Lecture 3 OUTLINE Semiconductor Basics cont d Carrier drift and diffusion PN Junction Diodes Electrostatics Capacitance Reading Chapter 2 1 2 2 EE105 Fall 2011 Lecture 3 Slide 1 Prof Salahuddin UC Berkeley Electrical Resistance I V W t homogeneously doped sample L V L Resistance R I Wt Unit ohms where is the resistivity EE105 Fall 2011 Lecture 3 Slide 2 Prof Salahuddin UC Berkeley Carrier Diffusion Due to thermally induced random motion mobile particles tend to move from a region of high concentration to a region of low concentration Analogy ink droplet in water Current flow due to mobile charge diffusion is proportional to the carrier concentration gradient The proportionality constant is the diffusion constant dp J p qD p dx Notation Dp hole diffusion constant cm2 s Dn electron diffusion constant cm2 s EE105 Fall 2011 Lecture 3 Slide 3 Prof Salahuddin UC Berkeley Diffusion Examples Linear concentration profile constant diffusion current Non linear concentration profile varying diffusion current x p N 1 L J p diff EE105 Fall 2011 p N exp dp qD p dx N qD p L Lecture 3 Slide 4 J p diff x Ld dp qD p dx qD p N x exp Ld Ld Prof Salahuddin UC Berkeley Diffusion Current Diffusion current within a semiconductor consists of hole and electron components dp dn J p diff qD p J n diff qDn dx dx dn dp J tot diff q Dn Dp dx dx The total current flowing in a semiconductor is the sum of drift current and diffusion current J tot J p drift J n drift J p diff J n diff EE105 Fall 2011 Lecture 3 Slide 5 Prof Salahuddin UC Berkeley The Einstein Relation The characteristic constants for drift and diffusion are related D kT q kT Note that 26mV at room temperature 300K q This is often referred to as the thermal voltage EE105 Fall 2011 Lecture 3 Slide 6 Prof Salahuddin UC Berkeley The PN Junction Diode When a P type semiconductor region and an N type semiconductor region are in contact a PN junction diode is formed V D ID EE105 Fall 2011 Lecture 3 Slide 7 Prof Salahuddin UC Berkeley Diode Operating Regions In order to understand the operation of a diode it is necessary to study its behavior in three operation regions equilibrium reverse bias and forward bias VD 0 EE105 Fall 2011 VD 0 Lecture 3 Slide 8 VD 0 Prof Salahuddin UC Berkeley Carrier Diffusion across the Junction Because of the differences in hole and electron concentrations on each side of the junction carriers diffuse across the junction Notation nn electron concentration on N type side cm 3 pn hole concentration on N type side cm 3 pp hole concentration on P type side cm 3 np electron concentration on P type side cm 3 EE105 Fall 2011 Lecture 3 Slide 9 Prof Salahuddin UC Berkeley Depletion Region As conduction electrons and holes diffuse across the junction they leave behind ionized dopants Thus a region that is depleted of mobile carriers is formed The charge density in the depletion region is not zero The carriers which diffuse across the junction recombine with majority carriers i e they are annihilated quasiquasineutral neutral region width Wdep region EE105 Fall 2011 Lecture 3 Slide 10 Prof Salahuddin UC Berkeley The Depletion Approximation Because charge density 0 in the depletion region a large E field exists in this region In the depletion region on the N side dE qN D dx si si qN D x b E si x qND a b qNA x In the depletion region on the P side dE qN A dx si si qN A a x E si aN A bN D EE105 Fall 2011 Lecture 3 Slide 11 Prof Salahuddin UC Berkeley Carrier Drift across the Junction EE105 Fall 2011 Lecture 3 Slide 12 Prof Salahuddin UC Berkeley PN Junction in Equilibrium In equilibrium the drift and diffusion components of current are balanced therefore the net current flowing across the junction is zero J p drift J p diff J n drift J n diff J tot J p drift J n drift J p diff J n diff 0 EE105 Fall 2011 Lecture 3 Slide 13 Prof Salahuddin UC Berkeley Built in Potential V0 Because there is a large electric field in the depletion region there is a significant potential drop across this region qp p E qD p x2 p dV D p x1 dp dx dp dV p p D p dx dx pp dp p pn V x1 V x2 Dp p ln pp pn kT N ln 2 A q ni N D kT N A N D V0 ln 2 q ni EE105 Fall 2011 Lecture 3 Slide 14 Unit Volts Prof Salahuddin UC Berkeley Built In Potential Example Estimate the built in potential for PN junction below Note that EE105 Fall 2011 kT ln 10 26mV 2 3 60mV q N P ND 1018 cm 3 NA 1015 cm 3 Lecture 3 Slide 15 Prof Salahuddin UC Berkeley PN Junction under Forward Bias A forward bias decreases the potential drop across the junction As a result the magnitude of the electric field decreases and the width of the depletion region narrows x qND a b qNA x ID V x V0 b EE105 Fall 2011 0 a x Lecture 3 Slide 16 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 3 Slide 17 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 3 Slide 18 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 …
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