Slide 1Review the FollowingFirst AssignmentSecond AssignmentSchedule Changes Due to University Weather ClosingsDrift CurrentDrift current resistanceDrift current resistance (cont.)Drift current resistance (cont.)Net intrinsic mobilityLattice mobilityNet extrinsic mobilityNet silicon extr resistivity (cont.)Ionized impurity mobility functionSlide 15Exp. m(T=300K) model for P, As and B in Si1Exp. mobility model function for Si1Carrier mobility functions (cont.)Carrier mobility functions (ex.)Net silicon (ex- trinsic) resistivitySlide 21Net silicon extr resistivity (cont.)Net silicon (com- pensated) res.Slide 24SummaryEquipartition theoremCarrier velocity saturation1Carrier velocity2Carrier velocity saturation (cont.)ReferencesReferencesEE 5340Semiconductor Device TheoryLecture 06 – Spring 2011Professor Ronald L. [email protected]://www.uta.edu/ronc©rlc L06-10Feb20112Review the Following•R. L. Carter’s web page:–www.uta.edu/ronc/•EE 5340 web page and syllabus. (Refresh all EE 5340 pages when downloading to assure the latest version.) All links at:–www.uta.edu/ronc/5340/syllabus.htm•University and College Ethics Policies–www.uta.edu/studentaffairs/conduct/•Makeup lecture at noon Friday (1/28) in 108 Nedderman Hall. This will be available on the web.©rlc L06-10Feb20113First Assignment•Send e-mail to [email protected]–On the subject line, put “5340 e-mail”–In the body of message include•email address: ______________________•Your Name*: _______________________•Last four digits of your Student ID: _____* Your name as it appears in the UTA Record - no more, no less©rlc L06-10Feb20114Second Assignment•Submit a signed copy of the document posted at www.uta.edu/ee/COE%20Ethics%20Statement%20Fall%2007.pdf©rlc L06-10Feb20115Schedule Changes Due to University Weather Closings•Make-up class will be held Friday, February 11 at 12 noon in 108 Nedderman Hall.•Additional changes will be announced as necessary.•Syllabus and lecture dates postings have been updated.•Project Assignment has been posted in the initial version.©rlc L06-10Feb20116Drift Current•The drift current density (amp/cm2) is given by the point form of Ohm LawJ = (nqmn+pqmp)(Exi+ Eyj+ Ezk), soJ = (sn + sp)E = sE, wheres = nqmn+pqmp defines the conductivity•The net current is- SdJI©rlc L06-10Feb20117Drift currentresistance•Given: a semiconductor resistor with length, l, and cross-section, A. What is the resistance?•As stated previously, the conductivity, s = nqmn + pqmp•So the resistivity, r = 1/s = 1/(nqmn + pqmp)©rlc L06-10Feb20118Drift currentresistance (cont.)•Consequently, sinceR = rl/AR = (nqmn + pqmp)-1(l/A)•For n >> p, (an n-type extrinsic s/c)R = l/(nqmnA)•For p >> n, (a p-type extrinsic s/c) R = l/(pqmpA)©rlc L06-10Feb20119Drift currentresistance (cont.)•Note: for an extrinsic semiconductor and multiple scattering mechanisms, sinceR = l/(nqmnA) or l/(pqmpA), and(mn or p total)-1 = S mi-1, thenRtotal = S Ri (series Rs)•The individual scattering mechanisms are: Lattice, ionized impurity, etc.©rlc L06-10Feb201110Net intrinsicmobility•Considering only lattice scatteringonly, , 11is mobility total thelatticetotal©rlc L06-10Feb201111Lattice mobility•The mlattice is the lattice scattering mobility due to thermal vibrations•Simple theory gives mlattice ~ T-3/2•Experimentally mn,lattice ~ T-n where n = 2.42 for electrons and 2.2 for holes•Consequently, the model equation is mlattice(T) = mlattice(300)(T/300)-n©rlc L06-10Feb201112Net extrinsicmobility•Considering only lattice and impurity scatteringimpuritylatticetotal111is mobility total the©rlc L06-10Feb201113Net silicon extrresistivity (cont.)•Since r = (nqmn + pqmp)-1, and mn > mp, (m = qt/m*) we have rp > rn•Note that since1.6(high conc.) < rp/rn < 3(low conc.), so1.6(high conc.) < mn/mp < 3(low conc.)©rlc L06-10Feb201114Ionized impuritymobility function•The mimpur is the scattering mobility due to ionized impurities•Simple theory gives mimpur ~ T3/2/Nimpur•Consequently, the model equation is mimpur(T) = mimpur(300)(T/300)3/2©rlc L06-10Feb201115Figure 1.17 (p. 32 in M&K1) Low-field mobility in silicon as a function of temperature for electrons (a), and for holes (b). The solid lines represent the theoretical predictions for pure lattice scattering [5].©rlc L06-10Feb201116Exp. m(T=300K) modelfor P, As and B in Si10500100015001.E+13 1.E+15 1.E+17 1.E+19Doping Concentration (cm^-3)M obilit y (cm^2/ V- sec)PAsB©rlc L06-10Feb201117Exp. mobility modelfunction for Si1Parameter As P Bmmin52.2 68.5 44.9mmax1417 1414 470.5Nref9.68e16 9.20e16 2.23e17a 0.680 0.711 0.719refa,dminpn,maxpn,minpn,pn,NN1©rlc L06-10Feb201118Carrier mobilityfunctions (cont.)•The parameter mmax models 1/tlattice the thermal collision rate•The parameters mmin, Nref and a model 1/timpur the impurity collision rate•The function is approximately of the ideal theoretical form: 1/mtotal = 1/mthermal + 1/mimpurity©rlc L06-10Feb201119Carrier mobilityfunctions (ex.)•Let Nd = 1.78E17/cm3 of phosphorous, so mmin = 68.5, mmax = 1414, Nref = 9.20e16 and a = 0.711. –Thus mn = 586 cm2/V-s•Let Na = 5.62E17/cm3 of boron, so mmin = 44.9, mmax = 470.5, Nref = 9.68e16 and a = 0.680. –Thus mp = 189 cm2/V-s©rlc L06-10Feb201120Net silicon (ex-trinsic) resistivity•Since r = s-1 = (nqmn + pqmp)-1•The net conductivity can be obtained by using the model equation for the mobilities as functions of doping concentrations.•The model function gives agreement with the measured s(Nimpur)Figure 1.15 (p. 29) M&K Dopant density versus resistivity at 23°C (296 K) for silicon doped with phosphorus and with boron. The curves can be used with little error to represent conditions at 300 K. [W. R. Thurber, R. L. Mattis, and Y. M. Liu, National Bureau of Standards Special Publication 400–64, 42 (May 1981).]©rlc L06-10Feb201121©rlc L06-10Feb201122Net silicon extrresistivity (cont.)•Since r = (nqmn + pqmp)-1, and mn > mp, (m = qt/m*) we have rp > rn, for the same NI•Note that since1.6(high conc.) < rp/rn < 3(low conc.), so1.6(high conc.) < mn/mp < 3(low conc.)©rlc L06-10Feb201123Net silicon (com-pensated) res.•For an n-type (n >> p) compensated semiconductor, r = (nqmn)-1•But now n = N  Nd - Na, and the mobility must be considered to be determined by the total ionized impurity scattering Nd + Na  NI•Consequently, a