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1 Surfce nd Interfce Science Physics 627; Chemistry 542 Lectures 4 Feb 3, 2013 Determining Surfce Structure Diffrction methods: LEED; RHEED Rel Spce: STEM References nd Resources: Woodruff nd Delchr (2 nd ed.), pp Wikipedi (!)

2 Electrons in the ~ ev rnge hve wvelengths comprble to lttice dimensions h / p (de Broglie Reltion) 2 E kinetic p / 2m (Free electron energy-momentum reltion) p 2mE kinetic nd h / 2mEkinetic Now, put in numbers! h If we express E in ev: nd in Ǻ: We get: J 34 s 1Å 110 m eV (in Å) 12.4 / m Ekinetic (in ev) kg 19 J Universl Curve Therefore E kinetic = 36 ev (esy to do!) gives = 2.1 Ǻ!! Just bout right!!!

3 Bsic ide of LEED: Scttering off two dimensionl rry of toms. If d = n, we get constructive interference! Wht hppens to Θ when is chnged? Why two dimensionl, not 3D??

4 Low Energy Electron Diffrction (LEED) LEED is n importnt diffrction technique for the determintion of surfce structures. It my be used in one of two wys. Qulittively : The diffrction pttern is recorded. An nlysis of the spot positions yields informtion on the size, symmetry nd rottionl lignment of the surfce unit cell. Quntittively : The intensities of the vrious diffrcted bems re recorded s function of the incident electron energy to generte I-V curves which, by comprison with clculted curves, gives ccurte informtion on tomic positions.

5 Schemtic digrm of LEED pprtus Commercil LEED pprtus LEED pprtus mounted in UHV chmber

6 (10) (01) (01) (10) LEED diffrction ptterns from W(100) t two different energies (Which is higher energy???) (Wht s the rtio of energies??)

7 Rel nd reciprocl spce pictures of unit cells Rel Spce Reciprocl Spce k j i k j i 2 * (i, j, k cycl.) * 1 * ẑ Generl for 3D In 2D, use: z ˆ * 3 z y x ˆ ; ˆ ; ˆ Consider: x x z y x z y ˆ 2 ˆ 2 ˆ ˆ ˆ ˆ ˆ * 1

8 Superstructures

9 First compliction: Scttering from different lyers prllel to the surfce cn interfere constructively or destructively Interference between different lyers (single scttering) I-V curve (intensity profile) for Ni(100)

10 Second compliction: Multiple scttering

11 How to get quntittive results from LEED The inspection of the LEED pttern gives qulittive picture of the surfce periodicity i.e. the size of the surfce unit cell nd to certin degree of surfce symmetries. It will give no informtion bout the tomic rrngement within surfce unit cell or the sites of dsorbed toms. A more quntittive nlysis of LEED experimentl dt cn be chieved by nlysis of I-V curves (mesurements of the intensity versus incident electron energy). These curves re then compred to computer clcultions bsed on the ssumption of prticulr model. The model is chnged in n itertive process until stisfctory greement between experimentl nd theoreticl curves is chieved. A quntittive mesure for this greement is the so clled relibility- or R-fctor, for exmple: where nd V oi is the imginry prt of the electron self-energy

12 Theory vs. experiment (red) for I-V profiles for Al(111)

13 Summry

14 Reflection High Energy Electron Diffrction (RHEED) High energy electrons (10 30 kev) Grzing incidence geometry Widely used to monitor epitxil growth Not s well understood quntittively s LEED No energy filtering

15 MBE pprtus with RHEED

16 RHEED experimentl geometry

17 (Schemtic) origin of RHEED oscilltions

18 A RHEED pttern from TiO 2 (110) Streked RHEED pttern from the TiO 2 (110) surfce. The smple hd terrced surfce, which cused noticeble streking compred to the RHEED pttern from the flt TiO 2 (110) surfce shown to the left.

19 RHEED summry

20 Scnning tunneling microscopy (STM)

21 Quntum tunneling

22 The STM mesures chrge density, not directly tomic positions

23 STM of Si(111) (7x7) t good (top left) nd optiml (right) resolution Clculted (left) STM pictures for the surfce structure t right

24 Atomic mnipultion using the STM tip

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26 The influence of bis: Si(100) (1x2)

27 Spectroscopy: Si(111) dtom sites A, corner holes B vcncy sites C

28 Atomic force microscopy (AFM) AFM imge of NCl