Lecture #10Poisson’s EquationCharge Density in a SemiconductorWork FunctionMetal-Semiconductor ContactsIdeal MS Contact: FM > FS, n-typeIdeal MS Contact: FM < FS, n-typeIdeal MS Contact: FM < FS, p-typeEffect of Interface States on FBnSchottky Barrier Heights: Metal on SiSchottky Barrier Heights: Silicide on SiThe Depletion ApproximationElectrostaticsDepleted Layer Width, WSummary: Schottky Diode (n-type Si)Summary: Schottky Diode (p-type Si)EE130 Lecture 10, Slide 1Spring 2007Lecture #10OUTLINE• Poisson’s Equation• Work function• Metal-Semiconductor Contacts– equilibrium energy-band diagram– depletion-layer widthRead: Chapter 5.1.2,14.1, 14.2EE130 Lecture 10, Slide 2Spring 2007Gauss’s Law:s : permittivity (F/cm) : charge density (C/cm3)Poisson’s EquationE(x) E(x+x)xarea AEE130 Lecture 10, Slide 3Spring 2007Charge Density in a Semiconductor•Assuming the dopants are completely ionized: = q (p – n + ND – NA)EE130 Lecture 10, Slide 4Spring 2007Work FunctionM: metal work function S: semiconductor work function0: vacuum energy levelEE130 Lecture 10, Slide 5Spring 2007There are 2 kinds of metal-semiconductor contacts: •rectifying “Schottky diode”•non-rectifying“ohmic contact”Metal-Semiconductor ContactsEE130 Lecture 10, Slide 6Spring 2007Ideal MS Contact: M > S, n-typeMBnBand diagram instantly after contact formation:Equilibrium band diagram:Schottky Barrier :EE130 Lecture 10, Slide 7Spring 2007Ideal MS Contact: M < S, n-typeBand diagram instantly after contact formation:Equilibrium band diagram:EE130 Lecture 10, Slide 8Spring 2007Ideal MS Contact: M < S, p-typeMSiBpWqVbi = Bp– (EF – Ev)FBp-type SimetalEvEFEcEoBp =+ EG -MEE130 Lecture 10, Slide 9Spring 2007Effect of Interface States on BnEoMSiBnWqVbi = B – (Ec – EF)FBn-type SimetalEvEFEcM >S• Ideal MS contact:Bn =M – • Real MS contacts: A high density of allowed energy states in the band gap at the MS interface pins EF to the range 0.4 eV to 0.9 eV below EcEE130 Lecture 10, Slide 10Spring 2007-Bn tends to increase with increasing metal work functionSchottky Barrier Heights: Metal on SiEE130 Lecture 10, Slide 11Spring 2007Silicide-Si interfaces are more stable than metal-silicon interfaces. After metal is deposited on Si, a thermal annealing step is applied to form a silicide-Si contact. The term metal-silicon contact includes silicide-Si contacts.Schottky Barrier Heights: Silicide on SiEE130 Lecture 10, Slide 12Spring 2007The Depletion Approximation The semiconductor is depleted of mobile carriers to a depth W In the depleted region (0 x W ): = q (ND – NA) Beyond the depleted region (x > W ): = 0EE130 Lecture 10, Slide 13Spring 2007Electrostatics•Poisson’s equation:•The solution is:ss DqNx xWqNxDs xdxxV )( EEEEE130 Lecture 10, Slide 14Spring 2007Depleted Layer Width, W 2 DbisqNVW 202xWKqNxVSDAt x = 0, V = -Vbi• W decreases with increasing NDEE130 Lecture 10, Slide 15Spring 2007Summary: Schottky Diode (n-type Si)Equilibrium (VA = 0)-> EF continuous, constantBn =M – EoMSiBnWqVbi = Bn – (Ec – EF)FBn-type SimetalEvEFEcM >S 2DbisqNVWDepletion width:EE130 Lecture 10, Slide 16Spring 2007Summary: Schottky Diode (p-type Si)MSiBpWqVbi = Bp– (EF – Ev)FBp-type SimetalEvEFEcEoM <SEquilibrium (VA = 0)-> EF continuous, constantBp =+ EG -M 2AbisqNVWDepletion
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