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Start: Lecture #10, 11/12/2009ppSince np=ni2, pnSchematic of the junction terminology Position of the metallurgical (diffused) junctionpnExcess holes in Excess electrons usedthe n-materialin the p-materialDepletion widthHow much current flows through a diode when we apply a voltageWe know that the concentrations of holes in the p side and the concentration of holes on the n side of a p-n junction pjare related by Vo:Note that this means that as you apply a positive voltage the number of excess holespositive voltage, the number of excess holes on the n side increases exponentiallyNow, we can find the excess minority carrier concentration on both p and n-side of the depletion width by subtracting:width by subtracting:Since we know that the excess carrier concentration drops off to zero as we get further away from the junction, we can define diffusion lengths Lnand Lpfor l t d h l ti l d ti l d ith di telectrons and holes, respectively and assume an exponential decay with distance. These diffusion lengths depend on the dopant concentration (recombination).Usually the n and p regions are long with respect to Land Land:Usually, the n and p regions are long with respect to Lnand Lpand:Diffusion profile of excess minority carriersThese are the excess hole and electron concentrations as a function of distance xnand xpfrom the junctionFinally, the total diode current is the sum of the hole and electron currents across the p-n junction and is given by:and is given by:Area of junction diffusivity diffusion length Applied voltage Temperature (K)L=DL=DCan also be substituted for LFor those interested, here are three ways of deriving the diodeof deriving the diode equationDiode Breakdown EffectsDiode Breakdown Effects:When we apply a large reverseWhen we apply a large reverse bias (negative voltage) onto a diode, it eventually breaks down and conducts again. That voltage pnis called the reverse breakdown voltage Vbr.There are twoThere are two common breakdown mechanisms: Tunneling and pngAvalanche MultiplicationAvalanche MultiplicationIf a high enough voltage is applied toIf a high enough voltage is applied to the depletion region, minority carriers are accelerated through this region and are energetic enough to generate secondary electrons. This results in an “avalanche” effect which amplifies the number of free carriers in the depletion region and results in breakdownregion and results in breakdownImpact ionizationNote: Avalanche photodiodes are often used as sensitive optical sensors with built-in gain. They are typically biased totypically biased to 100VHigher fields occur at small dltidepletion widths and large reverse biasesbiasesFSiVbr= Ebr2/2qNdFor Si, 3x105V/cmNarrower depletion widthsWider depletion widthsPlot of breakdown characteristics as a function of dopant concentrationTunneling or Zener breakdown:At a high enough voltage, if W is narrow enough, it is possible for electrons to tunnel from the valence band ofNote: Zener diodes are oftenpossible for electrons to tunnel from the valence band of the p-side of the diode directly to the conduction band of the n-side of the diodediodes are often used as voltage control devicesVTThe mechanism for this process is field ionization, which requires very short W and high fields ofThis results in a very sharp increase in current at the tunneling voltage VTwhich requires very short W and high fields of >106V/cm in the junction. There is not enough distance for impact ionization if Ndand Naare highMetal‐Semiconductor JunctionsMetal 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 IgenFor 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 ppNote that the last part of this equation is very similar to the regular p-n diode current equation.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.Field‐Effect Devices: Introgridvacuum~2400K(-)Field effect devices: The electric field of a gate or grid is used to modulate theanodevacuum(+)()of a gate or grid is used to modulate the number of charges (I.e. electron current) moving from the source to the drain.electronsIn a triode, the charges are electrons accelerated through a vacuum. N-type Si channelMOS capacitorEnd: Lecture #10,


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CALTECH APH 9A - Lecture #10

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