Optoelectronics I Lecture : Background dconcepts M. Soroosh Assistant Professor of Electronics Shahid Chamran University 1
Face Centered Crystal (FCC) Body Centered Crystal (BCC) Bragg s Law William Lawrence Bragg interpreted the x-ray scattering as the reflection of the incident x-ray beam from a unique set of planes of atoms within the crystal. There are two conditions for constructive interference of the scattered x-rays: 1) The angle of incidence must equal the angle of reflection of the outgoing wave. ) The difference in path lengths must be an integral number of wavelengths. Bragg s Law: nλ =d sinθ (n = integer) Zinc Blend (ZB) Each atom has four covalent bonds, but bonds with atoms of other type. Zinc Blend lattice cell: GaAs, InP, AlAs, GaP, ZnS, Ga As
Energy Levels In solid state physics, aband gap, also called an energy gap or bandgap, isanenergyrangeinasolid where no electron states can exist. In graphs of the electronic band structure of solids, the band gap generally refers to the energy difference (in electron volts) between the top of the valence band and the bottom of the conduction band in insulators and semiconductors. This is equivalent to the energy required to free an outer shell electron from its orbit about the nucleus to become a mobile charge carrier, able to move freely within the solid material, so the band gap is a major factor determining the electrical conductivity of a solid. Substances with large band gaps are generally insulators, those with smaller band gaps are semiconductors, while conductors either have very small band gaps or none, because the valence and conduction bands overlap. TO AN ARRAY OF ATOMS Electrons in a periodic array merge into regions where energy value is allowed in Schrödinger s Eq., or not: those permitted by Schrödinger s Eq. called bands - bands can overlap those not permitted are called forbidden regions or Band Gaps A filled band does not allow current flow: in an insulator, lower band filled, upper is not. In a metal, bands overlap and partially filled. Semiconductors are insulators at 0 K Electrons inconduction band act free (i.e., no potential) ti E v E c E v Metal Insulator E c Band Gap Conduction Band Valence Band E c E v E c E v Semicon. Band-Gap Shrinkage 3
Compound Semiconductors Immiscible Region 4
Wavelength Range for Epitaxy Materials 400 650 780 807 980 1310 1550 InP GaInAs/InP AlInGaAs/InP GaAsSb/GaAs InGaNAs/GaAs GaAs InGaAs/GaAs AlGaAs/GaAs AlGaInP/GaAs GaInN/GaN QDs 00 400 600 800 1000 100 1400 1600 Wavelength, nm Quantum dots Electron levels Hole levels hυ 5
Debye Length Debye sphere is a volume whose radius is the Debye length, in which there is a sphere of influence, and outside of which charges are screened. Reciprocal Lattice The reciprocal lattices is the collection of points that represent allowed values of wave vectors for Fourier series and Fourier transforms with the periodicity of the lattice. The value of k allowed for any vector is given by Brillouine Zone Valley Band Structure 6
Direct and Indirect Bandgap Effective Mass The effective mass has nothing to do with a real mass; itisamathematical contraption. However, if we know the dispersion curves (either from involved calculations or from measurements), we can put a number to the effective masses and find that they are not too different from the real masses. Ifweusetheeffectivemassm * of electrons and holes instead of their real mass m, we may consider their behavior to be identical to that of electrons (or holes) in the free electron gas model. 7
Charge carriers in semiconductors Effective mass E k p = mv = hk 1 h E = mv = k m d E h = dk m h m* = d E dk Phonon In physics, aphonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, suchassolids and some liquids. Often referred to as a quasiparticle, [1] it represents an excited state in the quantum mechanical quantization of the modes of vibrations of elastic structures of interacting particles. Phonons play a major role in many of the physical properties of condensed matter, such as thermal conductivity and electrical conductivity. The study of phonons is an important part of condensed matter physics. 8
Scattering Velocity Saturation Inter-valley scattering Mobility ln(μ) μ I μ L ln( T ) This equation is called as Mattheisen s rule. 1 1 1 = + μt μl μi 9
Mobility variation with temperature μ μ T T High temperature Low temperaturet 1 1 1 = + μt μl μi ln(μ) μ I μ L Peak depends on the density of impurities This equation is called as Mattheisen s rule. ln( T ) Homojunction/Heterojunction Quantum/Newtonian Physics Classic Large Scale, Length>100nm Continues Energies for particle Having a macroscopic View Quantum Atomic Scale, Length<100nm Discrete Energies for particles Having a microscopic view 10