EE 5340 Semiconductor Device Theory Lecture 7 - Fall 2009 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc

Second Assignment Please print and bring to class a signed copy of the document appearing at http://www.uta.edu/ee/COE%20Ethics%20Statement%20Fall%2007.pdf L 07 Sept 15

Diffused or Implanted IC Resistor (Fig 2.451) L 07 Sept 15

An IC Resistor with L = 8W (M&K)1 L 07 Sept 15

Typical IC doping profile (M&K Fig. 2.441) L 07 Sept 15

Mobilities** L 07 Sept 15

IC Resistor Conductance L 07 Sept 15

An IC Resistor with Ns = 8, R = 8Rs (M&K)1 L 07 Sept 15

The effect of lateral diffusion (M&K1) L 07 Sept 15

A serpentine pattern IC Resistor (M&K1) R = NSRS + 0.65NCRS note: RC = 0.65RS L 07 Sept 15

Fermi Energy The equilibrium carrier concentration ahd the Fermi energy are related as The potential f = (Ef-Efi)/q If not in equilibrium, a quasi-Fermi level (imref) is used L 07 Sept 16

Electron quasi-Fermi Energy (n = no + n) L 07 Sept 16

Hole quasi-Fermi Energy (p = po + p) L 07 Sept 16

Ex-field when Ef - Efi not constant Since f = (Ef - Efi)/q = Vt ln(no/ni) When Ef - Efi = is position dependent, Ex = -df/dx = -[d(Ef-Efi)/dx] = - Vt d[ln(no/ni)]/dx If non-equilibrium fn = (Efn-Efi)/q = Vt ln(n/ni), etc Exn = -[dfn/dx] = -Vt d[ln(n/ni)]/dx L 07 Sept 16

Si and Al and model (approx. to scale) metal n-type s/c p-type s/c Eo Eo Eo qcsi~ 4.05 eV qcsi~ 4.05 eV qfm,Al ~ 4.1 eV qfs,n qfs,p Ec Ec EFm EFn EFi EFi EFp Ev Ev L 07 Sept 16

Making contact be- tween metal & s/c Equate the EF in the metal and s/c materials far from the junction Eo(the free level), must be continuous across the jctn. N.B.: qc = 4.05 eV (Si), and qf = qc + Ec - EF Eo qc (electron affinity) qf (work function) Ec EF EFi qfF Ev L 07 Sept 15

Equilibrium Boundary Conditions w/ contact No discontinuity in the free level, Eo at the metal/semiconductor interface. EF,metal = EF,semiconductor to bring the electron populations in the metal and semiconductor to thermal equilibrium. Eo - EC = qcsemiconductor in all of the s/c. Eo - EF,metal = qfmetal throughout metal. L 07 Sept 16

Ideal metal to n-type barrier diode (fm>fs,Va=0) n-type s/c No disc in Eo Ex=0 in metal ==> Eoflat fBn=fm- cs = elec mtl to s/c barr fi=fBn-fn= fm-fs elect s/c to mtl barr Eo qfm qcs qfi qfBn qfs,n Ec EFm EFn EFi Depl reg Ev qf’n L 07 Sept 16

References 1Device Electronics for Integrated Circuits, 2 ed., by Muller and Kamins, Wiley, New York, 1986. See Semiconductor Device Fundamentals, by Pierret, Addison-Wesley, 1996, for another treatment of the m model. 2Physics of Semiconductor Devices, by S. M. Sze, Wiley, New York, 1981. 3Semiconductor Physics & Devices, 2nd ed., by Neamen, Irwin, Chicago, 1997. L 07 Sept 15