Chapter 4 PN Junctions

Transcription

1 /5/14 Chater 4 Junction 4.1 Builing Block of the Junction Theory Donor ion V + I -tye -tye I ioe ymbol Revere bia Forwar bia V junction i reent in erha every emiconuctor evice. Slie (a) Energy Ban Diagram of a Junction -region -region E f E f i contant at equilibrium (b) E c E c E f E v E c an E v are known relative to E f E v (c) E c E f E v E c an E v are mooth, the eact hae to be etermine. () eutral -region Deletion layer eutral -region E c E f E v A eletion layer eit at the junction where n an. Slie

2 /5/ Built-in otential (a) -tye -tye a a (b) q bi E c E f E v V bi (c) Can the built-in otential be meaure with a voltmeter? Slie Built-in otential -region -region n i n n a e e q A kt c qb kt c kt c A ln q B kt q ln n c a i bi B A kt q c ln ni a ln c bi kt q ln a ni Slie

3 /5/14 Gau Law: oion Equation : ermittivity (~1 o for Si) : charge enity (C/cm 3 ) E() E( + ) oion equation Slie Deletion-Layer Moel 4..1 Fiel an otential in the Deletion Layer eutral Region Deletion Layer n eutral Region On the -ie of the eletion layer, = q a E q a q n q a qa qa E ( ) C 1 ( ) E n On the -ie, = q q E ) ( - ) ( Slie

4 /5/ Fiel an otential in the Deletion Layer eutral Region Deletion Layer n eutral Region The electric fiel i continuou at =. a = Which ie of the junction i elete more? A one-ie junction i calle a + junction or + junction Slie Fiel an otential in the Deletion Layer On the -ie, E qa V ( ) ( ) bi n V Arbitrarily chooe the voltage at = a V =. bi, built-in otential n E c E f E v V On the -ie, q ) D ( ) q bi ( ) ( Slie

5 /5/14 W e 4.. Deletion-Layer With eutral Region Deletion Layer eutral Region n V i continuou at = We bi 1 1 q a If a >>, a in a + junction, bi q a What about a + junction? W e bi q where a 1 lighter oant enity Slie EXAMLE: A + junction ha a =1 cm -3 an =1 17 cm -3. What i a) it built in otential, b)w e, c), an )? Solution: 17 a) kt a 1 1 cm bi ln.6v ln 6 q n 1 cm b) W e bi q 6 i / 1V.1 μm c) W e.1 μm ) a μm 1. Å Slie

6 /5/14 V Revere-Biae Junction E c q bi E c E f W e ( bi Vr ) otential barrier q q E f E v E v (a) V = E c a 1 lighter oant enity E c E fn q bi + qv qv E f E v Doe the eletion layer wien or hrink with increaing revere bia? E v (b) revere-biae Slie Caacitance-Voltage Characteritic a Conuctor Inulator Conuctor W e Revere biae junction i a caacitor. C e A W e I C e a goo thing? How to minimize junction caacitance? Slie

7 /5/ Caacitance-Voltage Characteritic C 1 e W A e ( bi V ) q A S 1/C e Caacitance ata Sloe = /q A bi Increaing revere bia V r From thi C-V ata can a an be etermine? Slie EXAMLE: If the loe of the line in the reviou lie i 1 3 F - V -1, the intercet i.84v, an A i 1 m, fin the lighter an heavier oing concentration l an h. Solution: l /( loe q A /( cm 3 ) cm ) kt hl n bi ln 1 i kt cm h e e 15 q n 61 i l q bi I thi an accurate way to etermine l? h?.84 Slie

8 /5/ Junction Breakown I V B, breakown voltage Small leakage Current Forwar Current V R A R C A 3.7 V IC Zener ioe B D A Zener ioe i eigne to oerate in the breakown moe. Slie eak Electric Fiel eutral Region increaing revere bia + a (a) E E increaing revere bia E q E( ) ( bi Vr ) 1/ (b) V B q crit E bi Slie

9 /5/ Tunneling Breakown Fille State - Emty State E c Dominant if both ie of a junction are very heavily oe. E v J G e H / ε I V E E crit 1 6 V/cm Breakown Slie E c E f E v electron-hole air generation Avalanche Breakown imact ionization: an energetic original electron electron generating electron an hole, which can alo caue imact ionization. Imact ionization + oitive feebackavalanche breakown V B Ecrit q E c E fn V B 1 1 a 1 Slie

10 /5/ Forwar Bia Carrier Injection V= V = I= Forwar biae V + E c q bi E f E v q bi qv E fn - qv E c E f Drift an iffuion cancel out Minority carrier injection + E v Slie Forwar Bia Quai-equilibrium Bounary Conition E fn fn n( ) ce ( E E c fn )/ kt E cc E f EE v v e n c ( E E c f )/ kt e ( E Ef)/ kt e ( E n fn E e f )/ kt qv kt fn / The minority carrier enitie are raie by e qv/kt Which ie get more carrier injection? Moern Semiconuctor Device for Integrate Circuit (C. Hu) Slie

11 /5/ Carrier Injection Uner Forwar Bia Quai-equilibrium Bounary Conition n qv kt ( ) ne qv kt ( ) e i n a i n e qv kt e qv kt qv kt n( ) n( ) n n ( e 1) qv kt ( ) ( ) ( e 1) Slie EXAMLE: Carrier Injection A junction ha a =1 19 cm -3 an =1 16 cm -3. The alie voltage i.6 V. Quetion: What are the minority carrier concentration at the eletion-region ege? Solution: n( ) n ( ) qv kt e 1 e 1 cm qv kt e 1 e 1 cm Quetion: What are the ece minority carrier concentration? Solution: n( ) n( ) n cm ( ) ( ) cm -3 Slie

12 /5/ Current Continuity Equation J () area A J ( + ) J ( ) J ( ) A A A q q J ( ) J ( ) q Volume = A J q Slie Current Continuity Equation qd J q q Minority rift current i negligible; J = qd / D L n n L n L an L n are the iffuion length L D L n D n n Slie

13 /5/ Forwar Biae Junction-- Ece Carrier + L - ( ) ( ) qv / kt ( e 1) ( ) Ae / L Be / L ( ) ( e qv / kt 1) e / L, Slie Ece Carrier Ditribution 1. -ie a = 1 17 cm -3 n ' e /L n.5 -ie = 1 17 cm -3 ' e /L 3L n L n L n L L 3L 4L ( ) n( ) n ( e ( e qv / kt qv / kt 1) e 1) e / L / L n,, Slie

14 /5/14 EXAMLE: Carrier Ditribution in Forwar-biae Dioe -tye = 5 cm -3 D =1 cm / = 1 -tye a = 1 17 cm -3 D n =36.4cm / n = Sketch n'() on the -ie. n( ) n qv kt ni qv / kt ( e 1) ( e 1) e 1 cm 17 a 1 -ie 1 13 cm -3 n ( = ) -ie (= n ) Slie EXAMLE: Carrier Ditribution in Forwar-biae Dioe How oe L n comare with a tyical evice ize? L n D n n μm What i '() on the -ie? Slie

15 /5/ Dioe I-V Characteritic J total J total J = J total J n J n = J total J -ie J n J -ie J n -ie J -ie J J ( ) qv kt qd q ( e 1) L n( ) n qv kt n qdn q n ( e 1) Ln D D e e L Ln D D n qv kt Total current J ( ) J n( ) q q n ( e 1) L L n J at all Slie The Junction a a Temerature Senor qv kt I I( e 1) I Aqn i D L Dn L n a What caue the IV curve to hift to lower V at higher T? Slie

16 /5/ Contribution from the Deletion Region n n e qv / kt i et recombination (generation) rate: n i ( e e qv / kt 1) qnw qv / kt i e qv / kt I I( e 1) A ( e 1) τ e I leakage I qnw i A τ e e Sace-Charge Region (SCR) current Uner forwar bia, SCR current i an etra current with a loe 1mV/ecae Slie Charge Storage -ie 1 13 cm -3 -ie Q I n' I Q Q I What i the relationhi between (charge-torage time) an (carrier lifetime)? Slie

17 /5/ Small-ignal Moel of the Dioe V I R C 1 G R q kt I V V I qv / kt I ( e ) I qv / kt ( e 1) DC / kt q V I e qv / kt What i G at 3K an I DC = 1 ma? C Diffuion Caacitance: Q V I V G I DC / kt q Which i larger, iffuion or eletion caacitance? Slie art II: Alication to Otoelectronic Device 4.1 Solar Cell Solar Cell i alo known a hotovoltaic cell. Convert unlight to electricity with 1-3% converion efficiency. 1 m olar cell generate about 15 W eak or 5 W continuou ower. Low cot an high efficiency are neee for wie eloyment. Slie

18 /5/ Solar Cell Baic light Short Circuit I c I Dark IV Eq.(4.9.4) -.7 V V E c Solar Cell IV Eq.(4.1.1) E v + (a) I c Maimum ower-outut I qv kt I ( e 1) I c Slie Direct-Ga an Inirect-Ga Semiconuctor Electron have both article an wave roertie. An electron ha energy E an wave vector k. irect-ga emiconuctor inirect-ga emiconuctor Slie

19 /5/ Light Abortion Light intenity () e α(1/cm): abortion coefficient - 1/α : light enetration eth hc hoton Energy (ev) 1.4 ( m) A thinner layer of irect-ga emiconuctor can aborb mot of olar raiation than inirect-ga emiconuctor. But Si Slie Short-Circuit Current an Oen-Circuit Voltage J () area A J ( + ) If light hine on the -tye emiconuctor an generate hole (an electron) at the rate of G -1 cm -3, Volume = A L G D If the amle i uniform (no junction), / = = GL /D = G Slie

20 /5/14 Solar Cell Short-Circuit Current, I c Aume very thin + layer an carrier generation in region only. + ' L I c G J ( ) L qd ( ) G D G ( ) G(1 e I c D ( ) / q Ge L AJ () AqL G i really not uniform. L nee be larger than the light enetration eth to collect mot of the generate carrier. G / L ) Slie L Oen-Circuit Voltage Total current i I SC lu the V ioe (ark) current: n D i qv / kt I Aq ( e 1) AqLG L Solve for the oen-circuit voltage (V oc ) by etting I= qv / (auming e oc kt 1) n D i qvoc / kt e LG L V oc kt q ln( G / n i ) How to raie V oc? Slie

21 /5/ Outut ower A articular oerating oint on the olar cell I-V curve maimize the outut ower (I V). Outut ow er I c V oc FF Si olar cell with 15-% efficiency ominate the market now Theoretically, the highet efficiency (~4%) can be obtaine with 1.9eV >Eg>1.eV. Larger Eg lea to too low Ic (low light abortion); maller Eg lea to too low Voc. Tanem olar cell get 35% efficiency uing large an mall Eg material tailore to the hort an long wavelength olar light. Moern Semiconuctor Device for Integrate Circuit (C. Hu) Slie Light Emitting Dioe an Soli-State Lighting Light emitting ioe (LED) LED are mae of comoun emiconuctor uch a In an Ga. Light i emitte when electron an hole unergo raiative recombination. E c Raiative recombination E v on-raiative recombination through tra Slie

22 /5/14 Direct an Inirect Ban Ga Tra Direct ban ga Eamle: GaA Direct recombination i efficient a k conervation i atifie. Inirect ban ga Eamle: Si Direct recombination i rare a k conervation i not atifie Slie LED Material an Structure LED wavelength ( m) 1.4 hoton energy 1.4 ( ev ) E g Slie

23 /5/ LED Material an Structure comoun emiconuctor E g (ev) Wavelength (μm) Color Lattice contant (Å) InA In infrare 3.45 In GaA Ga re Re Yellow yellow Green blue violet Blue Al Ga Al 6.. UV 3.11 Light-emitting ioe material binary emiconuctor: - E: GaA, efficient emitter ternary emiconuctor : -E: GaA 1-, tunable E g (to vary the color) quaternary emiconuctor: -E: AlInGa, tunable E g an lattice contant (for growing high quality eitaial film on ineenive ubtrate) Slie Common LED Sectral range Material Sytem Subtrate Eamle Alication Infrare InGaA In Otical communication Infrare -Re GaA GaA Inicator lam. Remote control Re- Yellow Green- Blue AlInGa InGa GaA or Ga Ga or ahire Otical communication. High-brightne traffic ignal light High brightne ignal light. Vieo billboar AlInGa Quantun Well Blue-UV AlInGa Ga or ahire Soli-tate lighting Re- Blue Organic emiconuctor gla Dilay Slie

24 /5/ Soli-State Lighting luminoity (lumen, lm): a meaure of viible light energy normalize to the enitivity of the human eye at ifferent wavelength Incanecent lam Comact fluorecent lam Tube fluorecent lam White LED Theoretical limit at eak of eye enitivity ( λ=555nm) Theoretical limit (white light) ? 683 ~34 Luminou efficacy of lam in lumen/watt Organic Light Emitting Dioe (OLED) : ha lower efficacy than nitrie or aluminie bae comoun emiconuctor LED. Term: luminoity meaure in lumen. luminou efficacy, Slie Dioe Laer Light Amlification (a) Abortion () et Light Abortion (b) Sontaneou Emiion (c) Stimulate Emiion (e) et Light Amlification Light amlification require oulation inverion: electron occuation robability i larger for higher E tate than lower E tate. Stimulate emiion: emitte hoton ha ientical frequency an irectionality a the timulating hoton; light wave i amlifie. Slie

25 /5/ Light Amlification in Dioe oulation inverion i achieve when qv E E E fn f g Equilibrium, V= oulation inverion, qv > Eg Slie Otical Feeback an Laer light out Cleave crytal lane + + Laer threhol i reache (light intenity grow by feeback) when R R G 1 1 R1, R: reflectivitie of the two en G : light amlification factor (gain) for a roun-tri travel of the light through the ioe Light intenity grow until R, when the light intenity 1R G 1 i jut large enough to timulate carrier recombination at the ame rate the carrier are injecte by the ioe current. Slie

26 /5/ Otical Feeback an Laer Dioe Ditribute Bragg reflector (DBR) reflect light with multi-layer of emiconuctor. Vertical-cavity urfaceemitting laer (VCSEL) i hown on the left. Quantum-well laer ha maller threhol current becaue fewer carrier are neee to achieve oulation inverion in the mall volume of the thin mall-eg well. Moern Semiconuctor Device for Integrate Circuit (C. Hu) Slie Laer Alication Re ioe laer: CD, DVD reaer/writer Blue ioe laer: Blu-ray DVD (higher torage enity) 1.55 m infrare ioe laer: Fiber-otic communication 4.15 hotoioe hotoioe: Revere biae ioe. Detect hotogenerate current (imilar to Ic of olar cell) for otical communication, DVD reaer, etc. Avalanche hotoioe: hotoioe oerating near avalanche breakown amlifie hotocurrent by imact ionization. Slie

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