specular reflectivity and off-specular scattering tools for roughness investigation

LEUVENInstituut voor

Kern- en Stralingsfysica

Specular reflectivity and off-specular Specular reflectivity and off-specular scatteringscattering

Tools for roughness investigationTools for roughness investigation

Hugues Guerault 15/12/2000Hugues Guerault 15/12/2000


Kern- en StralingsfysicaOutlineOutline

Introduction

Flat surface/interface - Dynamical theoryLayer thickness and electronic density determination

Rough surface/interface - Kinematical theoryRoughness and diffuseness (Non-)periodic roughnessDifferential cross-section Correlation lengths

Investigation geometriesSpecular reflectivity (specular scan)Off-specular scattering (longitudinal, transverse and detector scans)

Conclusions


Kern- en StralingsfysicaIntroductionIntroduction

Increasing ability to structure solids in 1, 2 or 3D at nanoscopic scale Mesoscopic layered superstructures (multilayers, superlattices, layered gratings, quantum wires –and dots)

Perfection depends on Perfection of the superstructure (grating shape, periodicity, layer thickness) Interface quality (roughness, interdiffusion)

Crystalline properties (strain, defects, mosaicity,…)

Roughness affects the physical behavior of interfaces Optical : reduces the specular reflectivity – creates diffuse scattering Magnetic : changes the interface magnetization Electronic : disturbs the band structure in semiconductor devices (resistivity)



Transfer Matrix [M]ij M=R01T1R12……………TN-1RNN-1TNRNS

Reflection coefficient r=M12/M22 Absolute Reflectivity R=r.r*

Transmission coefficient t=1/M22

At p,p+1 interface (Rp,p+1 : Refraction Matrix ; pp, mp Fresnel coef.)

Electric field in layer p

)())()(( ykwtipppp

pyezUzUE

Dynamical TheoryDynamical Theory

)()()( 11 pppppp

pppp zUzU

pmmp

zU

1pp,R

Through the layer p (Tp : Translation Matrix)

)()(0

0)(,

,

1 pppphik

hik

pp zUzUe

ezUpzp

pzp

pT

SubstrateN

p+1

p

2

10 Air (n=1)

ZS

Zp

hn- +kn


Kern- en StralingsfysicaN=1 , N=2N=1 , N=2

Single Layer

R=r.r* max. each time

As Then

(Kiessig fringes)

hp

qqqqkz

czzz

212 2

2

11

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.01E-6

1E-5

1E-4

1E-3

0.01

0.1

1

10

2

c2

p2

Log(

Refle

ctiv

ity)

Grazing incidence (degree)

W // Si 8 nm 15 nm

0 20 40 60 80

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

W (8 nm) // Si

(/2h)2

4sin4

1 zq2

222

2

hpc

For <c Total external reflection

For p=0, =c leading to el via

Bilayer 2 oscillation frequencies are evidenced

0 1 2 31E-6

1E-5

1E-4

1E-3

0.01

0.1

1

10


Log(R

eflec

tivity

)

CuO2 (5,5 nm) // Cu (45 nm) // Si

Cu thickness

CuO2 thickness

hiq

hiq

z

z

errerr

MMr

1

1

21201

21201

22

12

1

el

cel r2

2


Kern- en StralingsfysicaKinematical TheoryKinematical Theory

Born approximations No multiple reflectionsNo refractionR function of d/dz

dzedzzd

qrr ziq

z

z )(2

0 )(4

Rough interfaces Dynamical theory not appropriated anymore

)](')('[)(

)(*. zzTFqRqRrrR

zF

z

100 200 300 400

Aut

ocor

rela

tion

Func

tion

z (A)0 1 2 3 4

1E-6

1E-5

1E-4

1E-3

0.01

0.1

1

Log

(Ref

lect

ivity

)


Substrate

100 A

300 A

TF-1 Disturbance of el at interface


Kern- en StralingsfysicaInterface disturbanceInterface disturbance

What kind of disturbance ?

Rough interface Diffuse interface

Diffuseness / Graded interface

Graded composition (electronic density) from j to i layer with l steps

2

0.5 1.0 1.5 2.0

Log

(Refl

ectiv

ity)

Grazing incidence

2

No roughness without diffuseness with diffuseness (3 nm)

Fe (10 nm) / Co (22 nm)

Fe (10 nm) / Ag (22 nm)



If Then WiqWiq zz eWpdWe ).(.

Differential cross-sectionDifferential cross-section

)'(20 )'()(' rrQierrdrdrr

dd

dd

qLLrrQR

zyx

2

4*.)(

))','(),(())(2

220 yxUyxUiqYqXqi

z

el mmzyx dxdyedXdYeq

rdd

))','(),(( yxUyxUiqyx

mmzeLL

Um+1(x,y)

Um (x,y)

Um (x’,y’)hm

ideal

zm+1

zm

Q qz

Differential cross-section (detected intensity) depends on p(W=Um(x,y)) (Height distribution at

interfaces)

)','(),( yxUyxUW mm

kin ksc

Q

q//(x,y)

qz



Discrete Height Distribution

Kiessig fringes function of D

Flat substrate

Pure specular

)2)(2...(... yxYiqXiq qqdYeeXd

dd yx

1 Wiqze

44

22 116)(z

yxz

el

qqq

qQR

)()()( 2211 UpUpWp

Periodic RoughnessPeriodic Roughness

1)0( Wp

SubiQDiQdp

coh ReppeQR )()( 212

U1

U2

D



Two contributions

Specular contribution observed in the specular direction

Diffuse contribution observed when Q(x,y)0

Random Height Distribution

Gaussian height distribution

Non-periodic RoughnessNon-periodic Roughness

0),( yxUm

2))','(),((),( yxUyxUYXg mm

)','(),(22),( 2 yxUyxUYXg

Height-Height correlation function

22 ),( yxUm

2

2

2

21)(

u

eWp

2)(

2

22 RgqWqWiq

zz

z eee

dd

flat

qyx

q

z

yxel

spe ddeqqe

qLLr

dd

zz

2222

2

220

24

)(),(2

220 1

222 YqXqiYXCqq

z

yxel

diff

yxzz eedXdYeq

LLrdd

+

),(22)( 2 YXCRg zz



Height-Height correlation function

where h : roughness exponent : lateral correlation length

hR

zz eRC

2

2)(

Correlation LengthsCorrelation Lengths

Increasing and decreasing roughness in periodic multilayers

: vertical correlation length No Increasing Partial Identical replication roughness replication replication

kj ZZ

kk

jj

j

kjk eRCRCRC )()(

21)(


Kern- en StralingsfysicaSpecular reflectivitySpecular reflectivity

0 1 2 3 41E-7

1E-6

1E-5

1E-4

1E-3

0.01

0.1

1

10

Grazing incidence angle (degree)

Log(

Ref

lect

ivity

)

CoSi2 (15 nm) // Si * Flat surface Vacuum/CoSi2

=0

* Rough interface CoSi2/Si no roughness 5A 10 A

0 1 2 3 41E-7

1E-6

1E-5

1E-4

1E-3

0.01

0.1

1

10 CoSi2 (15 nm) // Si

Log(

Ref

lect

ivity

)

Grazing incidence angle (degree)

* Rough Surface Vacuum/CoSi2 no roughness 5A 10 A

* Flat interface CoSi2/Si=0

0 1 2 3 4 51E-8

1E-7

1E-6

1E-5

1E-4

1E-3

0.01

0.1

1

10[a-Si / W] multilayersN=20 d=70 A =20

Log(R

eflec

tivity

)

Incident angle (degree)

No roughness [W/a-Si]=5 A



Transverse scan (Rocking curve) at 2=2º

Si layer (64 nm) on Si substrate =7A , h=0.2 , various

Large lateral correlation at interface

Specular peak

Yoneda wings : each time i or f = c

Off-specular (diffuse) scatteringOff-specular (diffuse) scattering

-2.0x10-3 -1.0x10-3 0.0 1.0x10-3 2.0x10-3

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Longitudinaldiffuse scan

0=0.1

Specularreflectivity

qx(A-1)

q z(A-1)

inaccessible q-area inaccessible q-area

rocking curve2=1.5

detector scan=0.9

0 1 2

Log

[Inte

nsity

(arb

. unit

s)]

scan

=7000 A =2000 A =500 A

Yoneda Wings



Si (30 nm) // Ge (50 nm) // SiO2 (1.5 nm)Schlomka et al. PRB 51(4) 1995

Offset (longitudinal) scan Detector scan

Longitudinal and detector scansLongitudinal and detector scans

Curve depends on i (penetration depth)i < c No penetration

Increasing i different modulations

Specular contribution of the diffuse scattering

Same oscillations than reflectivity curve


Kern- en StralingsfysicaConclusionsConclusions

Grazing Incidence X-Ray Reflection Surface/interface investigation at atomic scale Non destructive technique

Vertical periodicity & in-plane morphology Layer thickness, electronic density profile (composition

profile) Surface and interface roughness In-plane and between plane correlations No information on the crystalline structure

Application 01/2001: Collaboration IKS / VSM / IMEC Roughness characterization of Co1-xNixSi2 layers

(MBE) Roughness influence on the resistivity

specular reflectivity and off-specular scattering tools for roughness investigation

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