Lecture 12: HEMT AC Properties

Transcription

1 Lecure : HEMT A Proeres Quas-sac oeraon Transcaacances -araeers Non-quas ac effecs Parasc ressances / caacancs f f ax ean ue for aer 6: { sk MEFET ars} (.e. sk an MEFET ars brefl rea N ars) Lecure Hh ee evces 0

2 Quas-ac oluon I rf + onnu nonlnear no eneral analc soluon exss n u u x x x u x Assue quas-sac soluons: annel oenal (an hus he annel are) reacs nsanounsl o an anes n v s v s. a=0 v s () I = V T = = Lecure Hh ee evces 0

3 Non-Quas-ac oluon Ths aroa s onl reall accurae for escales loner ha he nrnsc rans e r Q I hares has o be sule fro he source ransen nvolves a are-fron s sll a ver useful aroxaon! u (0 ) v V n u u x x T x u x a=0 a=0 v s () I u ( 0 ) a u (0 ) = V T = = Lecure Hh ee evces 0

4 Ternal ares Neave annel ares ves ono ran an source ares Posve are on ae ernal o ake evce neural ae are: Q ( ) L L x Wox uh x x uh (0 ) av s v v WLoxv s VT L 0 0 Q Q Q a a a Q efnon of ran are: I L Wox Q ( ) xu H ox s T L Q x xx WL v V Q V s =0.5V V s =.0V Q Q x 6a a 8a 4 5 a V =0.7V Q Q V =0.V V T =-0.5V In sauraon: a=0 Q /Q =40/ Q V (V) V (V) Lecure Hh ee evces 0 4 Q

5 Transcaacances Q V Q V Q V WL WL Q V ox WL ox 5 WL ox 4a a a a a a 4a a ox 5 a 8a 9a a a a Noe ha Lecure Hh ee evces 0 5

6 nues excercse Q V WL ox a a a Q V WL ox 5 4a a a a I a=0 V Wha s he hscal reason ha n sauraon =0 an > 0?? Lecure Hh ee evces 0 6

7 Q v Lare an sall snal Moel oon ource ( ) v I v v s ( ) v s ( ) v s v v s vs v s vs Q v ( ) v ( ) vs( ) v s I s s v v s vs v s vs s oon source: v s 0 v v s v v s For sall snal : I 0 I V v s V I V V V vs vs V v s I V V v v v v W W ox n oxn V VT a V VT L L Lecure Hh ee evces 0 7 a

8 Quas-sac oon ource all nal -araeers v v s s v s v s v s v s v s v e e j j v s v e s e j j v v s s j j j j As wh he HBT we can also ransfor -araeers o an araeers Lecure Hh ee evces 0 8

9 All nne caacances Q V Q Q Q + Q +Q +Q + V Q -Q +Q -Q x Q -Q Q / V x x = f x= x =- oherwse x Q -Q +Q -Q Q+Q Q -Q V Known: Q Q Q Lecure Hh ee evces 0 9 V Q Q +Q +Q =0 s s V Q an solve for all x s s ss V Q s s ss s 0 0 V s

10 all nal Hbr- oel v v s s v s = s =0 j j j j - (-)v - + ae v s ran s s v s ource = Lecure Hh ee evces 0 0

11 Trans Te (arb uns) Quas ac rans e f rs Q I n L 4 a a V a a VT Lnear auraon We exec non-quas-sac effecs o be oran for hh frequences Or when he ranssor s ee n he lnear reon sall! V (V) Lecure Hh ee evces 0

12 all snal non-quas sac n u u x x U H j I W n I ox x u x U H Assue sall snal snusoal erurbaon: u x UH x u xe j x I x xe H j / U U Iˆ ju U Iˆ ju / H H / Î s he ofe Bessel funcon H Exress Î as a seres exanson an solve for u (x) fro bounar conons (ver eous alebra see ) H / H Lecure Hh ee evces 0

13 Non : hannel essance N N j j j j j j / 0 a a j / 0 / 0 a a j / 0 Essenall all correcons are zero/sall f << 0... Afer len of alebra one obans he N -araeers V V 0 n L 4 a a 5 ( a) T 0 s ae Exce for he annel ressance: ource s r e a 5a 0a a 0 a a s N r r oran when s sall.e. No full lnear reon / sall V s ae s r r ran j( / 0 ) Lecure Hh ee evces 0 ource

14 uar hbr ran ae Quas-ac ran v v ource s s ource ( j / 0 ) ae r s r Non Quas-ac ource ran j( / 0 ) s 5 + v - In sauraon:a=0 4 j v Lecure Hh ee evces 0 4

15 Parascs: ource ran an ae essance ource ran Two ars: conac ressance annel ressance ror o acve reon c lea lea c H coh L W lea HLs / W H ae-eal shee ressance: ae ressance (slar o base ressance for a HBT): W L H H Lecure Hh ee evces 0 5

16 Exrnsc an nrnsc I When easurn he evce ransconucance One easures =I /V s The nrnsc evce ransconucance s =I /V s ( ) V s V s ( ) The easure exrnsc s saller han ue o s an! (For hose of ou who have one crcu esn s a source eenerac ressance) Lecure Hh ee evces 0 6

17 Parascs caacances s = s All caacances are have relae woernal arallell-lae lke caacances s No ranssor effec so x = x Parasc caacances are n arallell o evce caacances: s oe arasc can be he onan caacance e.. =0 for a=0 = s Lecure Hh ee evces 0 7

18 f f ax Lecure Hh ee evces 0 s j j j j. eerne []. onver o [z]. A ressances an arasc caacances 4. alculae h f 5. alculae U f ax ax 8 8 f f f f f 4 a a a ox WL V Q h =: f U=: f ax