EE40 Lecture 32 Prof Chang Hasnain 11 21 07 Reading Supplementary Reader EE40 Fall 2007 Slide 1 Prof Chang Hasnain Electron and Hole Densities in Doped Si Instrinsic undoped Si n p ni np ni 2 N doped Si Assume each dopant contribute to one electron n N d N c e E f Ec kT p ni 2 N d p doped Si Assume each dopant contribute to one hole p N a N v e Ev E f kT p ni 2 N a EE40 Fall 2007 Slide 2 Prof Chang Hasnain Summary of n and p type silicon Pure silicon is an insulator At high temperatures it conducts weakly If we add an impurity with extra electrons e g arsenic phosphorus these extra electrons are set free and we have a pretty good conductor n type silicon If we add an impurity with a deficit of electrons e g boron then bonding electrons are missing holes and the resulting holes can move around again a pretty good conductor p type silicon Now what is really interesting is when we join n type and p type silicon that is make a pn junction It has interesting electrical properties EE40 Fall 2007 Slide 3 Prof Chang Hasnain Junctions of n and p type Regions p n junctions form the essential basis of all semiconductor devices A silicon chip may have 108 to 109 p n junctions today How do they behave What happens to the electrons and holes What is the electrical circuit model for such junctions n and p regions are brought into contact Note that the textbook has a very good explanation EE40 Fall 2007 Slide 4 Prof Chang Hasnain The pn Junction Diode Schematic diagram p type net acceptor concentration NA n type net donor concentration ND cross sectional area AD Physical structure an example For simplicity assume that the doping profile changes abruptly at the junction EE40 Fall 2007 Circuit symbol ID ID VD metal SiO2 VD SiO2 p type Si n type Si metal Slide 5 Prof Chang Hasnain Depletion Region Approximation 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 Fall 2007 Slide 6 Prof Chang Hasnain 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 Fall 2007 Slide 7 Prof Chang Hasnain 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 Fall 2007 Slide 8 Prof Chang Hasnain Two Governing Laws Gauss s Law describes the relationship of charge density and electric field r r Qencl 1 dV S E dA V dE dx 1 x E x E x0 x dx x0 Poisson s Equation describes the relationship between electric field distribution and electric potential d 2 x dE x x 2 dx dx x x x0 E x dx x0 EE40 Fall 2007 Slide 9 Prof Chang Hasnain qN a 0 x qN d Depletion Approximation 1 x x 0 and x 0 x x x x p0 0 x x n 0 0 p0 o x p E0 x qN a x x po s xno E0 x x E0 x n0 qNd n x x no xpo x x po x 0 qN a 0 x qN d dx E0 xno xno x 0 s s qN d x xno s Gauss s Law E 0 x p n xpo 0 x xno xno x x EE40 Fall 2007 Slide 10 Prof Chang Hasnain Depletion Approximation 2 p xpo 2 s xno2 qNa 2 s xno n xpo2 0 x n 1017 p 105 P 10 n 104 18 xpo EE40 Fall 2007 x qNa x po qNd xno E0 0 s s Poisson s Equation qNd E0 x Slide 11 xno x Prof Chang Hasnain EE40 Lecture 33 Prof Chang Hasnain 11 26 07 Reading Supplementary Reader EE40 Fall 2007 Slide 12 Prof Chang Hasnain Depletion Approximation 3 x x x po x po 0 x E0 x dx 0 x po qN a x x po dx 0 s x qN a x x dx x dx xpo po s x po 0 x qN a x x po 2 2 s x po x 0 x x 0 0 0 x E0 x dx 0 0 qN d qN a x xno dx 0 x po 2 s 2 s x x qN d qN a x dx xno dx x po 2 0 0 s 2 s qN d qN a 2 0 x x 2 xno x x po 2 2 s 2 s EE40 Fall 2007 Slide 13 0 x xno Prof Chang Hasnain Effect of Applied Voltage VD p 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 Fall 2007 Slide 14 Prof Chang Hasnain Depletion Approx with VD 0 reverse bias p xp xpo E0 x n xno x n x qNa x po qNd xno E0 0 s s Higher barrier and few holes in np 105 type lead to little current 0 x qNa qNd bi qVD Built in potential bi xno2 xpo2 2 s 2 s n 1017 P 1018 bi n 104 x xp xpo xnoxn EE40 Fall 2007 Slide 15 Prof Chang Hasnain Depletion Approx with VD 0 forward bias p xpo x E0 x p xnxno n x qNa x po qNd xno E0 0 s s Poisson s Equation Lower barrier and large hole electron density at the right places lead to large current 0 x qNa qNd Built in potential bi xno2 xpo2 P 10 18 n …
View Full Document
Unlocking...