4H silicon carbide particle detectors: study of the defects induced by high energy neutron irradiation

During the last decade advances in the field of sensor design and improved base materials have pushed the radiation hardness of the current silicon detector technology to impressive performance. It should allow operation of the tracking systems of the Large Hadron Collider (LHC) experiments at nominal luminosity (1034 cm-2s-1) for about 10 years. The current silicon detectors are unable to cope with such an environment. Silicon carbide (SiC), which has recently been recognized as potentially radiation hard, is now studied. In this work it was analyzed the effect of high energy neutron irradiation on 4H-SiC particle detectors. Schottky and junction particle detectors were irradiated with 1 MeV neutrons up to fluence of 1016 cm-2. It is well known that the degradation of the detectors with irradiation, independently of the structure used for their realization, is caused by lattice defects, like creation of point-like defect, dopant deactivation and dead layer formation and that a crucial aspect for the understanding of the defect kinetics at a microscopic level is the correct identification of the crystal defects in terms of their electrical activity. In order to clarify the defect kinetic it were carried out a thermal transient spectroscopy (DLTS and PICTS) analysis of different samples irradiated at increasing fluences. The defect evolution was correlated with the transport properties of the irradiated detector, always comparing with the un-irradiated one. The charge collection efficiency degradation of Schottky detectors induced by neutron irradiation was related to the increasing concentration of defects as function of the neutron fluence.

Synthesis and characterization of implants for bone substitutions made of biomedical apatites containing silicon

In the last decades the development of bone substitutes characterized by a superior biomimetism has become of particular interest, owing to the increasing economic and societal impact of the bone diseases. In the present work of research the development of bone substitutes characterized by improved biomimetism, has been faced in a chemical, structural and morphological perspective. From a chemical point of view, it has been developed the synthesis of hydroxyapatite powders, exhibiting multiple ionic substitutions in both cationic and anionic sites, so to simulate the chemical composition of the natural bone. Particular emphasis has been given to the effect of silicon on the chemical-physical and solubility properties of the obtained hydroxyapatites. From a structural point of view, it has been developed the synthesis of ceramic composite materials, based on hydroxyapatite and calcium silicates, employed both as a reinforcing phase, to raise the mechanical strength of the composite compared to hydroxyapatite, and as a bioactive phase, able to increase the bioactivity properties of the whole ceramic. Finally the unique morphological features of the bone were mimicked by taking inspiration by Nature, so that native wood structures were treated in chemical and thermal way to obtain hydroxyapatite porous materials characterized by the same morphology as the native wood. The results obtained in the present work were positive in all the three different areas of investigation, so to cover the three different aspects of biomimetism, chemical, structural and morphological. Anyway, only at the convergence of the three different fields it is possible to find out the best solutions to develop the ideal bone-like scaffold. Thus, the future activity should be devoted to solve the problems at the borderline between the different research lines, which hamper this convergence and in consequence, the achievement of a bone scaffold able to mimic the various aspects exhibited by the bone tissue

Study of silicon-on-insulator multiple-gate MOS structures including band-gap engineering and self heating effects

The progresses of electron devices integration have proceeded for more than 40 years following the well–known Moore’s law, which states that the transistors density on chip doubles every 24 months. This trend has been possible due to the downsizing of the MOSFET dimensions (scaling); however, new issues and new challenges are arising, and the conventional ”bulk” architecture is becoming inadequate in order to face them. In order to overcome the limitations related to conventional structures, the researchers community is preparing different solutions, that need to be assessed. Possible solutions currently under scrutiny are represented by: • devices incorporating materials with properties different from those of silicon, for the channel and the source/drain regions; • new architectures as Silicon–On–Insulator (SOI) transistors: the body thickness of Ultra-Thin-Body SOI devices is a new design parameter, and it permits to keep under control Short–Channel–Effects without adopting high doping level in the channel. Among the solutions proposed in order to overcome the difficulties related to scaling, we can highlight heterojunctions at the channel edge, obtained by adopting for the source/drain regions materials with band–gap different from that of the channel material. This solution allows to increase the injection velocity of the particles travelling from the source into the channel, and therefore increase the performance of the transistor in terms of provided drain current. The first part of this thesis work addresses the use of heterojunctions in SOI transistors: chapter 3 outlines the basics of the heterojunctions theory and the adoption of such approach in older technologies as the heterojunction–bipolar–transistors; moreover the modifications introduced in the Monte Carlo code in order to simulate conduction band discontinuities are described, and the simulations performed on unidimensional simplified structures in order to validate them as well. Chapter 4 presents the results obtained from the Monte Carlo simulations performed on double–gate SOI transistors featuring conduction band offsets between the source and drain regions and the channel. In particular, attention has been focused on the drain current and to internal quantities as inversion charge, potential energy and carrier velocities. Both graded and abrupt discontinuities have been considered. The scaling of devices dimensions and the adoption of innovative architectures have consequences on the power dissipation as well. In SOI technologies the channel is thermally insulated from the underlying substrate by a SiO2 buried–oxide layer; this SiO2 layer features a thermal conductivity that is two orders of magnitude lower than the silicon one, and it impedes the dissipation of the heat generated in the active region. Moreover, the thermal conductivity of thin semiconductor films is much lower than that of silicon bulk, due to phonon confinement and boundary scattering. All these aspects cause severe self–heating effects, that detrimentally impact the carrier mobility and therefore the saturation drive current for high–performance transistors; as a consequence, thermal device design is becoming a fundamental part of integrated circuit engineering. The second part of this thesis discusses the problem of self–heating in SOI transistors. Chapter 5 describes the causes of heat generation and dissipation in SOI devices, and it provides a brief overview on the methods that have been proposed in order to model these phenomena. In order to understand how this problem impacts the performance of different SOI architectures, three–dimensional electro–thermal simulations have been applied to the analysis of SHE in planar single and double–gate SOI transistors as well as FinFET, featuring the same isothermal electrical characteristics. In chapter 6 the same simulation approach is extensively employed to study the impact of SHE on the performance of a FinFET representative of the high–performance transistor of the 45 nm technology node. Its effects on the ON–current, the maximum temperatures reached inside the device and the thermal resistance associated to the device itself, as well as the dependence of SHE on the main geometrical parameters have been analyzed. Furthermore, the consequences on self–heating of technological solutions such as raised S/D extensions regions or reduction of fin height are explored as well. Finally, conclusions are drawn in chapter 7.

The incomplete ionization of substitutional dopants in Silicon Carbide

This thesis analyzes theoretically and computationally the phenomenon of partial ionization of the substitutional dopants in Silicon Carbide at thermal equilibrium. It is based on the solution of the charge neutrality equation and takes into account the following phenomena: several energy levels in the bandgap; Fermi-Dirac statistics for free carriers; screening effects on the dopant ionization energies; the formation of impurity bands. A self-consistent model and a corresponding simulation software have been realized. A preliminary comparison of our calculations with existing experimental results is carried out.

Silicon-containing block copolymers with well-defined, branched architectures

In the past decade, block copolymers (BCPs) have attracted increasing scientific and technological interest because of their inherent capability to spontaneously self-assemble into ordered arrays of nanostructures. The importance of nanostructures in a number of applications has fostered the need for well-defined, complex macromolecular architectures. In this thesis, the influence of macromolecular architecture on the bulk morphologies of novel linear-hyperbranched and linear brush-like diblock copolymer structure is investigated. An innovative, generally applicable strategy for the preparation of these defined diblock copolymers, consisting of linear polystyrene and branched polycarbosilane blocks, is demonstrated. Furthermore, complete characterization and solid-state morphological studies are provided. Finally, the concept is extended to linear-hyperbrached and linear brush-like polyalkoxysilanes. A shift of the classical phase boundaries to higher PS weight fractions as well as the appearance of new morphologies confirms the dramatic effect that polymer topology has on the morphology of BCPs.

Fiber-Optic Technologies for Wireline and Wireless In-building Networks

This doctoral dissertation aims to establish fiber-optic technologies overcoming the limiting issues of data communications in indoor environments. Specific applications are broadband mobile distribution in different in-building scenarios and high-speed digital transmission over short-range wired optical systems. Two key enabling technologies are considered: Radio over Fiber (RoF) techniques over standard silica fibers for distributed antenna systems (DAS) and plastic optical fibers (POFs) for short-range communications. Hence, the objectives and achievements of this thesis are related to the application of RoF and POF technologies in different in-building scenarios. On one hand, a theoretical and experimental analysis combined with demonstration activities has been performed on cost-effective RoF systems. An extensive modeling on modal noise impact both on linear and non-linear characteristics of RoF link over silica multimode fiber has been performed to achieve link design rules for an optimum choice of the transmitter, receiver and launching technique. A successful transmission of Long Term Evolution (LTE) mobile signals on the resulting optimized RoF system over silica multimode fiber employing a Fabry-Perot LD, central launch technique and a photodiode with a built-in ball lens was demonstrated up to 525m with performances well compliant with standard requirements. On the other hand, digital signal processing techniques to overcome the bandwidth limitation of POF have been investigated. An uncoded net bit-rate of 5.15Gbit/s was obtained on a 50m long POF link employing an eye-safe transmitter, a silicon photodiode, and DMT modulation with bit and power loading algorithm. With the insertion of 3x2N quadrature amplitude modulation constellation formats, an uncoded net-bit-rate of 5.4Gbit/s was obtained on a 50 m long POF link employing an eye-safe transmitter and a silicon avalanche photodiode. Moreover, simultaneous transmission of baseband 2Gbit/s with DMT and 200Mbit/s with an ultra-wideband radio signal has been validated over a 50m long POF link.

Advanced Numerical Simulation of Silicon-Based Solar Cells

Photovoltaic (PV) conversion is the direct production of electrical energy from sun without involving the emission of polluting substances. In order to be competitive with other energy sources, cost of the PV technology must be reduced ensuring adequate conversion efficiencies. These goals have motivated the interest of researchers in investigating advanced designs of crystalline silicon solar (c-Si) cells. Since lowering the cost of PV devices involves the reduction of the volume of semiconductor, an effective light trapping strategy aimed at increasing the photon absorption is required. Modeling of solar cells by electro-optical numerical simulation is helpful to predict the performance of future generations devices exhibiting advanced light-trapping schemes and to provide new and more specific guidelines to industry. The approaches to optical simulation commonly adopted for c-Si solar cells may lead to inaccurate results in case of thin film and nano-stuctured solar cells. On the other hand, rigorous solvers of Maxwell equations are really cpu- and memory-intensive. Recently, in optical simulation of solar cells, the RCWA method has gained relevance, providing a good trade-off between accuracy and computational resources requirement. This thesis is a contribution to the numerical simulation of advanced silicon solar cells by means of a state-of-the-art numerical 2-D/3-D device simulator, that has been successfully applied to the simulation of selective emitter and the rear point contact solar cells, for which the multi-dimensionality of the transport model is required in order to properly account for all physical competing mechanisms. In the second part of the thesis, the optical problems is discussed. Two novel and computationally efficient RCWA implementations for 2-D simulation domains as well as a third RCWA for 3-D structures based on an eigenvalues calculation approach have been presented. The proposed simulators have been validated in terms of accuracy, numerical convergence, computation time and correctness of results.

Manufacturing and characterization of amorphous silicon alloys passivation layers for silicon hetero-junction solar cells

Nel presente lavoro di tesi magistrale sono stati depositati e caratterizzati film sottili (circa 10 nm) di silicio amorfo idrogenato (a-Si:H), studiando in particolare leghe a basso contenuto di ossigeno e carbonio. Tali layer andranno ad essere implementati come strati di passivazione per wafer di Si monocristallino in celle solari ad eterogiunzione HIT (heterojunctions with intrinsic thin layer), con le quali recentemente è stato raggiunto il record di efficienza pari a 24.7% . La deposizione è avvenuta mediante PECVD (plasma enhanced chemical vapour deposition). Tecniche di spettroscopia ottica, come FT-IR (Fourier transform infrared spectroscopy) e SE (spettroscopic ellipsometry) sono state utilizzate per analizzare le configurazioni di legami eteronucleari (Si-H, Si-O, Si-C) e le proprietà strutturali dei film sottili: un nuovo metodo è stato implementato per calcolare i contenuti atomici di H, O e C da misure ottiche. In tal modo è stato possibile osservare come una bassa incorporazione (< 10%) di ossigeno e carbonio sia sufficiente ad aumentare la porosità ed il grado di disordine a lungo raggio del materiale: relativamente a quest’ultimo aspetto, è stata sviluppata una nuova tecnica per determinare dagli spettri ellisometrici l’energia di Urbach, che esprime la coda esponenziale interna al gap in semiconduttori amorfi e fornisce una stima degli stati elettronici in presenza di disordine reticolare. Nella seconda parte della tesi sono stati sviluppati esperimenti di annealing isocrono, in modo da studiare i processi di cristallizzazione e di effusione dell’idrogeno, correlandoli con la degradazione delle proprietà optoelettroniche. L’analisi dei differenti risultati ottenuti studiando queste particolari leghe (a-SiOx e a-SiCy) ha permesso di concludere che solo con una bassa percentuale di ossigeno o carbonio, i.e. < 3.5 %, è possibile migliorare la risposta termica dello specifico layer, ritardando i fenomeni di degradazione di circa 50°C.

Test di silicon photomultipliers (sipm) accoppiati a scintillatori

In questa tesi si riportano i risultati di uno studio della risoluzione temporale di un fotomoltiplicatore al Silicio (SiPM). La diffusione di questi rivelatori è in notevole aumento sia nelle ricerche di Fisica Nucleare e Subnucleare che nelle applicazioni mediche. I vantaggi sono legati alla loro insensibilità ai campi magnetici e ai facili modi di operazione (piccoli, robusti e con utilizzo a basso voltaggio). Usati sino ad ora per la misura di cariche, sono oggi di grande interesse per possibili applicazioni che richiedano alta risoluzione temporale (sistemi di tempo di volo, trigger, calorimetria). In questo studio sono stati studiati due tipi diversi di accoppiamento Scintillatore-SiPM: diretto o tramite fibre. Per queste analisi sono stati utilizzati diversi metodi di acquisizione e successivamente si sono incrociati i relativi risultati.

Silicon oxide nitride (sion) films per applicazioni fotovoltaiche

La ricerca, negli ultimi anni, si è concentrata sullo studio di materiali con energy gap più ampio del silicio amorfo a-Si per ridurre gli assorbimenti parassiti all'interno di celle fotovoltaiche ad eterogiunzione. In questo ambito, presso l'Università di Costanza, sono stati depositati layers di silicon oxynitride amorfo a-SiOxNy. Le promettenti aspettative di questo materiale legate all'elevato optical gap, superiore ai 2.0 eV, sono tuttavia ridimensionate dai problemi intrinseci alla struttura amorfa. Infatti la presenza di una grande quantit a di difetti limita fortemente la conducibilita e aumenta gli effetti di degradazione legati alla luce. In quest'ottica, nella presente tesi, sono stati riportati i risultati di analisi spettroscopiche eseguite presso il Dipartimento di Fisica e Astronomia di Bologna su campioni di silicon oxynitride nanocristallino nc-SiOxNy, analisi che hanno lo scopo di osservare come la struttura nanocristallina influisca sulle principali proprieta ottiche e sulla loro dipendenza da alcuni parametri di deposizione.

Variation of stable silicon isotopes: Analytical developments and applications in Precambrian geochemistry

Die vorliegende Dissertation behandelt die Gesamtgesteinsanalyse stabiler Siliziumisotope mit Hilfe einer „Multi Collector-ICP-MS“. Die Analysen fanden in Kooperation mit dem „Royal Museum for Central Africa“ in Belgien statt. Einer der Schwerpunkte des ersten Kapitels ist die erstmalige Analyse des δ30Si –Wertes an einem konventionellen Nu PlasmaTM „Multi-Collector ICP-MS“ Instrument, durch die Eliminierung der den 30Si “peak” überlagernden 14N16O Interferenz. Die Analyse von δ30Si wurde durch technische Modifikationen der Anlage erreicht, welche eine höherer Massenauflösung ermöglichten. Die sorgsame Charakterisierung eines adäquaten Referenzmaterials ist unabdingbar für die Abschätzung der Genauigkeit einer Messung. Die Bestimmung der „U.S. Geological Survey“ Referenzmaterialien bildet den zweiten Schwerpunkt dieses Kapitales. Die Analyse zweier hawaiianischer Standards (BHVO-1 and BHVO-2), belegt die präzise und genaue δ30Si Bestimmung und bietet Vergleichsdaten als Qualitätskontrolle für andere Labore. Das zweite Kapitel befasst sich mit kombinierter Silizium-/Sauerstoffisotope zur Untersuchung der Entstehung der Silizifizierung vulkanischer Gesteine des „Barberton Greenstone Belt“, Südafrika. Im Gegensatz zu heute, war die Silizifizierung der Oberflächennahen Schichten, einschließlich der „Chert“ Bildung, weitverbreitete Prozesse am präkambrischen Ozeanboden. Diese Horizonte sind Zeugen einer extremen Siliziummobilisierung in der Frühzeit der Erde. Dieses Kapitel behandelt die Analyse von Silizium- und Sauerstoffisotopen an drei unterschiedlichen Gesteinsprofilen mit unterschiedlich stark silizifizierten Basalten und überlagernden geschichteten „Cherts“ der 3.54, 3.45 und 3.33 Mill. Jr. alten Theespruit, Kromberg und Hooggenoeg Formationen. Siliziumisotope, Sauerstoffisotope und die SiO2-Gehalte demonstrieren in allen drei Gesteinsprofilen eine positive Korrelation mit dem Silizifizierungsgrad, jedoch mit unterschiedlichen Steigungen der δ30Si-δ18O-Verhältnisse. Meerwasser wird als Quelle des Siliziums für den Silizifizierungsprozess betrachtet. Berechnungen haben gezeigt, dass eine klassische Wasser-Gestein Wechselwirkung die Siliziumisotopenvariation nicht beeinflussen kann, da die Konzentration von Si im Meerwasser zu gering ist (49 ppm). Die Daten stimmen mit einer Zwei-Endglieder-Komponentenmischung überein, mit Basalt und „Chert“ als jeweilige Endglieder. Unsere gegenwärtigen Daten an den „Cherts“ bestätigen einen Anstieg der Isotopenzusammensetzung über der Zeit. Mögliche Faktoren, die für unterschiedliche Steigungen der δ30Si-δ18O Verhältnisse verantwortlich sein könnten sind Veränderungen in der Meerwasserisotopie, der Wassertemperatur oder sekundäre Alterationseffekte. Das letzte Kapitel beinhaltet potentielle Variationen in der Quellregion archaischer Granitoide: die Si-Isotopen Perspektive. Natriumhaltige Tonalit-Trondhjemit-Granodiorit (TTG) Intrusiva repräsentieren große Anteile der archaischen Kruste. Im Gegensatz dazu ist die heutige Kruste kaliumhaltiger (GMS-Gruppe: Granit-Monzonite-Syenite). Prozesse, die zu dem Wechsel von natriumhaltiger zu kaliumhaltiger Kruste führten sind die Thematik diesen Kapitels. Siliziumisotopenmessungen wurden hier kombiniert mit Haupt- und Spurenelementanalysen an unterschiedlichen Generationen der 3.55 bis 3.10 Mill. Yr. alten TTG und GMS Intrusiva aus dem Arbeitsgebiet. Die δ30Si-Werte in den unterschiedlichen Plutonit Generationen zeigen einen leichten Anstieg der Isotopie mit der Zeit, wobei natriumhaltige Intrusiva die niedrigste Si-Isotopenzusammensetzung aufweisen. Der leichte Anstieg in der Siliziumisotopenzusammensetzung über die Zeit könnte auf unterschiedliche Temperaturbedingungen in der Quellregion der Granitoide hinweisen. Die Entstehung von Na-reichen, leichten d30Si Granitoiden würde demnach bei höheren Temperaturen erfolgen. Die Ähnlichkeit der δ30Si-Werte in archaischen K-reichen Plutoniten und phanerozoischen K-reichen Plutoniten wird ebenfalls deutlich.

Studio delle proprieta ottiche di film di silicon oxynitrides (sion) per applicazioni fotovoltaiche

Nelle celle solari HIT (Heterojunction Intrinsic Thin layer) attualmente in circolazione il materiale maggiormente utilizzato è sicuramente il silicio, per la sua buona caratteristica di assorbimento e disponibilità in natura. Tuttavia, la struttura amorfa del silicio impiegato come emettitore, limita fortemente la conducibilità e aumenta gli effetti di degradazione legati all'esposizione alla luce. In quest'ottica, nel presente lavoro di tesi, vengono analizzati sottili layers di Silicon Oxynitride ossigenato, depositati in forma nanocristallina presso l'Università di Costanza su substrati in vetro, tramite PECVD (Plasma-Enhanced Chemical Vapor Deposition). Il materiale, che non presenta i difetti intrinseci della forma amorfa, è dal punto di vista delle proprietà fisiche fondamentali ancora poco conosciuto e rappresenta una possibile alternativa agli analoghi campioni in forma amorfa. Le misure e le analisi presentate in questa tesi, svolte presso il Dipartimento di Fisica e Astronomia di Bologna, sono finalizzate ad indagare le principali proprietà ottiche, quali l'energy gap e l'indice di rifrazione dei layers. I risultati ottenuti, espressi in funzione dei parametri di deposizione, mostrano che un aumento della concentrazione di ossigeno in fase di deposito implica un aumento lineare dell'ampiezza dell'energy gap e un calo dell'indice di rifrazione. Anche altri parametri come la potenza di deposito e il tempo di annealing sembrano giocare un ruolo importante sul valore dell'energy gap. I risultati appaiono inoltre essere in buon accordo con quanto ottenuto da studi precedenti su layers simili ma con una maggiore fase amorfa. In conclusione, la possibilità di regolare il valore dell'energy gap e l'indice di rifrazione in base ai parametri di deposizione, unita alle buone prerogative tipiche dei materiali cristallini, conferisce al materiale buone prospettive per applicazioni fotovoltaiche come emettitori in celle ad eterogiunzione o rivestimenti con proprietà antiriflettenti

Development of an X-ray spectrometric system and feasibility tests of Silicon Drift Detector for medical and space applications

The thesis work concerns X-ray spectrometry for both medical and space applications and is divided into two sections. The first section addresses an X-ray spectrometric system designed to study radiological beams and is devoted to the optimization of diagnostic procedures in medicine. A parametric semi-empirical model capable of efficiently reconstructing diagnostic X-ray spectra in 'middle power' computers was developed and tested. In addition, different silicon diode detectors were tested as real-time detectors in order to provide a real-time evaluation of the spectrum during diagnostic procedures. This project contributes to the field by presenting an improved simulation of a realistic X-ray beam emerging from a common X-ray tube with a complete and detailed spectrum that lends itself to further studies of added filtration, thus providing an optimized beam for different diagnostic applications in medicine. The second section describes the preliminary tests that have been carried out on the first version of an Application Specific Integrated Circuit (ASIC), integrated with large area position-sensitive Silicon Drift Detector (SDD) to be used on board future space missions. This technology has been developed for the ESA project: LOFT (Large Observatory for X-ray Timing), a new medium-class space mission that the European Space Agency has been assessing since February of 2011. The LOFT project was proposed as part of the Cosmic Vision Program (2015-2025).

Parallel Architectures for Many-Core Systems-On-Chip in Deep Sub-Micron Technology

Despite the several issues faced in the past, the evolutionary trend of silicon has kept its constant pace. Today an ever increasing number of cores is integrated onto the same die. Unfortunately, the extraordinary performance achievable by the many-core paradigm is limited by several factors. Memory bandwidth limitation, combined with inefficient synchronization mechanisms, can severely overcome the potential computation capabilities. Moreover, the huge HW/SW design space requires accurate and flexible tools to perform architectural explorations and validation of design choices. In this thesis we focus on the aforementioned aspects: a flexible and accurate Virtual Platform has been developed, targeting a reference many-core architecture. Such tool has been used to perform architectural explorations, focusing on instruction caching architecture and hybrid HW/SW synchronization mechanism. Beside architectural implications, another issue of embedded systems is considered: energy efficiency. Near Threshold Computing is a key research area in the Ultra-Low-Power domain, as it promises a tenfold improvement in energy efficiency compared to super-threshold operation and it mitigates thermal bottlenecks. The physical implications of modern deep sub-micron technology are severely limiting performance and reliability of modern designs. Reliability becomes a major obstacle when operating in NTC, especially memory operation becomes unreliable and can compromise system correctness. In the present work a novel hybrid memory architecture is devised to overcome reliability issues and at the same time improve energy efficiency by means of aggressive voltage scaling when allowed by workload requirements. Variability is another great drawback of near-threshold operation. The greatly increased sensitivity to threshold voltage variations in today a major concern for electronic devices. We introduce a variation-tolerant extension of the baseline many-core architecture. By means of micro-architectural knobs and a lightweight runtime control unit, the baseline architecture becomes dynamically tolerant to variations.