1Introduction to Semiconductor Devices and Circuit ModelReading:Chapter 2 of Howe and SodiniEE40 Summer 2005: Lecture 10 Instructor: Octavian Florescu2Electrical Resistancewhere ρis the resistivityResistanceWtLIVRρ=≡(Units: Ω)V+_LtWIhomogeneous sample(Units: Ω-cm)2EE40 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 crystalline In recent years, however, non-crystalline semiconductors have become commercially very importantpolycrystalline amorphous crystallineEE40 Summer 2005: Lecture 10 Instructor: Octavian Florescu4Semiconductor MaterialsElemental:Compound:3EE40 Summer 2005: Lecture 10 Instructor: Octavian Florescu5The Silicon Atom 14 electrons occupying the 1st 3 energy levels: 1s, 2s, 2p orbitals filled by 10 electrons 3s, 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 Crystal Each Si atom has 4 nearest neighbors lattice constant= 5.431Å4EE40 Summer 2005: Lecture 10 Instructor: Octavian Florescu7Compound SemiconductorsGaAs• “zinc blende” structure• III-V compound semiconductors: GaAs, GaP, GaN, etc.9 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 irradiation5EE40 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 = ni6EE40 Summer 2005: Lecture 10 Instructor: Octavian Florescu11Generation We 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 T Another type of generation process which can occur is optical generation The energy absorbed from a photon frees an electron from covalent bond In 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 Florescu12Recombination When 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” Æ semiconductor is heated2. to photon emission“optical recombination” Æ light is emitted Optical recombination is negligible in Si. It is significant in compound semiconductor materials, and is the basis for light-emitting diodes and laser diodes.7EE40 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-38EE40 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 Æ material is “n-type”If NA>> ND(so that NA– ND>> ni):DANNp −≅DAiNNnn−≅2andp >> n Æ material is “p-type”N-type and P-type Material9EE40 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 Scattering Mobile electrons and atoms in the Si lattice are always in random thermal motion. Average velocity of thermal motion for electrons in Si:~107cm/s @ 300K Electrons make frequent “collisions” with the vibrating atoms “lattice scattering” or “phonon scattering” Other scattering mechanisms: deflection by ionized impurity atoms deflection due to Coulombic force between carriers The average current in any
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