Lecture 6 Thermionic Engines
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1 Ltur 6 hrmioni ngins Rviw Rihrdson formul hrmioni ngins Shotty brrir nd diod pn juntion nd diod disussion.997 Copyright Gng Chn, MI For.997 Dirt Solr/hrml to ltril nrgy Convrsion WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI
2 Rviw: Frmi-Dir Distribution Avrg numbr of ltrons in th stt FRMI-DIRAC DISRIUIO f n 0,1 na ( μ )/( ) p μ Copyrigh t Gng Chn, MI For.997 Dirt Solr/hrml to K 100 K 300 K μ (V) ltril nrgy Convrsion 1 Frmi-Dir Distribution At 0K, μ is lld Frmi lvl, f f1 for <μ f0 for >μ WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI
3 WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI.997 Copyright Gng Chn, MI For.997 Dirt Solr/hrml to ltril nrgy Convrsion Rviw: ltron Dnsity ( ) d d d V f z y y y z z μ π π π π π π π p 8, / / / / / / 3 / / / / / / ( ) m z y h n μ μ κ p p h πm 3/ * d f D n ),, ( ) ( μ
4 0 1 /(π/) Gp g /(π/) 0 1/(π/) Donor nrgy Lvl.997 Copyright Gng Chn, MI Mtl Insultor Diffrnt Solids nrgy nrgy nrgy Frmi Lvl Smiondutor For.997 Dirt Solr/hrml to ltril nrgy Convrsion nrgy Aptor nrgy Lvl /(π/)0 1 n-typ p-typ Smiondutor Smiondutor π/) 0 1 /(π/) 0 1 /(π/) π/) WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI
5 Wor Funtion nd Affinity ltron Vuum Wor Funtion W.997 Copyright Gng Chn, MI Frmi Lvl f Mtl ltrods For. 997 Dirt Solr/hrml to ltril nrgy Convrsion Currnt Affinity ndgp g Light v f WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI
6 FRMI-DIRAC DISRIUIO Wor Funtion W Frmi Lvl μ 1000 K Vuum ltrons ust Outsid th Mtl p V 3 8 π π / π / π / π / π /.997 Copyright Gng Chn, MI π / π / π / π / For.997 Dirt Solr/hrml to 100 K 300 K μ W d d ltril nrgy Convrsion μ ( V) y y > 0 0 h ( ) z z d h m WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI m ltron prtil Flu Lving Surf v y f y z z f
7 p 3 8 π 3 8 π m π h π / ltron Flu Out of Surf π / π / π / π / π / π / d d d d d W ( ) p π / π / π / y h 1 dz m μ p 1 h h y p W m m.997 Copyright Gng Chn, MI For.997 Dirt Solr/hrml to y z ltril nrgy Convrsion ( ) z 1 WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI
8 ltril Currnt Dnsity m W W π h 3 m A 10 π ( ) p A p 3 h m K Rihrdson Formul or Rihrdson-Dushmn qution For hrmioni mission A Rihrdson Constnt.997 Copyright Gng Chn, MI ϕ (1 r) A p For.997 Dirt Solr/hrml to Mor Gnrl ltril nrgy Convrsion O.W. Rihrdson 198 obl Priz WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI
9 Contt Potntil.997 Copyright Gng Chn, MI For.997 Dirt Solr/hrml to o F F o W M W M W S χ qϕ n ) mtl nd smiondutor fr prt qϕ n ( ϕ ϕ' ) W W ' V ltril nrgy Convrsion M S W S qφ bi W S χ qϕ n b) mtl nd smiondutor in intimt ontt χ qϕ n Courtsy of sús dl Almo. Usd with prmission. WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI o F o v F v
10 Cthod A Vuum Diod Anod W V p.997 Copyright Gng Chn, MI W A p V For.997 Dirt Solr/hrml to ltril nrgy Convrsion W W -V (W -W ) At quilibrium, - 0 μ WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI
11 Cthod A hrmioni Gnrtor Anod W V V p.997 Copyright Gng Chn, MI > p W For.997 Dirt Solr/hrml to A ltril nrgy Convrsion o μ W V o W -V o μ -μ μ At quilibrium, - 0 WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI
12 .997 Copyright Gng C hn, MI For.997 Dirt Solr/hrm l to ltril nrgy Convrsion hrmioni Gnrtor o o W V V W W A V V W A ln 0 p p o W V ln 1 Opn Ciruit Voltg: WARR M. ROHSOW HA AD MASS RASFR LAORAORY, WARR M. ROHS MI OW HA AD MASS RASFR LAORAORY, MI
13 Cthod Anod R lod Undr Oprtion A A Powr Output W V V p W V p A P V A p.997 Copyright Gng Chn, MI For.997 Dirt Solr/hrml to ltril nrgy Convrsion p W W WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI
14 WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI.997 Copyright Gng Chn, MI For.997 Dirt Solr/hrml to ltril nrgy Convrsion Ht rnsfr: ltron Ht Flu z y m d d d 1 p 1 8 / / / 0 / / 3, μ π π π π π π h Kinti nrgy: otl Ht from Cthod to Anod: W W μ μ V q V W, otl Ht from Cthod to Anod: q W,
15 Cthod t Ht Input Anod.997 Copyright Gng Chn, MI R lod Q Q Q q, q, For.997 Dirt Solr/hrml to ltril nrgy Convrsion h rd ond Q rd --- Rdition ht trnsfr btwn thod nd nod Q ond ---Condution ht loss through lds, nd gs in btwn WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI
16 η Powr Q h Whn rdition is ngltd V W β β olr/hrml to y Convrsion.997 Copyright Gng Ch S.W. Angrist, Dirt nrgy Convrsion, Allyn nd on, oston, 1965 For.997 Dir ltril nr ffiiny hrml ffiiny - η t prnt θ 0.8 θ 0 θ 0. θ 0.4 θ 0.6 I V β Figur by MI OpnCoursWr. WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI
17 primntl Dmonstrtion.997 Copyright Gng Chn, MI Htsopoulos nd Ky, AP, Img rmovd du to opyright rstritions. Pls s Fig. 3 in Htsopoulos, Gorg., nd osph Ky. "Msurd hrml ffiinis of Diod Configurtion of hrmo ltron ngin." ournl of Applid Physis 9 (1958): For.997 Dirt Solr/hrml to ltril nrgy Convrsion WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI
18 Cthod > Rl Dvi Issus Du to Sp Chrg Additionl δ Anod Lrg wor funtion, high tmprtur Csium to rdu sp hrg, but rlibility problm Vuum oprtion or plsm oprtion (filld with gs).997 Copyright Gng Chn, MI For.997 Dirt Solr/hrml to ltril nrgy Convrsion μ W V o W μ WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI
19 Rnt rnds.997 Copyright Gng Chn, MI For.997DirtSolr/ hrmlto gtiv ltron Affinity Mtrils (Dimond) Smith t l., Dimond nd rltd mtrils, 15, 08 (006) gtiv ltron ffinity mtrils Smll gp dvis Solid-stt thrmionis ltril nrgy Convrsion Courtsy of lsvir, In., Usd with prmission. WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI
20 Vuum Wor Funtion W Frmi Lvl f Mtl Δ Shotty rrir Vuum Affinity ndgp g.997 Copyright Gng Chn, MI For.997 Dirt Solr/hrml to ltril nrgy Convrsion v -typ Smiondutor f Shotty rrir f Δ Mtl Smiondutor Intrf WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI
21 P-typ Shotty rrir.997 Copyright Gng Chn, MI For.997 Dirt Solr/hrml to Courtsy of Ptr Stllling. Usd with prmission. ltril nrgy Convrsion WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI
22 Shotty Diod f f Δ Rihrdson Formul Δ V A p p Copyright Gng Chn, MI f Δ Forwrd is Δ V V For.997 Dirt Solr/hrml to ltril nrgy Convrsion Rvrs is WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI
23 f n-yp v f v p-yp pn untion ltron nrgy Inrsingly gtiv n-yp uild-in Potntil Sp Chrg Rgion Hol nrgy Inrsingly Positiv.997 Copyright Gng Chn, MI For.997 Dirt Solr/hrml to ltril nrgy Convrsion n-yp Sp Chrg Rgion p-yp V bi p-yp WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI
24 .997 Copyright Gng Chn, MI For.997 Dirt Solr/hrml to ltril nrgy Convrsion pn untion sis n μ p v μ p p v v p i g n pn For nondgnrt smiondutor WARR M. ROHSOW HA AD MASS RASFR LAORAORY, WARR M. ROHS MI OW HA AD MASS RASFR LAORAORY, MI
25 pn untion sis: uilt-in Potntil ltron nrgy Inrsingly gtiv V bi n-yp uild-in Potntil Sp Chrg Rgion Hol nrgy Inrsingly Positiv p-yp p.997 Copyright Gng Chn, MI For.997 Dirt Solr/hrml to V bi ltril nrgy Convrsion D μ WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI, n μ, n ln D, ln p μ g v A, p, n g ln ln A D n i v A D
26 pn untion sis: Sp Chrg Rgion ltron nrgy Inrsingly gtiv V bi n-yp uild-in Potntil Sp Chrg Rgion Hol nrgy Inrsingly Positiv p-yp ε s A A D.997 Copyright Gng Chn, MI For. 997 DirtSolr/hrml to ltril nrgy Convrsion w On Sid Only w ε s Vbi Dby Lngth w ε s D V bi WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI
27 s pn untion I-V ( V / 1) Sturtion Currnt s v 1 A h τ h 1 h ---hol diffusivity (m /s) ---ltron diffusivity τ h ---hol rombintion tim τ ---ltron rombintion tim D τ G p κ.997 Copyright Gng Chn, MI For.997 Dirt Solr/hrml to ltril nrgy Convrsion WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI
28 s f Compr Shotty diod nd pn diod Δ V ( s p 1 C hol V diffusion A n-typ.997 Copyright Gng Chn, MI A Δ p For.997 Dirt Solr/hrml to ltril nrgy Convrsion s s C ψ ψ h p-typ ltron diffusion D v A D V / 1) v 1 A h τ h 1 D τ G p κ WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI
29 C hol V diffusion A n-typ C A ψ ψ h n.997 Copyright Gng Chn, MI p v For.997 Dirt Solr/hrml to A D p-typ ltron tron diffusion D D Currnt nd nrgy Distribution Posi itiv iv ltril nrgy Convrsion nrgy Sour Distribution A D 0 gtiv Positiv WARR M. ROHSOW HA AD MASS RASFR LAORAORY, MI
30 MI OpnCoursWr Dirt Solr/hrml to ltril nrgy Convrsion hnologis Fll 009 For informtion bout iting ths mtrils or our rms of Us, visit:
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