Lecture 4Energy Band DescriptionPN Junction under Reverse BiasSlide 4I-V characteristic from energy band descriptionSlide 6Minority Carrier Injection under Forward BiasMinority Carrier Concentrations at the Edges of the Depletion RegionDiode Current under Forward BiasCurrent Components under Forward BiasI-V Characteristic of a PN JunctionPractical PN JunctionsParallel PN JunctionsDiode Saturation Current ISSlide 15PN Junction Small-Signal CapacitanceVoltage-Dependent CapacitanceReverse-Biased Diode ApplicationReverse BreakdownReverse Breakdown MechanismsConstant-Voltage Diode Model for Large-Signal AnalysisExample: Diode DC Bias CalculationsSmall-Signal AnalysisDiode Model for Small-Signal AnalysisSmall Sinusoidal AnalysisEE105 Fall 2010 Lecture 4, Slide 1 Prof. Salahuddin, UC BerkeleyLecture 4OUTLINE•PN Junction Diodes–Electrostatics–Capacitance–I/V–Reverse Breakdown–Large and Small signal modelsReading: Chapter 2.2-2.3,3.2-3.4EE105 Fall 2011 Lecture 4, Slide 2 Prof. Salahuddin, UC BerkeleyEnergy Band DescriptionEE105 Fall 2011 Lecture 4, Slide 3 Prof. Salahuddin, UC BerkeleyPN Junction under Reverse Bias •A reverse bias increases the potential drop across the junction. As a result, the magnitude of the electric field in the depletion region increases and the width of the depletion region widens.EE105 Fall 2011 Lecture 4, Slide 4 Prof. Salahuddin, UC BerkeleyEnergy Band DescriptionEE105 Fall 2011 Lecture 4, Slide 5 Prof. Salahuddin, UC BerkeleyI-V characteristic from energy band descriptionEE105 Fall 2011 Lecture 4, Slide 6 Prof. Salahuddin, UC BerkeleyMathematical description of current flow in a p-n junction diodeEE105 Fall 2011 Lecture 4, Slide 7 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 4, Slide 8 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 exponentially with distance from the depletion region, to zero:TDDVVkTqVee// nTDLxAVVippppeNenxnxnnxn//201)()()(x'Notation:Ln electron diffusion length (cm) nTDLxVVnAinpndiffneeLNnqDxddnqDJ//2,1EE105 Fall 2011 Lecture 4, Slide 9 Prof. Salahuddin, UC BerkeleyDiode Current under Forward Bias•The current flowing across the junction is comprised of hole diffusion and electron diffusion components:•Assuming that the diffusion current components are constant within the depletion region (i.e. no recombination occurs in the depletion region): where1 2/pDpnAniSVVSt otLNDLNDqnJeJJTD0,0,0,0,xdiffnxdiffpxdriftnxdrif tptotJJJJJ 1/20,TDVVnAinxdiffneLNnqDJ 1/20,TDVVpDipxdiffpeLNnqDJEE105 Fall 2011 Lecture 4, Slide 10 Prof. Salahuddin, UC BerkeleyCurrent Components under Forward Bias•For a fixed bias voltage, Jtot is constant throughout the diode, but Jn(x) and Jp(x) vary with position.x0Jtota-bEE105 Fall 2011 Lecture 4, Slide 11 Prof. Salahuddin, UC BerkeleyI-V Characteristic of a PN Junction•Current increases exponentially with applied forward bias voltage, and “saturates” at a relatively small negative current level for reverse bias voltages. pDpnAniSSVVSDLNDLNDAqnAJIeIITD2/1“Ideal diode” equation:EE105 Fall 2011 Lecture 4, Slide 12 Prof. Salahuddin, UC BerkeleyPractical PN Junctions•Typically, pn junctions in IC devices are formed by counter-doping. The equations provided in class (and in the textbook) can be readily applied to such diodes if–NA net acceptor doping on p-side (NA-ND)p-side–ND net donor doping on n-side (ND-NA)n-side)1( kTVqSDDeIIDppAnniSNLDNLDAq nI2VD (V)ID (A)EE105 Fall 2011 Lecture 4, Slide 13 Prof. Salahuddin, UC BerkeleyParallel PN Junctions•Since the current flowing across a PN junction is proportional to its cross-sectional area, two identical PN junctions connected in parallel act effectively as a single PN junction with twice the cross-sectional area, hence twice the current.EE105 Fall 2011 Lecture 4, Slide 14 Prof. Salahuddin, UC BerkeleyDiode Saturation Current IS•IS can vary by orders of magnitude, depending on the diode area, semiconductor material, and net dopant concentrations.–typical range of values for Si PN diodes: 10-14 to 10-17 A/m2•In an asymmetrically doped PN junction, the term associated with the more heavily doped side is negligible:–If the P side is much more heavily doped,–If the N side is much more heavily doped,DppAnniSNLDNLDAqnI2DppiSNLDAqnI2AnniSNLDAqnI2EE105 Fall 2011 Lecture 4, Slide 15 Prof. Salahuddin, UC BerkeleyPN Junction under Reverse Bias •A reverse bias increases the potential drop across the junction. As a result, the magnitude of the electric field in the depletion region increases and the width of the depletion region widens. 112 0 RDAsidepVVNNqW EE105 Fall 2011 Lecture 4, Slide 16 Prof. Salahuddin, UC BerkeleyPN Junction Small-Signal Capacitance•A reverse-biased PN junction can be viewed as a capacitor, for incremental changes in applied voltage. depsijWCEE105 Fall 2011 Lecture 4, Slide 17 Prof. Salahuddin, UC BerkeleyVoltage-Dependent Capacitance•The depletion width (Wdep) and hence the junction capacitance (Cj) varies with VR.si 10-12 F/cm is the permittivity of silicon.0000121VNNNNqCVVCCDADAsijRjjVDEE105 Fall 2011 Lecture 4, Slide 18 Prof. Salahuddin, UC BerkeleyReverse-Biased Diode Application•A very important application of a reverse-biased PN junction is in a voltage controlled oscillator (VCO), which uses an LC tank.
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