Lecture 5 OUTLINE PN Junction Diodes I V Capacitance Reverse Breakdown Large and Small signal models Reading Chapter 2 2 2 3 3 2 3 4 EE105 Fall 2010 Lecture 5 Slide 1 Prof Salahuddin UC Berkeley Hole Diffusion x x 0 J p diff EE105 Fall 2011 qD p ni2 N D Lp e VD VT Lecture 4 Slide 2 1e x Lp Prof Salahuddin UC Berkeley Distribution of Diffusion Current J p diff qD p ni2 N D Lp e VD VT 1e x Lp J n diff qDn ni2 VD VT e 1 e x Ln N A Ln x b 0 a Assume No Recombination in the depletion region Known Total Current is the same everywhere EE105 Fall 2011 Lecture 4 Slide 3 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 J total J p diff qD p ni2 N D Lp e VD VT 1e x Lp J n diff qDn ni2 VD VT e 1 e x Ln N A Ln x b EE105 Fall 2011 0 Lecture 4 Slide 4 a 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 5 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 6 Prof Salahuddin UC Berkeley How to make sure that current flow in a forward biased p n junction diode is mainly due to electrons EE105 Fall 2011 Lecture 4 Slide 7 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 8 Dp I S Aqni L N p D 2 Dn I S Aqni Ln N A 2 Prof Salahuddin UC Berkeley Depletion Width on the P side x qND a b qNA qN E A a x si see slide 3 dV qN A a x dX si x V qN A a x 2 2 si V x V0 b EE105 Fall 2011 0 a x Lecture 4 Slide 9 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 10 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 11 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 12 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 13 1 2 1 LC 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 14 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 15 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 16 Prof Salahuddin UC Berkeley Constant Voltage Diode Model for Large Signal Analysis If VD VD on The diode operates as an open circuit If VD VD on The diode operates as a constant voltage source with value VD on EE105 Fall 2011 Lecture 4 Slide 17 Prof Salahuddin UC Berkeley Example Diode DC Bias Calculations IX VX I X R1 VD I X R1 VT ln IS I X 2 2mA for VX 3V I X 0 2mA for VX 1V This example shows the simplicity provided by a constant voltage model over an exponential model Using an exponential model iteration is needed to solve for current Using a constant voltage model only linear equations need to be solved EE105 Fall 2011 Lecture 4 Slide 18 Prof Salahuddin UC Berkeley Small Signal Analysis Small signal analysis is performed at a DC bias point by perturbing the voltage by a small amount and observing the resulting linear current perturbation If two points on the I V curve are very close the curve inbetween these points is well approximated by a straight line I D dI D VD dVD 2 3 x x e x 1 x 2 3 EE105 Fall 2011 Lecture 4 Slide 19 VD VD1 I s VD1 VT I D1 e VT VT Prof Salahuddin UC Berkeley Diode Model for Small Signal Analysis Since there is a linear relationship between the smallsignal current and small signal voltage of a diode the diode can be …
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