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K?o7LvnFill) //then the solid has a lower index than the filling medium, need to swap these two values for the equation to work properly
// variable nTEMP=nREF
// nREF=nFill
// nFill=nTEMP
// endif
fraction_filled=((1-P)*(nSi^2-n^2)/(nSi^2+2*n^2)+P*(nREF^2-n^2)/(nREF^2+2*n^2))/((nREF^2-n^2)/(nREF^2+2*n^2)-(nFill^2-n^2)/(nFIll^2+2*n^2))
print fraction_filled
GFraction=fraction_filled/P
if (GFraction>1)
DoAlert 0 ("Solid index too low. For this thickness and porosity, no amount of filling by a solid of index "+num2str(nFill)+" can yield EOT="+num2str(GEOTSolid)+" nm. Max possible EOT (nL): "+num2str(GThickness*Bruggeman(nSi, nfill,P)))
GFraction=NaN
endif
if (GFraction<0)
DoAlert 0 ("EOT too low. For this thickness and porosity, no amount of filling by a solid of index "+num2str(nFill)+" can yield the given EOT value. Even if the pores are completely empty, the EOT (nL) will be: "+num2str(GThickness*Bruggeman(nSi, 1,P))+" nm.")
GFraction=NaN
endif
GMassPerArea=fraction_filled*GThickness*1e-4*GSolidDensity
CalcSingleLayerSpectrum(GEOTSolid) //make simulated spectrum
Duplicate/O Spectrum Fill_Spectrum
EndMacro
Window CalculatePorosity() : Panel
PauseUpdate; Silent 1 // building window...
NewPanel /W=(624,44,887,349)
SetDrawLayer UserBack
SetDrawEnv linethick= 4,linefgc= (65535,0,0)
DrawLine 10,124,252,124
SetDrawEnv fstyle= 1
DrawText 33,147,"How much is in the pores?"
PopupMenu Liquid,pos={0,1},size={124,20},proc=SelectLiquid,title="Liquid used:"
PopupMenu Liquid,mode=7,popvalue="Ethanol",value= #"\"Ethanol;Water;Toluene;Hexane;Methanol;Acetone;Buffer\""
ValDisplay GnFill,pos={142,4},size={88,14},title="index:"
ValDisplay GnFill,limits={0,0,0},barmisc={0,1000},value= #"GnFill"
SetVariable SetEOT2,pos={6,46},size={239,15},title="EOT(nL) of layer in "
SetVariable SetEOT2,limits={1,Inf,1},value= GEOT2
SetVariable SetEOT1,pos={6,28},size={239,15},title="EOT(nL) of layer in Air"
SetVariable SetEOT1,limits={1,Inf,1},value= GEOT1
Button CalculatePorosity,pos={8,82},size={64,20},proc=GotoCalculatePorosity,title="calculate"
ValDisplay GThickness,pos={83,82},size={150,14},title="Thickness (nm):"
ValDisplay GThickness,format="%d",limits={0,0,0},barmisc={0,1000}
ValDisplay GThickness,value= #"GThickness"
ValDisplay GPorosity,pos={93,100},size={120,14},title="Porosity (%):"
ValDisplay GPorosity,format="%g",limits={0,0,0},barmisc={0,1000}
ValDisplay GPorosity,value= #"round((GPorosity)*1000)/10"
SetVariable SetSolidIndex,pos={12,150},size={239,15},title="Index of solid loaded:"
SetVariable SetSolidIndex,limits={1,10,0.01},value= GnSolid
SetVariable SetSolidDensity,pos={13,250},size={239,15},title="Density of solid loaded (g/ml):"
SetVariable SetSolidDensity,limits={0,20,0.1},value= GSolidDensity
SetVariable SetSolidEOT,pos={12,190},size={239,15},title="EOT (nL) of layer w/solid in air:"
SetVariable SetSolidEOT,limits={1,Inf,1},value= GEOTSolid
ValDisplay fraction_filled,pos={103,211},size={150,14},title="Fractional filing:"
ValDisplay fraction_filled,format="%f",limits={0,0,0},barmisc={0,1000}
ValDisplay fraction_filled,value= #"GFraction"
ValDisplay mass_loaded,pos={91,269},size={160,14},title="Mass loaded (mg/cm2):"
ValDisplay mass_loaded,limits={0,0,0},barmisc={0,1000},value= #"GMassPerArea"
Button CalculateFraction,pos={13,209},size={64,20},proc=GotoCalculateFractionalFilling,title="calculate"
SetVariable set_Si_index,pos={6,62},size={146,15},title="porous Si index"
SetVariable set_Si_index,limits={1,Inf,0.01},value= GnSi
PopupMenu REF_matrix,pos={100,167},size={129,20},proc=SelectLiquid,title="Measured in:"
PopupMenu REF_matrix,mode=7,popvalue="Buffer",value= #"\"Ethanol;Water;Toluene;Hexane;Methanol;Acetone;Buffer\""
EndMacro
Function UpdateCalculatePorosityPanel()
SVAR GFill_Liquid=GFill_Liquid
SVAR GMeasurement_Liquid=GMeasurement_Liquid
SetVariable SetEOT2, title="EOT(nL) of layer in "+GFill_Liquid
SetVariable SetSolidEOT, title="EOT (nL) of layer w/solid in "+GMeasurement_Liquid
End
//Macro MakeSpectrum(fill_index) //This calculates what the reflectivity spectrum should look like, given the refractive index of the filling material
// Variable fill_index
// DoubleLayerCalc(fill_index)
// //Spectrum=Spectrum*IRF //correct it to the instrument response function (or you can use a gaussian IRF=exp(-((x-800)/200)^2))
//EndMacro
Macro CalcSingleLayerSpectrum(fill_index) //This calculates what the reflectivity spectrum should look like, given a bulk refractive index, a porous Si index, the index of the material filling the pores, and a
//film thickness. It assumes the sample is immersed in the "fill liquid." Based on the standard optical model for reflectivity from a Fabry-Perot layer (ignoring multiple reflections), and using the
//two-componenet Bruggeman model to calculate refractive index. It assumes that the film has no absorption losses and that the index is constant with wavelength.
VARIABLE fill_index //index of whatever is filling the pores
//Make/D/N=6/O w_coef
//Variable A1, A2, A3, f1, f2, f3 //variables to pass to the function that calculates the spectrum, called "single_layer_interference"
Variable rhoa, rhob, layer1_2nL //local variables, in terms of the reflectivity equation
variable porous_Si_index=GnSi //this is the globally-defined refractive index for porous silicon
variable layer1_porosity=Gporosity //this is the globally-defined porosity for the porous Si film. Calculated by the routine "calculate_Porosity_fit"
//variable layer2_porosity=Gporosity //this is also the globally-defined porosity for the porous Si film. Calculated by the routine "calculate_Porosity_fit"
variable layer1_thickness=Gthickness //this is the globally-defined thickness of the porous Si film. Calculated by the routine "calculate_Porosity_fit"
//variable layer2_thickness=0 //assume zero, because in this program we only want to calculate a single-layer film
variable bulk_Si_index=4.1 //the usual value used. Assuming this doesn't change over the wavelength range here.
variable layer1_index
layer1_index=Bruggeman(porous_Si_index, fill_index,layer1_porosity)
rhoa=(fill_index-layer1_index)/(fill_index+layer1_index)
rhob=(layer1_index-bulk_Si_index)/(layer1_index+bulk_Si_index)
layer1_2nL=2*layer1_index*layer1_thickness
Spectrum=rhoa^2+rhob^2+2*rhoa*rhob*cos(2*pi*layer1_2nL/Wavelength)
EndMacro
//Macro DoubleLayerCalc(fill_index) //This calculates what the reflectivity spectrum should look like, given a bulk refractive index, a porous Si index, the index of the material filling the pores, and a film thickness. It was written for double-layers
////but in this program it only calculates the spectrum for single-layers (Layer 2 assumed to have zero thickness).
// VARIABLE fill_index //index of whatever is filling the pores
// Make/D/N=6/O w_coef
// Variable A1, A2, A3, f1, f2, f3 //variables to pass to the function that calculates the spectrum, called "double_layer_interference"
// Variable rhoa, rhob, rhoc, layer1_2nL, layer2_2nL //local variables, in terms of the reflectivity equation
// variable porous_Si_index=GnSi //this is the globally-defined refractive index for silicon
// variable layer1_porosity=Gporosity //this is the globally-defined porosity for the porous Si film. Calculated by the routine "calculate_Porosity_fit"
// variable layer2_porosity=Gporosity //this is also the globally-defined porosity for the porous Si film. Calculated by the routine "calculate_Porosity_fit"
// variable layer1_thickness=Gthickness //this is the globally-defined thickness of the porous Si film. Calculated by the routine "calculate_Porosity_fit"
// variable layer2_thickness=0 //assume zero, because in this program we only want to calculate a single-layer film
// variable bulk_Si_index=4.1 //the usual value used. Assuming this doesn't change over the wavelength range here.
// variable layer1_index
// variable layer2_index
// layer1_index=Bruggeman(porous_Si_index, fill_index,layer1_porosity)
// layer2_index=Bruggeman(porous_Si_index, fill_index,layer2_porosity)
// rhoa=(fill_index-layer1_index)/(fill_index+layer1_index)
// rhob=(layer1_index-layer2_index)/(layer1_index+layer2_index)
// rhoc=(layer2_index-bulk_Si_index)/(layer2_index+bulk_Si_index)
// layer1_2nL=2*layer1_index*layer1_thickness
// layer2_2nL=2*layer2_index*layer2_thickness
// A1=rhoa*rhob // this is equal to the layer1 FFT peak amplitude
// A2=rhob*rhoc // this is equal to the layer2 FFT peak amplitude
// A3=rhoa*rhoc //this is equal to the FFT peak amplitude representing both layers together
// f1=layer1_2nL //optical thickness of layer 1
// f2=layer2_2nL //optical thickness of layer 2
// f3=layer1_2nL+layer2_2nL //optical thickness of both layers together
// W_coef[0] = {A1,A2,A3,f1,f2,f3}
// spectrum=double_layer_interference(w_coef,wavelength)
//EndMacro
Function Bruggeman_old(nSi, nfill,P)
//for a given porosity, Si index, and index of the filling medium, provides the value of the refractive index of the layer, based on the Bruggeman effective medium model
variable P, nSi, nfill
Make/O/n=4000 n
n=1+x/600 //calculate refractive index in the range 1 to 7.7
Make/O/n=4000 Bruggeman_function=(1-P)*(nSi^2-n^2)/(nSi^2+2*n^2)+(P)*(nfill^2-n^2)/(nfill^2+2*n^2)
findlevel/Q Bruggeman_function, 0 //where this function crosses zero
return (n(V_LevelX))
End
Function Bruggeman(nSi, nfill,P)
//for a given porosity, porous Si index, and index of the filling medium, provides the value of the refractive index of the layer, based on the two-component Bruggeman effective medium model
//uses the exact solution
variable P, nSi, nfill
return (0.5*sqrt(2*nSi^2-nfill^2-3*P*nSi^2+3*P*nfill^2+sqrt(8*nSi^2*nfill^2+(-2*nSi^2+nfill^2+3*P*nSi^2-3*P*nfill^2)^2)))
End
Function double_layer_interference(w,x)
Wave w
Variable x
//This is the interference spectrum for a double layer, accd to Gordon Miskelly:
//R = [rhoa^2 + rhob^2 + rhoc^2 ] + 2rhoa*rhob*cos(2d1) + 2rhob*rhoc*cos(2d2) + 2rhoa*rhoc*cos(2(d1+d2))
//The treatment is taken from Thin-film Optical Filters, by H. A. McLeod, Adam Hilger Ltd, Bristol, 1986, p.49 (single reflection per layer)
//delta1=2*pi*layer1_index*layer1_thickness/wavelength[i] //phase relationship of layer 1
//delta2=2*pi*layer2_index*(total_thickness-layer1_thickness)/wavelength[i] //phase relationship of layer2
//rhoa=(solution_index-layer1_index)/(solution_index+layer1_index)
//rhob=(layer1_index-layer2_index)/(layer1_index+layer2_index)
//rhoc=(layer2_index-bulk_Si_index)/(layer2_index+bulk_Si_index)
//now there will be 3 peaks in the FFT of the spectrum, and their positions correspond to:
//2nL of layer 1, layer 2, and the combination layer1+layer2, respectively
//the intensities of the FFT peaks correspond to 2rhoa*rhob, 2rhob*rhoc, and 2rhoa*rhoc, respectively
//in terms of the variables in this program:
//f1=layer1_2nL
//f2=layer2_2nL
//f3=both_layers_2nL
//delta1=pi*f1/x
//delta2=pi*f2/x
//delta1+delta2=delta3=pi*f3/x
//A1=rhoa*rhob=layer1_FFT_amplitude
//A2=rhob*rhoc=layer2_FFT_amplitude
//A3=rhoa*rhoc=both_layers_FFT_amplitude
//rhoa^2+rhob^2+rhoc^2=(A1*A3/A2+A2*A3/A1+A1*A2/A3)
// f(x) =(A1*A3/A2+A1*A2/A3+A2*A3/A1)+2*A1*cos(2*pi*f1/x)+2*A2*cos(2*pi*f2/x)+2*A3*cos(2*pi*f3/x)
// the 6 coefficients for this function are passed to it from the W_coef wave:
//w[0] = A1
//w[1] = A2
//w[2] = A3
//w[3] = f1
//w[4] = f2
//w[5] = f3
if(w[0]==0 && w[1]==0)
//calculate result for a single layer Fabry-Perot film. Why this is needed:
//If the two layers have equal index, rhob will be zero. Unfortunately that means that w[0] and w[1] will be zero.
//this conditional is needed to avoid the divide by zero error that is therefore incurred in the double layer interference equation.
//For this special case the equation reduces to the single-layer Fabry-Perot equation. Mathematically, we assume that w[0] and w[1] are
//vanishingly small, but that their ratio is equal to 1 (they approach zero at the same rate).
return 2*w[2]+2*w[2]*cos(2*pi*w[5]/x)
else
return (w[0]*w[2]/w[1]+w[0]*w[1]/w[2]+w[1]*w[2]/w[0])+2*w[0]*cos(2*pi*w[3]/x)+2*w[1]*cos(2*pi*w[4]/x)+2*w[2]*cos(2*pi*w[5]/x)
endif
End
Function SelectSpectrum2DisplayPop(ctrlName,popNum,popStr) : PopupMenuControl
String ctrlName
Variable popNum
String popStr
CheckDisplayed/W=Graph0 $popStr
if(V_flag==1)//then the spectrum is already up, don't put up again
else
AppendtoGraph/W=Graph0 $popStr vs wavelength
if(cmpstr(popstr,"Fill_Spectrum")==0)
ModifyGraph rgb(Fill_Spectrum)=(26214,26214,26214)
endif
if(cmpstr(popstr,"Liquid_Spectrum")==0)
ModifyGraph rgb(Liquid_Spectrum)=(1,4,52428)
endif
if(cmpstr(popstr,"Air_Spectrum")==0)
ModifyGraph rgb(Air_Spectrum)=(0,43690,65535)
endif
endif
End
Function SelectSpectrum2RemovePop(ctrlName,popNum,popStr) : PopupMenuControl
String ctrlName
Variable popNum
String popStr
CheckDisplayed/W=Graph0 $popStr
if(V_flag==1)//then the selected spectrum is up, remove it
RemoveFromGraph/W=Graph0 $popStr
endif
End
Window Graph0() : Graph
PauseUpdate; Silent 1 // building window...
Display /W=(1,44,587,470) Air_Spectrum vs wavelength as "Spectrum"
AppendToGraph Liquid_Spectrum vs wavelength
ModifyGraph rgb(Air_Spectrum)=(0,43690,65535),rgb(Liquid_Spectrum)=(1,4,52428)
ModifyGraph mirror=2
Label left "\\Z14Reflectance"
Label bottom "\\Z14Wavelength, nm"
ShowInfo
ControlBar 50
PopupMenu display_spectrum,pos={6,2},size={141,20},proc=SelectSpectrum2DisplayPop,title="display:"
PopupMenu display_spectrum,mode=3,popvalue="Fill_Spectrum",value= #"Wavelist(\"*_Spectrum\",\";\",\"\")"
PopupMenu remove_spectrum,pos={4,24},size={143,20},proc=SelectSpectrum2RemovePop,title="remove:"
PopupMenu remove_spectrum,mode=3,popvalue="Fill_Spectrum",value= #"Wavelist(\"*spectrum\",\";\",\"WIN:Graph0\")"
EndMacro