Specular reflectivity and off-specular scattering Tools for roughness investigation Hugues Guerault 15/12/2000

Outline  Introduction  Flat surface/interface - Dynamical theory Layer thickness and electronic density determination  Rough surface/interface - Kinematical theory Roughness and diffuseness (Non-)periodic roughness Differential cross-section Correlation lengths  Investigation geometries Specular reflectivity (specular scan) Off-specular scattering (longitudinal, transverse and detector scans)  Conclusions

Introduction  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)

Dynamical Theory Electric field in layer p Substrate N p+1 p 2 1 0 Air (n=1) ZS Zp hn - + kn Through the layer p (Tp : Translation Matrix) At p,p+1 interface (Rp,p+1 : Refraction Matrix ; pp, mp Fresnel coef.) Transfer Matrix [M]ij M=R01T1R12……………TN-1RNN-1TNRNS Reflection coefficient r=M12/M22 Absolute Reflectivity R=r.r* Transmission coefficient t=1/M22

N=1 , N=2 Single Layer Bilayer 2 oscillation frequencies are evidenced R=r.r* max. each time As Then (Kiessig fringes) Cu thickness CuO2 thickness For <c  Total external reflection For p=0, =c leading to el via Bilayer 2 oscillation frequencies are evidenced

Kinematical Theory Rough interfaces Dynamical theory not appropriated anymore Born approximations No multiple reflections No refraction R function of d/dz Substrate 100 A 300 A TF-1 Disturbance of el at interface

Interface disturbance What kind of disturbance ? Rough interface Diffuse interface 2 Diffuseness / Graded interface Graded composition (electronic density) from j to i layer with l steps

Differential cross-section kin ksc Q q//(x,y) qz Um+1(x,y) Um (x,y) Um (x’,y’) hmideal zm+1 zm Q qz If Then Differential cross-section (detected intensity) depends on p(W=Um(x,y)) (Height distribution at interfaces)

Periodic Roughness Flat substrate Discrete Height Distribution D Pure specular Discrete Height Distribution Kiessig fringes function of D U1 U2 D

Non-periodic Roughness Random Height Distribution Gaussian height distribution Height-Height correlation function Two contributions Specular contribution observed in the specular direction Diffuse contribution observed when Q(x,y)0 +

Correlation Lengths Height-Height correlation function where h : roughness exponent  : lateral correlation length Increasing and decreasing roughness in periodic multilayers  : vertical correlation length No Increasing Partial Identical replication roughness replication replication

Specular reflectivity

Off-specular (diffuse) scattering inaccessible q-area rocking curve 2q=1.5 detector scan w=0.9 Transverse scan (Rocking curve) at 2=2º Si layer (64 nm) on Si substrate s=7 A , h=0.2 , various  Large lateral correlation  at interface  Specular peak Yoneda wings : each time ai or af = ac Yoneda Wings

Longitudinal and detector scans Si (30 nm) // Ge (50 nm) // SiO2 (1.5 nm) Schlomka et al. PRB 51(4) 1995 Offset (longitudinal) scan Detector scan Curve depends on ai (penetration depth) ai < ac No penetration Increasing ai  different modulations Specular contribution of the diffuse scattering Same oscillations than reflectivity curve

Conclusions 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