Week 7bElectrical ResistanceWhat is a Semiconductor?Semiconductor MaterialsThe Silicon AtomThe Si CrystalCompound SemiconductorsElectronic Properties of SiConduction Electrons and HolesDefinition of ParametersGenerationRecombinationGeneration and Recombination RatesPure SiDopingCharge-Carrier ConcentrationsN-type and P-type MaterialTerminologyCarrier ScatteringCarrier DriftDrift Velocity and Carrier MobilityCurrent DensityElectrical Conductivity sElectrical Resistivity rExampleExample (cont’d)Sheet Resistance RsIntegrated-Circuit ResistorsSummaryWeek 7b, Slide 1EECS42, Spring 2005 Prof. WhiteWeek 7bANNOUNCEMENTS• Reader with reference material from Howe & Sodini and from Rabaey et al available at Copy Central on Hearst Ave. near EuclidOUTLINE• Semiconductor materials• Properties of silicon•DopingReadingHowe & Sodini: Ch. 2.1-2.4.1Week 7b, Slide 2EECS42, Spring 2005 Prof. WhiteElectrical Resistancewhere ρis the resistivityResistanceWtLIVRρ=≡(Units: Ω)V+_LtWIhomogeneous sample(Units: Ω-cm)Week 7b, Slide 3EECS42, Spring 2005 Prof. WhiteWhat 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 crystallineWeek 7b, Slide 4EECS42, Spring 2005 Prof. WhiteWeek 7b, Slide 5EECS42, Spring 2005 Prof. WhiteSemiconductor MaterialsElemental:Compound:Week 7b, Slide 6EECS42, Spring 2005 Prof. WhiteThe 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 atomWeek 7b, Slide 7EECS42, Spring 2005 Prof. WhiteWeek 7b, Slide 8EECS42, Spring 2005 Prof. White“diamond cubic” latticeThe Si Crystal• Each Si atom has 4 nearest neighbors• lattice constant= 5.431ÅWeek 7b, Slide 9EECS42, Spring 2005 Prof. WhiteCompound Semiconductors• “zinc blende” structure• III-V compound semiconductors: GaAs, GaP, GaN, etc.9important for optoelectronics and high-speed ICsGaAsWeek 7b, Slide 10EECS42, Spring 2005 Prof. WhiteElectronic 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 irradiationWeek 7b, Slide 11EECS42, Spring 2005 Prof. WhiteConduction 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!Week 7b, Slide 12EECS42, Spring 2005 Prof. WhiteDefinition of Parametersn = number of mobile electrons per cm3p = number of holes per cm3ni= intrinsic carrier concentration (#/cm3)In a pure semiconductor,n = p = niWeek 7b, Slide 13EECS42, Spring 2005 Prof. WhiteGeneration• 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 > 0Week 7b, Slide 14EECS42, Spring 2005 Prof. WhiteWeek 7b, Slide 15EECS42, Spring 2005 Prof. WhiteRecombination• 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.Week 7b, Slide 16EECS42, Spring 2005 Prof. WhiteLate News – Silicon LaserIn October 2004 UCLA researchers reported makinga (Raman*) laser in a silicon waveguide, and in February2005 reported being able to modulate the optical outputby simply using a silicon pn-junction diode to injectloss-producing electrons into the laser cavity.Expectation: use of optical radiation to output informationfrom silicon chips (someday)•See photonics.com/dictionary web site for Raman effectdescriptionWeek 7b, Slide 17EECS42, Spring 2005 Prof. WhiteGeneration and Recombination Rates• The generation rate is dependent on temperature T, but it is independent of n and p :• The recombination rate is proportional to both n and p:• In steady state, a balance exists between the generation and recombination rates.• A special case of the steady-state condition is thermal equilibrium: no optical or electrical sourcesopticalthermalGTGG+=)()(2Tnnpi=)( TfnpRG=⇒=npR∝Week 7b, Slide 18EECS42, Spring 2005 Prof. Whiteni≅ 1010cm-3at room temperatureconductionPure SiWeek 7b, Slide 19EECS42, Spring 2005 Prof. WhiteDonors: 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-3Week 7b, Slide 20EECS42, Spring 2005 Prof. WhiteCharge-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) !Week 7b,
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