Lecture 3Electrical ResistanceCarrier DiffusionDiffusion ExamplesDiffusion CurrentThe Einstein RelationThe PN Junction DiodeDiode Operating RegionsCarrier Diffusion across the JunctionDepletion RegionThe Depletion ApproximationCarrier Drift across the JunctionPN Junction in EquilibriumBuilt-in Potential, V0Built-In Potential ExamplePN Junction under Forward BiasMinority Carrier Injection under Forward BiasMinority Carrier Concentrations at the Edges of the Depletion RegionDiode Current under Forward BiasEE105 Fall 2011 Lecture 3, Slide 1 Prof. Salahuddin, UC BerkeleyLecture 3OUTLINE•Semiconductor Basics (cont’d)–Carrier drift and diffusion•PN Junction Diodes–Electrostatics–CapacitanceReading: Chapter 2.1-2.2EE105 Fall 2011 Lecture 3, Slide 2 Prof. Salahuddin, UC BerkeleyElectrical Resistancewhere is the resistivity Resistance WtLIVR(Unit: ohms)V+_LtWIhomogeneously doped sampleEE105 Fall 2011 Lecture 3, Slide 3 Prof. Salahuddin, UC BerkeleyCarrier Diffusion•Due to thermally induced random motion, mobile particles tend to move from a region of high concentration to a region of low concentration. –Analogy: ink droplet in water •Current flow due to mobile charge diffusion is proportional to the carrier concentration gradient.–The proportionality constant is the diffusion constant.dxdpqDJppNotation:Dp hole diffusion constant (cm2/s)Dn electron diffusion constant (cm2/s)EE105 Fall 2011 Lecture 3, Slide 4 Prof. Salahuddin, UC BerkeleyDiffusion Examples•Non-linear concentration profile varying diffusion currentLNqDdxdpqDJppdiffp ,ddppdiffpLxLNqDdxdpqDJexp ,•Linear concentration profile constant diffusion currentdLxNp expLxNp 1EE105 Fall 2011 Lecture 3, Slide 5 Prof. Salahuddin, UC BerkeleyDiffusion Current•Diffusion current within a semiconductor consists of hole and electron components:•The total current flowing in a semiconductor is the sum of drift current and diffusion current:)( ,,,dxdpDdxdnDqJdxdnqDJdxdpqDJpndifftotndiffnpdiffpdiffndiffpdriftndriftptotJJJJJ,,,,EE105 Fall 2011 Lecture 3, Slide 6 Prof. Salahuddin, UC BerkeleyThe Einstein Relation•The characteristic constants for drift and diffusion are related:•Note that at room temperature (300K)–This is often referred to as the “thermal voltage”. qkTDmV26qkTEE105 Fall 2011 Lecture 3, Slide 7 Prof. Salahuddin, UC BerkeleyThe PN Junction Diode•When a P-type semiconductor region and an N-type semiconductor region are in contact, a PN junction diode is formed. VDID+–EE105 Fall 2011 Lecture 3, Slide 8 Prof. Salahuddin, UC BerkeleyDiode Operating Regions •In order to understand the operation of a diode, it is necessary to study its behavior in three operation regions: equilibrium, reverse bias, and forward bias.VD = 0 VD > 0VD < 0EE105 Fall 2011 Lecture 3, Slide 9 Prof. Salahuddin, UC BerkeleyCarrier Diffusion across the Junction•Because of the differences in hole and electron concentrations on each side of the junction, carriers diffuse across the junction: Notation:nn electron concentration on N-type side (cm-3)pn hole concentration on N-type side (cm-3)pp hole concentration on P-type side (cm-3)np electron concentration on P-type side (cm-3)EE105 Fall 2011 Lecture 3, Slide 10 Prof. Salahuddin, UC BerkeleyDepletion Region•As conduction electrons and holes diffuse across the junction, they leave behind ionized dopants. Thus, a region that is depleted of mobile carriers is formed.–The charge density in the depletion region is not zero.–The carriers which diffuse across the junction recombine with majority carriers, i.e. they are annihilated.width=Wdepquasi-neutral regionquasi-neutral regionEE105 Fall 2011 Lecture 3, Slide 11 Prof. Salahuddin, UC BerkeleyThe Depletion ApproximationIn the depletion region on the N side: bxqNEqNdxdEsiDsiDsi (x)x-qNAqNDIn the depletion region on the P side: xaqNEqNdxdEsiAsiAsi DAbNaN a-bBecause charge density ≠ 0 in the depletion region, a large E-field exists in this region:EE105 Fall 2011 Lecture 3, Slide 12 Prof. Salahuddin, UC BerkeleyCarrier Drift across the JunctionEE105 Fall 2011 Lecture 3, Slide 13 Prof. Salahuddin, UC BerkeleyPN Junction in Equilibrium•In equilibrium, the drift and diffusion components of current are balanced; therefore the net current flowing across the junction is zero.diffndriftndiffpdriftpJJJJ,,,,0,,,,diffndiffpdriftndriftptotJJJJJEE105 Fall 2011 Lecture 3, Slide 14 Prof. Salahuddin, UC BerkeleyBuilt-in Potential, V0•Because there is a large electric field in the depletion region, there is a significant potential drop across this region: DiAnppppppxxpppppNnNqkTppDxVxVpdpDdVdxdpDdxdVpdxdpqDEqppn/lnln)()( 22121 ln 20iDAnNNqkTV (Unit: Volts)EE105 Fall 2011 Lecture 3, Slide 15 Prof. Salahuddin, UC BerkeleyBuilt-In Potential Example•Estimate the built-in potential for PN junction below.–Note that N PND = 1018 cm-3NA = 1015 cm-3mV603.2mV26)10ln( qkTEE105 Fall 2011 Lecture 3, Slide 16 Prof. Salahuddin, UC Berkeley•A forward bias decreases the potential drop across the junction. As a result, the magnitude of the electric field decreases and the width of the depletion region narrows.PN Junction under Forward Bias (x)x-qNAqNDa-bV(x)xa-bV0ID0EE105 Fall 2011 Lecture 3, Slide 17 Prof. Salahuddin, UC BerkeleyMinority Carrier Injection under Forward Bias•The potential barrier to carrier diffusion is decreased by a forward bias; thus, carriers diffuse across the junction.–The carriers which diffuse across the junction become minority carriers in the quasi-neutral regions; they recombine with majority carriers, “dying out” with distance.np(x)np0AipNnn20Equilbrium concentration of electrons on the P side:edge of depletion regionx'0 x'EE105 Fall 2011 Lecture 3, Slide 18 Prof. Salahuddin, UC BerkeleyMinority Carrier Concentrations at the Edges of the Depletion Region•The minority-carrier concentrations at the edges of the depletion region are changed by the factor –There is an excess concentration (pn, np) of minority carriers in the quasi-neutral regions, under forward bias.•Within the quasi-neutral regions, the excess minority-carrier concentrations decay
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