E as questões?.

E as questões?

Resumo anterior Aplicações de Raio-X Luz sincrotron
Área Analítica, difração, Lei de Bragg, Fator de Estrutura Geométrico. Área de Imagem, radiografia Luz sincrotron Óptica de raio-x, policapilaridade Microscopia de raio-x Laser de raio-x (brandos e duros)

Desde que vimos como são as diferentes formas dos cristais, vejamos como são formados De ligações a bandas

Formação de um sólido Átomos livres Configuração eletrônica dos átomos
Aproximação dos átomos Diferentes tipos de forças interatômicas: coulômbica, repulsão, covalente Formação de bandas de energia Formação de sólidos Diferentes tipos de sólidos: metal, isolante, semicondutor

Diferentes tipos de forças interatômicas
Eletrostática ~ 20 kJ/mol Correlated motions of electrons in neighboring atoms create temporary dipoles of the same orientation - the atoms attract. This attraction is called a 'Van der Waals' force. In the force field, it is approximated with a 'Lennard-Jones' function. You can see how the two oxygen molecules attract each other. This takes a long time, the Van der Waals forces are weak. van der Waals – 4 kJ/mol

Diferentes tipos de forças interatômicas
Hidrogênica 12 – 30 kJ/mol Materiais duros, alto ponto de fusão, diamante, silício, quartzo Covalente ~ 350 kJ/mol As stated by the previous answerer, these are all intermolecular forces London forces: AKA Van der Waals or Dispersion forces Present in all atoms and molecules occurs when electrons "sloshing", creating an instantaneous dipole (meaning there is an unequal electron distribution, there are more electrons on one side of the atom/molecule than the other resulting in a partial charge on the atom, which in turn, induces neighboring atoms to do the same. VERY weak Dipole-dipole forces - present only in polar molecules (permanent dipoles) Polar molecules have a partially negative charge on one end and a partiall negative charge on the other end. So one polar molecules positive side is going to be attracted to another polar molecules negative end Hydrogen bonding: a special class of strong dipole-dipole interactions hydrogen bonding is a result of a large difference in electronegatiivity between hydrogen and Nitrogen, Oxygen, and Fluorine. This means that the hydrogen has a fairly large partial positive charge Basically, because N,F, and O have large electronegativity, they pull the electron closer to them, and away from the hydrogen, causing the hydrogen to have a partially positive charge Strong ionic attraction Recall lattice energy and its relations to properties of solid. The more ionic, the higher the lattice energy. Examine the following list and see if you can explain the observed values by way of ionic attraction: LiF, 1036; LiI, 737; KF, 821; MgF2, 2957 kJ/mol. Intermediate dipole-dipole forces Substances whose molecules have dipole moment have higher melting point or boiling point than those of similar molecular mass, but their molecules have no dipole moment. Weak London dispersion forces or van der Waal's force These forces alway operate in any substance. The force arisen from induced dipole and the interaction is weaker than the dipole-dipole interaction. In general, the heavier the molecule, the stronger the van der Waal's force of interaction. For example, the boiling points of inert gases increase as their atomic masses increases due to stronger Landon dispersion interactions. Hydrogen bond Certain substances such as H2O, HF, NH3 form hydrogen bonds, and the formation of which affects properties (mp, bp, solubility) of substance. Other compounds containing OH and NH2 groups also form hydrogen bonds. Molecules of many organic compounds such as alcohols, acids, amines, and aminoacids contain these groups, and thus hydrogen bonding plays a important role in biological science. Covalent bonding Covalent is really intramolecular force rather than intermolecular force. It is mentioned here, because some solids are formed due to covalent bonding. For example, in diamond, silicon, quartz etc., the all atoms in the entire crystal are linked together by covalent bonding. These solids are hard, brittle, and have high melting points. Covalent bonding holds atoms tighter than ionic attraction. Metallic bonding Forces between atom in metallic solids belong to another category. Valence electrons in metals are rampant. They are not restricted to certain atoms or bonds. Rather they run freely in the entire solid, providing good conductivity for heat and electric energy. These behaviour of electrons give special properties such as ductility and mechanical strength to metals. INTERMOLECULAR BONDING - HYDROGEN BONDS This page explains the origin of hydrogen bonding - a relatively strong form of intermolecular attraction. If you are also interested in the weaker intermolecular forces (van der Waals dispersion forces and dipole-dipole interactions), there is a link at the bottom of the page. The evidence for hydrogen bonding Many elements form compounds with hydrogen. If you plot the boiling points of the compounds of the Group 4 elements with hydrogen, you find that the boiling points increase as you go down the group. The increase in boiling point happens because the molecules are getting larger with more electrons, and so van der Waals dispersion forces become greater. Outras forças fracas ou desprezíveis: magnética e gravitacional

Principais tipos de ligações
Argon xstal: Van der Waals Iônica Metálica Covalente E/kJ/mol r/Å -0.5 +0.5 1 2 3 4 5 repulsão soma atração Sodium xstal: Kittel Carbon xstal;

Alguns tipos de ligações
Na+ Cl- Ligação Iônica Cl : Cl Ligação covalente não-polar [H : Cl] Ligação covalente polar

Num sólido iônico

Formação de bandas

Átomo de hidrogênio

Molécula de hidrogênio
Valence Bond Model vs. Molecular Orbital Theory Because arguments based on atomic orbitals focus on the bonds formed between valence electrons on an atom, they are often said to involve a valence-bond theory. The valence-bond model can't adequately explain the fact that some molecules contains two equivalent bonds with a bond order between that of a single bond and a double bond. The best it can do is suggest that these molecules are mixtures, or hybrids, of the two Lewis structures that can be written for these molecules. This problem, and many others, can be overcome by using a more sophisticated model of bonding based on molecular orbitals. Molecular orbital theory is more powerful than valence-bond theory because the orbitals reflect the geometry of the molecule to which they are applied. But this power carries a significant cost in terms of the ease with which the model can be visualized. Forming Molecular Orbitals Molecular orbitals are obtained by combining the atomic orbitals on the atoms in the molecule. Consider the H2 molecule, for example. One of the molecular orbitals in this molecule is constructed by adding the mathematical functions for the two 1s atomic orbitals that come together to form this molecule. Another orbital is formed by subtracting one of these functions from the other, as shown in the figure below. One of these orbitals is called a bonding molecular orbital because electrons in this orbital spend most of their time in the region directly between the two nuclei. It is called a sigma ( ) molecular orbital because it looks like an s orbital when viewed along the H-H bond. Electrons placed in the other orbital spend most of their time away from the region between the two nuclei. This orbital is therefore an antibonding, or sigma star ( *), molecular orbital. The bonding molecular orbital concentrates electrons in the region directly between the two nuclei. Placing an electron in this orbital therefore stabilizes the H2 molecule. Since the * antibonding molecular orbital forces the electron to spend most of its time away from the area between the nuclei, placing an electron in this orbital makes the molecule less stable. Electrons are added to molecular orbitals, one at a time, starting with the lowest energy molecular orbital. The two electrons associated with a pair of hydrogen atoms are placed in the lowest energy, or bonding, molecular orbital, as shown in the figure below. This diagram suggests that the energy of an H2 molecule is lower than that of a pair of isolated atoms. As a result, the H2 molecule is more stable than a pair of isolated atoms. Using the Molecular Orbital Model to Explain Why Some Molecules Do Not Exist This molecular orbital model can be used to explain why He2 molecules don't exist. Combining a pair of helium atoms with 1s2 electron configurations would produce a molecule with a pair of electrons in both the bonding and the * antibonding molecular orbitals. The total energy of an He2 molecule would be essentially the same as the energy of a pair of isolated helium atoms, and there would be nothing to hold the helium atoms together to form a molecule.

Distribuição de elétrons e energias de OM

Distribuição de carga homo-heteropolar (ligante)

Distribuição de carga e distribuição de ligação (anti-ligante)

Lítio 1s22s

Formação de bandas de energia, número de estados
Átomos de Na (1s22s22p63s) Número atômico 11 N átomos (1023 átomos/cm3) 2 átomos 3 átomos

Bandas de energia do Na com N átomos
Átomos de Na (1s22s22p63s) Número atômico 11 2(2l+1)elétrons 2 = fator de orientação do spin 2l = número de possíveis orientações do momento angular orbital 2(2l+1)N = capacidade de cada banda para N átomos

Classificação de sólidos
Metal Semicondutor Isolante

Zonas de Brillouin the first Brillouin zone is a uniquely defined primitive cell in reciprocal space

1ª 2ª 3ª SC FCC BCC

Em termos de bandas http://en.wikipedia.org/wiki/Brillouin_zone
In mathematics and solid state physics, the first Brillouin zone is a uniquely defined primitive cell of the reciprocal lattice in the frequency domain. It is found by the same method as for the Wigner-Seitz cell in the Bravais lattice. The importance of the Brillouin zone stems from the Bloch wave description of waves in a periodic medium, in which it is found that the solutions can be completely characterized by their behavior in a single Brillouin zone. Taking surfaces at the same distance from one element of the lattice and its neighbours, the volume included is the first Brillouin zone. Another definition is as the set of points in k-space that can be reached from the origin without crossing any Bragg plane. Equivalently, this is the Voronoi cell around the origin of the reciprocal lattice. There are also second, third, etc., Brillouin zones, corresponding to a sequence of disjoint regions (all with the same volume) at increasing distances from the origin, but these are used more rarely. As a result, the first Brillouin zone is often called simply the Brillouin zone. (In general, the n-th Brillouin zone consist of the set of points that can be reached from the origin by crossing n − 1 Bragg planes.) A related concept is that of the irreducible Brillouin zone, which is the first Brillouin zone reduced by all of the symmetries in the point group of the lattice. The concept of a Brillouin zone was developed by Leon Brillouin ( ), a French physicist.

Outra representação Schematic band diagrams for an insulator, a semiconductor, and a metal.

Formação de bandas de energia a partir dos níveis de energia dos átomos constituintes

Exemplo configuração banda de energia do Li

Estrutura de banda de isolante e semicondutor (cristal molecular)

Bandas de energia de níveis permitidos no diamante
1s22s22p2

Diamante colorido por doadores
The band structure of blue and yellow diamonds A pure diamond crystal is translucent, as it is composed only of carbon atoms, each of which has four valence electrons. In a yellow diamond, a few carbon atoms per million have been replaced by nitrogen atoms, each containing five valence electrons. The structure of the diamond crystal does not change significantly, but the extra electrons occupy a donor level. The nitrogen donor level energy in a diamond is large, peaking at about 4 eV. With a concentration of a few nitrogen atoms per million, instead of a clean "spike" donor level energy, the nitrogen donor level energy broadens into a band because of a number of complex factors, including thermal vibrations. This broadened donor energy band results in the difference between donor and conduction bands being as low as 2.2 eV. The most likely transition allows incident light with energy of 4 eV per photon to excite electrons from the donor level to the conduction band. However, it is possible for electrons to be excited to the conduction band with energy of 2.2 eV and upwards. This means that blue and violet light are absorbed from the full spectrum of light normally transmitted, and the resulting color is yellow. Unlike blue boron-doped diamonds, which conduct electricity, nitrogen-doped diamonds remain insulators. This is because nitrogen is a deep impurity: a relatively high energy (2.2 eV, as compared with 0.4 eV for boron) is required to excite electrons from the donor energy level to the conduction band, and only a fraction of the available electrons are freed to carry a charge. An extremely rare green color can result from a higher nitrogen content of about 1 atom per 1000 atoms of carbon. At even higher nitrogen concentrations, the donor level broadens so that all visible light can be absorbed, resulting in a black color. Synthetic blue diamonds are created by adding boron as an impurity. Boron is trivalent, having three valence electrons; where a boron atom replaces a carbon atom in the diamond structure there is one fewer electron than usual. This missing electron, or hole, creates an acceptor energy level above the valence band. The boron acceptor energy is only 0.4 eV, so light of any energy can be absorbed during excitation. The boron acceptor band is broadened, and the absorption tapers off throughout the visible light energies, resulting in stronger absorption at the red end of the spectrum. At a level of one or a few boron atoms for every million carbon atoms, an attractive blue color results. Natural diamonds of this color, such as the Hope Diamond, are rare and highly priced. Boron has one less electron than carbon, and the presence of a few boron atoms per million carbon atoms in diamond leads to a hole with an energy level within the band gap. This is called an "acceptor" level since it can accept an electron from the full valence band. « Previous Next » webexhibits.org/causesofcolor — Bibliography — About — Credits & Feedback Electrons can be donated to the empty conduction band. The valence band is completely filled. At minute concentrations of nitrogen, the energy required to excite an electron from the donor level to the conduction band is 4 eV, an energy that is greater than the visible light range (left). The diamond will be colorless. At a few nitrogen atoms per million carbon atoms, the donor level is broadened as at the right of this figure, and energies greater than 2.2 eV can excite an electron from the donor level to the conduction band. The absorption of these higher energies (blue and violet light) results in the yellow color of the diamond.

Teoria de Bandas : duas maneiras
Duas aproximações para encontrar as energias dos elétrons associados com os átomos numa rede periódica. 1.- Aproximação de elétron ligado (energia de átomos singulares) Os átomos isolados são reunidos para formar um sólido. 2.- Aproximação de elétron livre (não ligado) (E = p2/2m) Elétrons livres modificado por um potencial periódico, i.e. rede de íons. Ambas as aproximações resultam em níveis de energia agrupados com regiões de energia permitida e proibidas. Bandas de energia se sobrepõem em metais. Bandas de energia não se sobrepõem (ou possuem região proibida) para semicondutores e isolantes. There are two approaches to finding the electron energies associated with atoms in a periodic lattice. Approach #1: “Bound” Electron Approach (single atom energies!) Isolated atoms brought close together to form a solid. Approach #2: “Unbound” or Free Electron Approach (E = p2/2m) Free electrons modified by a periodic potential (i.e. lattice ions). Both approaches result in grouped energy levels with allowed and forbidden energy regions. Energy bands overlap for metals. Energy bands do not overlap (or have a “gap”) for semiconductors Ver Charles Kittel – Introduction to Solid State Physics

A wide range of energies can cause electrons to be excited from the valence band to the conduction band (absorption; figure shows electronic transitions, A, and corresponding absorption spectrum, B).

Excited electrons will drop from the bottom of the conduction band into the top of the valence band with the emission of light with a very narrow band width (emission; figure shows an electronic transition, A, and corresponding emission spectrum, B)

Diagrama de Banda: Isolante com Egap grande
Banda de condução (vazio) T > 0 EC Egap EF EV Banda de valência (cheio) Fermi Energies for Metals The Fermi energy is the maximum energy occupied by an electron at 0K. By the Pauli exclusion principle, we know that the electrons will fill all available energy levels, and the top of that "Fermi sea" of electrons is called the Fermi energy or Fermi level. An important parameter in the band theory is the Fermi level, the top of the available electron energy levels at low temperatures. The position of the Fermi level with the relation to the conduction band is a crucial factor in determining electrical properties. Fermi Level "Fermi level" is the term used to describe the top of the collection of electron energy levels at absolute zero temperature. This concept comes from Fermi-Dirac statistics. Electrons are fermions and by the Pauli exclusion principle cannot exist in identical energy states. So at absolute zero they pack into the lowest available energy states and build up a "Fermi sea" of electron energy states. The Fermi level is the surface of that sea at absolute zero where no electrons will have enough energy to rise above the surface. The concept of the Fermi energy is a crucially important concept for the understanding of the electrical and thermal properties of solids. Both ordinary electrical and thermal processes involve energies of a small fraction of an electron volt. But the Fermi energies of metals are on the order of electron volts. This implies that the vast majority of the electrons cannot receive energy from those processes because there are no available energy states for them to go to within a fraction of an electron volt of their present energy. Limited to a tiny depth of energy, these interactions are limited to "ripples on the Fermi sea". At higher temperatures a certain fraction, characterized by the Fermi function, will exist above the Fermi level. The Fermi level plays an important role in the band theory of solids. In doped semiconductors, p-type and n-type, the Fermi level is shifted by the impurities, illustrated by their band gaps. The Fermi level is referred to as the electron chemical potential in other contexts.In metals, the Fermi energy gives us information about the velocities of the electrons which participate in ordinary electrical conduction. The amount of energy which can be given to an electron in such conduction processes is on the order of micro-electron volts (see copper wire example), so only those electrons very close to the Fermi energy can participate. The Fermi velocity of these conduction electrons can be calculated from the Fermi energy. Table This speed is a part of the microscopic Ohm's Law for electrical conduction. For a metal, the density of conduction electrons can be implied from the Fermi energy. The Fermi energy also plays an important role in understanding the mystery of why electrons do not contribute significantly to the specific heat of solids at ordinary temperatures, while they are dominant contributors to thermal conductivity and electrical conductivity. Since only a tiny fraction of the electrons in a metal are within the thermal energy kT of the Fermi energy, they are "frozen out" of the heat capacity by the Pauli principle. At very low temperatures, the electron specific heat becomes significant. Fermi energies for metals Table of Fermi energies Em T = 0, a banda de valência inferior é preenchida com elétrons e a banda de condução está vazia, conseqüentemente condutividade zero. A energia de Fermi EF está no meio da banda proibida (2-10 eV) entre as bandas de condução e valência. Em T > 0, os elétrons não são termicamente excitados da banda de valência à banda de condução, conseqüentemente também condutividade zero.

Diagrama de Bandas: Função de preenchimento de Fermi-Dirac
Probabilidade dos elétrons (férmions) serem encontrados em vários níveis de energia. Em TA, E – EF = 0.05 eV  f(E) = E – EF = 7.5 eV  f(E) = 10 –129 Efeito enorme da dependência exponencial T > 0 T >> 0 T = 0 K Em T = 0 K, elétrons tem 100% probabilidade de estar abaixo da energia de Fermi EF e 0% probabilidade de estar acima de EF. Em T > 0 K, probabilidade diminui abaixo de EF e aumenta acima de EF, provocando que a função degrau passe a ser mais suave (escorregadia?). Fermi :

Diagrama de Banda: Metal
preenchimento da banda. Função de preenchimento Banda de energia a ser preenchida EC,V EC,V EF EF T > 0 T = 0 K Em T = 0, níveis de energia abaixo de EF são preenchidos com elétrons, entretanto todos os níveis acima de EF estão vazios. Os elétrons são livres para se movimentar dentro dos estados vazios da banda de condução com somente um pequeno campo elétrico aplicado E, teremos alta condutividade elétrica. Em T > 0, os elétrons tem uma probabilidade de serem termicamente excitados a partir de níveis abaixo do nível de energia de Fermi para acima. At T = 0, all levels in conduction band below the Fermi energy EF are filled with electrons, while all levels above EF are empty. Electrons are free to move into “empty” states of conduction band with only a small electric field E, leading to high electrical conductivity! At T > 0, electrons have a probability to be thermally “excited” from below the Fermi energy to above it.

Junção pn, diodos, LED’s e diodos lasers
Semicondutor tipo p, tipo n Junção pn, circuitos diretos e reversos Equações de transporte LED OLED Diodo laser

Diagrama de Bandas: Semicondutor sem Dopante
EF EC EV Banda de condução (Parcialmente preenchida) Banda de valência (Parcialmente vazia) T > 0 What happens to the conductivity for T > 0? How would the band diagram look for lower & higher temperatures? Em T = 0, A banda de valência é preenchida com elétrons e a banda de condução está vazia, resultando em condutividade zero. Em T > 0, elétrons podem ser termicamente excitados da banda de valência para a banda de condução, resultando em banda de valência parcialmente vazia e banda de condução parcialmente preenchida.

Diagrama de Banda: Semicondutor com dopante doador
Aumenta a condutividade de um semicondutor pela adição de uma pequena quantidade de outro material denominado dopante (ao invés de aquecer-lo) Para o Si que é do grupo IV, adiciona-se um elemento do grupo V para “doar” um elétron e fazer Si tipo -n (temos mais elétron negativos O elétron“Extra” está fracamente ligado, com nível de energia de doador ED justamente abaixo da banda de condução EC. elétrons resultantes na banda de condução, promovem um aumento da condutividade pelo aumento da densidade de portadores livres n. O nível de Fermi EF se desloca para EC devido a que há mais portadores. EC EV EF ED Egap~ 1 eV n-type Si

Porção da tabela periódica – semicondutores
Portion of the periodic table emphasizing the formation of 1:1 AZ solids that are isoelectronic with the Group 14 solids. Complementary pairs are indicated with similar shading: for example Ge, GaAs, ZnSe, and CuBr.

Semicondutor tipo -n

Diagrama de Banda: Semicondutor com dopante aceitador
Para o Si, do grupo IV, adiciona-se um elemento do grupo III para aceitar um elétron e teremos o Si tipo -p (mais buracos positivos). Elétrons “perdidos” são armadilhados num nível de energia aceitador EA justamente acima da banda de valência EV. Os buracos na banda de valência aumentam fortemente a condutividade elétrica. O nível de Fermi EF é deslocado para abaixo na direção de EV devido a que há poucos portadores. EC EF EA EV p-type Si

Porção da tabela periódica – semicon.
Portion of the periodic table emphasizing the formation of 1:1 AZ solids that are isoelectronic with the Group 14 solids. Complementary pairs are indicated with similar shading: for example Ge, GaAs, ZnSe, and CuBr.

Semicondutor tipo -p

Junção pn

Junção pn : Diagrama de Banda
regiões pn se “tocam” & portadores livres se movimentam Em equilíbrio, os níveis de Fermi (ou densidade de portadores de carga) devem se igualar. Devido à difusão, os elétrons se movimentam do lado n para p e os buracos do lado p para n. Zona de Depleção, ela ocorre na junção onde permanecem íons parados. Isto resulta num campo elétrico (103 a 105 V/cm), que se opõe a uma maior difusão. Tipo-n elétrons EC EF EF EV buracos Tipo -p regiões pn em equilíbrio – – EC – – + – + – EF + + – – + + – + – – Junção pn: + + – + + + EV Zona de Depleção

Exemplo de mudança da banda de energia pela composição: AlxGa1-xAs
Introduction (Band Diagram of AlGaAs) The electronic properties of the ternary-compound semiconductor, AlGaAs, depend on the alloy composition. This applet shows a single information in three different ways: In the top diagram, the minimum energies of the conduction band valleys, the Gamma-, L- and X-point valleys, are plotted as a function of the Al composition. The reference energy is the top of the valence band, i.e., E = Ev = 0 eV. The lower-left diagram shows the E-K diagram (Energy - K vector diagram). It shows the three important conduction band valleys (Gamma, L, and X valleys) and the light-hole (lh) and heavy-hole (hh) bands in the K-space (reciprocal space). The lower-right diagram shows the conventional (simplified) energy band diagram of the semiconductor. Mathematical Analysis Minima of Conduction Band Valleys in [eV] at 300K: AlxGa1-xAs [ref:1] Eg(x) = x (0 < x < 0.45) (x-0.45)2 (0.45 < x < 1.0) EL(x) = x EX(x) = x2 E(k) Diagram : Effective Masses for AlxGa1-xAs [ref:1, 2] A) Conduction Band Valleys Eg(k) = h2k2/2mg* where, mg*/m0 = x (for Density of States); x (for Conductivity) kg = 2p/a (0, 0, 0) EL(k) = h2(k-kL)2/2mL* where, mL*/m0 = x (for DOS); x (for Conductivity) kL = 2p/a (1/2, 1/2, 1/2) EX(k) = h2(k-kX)2/2mX* where, mX*/m0 = x (for DOS); x (for Conductivity) kX = 2p/a (0, 0, 1-D) B) Valence Band Valleys Ehh(k) = h2k2/2mhh* where, mhh*/m0 = x Elh(k) = h2k2/2mlh* where, mlh*/m0 = x Eso(k) = h2k2/2mso* - Do where, mso*/m0 = x Do = x The Density of States effective mass for valence band, mvb, is found from mvb = (mlh*3/2 + mhh*3/2)2/3 Eso(k) is the split-off band and does not contribute to the DOS. Applet Tutorial As you mouse-drag the composition, as indicated by the magenta-colored vertical-line within the top diagram, the respective energy positions of the G-, X-, and L-point conduction band valleys change accordingly. The lowest energy of the three conduction band valleys defines the conduction band edge Ec in the energy-band diagram (lower-right). Applet Worksheet (AlGaAs) 1. Determine Eg for the different compositions of the AlGaAs alloy. Indicate if it is a direct band gap or an indirect band gap. Composition Eg Direct or Indirect Al0.1Ga0.9As _____ _____________ Al0.4Ga0.6As _____ _____________ Al0.5Ga0.5As _____ _____________ Al0.9Ga0.1As _____ _____________ 2. What physical significance or consequence does the direct or indirect bandgap have (i.e., in terms of the light emission efficiency) ? Explain ! 3. Would the Light Emitting Diodes and Laser Diodes be made from a direct bandgap materials or from the indrect bandgap materials ? (a) direct bandgap materials (b) indirect bandgap materials 4. Why is the indirect bandgap materials so inefficient compared with the direct gap materials ? Explain ! References 1. S. Adachi, "GaAs, AlAs, and AlGAAs: Material Parameters for Use in research and device Applications," J.App.Phys. 58(3), 1 Aug. 1985, R1. 2. S.M.Sze, PHYSICS OF SEMICONDUCTOR DEVICES, 2nd Ed., John Wiley & Sons, NY 1981 (ISBN ) pp 3. R.G. Hunsperger, INTEGRATED OPTICS: THEORY AND TECHNOLOGY, 3rd Ed., Springer-Verlag, NY 1991 (ISBN )

Fabricação de diodo pn Abordagem a partir do substrato até o produto final mostrando o processo de litografia

Similar a junção PN mas com uma camada intrínseca inserida
Diodo PIN Similar a junção PN mas com uma camada intrínseca inserida

Junção pn : Características I-V
Relação Corrente-Voltagem (I-V) Polarização direta: a corrente aumenta exponencialmente. Polarização Reversa: corrente de fuga pequeno ~Io. Junção pn retificadora somente deixa passar corrente numa direção. Polariz. direta Polarização reversa

Junção pn : Diagrama de Bandas sobre polarização
Polarização Direta: voltagem negativa no lado n promove a difusão de elétrons através do decréscimo do potencial da junção na região de depleção  maior corrente. Polarização Reversa: voltagem positiva no lado n inibe a difusão de elétrons através do incremento do potencial da junção na região de depleção  menor corrente. Polarização Direta Polarização Reversa Equilíbrio tipo -n tipo -p e– Portadores majoritários Portadores minoritários –V p-type n-type +V

Semicondutor: Densidade de Dopante via Efeito Hall
Pq útil? Determina tipo de portador de carga (elétron vs. buraco) e densidade de portadores n para um semicondutor. Como? Semicondutor num campo externo B, corrente através de um eixo, e medida da voltagem de Hall induzida VH ao longo do eixo perpendicular. Derivado da equação de Lorentz FE (qE) = FB (qvB). Densidade de portadores n = _______(corrente I) (campo magnético B)__________ (carga do portador q) (espessura t)(Voltagem Hall VH) buraco elétron carga + carga -

Dispositivos pn : LED e Célula Solar
Diodo emissor de luz = Light-emitting diode (LED) Converte sinal elétrico em luz: entra elétron  sai fóton Fonte de luz com vida longa, baixa potência, desenho compacto. Aplicações: luzes indicadores, mostradores grandes. Célula Solar Converte entrada de luz em sinal elétrico de saida: entra fóton  sai elétron (os elétrons gerados são barridos pelo campo E da junção pn). Fonte de energia renovável. LED Celula Solar

Curva característica de um LED

Diversos LED´s pela composição e cor
aluminium gallium arsenide (AlGaAs) - red and infrared aluminium gallium phosphide (AlGaP) - green aluminium gallium indium phosphide (AlGaInP) - high-brightness orange-red, orange, yellow, and green gallium arsenide phosphide (GaAsP) - red, orange-red, orange, and yellow gallium phosphide (GaP) - red, yellow and green gallium nitride (GaN) - green, pure green (or emerald green), and blue indium gallium nitride (InGaN) - near ultraviolet, bluish-green and blue silicon carbide (SiC) as substrate - blue silicon (Si) as substrate - blue (under development) sapphire (Al2O3) as substrate - blue zinc selenide (ZnSe) - blue diamond (C) - ultraviolet aluminium nitride (AlN), aluminium gallium nitride (AlGaN) - near to far ultraviolet

Formação de cores em LED´s
Azul => In, Ga, N Verde => GaP Vermelho => Ga, P, As Soluções sólidas de GaP1-xAsx, onde x varia de 1 a 0. Para x = 0.6, o LED é vermelho. O LED emite em laranja quando x = 0.35. Para x = 0.15 o LED emite amarelo. Para x = 0 o LED emite verde, i.e. GaP

Dispositivos: LED’s várias cores
Diagrama de cromaticidade CIE 1976 : caracteriza as cores por uma parâmetro de luminância Y e duas coordenadas de cores x e y. A luz branca pode ser criada usando LED’s amarelo e azul. 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 480 470 490 500 510 530 520 nm = verde 540 550 560 570 nm = amarelo 580 590 600 610 640 nm = vermelho violeta Azul-verde WHITE 2000 K 3000 5000 10,000 20,000 Incandescente Luz do dia 460 nm = azul

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 480 470 490 500 510 530 520 nm = verde 540 550 560 570 nm = amarelo 580 590 600 610 640 nm = vermelho violeta Azul-verde WHITE 2000 K 3000 5000 10,000 20,000 Incandescente Luz do dia 460 nm = azul

Color Temperature and Color Rendering Index (CRI)
Color temperature is how cool or warm the light source appears. Incandescent lamps have a warmer appearance than mercury vapor yard lights, for example. CRI is a relative measure of the shift in surface color of an object when lit by a particular lamp, compared with how the object would appear under a reference light source of similar color temperature. Commonly used as references are incandescent lamps (warm light sources) and natural daylight (a cool light source). Incandescent lamps and daylight have a CRI of 100, the highest possible CRI. The higher the CRI of the light source, the "truer" it renders color

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