berkley_半导体工艺讲义_03--硅器件物理

1Professor N Cheung, U.C. Berkeley Lecture 3EE143 F05 Electrical Resistance where ρ is the electrical resistivity Resistance Wt L I VR ρ=≡ (Unit: ohms) V + _ L t W I Material with resistivity ρ 2Professor N Cheung, U.C. Berkeley Lecture 3EE143 F05 Resistivity Range of Materials Si with dopants SiO2, Si3N4 1 Ω-m = 100 Ω-cm Adding parts/billion to parts/thousand of “dopants” to pure Si can change resistivity by 8 orders of magnitude ! 3Professor N Cheung, U.C. Berkeley Lecture 3EE143 F05 The Si Atom The Si Crystal High-performance semiconductor devices require defect-free crystals “diamond” structure 4Professor N Cheung, U.C. Berkeley Lecture 3EE143 F05 - + Top of valence band Bottom of conduction bandelectron hole Energy gap =1.12 eV Carrier Concentrations of Intrinsic (undoped) Si n (electron conc) = p (hole conc) = ni 5Professor N Cheung, U.C. Berkeley Lecture 3EE143 F05 Maximum 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 waferwafer 6Professor N Cheung, U.C. Berkeley Lecture 3EE143 F05 Donors: P, As, Sb Acceptors: B, Al, Ga, In 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. 7Professor N Cheung, U.C. Berkeley Lecture 3EE143 F05 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 DonorsDonors AcceptorsAcceptors 8Professor N Cheung, U.C. Berkeley Lecture 3EE143 F05 Semiconductor with both acceptors and donors has 4 kinds of charge carriers Ionized Donor Ionized Acceptor Immobile ; they DO NOT contribute to current flow with electric field is applied. However, they affect the local electric field Hole Electron Mobile; they contribute to current flow with electric field is applied. 9Professor N Cheung, U.C. Berkeley Lecture 3EE143 F05 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 Charge Neutrality Condition Valid for homogeneously doped semiconductor at thermal equilibrium 10Professor N Cheung, U.C. Berkeley Lecture 3EE143 F05 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: ND + p = NA + n 2) At thermal equilibrium, np = ni2 (“Law of Mass Action”) Note: Carrier concentrations depend on NET dopant concentration (ND - NA) ! Assume completely ionized 11Professor N Cheung, U.C. Berkeley Lecture 3EE143 F05 N-type and P-type Material If ND >> NA (so that ND – NA >> ni): AD NNn −≅ AD i NN np −≅ 2 and n >> p Æ material is “n-type” If NA >> ND (so that NA – ND >> ni): DA NNp −≅ DA i NN nn −≅ 2 and p >> n Æ material is “p-type” 12Professor N Cheung, U.C. Berkeley Lecture 3EE143 F05 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: E.g. Electrons drift in the direction opposite to the E-field Æ Current flows Average drift velocity = | v | = µ E Carrier mobility 1 2 3 4 5 electron E 1 23 4 5 electron E =0 13Professor N Cheung, U.C. Berkeley Lecture 3EE143 F05 Carrier 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. Berkeley Lecture 3EE143 F05 Mobile charge-carrier drift velocity is proportional to applied E-field: µn µp Carrier Mobility µ | v | = µ E Mobility depends on (ND + NA) ! (Unit: cm2/V•s) 15Professor N Cheung, U.C. Berkeley Lecture 3EE143 F05 Electrical Conductivity σ When an electric field is applied, current flows due to drift of mobile electrons and holes: EqnnvqJ nnn µ=−= )(electron current density: hole current density: EqppvqJ ppp µ=+= )( total current density: pn pnpn qpqn EJ EqpqnJJJ µµσ σ µµ +≡ = +=+= )( conductivity 16Professor N Cheung, U.C. Berkeley Lecture 3EE143 F05 (Unit: ohm-cm) Electrical Resistivity ρ pn qpqn µµσρ +=≡ 11 for n-type nqnµρ 1≅ for p-type pqpµρ 1≅ Note: This plot does not apply for compensated material! 17Professor N Cheung, U.C. Berkeley Lecture 3EE143 F05 Consider a Si sample doped with 1016/cm3 Boron. What is its electrical resistivity? Answer: NA = 1016/cm3 , ND = 0 (NA >> NDÆ p-type) Æ p ≈ 1016/cm3 and n ≈ 104/cm3 Example Calculation [ ] cm 4.1)450)(10)(106.1( 11 11619 −Ω=×= ≅+= −− ppn qpqpqn µµµρ From µ vs. ( NA + ND ) plot 18Professor N Cheung, U.C. Berkeley Lecture 3EE143 F05 * The sample is converted to n-type material by adding more donors than acceptors, and is said to be “compensated”. 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>>NAÆ n-type) Æ n ≈ 9x1016/cm3 and p ≈ 1.1x103/cm3 [ ] cm 12.0)600)(109)(106.1( 11 11619 −Ω=××= ≅+= −− npn qnqpqn µµµρ 19Professor N Cheung, U.C. Berkeley Lecture 3EE143 F05 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. 20Professor N Cheung, U.C. Berkeley Lecture 3EE143 F05 Sheet Resistance RS • 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 W LR Wt LR s== ρ t Rs ρ≡ Rs is the resistance when W = L (unit in ohms/square) if ρ is independent of depth x 21Professor N Cheung, U.C. Berkeley Lecture 3EE143 F05 RS when ρ(x) is function of depth x V + _ L t W I ρ1, dxρ2, dxρ3, dx …. ρn, dx dx)..(dx....dxdxdx R 1 n21 n321S σ+σ+σ=ρ++ρ+ρ+ρ= [ ]∫ ∫ + = = t pn tS dxxpxqxnxq dxx R 0 0 )()()()( 1 )( 1 µµ σ For a continuous σ(x) function: depth x 22Professor N Cheung, U.C. Berkeley Lecture 3EE143 F05 R ≅ 2.6Rs Electrical Resistance of Layout Patterns (Unit of RS: ohms/square) L=1µm W = 1µm R = Rs R = Rs/2 R = 2Rs R = 3Rs 1m 1mR = Rs Metal contact Top View 23Professor N Cheung, U.C. Berkeley Lecture 3EE143 F05 • The Four-Point Probe is used to measure Rs – 4 probes are arranged in-line with equal spacing s – 2 outer probes used to flow current I through the sample – 2 inner probes are used to sense the resultant voltage drop V with a voltmeter For a thin layer (t ≤ s/2), I VRs 532.4= (Typically, s ≈ 1 mm >>t) For derivation, see EE143 Lab Manual http://www-inst.eecs.berkeley.edu/~ee143/fa05/lab/four_point_probe.pdf If ρ is known, then Rs measurement can be used to determine t How to measure RS ? 24Professor N Cheung, U.C. Berkeley Lecture 3EE143 F05 Electron mobility vs. T Hole mobility vs. T For reference only