EECS 15 Sprig 4, Lecture 1 Lecture 1: P-N Diodes EECS 15 Sprig 4, Lecture 1 Aoucemets The Thursday lab sectio will be moved a hour later startig this week, so that the TA s ca atted lecture i aother class Readig: Start chapter 3 i the text 1
EECS 15 Sprig 4, Lecture 1 Cotext I the last few lectures, we looked at the carriers i a semicoductor, how may there are, ad how they move (trasport) Mass actio law, Doors, Acceptors Drift Diffusio I the this lecture, we will apply these cocepts to P-N diodes EECS 15 Sprig 4, Lecture 1 Trasport summary The umber of majority carriers i a eutral semicoductor goes accordig to the umber of Doors or acceptors, ad the umber of miority carriers is foud from the law of mass actio For -type material: i N d N a p For p-type material: p N a N d i p The total curret is give by the sum of drift ad diffusio: d J = J drift + J diff = qµ E + qd dx
EECS 15 Sprig 4, Lecture 1 Electrostatics summary I oe dimesio, the electrostatics equatios reduce to the E field growig or dimiishig depedig o the et charge: ρ( x') E( = E( x) + dx' ε x x Which ca also be writte as a differetial equatio for the potetial (voltage). d φ ( ρ( = dx ε EECS 15 Sprig 4, Lecture 1 Net Charge The et charge desity i a semicoductor is calculated from the umber of charge carriers ad fixed charges i a locatio: ρ( = q p( ( + N ( N ( ( ) If a regio does ot have the right umber of electros or holes to cacel the amout of charge from the dopats, the fixed charge of the dopats will ifluece the electric fields. d a 3
EECS 15 Sprig 4, Lecture 1 The chicke ad the Egg We eed to fid both the positio of the charges, which will create the E field, but the E field will also push the charges aroud. Fortuately, i most cases we will be able to break this up ito two simple cases: Regios where the mobile holes or electros are swept out by a E field, ad cotribute egligibly to the charge Regios where eutrality is maitaied, ad there is o E field The regios i which the amout of charge from mobile carriers is egligible are called depletio regios EECS 15 Sprig 4, Lecture 1 The PN juctio The PN juctio is just a semicoductor where oe regio doped with doors is ext to aother doped with acceptors. PN juctios are usually made by implatatio or diffusio, or sometimes by growig a semicoductor with dopats as a ew layer. P Type N Type 4
EECS 15 Sprig 4, Lecture 1 Neutrality Notice that if the electros ad holes were to just to stay where they were, the the whole volume would be eutral, ad there would be o electric field. However, there is a tremedous cocetratio gradiet at the joit, for both the electros ad the holes. Because of the large gradiet i the cocetratio, the electros will start to wader ito the p type material, ad the holes will start to wader ito the type material What stops the electros ad holes from spreadig out to a uiform cocetratio? P Type - - - - - + + + + N Type EECS 15 Sprig 4, Lecture 1 Establishmet of a potetial barrier What stops the carriers from spreadig out uiformly: The movemet of the carriers will cause a et charge to be developed, ad a opposig E field Excess carriers ( p > i ) will mea that recombiatio will be faster tha geeratio, ad the extra populatio will recombie ad go away. The ed result will be a regio depleted of electros ad holes, ad therefore left with a charge: P Type Fixed egative charges Fixed positive charges N Type 5
EECS 15 Sprig 4, Lecture 1 Drift ow opposes diffusio The E field which is established by the fixed charges left bare i the depletio regio stops the carriers from diffusig across. The diffusio is exactly balaced by the drift caused by the E field i thermal equilibrium. P Type Fixed egative charges Fixed positive charges N Type EECS 15 Sprig 4, Lecture 1 PN Juctio Fields p = Hole populatio I most cases, the populatios chage by may orders of magitude, so p quickly becomes small compared to N a P Type N a E Fixed egative charges Fixed positive charges p ( J p diff J p drift x p x p N Type = N i d = N d = N i a E J diff J drift Electro populatio + + Depletio Regio: mobile carrier desity << fixed charge up to ear the edges 6
EECS 15 Sprig 4, Lecture 1 Net Charge i Depletio Regio To solve for the electric fields, we eed to write dow the charge desity i the trasitio regio: ρ ( = q( p + N d N a I the p-side of the juctio, there are very few electros, some holes, ad the fixed acceptors: ρ q( p N ) < x ( a Sice the hole cocetratio is reduced o the p- side, the et charge is egative: ) x p < N a > p ρ ( < EECS 15 Sprig 4, Lecture 1 Charge o N-Side Aalogous to the p-side, the charge o the -side is give by: ( x ) q( + N ρ d < x < x The et charge here is positive sice: N d > ) ρ ( > = N d = N i a E J diff + + Depletio Regio 7
EECS 15 Sprig 4, Lecture 1 Carrier Cocetratio ad Potetial If we let the diode come to thermal equilibrium, the electro ad hole curret desities each must be zero everywhere: J ( = = q( µ E( + qd d( µ = ( E dx D d( dx q dφ( x = ( kt dx ) Where V th kt dφ( = q kt = q d( = V ( th d( ( EECS 15 Sprig 4, Lecture 1 Carrier Cocetratio ad Potetial () We have a equatio relatig the potetial to the carrier cocetratio kt dφ( = q If we itegrate the above equatio we have φ( φ( x d( = V ( ) = V ( l ( x ) We defie the potetial referece to be itrisic Si: th th d( ( φ( x ) = for ( x ) = i 8
EECS 15 Sprig 4, Lecture 1 Carrier Cocetratio Versus Potetial The carrier cocetratio is thus a fuctio of potetial x e φ ( / V ( ) = th i Check that for zero potetial, we have itrisic carrier cocetratio (referece). If we do a similar calculatio for holes, we arrive at a similar equatio p x e φ ( / V ( ) = th i Note that the law of mass actio is upheld at every poit x: φ ( / V ( / V ( p( i e th φ th = e = i EECS 15 Sprig 4, Lecture 1 The Dopig Chages Potetial Due to the logarithm, the potetial chages liearly for expoetial icrease i dopig: φ( = V th ( ( ( l = 6mV l 6mV l1 log 1 1 i ( φ( 6mV log 1 1 p( φ( 6mV log 1 1 Quick calculatio aid: For a p-type cocetratio of 1 16 cm -3, the potetial is -36 mv N-type materials have a positive potetial with respect to itrisic Si (To remember this: a type material eeds a positive potetial to keeps its electros from leakig out to the itrisic material ext to it!) i 9
EECS 15 Sprig 4, Lecture 1 PN diode equilibrium Voltage So i thermal equilibrium, at room temperature, a silico PN diode will have a potetial differece betwee the p ad sides of: ( p( φ 6mV log 6mV log i i φ ( p( 6mV log i EECS 15 Sprig 4, Lecture 1 Have we iveted a battery? Ca we haress the PN juctio ad tur it ito a battery? N D N A N DN A φbi φ φ p = V th l + l = Vth l i i i? Numerical example: φ bi 15 N DN A 1 1 = 6mV l = 6mV log 1 15 = i 6mV 1
EECS 15 Sprig 4, Lecture 1 Bad edge diagram If we draw a diagram of the eergies of the edges of the valece bad ad the coductio bad, we ca see that the Fermi level, the level that the electros are filled up to, is the same across the juctio. The potetial we calculated was the differece betwee the eergies of the coductio bad i the two regios. P type φ The Fermi level is always flat i thermal equilibrium N type EECS 15 Sprig 4, Lecture 1 Bad edge diagram If the p diode is lightly doped o each side, the the eutral regios have fewer carriers, the Fermi level is further from the bad edge i each case, ad the potetial differece is less. P type φ The Fermi level is always flat i thermal equilibrium N type 11
EECS 15 Sprig 4, Lecture 1 Abrupt juctio, full depletio model I may cases, it is sufficiet to cosider a abrupt chage from p type to type dopat If the umber of doors o the side, ad the umber of acceptors o the p side are >> i, the we ca make the approximatio that the et charge desity ρ( is: x p + qn d { { x Where x ad x p are the widths of the depletio regios extedig ito their respective doped regios qn a EECS 15 Sprig 4, Lecture 1 Forward bias Uder a forward bias, a voltage is applied which reduces the built i field, lettig the mobile carriers diffuse toward each other, ad built up a populatio which is larger tha the equilibrium populatio. The curret ca become very large (hudreds of amps for a big diode) φ Smaller tha equilibrium P type N type p > ( ( i 1
EECS 15 Sprig 4, Lecture 1 Reverse bias Uder a reverse bias, a voltage is applied which icreases the built i field, pullig the mobile carriers out of the depletio regio. The drift curret rises oly slightly, because oly the miority carriers ad geerated carriers get pulled across the regio. φ Larger tha equilibrium P type N type p < ( ( i EECS 15 Sprig 4, Lecture 1 Forward or reverse bias (abrupt juctio, full depletio model) Forward bias x p + qn d { { Depletio regio arrows x qn a Reverse Bias x p + qn d { { Depletio regio is larger qn a x I ay case: qn x = qn a p d x 13
EECS 15 Sprig 4, Lecture 1 Applicatio: rectifier The PN juctio ca block curret i oe directio, while lettig it pass if the voltage is reversed I the forward biased (curret passig) coditio, a voltage is applied to push the mobile carrier regios toward each other. They recombie at a higher rate, ad the diode coducts. I the reverse biased coditio, the mobile carriers are pulled away from each other, ad there is little curret. EECS 15 Sprig 4, Lecture 1 Applicatio: Solar Cell If we put a PN juctio i bright light, the light is absorbed by raisig electros from the valece bad to the coductio bad, thereby creatig a electro ad a hole for each photo absorbed. The excess electros ad holes get swept out of the depletio regio, ad there is a et curret. If the voltage is allowed to rise a little, the positive curret ad voltage act just like a battery, supplyig DC power. 14
EECS 15 Sprig 4, Lecture 1 Applicatio: Lightwave receiver (detector) Similarly to a solar cell, light hits a PN diode, ad electros ad holes are geerated. This causes a excess drift curret, ad ca be amplified to act as a receiver for optical sigals from a optical fiber. EECS 15 Sprig 4, Lecture 1 Applicatio: Light Emittig Diode I a LED, a diode made of a direct badgap semicoductor such as Gallium Arseide is forward biased. The excess holes ad electros the recombie, ad emit light. Semicoductor lasers for optical commuicatios work i a similar way. 15
EECS 15 Sprig 4, Lecture 1 PN Juctio Capacitor Uder thermal equilibrium or reverse bias, the PN juctio does ot draw ay curret But otice that a PN juctio stores charge i the space charge regio (trasitio regio) Sice the device is storig charge, it s actig like a capacitor Positive charge is stored i the -regio, ad egative charge is i the p-regio: qn x = qn a po d x o EECS 15 Sprig 4, Lecture 1 Reverse Biased PN Juctio What happes if we reverse-bias the PN juctio? + φ + V bi D V < D V D Sice o curret is flowig, the etire reverse biased potetial is dropped across the trasitio regio To accommodate the extra potetial, the charge i these regios must icrease If o curret is flowig, the oly way for the charge to icrease is to grow (shrik) the depletio regios 16
EECS 15 Sprig 4, Lecture 1 Curret Uder Reverse Bias p + VD φ p Uder thermal equilibrium curret is zero If we apply a reverse bias, we are icreasig the barrier agaist diffusio curret Drift curret is low sice the field oly moves miority carriers across juctio I fact, curret is ot zero but very small sice the miority carrier cocetratio is low. Miority carriers withi oe diffusio legth of juctio ca cotribute to a reverse bias curret. This is more or less idepedet of the applied bias φ φ + V E E φ p X X d V ) d ( D D EECS 15 Sprig 4, Lecture 1 Abrupt juctio, full depletio model For the Abrupt juctio, full depletio model of the PN diode, we ca fid the potetial as a fuctio of positio by itegratig over the charge distributio ρ( x p + qn d { { x Where x ad x p are the widths of the depletio regios extedig ito their respective doped regios qn a 17
EECS 15 Sprig 4, Lecture 1 Abrupt juctio, full depletio model We fid the potetial from: d φ ( ρ( = dx ε Itegratig twice, we fid: qna φ( = x + Apx + B x p p < x < ε qnd φ( = + x + A x + B < x < x ε I the ext lecture, we will use the boudary coditios to fid x, ad the values of the costats. x p 18