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Semiconductor Device Modeling and Characterization – EE5342 Lecture 7 – Spring 2011

Semiconductor Device Modeling and Characterization – EE5342 Lecture 7 – Spring 2011. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/. First Assignment. e-mail to listserv@listserv.uta.edu In the body of the message include subscribe EE5342

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Semiconductor Device Modeling and Characterization – EE5342 Lecture 7 – Spring 2011

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  1. Semiconductor Device Modeling and Characterization – EE5342 Lecture 7 – Spring 2011 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

  2. First Assignment • e-mail to listserv@listserv.uta.edu • In the body of the message include subscribe EE5342 • This will subscribe you to the EE5342 list. Will receive all EE5342 messages • If you have any questions, send to ronc@uta.edu, with EE5342 in subject line.

  3. Second Assignment • Submit a signed copy of the document that is posted at www.uta.edu/ee/COE%20Ethics%20Statement%20Fall%2007.pdf

  4. Schedule Changes Due to the University Closures last week • Plan to meet until noon some days in the next few weeks. This way we will make up the lost time. The first extended class will be Wednesday, February 9. • The MT will be postponed until Wednesday, February 16. All other due dates and tests will remain the same.

  5. Equipartitiontheorem • The thermodynamic energy per degree of freedom is kT/2 Consequently,

  6. Carrier velocitysaturation1 • The mobility relationship v = mE is limited to “low” fields • v < vth = (3kT/m*)1/2 defines “low” • v = moE[1+(E/Ec)b]-1/b, mo = v1/Ec for Si parameter electrons holes v1 (cm/s) 1.53E9 T-0.87 1.62E8 T-0.52 Ec (V/cm) 1.01 T1.55 1.24 T1.68 b 2.57E-2 T0.66 0.46 T0.17

  7. vdrift[cm/s]vs. E [V/cm](Sze2, fig. 29a)

  8. Carrier velocitysaturation (cont.) • At 300K, for electrons, mo = v1/Ec = 1.53E9(300)-0.87/1.01(300)1.55 = 1504 cm2/V-s, the low-field mobility • The maximum velocity (300K) is vsat = moEc = v1 =1.53E9 (300)-0.87 = 1.07E7 cm/s

  9. Diffusion ofcarriers • In a gradient of electrons or holes, p and n are not zero • Diffusion current,`J =`Jp +`Jn (note Dp and Dn are diffusion coefficients)

  10. Diffusion ofcarriers (cont.) • Note (p)x has the magnitude of dp/dx and points in the direction of increasing p (uphill) • The diffusion current points in the direction of decreasing p or n (downhill) and hence the - sign in the definition of`Jp and the + sign in the definition of`Jn

  11. Diffusion ofCarriers (cont.)

  12. Current densitycomponents

  13. Total currentdensity

  14. Doping gradient induced E-field • If N = Nd-Na = N(x), then so is Ef-Efi • Define f = (Ef-Efi)/q = (kT/q)ln(no/ni) • For equilibrium, Efi = constant, but • for dN/dx not equal to zero, • Ex = -df/dx =- [d(Ef-Efi)/dx](kT/q) = -(kT/q) d[ln(no/ni)]/dx = -(kT/q) (1/no)[dno/dx] = -(kT/q) (1/N)[dN/dx], N > 0

  15. Induced E-field(continued) • Let Vt = kT/q, then since • nopo = ni2 gives no/ni = ni/po • Ex = - Vt d[ln(no/ni)]/dx = - Vt d[ln(ni/po)]/dx = - Vt d[ln(ni/|N|)]/dx, N = -Na < 0 • Ex = - Vt (-1/po)dpo/dx = Vt(1/po)dpo/dx = Vt(1/Na)dNa/dx

  16. The Einsteinrelationship • For Ex = - Vt (1/no)dno/dx, and • Jn,x = nqmnEx + qDn(dn/dx)= 0 • This requires that nqmn[Vt (1/n)dn/dx] = qDn(dn/dx) • Which is satisfied if

  17. E - - Ec Ec Ef Efi gen rec Ev Ev + + k Direct carriergen/recomb (Excitation can be by light)

  18. Direct gen/recof excess carriers • Generation rates, Gn0 = Gp0 • Recombination rates, Rn0 = Rp0 • In equilibrium: Gn0 = Gp0 = Rn0 = Rp0 • In non-equilibrium condition: n = no + dn and p = po + dp, where nopo=ni2 and for dn and dp > 0, the recombination rates increase to R’n and R’p

  19. Direct rec forlow-level injection • Define low-level injection as dn = dp < no, for n-type, and dn = dp < po, for p-type • The recombination rates then are R’n = R’p = dn(t)/tn0, for p-type, and R’n = R’p = dp(t)/tp0, for n-type • Where tn0 and tp0 are the minority-carrier lifetimes

  20. Shockley-Read-Hall Recomb E Indirect, like Si, so intermediate state Ec Ec ET Ef Efi Ev Ev k

  21. S-R-H trapcharacteristics1 • The Shockley-Read-Hall Theory requires an intermediate “trap” site in order to conserve both E and p • If trap neutral when orbited (filled) by an excess electron - “donor-like” • Gives up electron with energy Ec - ET • “Donor-like” trap which has given up the extra electron is +q and “empty”

  22. S-R-H trapchar. (cont.) • If trap neutral when orbited (filled) by an excess hole - “acceptor-like” • Gives up hole with energy ET - Ev • “Acceptor-like” trap which has given up the extra hole is -q and “empty” • Balance of 4 processes of electron capture/emission and hole capture/ emission gives the recomb rates

  23. References • *Fundamentals of Semiconductor Theory and Device Physics, by Shyh Wang, Prentice Hall, 1989. • **Semiconductor Physics & Devices, by Donald A. Neamen, 2nd ed., Irwin, Chicago. • M&K = Device Electronics for Integrated Circuits, 3rd ed., by Richard S. Muller, Theodore I. Kamins, and Mansun Chan, John Wiley and Sons, New York, 2003. • 1Device Electronics for Integrated Circuits, 2 ed., by Muller and Kamins, Wiley, New York, 1986. • 2Physics of Semiconductor Devices, by S. M. Sze, Wiley, New York, 1981. • 3 Physics of Semiconductor Devices, Shur, Prentice-Hall, 1990.

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