EE143 F05 Lecture 3 Electrical Resistance V I W t Material with resistivity L Resistance V L R I Wt Unit ohms where is the electrical resistivity Professor N Cheung U C Berkeley 1 EE143 F05 Adding parts billion to parts thousand of dopants to pure Si can change resistivity by 8 orders of magnitude Professor N Cheung U C Berkeley Resistivity Range of Materials Lecture 3 Si with dopants SiO2 Si3N4 1 m 100 cm 2 EE143 F05 Lecture 3 The Si Atom The Si Crystal diamond structure High performance semiconductor devices require defect free crystals Professor N Cheung U C Berkeley 3 EE143 F05 Lecture 3 Carrier Concentrations of Intrinsic undoped Si electron Bottom of conduction band Energy gap 1 12 eV hole Top of valence band n electron conc p hole conc ni Professor N Cheung U C Berkeley 4 EE143 F05 Lecture 3 Purity of Device Grade Si wafer 99 999999999 so called eleven nines Maximum impurity allowed is equivalent to 1 mg of sugar dissolved in an Olympic size swimming pool pool Professor N Cheung U C Berkeley 5 EE143 F05 Lecture 3 Dopants in Si By substituting a Si atom with a special impurity atom Column V or Column III element a conduction electron or hole is created Donors P As Sb Professor N Cheung U C Berkeley Acceptors B Al Ga In 6 EE143 F05 Lecture 3 Energy Band Description of Electrons and Holes Contributed by Donors and Acceptors EC bottom of conduction band EV top of valence band ED Donor energy level EA Acceptor energy level At room temperature the dopants of interest are essentially fully ionized Donors Acceptors Professor N Cheung U C Berkeley 7 EE143 F05 Lecture 3 Semiconductor with both acceptors and donors has 4 kinds of charge carriers Hole Electron Ionized Donor Ionized Acceptor Professor N Cheung U C Berkeley Mobile they contribute to current flow with electric field is applied Immobile they DO NOT contribute to current flow with electric field is applied However they affect the local electric field 8 EE143 F05 Charge Neutrality Condition Lecture 3 Valid for homogeneously doped semiconductor at thermal equilibrium Even NA is not equal to ND microscopic volume surrounding any position x has zero net charge Si atom Ionized Donor Ionized Acceptor Hole Electron electron hole pair due to transition from valence band to conduction band Professor N Cheung U C Berkeley 9 EE143 F05 Lecture 3 How to Calculate Electron and Hole Concentrations for homogeneous Semiconductor n electron concentration cm 3 p hole concentration cm 3 ND donor concentration cm 3 NA acceptor concentration cm 3 1 Charge neutrality condition Assume completely ionized ND p NA n 2 At thermal equilibrium np ni2 Law of Mass Action Note Carrier concentrations depend on NET dopant concentration ND NA Professor N Cheung U C Berkeley 10 EE143 F05 Lecture 3 N type and P type Material If ND NA so that ND NA ni n ND N A and 2 ni p ND N A n p material is n type If NA ND so that NA ND ni p N A ND and 2 ni n N A ND p n material is p type Professor N Cheung U C Berkeley 11 EE143 F05 Lecture 3 Carrier 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 2 3 1 electron 4 5 3 2 1 electron 4 5 E 0 E E g Electrons drift in the direction opposite to the E field Current flows Average drift velocity v E Carrier mobility Professor N Cheung U C Berkeley 12 EE143 F05 Lecture 3 Carrier Mobility Mobile carriers are always in random thermal motion If no electric field is applied the average current in any direction is zero Si Mobility is reduced by collisions with the vibrating atoms phonon scattering deflection by ionized impurity atoms Professor N Cheung U C Berkeley B As 13 EE143 F05 Carrier Mobility Lecture 3 Mobile charge carrier drift velocity is proportional to applied E field v E n Mobility depends on ND NA Unit cm2 V s p Professor N Cheung U C Berkeley 14 EE143 F05 Lecture 3 Electrical Conductivity When an electric field is applied current flows due to drift of mobile electrons and holes electron current J q nv qn E n n n density hole current density total current density conductivity Professor N Cheung U C Berkeley J p q pv p qp p E J J n J p qn n qp p E J E qn n qp p 15 EE143 F05 Electrical Resistivity Lecture 3 1 1 qn n qp p 1 qn n for n type 1 qp p for p type Unit ohm cm Professor N Cheung U C Berkeley Note This plot does not apply for compensated material 16 EE143 F05 Lecture 3 Example Calculation Consider a Si sample doped with 1016 cm3 Boron What is its electrical resistivity Answer NA ND p type NA 1016 cm3 ND 0 p 1016 cm3 and n 104 cm3 1 1 qn n qp p qp p 1 6 10 19 16 10 450 1 1 4 cm From vs NA ND plot Professor N Cheung U C Berkeley 17 EE143 F05 Lecture 3 Example Dopant Compensation Consider the same Si sample with 1016 cm3 Boron doped additionally with 1017 cm3 Arsenic What is the new resistivity Answer NA 1016 cm3 ND 1017 cm3 ND NA n type n 9x1016 cm3 and p 1 1x103 cm3 1 1 qn n qp p qn n 1 6 10 19 9 10 600 16 1 0 12 cm The sample is converted to n type material by adding more donors than acceptors and is said to be compensated Professor N Cheung U C Berkeley 18 EE143 F05 Lecture 3 Summary of Doping Terminology intrinsic semiconductor undoped semiconductor extrinsic semiconductor doped semiconductor donor impurity atom that increases the electron concentration group V elements P As in Si acceptor impurity atom that increases the hole concentration group III elements B In in Si n type material semiconductor containing more electrons than holes p type material semiconductor containing more holes than electrons majority carrier the most abundant mobile carrier in a semiconductor minority carrier the least abundant mobile carrier in a semiconductor mobile carriers Charge carriers that contribute to current flow when electric field is applied Professor N Cheung U C Berkeley 19 EE143 F05 Lecture 3 Sheet Resistance RS L L Rs R W Wt Rs is the resistance when W L Rs t unit in ohms square if is independent of depth x The Rs value for a given layer e g doped Si metals in an IC or MEMS technology is used for design and layout of resistors for estimating values of parasitic resistance in a device or circuit Professor N Cheung U C Berkeley 20 EE143 F05 1 dx 2 dx 3 dx n dx Lecture 3 RS when x is function of depth x V I W t depth x L 1 dx dx dx dx 1 2 …
View Full Document
Unlocking...