ECE606: Solid State Devices Lecture 11 Interface States Recombination Carrier Transport

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1 C606: Sold State eves Leture Iterfae States Reombato Carrer Trasport Gerhard Klmek Outle ) SRH formula adapted to terfae states ) Surfae reombato depleto rego 3) Coluso

2 Surfae Reombato Curret R For sgle level bulk traps. bulk p = ( + ) + ( p + p ) pn T N T = ( p ) p N ( + ) + ( p + p ) T For sgle level terfae trap at R ( s ps ) T = ps d ( + ) + ( p + p ) s s s s s R C = V R d 3 Case : Morty Carrer Reombato R ( ) ( + )( p + ) s0 s0 s0 ps0 = IT d = ps s0 ( + + ) + ( p + p + p ) s0 s0 s s0 s0 s s s0 ps0it d s p + + s ps ps s0 s s0 p d ps s0 IT = s ps ps + + s0 s s0 oor doped s0 + s0 p s0 + p s0 4

3 Cosder the eomator p = + + = + + N s ps s s ps s s0 s s0 s p N ( ) β e = + + ( F ) β e = + + e ( ) β ps ( F ) β s e ( ) β ps ( ) β F F e e s x x = + e + ae x β F s0 + s0 p s0 + p s0 5 Cosder the eomator ( ) β ( ) β e ps e = + + N N = + e + s ( ) β ps ( ) β F F s e F ' F ps At = = + + N N s ps At = F >, x = 0 = + + small At = ' <, = + small + = F s F F ' 6

4 Approxmate the eomator ( ) β ( ) β e ps e = + + N N s F ' F ' for F F otherwse F F ' 7 Itegrated Reombato C R = R = C ps s0 IT p d p + + s ps s V V s0 s s0 F ' F ps s0 p d F F ' 8

5 Surfae Reombato Veloty F F ps s0 IT R p d ' 0 = p = s p g ps IT F F s s0 Surfae reombato veloty 9 Outle ) Nature of terfae states ) SRH formula adapted to terfae states 3) Surfae reombato depleto rego 4) Coluso 0

6 Case : Reombato epleto ( s ps ) IT ( ) R = s ps = β e e + = d ( + ) + ( p + p ) sit s s s s s β IT ps ps e ( ) β e s ( ) β d + d s ~0 p s ~0 R = s IT V ( ) β C e s e ps ( ) β + d Case : Reombato epleto R = = C s IT V s IT ( ) β + e s e ps ( ) s ps e e ( ) ( ) β β d d β + + s ~0 = φ s IT + ps dx s x + 0 P s ~0 = π β s ps IT

7 R Why do doors/aeptors ot at as R-G Ceters? p d ps s0 = s ps ps + + s0 s s0 p N s ps 0 = 0 R A p d ps s0 = s ps ps + + s0 s s0 p N s ps 0 A = A 0 F F ' 3 Summary π R = s ps IT β ' R = p ps IT F F s Iterfae (depleto) Iterfae (morty) R = N p p T Bulk (morty) 4

8 C606: Sold State eves Leture Carrer Trasport Gerhard Klmek Outle ) Overvew ) rft Curret 3) Physs of Moblty 4) Hgh feld effets 5) Coluso RF: Advaed eve Fudmetals, Pages

9 Curret Flow Through Semodutors epeds o hemal omposto, rystal struture, temperature, dopg, et. V I I = G V = q v A Carrer esty veloty Quatum Mehas + qulbrum Statstal Mehas apsulated to oepts of effetve masses ad oupato fators (Ch. -4) Trasport wth satterg, o-equlbrum Statstal Mehas apsulated to drft-dffuso equato wth reombato-geerato (Ch. 5 & 6) 7 No-equlbrum Systems Chapter 5 Chapter 6 vs. I V

10 Summary of Trasport quatos + ( A ) = q p + N N = J r + g t q p = r + g t q J N N N J = qµ + q N N N J P P P = qpµ q p P P P V I 9 Outle ) Overvew ) rft Curret 3) Physs of Moblty 4) Hgh feld effets 5) Coluso 0

11 Meag of ffetve Mass m 0 ħ d + U ψ = ψ rys x + U ext x m0 dx m ħ d + U φ = φ ext x m0 dx rft by letr feld. J = qµ d( m υ) m υ = q dt τ t qτ τ υ( t) = e m x x x x

12 rft by letr feld. qτ υ ( t) = e m t τ x x x x J qτ = ( t, - ps) m µ = qµ (Theory vald oe t > - ps) υ tme frto υ ( ) υ 3 Outle ) Overvew ) rft Curret 3) Physs of Moblty 4) Hgh feld effets 5) Coluso 4

13 Moblty ad Physs of Satterg Tme x x x x µ = qτ m m 0 m Ferm s Golde rule π τ ψ ( x) U ( x) ψ ( x) dx ħ 5 Phoo ad Iozed Impurty Satterg Iozed mpurty T τ ~ N 3 m 0 Hgher temperature, more phoo satterg m τ ~ T 3 6

14 Multple Satterg vets Iozed mpurty Phoo satterg others. µ = µ + µ ph ph II µ phµ II µ = µ + µ µ µ phµ II m m ph µ µ = + µ + II µ 0 = µ m + + ( NI N0 ) α II m = τ τ τ τ II ph s m = µ qτ Matthesso Rule. 7 Model for Iozed mpurty Satterg µ + µ N N α 0, = µ,m + ( I 0, ) m µ,m 8

15 Temperature-depedet Moblty 3 ~ T µ τ 9 Outle ) Overvew ) rft Curret 3) Physs of Moblty 4) Hgh Feld ffets 5) Coluso 30

16 Moblty at Hgh Felds? υ x x x x qτ υ = µ µ + C N 0 N m N What auses veloty saturato at hgh felds? Where does all the moblty formula deve smulator ome from? 3 Veloty Saturato S/Ge = 0 J = J + J = 0 J = J J > J + J = > 3 J + J J J = J J J

17 Veloty Overshoot & Iter-valley Trasfer Larger m Smaller m What type of satterg would you eed for ter-valley trasfer? 33 opg depedet Resstvty J = ρj J = q( µ + µ p p) ρ = q( µ + µ p) = for -type qµ N = for p-type qµ N p V A p 34

18 Coluso ) Posso ad drft-dffuso equatos form a omplete sem-lassal trasport model that a expla wde varety of deve pheomea. ) rft urret results from respose of eletros/holes to eletr feld. The physs of moblty s omplex ad materal depedet. 3) Costay of low-feld moblty a be heked by expermets. 35