SCANNING TUNNELING SPECTROSCOPY

Remove["Global`*"]

Highlights

Abstract

Off[General::spell,General::spell1];

Needs["Graphics`Arrow`"];

tera  = 10^12  ; micro = 10^-6;
giga  = 10^9   ; nano  = 10^-9; 
mega  = 10^6   ; pico  = 10^-12;
kilo  = 10^3   ; femto = 10^-15; 
milli = 10.^-3 ; atto  = 10^-18;

NSub = {
c   -> 2.99792458 10^8  , e     -> 1.6021773 10^-19,
h   -> 6.6260755 10.^-34, hbar  -> 1.05457 10.^-34 ,
K   -> 1.380658 10^-23  , me    -> 9.109389 10^-31 ,
mu0 -> 4. Pi 10^-7      , eps0  -> 8.85419 10^-12   };

ESi   =0.179 tera; rhoSi   =2330 ; nuSi   =0.28;
ESiO2 =0.06  tera; rhoSiO2 =2200 ; nuSiO2 =0.3;
ESi3N4=0.15  tera; rhoSi3N4=3100 ; nuSi3N4=0.24;
EAu   =0.08  tera; rhoAu   =19300; nuAu   =0.42;
ENi   =0.207 tera; rhoNi   =8900 ; nuNi   =0.41;
EW    =0.345 tera; rhoW    =19300; nuW    =0.28;
EPt   =0.17  tera; rhoPt   =21400; nuPt   =0.39;
EIr   =0.52  tera; rhoIr   =22500; nuIr   =0.3 ;
EHOPG =0.2   tera; rhoHOPG =2250 ; nuHOPG =0.3 ;
EPol  =0.001 tera; rhoPol  =1000 ; nuPol  =0.3 ;

xx     =0.8;
EPtIr  =xx 0.8 EPt+(1-xx) EIr;
rhoPtIr=xx rhoPt  +(1-xx) rhoIr;
nuPtIr =0.3;

opt= {
PlotRange  ->All,
AxesOrigin ->{0,0},
Frame      ->True,
GridLines  ->Automatic,           
DefaultFont->{"Times-Roman",8},
PlotStyle  ->{
Dashing[{.0001}],
Dashing[{.0200}],
Dashing[{.0200}],
Dashing[{.0200}],
Dashing[{.0200}],
Dashing[{.0200}]}};

Introduction

Scanning Tunneling Spectroscopy

Fermi-Dirac Statistics

Clear[f];
f[En_,EF_,v_,T_] =
N[1/(1+Exp[e(En-EF+v)/(K T)])/.NSub];

tblT = {4.2,77.,300.};

Fig12x1 = Plot[{
f[En,0.,0.,tblT[[1]]],
f[En,0.,0.,tblT[[2]]],
f[En,0.,0.,tblT[[3]]]},
{En,-.1,.1},
FrameLabel ->{"energy [eV]","Probability"},
Evaluate[opt]];

vb = 1;
Fig12x2 = Plot[
f[En,0,0,tblT[[3]]]-f[En,0,vb,tblT[[3]]],
{En,-2,1},
FrameLabel ->{"energy [eV]","Probability"},
Evaluate[opt]];

Print["side-wall width = ",
4 K tblT[[3]]/e/.NSub," [eV]"]

Clear[fc];
fc[En_,EF_,T_] = f[En,EF,0,T] (1.-f[En,EF,0,T]);

Fig12x3 = Plot[Evaluate[{
fc[En,0,tblT[[1]]],
fc[En,0,tblT[[2]]],
fc[En,0,tblT[[3]]]}],
{En,-.1,.1},
FrameLabel ->{"energy [eV]","Convolution"},
Evaluate[opt]];

Feenstra's Parameter

File Reading

Initialization

SetDirectory["/Users/sarid/papers/FinalBook1"];
name = "sts1601";

File Characterization

Clear[tbl1];
tbl1=ReadList[name,Number,RecordSeparators->{"\n"," "}];

dim1 = Dimensions[tbl1][[1]];
min1 = Min[tbl1];
max1 = Max[tbl1];
del1 = Max[tbl1]-Min[tbl1];
mid1 = tbl1[[dim1/2]]; 
Print["dimension = ",dim1];
Print["minimum   = ",min1];
Print["maximum   = ",max1];
Print["delta     = ",del1];
Print["middle    = ",mid1];

File Preparation

Averaging

Clear[tbl2,b1,b2];
nav = 5;
tbl2 = tbl1;
Do[
b1 = tbl2;
b2 = Table[N[(b1[[i-1]]+b1[[i]]+b1[[i+1]])/3],
{i,2,255}];
tbl2 = Join[{b2[[1]]},b2,{b2[[254]]}],
{n,1,nav}];

dim2 = Dimensions[tbl2][[1]];
del2 = Max[tbl2]-Min[tbl2];
Print["dimension = ",dim2 ];

Normalization

Clear[tbli];
tbli = Table[N[(tbl2[[n]]-tbl2[[dim1/2]])/del2],
{n,1,dim1,1}];

dimi = Dimensions[tbli][[1]];
mini = Min[tbli];
maxi = Max[tbli];
midi = tbli[[dimi]];
deli = Max[tbli]-Min[tbli]; 
Print["dimension = ",dimi];
Print["minimum   = ",mini];
Print["maximum   = ",maxi];
Print["delta     = ",deli];
Print["middle    = ",tbli[[dimi/2]]];

Voltage Information

vmax = 3.;
delv = 2 vmax/dim1;

Clear[tblv];
tblv = Table[(n-dim1/2) 2 vmax/dim1,{n,1,dim1}];

Print["goof = ",tblv[[1]]+vmax]

Spectroscopic Data

$i(v)$

tbliv = 
Table[{tblv[[n]],Abs[tbli[[n]]]},
{n,1,dim1}];

xlimit = .1;
ylimit = .3;
Fig12x4 = ListPlot[
tbliv,
PlotRange->{
{-vmax+xlimit,vmax-xlimit},
{0,ylimit}},
Frame->True,
PlotJoined->True,
GridLines->Automatic,
DefaultFont->{"Times-Roman",8},
FrameLabel ->{"Energy [eV]","i(v) [a.u.]"}];

$\partial i/\partial v$

c1 = 
N[Table[(tbli[[n+5]]-tbli[[n-5]])/delv,
{n,1+5,dim1-5}]];
c2 = {0,0,0,0,0};
c3 = {0,0,0,0,0};
tbldidv = Join[c2,c1,c3];

dimdidv = Dimensions[tbldidv][[1]];
Print["dimension = ",dimdidv];

tbldidvv = 
Table[{tblv[[n]],Abs[tbldidv[[n]]]},
{n,2,dim1}];

xlimit = .2;
ylimit = 3.;
Fig12x5 = 
ListPlot[tbldidvv,
PlotRange->{
{-vmax+xlimit,vmax-xlimit},
{0,ylimit}},
Frame->True,
PlotJoined->True,
GridLines->Automatic,
DefaultFont->{"Times-Roman",8},
FrameLabel ->{"Energy [eV]","di/dv [a.u.]"}];

$\partial \ln i/\partial \ln v$

dd = 
Max[tbli]/100;
tbldlnidlnvv = 
N[Table[{tblv[[n]],
Abs[tbldidv[[n]] tblv[[n]]]/
(Abs[tbli[[n]]]+dd)},
{n,1,dim1}]];

xlimit = .5;
ylimit = 110.;
dlnidlnvGraphics = 
ListPlot[tbldlnidlnvv,
PlotRange->{
{-vmax+xlimit,vmax-xlimit},
{0,ylimit}},
Frame->True,
PlotJoined ->True,
DefaultFont->{"Times-Roman",8},
GridLines  ->Automatic,
FrameLabel ->{"Energy [eV]",
"v/i di/dv [a.u.]"},
DisplayFunction->Identity];

Comparison of STS Results

tblx0 = {-3.33,-4.36,-6.05,-7.22,-7.34};

delE = 5.3;
tblx = tblx0+delE

z0=100.;
tblxGraphics = 
Plot[Evaluate[{
z0 fc[En,tblx[[1]],300.],
z0 fc[En,tblx[[2]],300.],
z0 fc[En,tblx[[3]],300.],
z0 fc[En,tblx[[4]],300.],
z0 fc[En,tblx[[5]],300.]}],
{En,-2.5,2.5},
PlotRange      ->All,
DisplayFunction->Identity];

Fig12x6 = 
Show[{dlnidlnvGraphics,tblxGraphics,
Graphics[{Thickness[0.01],
Text["t1g",{tblx[[1]],95}],
Text["t1u",{tblx[[2]],95}],
Text["hu",{tblx[[3]],95}],
Text["hg",{tblx[[4]]+.1,95}],
Text["gg",{tblx[[5]]-.1,95}],
Line[{{tblx[[1]],80},{tblx[[1]],90}}],
Line[{{tblx[[2]],80},{tblx[[2]],90}}],
Line[{{tblx[[3]],80},{tblx[[3]],90}}],
Line[{{tblx[[4]],80},{tblx[[4]],90}}],
Line[{{tblx[[5]],80},{tblx[[5]],90}}]}]},
Frame->True,
DisplayFunction->$DisplayFunction];