1µ P-N Junction Diodes ¸How do they work?(A little math)Movement of Electrons and Holes when Forming the JunctionCircles are charges free to move (Electrons and Holes)Squares are charges NOT free to move (Ionized Donor or Acceptor Atoms) Space Charge or Depletion RegionElectron diffusionHole diffusionHigh holeConcentrationHigh electronConcentrationLocal region ofpositive chargedue toimbalance inelectron-donorconcentrationsLocal region ofnegative chargedue toimbalance inhole-acceptorconcentrationsHigh holeConcentrationHigh electronConcentrationEMovement of Electrons and Holes when Forming the Junction Space Charge or Depletion RegionUniformly doped p-type and n-type semiconductors before the junction is formed.The electric field in the depletion region and the energy band diagram of a p-njunction in thermal equilibrium.E(a) A p-n junction with abrupt doping changes at the metallurgical junction.(b) Energy band diagram of an abrupt junction at thermal equilibrium.(c) Space charge distribution.(d) Rectangular approximation of the space charge distribution.2Movement of Electrons and Holes when Forming the Junction Space Charge or Depletion RegionSpace charge distribution in the depletion region at thermal equilibrium.Electric-field distribution.The shaded area corresponds to the built-in potential.ND -NAMovement of Electrons and Holes when Forming the JunctionNo net current flowin equilibriumEinstein RelationqkTDnn=µBuilt-in-PotentialMovement of Electrons and Holes when Forming the Junction¾ For NA=ND=1015/cm-3 in Silicon at room temperature,Vbi~ 0.6 V¾ For a non-degenerate semiconductor, |-qVbi|<|Eg|Note: This is not the diode turn-on voltage!This is the voltage required to reach a flat band diagramand sets an upper limit (typically an overestimate) for the voltage that can be applied to a diode before it burns itself up.Built-in-Potentialfunction ofimpurity concentrationMovement of Electrons and Holes when Forming the Junction Built-in potentials on the p-side and n-side of abrupt junctions in Si and GaAs as a function of impurity concentration.3Movement of Electrons and Holes when Forming the Junction Depletion Region ApproximationDepletion Region Approximation states that approximately no free carriers exist in the space charge region and no net charge exists outside of the depletion region ( known as the quasi-neutral region).within the quasi-neutral regionwithin the space charge regionKs: dielectric constantε0: permittivity of free spacePoisson’s EquationECEVEFEiECEVEFEip-Type Materialn-Type Material-qxVBI+++++++++ ++++++++++Thus,Movement of Electrons and Holes when Forming the Junction Depletion Region Approximation: Step Junction Solution0ερsKdxdE=Poisson’s EquationMovement of Electrons and Holes when Forming the Junction Depletion Region Approximation: Step Junction SolutionMovement of Electrons and Holes when Forming the Junction Depletion Region Approximation: Step Junction Solution4Movement of Electrons and Holes when Forming the Junction Depletion Region Approximation: Step Junction SolutionMovement of Electrons and Holes when Forming the Junction Depletion Region Approximation: Step Junction SolutionDiode under Forward Bias.mov Diode under no Bias.movDiode under Reverse Bias.movSchematic representation of depletion layer width and energy band diagrams of a p-n junction under various biasing conditions. Reverse-bias conditionForward-bias conditionThermal-equilibriumMovement of Electrons and Holes when Forming the Junction Depletion RegionForward bias Reverse biasMovement of Electrons and Holes when Forming the JunctionDepletion RegionCarrier distribution Energy band diagram5Fig. 4-8: Double-heterostructure configurationThus, only the boundary conditions change resulting indirect replacement of Vbiwith (Vbi-VA) with VA ≠0.Movement of Electrons and Holes when Forming the Junction Depletion Region Approximation: Step Junction SolutionMovement of Electrons and Holes when Forming the Junction Depletion Region Approximation: Step Junction Solution with VA ≠0Consider a p+n junction (heavily doped p-side, lightly doped n side)Movement of Electrons and Holes when Forming the Junction6Movement of Electrons and Holes when Forming the Junction Electron diffusion across a pn junctionMovement of Electrons and Holes when Forming the Junction Forward bias conditionMovement of Electrons and Holes when Forming the Junction Reverse bias condition7µ P-N Junction Diodes ¸Current Flowing through a DiodeI-V CharacteristicsQuantitative Analysis (Math, math and more math)p-n Junction I-V Characteristics In Equilibrium (no bias)Total current balances due to the sum of the individual componentsElectron Drift CurrentElectron DiffusionCurrentHole Drift CurrentHole Diffusion CurrentDiode under no Bias.movno net current!ECEVEFEip-Type Materialn-Type Material-qxVBI+++++++++ ++++++++++0=∇⋅+⋅=+= nDqnEqJJJnnDiffusionnDriftnnµno net current!p-n Junction I-V CharacteristicsECEVEFEin vs. Ep vs. E In Equilibrium (no bias)Total current balances due to the sum of the individual components0=∇⋅+⋅=+= pDqpEqJJJppDiffusionpDriftppµp-n Junction I-V Characteristics Forward Bias (VA> 0)IHole Drift CurrentElectron Drift CurrentElectron DiffusionCurrentHole Diffusion CurrentIPINDiode under Forward Bias.movCurrent flow is dominated by majority carriers flowingacross the junction and becoming minority carriersVACurrent flow is proportional to e(Va/Vref) due to the exponential decay of carriers into the majority carrier bandsLowering of potential hill by VAsurmount potential barrierPNIII+=8Hole Diffusion Current negligible due to large energy barrierHole Drift CurrentElectron Drift CurrentElectron Diffusion Current negligible due to large energy barrier Reverse Bias (VA< 0)Diode under Reverse Bias.movp-n Junction I-V CharacteristicsCurrent flow is constant due to thermally generated carriers swept out by Efields in the depletion regionCurrent flow is dominated by minority carriers flowing across the junction and becoming majority carriersIncrease of potential hill by VA Where does the Reverse Bias Current come from? ¾Generation near the depletion region edges “replenishes” the current source.p-n Junction I-V Characteristics Putting it all togetherp-n Junction I-V Characteristicsfor Ideal diodeVref= kT/q-I0−= 10kTqVexpIIηη: Diode Ideality Factorp-n Junction I-V