ECE Semiconductor Device and Material Characterization

Transcription

1 ECE 483 Semicoducor Device ad Maerial Characerizaio Dr. Ala Doolile School of Elecrical ad Comuer Egieerig Georgia Isiue of Techology As wih all of hese lecure slides, I am idebed o Dr. Dieer Schroder from Arizoa Sae Uiversiy for his geerous coribuios ad freely give resources. Mos of (>80%) he figures/slides i his lecure came from Dieer. Some of hese figures are coyrighed ad ca be foud wihi he class ex, Semicoducor Device ad Maerials Characerizaio. Every serious microelecroics sude should have a coy of his book! ECE 483 Dr. Ala Doolile

2 Doig Plasma esoace Free Carrier Absorio Ifrared Secroscoy Phoolumiescece all Measuremes Mageoresisace Time of Fligh ECE 483 Dr. Ala Doolile

3 Plasma esoace ad efleciviy Miimum Elecro/hole lasmas are esembles of free carriers ha ca, a cerai frequecies, oscillae i cocer as a grou. Such a lasma resoace exiss whose frequecy / wavelegh (νc/λ) is deermied by he free carrier desiy. * πc K sε Om λ lasma q Good for (or ) > ~0 8 cm -3 Sice lasma resoaces are hard o deec i racice, mos of he ime, free carrier desiies are deermied by emirical refleciviy miimums or free carrier absorio ( A B) C λ lasma ECE 483 Dr. Ala Doolile

4 Free Carrier Absorio Free carrier absorio occurs wihi he coducio or valace bad (o bewee). For examle a coducio elecro is absorbs a I hoo ad is romoed io a higher eergy sae sill iside he coducio bad q λ 3 α fc 3 4π ε Oc * ( m ) I racice, emirical fiig is used α fc Aλ Geerally measured usig Fourier Trasmissio Ifrared (FTI) Secromeer Good for (or ) > ~0 7 cm -3 ECE 483 Dr. Ala Doolile

5 Ifrared Secroscoy Measures doa coceraios (low emeraure) ad ca be used a room emeraure o measure free carrier absorio. Cryogeic emeraures are used o freeze carriers io heir doa groud sae I (very small eergy) ligh is used o excie elecros/holes io heir doa excied sae creaig shar absorio lies Absorio lie iesiy is calibraed o doa desiy Good for N A (or N D ) > ~0 cm -3 ECE 483 Dr. Ala Doolile

6 Ierferomeer Le source be cosπfx f: frequecy of ligh x: movable mirror locaio L L Cosrucive ierferece Maximum deecor ouu L L λ/4 Desrucive ierferece Zero deecor ouu L Movable Mirror Source Beam Slier L Fixed Mirror Samle Deecor L L L L λ/4 ECE 483 Dr. Ala Doolile

7 Fourier Trasform Ifrared Secroscoy Fourier rasform ifrared secroscoy (FTI) I ( x ) B( f )[ cosπxf ] Amliude I f ( x ) Acosπxf df B 0 I f ( x ) 0 B( f )[ cosπxf ]df Af ( f ) I( x ) cosπxf dx ω ω f f f Secrum (siy/y) I a Fourier secrum, frequecy badwidh deermies resoluio. siπxf πxf 0.8 f 0 3 cm x0 3 cm x (cm) Ierferogram ECE 483 Dr. Ala Doolile

8 Ierferogram - Secrum Ierferogram Secrum ECE 483 Dr. Ala Doolile

9 FTI Alicaios Deermie oxyge ad carbo desiy by rasmissio di ECE 483 Dr. Ala Doolile

10 Mobiliies Coduciviy Mobiliy: /qρ Majoriy carrier mobiliy; eed carrier coceraio ad resisiviy Drif Mobiliy: v d /ε Mioriy carrier mobiliy Need drif velociy ad elecric field (ayes-shockley exerime) all Mobiliy: /ρ Need all measureme all mobiliy does o ecessarily equal coduciviy mobiliy MOSFET Mobiliy: MOSFET mobiliy lowes, carriers are scaered a he Si-SiO ierface Ierface is microscoically rough ECE 483 Dr. Ala Doolile

11 Mobiliy Elecro/hole mobiliy is a measure of carrier scaerig i he semicoducor Laice scaerig Silico aoms Ioized imuriy scaerig Doa aoms Ierface scaerig Surface roughess a SiO /Si ierface Polar scaerig Silico bulk 3 MOSFET mobiliy (effecive mobiliy) 0.3 bulk mobiliy l i s Laice Scaerig: Si Vibraio Ioized Imuriy Scaerig: Doa aom Couresy of M.A. Gribelyuk, IBM. ECE 483 Dr. Ala Doolile

12 For bulk semicoducors, laice ad ioized imuriy scaerig domiae he mobiliy.5 T T ; i N.5 i Mobiliies Silico l Mobiliy (cm /V s) Doig Desiy (cm -3 ) i log log T Icreasig N i l (cm /V s) 000 T00 K 50 K 300 K 350 K 400 K 450 K 500 K -Silico N D (cm -3 ) ECE 483 Dr. Ala Doolile

13 Simle all Effec all effec is commoly used durig he develome of ew semicoducor maerial esisiviy, carrier coceraio AND mobiliy ca all be deermied simulaeously Lorez Force deflecio of free carriers by a alied mageic field Temeraure deede all is very owerful ad ca elucidae scaerig mechaisms (loig mobiliy vs T a ), ad deermie doa acivaio eergies Comesaed Doa Freeze ou regime Arrheius sloe resuls i E A Ucomesaed Doa Freeze ou regime Arrheius sloe resuls i E A / A moderae emeraures, ~ (N A - N D ) A elevaed emeraures, ~ i ECE 483 Dr. Ala Doolile

14 Volage iduced by curre I d w B all volage V V ρ Simle all Effec s I ε θ V I z y x 0 0 Lorez Force F q( ε v B) ε Bv x y dv V ε ydy dy 0 w w I qav x qwdv x I seady sae, he mageic force is balaced by he iduced elecric field BI qwd BI qwd BI qd dv BI all coefficie [m 3 /C or cm 3 /C] ECE 483 Dr. Ala Doolile

15 Simle all Effec esisiviy is simly foud from he volage dro alog he legh (o mageic field), ρ dw V s I ρ Carrier desiy r q ; r q (r ~ -, all scaerig facor) Mobiliy q r q r r ECE 483 Dr. Ala Doolile

16 ECE 483 Dr. Ala Doolile Deailed all Effec The all Coefficie for boh elecros ad holes rese i he same maerial is i geeral: ( ) ( ) ( ) ( ) B q B r

17 ECE 483 Dr. Ala Doolile Deailed all Effec The all Coefficie is i geeral: A low fields (B<</ ) Ad a high fields (B>>/ ) ( ) ( ) ( ) ( ) B q B r q r or q r q r ( ) q r he mea ime bewee collisios where τ is τ τ r

18 ECE 483 Dr. Ala Doolile Two Layer all Effec Someimes, a semicoducor has wo differe coducio layers (surface iversio, fermi-level iig, subsrae layers, - jucios or / or / layers) The all coefficie is he a weighed sum of boh layers ad ca be eiher osiive or egaive leadig o cofusio (show for he low B field limi): ad where oal oal oal oal oal

19 ECE 483 Dr. Ala Doolile Two Layer all Effec (more deail) The all coefficie is he a weighed sum of boh layers ad ca be eiher osiive or egaive leadig o cofusio: ( ) ( ) [ ] ( ) ( ) B B oal Low B Field igh B Field ad where oal oal oal oal oal oal

20 ECE 483 Dr. Ala Doolile Two Layer all Effec (more deail) The all coefficie is he a weighed sum of boh layers ad ca be eiher osiive or egaive leadig o cofusio (geerally): ( ) ( ) [ ] ( ) ( ) B B oal

21 all Effec Measuremes Two aroaches: all Bar (5 or 6 coacs) 3 4 (6) 5 Va der Pauw cofiguraio Based o Coformal maig heory Coacs assumed oi sources Uiform hickess Cao coai isolaed (ierior) holes 4 3 ECE 483 Dr. Ala Doolile

22 all Effec Measuremes 4 3 Va der Pauw cofiguraio Measure resisiviy firs by erimeer measuremes Examle: deermie,34 where curre goes i ad leaves ad volage is measured bewee ermials 3 ad 4. Nex deermie 3,4 where curre goes i ad leaves 3 ad volage is measured bewee ermials ad 4. Use: π,34 ρ l() 3,4 F where F is a symmery erm derived from coformal maig heory F is deermied from: l() F r F e r where r cosh l(),34 3,4 Differs some from your ex. For deails see h:// ECE 483 Dr. Ala Doolile

23 all Effec Measuremes 4 Va der Pauw cofiguraio 3 Now measure he all volage usig Crossig cofiguraios Examle: Aly he mageic field ad deermie V 3,4P where curre goes i ad leaves 3 ad volage is measured bewee ermials ad 4. Nex reverse he field ad deermie V 3,4N agai. To fid he shee coceraio (#/cm ) use: ρ q V IB ( ) 3,4P V3,4N where we have ieioally lef ou he roorioaliy cosa I realiy, 8 resisiviy ad eigh hall volage measuremes are made o reduce coac relaed offse volage errors resulig i a equaio ha is of he form: ρ q 8 ( 8x0 ) IB [( V ) ( ) ( ) ( )] 3,4P V3,4N V3,4P V3,4N V4,3P V4,3N V4,3P V4,3N See ex for imora samle geomery cosideraios (if igored, sigifica error ca resul) Differs some from your ex. For deails see h:// ECE 483 Dr. Ala Doolile

24 -V dr ayes - Shockley Exerime Allows mobiliy, diffusio cosa, ad mioriy carrier lifeime o be deermied L Elecric field Subsrae d Emier Collecor V i ( x, ) V ou N 4πD e (x,)/ (x,0) ( x v) 4D τ Time (s) Theory Exerime ECE 483 Dr. Ala Doolile

25 -V dr ayes - Shockley Exerime Allows mobiliy, diffusio cosa, ad mioriy carrier lifeime o be deermied L Elecric field Subsrae d Emier Collecor V i V ou If a leas wo leghs ad wo imes are measured, he FWM of he ime lo, ca be used o (x,)/ (x,0) Time (s) Theory Exerime d d ( d ) d / vdrif ; ; D ; τ 3 ε 6 l d d l( V ou / V d d ) 0.5l( ou d / d ) ECE 483 Dr. Ala Doolile

26 ayes Shockley Exerime ( x, ) N ( x v) ex 4πD 4D τ (x,) (cm -3 ) s τ 0 s s s 0.5 s 0. s (x,) (cm -3 ) d0.05 cm 0.05 cm cm 0. cm Time (s) Time (s) ECE 483 Dr. Ala Doolile

27 MOSFET Effecive Mobiliy Effecive mobiliy deermied from drai curre drai volage characerisics The MOSFET drai curre for small V D (50-00 mv) is Deermie g d I D / V D for low V D Solve for eff I ( W / L) Q V ( W / L) C ( V V ) V D eff N D eff ox G T D eff Lgd WQ Need g d, Q N, V T N WC Lg d ox ( VG VT ) Drai Curre (A) L0.4 m, W5 m ox 9 m Sauraed V G 3 V.5 V.5 V Liear 0.75 V Drai Volage (V) ECE 483 Dr. Ala Doolile

28 MOSFET Effecive Mobiliy I D -V D g d ; C GC -V G Q N ; I D -V G V T I D (A) V G 5 V 4.5 V 4 V 3.5 V 3 V.5 V V.5 V V C GC (F/cm ) QN (C/cm ) V D (V) V G (V) Q N V G C GC dv G ECE 483 Dr. Ala Doolile

29 MOSFET Effecive Mobiliy eff (cm /V s) o o / eff.3.. Sloe θ V G -V T (V) V G -V T (V) eff o θ ( V V G T ) o low-field mobiliy; θ mobiliy degradaio facor ECE 483 Dr. Ala Doolile

30 eview Quesios Wha are he differe mobiliies? Why is he MOS effecive mobiliy less ha he bulk mobiliy? ow is eff mos commoly deermied? Why does he all mobiliy differ from he coduciviy mobiliy ow does a all mobiliy measureme work? ow does he ayes-shockley exerime work? Wha is deermied wih he ayes-shockley exerime? For wha is he ime-of-fligh echique used? ECE 483 Dr. Ala Doolile