Start: Lecture #11‐12, 11/17‐19/2009Metal‐Semiconductor Junctions (again for review)Metal semiconductor contacts: p-semiconductor case:ElectronP-typeElectron affinityWork functionIonization energyWhen a metal is deposited on a semiconductor directly the work function of the metal and the Fermi level of the semiconductor must line up againMetal semiconductor contacts: n-semiconductor case:In this case, the metal behaves very much like a heavily doped p+layer, and the semiconductor is depleted of electronsNN-typeThe work function of a metalA depletion layer is formed because of the band-bendingThe work function of a metal is defined as the energy for its (free) electrons to escape into vacuumAgain, when we apply a voltage, diffusion current will give rise to an exponential increase of the currentAnd in reverse bias, the current flow is limited to Igen1.Equilibrium(noappliedvoltage,nocurrent):Metal-Semiconductor (Schottky) Diode Current: derivation for metal on n-semi.1.Equilibrium(noappliedvoltage,nocurrent):(a) ns= NCe−qφB/k T, is the surface density of electrons in conduction band atM-S junction(b)v≈v/4istheaveragevelocityofelectronsintheconductionbandto(b)vm≈vth/4istheaveragevelocityofelectronsintheconductionbandto-wards the metal(c) Electron current from conduction band to metal is, Jo,C→M=qvthNC4e−qφB/kTIn equilibrium, the current of electrons escaping the metal and entering thesemiconductor conduction band (M → C) must exactly balance the electroncurrent from the semiconductor conduction band into the metal (C → M),Jo,M→C= −Jo,M→C.o,M→Co,M→C2. Applied Voltage, Vf(quasi-equilibrium):(a)n=NCeq(Vf−φB)/kTisthesurfacedensityofelectronsinconductionband(a)ns=NCeq(fφB)/,isthesurfacedensityofelectronsinconductionbandat M-S junction(b) JC→M=qvthNC4eq(Vf−φB)/kT(c) The electron flow from the metal to the semiconductor is unchanged a s thereibdbdiihldilhihldiisnoband-bendinginthemetaldue toits extremelyhighelectrondensity,JM→C= −qvthNC4e−qφB/kT(d) Total current is then, Jn= JC→M+ JM→C=qvthNC4eqφB)/kT(eqVf/k T− 1).Comment on Analysis:(a)Wehave neglected the flow of holes from the valence band into the metal(a)We have neglected the flow of holes from the valence band into the metal in our analysis on the previous page of the metal-n Schottky diode. This can be done because the electron current turns out to be orders of magnitude larger than the hole current for such a “metal-n” Schottky diode (f t lS h ttkdi d th h l t ld l b id d)(for a metal-p Schottkydiode, the hole current would only be considered). As a result, Schottky diodes are termed “majority carrier devices”.(b) The Schottky diode can be made to behave similar to an ohmic contact (i li IV h t i ti ) if th i t f th j ti b(i.e., linear I-V characteristics), if the resistance of the junction can be made very small for both positive and negative applied voltages (the circuit resistance is then dominated by the series resistance of the external contact wires or the bulk resistivity of the semiconductor material itself, and not the yjunction). This can be done by choosing a metal-semiconductor combination that has a small barrier height.For a Metal-Semiconductor (Schottky) diode, the I-V relationship can be described by:Current Crossectional Area barrier height voltage ideality factorN = ideality factor which ranges from 1-2B = Schottky barrier height ~0.85 for a typical Si surface with a Pt contact This value depends on the surface of Si and the work function of the metal chosenB = constant describing the junction propertiesgj pp*Note that the last part of this equation is very similar to the regular p-n diode current pq y gpequation.Surface depletion and Fermi level pinningMany semiconductors, such as GaAs have dangling bonds on the surface, and this pins the Fermi level to a fixed value of ~0.8eV below the conduction band. This results in band bending and surface depletion even if there is no metal on the surface.In InAs, the Fermi level is pinned above the conduction band edge. This means that this material is ideal for constructing ohmic contacts.MOS‐CapacitorMOS capacitorCharge balance of a MOS capacitor. –Q = +Q“M-O-P” (metal-oxide-p-semi)Substitute the definition of Eiand EfDerivation of the depletion width of a MOS capacitor (on p-doped semiconductor)NA>>NDIntegrateNote that this is the permittivity of the oxideIntegrate againDepletion width into the semiconductorDepletion width of MOS capacitorAs is the case in typical Schottky diodes and p-n di d h d l i id hdiodes, the depletion width changes as a function of the square root of the dopant concentrationThis assumes zero biasCharge distribution with different applied voltagesNote that the charge associated with inversion resides in an extremely narrow channel immediately adjacent to the oxideInfluence of a gate voltageThe voltageThe voltage drop through the oxide must biddbe consideredThe difference in the dielectric displacement field (D=E) across the interface between the oxide and the semiconductor must be equal to the interface trapped charge (which is 0 for a good gate oxide!); assuming 0 trapped charge!; ESis the E-field at the semiconductor surfaceSince:Since:N t b tit tNext, we substitute the depletion derivationExample problemExample problem.End: Lecture #11‐12,