In [1]:
import numpy as np
import escape as esc

esc.require("0.9.8")

Loading material database from C:\dev\escape-core\python\src\escape\scattering\..\data\mdb\materials.db

Interfacial Roughness and Proximity Effects in Superconductor/Ferromagnet CuNi/Nb Heterostructures¶

This notebook fits a multilayer specular X-ray reflectivity example with interfacial roughness and proximity effects. It is a good reference for how structural parameters, roughness, and resolution corrections enter a realistic reflectivity workflow.

Authors: Yu. Khaydukov, R. Morari, O. Soltwedel, T. Keller, G. Christiani, G. Logvenov, M. Kupriyanov, A. Sidorenko, and B. Keimer

Citation: Journal of Applied Physics 118, 213905 (2015); doi: 10.1063/1.4936789

In this study, we present the results of fitting experimental data from the publication mentioned above. We selected data from two samples, where the CuNi layers differ in terms of thickness and roughness, to showcase the capabilities of a simultaneous fit with shared parameters. Rather than fitting the Scattering Length Densities (SLDs), we will focus on fitting the mass densities of the layer compounds.

This notebook also demonstrates how to add temporary records to the default material database. This approach allows new material records to be kept within the notebook alongside the code, rather than creating a new local material database.

In [2]:
src = esc.xrays(0.1540562, "nm")

Capping = {
    "name": "Capping",
    "type": "amorphous",
    "density": 2.32,
    "atoms": [
        {"Si": {"repeat": 1}},
    ],
}

CuNi = {
    "name": "CuNi",
    "type": "amorphous",
    "density": 8.93,
    "atoms": [
        {"Cu": {"repeat": 1}},
        {"Ni": {"repeat": 1}},
    ],
}

SiO2 = {
    "name": "SiO2",
    "type": "amorphous",
    "density": 2.62,
    "atoms": [
        {"Si": {"repeat": 1}},
        {"O": {"repeat": 2}},
    ],
}

from escape.scattering.mdb import default_mdb

default_mdb.add(Capping)
default_mdb.add(CuNi)
default_mdb.add(SiO2)
In [3]:
Cap_common = esc.amorphous("Capping", density="mdb")
CuNi_common = esc.amorphous("CuNi", density="mdb")

SiO2Lay = esc.layer(
    "SiO2", thkn="3+-2nm", rough="1+-1nm", bydensity=True
)
NbLay = esc.layer("Nb", thkn="10+-2nm", rough="1+-1nm", bydensity=True)
Sub = esc.substrate("Si", rough="1+-1nm", bydensity=True)

sample_10 = esc.multilayer(
    formula="Cap_common(10+-8nm,1+-1nm)/CuNi_common(10+-5nm,1+-1nm)/NbLay/SiO2Lay//Sub",
    bydensity=True,
    globals=globals(),
)
sample_21 = esc.multilayer(
    formula="Cap_common(10+-8nm,1+-1nm)/CuNi_common(30+-5nm,1+-1nm)/NbLay/SiO2Lay//Sub",
    bydensity=True,
    globals=globals(),
)

w10 = sample_10.show(source=src)
w21 = sample_21.show(source=src)
esc.show(w10, w21)
Out[3]:
In [4]:
Qz = esc.var("qz")

fwhm_10 = esc.par("FWHM_10", 0.005, userlim=[0.003, 0.03], fixed=False)
fwhm_21 = esc.par("FWHM_21", 0.005, userlim=[0.003, 0.03], fixed=False)

specrefl_10 = esc.specrefl(Qz, sample_10, "matrix", source=src)
specrefl_10 = esc.average_normal(specrefl_10, fwhm_10, Qz)

specrefl_21 = esc.specrefl(Qz, sample_21, "matrix", source=src)
specrefl_21 = esc.average_normal(specrefl_21, fwhm_21, Qz)
In [5]:
B10 = esc.par("Bgr 10", 1, scale=1e-6, userlim=[0, 5])
B21 = esc.par("Bgr 21", 1, scale=1e-6, userlim=[0, 5])
I10 = specrefl_10 + B10
I21 = specrefl_21 + B21
In [6]:
qz, y, err = np.loadtxt(
    "data/JAP15/XRR/Silicon/s10/ASCII/Si10.dat", unpack=True, skiprows=2
)
qz = qz * 10
dobj10 = esc.data(qz, y, err, copy=True)


qz, y, err = np.loadtxt(
    "data/JAP15/XRR/Silicon/s21/ASCII/Si21.dat", unpack=True, skiprows=2
)
qz = qz * 10
dobj21 = esc.data(qz, y, err, copy=True)
In [7]:
mobj10 = esc.model(I10, dobj10, residuals_scale="sqrt", weight_type="none", cost_weight=1.0, normalize_cost=True)
mobj21 = esc.model(I21, dobj21, residuals_scale="sqrt", weight_type="none", cost_weight=1.0, normalize_cost=True)
In [8]:
opt = esc.diffevol(
    [mobj10, mobj21],
    popsize=7,
    maxiter=50,
    ftol=1e-3,
    nupdate=1,
    strategy="best1bin",
    polish_final_maxiter=50,
    polish_candidate_maxiter=0,
)
opt()
opt.show().config_model(ylog=True)
Out[8]:
In [9]:
opt
Out[9]:
Name: Differential Evolution	Parameters number:         22
Parameter           	Value          	+-	Error     	Units     	Fixed
FWHM_10             	      0.0069825	+-	0.00077151	          	    0
Capping density     	         2.9796	+-	0.0041344 	g/cm^3    	    0
Cap_common Thickness	         12.214	+-	0.0073694 	nm        	    0
Cap_common Roughness	            1.5	+-	0         	nm        	    0
CuNi density        	         9.4693	+-	0.0010195 	g/cm^3    	    0
CuNi_common Thickness	         13.849	+-	0.088585  	nm        	    0
CuNi_common Roughness	        0.66725	+-	0.0025419 	nm        	    0
Nb Density          	         8.9907	+-	0.0083987 	          	    0
Layer: Thickness    	             12	+-	0.11427   	nm        	    0
Layer: Roughness Sigma	              2	+-	0         	nm        	    0
SiO2 Density        	         1.8188	+-	0.24649   	          	    0
Layer: Thickness    	         1.9217	+-	0.084548  	nm        	    0
Layer: Roughness Sigma	         1.6308	+-	0.029865  	nm        	    0
Si Density          	          3.495	+-	0         	          	    0
Substrate: Roughness Sigma	        0.78057	+-	0.059601  	nm        	    0
Bgr 10              	         4.5164	+-	0.15488   	x1e-06	   	    0
FWHM_21             	       0.016671	+-	0.00021063	          	    0
Cap_common Thickness	         8.5979	+-	0.0074399 	nm        	    0
Cap_common Roughness	            1.5	+-	0         	nm        	    0
CuNi_common Thickness	         32.944	+-	0.088769  	nm        	    0
CuNi_common Roughness	        0.60802	+-	0.0026498 	nm        	    0
Bgr 21              	              5	+-	0.24562   	x1e-06	   	    0
In [10]:
w10 = sample_10.show(source=src)
w21 = sample_21.show(source=src)
esc.show(w10, w21)
Out[10]:
In [ ]: