Overview of Silicon p-n Junctionsp-n Junctions (Diodes)p-n Junctions (Diodes)p-n Junctions (Diodes)Charge DensityElectric FieldPotentialBand DiagramAsymmetric Doping (NA=4ND)p-n Junction Band Diagramp-n Junction – No Applied Biasp-n Junction – Reverse Biasedp-n Junction – Forward Biasedp-n Junction Diodep-n Junction DiodeCurve Fitting Exponential Data (In MATLAB)Size of the Depletion RegionSize of the Depletion RegionReverse-Biased p-n Junction CapacitanceSmall-Signal Reverse-Biased CapacitanceSmall-Signal Reverse-Biased CapacitanceSmall-Signal Reverse-Biased CapacitanceSmall-Signal Reverse-Biased CapacitanceLarge-Signal Reverse-Biased Junction CapacitanceForward-Biased Junction CapacitanceSmall-Signal Junction ResistanceSmall-Signal Equivalent ModelBipolar Junction Transistors (BJTs)BJT Band DiagramBJT EquationsDesignable BJT Parameters1Overview of Silicon p-n JunctionsDr. David W. GrahamWest Virginia UniversityLane Department of Computer Science and Electrical Engineering© 2009 David W. Graham2p-n Junctions (Diodes)p-n Junctions (Diodes)• Fundamental semiconductor device• In every type of transistor• Useful circuit elements (one-way valve)• Light emitting diodes (LEDs)• Light sensors (imagers)3p-n Junctions (Diodes)++++++++++++++++++++++++––––––––––––––––––––––––––––––––––––––––––––––––++++++++++++++++++++++++p-type n-typeBring p-type and n-type material into contact4p-n Junctions (Diodes)++++++++++++++++++++++++–––––––––––––––––––––––––––––––––––––––++++++++++++++++++++++++p-type n-type• All the h+ from the p-type side and e- from the n-type side undergo diffusion→ Move towards the opposite side (less concentration)• When the carriers get to the other side, they become minority carriers• Recombination → The minority carriers are quickly annihilated by the large number of majority carriers• All the carriers on both sides of the junction are depleted from the material leaving• Only charged, stationary particles (within a given region)• A net electric fieldÆThis area is known as the depletion region (depleted of carriers)ÆSize of the depletion region depends on the diffusion length–––––––––Depletion Region––––––––––––––––––––––––+++++++++++++++––––––––––––––––––––––––+++++++++++++++–––++++++++++++++++++++++++–––––––––––––––5Charge Density++++++++++++++++++++++++–––––––––––––––––––––––––––––––––––––––++++++++++++++++++++++++p-type n-type–––––––––Depletion Region––––––––––––––––––––––––+++++++++++++++––––––––––––––––––––––––+++++++++++++++–––++++++++++++++++++++++++–––––––––––––––The remaining stationary charged particles results in areas with a net chargeCharge Densitypnxxw+=xρ(x)qND-qNAxnxpx=06Electric Field• Areas with opposing charge densities creates an E-field• Total areas of charge are equal (but opposite)• E-field is the integral of the charge density• Poisson’s Equationε is the permittivity of SiliconCharge Density()()0ερερSKxxdxdE==xρ(x)qND-qNAxnxpx=0Electric FieldExxnxpx=0()wVVxqNxqNEdxdVEAbinDpA−−=−=−=−=2maxεε7Potential()xEdxd−=ψ• E-field sets up a potential difference• Potential is the negative of the integral of the E-fieldCharge Densityxρ(x)qND-qNAxnxpx=0Electric FieldExxnxpx=0PotentialψxVbixnxpx=0Built-In Potential•Integrate the E-field within the depletion region•Use the Einstein RelationmVqkTUnNNqkTVTiDAbi9.25ln2==⎟⎟⎠⎞⎜⎜⎝⎛= LetVbi typically in the range of 0.6-0.7V8Band Diagram• Line up the Fermi levels• Draw a smooth curve to connect themECEfEVBand Diagram PotentialψxVbixnxpx=0Charge Densityxρ(x)qND-qNAxnxpx=0Electric FieldExxnxpx=09Asymmetric Doping (NA =4ND )Exxnxpx=0ψxVbixnxpx=0xρ(x)qND-qNAxnxpx=010p-n Junction Band DiagrampnVAECEfEVp-typen-typeVA is the applied biasp nDepletion Region11p-n Junction – No Applied BiaspnVAIf VA = 0ECEfEVECEfEV• Any e- or h+ that wanders into the depletion region will be swept to the other side via the E-field• Some e- and h+ have sufficient energy to diffuse across the depletion region• If no applied voltageIdrift = Idiffp nDepletion Region12p-n Junction – Reverse BiasedpnVAIf VA < 0• Barrier is increased• No diffusion current occurs (not sufficient energy to cross the barrier)• Drift may still occur• Any generation that occurs inside the depletion region adds to the drift current• All current is drift currentReverse BiasedECEfEVp nDepletion RegionExpands13p-n Junction – Forward BiasedpnVAIf VA > 0• Barrier is reduced, so more e- and h+ may diffuse across• Increasing VA increases the e- and h+ that have sufficient energy to cross the boundary in an exponential relationship (Boltzmann Distributions)→Exponential increase in diffusion current• Drift current remains the sameForward BiasedECEfEVp nDepletion RegionShrinks14p-n Junction Diode()10−=TAnUVeIICombination of drift and generationDiffusion DriftqkTUT=→ Thermal voltage = 25.86mV⎩⎨⎧=21n⎟⎟⎠⎞⎜⎜⎝⎛+=DippAinnNnLDNnLDqAI220Cq1910602.1−×=A = cross-sectional area15p-n Junction Diode()⎩⎨⎧−≈−=0001IeIeIITATAnUVnUVfor VA > 0for VA < 0I-I0VA()1100−=−=TATAnUVnUVeIIeII()()()()()()000lnlnlnlnlnlnlnInUVIIeIeIITAnUVnUVTATA+=+==⎟⎟⎠⎞⎜⎜⎝⎛ln(I)ln(I0)VAnkTqnUT=116Curve Fitting Exponential Data (In MATLAB)TAnUVeII0≈Curve Fitting Exponential Data (In MATLAB)• Given I and V (vectors of data)• Use the MATLAB functions•polyfit – function to fit a polynomial (find the coefficients)•polyval – function to plot a polynomial with given coefficients and x values[A] = polyfit(V,log(I),1);% polyfit(independent_var,dependent_var,polynomial_order)% A(1) = slope% A(2) = intercept[I_fit] = polyval(A,V);% draws the curve-fit line17Size of the Depletion Region()()()()()210210210222⎥⎦⎤⎢⎣⎡−+=+==⎥⎦⎤⎢⎣⎡−+=⎥⎦⎤⎢⎣⎡−+=AbiDADAspnnADAbiDAADspAbiDADAsnVVNNNNqKxxwxNNVVNNNNqKxVVNNNNqKxεεεVA = Applied voltage= 0 under equilibrium