Lecture 4 OUTLINE PN Junction Diodes Electrostatics Capacitance I V Reverse Breakdown Large and Small signal models Reading Chapter 2 2 2 3 3 2 3 4 EE105 Fall 2010 Lecture 4 Slide 1 Prof Salahuddin UC Berkeley Energy Band Description EE105 Fall 2011 Lecture 4 Slide 2 Prof Salahuddin UC Berkeley PN 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 3 Prof Salahuddin UC Berkeley Energy Band Description EE105 Fall 2011 Lecture 4 Slide 4 Prof Salahuddin UC Berkeley I V characteristic from energy band description EE105 Fall 2011 Lecture 4 Slide 5 Prof Salahuddin UC Berkeley Mathematical description of current flow in a p n junction diode EE105 Fall 2011 Lecture 4 Slide 6 Prof Salahuddin UC Berkeley Minority 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 np0 0 EE105 Fall 2011 x edge of depletion region x Equilbrium concentration n p0 of electrons on the P side Lecture 4 Slide 7 ni2 NA Prof Salahuddin UC Berkeley Minority Carrier Concentrations at the Edges of the Depletion Region The minority carrier concentrations at the edgesqVof kT V e the depletion region are changed by the factor e D D VT 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 minoritycarrier concentrations decay exponentially with distance from the depletion region to zero n p x n p 0 n p x n p x 2 i VD VT n e NA e 1 x Ln J n diff Notation Ln electron diffusion length cm dn p qDn ni2 VD VT qDn e 1 e x Ln dx N A Ln x EE105 Fall 2011 Lecture 4 Slide 8 Prof Salahuddin UC Berkeley Diode Current under Forward Bias The current flowing across the junction is comprised of hole diffusion and electron diffusion components J tot J p drift x 0 J n drift x 0 J p diff x 0 J n diff x 0 Assuming that the diffusion current components are constant within the depletion region i e no recombination occurs in the depletion region J n diff x 0 qDn ni2 VD VT e 1 N A Ln VD VT J tot J S e EE105 Fall 2011 J p diff x 0 qD p ni2 N D Lp e VD VT 1 Dn Dp 1 where J S qn N L N L D p A n 2 i Lecture 4 Slide 9 Prof Salahuddin UC Berkeley Current Components under Forward Bias For a fixed bias voltage Jtot is constant throughout the diode but Jn x and Jp x vary with position Jtot b EE105 Fall 2011 Lecture 4 Slide 10 0 a x Prof Salahuddin UC Berkeley I 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 Ideal diode equation I D I S eVD VT 1 Dn Dp I S AJ S Aqn N L N L D p A n 2 i EE105 Fall 2011 Lecture 4 Slide 11 Prof Salahuddin UC Berkeley Practical 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 ID A I D I S e qVD kT 1 Dn Dp I S Aqni L N L N n A p D 2 VD V EE105 Fall 2011 Lecture 4 Slide 12 Prof Salahuddin UC Berkeley Parallel 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 13 Prof Salahuddin UC Berkeley Diode Saturation Current IS Dn Dp I S Aqni L N L N n A p D 2 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 EE105 Fall 2011 Lecture 4 Slide 14 Dp I S Aqni L N p D 2 Dn I S Aqni Ln N A 2 Prof Salahuddin UC Berkeley PN 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 Wdep 2 si q EE105 Fall 2011 1 1 V0 VR NA ND Lecture 4 Slide 15 Prof Salahuddin UC Berkeley PN Junction Small Signal Capacitance A reverse biased PN junction can be viewed as a capacitor for incremental changes in applied voltage si Cj Wdep EE105 Fall 2011 Lecture 4 Slide 16 Prof Salahuddin UC Berkeley Voltage Dependent Capacitance The depletion width Wdep and hence the junction capacitance Cj varies with VR Cj VD C j0 VR 1 V0 si q N A N D 1 C j0 2 N A N D V0 si 10 12 F cm is the permittivity of silicon EE105 Fall 2011 Lecture 4 Slide 17 Prof Salahuddin UC Berkeley Reverse 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 By changing VR we can change C which changes the oscillation frequency f res EE105 Fall 2011 Lecture 4 Slide 18 1 2 1 LC Prof Salahuddin UC Berkeley Reverse Breakdown As the reverse bias voltage increases the electric field in the depletion region increases Eventually it can become large enough to cause the junction to break down so that a large reverse current flows breakdown voltage EE105 Fall 2011 Lecture 4 Slide 19 Prof Salahuddin UC Berkeley Reverse Breakdown Mechanisms a Zener breakdown occurs when the electric field is sufficiently high to pull an electron out of a covalent bond to generate an electron hole pair b Avalanche breakdown occurs when electrons and holes gain sufficient kinetic energy due to acceleration by the E field in between scattering events to cause electronhole pair generation upon colliding with the lattice EE105 Fall 2011 Lecture 4 Slide 20 Prof Salahuddin UC Berkeley Constant Voltage Diode Model for Large Signal Analysis If VD VD on The diode operates …
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