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ELECTRONIC TRANSPORT IN

QUANTIZED LOW DIMENSIONAL

SEMICONDUCTOR SYSTEMS ANDMETAL NANOPARTICLES

SanjuSanjuSanjuSanju ShresthaShresthaShresthaShrestha

Tribhuvan University,

Kathmandu, Nepal


2/45

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::::


3/45

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


16/45

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.


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


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.


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


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


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

- 0.20.8


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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


36/45

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


40/45

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.


42/45

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....


43/45

-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)


44/45

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

44


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