1EE130 Lecture 9, Slide 1Spring 2003Lecture #9OUTLINE–Metal-semiconductor contacts (cont.)» I-V characteristics» practical ohmic contacts» small-signal capacitanceReading: Finish Chapter 14EE130 Lecture 9, Slide 2Spring 2003Review: Schottky Diode (n-type Si)Equilibrium (VA= 0)-> EFcontinuous, constant ΦBn= ΦM–χEoΦMχSiΦBnWqVbi= ΦBn–(Ec– EF)FBn-type SimetalEvEFEcΦM > ΦS2EE130 Lecture 9, Slide 3Spring 2003Schottky Diode (p-type Si)ΦMχSiΦBpWqVbi= ΦBp–(EF– Ev)FBp-type SimetalEvEFEcEoΦM < ΦSEquilibrium (VA= 0)-> EFcontinuous, constantΦBp=χ + EG- ΦMEE130 Lecture 9, Slide 4Spring 2003Depleted Layer Width, W )(2 DAbisqNVVW−=⇒ε() ()202xWKqNxVSD−−=εAt x = 0, V = - (Vbi- VA)• W increases with increasing –VA• W decreases with increasing NDLast time, we found that-(Vbi- VA)3EE130 Lecture 9, Slide 5Spring 2003W for p-type Semiconductor )(2 AbiAsqNVVW+=⇒ε() ()202xWKqNxVSA−=εAt x = 0, V = Vbi+ VA• W increases with increasing VA• W decreases with increasing NAEE130 Lecture 9, Slide 6Spring 2003Current Flow in a Schottky Diode• Diode current is determined by majority-carrier flow across the MS junction– Under forward bias, majority-carrier diffusion from the semiconductor into the metal dominates the current – Under reverse bias, majority-carrier diffusion from the metal into the semiconductor dominates the current4EE130 Lecture 9, Slide 7Spring 2003Thermionic Emission Theory• Electrons can cross the junction if• The current for electrons at a given velocity is:• So, the total current over the barrier is:()AbixxVVqmvKE −≥=221()AbinxVVmqvv −≡≥*min2)(, xxvMsvnqAvIx−=→•∫−∞−→•−=min)(vxxxMsdvvnvqAIEE130 Lecture 9, Slide 8Spring 2003Schottky Diode I - V• Given that• We obtain• In the other direction, we always see the same barrier ΦBn:• Therefore2//2//232A/cm 120 where, 4kTqSkTqVSkTqVkTqnMSBAABeJeJATeeAThkqmIΦ−Φ−→•≈==π()()()2*2//32*4xncFvkTmkTEEnxeehkTmvn−−=π()0=−=→•→• AMSSMVIISSkTqVSJATIeIIA2/ where)1( =−=5EE130 Lecture 9, Slide 9Spring 2003•ISof a Schottky diode is 103to 108times larger than a pnjunction diode, depending on ΦB.⇒ Schottky diodes are preferred rectifiers for low voltage, high current applications.Applications of Schottky DiodesEE130 Lecture 9, Slide 10Spring 2003Practical Ohmic Contact• In practice, most M-S contacts are rectifying• To achieve a contact which conducts easily in both directions, we dope the semiconductor very heavilyÆ W is so narrow that carriers can tunnel directly through the barrier6EE130 Lecture 9, Slide 11Spring 2003DABnNVHnDthxDMSonnsemkTqNPvqNJmmhmH/)(13/292/Vcm /104.5/4−Φ−→−−=≈×==πεπ- -- -VDBnsqNWΦ≅ε2DABnNVHeP)(y probabilit tunneling−Φ−=EvEc, EFEFMEvEc, EFSΦBn–VAEE130 Lecture 9, Slide 12Spring 2003Specific Contact Resistance7EE130 Lecture 9, Slide 13Spring 2003Voltage Drop across an Ohmic ContactEE130 Lecture 9, Slide 14Spring 2003Review: MS-Contact Charge Distribution• In a Schottky contact, charge is stored on either side of the MS junction• This charge is modulated by the applied voltage8EE130 Lecture 9, Slide 15Spring 2003AWCsε= Schottky Diode: Small-Signal Capacitance• If an A.C. voltage is applied in series with the D.C. bias VA, the charge stored in the Schottky contact will be modulated → displacement current will flowEE130 Lecture 9, Slide 16Spring 2003Once Vbiis known, ΦΒncan be determined:22)(21AqNVVCsDAbiε−=DcBnFBFcBnbiln)(NNkTqEEqqV −Φ=−−Φ=Using C-V Data to Determine ΦB9EE130 Lecture 9, Slide 17Spring
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