May 29, 2018, 8:45~10:15 IB011 Advanced Lecture on Semiconductor Electronics #7

Transcription

1 May 9, 8, 8:5~:5 I Advanced Lecue on Semconduco leconcs #7 # Dae Chape 7 May 9 Chape 5.Deec and Cae Cae Scaeng Ionzed mpuy scaeng, Alloy scaeng, Neual mpuy scaeng, Ineace oughness scaeng, Auge /

2 Scaeng mechansm and he low eld elecon mobly Mahessen s ule oal hp:// /

3 Mobly as a uncon o mpuy concenaon hp:// h nceasng mpuy concenaon, scaeng pobably ncease. Mobly deceases. /

4 Tempeaue dependence o AlGaAs/GaAs wo dmensonal elecon gas mobly Doped laye and channel laye ae sepaaed. Impuy scaeng can be mnmzed. hp:// hp:// /

5 Hgh eld anspo A hgh elecc eld v d F. S. J. Peaon e al., Mae. Sc. ng., R55. 5/

6 Fomulazaon o anson pocess Fem s Golden ule Fem s Golden ule Geneal omalsm eplanng pobably o anson o pacle om one sae o anohe by peubaon ample o scaeng n semconduco *Impuy scaeng lecon s momenum changes bu enegy does no change. *Phonon scaeng oh momenum and enegy o elecon change. *Absopon o phoon lecons n sold s eced and sh o hghe enegy sae by absobng phoon enegy. *Sponaneous emsson Tanson om eced sae o gound sae by emng phoon *Smulaed emsson Tanson om eced sae o gound sae ggeed by elecc eld o lgh. avelengh and phase o emed phoon s he same as ha o ncden lgh. Scaeng by me-ndependen sac poenal Impuy scaeng, alloy scaeng. negy o pacle does no change by scaeng. Scaeng by me-dependen hamonc oscllao wh he em cos q scaeng by phonon o phoon. negy o pacle changes by q negy o phonon o phoon 6/

7 Fem s Golden ule Scaeng by sac poenal Impuy, alloy Hamlonan=Non peubaon em+peubaon em ae = Hˆ Hˆ ˆ gen sae and enegy o non peubaon em Hˆ, lecon sae beoe peubaon s. <, ep >, [ Hˆ ˆ ] pandng he wave uncon by non peubaon em a Subsung no Schlödnge eq. Delee non peubaon em [ Hˆ ˆ ] a a da ep a ˆ ep d Jus beoe peubaonnal us ae peubaon nal * Mulply om le and negae. Only em emans. da d da * ep a ep d a ˆ ep, ˆ d a ep ˆ Impuy avenumbe o elecon 7/

8 Fem s Golden ule Scaeng by sac poenal Impuy, alloy da d Fs ode appomaon da d ˆ I we assume o be consan, a ˆ ep ep a Pobably o ndng elecons n a nal sae s ˆ A =, nal value o a =δ Fem s Golden Rule ˆ a ep d ep d ˆ a ep sn ˆ ep sn sn sn c,sn c sn c d sn c d sn c a Fem s Golden Rule Tanson pobably om nal o nal sae s 8/

9 Fem s Golden ule Scaeng by vbang poenal Phonon scaeng, Absopon and emsson o phoon ep ˆep cos ˆ ˆ bang poenal wh he angula equency lecomagnec eld Lace vbaon Consan ep ep ep ep ep ep ˆ d d a Fem s Golden Rule Pobably o ndng elecon a nal sae s sn sn cos sn sn c c c c a Ths em can be negleced., N Tanson pobably by vbang poenal s 9/

10 Fem s Golden Rule Tanson pobably by sac poenal N Tanson pobably by vbang poenal N, /

11 Ionzed mpuy scaeng Sac poenal Poenal enegy o onzed mpuy e In a sold, caes havng oppose chage suound, heeoe poenal s moded. e need o omulae sceened Coulomb poenal. o e nd Toal poenal = poenal by mpuy + poenal by nduced cae o e nd Toal chage = mpuy chage +nduced cae chage Change o delecc consan by sceenng e nd ee Chage dsbuon n -space ep Posson s equaon e Fee cae densy s n. Induced cae chage s eo n e n e ep nd o T T eo n e o n e T T Change o delecc consan s e nd n e ee, T o o o lecon ollows olzmann s dsbuon. n e o e ne T /

12 Ionzed mpuy scaeng Sac poenal Sceened Coulomb poenal Chage densy o mpuy wh chage q e q q lecc poenal e Foue ansom o δ uncon s. q ne Tansom om eal space o space e q, e ee, T q o Invese Foue ansom e o q q ep d q d sn e o dcos e sn cos cos ddd q q o ep Inegal omula sn a d ep ab b lecosac poenal whou sceenng lecosac poenal wh sceenng /

13 Ionzed mpuy scaeng Sac poenal Change o poenal enegy by sceenng Poenal enegy ab. un ab. un hou sceeng p Sceenng coecen h sceenng ne T /

14 avenumbe o elecon How o calculae anson pobably =,? Sceened poenal enegy Ze ep Ma elemen o anson pobably * sn cos ep ep cos cos ep ep cos sn ep Ze Ze d d Ze d d Ze d d d e Ze d M Then, sn, Ze Ionzed mpuy scaeng Sac poenal /

15 Ionzed mpuy scaeng Sac poenal Relaaon me by sac poenal s d cos, Concenaon o mpuy s N. Aveage elaaon me s N Ze 8 * m e m* T Mobly s mp * 8m T ln * 8m T T Chap.6, p. Q: lecon mobly o hgh puy n-s a T=K s cm /s. I sngle dono Z= s doped wh an elecon concenaon o 7cm -, mobly deemned by mpuy scaeng s 95 cm /s. All he mpuy ae onzed. I double dono Z= s doped wh an concenaon o 7cm -, calculae he mobly a oom empeaue. 95 Z N,, o 89cm 95 / s 5/

16 Alloy scaeng Sac poenal Consde alloy A - A A all Sold lne :eal poenal oen lne :aveage poenal ach poenal s dened as A and. Poenal o alloys s all. negy deence n aom A and aom s all A A all all A A A A all Dsance o aom s. Scaeng poenal s,, all d e M M, Tanson pobably s Scaeng poenal speads n. e M N d 6/

17 9 N N ample o cc Lace consan s a. Dsance o neaes neghbo s a olume o un cell s a Tanson pobably s 9 all A N Tanson pobably a A a 9 all N Rao o A n un cell s ao o s In oal, 9 all o N Aveage elaaon me s.75 9 * T m all Tempeaue dependence * T m e alloy Q: Invese o he aveage elaaon me n Al. Ga.7 As a K s.s -. Caclulae mobly a 77 K and K deemned by alloy scaeng, assumng m*=.7m. s cm K s cm K /.6 77 /. Alloy scaeng Sac poenal 7/

18 Ohe sac poenal scaeng Neual mpuy scaeng and deec scaeng N M m * T.75 Suace oughness scaeng q Auge pocess and mpac onzaon * m e sc N dep d cos q q ep q N s T. Ando, J. Phys. Soc. Japan, Inal : wo elecons and one hole =Cn C:Auge coecen Fnal :one elecon evese pocess Avalanche phoodode Auge Impac onzaon In sead o emng phoon, ecess enegy s used o ece conducon band elecon. 8/

19 Auge coecen and bandgap K. A. ulashevch and S. Yu Kapov, Phys.Sa.Sol.c, /

20 Auge pocess =ogn o powe sauaon n opcal communcaon LD /

21 Impac Ionzaon=pncple o Avalanche Phoo Dode lecode SO I ph R H : Invesgae when mpac onzaon sas. h > g n + p e h + š p + a h + e c e v ne lecode h + n + p š b Avalanche egon a b Absopon egon Avalanche egon c a A pcoal vew o mpac onzaon pocesses eleasng HPs and he esulng avalanche mulplcaon. b Impac o an enegec conducon elecon wh cysal vbaons anses he elecons nec enegy o a valence elecon and heeby eces o he conducon band. 999 S.O. Kasap, Opoeleconcs Pence Hall a A schemac llusaon o he sucue o an avalanche phoodode APD based o avalanche gan. b The ne space chage densy acoss he phoodode. c The eld acoss he dode and he dencaon o absopon and mulplcaon egons. 999 S.O. Kasap, Opoeleconcs Pence Hall /