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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
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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)
0 Air (n=1) 1 2 + - kn p hn Zp p+1 N ZS Substrate Dynamical Theory Electric field in layer p Through the layer p(Tp : Translation Matrix) At p,p+1 interface(Rp,p+1 : Refraction Matrix ; pp, mp Fresnel coef.) Transfer Matrix [M]ijM=R01T1R12……………TN-1RNN-1TNRNS Reflection coefficientr=M12/M22 Absolute Reflectivity R=r.r* Transmission coefficientt=1/M22
Cu thickness CuO2 thickness N=1 , N=2 Single Layer R=r.r* max. each time As Then (Kiessig fringes) For <c Total external reflection For p=0, =c leading to el via Bilayer2 oscillation frequencies are evidenced
300 A 100 A TF-1 Substrate Disturbance of el at interface Kinematical Theory Rough interfaces Dynamical theory not appropriated anymore Born approximations No multiple reflections No refraction R function of d/dz
2 Interface disturbance What kind of disturbance ? Rough interface Diffuse interface Diffuseness / Graded interface Graded composition (electronic density) from j to i layer with l steps
Um+1(x,y) zm+1 Q qz hmideal Um (x’,y’) zm kin ksc Um (x,y) q//(x,y) Q qz Differential cross-section If Then Differential cross-section (detected intensity) depends on p(W=Um(x,y)) (Height distribution at interfaces)
U1 D U2 Periodic Roughness Flat substrate Pure specular Discrete Height Distribution Kiessig fringes function of 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
detector scan w=0.9 rocking curve 2q=1.5 inaccessible q-area inaccessible q-area Yoneda Wings Off-specular (diffuse) scattering Transverse scan (Rocking curve) at 2=2º Si layer (64 nm) on Si substrate s=7A , h=0.2 , various Large lateral correlation at interface Specular peak Yoneda wings : each time ai or af = ac
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