simulator was extensively used by this group for the study of III-V SBDs in [Gonz93], [Gonz97], [Shik04], [Pére04], [Pére05], [Shik06] and in Sibased SBDs in [Mart96], [Reng07], [Pasc07], [Pasc09]. It was extended to the current version of the 2D-MC simulator and extensively used in the study of HEMTs by Dr. J. Mateos [Mate99], [Mate00a], [Mate00b], [Mate04a], [Mate04b], [Vasa10] and was later modified by this author to include the gate leakage current in [Moro14]. This 2D-MC simulator has also proven its power in the study of ballistic devices [Mate03], [Iñig07] and self-switching nanodiodes [Iñig07], [Iñig08], [Iñig11] as well as in the experimental field as a powerful simulation tool for developing new applications at THz frequencies [Sang13], [Dahe16]. This 2D-MC simulator has been extensively used throughout this work to study PSBDs anddevelop the compact models that have been applied for the design of the multipliers and mixers fabricated in LERMA-LPN.
The flow chart of the ensemble 2D-MC simulations is illustrated in Fig. 2.1. The first point of a MC simulation is the definition of the SC physical properties, the SC layers and their geometries, the position of the metallic contacts and the physical parameters of the system (temperature, boundary conditions). Three non-parabolic spherical valleys (Γ, L, and X) are used to model the conduction band of the GaAs semiconductor layers [Fisc91]. The Schottky and the ohmic contacts as well as the boundary conditions of the structure are simulated as in [Gonz96], [Gonz97], [Mate00a], [Mate00b], [Mate04b], [Mate04b]. The Schottky contact is simulated as a perfect absorbing boundary, that is, all the carriers reaching the metal contact leave the structure and no carriers are injected from the metal into the semiconductor. This condition leads to the modification of the Maxwellian velocity distribution of the electrons at some tens of nanometers from the Schottky interface to a perfect hemi-Maxwellian distribution at the interface [Bacc76], [Mazi87], [Trav10]. Regarding the ohmic contact model, it imposes charge neutrality in the proximities of the electrode by injecting carriers with the appropriate thermal distribution (velocity-weighted hemi-Maxwellian) at the lattice temperature [Gonz97]. A mesh of the 2D structure is required to define the nodes where the Poisson equation is solved and the mesh where the electric field is calculated. The mesh size is defined in accordance with the Debye’s length of the SC [Jaco89], which is around 1 to 5 nm in GaAs at the practical doping levels. A time discretization of the simulation using a time step, dt, is also required in ensemble 2D-MC simulations to define the instants at which the electrical field is updated and the data of each carrier is stored (both for having transient and average values of the different quantities: electron concentration, velocity, energy, electric potential and field, etc. ). The choice of the time step is limited by the plasma frequency [Hock88] and the dielectric relaxation time [Tiwa92] of the SC, a value of around 1 to 2 fs is usually used in our GaAs simulations. The initial number of particles and their position is defined in accordance with the doping of each mesh and the initial kinetic energy associated to each particle is randomly defined following the Maxwell-Bolzmann distribution. However the number of particles within the device changes during the simulation due to the entrance and exit of electrons through the electrodes. The total simulation time T=N·dt has to be also chosen, where N is the number of time steps to be computed before finishing the simulation.
Once the structure is defined, the Poisson equation is solved by LU decomposition [Mate96] at T=0 to obtain the electric potential at each node of the mesh and the electric field in each cell. The particles’ simulation loop is initiated by moving each electron during a random period of time under the electric field of the mesh where it is placed. The free flight time is randomly obtained in accordance with the energy dependent scattering probabilities of such electron in the defined SC (whose properties depend on the mesh where the electron is moving). When the free flight ends, if the time step has not finished, the electron suffers a scattering mechanism (considered instantaneous), that is also randomly selected according to the scattering probabilities associated with the energy of the electron at that time instant.

Table of contents :

1 THE SUBMILLIMETER RANGE FOR PLANETARY SCIENCE 
1.1 THE HETERODYNE DETECTION
1.1.1 THZ FREQUENCY MIXERS
1.1.2 THZ LOCAL OSCILLATOR
1.1.3 SPACE MISSIONS AND THZ SCIENCE
1.2 THE JUICE PROJECT BASELINE
1.2.1 THE SUBMILLIMETER WAVE INSTRUMENT (SWI)
1.3 DESIGN AND OPTIMIZATION OF PSBD-BASED MMIC MODULES
1.4 STRUCTURE AND OBJECTIVES OF THIS PHD WORK
PART 1: PLANAR SHOTTKY BARRIER DIODES MODELING
2 ANALYTICAL MODEL OF PLANAR SCHOTTKY BARRIER DIODES 
2.1 THE TWO-DIMENSIONAL MONTE CARLO SIMULATOR
2.1.1 PSBD STRUCTURE IN MONTE CARLO SIMULATIONS
2.2 THE CURRENT TRANSPORT AND CAPACITANCE MODEL IN PSBDS
2.2.1 BUILT-IN VOLTAGE AND BARRIER HEIGHT RELATIONSHIP
2.2.2 ANALYTICAL MODEL OF CURRENT TRANSPORT IN PSBDS
2.2.3 RESISTANCE MODEL OF PSBDS
2.2.4 CAPACITANCE ANALYTICAL MODEL IN PSBDS
2.3 THE ANALYTICAL MODEL IN HARMONIC BALANCE SIMULATIONS
2.3.1 SINGLE VARACTOR PSBD SIMULATIONS FOR DOUBLERS
2.3.2 ANTIPARALLEL VARISTOR PSBDS SIMULATIONS FOR MIXERS
2.4 CONCLUSIONS
PART 2: THE JUICE-SWI PROJECT
3 A POWER-COMBINED 300 GHZ FREQUENCY DOUBLER
3.1 THE 300 GHZ FREQUENCY DOUBLER CHIP
3.1.1 DESCRIPTION OF THE VIRTUAL DEVICE
3.1.2 DESCRIPTION OF THE MECHANICAL BLOCK
3.1.3 EXPERIMENTAL RESULTS
3.1.4 EXPERIMENTAL COMPARISON BETWEEN PSBD PHYSICAL MODELS
3.2 A POWER-COMBINED 300 GHZ FREQUENCY DOUBLER
3.2.1 QUADRATURE HYBRID COUPLER
3.2.2 DESCRIPTION OF THE MATCHING NETWORK DESIGN
3.2.3 MECHANICAL BLOCK DESIGN: DC CIRCUIT
3.2.4 EXPERIMENTAL RF PERFORMANCE
3.2.5 COMPARISON WITH ADS-HFSS INDIVIDUAL SIMULATIONS
3.3 CONCLUSIONS
4 A 600 GHZ FREQUENCY DOUBLER 
4.1 TWO-ANODES 600 GHZ TWO ANODES FREQUENCY DOUBLER
4.1.1 VIRTUAL DEVICE
4.1.2 MECHANICAL BLOCK
4.1.3 EXPERIMENTAL DEVICE
4.1.4 SIMULATIONS OF THE TWO-ANODES 600 GHZ FREQUENCY DOUBLER
4.1.5 EXPERIMENTAL COMPARISON WITH COMBINED SIMULATIONS OF THE 300 GHZ POWER-COMBINED AND 600 GHZ DOUBLERS
4.2 A 600 GHZ FOUR ANODES FREQUENCY DOUBLER
4.2.1 OPTIMIZATION OF THE PSBDS PROPERTIES
4.2.2 VIRTUAL DESIGN IN ADS-HFSS
4.2.3 VIRTUAL ADS-HFSS COMPARISON BETWEEN THE 600 GHZ TWO AND FOUR ANODES
DOUBLERS
4.2.4 COMPARISON WITH ADS-HFSS INDIVIDUAL SIMULATIONS
4.2.5 EXPERIMENTAL COMPARISON WITH COMBINED SIMULATIONS OF THE 300 GHZ AND
THE 600 GHZ FOUR ANODES DOUBLER
4.3 CONCLUSIONS
5 A 600 GHZ FREQUENCY RECEIVER 
5.1 QUALITATIVE DESCRIPTION OF THE DEVICE
5.1.1 IF ADAPTER CIRCUIT
5.2 ANALYSIS OF THE PSBDS IMPEDANCE MATCHING IN THE 600 GHZ MIXER
5.3 ANALYSIS OF THE PSBDS PERFORMANCES
5.3.1 ANALYSIS OF THE 3· CM -3 EPILAYER DOPING
5.3.2 ANALYSIS OF THE 5·1017 CM -3 EPILAYER DOPING
5.3.3 IMPROVEMENT OF THE 600 GHZ SUBHARMONIC MIXER PERFORMANCE
5.4 CONCLUSIONS
6 A 1.2 THZ SUB-HARMONIC BIASABLE FREQUENCY MIXER 
6.1 OPTIMIZATION OF THE PSBDS PROPERTIES
6.1.1 ANALYSIS OF THE 3· CM -3 EPILAYER DOPING
6.1.2 ANALYSIS OF THE 5· CM -3 EPILAYER DOPING
6.2 DESCRIPTION OF TWO DIFFERENT 1.2 THZ MIXER CHIP DESIGNS
6.2.1 IN-CHANNEL AND OUT-CHANNEL DESIGNS OF THE CHIP
6.2.2 LO ANTENNA AND HAMMER FILTER
6.2.3 DC GROUND STRUCTURE
6.2.4 RF FILTER AND ANTENNA
6.3 MECHANICAL BLOCK: IF AND DC CIRCUITS
6.3.1 IF CIRCUIT
6.3.2 DC CIRCUIT
6.4 THEORETICAL COMPARISON IN ADS-HFSS SIMULATIONS
6.4.1 CONVERSION LOSS AND NOISE TEMPERATURE OF THE RECEIVER
6.4.2 NOISE IN SCHOTTKY MIXERS
6.4.3 NOISE TEMPERATURE IN ADS SIMULATIONS
6.4.4 SIMULATED CONVERSION LOSS IN THE 1.2 THZ MIXER CHIPS
6.4.5 SIMULATED NOISE TEMPERATURE IN THE 1.2 THZ MIXER CHIPS
6.4.6 ANALYSIS OF THE BIAS PERFORMANCES AND THE RLC EQUIVALENT CIRCUIT
6.4.7 CONCLUSIONS
6.5 EXPERIMENTAL DEVICE
6.5.1 I-V CHARACTERISTICS OF THE DIODES
6.5.2 THE Y-FACTOR FOR EXPERIMENTAL MEASUREMENT
6.5.3 RF RESULTS OF THE 1.2 THZ RECEIVER AT 300 K
6.5.4 RF RESULTS OF THE 1.2 THZ RECEIVER AT 160 K
6.6 COMPARISON WITH ADS-HFSS INDIVIDUAL SIMULATIONS
6.7 SIMULTANEOUS SIMULATION OF THE 600 GHZ DOUBLER AND THE 1.2 THZ MIXER
6.7.1 SIMULTANEOUS SIMULATIONS WITH THE 600 GHZ TWO ANODES DOUBLER
6.7.2 SIMULTANEOUS SIMULATIONS WITH THE 600 GHZ FOUR ANODES DOUBLER
6.7.3 SIMULTANEOUS SIMULATIONS OF THE 1.2 THZ MIXER WITH HIGHLY DOPED PSBDS
6.8 UPDATED EXPERIMENTAL STATUS OF THE 1.2 THZ RECEIVER
6.8.1 LOCAL OSCILLATOR CHAIN
6.8.2 I-V CHARACTERISTICS OF THE NEW SET OF PSBDS 1.2 THZ CHIPS
6.8.3 UPDATED RESULTS OF THE 1.2 THZ RECEIVER AT 150 K
6.9 CONCLUSIONS
7 CONCLUSIONS AND PERSPECTIVES 
BIBLIOGRAPHY 

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