Lecture 4: Heterojunction pn-diode

Transcription

1 Lecture 4: Heterojuctio -ioe Lecture 4, High See Devices 16 1

2 Lecture 4: Heterojuctio P-ioe + heterojuctio uer equilibrium + heterojuctio uer exterl s Gre heterojuctios + gre heterojuctio: Curret -tye IP + - tye I.53 G.47 As -tye I.53 G.47 As Forms olr trsistor. Reig Guie i Liu: 73-93, 11-16, Lecture 4, High See Devices 16

3 Bsic + structure omeclture + DE c F Covetio: Citl or lower cse eotes mgitue o bg E F E E g DE v E g Abrut oig roiles: +, - + P- + P + (citl letter lrger bg. + higher oig) E x x F < i E <E v F > i E <E c Gre (bg) juctios re lso ossible Therml Eqiuilibrium: Fermi level ees to be costt! Chrge trser orms buil i otetil Lecture 4, High See Devices 16 3

4 -x <x< From chrge istributio to otetil r ε x = e V -x -x x -x -x x -x -x x ρ(x) = ε x = q ε (x + x ) V x = q ε x + x x <x<x ρ(x) = ε x = q ε (x x) V x = q ε x x x + φ ε x x = ρ ε ε x = 1 ρ x x ε ε x x = V(x) V x = ε x x V x o = φ = V() φ = V V() φ + φ = qv Lecture 4, High See Devices 16 4

5 Drw + bs eutrl Regio Deletio Regio eutrl Regio E C x = E c x qv(x) + E v x = E v x qv(x) o exterl s: =, = x=- = x= 1. Obti/Clculte E g, DE c,f F. Determie,,, E g DE v DE c E g F E g DE e q c F q e 1 e F e q Lecture 4, High See Devices 16 5

6 Exmle tyicl + juctio Exmle: + : IGAs ( A =1e19 cm -3 V =6e18) : IP D =(e17 cm -3 C =3e17) DE c =.5 ev E g =.75 ev 1. Obti/Clculte E g, DE c,f F. Determie,,, E E c kt l C + c c 1/4 Φ =. mev o-egeerte (+) Φ P = 8. mev Degeerte (-) E g DE e q c F q e 1 e F e q Lecture 4, High See Devices 16 6

7 Built i otetil: + juctio DE c F The buil i otetil is the sertio betwee the two ermilevels beore equlibrium! E g E g F DE v E E g g F DE DE q c F v F q q F F F Homojuctio Heterojuctio Lecture 4, High See Devices 16 7

8 miute exercise rw equilibrium bs E E E x x x x x x Lecture 4, High See Devices 16 8

9 Gre Juctio: + + grig E c (x) Bs vries grully i the -sie over istce gre I eletio regio > gre we c clculte,, i the sme wy s beore! Resultig bs sum o electrosttic otetil vritio b-g vritio E v (x) E C x = E c x qv(x) E v x = E v x qv(x) gre Lecture 4, High See Devices 16 9

10 miute excercise gre juctio - E c Sketch the b igrm i equlibrium! + E v Lecture 4, High See Devices 16 1

11 + - juctio uer exterl s eutrl Regio Deletio Regio eutrl Regio Extrl s icreses otetil ierece betwee the two reservoirs: + DE=qV -V φ φ φ φ E x=- Reservoir or holes = +V - x= Reservoir or Electros -qv E V P V V V V ivies ito two rts, V V egtive V lrger eletio regio (reverse se juctio) V e e V Qusi-ermi levels or the reservoirs e q V V e q Lecture 4, High See Devices 16 11

12 Curret clcultio: Crrier Cocetrtio Gre Juctio Positive Bis - E +qv E E Assume o recomtio smll currets: the qusi ermi levels re costt i the elete regio E E ex c kt ( ( ) ) ( ( c qv )ex kt qv )ex kt ( ( ) ) WG i G i E E Positive V : Icrese i miority crrier cocetrtio t eges o eletio regio - egtive V : Decrese i miority crrier cocetrtio Lecture 4, High See Devices 16 1

13 Gre juctios: Crrier Cocetrtio E - Recomtio, () E V x Recomtio Ijecte crriers will iuse recome with mjority crriers D x x x x L L D () = excess electro cocetrtio L = miority electro iusio legth x x x L Holes o -sie Lecture 4, High See Devices 16 13

14 Gre juctios: Evlutio o curret (Log ioe) - δ x = Ae x x δ = () L L + Be δ = : B= E E V miority (), () J J qd q e x x qd qe x x qd x qd x x Hole curret Electro curret I D WG G D i D i qv qa ex 1 L L kt D >D, i WG << i G Lecture 4, High See Devices 16 14

15 Gre juctios: Short ioe (), () I short ioe the excess electro/hole cocetrtios re orce to zero ue to eitxil thickesses ( ) ( ) B E - B - E δ x δ L = δ = δ E = x sih E x L δ x = sih E x L sih x = ex e x sih x x + O(x ) I D WG G D i D i qv qa ex 1 E B P kt Lecture 4, High See Devices 16 15