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Resolved, 2022/2023, 2n quadrimestre

© 2022 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0, In this paper, we present a study of the laser scribing of WOx, VOx, and MoOx films, deposited onto crystalline silicon, with three different wavelengths (355 nm, 532 nm, and 1064 nm) and in two temporal regimes in pulse width, picosecond and nanosecond. For each case, we measure the fluence threshold to remove the transition metal oxides (TMO) film and the fluence threshold to induce damage in the crystalline silicon substrate. The relation between the process parameters and the morphological changes produced in the oxide films is also analysed. The selection of the proper laser source allows a wide parametric window, leading to the complete removal of the TMO films without alteration of the crystalline silicon substrate. Morphological changes of the ablated regions were characterized through confocal microscopy and the relationships between the dimensions of the craters and the ablation parameters were analysed. Finally, we present results on the isolation of diodes and their electrical characteristics, showing the quality of the laser scribing processes., Partial financial support for this work has been provided by the Spanish Ministry of Science and Innovation under the projects CHENOC (ENE2016–78933-C4–1-R and ENE2016–78933-C4–4-R) and SCALED (PID2019–109215RB-C41 and PID2019–109215RB-C44)., Peer Reviewed, Postprint (author's final draft)

In this paper, we present a study of the laser scribing of WOx, VOx, and MoOx films, deposited onto crystalline silicon, with three different wavelengths (355 nm, 532 nm, and 1064 nm) and in two temporal regimes in pulse width, picosecond and nanosecond. For each case, we measure the fluence threshold to remove the transition metal oxides (TMO) film and the fluence threshold to induce damage in the crystalline silicon substrate. The relation between the process parameters and the morphological changes produced in the oxide films is also analysed. The selection of the proper laser source allows a wide parametric window, leading to the complete removal of the TMO films without alteration of the crystalline silicon substrate. Morphological changes of the ablated regions were characterized through confocal microscopy and the relationships between the dimensions of the craters and the ablation parameters were analysed. Finally, we present results on the isolation of diodes and their electrical characteristics, showing the quality of the laser scribing processes.

© 2022 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0, Transition metal oxide (TMOs) layers have interesting properties as selective contacts, i.e., hole or electron transport layers for novel semiconductor devices. Especially, oxides of molybdenum (MoO3), vanadium (V2O5), and tungsten (WO3) show good bahaviour acting as front hole-selective contacts for n-type crystalline-silicon heterojunction solar cells. Laser scribing has been widely used for thin-film ablation and seems the appropriate technology for device manufacturing with such non-conventional materials. In this work, we study the laser scribing of non-stoichiometric evaporated WOx, VOx, and MoOx films with three different wavelengths (1064, 532, and 355 nm) with pulse duration in the nanosecond and picosecond regimes. The selection of the proper laser source allows a wide parametric window, with complete removal of the TMO films and no alteration of the silicon substrate. The results on the isolation of diodes and their electrical characteristics show the quality of the laser scribing processes., Partial financial support has been provided by the Spanish Ministry of Science and Innovation under the projects CHENOC (ENE2016–78933-C4–1-R and ENE2016– 78933-C4–4-R) and SCALED (PID2019–109215RB-C41 and PID2019–109215RB-C44)., Peer Reviewed, Postprint (published version)

Resolved, 2021/2022

Resolved, 2021/2022

Resolved

Resolved

Resolved

Cu(In,Ga)Se2 (CIGS) technology is one of the best absorber materials with record efficiencies among photovoltaic thin-film technologies (22.3% at lab scale and 16% at large commercial module). Although research on this material was originally motivated by low-cost, glass-glass applications focusing to fixed photovoltaic structures, the high efficiency values make CIGS an interesting alternative for low concentration systems. In this paper a 2D model for Cu(In,Ga)Se2 (CIGS) solar cells under low solar concentration is described and contrasted with experimental data. Using simulation, the effect of front electric contact design parameters: finger width, finger separation, and number of buses are analyzed for solar concentrations from 1 up to 10 suns. Efficiency maps allowing front contact grid optimization are shown and analyzed for each concentration factor (Cx), assessing the viability of CIGS solar cells for low concentration applications, where commercial CIGS solar cells may exhibit 35% of electrical power increases with proper front grid optimization under low concentration respect to conventional grid design., Preprint

In this work, we report on improving efficiency of DopLa cells fabricated on p-type substrates. This type of solar cells has all the highly-doped regions based on laser doping from dielectric films resulting in a very simple fabrication process. Depending on the dopant type, emitter regions or high/low doping junctions related to base contacts can be created. The emitter regions are located at the rear surface in order to be contacted by a continuous metal film without penalizing in shadowing losses, while the front surface shows a typical finger grid configuration with the base contacts under the metal. In a previous work, the reported efficiency was limited by optical losses at the front planar surface. As a consequence, we focus on the introduction of a texturized front surface to the device. Firstly, we characterize the contact formation by laser processing on texturized surfaces by SEM image showing that the size of the contacted region is difficult to determine. By measuring contact resistance and surface recombination velocity, we deduce that the laser process of such surfaces leads to a contacted region which is smaller than the one where passivation is lost. The obtained information is included in 3D simulations to get the optimum size of the contacts, i.e. optimum laser power. Additionally, a new front grid metallization is introduced in order to reduce shadowing. Due to the rear emitter configuration of these devices, front surface recombination is crucial for collecting photogenerated carriers. Thus, optimum laser power is very close to the minimum to obtain a reliable contact. Finally, 2x2 cm 2 solar cells are fabricated with a best efficiency of 17.0 %., Peer Reviewed, Postprint (published version)

Laser firing processes have emerged as a technologically feasible approach for the fabrication of local point contacts or local doped regions in advanced high-efficiency crystalline-Si (c-Si) solar cells. In this work, we analyze the local impact induced by the laser pulse on the passivation layers, which are commonly present in advanced c-Si solar cell architectures to reduce surface recombination. We use microphotoluminescence (PL) measurements with a spatial resolution of 7 mu m to evaluate the passivation performance at the surroundings of laser-processed regions (LPRs). In particular, we have studied LPRs performed on SiCx/Al2O3- and Al2O3 passivated c-Si wafers by an infrared (1064 nm) laser. Micro-PL results show that passivation quality of c-Si surface is affected up to about 100 mu m away from the LPR border and that the extension of this damaged zone is correlated with the laser power and to the presence of capping layers. In the final part of the work, the observed decrease in passivation quality is included in an improved 3-D simulation model that gives accurate information about the recombination velocities associated with the studied LPRs., Peer Reviewed, Postprint (author's final draft)

Resolved

One of the most common strategies in high-efficiency crystalline silicon (c-Si) solar cells for the rear surface is the combination of a dielectric passivation with a point-like contact to the base. In such devices, the trade-off between surface passivation and ohmic losses determines the optimum distance between contacts or pitch. Given a certain pitch, the series resistance related to majority carrier flow through the base and the rear point-like contact (Rbase) is commonly calculated a-priori and not crosschecked in finished devices, since typical techniques to measure series resistance lead to an unique value that includes all ohmic losses. In this work, we present a novel method to measure Rbase using impedance spectroscopy (IS) analysis. The IS data at high frequencies allow to determine Rbase due to the presence of the capacitor formed by the metal/dielectric/semiconductor structure that covers most of the rear surface. The method is validated by device simulations where the dependence of Rbase on carrier injection, base resistivity and pitch are reproduced. Finally, Rbase is measured on finished devices. As a result, a more accurate value of the contacted area is deduced which is a valuable information for further device optimization., Peer Reviewed, Postprint (author's final draft)

The devices will be fabricated using the clean room facilities located at the Dept of Eng Electrònica and the Center for Research in Nanoengineering (CrNE) of the UPC, This work is a slight research on silicon heterojunction solar cells which have been of great interest recently. The aim is to span fabrication, characterization and simulation and to reach a broad but shallow knowledge about this devices. Within heterojunction solar cells, this work is particularly focused on amorphous silicon/crystalline silicon (a-Si/c-Si) heterojunction solar cells and Transition-Metal-Oxide (TMO) silicon heterojunction solar cells (TMO/c-Si). TMO started being of interest very recently because they can substitute a-Si in a solar cell lowering fabrication costs while achieving relatively good performance. Unlikely, it is not clear why it can play the same role as a-Si since they are very different materials. Therefore simulating TMO based devices is still far from being reliable. Simulations of a-Si heterojunction solar cells have been performed since it seems to be the starting point of the road to simulating TMO. The fabrication and characterization processes are almost the same for the two types of solar cell. Since the final aim is to understand TMO heterojunction solar cells, this part is dedicated to them. Three different TMOs heterojunction solar cells have been fabricated and characterized which are M oOx , W Ox and V2 O5 while the simulation has focused on a-Si. The work has been carried out collaborating with a research group from electronics department of the UPC (Universitat Politèctica de Cataunya). Silvaco ATLAS electronic device simulator has been used to reproduce the a-Si HIT (Heterojuntion with Intrinsic Thin layer) solar cell figures of merit., En este proyecto se estudian células solares de heterounión de silicio cristalino. El objetivo es hacer un seguimiento de su fabricación, caracterización y llevar a cabo una simulación para conseguir una amplia pincelada de conocimiento sobre estos dispositivos. En concreto, los dos tipos de células solares en las que nos centraremos son células de heterounión silicio cristalino (c-Si) con silicio amorfo (a-Si) y c-Si con diferentes óxidos de metales de transición (TMO). La idea es utilizar metales de transición en vez de silicio amorfo (a-Si) para abaratar el proceso de fabricación manteniendo una buena eficiencia. Desgraciadamente, todavía no se conoce el funcionamiento exacto de las células con TMOs, por lo tanto en la simulación nos centraremos en las células de a-Si / c-Si. En cambio el proceso de fabricación y caracterización está dedicado mayoritariamente a las células TMO / c-Si con el objectivo de entender major la interacción que hay entre ellos., En aquest projecte s’estudien cèl·lules solars d’heterounió de silici cristal·lí. L’objectiu és fer un seguiment de la seva fabricació, caracterització i dur a terme una simulació per aconseguir un amplia pinzellada de coneixement sobre aquests dispositius. En concret, els dos tipus de cèl·lules solars en les que ens centrarem són cèl·lules d’heterounió silici cristal·lí (c-Si) amb silici amorf (a-Si) i c-Si amb diferents òxids de metalls de transició (TMO). La idea és utilitzar metalls de transició en comptes de silici amorf (a-Si) per abaratir el procés de fabricació mantenint una bona eficiència. Malauradament, encara no es coneix el funcionament exacte de les cèl·lules amb TMOs, per tant en la part de simulació ens centrarem en les cèl·lules de a-Si/c-Si. En canvi el procés de fabricació i caracterització està dedicat majoritàriament a les cèl·lules TMO/c-Si per entendre millor la interacció que hi ha entre ells.

This paper presents an 3D TCAD model of crystalline Silicon (c-Si) solar cells. Physical parameters used in the model are discussed. Simulation results are compared to experimental current-voltage curves and solar cell figures of merit namely open-circuit voltage, short-circuit current density, fill factor, and conversion efficiency, allowing us to determine an optimum design for these devices. Particularly, the model is applied to conventional p-type c-Si solar cells with rear contacts based on Laser-Firing technique and to Doped by Laser (DopLa) crystalline Silicon solar cells., Peer Reviewed, Postprint (published version)

Resolved

In this work 3D simulations are used to study the impact of technological parameters on device performance of c-Si interdigitated back-contacted IBC solar cells with point-like doped contacts. In these cells, the highly-doped regions are defined in a point-like structure instead of the more classical arrangement of fully doped fingers. Numerical simulations allow us to optimize rear contact geometry, i.e. optimum pitch between contacts, depending on the substrate resistivity and the passivation quality of base contacts. Results show a trade-off between recombination and base resistive losses demonstrating limit efficiencies over 27% for a perfectly passivated structure on p- and n-type substrates. More realistic devices where state-of-the-art surface passivation is considered reach efficiencies beyond 22% on 2 +- 1 ohmcm substrates with optimum pitch values of 200 +- 50 µm., Peer Reviewed, Postprint (published version)

Resolved

In this paper we introduce a new crystalline silicon (c-Si) solar cell fabrication technology based on the laser processing of dielectric films to create all the highly-doped regions. We call it DopLaCell (Doped by Laser Cell) structure. The resulting fabrication process can be simplified to just four steps: wafer cleaning, film depositions, laser processing and metallization. We used phosphorus-doped silicon carbide stacks (SiCx(n)) and aluminium oxide/silicon carbide (Al2O3/SiCx) stacks for the creation of n+ and p+ regions respectively. As a proof of concept, 1x1 cm2 solar cells were fabricated on 0.45 Wcm p-type substrates with promising results. The main feature of DopLaCell structure is the location of the emitter at the rear surface consisting of a point-like laser processed n+ regions combined with an induced inversion layer in between based on the fixed charge density of the SiCx(n) stacks. Solar cells with distance between rear emitter regions or pitch ranging from 200 to 350 μm are characterized resulting in a strong decrease of Fill Factor (FF) from 75.4 to 59.7 %. Suns-Voc measurements show excellent pseudo-FF (p-FF) values beyond 81% in all devices demonstrating the high quality of laser doping process and the actual limitation of FF by ohmic losses. Device modelling through 3D simulations demonstrates that these ohmic losses are related to the high sheet resistance of the inversion layer induced in-between n+ regions. We conclude that there is room for improvement to fully develop the potential of this new structure, particularly for low resistivity n-type substrates where the high fixed charge densities of Al2O3 can help to improve FF., Peer Reviewed, Postprint (published version)

Rear surface of high-efficiency crystalline silicon solar cells is based on a combination of dielectric passivation and point-like contacts. In this work, we develop a 3D model for these devices based on 2.2 Ωcm p-type crystalline silicon substrates. We validate the model by comparison with experimental results allowing us to determine an optimum design for the rear pattern. Additionally, the 3D model results are compared with the ones deduced from a simpler and widely used 1D model. Although the maximum efficiency predicted by both models is approximately the same, large deviations are observed in open-circuit voltage and fill factor. 1D simulations overestimate open-circuit voltage because Dember and electrochemical potential drops are not taken into account. On the contrary, fill factor is underestimated because of higher ohmic losses along the base when 1D analytical model is used. These deviations are larger for relatively low-doped substrates, as the ones used in the experimental samples reported hereby, and poor passivated contacts. As a result, 1D models could mislead to too short optimum rear contact spacing., Peer Reviewed, Postprint (published version)

Resolved

Projecte realitzat en el marc d’un programa de mobilitat amb Microwave Remote Sensing Laboratory de la University of Massachusetts Amherst, [ANGLÈS] Frequency Modulated Continuous Wave radars suffer from an undesirable effect called transmitter leakage. The power leak between transmitter and receiver due to the lack isolation impairs reception performance. The leak, which is orders of magnitude stronger than the desired target echoes, drives the receptor into saturation due to its non-linear characteristics. Since the echoes and leakage are extremely close in frequency it is impossible to use filters to get rid of this problem. Traditionally, the way to increase the isolation has been to use separate antennas to transmission and reception instead of a single one. However, this method presents some drawbacks, e.g. an increase of bulkiness and price. A more elaborate approach is cancelling (subtracting) the leakage before it reaches the receiver. The cancellation system takes advantage of the fact that the leakage and the transmitted signal are of the same form. Subtracting the leakage effectively requires a degree of precision rarely achieved by manual adjustment. This work presents detailed description of a design operating at UHF that uses feedback as a way to achieve a high degree of leakage cancellation. The design validity is demonstrated in a series of tests that quantify the degree of leakage cancellation and assess how different targets are affected by the system., [CASTELLÀ] Los radares de onda continua modulados en frecuencia (FMCW) sufren un efecto generalmente no deseado llamado fuga de transmisión. La fuga de potencia de transmisor a receptor debido a la falta de aislamiento entre estos puede llegar a degradar la calidad de la recepción. La fuga, generalmente con una potencia órdenes de magnitud mayor a la eco útil , satura el receptor debido a sus características no lineales . Debido a que normalmente la fuga y el eco son muy cercanos en frecuencia no se pueden utilizar filtros para solucionar el problema. Tradicionalmente, la manera de aumentar considerablemente el aislamiento ha sido utilizar antenas separadas por el transmisor y el receptor en vez de una sola. Este método presenta algunos inconvenientes como el incremento del peso, volumen y el precio del sistema. Un método más elaborado es cancelar (restar) la fuga justo antes de que llegue al receptor. El dispositivo de cancelación se sirve del hecho de que la fuga y la señal transmitida son de la misma forma excepto en la amplitud y fase. Restar la fuga de una manera efectiva requiere una precisión raramente lograda con ajustes manuales. En este trabajo se presenta una descripción detallada de un sistema realimentado que consigue un alto grado de cancelación. La validez del diseño se demuestra en usa serie de pruebas que determinan cómo este cancela la fuga y como el eco útil se ve afectado., [CATALÀ] Els radars d'ona contínua modulats en freqüència (FMCW) pateixen un efecte generalment no desitjat anomenat fuga de transmissió. La fuga de potència de transmissor a receptor a causa de la falta d'aïllament entre aquests pot arribar a degradar la qualitat de la recepció. La fuga, generalment amb una potència ordres de magnitud major a l'eco útil, satura el receptor degut a les seves característiques no lineals. Degut a que normalment la fuga i l'eco són molt propers en freqüència no es poden utilitzar filtres per solucionar el problema. Tradicionalment, la manera d'augmentar considerablement l'aïllament ha sigut utilitzar antenes separades pel transmissor i pel receptor en comptes d'una sola. Aquest mètode presenta alguns inconvenients com l'increment del pes,volum i el preu del sistema. Un mètode més elaborat és cancel·lar (restar) la fuga just abans que arribi al receptor. El dispositiu de cancel·lació es serveix del fet que la fuga i el senyal transmès són de la mateixa forma excepte en l'amplitud i fase. Restar la fuga d'una manera efectiva requereix una precisió rarament aconseguida amb ajustaments manuals. En aquest treball es presenta una descripció detallada d'un sistema realimentat que aconsegueix un alt grau de cancel·lació. La validesa del disseny es demostra en usa sèrie de tests que determinen com aquest cancel·la la fuga i com l'eco útil es veu afectat.

The back-contact back-junction BC-BJ solar cell concept is a promising photovoltaic structure for both laboratory and industrial c-Si solar cells. High efficiency devices based on this concept have been reported in the past using either diffused regions or applying the heterojunction with intrinsic thin layer HIT concept to perform both base and emitter contacts. In this work we use 3D numerical simulations to study the impact of technological parameters on device performance of c-Si(p) BC-BJ solar cells with point-like doped contacts. Numerical simulations allow us to optimize rear contact geometry as a trade-off between recombination and base resistive losses, leading to photovoltaic efficiencies higher than 18.3% and up to 22.3% on 2.2 cm FZ substrates depending on the back contact pattern and the passivation quality of base contacts., Peer Reviewed, Postprint (published version)

Català: Són molts els fabricants que utilitzen programes comercials que integren mòduls d'extracció per estimar els paràmetres que modelen els seus dispositius en simuladors de circuits. L'objectiu del present treball és el desenvolupament d'una aplicació capaç d'estimar els paràmetres SPICE que modelen el transistor bipolar, tot això a partir de mesures experimentals reals proporcionades pel fabricant del dispositiu. A més, s'ofereix un compendi de mètodes i tècniques en forma de manual, on es descriu de manera detallada la teoria, si fa o no fa confidencial, amagada darrere de l'extracció de paràmetres en dispositius semiconductors., Castellano: Son muchos los fabricantes que utilizan programas comerciales que integran módulos de extracción para estimar los parámetros que modelan sus dispositivos en simuladores de circuitos. El objetivo del presente trabajo es el desarrollo de una aplicación capaz de estimar los parámetros SPICE que modelan el transistor bipolar, todo ello a partir de medidas experimentales reales proporcionadas por el fabricante del dispositivo. Además, se ofrece un compendio de métodos y técnicas en forma de manual, donde se describe de manera detallada la teoría, poco más o menos confidencial, escondida detrás de la extracción de parámetros en dispositivos semiconductores., English: They are many manufacturers that use commercial programs that integrate extraction modules to estimate the parameters that model their devices in electronic circuit simulators. The objective of the present work is the development of an application able to estimate the parameters SPICE that model the bipolar transistor, everything it starting from experimental real measures provided by the manufacturer of the device. Also, this work offers a summary of methods and technical in manual form, where it is described in a detailed way the theory, not very more or less confidential, hidden behind the extraction of parameters in devices semiconductors.

Time-to-market is a critical issue for nowadays integrated circuits manufacturers. In this paper the Via-Configurable Transistor Array regular layout fabric (VCTA), which aims to minimize the time-to-market and its associated costs, is studied for a Delay-Locked Loop design (DLL). The comparison with a full custom design demonstrates that VCTA can be used without loss of functionality while accelerating the design time. Layout implementations, in 90 nm CMOS process, as well as the delay, energy and jitter electrical simulations are provided., Peer Reviewed, Postprint (published version)

This paper presents an analytical model for high-frequency noise of high-speed SiGe heterojunction bipolar transistors (HBTs). The model allows circuit level noise parameters to be obtained: the minimum noise figure, the noise resistance and the optimum admittance for different bias and frequencies up to 64 GHz, including the quasi-saturation effect. The noise parameters are determined directly from y-parameters. The analytical model is verified through comparison with TCAD simulation results of the noise parameters using the field impedance method as well as with measured data. The paper also reviews for 200 GHz SiGe HBTs the latest y-parameters-based analytical noise models. Their bias and frequency dependence is calculated and compared with device simulation., Postprint (published version)

Català: El present treball es desenvolupa entorn de la modelització d'un transistor bipolar de doble heterounió (DHBT). En concret, s'estudia un dispositiu Tipus-I basat en la utilització de materials semiconductors III-V com són el InP (fosfur d?indi) i InGaAs (aliatge ternari d'indi, gal-li i arseni). Per dur a terme totes les simulacions d'aquesta tesi, s'ha fet ús del simulador numèric ATLAS de la companyia SILVACO. Amb l'objectiu d'avaluar la bondat del model, es realitza una comparació amb valors experimentals i amb resultats de simulacions realitzades amb l'eina TCAD DESSIS de Synopsys del comportament en contínua del dispositiu. S'analitzen el models i paràmetres de transport i les propietats físiques del dispositiu estudiant i discutint els models disponibles a la literatura i la forma d'implementar-los al simulador. Finalment, es procedeix a analitzar el nivell d'influència de certs factors (paràmetres de transport com la movilitat de portadors o propietats físiques com per exemple el fenomen del band gap narrowing) sobre el comportament en contínua del dispositiu. Per últim, s'estudia l'impacte de l'escalat de diferents regions., Castellano: El presente trabajo se desarrolla en torno a la modelización de un transistor bipolar de doble heterounión (DHBT). En concreto, se estudia un dispositivo Tipo-I basado en la utilización de materiales semiconductores III-V como son el InP (fosfuro de indio) e InGaAs (aleación ternaria de indio, galio y arsenio). Para llevar a cabo todas las simulaciones de esta tesis, se ha hecho uso del simulador numérico ATLAS de la compañía SILVACO. Con el objetivo de evaluar la bondad del modelo, se realiza una comparación con valores experimentales y con resultados de simulaciones realizadas con la herramienta TCAD DESSIS de Synopsys del comportamiento en continua del dispositivo. Se analizan los modelos y parámetros de transporte y las propiedades físicas del dispositivo estudiando y discutiendo los modelos disponibles en la literatura y la forma de implementarlos en el simulador. Finalmente, se procede a analizar el nivel de influencia de ciertos factores (parámetros de transporte como la movilidad de portadores ó propiedades físicas como por ejemplo el fenómeno del band gap narrowing) sobre el comportamiento en continua del dispositivo. Por último se estudia el impacto del escalado de diferentes regiones del mismo., English: A double heterojunction bipolar transistor (DHBT) modeling has been developed in this work. In particular, a Type-I device is studied, which is based on the use of III-V semiconductor materials such as InP (indium phosphide) and InGaAs (ternary alloy of indium, gallium and arsenic). ATLAS numerical simulator from SILVACO company has been used to carry out all simulations in this thesis. In order to evaluate the model accuracy, a comparison is made with experimental data and simulation results from DESSIS TCAD tool from Synopsys. This exercise is focused on DC behavior of the device. Transport model and device physical propierties have been analyzed by means of studying and discussing the available models in the literature and its implementation in the simulator. Finally, relative impact of certain factors (transport parameters such as carrier mobility or physical properties as for instance band gap narrowing) has been analyzed over DC behavior of the device. To conclude, DHBT is vertically scaled with the purpose of studying the influence.

El transistor bipolar, com altres dispositius semiconductors, utilitza models matemàtics per simular el seu comportament elèctric. El model matemàtic, o model compacte del dispositiu semiconductor, equival a un circuit electrònic amb un conjunt de paràmetres que emula el comportament del dispositiu. Per tant, la obtenció d’aquest model, és clau en el disseny de circuits que incorporin aquests dispositius. El dispositiu bipolar amb el que s’ha treballat en aquest projecte, és el transistor bipolar d’heterounió. Hi ha diferents models compactes de transistor, i la tria del model que es vol utilitzar es pot fer seguint tres criteris: Depenent de l’aplicació: models del transistor que s’empren en circuits determinats, com per exemple circuits d’alta freqüència o circuits de potència. Depenent del fabricant: models del transistor que dona el fabricant del circuit que es vol dissenyar. Depenent de la precisió: models del transistor mes complexos, solen ser mes precisos. Els models poden estar orientats a la mateixa aplicació, però alguns són més fidels a la realitat, ja que n’hi ha que ometen, per exemple, nolinealitats.