Análisis y diseño de multiplicadores y mezcladores mediante el método de Monte Carlo en la banda de THz = Analysis and design of multipliers and mixers via Monte Carlo modelling at THz bands

La región del espectro electromagnético comprendida entre 100 GHz y 10 THz alberga una gran variedad de aplicaciones en campos tan dispares como la radioastronomía, espectroscopíamolecular, medicina, seguridad, radar, etc. Los principales inconvenientes en el desarrollo de estas aplicaciones son los altos costes de producción de los sistemas trabajando a estas frecuencias, su costoso mantenimiento, gran volumen y baja fiabilidad. Entre las diferentes tecnologías a frecuencias de THz, la tecnología de los diodos Schottky juega un importante papel debido a su madurez y a la sencillez de estos dispositivos. Además, los diodos Schottky pueden operar tanto a temperatura ambiente como a temperaturas criogénicas, con altas eficiencias cuando se usan como multiplicadores y con moderadas temperaturas de ruido en mezcladores. El principal objetivo de esta tesis doctoral es analizar los fenómenos físicos responsables de las características eléctricas y del ruido en los diodos Schottky, así como analizar y diseñar circuitos multiplicadores y mezcladores en bandas milimétricas y submilimétricas. La primera parte de la tesis presenta un análisis de los fenómenos físicos que limitan el comportamiento de los diodos Schottky de GaAs y GaN y de las características del espectro de ruido de estos dispositivos. Para llevar a cabo este análisis, un modelo del diodo basado en la técnica de Monte Carlo se ha considerado como referencia debido a la elevada precisión y fiabilidad de este modelo. Además, el modelo de Monte Carlo permite calcular directamente el espectro de ruido de los diodos sin necesidad de utilizar ningún modelo analítico o empírico. Se han analizado fenómenos físicos como saturación de la velocidad, inercia de los portadores, dependencia de la movilidad electrónica con la longitud de la epicapa, resonancias del plasma y efectos no locales y no estacionarios. También se ha presentado un completo análisis del espectro de ruido para diodos Schottky de GaAs y GaN operando tanto en condiciones estáticas como variables con el tiempo. Los resultados obtenidos en esta parte de la tesis contribuyen a mejorar la comprensión de la respuesta eléctrica y del ruido de los diodos Schottky en condiciones de altas frecuencias y/o altos campos eléctricos. También, estos resultados han ayudado a determinar las limitaciones de modelos numéricos y analíticos usados en el análisis de la respuesta eléctrica y del ruido electrónico en los diodos Schottky. La segunda parte de la tesis está dedicada al análisis de multiplicadores y mezcladores mediante una herramienta de simulación de circuitos basada en la técnica de balance armónico. Diferentes modelos basados en circuitos equivalentes del dispositivo, en las ecuaciones de arrastre-difusión y en la técnica de Monte Carlo se han considerado en este análisis. El modelo de Monte Carlo acoplado a la técnica de balance armónico se ha usado como referencia para evaluar las limitaciones y el rango de validez de modelos basados en circuitos equivalentes y en las ecuaciones de arrastredifusión para el diseño de circuitos multiplicadores y mezcladores. Una notable característica de esta herramienta de simulación es que permite diseñar circuitos Schottky teniendo en cuenta tanto la respuesta eléctrica como el ruido generado en los dispositivos. Los resultados de las simulaciones presentados en esta parte de la tesis, tanto paramultiplicadores comomezcladores, se han comparado con resultados experimentales publicados en la literatura. El simulador que integra el modelo de Monte Carlo con la técnica de balance armónico permite analizar y diseñar circuitos a frecuencias superiores a 1 THz. ABSTRACT The terahertz region of the electromagnetic spectrum(100 GHz-10 THz) presents a wide range of applications such as radio-astronomy, molecular spectroscopy, medicine, security and radar, among others. The main obstacles for the development of these applications are the high production cost of the systems working at these frequencies, highmaintenance, high volume and low reliability. Among the different THz technologies, Schottky technology plays an important rule due to its maturity and the inherent simplicity of these devices. Besides, Schottky diodes can operate at both room and cryogenic temperatures, with high efficiency in multipliers and moderate noise temperature in mixers. This PhD. thesis is mainly concerned with the analysis of the physical processes responsible for the characteristics of the electrical response and noise of Schottky diodes, as well as the analysis and design of frequency multipliers and mixers at millimeter and submillimeter wavelengths. The first part of the thesis deals with the analysis of the physical phenomena limiting the electrical performance of GaAs and GaN Schottky diodes and their noise performance. To carry out this analysis, a Monte Carlo model of the diode has been used as a reference due to the high accuracy and reliability of this diode model at millimeter and submillimter wavelengths. Besides, the Monte Carlo model provides a direct description of the noise spectra of the devices without the necessity of any additional analytical or empirical model. Physical phenomena like velocity saturation, carrier inertia, dependence of the electron mobility on the epilayer length, plasma resonance and nonlocal effects in time and space have been analysed. Also, a complete analysis of the current noise spectra of GaAs and GaN Schottky diodes operating under static and time varying conditions is presented in this part of the thesis. The obtained results provide a better understanding of the electrical and the noise responses of Schottky diodes under high frequency and/or high electric field conditions. Also these results have helped to determine the limitations of numerical and analytical models used in the analysis of the electrical and the noise responses of these devices. The second part of the thesis is devoted to the analysis of frequency multipliers and mixers by means of an in-house circuit simulation tool based on the harmonic balance technique. Different lumped equivalent circuits, drift-diffusion and Monte Carlo models have been considered in this analysis. The Monte Carlo model coupled to the harmonic balance technique has been used as a reference to evaluate the limitations and range of validity of lumped equivalent circuit and driftdiffusion models for the design of frequency multipliers and mixers. A remarkable feature of this reference simulation tool is that it enables the design of Schottky circuits from both electrical and noise considerations. The simulation results presented in this part of the thesis for both multipliers and mixers have been compared with measured results available in the literature. In addition, the Monte Carlo simulation tool allows the analysis and design of circuits above 1 THz.

The effects of school mobility in pre -assessment grade levels on student performance and school accountability in urban Title I schools

This study examined the effects of student mobility and educational enrollment experiences on academic achievement. The educational progress, school enrollments and transfers of inner-city elementary students were tracked over a four-year period. Student achievement was measured by criterion-referenced reading tests administered in the second semester of the third grade. It further analyzed the degree to which the switch to different basal reading textbooks interrupted the continuity of education thereby contributing to the detrimental effects of intra-district mobility. ^ Mobility histories of 2,913 third grade students were collected to evaluate the number of times each student entered or withdrew from a Miami-Dade County Public School beginning in August 2000 through March 2004, and distinguished between transfers that occurred during the academic school year and those that occurred during summer months. Data were analyzed using Pearson correlations and multiple regressions to determine if school mobility contributed to performance on the Florida Comprehensive Assessment Third Grade Reading Test (FCAT). Transferring from one school to another was found to have a significant negative impact on student test scores. Transfers within the academic school year were more detrimental than transfers that occurred during the summer months. Third grade students who transferred into schools that used the same reading textbook series were found to have significantly higher FCAT reading scores than third graders who transferred into schools that used different reading textbooks. ^ The effects of mobility rates on overall school performance were also examined. Data was collected on 124 Title I elementary schools to determine the degree to which mobility affected school accountability scores. Title I schools with high student mobility rates had significantly lower accountability scores than schools with lower student mobility rates. ^ The results of this study highlight the impact of education and housing policy and imply a need for programs and practices that promote stability in the early elementary years. ^

First principles calculation of electron-phonon and alloy scattering in strained SiGe

First-principles electronic structure methods are used to predict the mobility of n-type carrier scattering in strained SiGe. We consider the effects of strain on the electron-phonon deformation potentials and the alloy scattering parameters. We calculate the electron-phonon matrix elements and fit them up to second order in strain. We find, as expected, that the main effect of strain on mobility comes from the breaking of the degeneracy of the six Δ and L valleys, and the choice of transport direction. The non-linear effects on the electron-phonon coupling of the Δ valley due to shear strain are found to reduce the mobility of Si-like SiGe by 50% per % strain. We find increases in mobility between 2 and 11 times that of unstrained SiGe for certain fixed Ge compositions, which should enhance the thermoelectric figure of merit in the same order, and could be important for piezoresistive applications.

AuxAg1-x alloy seeds: A way to control growth, morphology and defect formation in Ge nanowires

Germanium (Ge) nanowires are of current research interest for high speed nanoelectronic devices due to the lower band gap and high carrier mobility compatible with high K-dielectrics and larger excitonic Bohr radius ensuing a more pronounced quantum confinement effect [1-6]. A general way for the growth of Ge nanowires is to use liquid or a solid growth promoters in a bottom-up approach which allow control of the aspect ratio, diameter, and structure of 1D crystals via external parameters, such as precursor feedstock, temperature, operating pressure, precursor flow rate etc [3, 7-11]. The Solid-phase seeding is preferred for more control processing of the nanomaterials and potential suppression of the unintentional incorporation of high dopant concentrations in semiconductor nanowires and unrequired compositional tailing of the seed-nanowire interface [2, 5, 9, 12]. There are therefore distinct features of the solid phase seeding mechanism that potentially offer opportunities for the controlled processing of nanomaterials with new physical properties. A superior control over the growth kinetics of nanowires could be achieved by controlling the inherent growth constraints instead of external parameters which always account for instrumental inaccuracy. The high dopant concentrations in semiconductor nanowires can result from unintentional incorporation of atoms from the metal seed material, as described for the Al catalyzed VLS growth of Si nanowires [13] which can in turn be depressed by solid-phase seeding. In addition, the creation of very sharp interfaces between group IV semiconductor segments has been achieved by solid seeds [14], whereas the traditionally used liquid Au particles often leads to compositional tailing of the interface [15] . Korgel et al. also described the superior size retention of metal seeds in a SFSS nanowire growth process, when compared to a SFLS process using Au colloids [12]. Here in this work we have used silver and alloy seed particle with different compositions to manipulate the growth of nanowires in sub-eutectic regime. The solid seeding approach also gives an opportunity to influence the crystallinity of the nanowires independent of the substrate. Taking advantage of the readily formation of stacking faults in metal nanoparticles, lamellar twins in nanowires could be formed.

Epitaxial growth of molecular crystals on van der Waals substrates for high-performance organic electronics

Epitaxial van der Waals (vdW) heterostructures of organic and layered materials are demonstrated to create high-performance organic electronic devices. High-quality rubrene films with large single-crystalline domains are grown on h-BN dielectric layers via vdW epitaxy. In addition, high carrier mobility comparable to free-standing single-crystal counterparts is achieved by forming interfacial electrical contacts with graphene electrodes.

Atomic resolution studies of oxide superlattices and ultrathin films

The ability to grow ultrathin films layer-by-layer with well-defined epitaxial relationships has allowed research groups worldwide to grow a range of artificial films and superlattices, first for semiconductors, and now with oxides. In the oxides thin film research community, there have been concerted efforts recently to develop a number of epitaxial oxide systems grown on single crystal oxide substrates that display a wide variety of novel interfacial functionality, such as enhanced ferromagnetic ordering, increased charge carrier density, increased optical absorption, etc, at interfaces. The magnitude of these novel properties is dependent upon the structure of thin films, especially interface sharpness, intermixing, defects, and strain, layering sequence in the case of superlattices and the density of interfaces relative to the film thicknesses. To understand the relationship between the interfacial thin film oxide atomic structure and its properties, atomic scale characterization is required. Transmission electron microscopy (TEM) offers the ability to study interfaces of films at high resolution. Scanning transmission electron microscopy (STEM) allows for real space imaging of materials with directly interpretable atomic number contrast. Electron energy loss spectroscopy (EELS), together with STEM, can probe the local chemical composition as well as local electronic states of transition metals and oxygen. Both techniques have been significantly improved by aberration correctors, which reduce the probe size to 1 Å, or less. Aberration correctors have thus made it possible to resolve individual atomic columns, and possibly probe the electronic structure at atomic scales. Separately, using electron probe forming lenses, structural information such as the crystal structure, strain, lattice mismatches, and superlattice ordering can be measured by nanoarea electron diffraction (NED). The combination of STEM, EELS, and NED techniques allows us to gain a fundamental understanding of the properties of oxide superlattices and ultrathin films and their relationship with the corresponding atomic and electronic structure. In this dissertation, I use the aforementioned electron microscopy techniques to investigate several oxide superlattice and ultrathin film systems. The major findings are summarized below. These results were obtained with stringent specimen preparation methods that I developed for high resolution studies, which are described in Chapter 2. The essential materials background and description of electron microscopy techniques are given in Chapter 1 and 2. In a LaMnO3-SrMnO3 superlattice, we demonstrate the interface of LaMnO3-SrMnO3 is sharper than the SrMnO3-LaMnO3 interface. Extra spectral weights in EELS are confined to the sharp interface, whereas at the rougher interface, the extra states are either not present or are not confined to the interface. Both the structural and electronic asymmetries correspond to asymmetric magnetic ordering at low temperature. In a short period LaMnO3-SrTiO3 superlattice for optical applications, we discovered a modified band structure in SrTiO3 ultrathin films relative to thick films and a SrTiO3 substrate, due to charge leakage from LaMnO3 in SrTiO3. This was measured by chemical shifts of the Ti L and O K edges using atomic scale EELS. The interfacial sharpness of LaAlO3 films grown on SrTiO3 was investigated by the STEM/EELS technique together with electron diffraction. This interface, when prepared under specific conditions, is conductive with high carrier mobility. Several suggestions for the conductive interface have been proposed, including a polar catastrophe model, where a large built-in electric field in LaAlO3 films results in electron charge transfer into the SrTiO3 substrate. Other suggested possibilities include oxygen vacancies at the interface and/or oxygen vacancies in the substrate. The abruptness of the interface as well as extent of intermixing has not been thoroughly investigated at high resolution, even though this can strongly influence the electrical transport properties. We found clear evidence for cation intermixing through the LaAlO3-SrTiO3 interface with high spatial resolution EELS and STEM, which contributes to the conduction at the interface. We also found structural defects, such as misfit dislocations, which leads to increased intermixing over coherent interfaces.

Interface roughness in short-period InGaAs/InP superlattices

Electron mobility was studied in lattice-matched short-period InGaAs/InP superlattices as a function of the width of the wells. The decreasing mobility with decreasing well width was shown to occur due to the interface roughness. The roughnesses of InGaAs/InP and GaAs/AlGaAs interfaces were compared. Much smoother InGaAs/InP interfaces resulted in higher electron mobility limited by interface roughness.

Low-frequency noise and static analysis of the impact of the TiN metal gate thicknesses on n- and p-channel MuGFETs

The impact of the titanium nitride (TIN) gate electrode thickness has been investigated in n and p channel SOI multiple gate field effect transistors (MuGFETs) through low frequency noise charge pumping and static measurements as well as capacitance-voltage curves The results suggest that a thicker TIN metal gate electrode gives rise to a higher EOT a lower mobility and a higher interface trap density The devices have also been studied for different back gate biases where the GIFBE onset occurs at lower front-gate voltage for thinner TIN metal gate thickness and at higher V(GF) In addition it is demonstrated that post deposition nitridation of the MOCVD HfSiO gate dielectric exhibits an unexpected trend with TIN gate electrode thickness where a continuous variation of EOT and an increase on the degradation of the interface quality are observed (C) 2010 Elsevier Ltd All rights reserved

Temperature dependence of polaronic transport through single molecules and quantum dots

Motivated by recent experiments on electric transport through single molecules and quantum dots, we investigate a model for transport that allows for significant coupling between the electrons and a boson mode isolated on the molecule or dot. We focus our attention on the temperature-dependent properties of the transport. In the Holstein picture for polaronic transport in molecular crystals the temperature dependence of the conductivity exhibits a crossover from coherent (band) to incoherent (hopping) transport. Here, the temperature dependence of the differential conductance on resonance does not show such a crossover, but is mostly determined by the lifetime of the resonant level on the molecule or dot.

Caracterização morfodinâmica do litoral Norte Fluminense, RJ, Brasil

A morfologia das praias é reflexo da ação hidrodinfunica com o tipo de sedimento disponível. Esta interação se dá a partir da base de ação das ondas, tornando-se mais efetiva na zona de arrebentação onde a energia é dissipada, originando na zona de surfe que se estende em direção à linha de costa até Q limite do espraiamento na face de praia. O objetivo deste trabalho é apresentar as características morfodinâmicas do litoral NE do Estado do Rio de Janeiro, baseando-se na análise da variação espaço Hemporal de perfis de praia, na morfologia da plataforma continental e em fotos aéreas. Os perfis de praia foram levantados durante cinco anos pela PETROBRÁS S/A, em oito estações ao longo do litoral. O comportamento morfodinâmico distinto de setores do litoral estudado é função do padrão de ondas e direção da linha de costa, morfologia da plataforma interna controlando a extensão da zona de surfe e o número de zonas de arrebentação, características dos sedimentos e gradiente da face de praia. Foram reconhecidos quatro compartimentos morfodinâmicos distintos, com base na morfologia dos perfis praiais e plataforma interna, no índice de mobilidade da linha de praia, granulometria x gradiente da face de praia e o parâmetro Q. Os quatro compartimentos são: Atafona/Foz do Rio Paraíba do Sul - estágio morfodinâmico intermediário a dissipativo, com o maior índice de mobilidade e elevada taxa de erosão; Sul de Atafona-Cabo de São Tomé - estágio intermediário a refletivo com baixo índice de mobilidade da praia; Cabo de São Tomé - estágio refletivo a intermediário com alto índice de mobilidade da praia; Cabo de São Tomé-Cabiúnas - estágio refletivo com baixo índice de mobilidade.

Characterization of processed materials by electrical currents: development of equipment and applications

Dissertação para obtenção do Grau de Mestre em Engenharia Mecânica

Al-doped ZnO ceramic sputtering targets based on nanocrystalline powders produced by emulsion detonation synthesis – deposition and application as a transparent conductive oxide material

Transparent conducting oxides (TCOs) have been largely used in the optoelectronic industry due to their singular combination of low electrical resistivity and high optical transmittance. They are usually deposited by magnetron sputtering systems being applied in several devices, specifically thin film solar cells (TFSCs). Sputtering targets are crucial components of the sputtering process, with many of the sputtered films properties dependent on the targets characteristics. The present thesis focuses on the development of high quality conductive Al-doped ZnO (AZO) ceramic sputtering targets based on nanostructured powders produced by emulsion detonation synthesis method (EDSM), and their application as a TCO. In this sense, the influence of several processing parameters was investigated from the targets raw-materials synthesis to the application of sputtered films in optoelectronic devices. The optimized manufactured AZO targets present a final density above 99 % with controlled grain size, an homogeneous microstructure with a well dispersed ZnAl2O4 spinel phase, and electrical resistivities of ~4 × 10-4 Ωcm independently on the Al-doping level among 0.5 and 2.0 wt. % Al2O3. Sintering conditions proved to have a great influence on the properties of the targets and their performance as a sputtering target. It was demonstrated that both deposition process and final properties of the films are related with the targets characteristics, which in turn depends on the initial powder properties. In parallel, the influence of several deposition parameters in the film´s properties sputtered from these targets was investigated. The sputtered AZO TCOs showed electrical properties at room temperature that are superior to simple oxides and comparable to a reference TCO – indium tin oxide (ITO), namely low electrical resistivity of 5.45 × 10-4 Ωcm, high carrier mobility (29.4 cm2V-1s-1), and high charge carrier concentration (3.97 × 1020 cm-3), and also average transmittance in the visible region > 80 %. These superior properties allowed their successful application in different optoelectronic devices.

Boron Leaching Decreases withIncreases on Soil pH

ABSTRACT Management of boron fertilization depends on the magnitude of B leaching in the soil profile, which varies proportionally with the concentration of B in the soil solution, which, in turn, decreases as the soil pH increases due to the higher sorption of B on soil solid surfaces. The objective of this study was to quantify the effect of liming and rates of B applied to the soil on B leaching. The experiment was carried out in the laboratory in 2012, and treatments consisted of a factorial combination of two rates of liming (without and with lime to raise the soil pH to 6.0) and five rates of B (0, 10, 20, 50 and 100 mg kg-1, as boric acid). A Typic Rhodudalf was used, containing 790 g kg-1 clay and 23 g kg-1 organic matter; the pH(H2O) was 4.6. Experimental units were composed of PVC leaching columns (0.10 m in diameter) containing 1.42 kg of soil (dry base). Boron was manually mixed with the top 0.15 m of the soil. After that, every seven days for 15 weeks, 300 mL of distilled water were added to the top of each column. In the percolated solution, both the volume and concentration of B were measured. Leaching of B decreased with increased soil pH and, averaged across the B rates applied, was 58 % higher from unlimed (pH 4.6) than from limed (pH 6.6) samples as a result of the increase in B sorption with higher soil pH. In spite of its high vertical mobility, the residual effect of B was high in this oxisol, mainly in the limed samples where 80 % of B applied at the two highest rates remained in the soil, even after 15 water percolations. Total recovery of applied B, including leached B plus B extracted from the soil after all percolations, was less than 50 %, showing that not all sorbed B was quantified by the hot water extraction method.

Ionsonde Measurement Trend

Time series analysis has gone through different developmental stages before the current modern approaches. These can broadly categorized as the classical time series analysis and modern time series analysis approach. In the classical one, the basic target of the analysis is to describe the major behaviour of the series without necessarily dealing with the underlying structures. On the contrary, the modern approaches strives to summarize the behaviour of the series going through its underlying structure so that the series can be represented explicitly. In other words, such approach of time series analysis tries to study the series structurally. The components of the series that make up the observation such as the trend, seasonality, regression and disturbance terms are modelled explicitly before putting everything together in to a single state space model which give the natural interpretation of the series. The target of this diploma work is to practically apply the modern approach of time series analysis known as the state space approach, more specifically, the dynamic linear model, to make trend analysis over Ionosonde measurement data. The data is time series of the peak height of F2 layer symbolized by hmF2 which is the height of high electron density. In addition, the work also targets to investigate the connection between solar activity and the peak height of F2 layer. Based on the result found, the peak height of the F2 layer has shown a decrease during the observation period and also shows a nonlinear positive correlation with solar activity.

NMR studies of the exchange reactions of CH3CN.BX3 with excess CH3CN /|nJoseph Fogelman. -- 260 St. Catharines, Ont. : [s. n.],

Exchange reactions between molecular complexes and excess acid or base are well known and have been extensively surveyed in the literature(l). Since the exchange mechanism will, in some way involve the breaking of the labile donor-acceptor bond, it follows that a discussion of the factors relating to bonding in molecular complexes will be relevant. In general, a strong Lewis base and a strong Lewis acid form a stable adduct provided that certain stereochemical requirements are met. A strong Lewis base has the following characteristics (1),(2) (i) high electron density at the donor site. (ii) a non-bonded electron pair which has a low ionization potential (iii) electron donating substituents at the donor atom site. (iv) facile approach of the site of the Lewis base to the acceptor site as dictated by the steric hindrance of the substituents. Examples of typical Lewis bases are ethers, nitriles, ketones, alcohols, amines and phosphines. For a strong Lewis acid, the following properties are important:( i) low electron density at the acceptor site. (ii) electron withdrawing substituents. (iii) substituents which do not interfere with the close approach of the Lewis base. (iv) availability of a vacant orbital capable of accepting the lone electron pair of the donor atom. Examples of Lewis acids are the group III and IV halides such (M=B, AI, Ga, In) and MX4 - (M=Si, Ge, Sn, Pb). The relative bond strengths of molecular complexes have been investigated by:- (i) (ii) (iii) (iv) (v] (vi) dipole moment measurements (3). shifts of the carbonyl peaks in the IIIR. (4) ,(5), (6) .. NMR chemical shift data (4),(7),(8),(9). D.V. and visible spectrophotometric shifts (10),(11). equilibrium constant data (12), (13). heats of dissociation and heats of reactions (l~), (16), (17), (18), (19). Many experiments have bben carried out on boron trihalides in order to determine their relative acid strengths. Using pyridine, nitrobenzene, acetonitrile and trimethylamine as reference Lewis bases, it was found that the acid strength varied in order:RBx3 > BC1 3 >BF 3 • For the acetonitrile-boron trihalide and trimethylamine boron trihalide complexes in nitrobenzene, an-NMR study (7) showed that the shift to lower field was. greatest for the BB~3 adduct ~n~ smallest for the BF 3 which is in agreement with the acid strengths. If electronegativities of the substituents were the only important effect, and since c~ Br ,one would expect the electron density at the boron nucleus to vary as BF3electron pair on the halogen and the vacant orbital on the boron site. The degree of back-bonding varies inversely as the bo~on halogen distance and one would therefore expect the B-F bond to exhibit greater back-bonding character than the B-Cl or B-Br bonds. Since back-bonding transfers electron density from substituent to the boron atom site, this process would be expected to weaken the Lewis acid strength. This explains the Lewis acid strength increasing in the order BF 3 BC1 3 BBr 3 . When the acetonitrile boron trihalide complex is formed, the boron atom undergoes ~_cbange of hybridization from sp2 to sp3. From a linear relationship between the heat of formation of ethyl acetate adducts and the shift in the carbonyl I.R. stretch, Drago (22) et al have proposed that the angular di~tortion of the X-B-X bonds from sp2 (12 ) to sp3 (10 hybridization is proportional to the amount of charge transferred, i.e. to the nature of the base, and they have rejected the earlier concept of reorganization energy in explaining the formation of the adduct bond (19).