Surface and Interface Science Physics 627; Chemistry 542. Lecture 10 March 1, 2013

Transcription

1 Suface and Inteface Science Physics 67; Chemisty 54 Lectue 0 Mach, 03 Int t Electnic Ppeties: Wk Functin,Theminic Electn Emissin, Field Emissin Refeences: ) Wduff & Delcha, Pp. 40-4; ) Zangwill Pp ) C. Heing and M.N. Nichlas, Theminic Emissin Rev. Md. Phys, 85 (949) 4) A. Mdins, Field, Theminic, and Secnday Electn Spectscpy (Plenum, NY, 984) 5) L.N. Dbetsv and M.V. Gmyunva Emissin Electnics (Kete Pess, Jeusalem, 97)

2 Wk Functin Unifm Suface Tue wk functin, e, f cnduct is diffeence between electchemical ptential,, f electn just inside cnduct and the electstatic ptential enegy (-e ) f an electn in the vacuum just utside. is wk equied t bing an electn fm infinity t slid -e I e -e G n e / T, P e e Nte: is functin f intenal AND suface/extenal (e.g., shifting chages, diples) cnditins. Can define quantity which is functin f intenal state f the slid. Chemical ptential f electns: e I Aveage electstatic ptential inside e []

3 Wk Functin The Femi enegy [E F ], the highest filled bital in a cnduct at T = 0 K, is measued with espect t e I and is equivalent t. e e e We can wite: equivalently: I / e depends n suface stuctue and adsbed layes. The vaiatin in f a slid is cntained in. What d we mean by ptential just utside the suface??? The ptential expeienced by an electn just utside a cnduct is: kee V ( ) 4 9 k e whee Nm /C F a unifm suface, this cespnds t in () (V() 0 as mv ange f > 0 3 Ang.]) -F In pesence f electic field -F k e / e V ( ) F dv kee 4 0 d F / 5 / / ef F k e [in.90 / 4 F 5 S f F = 0 4 V/m (00V/cm), =.9 x 0-7 m; = 3.8 mv

4 Wk Functin Plycystalline Suface patches f diffeent wk functin patches f diffeent suface ptential F small distance abve ith patch electstatic ptential is i At distances lage w//t patch dimensin: f i i S mean wk functin is given by: e f e i i At lw field, electn emissin cntlled by: i e At high field (applied field >> patch field) electn emissin elated t individual patches e i. i i j k i j On eal sufaces, patch dimensin <~ 00Ang, if ~ ev then patch field F ~ V/0-6 cm ~ x 0 6 V/cm.

5 Wk Functin Facts that influence wk functin diffeences n clean sufaces adsbed layes suface diple SMOOTH SURFACE: Electn density spillve OUTSIDE ROUGH SURFACE: Smthing cntibutin lwes Example: W e (0) 5.70 () 4.93 () 4.39 (6) 4.30

6 Wk Functin Wk functin change upn adsptin Chage tansfe at inteface: electpsitive (K, Na, ) Electnegative (Cl, O, F, ) Mdel diple laye as paallel plate capacit: = n/ = diple mment (C.m) n = suface density (m - ) = 8.85 X 0 - C/Vm Suppse =.5 V f x 0 5 /cm O atms n W(00). What is? F mlecules with pemanent diple mments:

7 Vacuum level nea a suface

8 Multiple Expansin f the Electstatic Ptential:

9 0 ' ') ( ') (cs ') ( 4 n n n n d P Q d V mn 4 ' ') ( 4 ) ( ˆ 4 ' ') ( ' ˆ 4 ' ') ( ' 'cs 4 ) ( p d d V dip ' ) ' ( ' d p Multiple Expansin f the Electstatic Ptential:

10 Vacuum level nea a suface V ( x) C V ( x) (paallel plate) x n (multiple) V ( x) x (diple) x L x L x L

11 Vacuum level nea a suface -+ Intefac e diple injectin baies educed

12 Theminic emissin RICHARDSON S EQUATION Cuent density: = eflectin cefficient Richadsn plt: Electn Emissin j A ( ) T exp e / kt A 4 mek 3 h Amp 0.4 cm deg ln(j/t ) vs. /T staight line ln(j/t ) Schttky Plt /T (K - ) e e bf / ln j vs F / staight line

13 Electn Emissin Field emissin Electn tunneling thugh lw, thin baie Field emissin when F >~ 3 x 0 7 V/cm ~ 0.3 V/Ang Geneal elatin f electn emissin in high field: j e P given by WKB appximatin t(y), f(y) slwly vaying elliptic functins 0 P( Ez, F) v( Ez ) dez /3 P cnst. exp m / / l 0 ( V E z ) / dz Appximate baie by tiangle A ~ 3/ 3/ / P ~ cnst. exp m / F Fwle-Ndheim Eqn, including ptential baie: 3/ 6 F 7 f ( y) j.540 t ( y)exp F F / ~ 3/ F whee (V-E z ) 3/ I b Altenatively: a exp V with F = cv cv l ~ /F y e 3/ F / -efz

14 Electn Emissin Field Emissin Micscpe Get high field by placing shap Tip at cente f spheical tube. Mag: R/ ~ 5cm/0-5 cm ~ 500,000 F = cv; c ~ 5/ F ~ 5 x 0 7 V/cm F V =,500 Vlts. (0) () [typ] W single cystal wie as tip. Typical patten n phsph sceen

15 Electn Emissin Field Emissin Micscpe Field emissin ppeties

16 Electn Emissin Secnday Electn Emissin Electns emitted fm sufaces afte electn bmbadment In geneal cmplicated phenmenn invlving seveal inteelated pcesses Geneally classify secndaies int thee categies: (I) Elastic ; (II) Inelastic; (III) tue secndaies (KE < 50 ev) e - Retading gid cllect Ttal cefficient f secnday emissin, = j /j i I II III = + j i Enegy, E p F metals, max values: ~ 0. (E p ~ ev); ~ 0.0 (lage E p ) ~ 0.3 t 0.4 ~ 0.5 t.8 (E p ~ few hunded ev) F insulats, can be MUCH highe (~ 0!!!!) j

17 Secnday Electn Emissin Establishment f stable ptential f insulats Electn Emissin F metals and semicnducts: Celatin between and density, (NOTE: depends n wk functin, temp, angle f incidence,.)