1Professor N Cheung, U.C. BerkeleyLecture 3EE143 F05Electrical Resistancewhere ρis the electrical resistivityResistanceWtLIVRρ=≡(Unit: ohms)V+_LtWIMaterial with resistivity ρ2Professor N Cheung, U.C. BerkeleyLecture 3EE143 F05Resistivity Range of MaterialsSi with dopantsSiO2, Si3N41 Ω-m = 100 Ω-cmAdding parts/billionto parts/thousandof “dopants” to pure Si can changeresistivity by 8 orders of magnitude !3Professor N Cheung, U.C. BerkeleyLecture 3EE143 F05The Si AtomThe Si CrystalHigh-performance semiconductor devices require defect-free crystals“diamond” structure4Professor N Cheung, U.C. BerkeleyLecture 3EE143 F05-+Top of valence bandBottom of conduction bandelectronholeEnergy gap=1.12 eVCarrier Concentrations of Intrinsic (undoped) Sin (electron conc)= p (hole conc) = ni5Professor N Cheung, U.C. BerkeleyLecture 3EE143 F05Maximum impurity allowed is equivalent to 1 mg of sugar dissolved in an Olympic-size swimming pool.Maximum impurity allowed is equivalent to 1 mg of sugar dissolved in an Olympic-size swimming pool..99.999999999 % (so99.999999999 % (so--called “eleven nines” ) !!called “eleven nines” ) !!Purity of DevicePurity of Device--Grade Grade Si Si waferwafer6Professor N Cheung, U.C. BerkeleyLecture 3EE143 F05Donors: P, As, SbAcceptors: B, Al, Ga, InDopants in SiBy substituting a Si atom with a special impurity atom (Column Vor Column III element), a conduction electron or hole is created.7Professor N Cheung, U.C. BerkeleyLecture 3EE143 F05Energy Band Description of Electrons and Holes Contributed by Donors and AcceptorsEC= bottom of conduction bandEV= top of valence bandED= Donor energy levelEA= Acceptor energy levelAt room temperature, the dopants of interestare essentially fully ionizedDonorsDonorsAcceptorsAcceptors8Professor N Cheung, U.C. BerkeleyLecture 3EE143 F05Semiconductor with both acceptors and donors has 4 kinds of charge carriersIonized DonorIonizedAcceptorImmobile ; they DO NOTcontribute to current flow with electric field is applied. However, they affect the local electric fieldHoleElectronMobile; they contribute to current flow with electric field is applied.9Professor N Cheung, U.C. BerkeleyLecture 3EE143 F05Even NAis not equal to ND,microscopic volume surroundingany position x has zero net chargeSi atomIonized DonorIonizedAcceptorHoleElectronelectron-hole pair due to transition fromvalence band to conduction bandCharge Neutrality ConditionValid for homogeneously doped semiconductor at thermal equilibrium10Professor N Cheung, U.C. BerkeleyLecture 3EE143 F05How to Calculate Electron and Hole Concentrationsfor homogeneous Semiconductorn: electron concentration (cm-3)p : hole concentration (cm-3)ND: donor concentration (cm-3)NA: acceptor concentration (cm-3)1) Charge neutrality condition: ND+ p = NA+ n2) At thermal equilibrium, np = ni2 (“Law of Mass Action”)Note: Carrier concentrations depend on NET dopant concentration (ND- NA) !Assume completely ionized11Professor N Cheung, U.C. BerkeleyLecture 3EE143 F05N-type and P-type MaterialIf 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”12Professor N Cheung, U.C. BerkeleyLecture 3EE143 F05Carrier Drift• When an electric field is applied to a semiconductor, mobile carriers will be accelerated by the electrostatic force. This force superimposes on the random thermal motion of carriers:E.g. Electrons drift in the direction opposite to the E-fieldÆ Current flowsAverage drift velocity = | v | = µECarrier mobility12345electronE12345electronE=013Professor N Cheung, U.C. BerkeleyLecture 3EE143 F05Carrier Mobility• Mobile carriers are always in random thermal motion. If no electric field is applied, the average current in any direction is zero. • Mobility is reduced by– collisions with the vibrating atoms• “phonon scattering”– deflection by ionized impurity atoms-Si-As+-B--14Professor N Cheung, U.C. BerkeleyLecture 3EE143 F05Mobile charge-carrier drift velocity is proportional to applied E-field:µnµpCarrier Mobility µ| v | = µEMobility depends on (ND+ NA) !(Unit: cm2/V•s)15Professor N Cheung, U.C. BerkeleyLecture 3EE143 F05Electrical Conductivity σWhen an electric field is applied, current flows due to drift of mobile electrons and holes:EqnnvqJnnnµ=−=)(electron current density:hole current density:EqppvqJpppµ=+=)(total current density:pnpnpnqpqnEJEqpqnJJJµµσσµµ+≡=+=+=)(conductivity16Professor N Cheung, U.C. BerkeleyLecture 3EE143 F05(Unit: ohm-cm)Electrical Resistivityρpnqpqnµµσρ+=≡11for n-typenqnµρ1≅for p-typepqpµρ1≅Note: This plot does not apply for compensated material!17Professor N Cheung, U.C. BerkeleyLecture 3EE143 F05Consider a Si sample doped with 1016/cm3Boron.What is its electrical resistivity?Answer:NA= 1016/cm3, ND= 0 (NA>> NDÆ p-type)Æ p ≈ 1016/cm3and n ≈ 104/cm3Example Calculation []cm 4.1)450)(10)(106.1(1111619−Ω=×=≅+=−−ppnqpqpqnµµµρFrom µvs. ( NA+ ND) plot18Professor N Cheung, U.C. BerkeleyLecture 3EE143 F05* The sample is converted to n-type material by adding more donors than acceptors, and is said to be “compensated”.Example: Dopant CompensationConsider the same Si sample (with 1016/cm3Boron), doped additionally with 1017/cm3Arsenic. What is the new resistivity?Answer:NA= 1016/cm3, ND= 1017/cm3 (ND>>NAÆ n-type)Æ n ≈ 9x1016/cm3and p ≈ 1.1x103/cm3[]cm 12.0)600)(109)(106.1(1111619−Ω=××=≅+=−−npnqnqpqnµµµρ19Professor N Cheung, U.C. BerkeleyLecture 3EE143 F05Summary of Doping Terminologyintrinsic semiconductor: undoped semiconductorextrinsicsemiconductor: doped semiconductordonor: impurity atom that increases the electron concentrationgroup V elements (P, As)in Siacceptor: impurity atom that increases the hole concentrationgroup III elements (B, In) in Sin-type material: semiconductor containing more electrons than holesp-typematerial: semiconductor containing more holes than electronsmajority carrier: the most abundant mobile carrier in a semiconductor minority carrier: the least abundant mobile carrier in a semiconductormobile carriers: Charge carriers that contribute to current flow when electric field is applied.20Professor N Cheung, U.C. BerkeleyLecture 3EE143 F05Sheet Resistance RS• The Rsvalue for a given layer (e.g. doped Si, metals) in an IC or MEMS technology is used– for
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