SKP Eng Sanju
Transcript of SKP Eng Sanju
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ELECTRONIC TRANSPORT IN
QUANTIZED LOW DIMENSIONAL
SEMICONDUCTOR SYSTEMS ANDMETAL NANOPARTICLES
SanjuSanjuSanjuSanju ShresthaShresthaShresthaShrestha
Tribhuvan University,
Kathmandu, Nepal
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Compound/Elemental SemiconductorCompound/Elemental SemiconductorCompound/Elemental SemiconductorCompound/Elemental Semiconductor
E
(Ef,0)
(Ef,kf)
kfElectron &
photon
Electron,
photon &
k(E
f
(E
ph
ph
f
interaction phononinteraction
nergy andnergy andnergy andnergy andmomentummomentummomentummomentumconservationconservationconservationconservation
GaAsGaAsGaAsGaAs SiSiSiSi
direct & Indirectdirect & Indirectdirect & Indirectdirect & Indirect bandgapbandgapbandgapbandgap::::
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3
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LOW DIMENSIONAL ELECTRONTRANSPORTSpatial confinement
Quantum well Quantum well wire :
Anderson in 1960
Heterojunction: Sakaki in1980 Sakaki H., Jpn. J.Appl. Phys. 19, L735(1980).
Quantum dot
4
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3D
bulk
2D
quantum well
1D
quantum wire
0 D
quantum dot
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Only fixedOnly fixedOnly fixedOnly fixedvalues ofvalues ofvalues ofvalues of
energyenergyenergyenergy
allowedallowedallowedallowed
Electron in a potential boxElectron in a potential boxElectron in a potential boxElectron in a potential box
GeorgeGeorgeGeorgeGeorge TookerTookerTookerTooker
R
Man in a boxMan in a boxMan in a boxMan in a boxZero energyZero energyZero energyZero energy
not allowednot allowednot allowednot allowed
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k
k
k
k
kk
k
3
1
2
E
E
N(E)
E
E
E
N(E)
1
2
3 E E E
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DENSITY OF STATES
TheThe numbernumber ofof availableavailable electronicelectronic statesstates perper
unitunit volumevolume perper unitunit energyenergy aroundaround anan energyenergyE
( ) ( ) = EEEN 1
Quantum numberQuantum number
In bulk 3D materials, It is given by volume of a
spherical shell having radius k and thickness
dk
szyx
zyx kkk ,,=
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DENSITY OF STATES FOR 3D, 2D, 1D AND 0D
STRUCTURES
( ) ( )0*
32
212
1
23
*
D3zyx
EmENkkn
Em
ENk,k,k
==
== h
( ) ( )
( ) ( ) ( )0D0
212
1
21
*
D1z
EEENl,m,n
Em
ENk,m,n
==
==
h
h
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dN/dE = dN/dk .
dk/dE
k2222
. 1/k
k or E 1/21/21/21/2
dN dE = dN dk . dk dE
3D
A spherical shell of radius k and thickness
dk
A circular discof radius k and
thickness dk
kx
ky
kz
E
N
dN/dE = dN/dk . dk/dE
= 1 . 1/k
= 1/k or 1/E1/21/21/21/2
= k . 1/k
= 1 or
constant
2D
1D
A slit ofthickness dk
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DOS VERSES ENERGY
E
N(E)
N(E)
E
N(E)
N(E)
E
N(E)
E
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DISTRIBUTION FUNCTIONNag B.R., Electron Transport in Compound
semiconductors(1980).
MaxwellMaxwell-- BoltzmannBoltzmann
( )
=
TK
EEeEf FMB
FermiFermi-- DirectDirect
BoseBose-- EinsteinEinstein
( )
+
=
TK
EEEf
B
F
FD
exp1
1
( )
=
TK
EEEf
B
F
BE
exp1
1
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BulkBulkBulkBulk How atoms are arranged inHow atoms are arranged inHow atoms are arranged inHow atoms are arranged in
crystal structurecrystal structurecrystal structurecrystal structure
MoleculesMoleculesMoleculesMolecules Constituent atoms andConstituent atoms andConstituent atoms andConstituent atoms and
BulkBulkBulkBulk MoleculesMoleculesMoleculesMolecules ---- AtomsAtomsAtomsAtoms
how these are bondedhow these are bondedhow these are bondedhow these are bonded
AtomsAtomsAtomsAtoms Properties depend uponProperties depend uponProperties depend uponProperties depend upon
atomic numberatomic numberatomic numberatomic number
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At what size quantum confinement becomesAt what size quantum confinement becomesAt what size quantum confinement becomesAt what size quantum confinement becomes
importantimportantimportantimportant
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Critical dimension for the quantum dot =Critical dimension for the quantum dot =Critical dimension for the quantum dot =Critical dimension for the quantum dot =
Electron wave lengthElectron wave lengthElectron wave lengthElectron wave length
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In absence of any perturbation, the total motion ofIn absence of any perturbation, the total motion of
electrons gets cancelledelectrons gets cancelled-- Brownian motionBrownian motion..
Presence of external perturbationPresence of external perturbation
Magnetic fieldMagnetic field
Electric fieldElectric field
Temperature gradientTemperature gradient
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TRANSPORT PARAMETERS
Electronic and thermalElectronic and thermal
MobilityMobilityElectrical ConductivityElectrical Conductivity
Electronic Thermal conductivityElectronic Thermal conductivity
Lattice Thermal conductivityLattice Thermal conductivity
Thermoelectric Figure of meritThermoelectric Figure of merit
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Transport ParametersTransport ParametersTransport ParametersTransport ParametersTransport ParametersTransport ParametersTransport ParametersTransport Parameters
NagNag BB..RR..,, ElectronElectron TransportTransport inin CompoundCompound semiconductors,semiconductors, SpringerSpringer SeriesSeriesinin SolidSolid StateState Sciences,Sciences, eded.. byby MM..CardonaCardona,, PP..FuldeFulde andand HH..JJ..OuessierOuessier(Springer,(Springer, Berlin)Berlin) ((19801980))..
MobilityMobilityMobilityMobilityMobilityMobilityMobilityMobility
*m
e=
Electrical ConductivityElectrical ConductivityElectrical ConductivityElectrical ConductivityElectrical ConductivityElectrical ConductivityElectrical ConductivityElectrical Conductivity
=*m
ne2
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Electronic Thermal ConductivityElectronic Thermal ConductivityElectronic Thermal ConductivityElectronic Thermal ConductivityElectronic Thermal ConductivityElectronic Thermal ConductivityElectronic Thermal ConductivityElectronic Thermal Conductivity,,
Smith R.A., Semiconductors, Academic Publishers,Smith R.A., Semiconductors, Academic Publishers, IIndIInd edition pp.147edition pp.147(1989).(1989).
wherewhere LotentzLotentz ratioratio
L= =
= Le
2
2
e
k222
22
k
Callaway J., Phys. Rev. 113,1046 (1959).Callaway J., Phys. Rev. 113,1046 (1959).
Total Thermal ConductivityTotal Thermal ConductivityTotal Thermal ConductivityTotal Thermal ConductivityTotal Thermal ConductivityTotal Thermal ConductivityTotal Thermal ConductivityTotal Thermal Conductivity
( )x
1e
exT
2
kkT
T
0
2x
xC
43
2
B
3
Blatt
D
=
h
latte +=
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SeebeckSeebeckSeebeckSeebeckSeebeckSeebeckSeebeckSeebeck CoefficientCoefficientCoefficientCoefficientCoefficientCoefficientCoefficientCoefficient
Nag B.R., Electron Transport in Compound semiconductors (1980).Nag B.R., Electron Transport in Compound semiconductors (1980).
+=
=
TkTk
E
e
k
TS
BB
FB
z
EgliEgli P.EdP.Ed., Thermoelectricity (Wiley, New York) (1961).., Thermoelectricity (Wiley, New York) (1961).
Harmon C. andHarmon C. and HonigHonig J.M., J. Appl. Phys. 33, 3178J.M., J. Appl. Phys. 33, 3178--3188 (1962).3188 (1962).
Rowe D.M. andRowe D.M. and BhandariBhandari C.M., ModernC.M., Modern ThermoelectricsThermoelectrics (Reston, Reston(Reston, Reston
VA), (1983).VA), (1983).
= 2SZ
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Comparative studies ofComparative studies ofComparative studies ofComparative studies ofReducedReducedReducedReduced
Dimensionality onDimensionality onDimensionality onDimensionality onelectron transport atelectron transport atelectron transport atelectron transport at
&&&&Systems at LowSystems at LowSystems at LowSystems at LowTemperaturesTemperaturesTemperaturesTemperatures
AsGaGaAs/Al x)-(1x As/InInGa x)-(1x
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Why GaAs?
Large band structure: high temperature performanceand radiation hardness
Direct bandgap: excellent optical properties as well assuperior electron transport in the conduction band
The band a in eneral decreases as the tem erature
increases: The band gap of GaAs, for examples, is1.51eV at and 1.43eV at room temperatures
Importance for both electronic and optoelectronicdevices
The material has high mobility suitable for high speeddevices
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101
102
103
104
105
106 2D EG
GaAs
n2D
=1x1014
m-2
in
pzac
m
obility
m
2V-1S
-1
102
103
104
105
106
sr
in
pz
1D EG
GaAs
n1D
=1x107m
-1
m
obility
m
2V-
1S-
1
Variation of 2D EG dc mobility versus
temperature for GaAs for various scatteringmechanisms such as acoustic phonon viadeformation potential (ac), piezoelectric (pz),ionized impurity (in), alloy disorder (all) and
surface roughness (sr) scatteringmechanisms.
Variation of 1D EG dc mobility versus
temperature for GaAs for various scatteringmechanisms such as acoustic phonon viadeformation potential (ac), piezoelectric (pz),ionized impurity (in) and surface roughness(sr) scattering mechanisms.
0 40 80 120 16010
-1
100
Temperature K
0 40 80 120 16010
1
ac
Temperature K
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8
12
16
2
1
2D EG
1: GaAs: ac+pz+in+sr
2: InGaAs: ac+pz+in+all+srn
2D=1x10
14m
-2
dc
m
obi
lity
m
2V-1S
-1
100
200
300
400
500
600 2
1
1D EG
1: GaAs
2: InGaAs
ac+pz+in+sr
n1D
=1x107m
-1dc
m
ob
ility
m
2V-1S-1
Variation of 2D EG dc mobility versus
temperature for GaAs (1) and InGaAs (2)with various scattering mechanisms such as acoustic phonon viadeformation potential (ac), piezoelectric(pz), ionized impurity (in) and surfaceroughness (sr) scattering mechanisms.
Variation of 1D EG dc mobility versus
temperature for GaAs (1) and InGaAs (2)with various scattering mechanisms such as acoustic phonon viadeformation potential (ac), piezoelectric(pz), ionized impurity (in) and surfaceroughness (sr) scattering mechanisms.
0 40 80 120 160
Temperature K
0 40 80 120 1600
Temperature K
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2
4
6
8
10
1
2
r
im
1
2
2D EG
= 60GHZ
1: GaAs: ac+pz+in+sr
2: InGaAs: ac+pz+in+all+sr
n2D
=1x1014
m-2
ac
m
ob
ility
m
2V-
1S-
1
0
4
8
12
16
2
2
1
1
r
im
1: GaAs
2: InGaAs
ac+pz+in+srn
1D=1x10
7m
-1
1D EG
= 60GHz
ac
mo
bility
m
2V-1S-1
Variation of 2D EG ac mobility versustemperature at constant frequency 60GHz forGaAs (1) and InGaAs (2) with various
scattering mechanisms such as acousticphonon via deformation potential (ac),piezoelectric (pz), ionized impurity (in), alloydisorder (all) and surface roughness (sr)
scattering mechanisms.
Variation of 1D EG ac mobility versustemperature at constant frequency 60GHz for
GaAs (1) and InGaAs (2) with various scattering mechanisms such as acousticphonon via deformation potential (ac),piezoelectric (pz), ionized impurity (in) and
surface roughness (sr) scatteringmechanisms.
0 40 80 120 1600
Temperature K
0 40 80 120 160
Temperature K
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0
4
8
12
16
2
2
1
1
r
im
2D EG
T= 77K
1: GaAs: ac+pz+in+sr
2: InGaAs: ac+pz+in+all+sr
n2D
=1x1014
m-2
ac
m
obility
m
2V-1S-1
0
20
40
60
80
100
1
2
2
1
r
im
1D EG
T= 77K
1: GaAs
2: InGaAsac+pz+in+sr
n1D
=1x107m
-1ac
m
obility
m
2V-
1S-
1
Variation of 2D EG ac mobility versusfrequency at constant temperature 77K
for GaAs (1) and InGaAs (2) with variousscattering mechanisms such as acousticphonon via deformation potential (ac),piezoelectric (pz), ionized impurity (in),alloy disorder (all) and surfaceroughness (sr) scattering mechanisms.
Variation of 1D EG ac mobility versusfrequency at constant temperature 77K
for GaAs (1) and InGaAs (2) with variousscattering mechanisms such as acousticphonon via deformation potential (ac),piezoelectric (pz), ionized impurity (in)and surface roughness (sr) scatteringmechanisms.
0 40 80 120 160
Frequency GHz
0 40 80 120 160
Frequency GHz
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BAND STRUCTURE EFFECTS ONBAND STRUCTURE EFFECTS ONBAND STRUCTURE EFFECTS ONBAND STRUCTURE EFFECTS ON
ELECTRICAL AND THERMALELECTRICAL AND THERMALELECTRICAL AND THERMALELECTRICAL AND THERMALPROPERTIES OF MERCURY CADMIUMPROPERTIES OF MERCURY CADMIUMPROPERTIES OF MERCURY CADMIUMPROPERTIES OF MERCURY CADMIUM
UNDERUNDERUNDERUNDER MAGNETIC QUANTIZATION INMAGNETIC QUANTIZATION INMAGNETIC QUANTIZATION INMAGNETIC QUANTIZATION IN
LONGITUDINAL CONFIGURATIONLONGITUDINAL CONFIGURATIONLONGITUDINAL CONFIGURATIONLONGITUDINAL CONFIGURATION
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WHY MERCURY CADMIUM TELLURIDE (MCT)?
alloy semiconductor: adjustable bandgap
very narrow and direct bandgap for intrinsicoperation, as it is associated with a high
absorption coefficient and a moderate dielectriccoefficient/index of refraction: good applicant invarious electronics and optoelectronics devices
low effective mass: electrons would occupy thelowest Landau levels at a reasonable highmagnetic field,
very high mobility of MCT: hence, good applicantfor thermoelectric devices such as cooler,refrigerator etc
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10
100
1000
hypernonp
para
T=77K
in+all+ac+pz+pop
n=1020
m-3
Condu
ctivitym
2V-1S-1
100
hyper
nonp
paraB=4Tin+all+ac+pz+pop
n=1020
m-3
Con
ductivitym
2V-1S-1
VARIATION OF CONDUCTIVITY WITHTEMPERATURE AT CONSTANT MAGNETIC
FIELD 4T FOR NONDEGENERATE N- HG0.8CD0.2TE WITH VARIOUS SCATTERINGMECHANISMS SUCH AS IONIZED IMPURITY(IN), ALLOY DISORDER (ALL), ACOUSTICPHONON VIA DEFORMATION POTENTIAL(AC), PIEZOELECTRIC (PZ) AND POLAROPTICAL PHONON (POP) SCATTERING
MECHANISMS.
VARIATION OF CONDUCTIVITY WITH MAGNETICFIELD AT CONSTANT TEMPERATURE 77K FOR
NONDEGENERATE N-HG0.8CD0.2TE WITHVARIOUS SCATTERING MECHANISMS SUCH ASIONIZED IMPURITY (IN), ALLOY DISORDER(ALL), ACOUSTIC PHONON VIA DEFORMATIONPOTENTIAL (AC), PIEZOELECTRIC (PZ) ANDPOLAR OPTICAL PHONON (POP) SCATTERING
MECHANISMS.
0 5 10 15 20
Magnetic Field T
0 50 100 150 200 250 300
Temperature K
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-4
0
4
8
12
hypernonp
para
B=4T
n=1020
m-3
Ferm
iEn
ergy
Level(
)
0
4
8
12
hypernonp
para
T=77K
n=1020
m-3
Ferm
iEnergy
Level(
)
Variation of Fermi Energy Level (
) with temperature at constantmagnetic field 4T for
nondegenerate n-Hg0.8Cd0.2Te.
Variation of Fermi Energy Level (
) with magnetic field at constanttemperature 77K for
nondegenerate n-Hg0.8Cd0.2Te.
0 50 100 150 200 250 300-8
Temperature K
0 5 10 15 20
-4
Magnetic Field T
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0.56
0.60
0.64
0.68
0.72
hypernonp
para
B=4T
in+all+ac+pz+pop
n=1020
m-3
Seebeck
Coefficientm
eVK-
1
0.5
0.6
0.7
0.8hypernonp
paraT=77Kin+all+ac+pz+pop
n=1020
m-3
Seeb
eck
Coefficientm
eVK-1
Variation of Seebeck coefficient
with temperature at constant
magnetic field 4T for nondegenerate n-Hg0.8Cd0.2Te .
Variation of Seebeck coefficient
with magnetic field at constant
temperature 77K for nondegenerate n-Hg0.8Cd0.2Te .
0 50 100 150 200 250 300
Temperature K
0 5 10 15 20
Magnetic Field T
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0
40
80
120
160
B=4T
in+all+ac+pz
n=1020
m-3
AC+PZ nonp
hyper
para
Z
Tx
10-6
0
1
2
3
4
5
hyper
nonp
para
T=30K
in+all+ac+pz
n=1020
m-3
AC+PZ
ZT
x10-
6
Variation of with temperature at
constant magnetic field 4T for
nondegenerate n-Hg0.8Cd0.2Te.Boundary scatterings due to
acoustic phonon (AC) and
piezoelectric (PZ) are included for
lattice thermal conductivity.
Variation of with magnetic field at
constant temperature 30K for
nondegenerate n-Hg0.8Cd0.2Te.Boundary scatterings due to
acoustic phonon (AC) and
piezoelectric (PZ) are included for
lattice thermal conductivity.
20 40 60 80 100
Temperature K
0 5 10 15 20
Magnetic Field T
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MAGNITUDE AND TIME RESPONSE OFELECTRONIC AND TOPOGRAPHICAL
CHANGES DURING HYDROGEN
SENSING IN SIZE SELECTED
PALLADIUM NANOPARTICLES
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TETRAHEDRAL VOID: SHOWING THECHANGE IN THE LATTICE CONSTANTWHEN THE VOID SPACE IS OCCUPIEDBY AN ATOM OF SIZE LARGER THANTHE VOID.
Octahedral void: showing that there is
no change in the lattice constant as the
size of the atom inside the void space
is smaller than the void.
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PHASE TRANSITION IN PDNANOPARTICLES WITH THE ABSORPTION
OF H: RESULT THE CHANGE IN ELECTRICAL
RESISTANCE AND THE PROPERTY IS USED
IN THE DETECTION OF H.
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-15
-10
-5
0
5
Pd15 CH =4% T = 20oC
R/R0%
Sensing response of sample Pd15 at forSensing response of sample Pd15 at forSensing response of sample Pd15 at forSensing response of sample Pd15 at for .... Solid andSolid andSolid andSolid and
dotted line represent gas on and off conditions.dotted line represent gas on and off conditions.dotted line represent gas on and off conditions.dotted line represent gas on and off conditions.
0 500 1000 1500 2000 2500 3000-25
-20
Time (s)
PdH with a rate constant k
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PdH with a rate constant k1
-PdH with a reaction rate constant k2
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0
20
0 100 200 300
0
20
Fitted curve
EE
Pd15
CH: 4%
T: 20oC0%
t>>>>>>>> =11.200.63 =7.50
t
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6
8
10
12
15 20 25
30
60
90(a)
(s)
CH: 4%
T: 20oC
%%%%
Electronic Effect
32
40
48
15 20 25
40
80
120
0000
(b) Topographical Effect
(s)
||||
||||%%%%
CH: 4%
T: 20oC
15 20 25
Nanoparticle Size (nm)
15 20 25
Nanoparticle Size (nm)
(a) and (b) Magnitude and response time for EE and TE, respectively, as
a function of nanoparticle size at 20o C and CH: 4%. in Fig. (b) is the
delay time for TE. It may be noted that is negative hence only the
magnitude of it is shown. Error bar represents the deviation from the
mean value in the fitting. The curves show only the nature of the trend.
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4
8
12
20 30 40 50 60
8
10
12
14
16
(a)
Electronic Effect
((((s))))
%%%% Pd15
CH: 4%
0
15
30
20 40 60
0
80
160
(b)
((((s))))
0000
Topographical Effect
||||
|%|%|%|%
Pd15
CH: 4%
Temperature (o
C)
20 40 60
Temperature (o
C)
(a)(a)(a)(a) andandandand (b)(b)(b)(b) MagnitudeMagnitudeMagnitudeMagnitude andandandand responseresponseresponseresponse timetimetimetime forforforfor EEEEEEEE andandandand TE,TE,TE,TE, respectively,respectively,respectively,respectively, forforforfor
samplesamplesamplesample PdPdPdPd15151515 asasasas aaaa functionfunctionfunctionfunction ofofofof temperaturetemperaturetemperaturetemperature atatatat CCCCHHHH====4444%%%% inininin Fig FigFigFig.... (b)(b)(b)(b) isisisis thethethethe
delaydelaydelaydelay timetimetimetime forforforfor TETETETE.... ItItItIt isisisis notednotednotednoted thatthatthatthat isisisis negativenegativenegativenegative hencehencehencehence onlyonlyonlyonly thethethethe magnitudemagnitudemagnitudemagnitude ofofofofitititit isisisis shownshownshownshown.... ErrorErrorErrorError barbarbarbar representsrepresentsrepresentsrepresents thethethethe deviationdeviationdeviationdeviation fromfromfromfrom thethethethe meanmeanmeanmean valuevaluevaluevalue inininin thethethethe
fittingfittingfittingfitting.... TheTheTheThe curvescurvescurvescurves showshowshowshow onlyonlyonlyonly thethethethe naturenaturenaturenature ofofofof thethethethe trendtrendtrendtrend....
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-0.09
-0.06
-0.03Electronic Effect
ln(R
/R0)-
1
E=14.90 meV
Pd15
CH=4%
-172.85492
(a)
0.0
0.2
0.4(b)
Pd15
CH=4%
Topographical Effect
ln(R
/R0)-
1
(a)a)a)a) AAAA plotplotplotplot showingshowingshowingshowing variationvariationvariationvariation ofofofof lnlnlnln(R(R(R(REEEE/R/R/R/R0000))))----1111 versusversusversusversus TTTT----1111 forforforfor samplesamplesamplesample PdPdPdPd15151515 atatatat
CCCCHHHH====4444%%%%,,,, withwithwithwith givengivengivengiven activationactivationactivationactivation energyenergyenergyenergy 14141414....90909090meVmeVmeVmeV.... (b)(b)(b)(b) VariationVariationVariationVariation ofofofof
lnlnlnln(R(R(R(REEEE/R/R/R/R0000))))----1111 versusversusversusversus TTTT----((((1111////2222))))forforforfor PdPdPdPd15151515....
0.0030 0.0032 0.0034
(Temperature)-1 (K-1)
0.055 0.056 0.057 0.058
(Temperature)-1/2 (K-1/2)
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ACKNOWLEDGEMENT
I am grateful to,
Prof. C. K. Sarkar, Dept. of ETCE, JadavpurUniversity, Kolkata
,
Indian National Science Academy, New Delhi
Prof. B. R. Mehta, TFL, Physics Department,,,,
IITD
TWAS
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