Introduction to Semiconductor Devices and Circuit ModelReading:Chapter 2 of Howe and SodiniEE40 Summer 2005: Lecture 10 Instructor: Octavian Florescu2Electrical Resistancewhere ρρρρis the resistivityResistanceWtLIVRρ=≡(Units: ΩΩΩΩ)V+_LtWIhomogeneous sample(Units: ΩΩΩΩ-cm)EE40 Summer 2005: Lecture 10 Instructor: Octavian Florescu3What is a Semiconductor?Low resistivity => “conductor”High resistivity => “insulator”Intermediate resistivity => “semiconductor”Generally, the semiconductor material used in integrated-circuit devices is crystallineIn recent years, however, non-crystalline semiconductors have become commercially very importantpolycrystalline amorphous crystallineEE40 Summer 2005: Lecture 10 Instructor: Octavian Florescu4Semiconductor MaterialsElemental:Compound:EE40 Summer 2005: Lecture 10 Instructor: Octavian Florescu5The Silicon Atom14 electrons occupying the 1st 3 energy levels:1s, 2s, 2p orbitals filled by 10 electrons3s, 3p orbitals filled by 4 electronsTo minimize the overall energy, the 3s and 3p orbitals hybridize to form 4 tetrahedral 3sp orbitalsEach has one electron and is capable of forming a bond with a neighboring atomEE40 Summer 2005: Lecture 10 Instructor: Octavian Florescu6“diamond cubic” latticeThe Si CrystalEach Si atom has 4 nearest neighborslattice constant= 5.431ÅEE40 Summer 2005: Lecture 10 Instructor: Octavian Florescu7Compound SemiconductorsGaAs• “zinc blende” structure• III-V compound semiconductors: GaAs, GaP, GaN, etc. important for optoelectronics and high-speed ICsEE40 Summer 2005: Lecture 10 Instructor: Octavian Florescu8Electronic Properties of Si•••• Silicon is a semiconductor material.Pure Si has relatively high resistivity at room temperature.•••• There are 2 types of mobile charge-carriers in Si:Conduction electrons are negatively charged.Holes are positively charged. They are an “absence of electrons”.•••• The concentration of conduction electrons & holesin a semiconductor can be affected in several ways:1.by adding special impurity atoms (dopants)2.by applying an electric field3.by changing the temperature4.by irradiationEE40 Summer 2005: Lecture 10 Instructor: Octavian Florescu9Conduction Electrons and HolesSi Si SiSi Si SiSi Si SiWhen an electron breaks loose and becomes a conduction electron, a hole is also created.2-D representationNote: A hole (along with its associated positive charge) is mobile!EE40 Summer 2005: Lecture 10 Instructor: Octavian Florescu10Definition of Parametersn = number of mobile electrons per cm3p = number of holes per cm3ni= intrinsic carrier concentration (#/cm3)In a pure semiconductor,n = p = niEE40 Summer 2005: Lecture 10 Instructor: Octavian Florescu11GenerationWe have seen that conduction (mobile) electrons and holes can be created in pure (intrinsic) silicon by thermal generation. Thermal generation rate increases exponentially with temperature TAnother type of generation process which can occur is optical generationThe energy absorbed from a photon frees an electron from covalent bondIn Si, the minimum energy required is 1.1eV, which corresponds to ~1 µm wavelength (infrared region). 1 eV = energy gained byan electron falling through 1 V potential = qeV = 1.6 x 10-19C x1 V = 1.6 x 10-19J. Note that conduction electrons and holes are continuously generated, if T > 0EE40 Summer 2005: Lecture 10 Instructor: Octavian Florescu12RecombinationWhen a conduction electron and hole meet, each one is eliminated, a process called “recombination”. The energy lost by the conduction electron (when it “falls”back into the covalent bond) can be released in two ways:1.to the semiconductor lattice (vibrations)“thermal recombination” semiconductor is heated2.to photon emission“optical recombination” light is emittedOptical recombination is negligible in Si. It is significant in compound semiconductor materials, and is the basis for light-emitting diodes and laser diodes.EE40 Summer 2005: Lecture 10 Instructor: Octavian Florescu13ni≅≅≅≅ 1010cm-3at room temperatureconductionPure SiEE40 Summer 2005: Lecture 10 Instructor: Octavian Florescu14Donors: P, As, Sb Acceptors: B, Al, Ga, InDopingBy substituting a Si atom with a special impurity atom (Column Vor Column III element), a conduction electron or hole is created.Dopant concentrations typically range from 1014cm-3to 1020cm-3EE40 Summer 2005: Lecture 10 Instructor: Octavian Florescu15Charge-Carrier ConcentrationsND: ionized donor concentration (cm-3)NA: ionized acceptor concentration (cm-3)Charge neutrality condition: ND+ p = NA+ nAt thermal equilibrium, np = ni2 (“Law of Mass Action”)Note: Carrier concentrations depend on net dopant concentration (ND- NA) !EE40 Summer 2005: Lecture 10 Instructor: Octavian Florescu16If ND>> NA(so that ND– NA>> ni):ADNNn−≅ADiNNnp−≅2andn >> p material is “n-type”If NA>> ND(so that NA– ND>> ni):DANNp−≅DAiNNnn−≅2andp >> n material is “p-type”N-type and P-type MaterialEE40 Summer 2005: Lecture 10 Instructor: Octavian Florescu17intrinsic semiconductor: “undoped” semiconductorelectrical properties are native to the materialextrinsic semiconductor: doped semiconductorelectrical properties are controlled by the added impurity atomsdonor: impurity atom that increases the electron concentrationgroup V elements (P, As)acceptor: impurity atom that increases the hole concentrationgroup III elements (B, In)n-type material: semiconductor containing more electrons than holesp-typematerial: semiconductor containing more holes than electronsmajority carrier: the most abundant carrier in a semiconductor sampleminority carrier: the least abundant carrier in a semiconductor sampleTerminologyEE40 Summer 2005: Lecture 10 Instructor: Octavian Florescu18Carrier ScatteringMobile electrons and atoms in the Si lattice are always in random thermal motion.Average velocity of thermal motion for electrons in Si:~107cm/s @ 300KElectrons make frequent “collisions” with the vibrating atoms“lattice scattering” or “phonon scattering”Other scattering mechanisms:deflection by
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