Lecture 11 OUTLINE The pn Junction Diode Uses Rectification parts of transistors light emitting diodes and lasers solar cells electrically variable capacitor varactor diode voltage reference zener diode Depletion region junction capacitance I V characteristic Circuit applications and analysis Reference Reading Hambley Chapter 10 1 to 10 4 Howe and Sodini Chapter 3 3 3 6 EE40 Summer 2006 Lecture 11 Instructor Octavian Florescu 1 The pn Junction Diode Schematic diagram p type net acceptor concentration NA Circuit symbol ID n type net donor concentration ND cross sectional area AD Physical structure an example VD ID metal SiO2 SiO2 For simplicity assume that the doping profile changes abruptly at the junction EE40 Summer 2006 Lecture 11 VD p type Si n type Si metal Instructor Octavian Florescu 2 Depletion Region When the junction is first formed mobile carriers diffuse across the junction due to the concentration gradients Holes diffuse from the p side to the n side leaving behind negatively charged immobile acceptor ions Electrons diffuse from the n side to the p side leaving behind positively charged immobile donor ions acceptor ions p donor ions n A region depleted of mobile carriers is formed at the junction The space charge due to immobile ions in the depletion region establishes an electric field that opposes carrier diffusion EE40 Summer 2006 Lecture 11 Instructor Octavian Florescu 3 Charge Density Distribution Charge is stored in the depletion region acceptor ions p quasi neutral p region donor ions n depletion region quasi neutral n region charge density C cm3 distance EE40 Summer 2006 Lecture 11 Instructor Octavian Florescu 4 Doping Typical doping densities 1016 1019 cm 3 Atomic density for Si 5 x 1022 atoms cm3 1018 cm 3 is 1 in 50 000 two persons in entire Berkeley wearing a green hat P n junction effect is like EE40 Summer 2006 Lecture 11 Instructor Octavian Florescu 5 Electric Field and Built In Potential 0 p n electric field V cm distance No net current flows across the junction when the externally applied voltage is 0 V 0 potential V kT N A N D ln 2 q ni kT ln 10 60 mV for T 300K q distance built in potential 0 EE40 Summer 2006 Lecture 11 Instructor Octavian Florescu 6 Effect of Applied Voltage p VD n The quasi neutral p and n regions have low resistivity whereas the depletion region has high resistivity Thus when an external voltage VD is applied across the diode almost all of this voltage is dropped across the depletion region Think of a voltage divider circuit If VD 0 forward bias the potential barrier to carrier diffusion is reduced by the applied voltage If VD 0 reverse bias the potential barrier to carrier diffusion is increased by the applied voltage EE40 Summer 2006 Lecture 11 Instructor Octavian Florescu 7 Forward Bias As VD increases the potential barrier to carrier diffusion across the junction decreases and current increases exponentially VD 0 p n The carriers that diffuse across the junction become minority carriers in the quasi neutral regions they then recombine with majority carriers dying out with distance ID Amperes VD Volts Hence the width of the depletion region decreases EE40 Summer 2006 Lecture 11 Instructor Octavian Florescu 8 Reverse Bias As VD increases the potential barrier to carrier diffusion across the junction increases thus no carriers diffuse across the junction VD 0 p A very small amount of reverse current ID 0 does flow due to minority carriers diffusing from the quasi neutral regions into the depletion region and drifting across the junction ID Amperes n VD Volts Hence the width of the depletion region increases EE40 Summer 2006 Lecture 11 Instructor Octavian Florescu 9 I V Characteristic Exponential diode equation I D I S e qVD kT 1 ID A kT 0 026 Volts for T 300K q VD V IS is the diode saturation current function of ni2 AD NA ND length of quasi neutral regions typical range of values 10 14 to 10 17 A m2 Note that e0 6 0 026 1010 and e0 72 0 026 1012 ID is in the mA range for VD in the range 0 6 to 0 7 V typically EE40 Summer 2006 Lecture 11 Instructor Octavian Florescu 10 Depletion Region Width Wj The width of the depletion region is a function of the bias voltage and is dependent on NA and ND Wj NA ND N AND 2 Si q 0 VD If one side is much more heavily doped than the other which is commonly the case then this can be simplified Wj 2 Si 0 VD qN Si 10 12 F cm where N is the doping concentration on the more lightly doped side EE40 Summer 2006 Lecture 11 Instructor Octavian Florescu 11 Junction Capacitance VD p n charge density C cm3 distance The charge stored in the depletion region changes with applied voltage This is modeled as junction capacitance Cj EE40 Summer 2006 Lecture 11 AD Si Wj Instructor Octavian Florescu 12 Summary pn Junction Diode Electrostatics A depletion region in which n and p are each much smaller than the net dopant concentration is formed at the junction between p and n type regions A built in potential barrier voltage drop exists across the depletion region opposing carrier diffusion due to a kT N A N D concentration gradient across the junction 0 ln q n2 At equilibrium VD 0 no net current flows across the junction Width of depletion region W j i 2 Si 0 VD qN decreases with increasing forward bias p type region biased at higher potential than n type region increases with increasing reverse bias n type region biased at higher potential than p type region Charge stored in depletion region capacitance C j EE40 Summer 2006 Lecture 11 AD Si Wj Instructor Octavian Florescu 13 Summary pn Junction Diode I V Under forward bias the potential barrier is reduced so that carriers flow by diffusion across the junction Current increases exponentially with increasing forward bias The carriers become minority carriers once they cross the junction as they diffuse in the quasi neutral regions they recombine with majority carriers supplied by the metal contacts injection of minority carriers Under reverse bias the potential barrier is increased so that negligible carriers flow across the junction If a minority carrier enters the depletion region by thermal generation or diffusion from the quasi neutral regions it will be swept across the junction by the built in electric field ID A collection of minority carriers reverse current VD V EE40 Summer 2006 Lecture 11 Instructor Octavian Florescu 14 pn Junction Reverse Breakdown As the reverse bias voltage increases the peak electric field in the depletion region increases When the
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