奈米線之製備及其熱、電傳導與熱力學性質之研究

國立交通大學

電子物理學系

博士論文

奈米線之製備及其熱、電傳導與熱力學性質之研究

Fabrication and Investigation of transport and

thermodynamic properties of nanowires

學

號： 9221809

研 究

生： 歐敏男

指 導 教 授： 楊宗哲 (Dr. Yang, Tzong-Jer) 教授

陳洋元 (Dr. Chen, Yang-Yuan) 教授

奈米線之製備及其熱、電傳導與熱力學性質之研究 學生：歐敏男 指導教授：楊宗哲 教授 陳洋元 教授

國立交通大學電子物理學系﹙研究所﹚碩士班

摘要

許多實驗結果顯示低維度材料具有與塊狀材料迥異的特性，這些性質的改變 可能肇因於材料尺寸的縮減。以一維量子線之奈米線為例，其電子能態的分佈受 到量子侷限限效應的改變，或因表面原子的比例增加，這些都可能是導致材料 熱、電、磁等性質改變的原因。為了研究奈米線的各種物理性質，我們分別利用 自組構與微影製程這兩種方法製備群聚之奈米線陣列及單一鎳奈米線。我們以電 化學沉積法讓材料填充於陽極氧化鋁(AAO)模板的孔洞中，製作奈米線陣列。以 此方法我們製作六角形排列之鐵(Fe)與三碲化二鉍(Bi2Te3)奈米線陣列，用以研究 其群聚之磁性與電性。其中鐵奈米線之線徑約60 及 200 奈米，而三碲化二鉍奈 米線之線徑則約60 奈米。X 光繞射顯示，60 奈米的鐵與三碲化二鉍奈米線陣列 均具有較好的結晶性，而線徑約200 奈米之鐵奈米線陣列，並無此明顯特徵。進 一步的磁性量測結果顯示，60 奈米鐵之飽合場較小且矯頑場較大，顯示 60 奈米 鐵確實具有較強之磁異向性能，此外其在小外加磁場中磁阻的變化與外加磁場大 小呈現平方關係，與材料之退磁場效應相關。 金屬的許多特性均與電子的行為相關，如金屬的熱傳導主要來自電子的貢 獻，因此金屬材料的電導率與熱導率比值遵守 Wiedemann-Franz 定律，研究單 一鎳奈米線之熱導性與電導性可以獲得電子與聲子在一維材料中的傳輸行為，並 進一步瞭解電子在材料中的特性。我們整合光與電子束微影製程、薄膜沉積及蝕

刻技術用以製備一根懸橋結構之鎳奈米線，其截面為100 奈米厚及 180 奈米寬之

矩形，長約35 微米。磁阻之量測顯示單一之鎳奈米線仍保有鐵磁性，其矯頑場

約500 Oe。我們用自行開發的電性量測系統與三倍頻技術(3ω technique)量測此

鎳奈米線在溫度15~300 K 之間的電阻率、熱傳導率與比熱，其室溫電阻率約為

36 μΩ-cm，殘餘電阻率約 17 μΩ-cm，因此其 RRR ~ 2 (Residual Resistivity Ratio)， 較一般塊材小，顯示此奈米線中具有許多雜質與缺陷，使電子受到嚴重的散射。

熱導率量測之結果亦顯示奈米線之室溫熱導率約為塊材的20%，且其值隨溫度下

降而下降，明顯與塊材不同。熱傳導率與電導率的量測結果顯示奈米線其電聲子

傳導特性僅於75-300 K 之間符合接近 Wiedemann-Franz 定律，顯示鎳奈米線中

Fabrication and Investigation of transport and thermodynamic properties

of nanowires

student：

Min-Nan

Ou

Advisors： Dr. Yang, Tzong-Jer

Dr. Chen, Yang-Yuan

Department of Electrophysics

National Chiao Tung University

Abstract

There are experiments revealing changes of physical properties in

low dimensional materials likely due to size reduction. In quasi one

dimension nanowires, the quantum confinement and surface effect may

affect their magnetism, transport, and thermodynamic properties. To

evaluate these one-dimensional properties a bottom-up method was used

to fabricate iron and Bi

2

Te

3

nanowires in an AAO template using

chemical electrodeposition. The average diameters of two highly

ordered iron nanowires are about 60 and 200 nm, respectively, and that of

Bi

2

Te

3

nanowires is 60 nm. Magnetization measurements show a larger

anisotropic magnetization in both 60-nm nanowires. It is illustrated by

the formation of magnetic easy axis and preferred crystal orientation of

[110] along the longitudinal axes of nanowires. The quadratic magnetic

field dependence of normalized magnetoresistance (MR) at low field is

attributed to the additional effect of demagnetization in low dimensional

systems.

nanowires for the direct study of transport and thermodynamic properties

in one wire. Optic, e-beam lithography, thermal evaporation, and

etching techniques were applied to construct individual and sagging

nickel nanowires on a silicon wafer. The thermal conductivity of the

sagging nickel nanowire was measured between 15 and 300 K. The

room temperature and 0.5 K electrical resistivity are about 36 μΩ-cm and

17 μΩ-cm respectively, giving a low residual resistivity ratio (RRR) of

only 2. As compared to the bulk Ni，this result indicates that the

conductive electrons are strongly scattered by defects and impurities. The

temperature dependence of thermal conductivity and Lorenz number also

significantly differ from that of the bulk. Transport measurement data

on the nickel nanowire show that at 75- 300 K, it follows the

Wiedemann-Franz law, whereas the agreement break down below 75 K

indicating that the thermal current is more suppressed than the electrical

current in the one dimension system.

誌謝

論文完成了，接下來才是最困難的部份，要把所有我在中央研究院物理所這 八年中所有該感謝的人一一列出，並將對他們的感謝之語寫下來，內容可能比論 文本文還長!回憶八年前，為了拓展自己科學研究的寬度，離開了中山大學物理 所，也離開了周雄老師的保護傘，帶著忐忑不安的心來到物理所陳洋元老師的實 驗室，首先面對的是完全不同的人際關係、以及新的實驗設備，面臨的是極度嚴 酷的挑戰，幸運的是有老師的支持-在生活上，老師盡可能的照顧大家並且給予 我們最好的福利，在實驗上，不免要求嚴格。而這正是從事科學研究最重要的基 本精神-在該謹慎的地方要求嚴謹，也才是迫使一個人蛻變的真實力量，而我就 是在這樣開放又嚴謹的環境下學習科學。之後在陳老師的鼓勵下進入交通大學電 子物理所攻讀博士班，這段期間在陳洋元及楊宗哲老師的諄諄教誨下，使我在各 方面均有長足的進步，過去八年，不僅在物理知識上收穫豐實，並培養了積極與 樂觀的研究態度，老師們對我的影響深遠，在這裡，由衷地再跟兩位老師說聲感 謝。 在這幾年的漫長時間裡，經歷了許多人生的大事，結婚、兩個小孩的出生， 這一切都不是我個人的力量足以承擔的，很感謝老師們這段期間給予我最大的支 持及體諒，更要感謝爸、媽、大妹、小妹以及整個家族給我的支持，雖然遇到了 很多困難，但也總算有驚無險的度過了，更感謝文娟及我的岳父母，不辭辛勞的 為我照顧兩個頑皮的小孩，也感謝兩個可愛的小孩昱辰、昱謙，在爸爸為實驗及 課業憂煩時帶給我歡樂，而這些人的支持是讓我繼續走向科學研究之路最大的助 力。當然不能忘記在奈米材料與低溫物理實驗室一起工作的夥伴，要感謝的人很 多，尤其在與王昌仁博士共事的幾年，讓我學習到許多的實驗技術，也要感謝董 崇禮博士及何建民教授為我修改文章，特別是何老師超導領域豐富的閱歷，擴展 了我的研究領域。感謝陳正龍在成長孔洞氧化鋁材料上的專業協助，尤其是他的

徒弟-林岱樺、林育竹，她們總是能為我成長出需要的奈米線樣品，此外，因為 李秉中與吳欣航的努力，我們正一步一步地完成我們的夢幻電路，也要感謝陳虹 圻學弟不厭其煩的為我測試各種『創意製程』，以及學弟劉佳誠在電子電路上的 協助，很懷念跟蔡傳博一起量測與修改比熱系統的日子，很幸運有機會一起與張 玉貴博士完成準分子雷射鍍膜系統，謝謝實驗室的所有成員黃柏翰、蔡尚任、洪 圖均、陳伯仲、林宜欣、郭玲如、曾文彥、黃偉嘉、周宗輝、吳炳賢、洪慈蓮、 熊德智與過去諸多在實驗與生活上幫助過我的成員陪我走過這一段歲月。也感謝 黃斯衍、徐豐麒在物理觀念及實驗技巧給與我許多建議，很榮幸，能與你們一起 在這個開放的研究環境裡討論科學問題。特別要感謝物理所陳啟東老師、『量子 電子元件實驗室』及『奈米核心設施中心』的相關成員在製備單一鎳奈米線樣品 中，於各種微影製程上的大力協助，特別要感謝賴水金學弟在電子束微影製程上 的指導。我的博士論文在這許多人的幫助下也才得以順利完成。 Here, also,

I sincerely thank Dr. Sergey R. Harutyunyan and Sonnathi Neeleshwar for discussion on experiment and interesting issues in physics.

Contents

中文摘要 ……… i

Abstract ………

iii

誌謝

……… v

Contents ………

vii

Tables ………

ix

Figures ………

x

1. Introduction………

1

2. Theorem………

5

2.1 Thermal

conduction……… 6

2.1.1 Kinetic theory of ideal particles……… 7

2.1.2 Thermal conductivity of metals………

8

2.2 Magnetism………

18

2.3 Thermoelectricity………

20

3. Experimental

facilities

and measurement methods…… 26

3.1

Introduction to experimental equipments……… 27

3.1.1 X-ray diffraction (XRD) ……… 27

3.1.2 Scanning electron microscope (SEM) ……… 28

3.1.3 M a g n e t i c P r o p e r t y M e a s u r e m e n t S y s t e m

(MPMS) ……… 29

3.1.4 P h y s i c a l P r o p e r t y M e a s u r e m e n t S y s t e m

(PPMS) ……… 29

3.1.5 Cryostat system……… 30

3.2

Electric property measurement methods……… 31

3.2.1 Four-probe method……… 31

3.2.2 Self-heating 3ω method……… 34

4. Nanowires

fabrication………

41

4.1 Bottom-up

method………

42

4.1.1 Fabrication of nano-scale porous template……… 42

4.1.2 Fabricate nanowires by electodeposition……… 49

4.2 Top-down

method………

50

4.2.1 Lithography……… 50

4.2.2 Thin film deposition system……… 58

4.2.3 Etching……… 59

5.

Results and Discussion……… 62

5.1

AAO template fabrication……… 63

5.2

Imbedded iron nanowires……… 66

5.2.1 Synthesis of nanowire arrays……… 66

5.2.2 XRD of Imbedded FeNWs in AAO……… 71

5.2.3 Electronic transport properties……… 72

5.2.4 Magnetic properties……… 75

5.3

A test for 3ω method: 3

rd

harmonic signal of Platinum

ire

77

5.4

Individual nickel nanowire……… 78

5.4.1 Sample preparation and sagging structure constructing 78

5.4.2 Electronic and thermal Transport Properties……… 85

5.4.3 Specific heat……… 98

5.5 Bi

2

Te

3

nanowire……… 99

6. Conclusions………

102

Reference ………

104

Tables

TABLE 2.1 Thermal conductivities of pure metals at 273 K.

20

TABLE 5.1 The calculate results for thermal conductivity and

specific heat from the fitting parameters K and G in

Figure 5.12.

78

TABLE 5.2 An illustration for the NiNW resistance R

NiNW

between

each pair of pins for 4-probe measurements at room

temperature. The definition of pin number shows in

Figure 5.17

Figures

Figure 1.1

(a) below a certain wire diameter, a semimetal to

semiconductor transition occurs in Bi-nanowire. (b)

Measured temperature dependence of the resistance ratio

R(T)/R(300) of Bi-nanowire of various diameter.

4

Figure 2.1

Temperature dependence of normalized Lorenze number

_{for monovalent metals.}

15

Figure 2.2

Thermal conductivity of very low and high residual

resistivity silver, showing the influence of the residual

resistivity on the low-temperature thermal conductivity.

15

Figure 2.3

Schematic phonon dispersion curves for a given direction

of

qK

of (a) monatomic lattice and (b) diatomic lattice.

The lattice parameter is denoted a

0

.

16

Figure 2.4 A typical hysteresis loop of a ferromagnetic material.

19

Figure 2.5

Progress in the figure of merit of thermoelectric materials

_{at room temperature.}

20

Figure 2.6

Definition of the thermaoelectric effects. The

conductors A and B are joined at junctions 1 and 2. (a)

If these junctions are at different temperature, a Seebeck

voltage appears across an opening in one of the

conductor. (b) If a current is passed, there is Peltier

cooling at one junction and Peltier heating at the other.

21

Figure 2.7

(a) The actual commercial thermaoelectric device. (b)

and (c) are the cooler and power generator, respectively.

22

Figure 2.8

Electronic density of states for (a) bulk 3D crystal, (b)

2D quantum well, (c) 1D nanowire and (d) OD quantum

dot.

24

Figure 3.1

The sketch of the homemade sample holder with copper

base and two layer shields.

30

Figure 3.2

The sketch for the conditions of leads connection from

sample to instruments and the effective circuits. Inset (a)

is the 2-probe method. Inset (b) is the 4-probe method.

Figure 3.3

The typical arrangement for thermal conductance

measurement. Usually, the large bulk sample is fixed on

a high thermal conductive heat sink. The heater is placed

on top of sample to provide a steady heat flow by a

power P, which generate a stable temperature gradient

cross the sample. The temperature different ΔT then is

measured with a set of thermometry, since the thermal

conductivity κ can be calculate with the simple formula

κ=P/ΔT.

35

Figure 3.4

The sketch for sagging structure and the temperature

distribution of a wire. As shows in the right figure, a

sagging wire presents a temperature gradient by injecting

a current into wire. For an appropriate applied current,

the temperature of end points of the wire contacting with

heat sink is keeping the same with heat sink.

36

Figure 3.5

The schematic sketch of measurement setup and settling

_{of specimen.}

40

Figure 4.1

Relationship between pore diameter and growth rate of

_{anodic alumina membrane and anodic voltage.}

44

Figure 4.2

The setup scheme for the fabrication of nano-porous

template. sThe materials of anode and cathode

electrode are copper and platinum, respectively. This

whole set were placing on a temperature and stirrer

controller in a refrigerator.

45

Figure 4.3

Three top-views and one side-view of anodic alumina

_{membrane with pore size ~60, 20, and 10 nm.}

47

Figure 4.4

The scheme of a whole procedure to deposit nanowires in

_{AAO template.}

48

Figure 4.5

The scheme of experimental

_{electrodeposition setup.}

arrangement of

49

Figure 4.6

The typical sequences of process steps are given as

above. It is typical for most silicon substrate fabrication

steps.

52

Figure 4.7

The much nonmetal material is not performed by

procedure as figure 4.7, since essentially all suitable

metal etchants attack those materials as well. Therefore,

fabrication scheme above is typically used.

53

Figure 4.8

For that of high temperature deposition process, the

substrate etching procedure usually is choosing to solve

the difficulty.

Figure 4.9

The selected resists and exposure devices may change

the pattern resolution of by the typical sequences of

process steps. Inset (a) is the resist cross section of

positive and negative resist. The solubility of the exposed

areas increases for a positive resist, while it decreases in

negative resist. Inset (b) is the resist profile of different

resist.

57

Figure

4.10

The sketch of a reactive ion etching (RIE) device, which

performed a high selectivity and uniformity for etching

process.

60

Figure 5.1

The SEM images for the 60 nm template. The (a) and (b)

are the top and back side view, respectively. It shows that

the average pore size is about 60 nm. The (c) and (d)

shows a cross section view in different magnification,

which shows that the thickness of template is about 70

μm.

64

Figure 5.2

The SEM images for the 20 nm template. The (a) and

(b) are the top view in different magnification. It shows

that the average pore size is about 20 nm. The (c) is back

side view. The (d) shows a cross section view, which

shows that the thickness of template could be over 100

μm.

65

Figure 5.3

OM images of the iron-filled AAO templates. Images

are (a) and (b) the as grow sample without mechanical

polish of 60 nm template, (c) the as grow sample without

mechanical polish of 200 nm template, and (d) the

sample performed with polishing. The silver parts

indicate the filling of iron.

67

Figure 5.4

SEM images of the iron-filled AAOtemplates with pore

diameter about 200 nm. Images are (a) and (b) the top

view by different magnification after mechanical polish

of 200 nm template, (c) the top view without mechanical

polish, and (d) the side view. The white spots and color

indicate the filling of iron.

68

Figure 5.5

SEM images of the iron-filled AAO templates with pore

diameter about 60 nm. Images are (a) the top view of as

grow one, (b) the top view after mechanical polish, and

(c) the side view. The white spots and color indicate

the filling of iron.

69

Figure 5.6

The EDS of imbedded iron nanowires. Inset (a) and are

the electrons spotting on top and side of AAO

respectively.

Figure 5.7

X-ray diffraction patterns of film, 200-nm, and 60-nm

NWs. Insets (a) and (b) are the Crosse section view of

200 and 60 nm NW arrays respectively. The white

spots represent the nano-pores filled with α-Fe. Inset (c)

is the side view of home-made empty AAO template.

71

Figure 5.8

Arrangement of electrodes. (a) is the sketch of 4-probe

method for the imbedded iron nanowires, while the (b) is

the real image of this sample.

72

Figure 5.9

The resistance of 60-nm and 200-nm nanowires

_{measured with quasi-four probe.}

73

Figure

5.10

Magneto-resistance of NW arrays, with the current

applied on longitudinal axis of Fe NWs and

perpendicular to applied magnetic field. Inset (a):

transport measurement setup. The 200 nm gold layers are

deposited onto both top and bottom sides of samples to

serve as the electrodes. Inset (b): the normalized MR/ΔR

ratio of 60 and 200-nm NWs. The parabolic fitting

based on Eq. (2) for 60-nm NWs is represented by the

solid line.

74

Figure

5.11

Hysteresis loops of the NW arrays with magnetic field

parallel (//) and perpendicular (⊥) to longitudinal axis of

NWs: (a) 200-nm and (b) 60-nm NWs.

76

Figure

5.12

The frequency dependence 3ω-signal (T ~ 300 K) of

platinum wire was fitted with inserted equation. Thermal

conductivity κ and specific heat C

p

can be calculated

with two coefficients K and G.

77

Figure

5.13

the diagram for primary chip and the patter design for

NiNW. They are inset (a) and (b) the sketch for the

primary chip, inset (c) the center image of the primary

chip, and (d) the four nano ditch pattern.

81

Figure

5.14

the pattern defined and etching results. Inset (a) shows

the sequence of e-beam exposure, develop, deposition,

and lift-off process. Inset (b) shows the etching results

with CF

4

by RIE.

82

Figure

5.15

The detail steps of lithography and etching processes for

the sagging nickel nanowire.

83

Figure

5.16

The SEM image of sagging Ni-NW with dimensions 100

nm in thickness, 180 nm in width, and 35 μm in length.

Inset (a) and (b) are the top view with different

magnification. Inset (c) is the image at the tile angle 45

o

.

Figure

5.17

The sketch of the measurement arrangement for both

electrical and thermodynamic properties. L

5

and L

6

is

the nickel leading pad, which there is not junction in each

pad, although it is denoted in two different colors. L

1

, L

2

,

L

3

and L

4

is the gold leading pad. There are two junctions

presented. One locates at the interface between L

1

and

L

5

, and the other one between L

6

and L

4

.

86

Figure

5.18

The current dependence of 1

st

harmonic signal. Open

circle is the data. Solid line is the fitting result.

87

Figure

5.19

The temperature coefficient of the NiNW (solid circle) is

much small than that of bulk, meanwhile the trend them

are totally different.

87

Figure

5.20

The resistivity ρ(T) of the Ni-NW (solid circles) and the

bulk (open circles) from White et al. The solid line is the

fitting results by Bloch-Gruneisen formula. Inset: the

resistivity in low temperature range, which is agreed with

the T

2

fitting curve (solid line in inset).

88

Figure

5.21

The magnetoresistance of Ni-NW with magnetic field

perpendicular to applied current.

89

Figure

5.22

The current dependence 3

rd

harmonic signal at 300 K.

The inset shows the linear dependence, which agree with

equation 3.6.

93

Figure

5.23

The current dependence 3

rd

harmonic signal at 10 K.

93

Figure

5.24

The frequency dependent 3

rd

harmonic signal. Insets (a)

to (e) are five data performed at 15, 85, 155,225, and 295

K to show the dependence and the fitting results. Inset (f)

collects those five fitting to show the trend of

temperature relationship.

94

Figure

5.25

The thermal conductivity k(T) of the Ni-NW (solid

circles), the calculated k

E

(solid line) and the k

PH

(open

circles). Inset: the thermal conductivity k(T) of the pure

bulk Ni

[12]

.

96

Figure

5.26

The Lorenz number L(T) of the Ni-NW (solid circles)

and the pure bulk Ni (open circles)

[108, 113]

.

97

Figure

5.27

The specific heat of Ni-NW and the bulk.

98

Figure

5.28

The XRD pattern of BiTe alloy with diameter ~60 nm.

This result suggests a strong crystal texture, with the

[110] direction aligned along the longitudinal axis.

Figure

5.29

The High Resolution TEM analysis. (a) A top-view SEM

image of 60-nm Bi

2

Te

3

-alloy nanowire. (b) and (c) are

TEM images and electronic diffraction pattern of

free-standing nanowire.

100

Figure

5.30

The resistance of BiTe-alloy nanowire with diameter ~60

nm.

101

Figure

5.31

The electrodes for four-probe resistance measurement

were obtained by e-beam lithograph technique.

101

Chapter 1

Introduction

Metal and semiconductor nanowires (NW) exhibit much different behaviors from those of the bulk, because of quantum confinement and surface effects, distribution of electron energy states, diameter dependence of band gap, enhanced surface scattering of electrons and phonons, large surface to volume ratio and large aspect ratio. Some of their unique mechanical, electrical, magnetic and thermal properties make them become fundamental building blocks for both nano-science and nano-technology in electronic and magnetic materials, as well as biologic sensor and recording media. Consequently, nanowires become an important one-dimensional system in research.

Ferromagnetic NW arrays have attracted special attention owing to their great potential applications in high density magnetic storage media, high sensitivity magnetic sensor and biologic technology [1-4]. For example, perpendicular magnetic recording (PMR) of nanowire arrays could overcome the thermal instability limit of superparamagnetism. Modern magnetic storage devices made by these materials can have bit densities in excess of 100 Gbit/in2 [5-7]. Indeed, extensive research has been focused on magnetic nanowires in recent years [8-15] for their great

importance on the production of magnetic devices. In this required, better understanding of their magnetism, electrical transport and fundamental

low-dimensional properties is a pressing issue.

convert the heat energy to electric power. The energy conversion efficiency of thermoelectric materials is judged by a figure-of-merit,

2 L e 2 L 0 S ZT T S T ( ) L T ne σ = κ + κ = _κ + μ , (1.1)

where n, S, L0, e, κL, κe and σ are the carrier density, seebeck coefficient, Lorenz

number, electronic charge, lattice thermal conductivity, electronic thermal conductivity and electrical conductivity, respectively. Clearly, the transports properties of nanowires are critically important to enhance dominate the efficiency of thermoelectric materials.

The characteristic transport properties of nano-crystalline materials are sensitive to the number of interfaces, random atomic arrangements, impurities, and defects. In consequence, the effective number of conduction electrons are limited to those, which pass or tunnel through all the boundaries along the mean free path (mfp), resulting in additional resistivities [16-18]. The grain size and transverse dimensions in nanowires are comparable to mfp leading to the enhanced contribution of normal (N-processes) electron-phonon and electron-electron scattering at low temperatures

[19], because in this case each scattering is followed by a collision with the surface. There is also a considerable s-d scattering in ferromagnets, particularly in Ni [20, 21], which, for its turn, increases the number of N-processes, leading to redistribution of energy between hot and cold electrons. Thus, in nanowires the behavior of charge current may differ from the behavior of heat current, even if the heat carriers are also charged particles, giving rise to the violation of Wiedemann-Franz law (WF). Recently, the behavior of the Lorenz number (L) in disordered systems has become the topic of several theoretical treatments, which suggest the deviation from the WF

law in nonmagnetic granular metals [22, 23], and the correction ΔL of Lorenz number have to be positive. In addition, there are theoretical supports that a decreasing diameter will also cause changes of electron band structure, then the thermopower (Figure 1.1a).

Since, from the microscopic view, understanding of the electron and phonon transport mechanisms in an individual nanowire is important for the study of low-dimensional thermoelectric materials, the size reduction may be a new factor to improve the thermoelectric properties, such as seebeck coefficient (S), electrical conductivity (σ) and thermal conductivity (κ). One experimental result showed that bismuth nanowires experience a semimetal-to-semiconductor transition. Figure 1.1b shows a temperature dependent resistance with varies size of bismuth-nanowire [24]. Moreover, there is a further prediction that the segment nanowires may deeply reduce phonon transport in nanowires. To achieve these object there are two efforts required. The first one is the preparation of one-dimensional materials. The other one is the construction of a transport property measurement system.

For sample preparation, the porous anodic aluminum oxide (AAO) is considered to be a template for growing nanowire because of its high-density and uniformity of pores. This kind of bottom-up method is to fill thermoelectric materials such as bismuth and Bi2Te3 into AAO template by chemical electrodeposition, as already

demonstrated by several groups. Such a combination of AAO and electrodeposition technique provides a high quality and low cost approach in synthesizing low dimensional materials for both scientific research and applications [25, 26].

Although fabrications of nanowire arrays and their magnetic properties have been widely studied [27-31], magneto transport properties have been seldom reported. Especially, most of transport studies on nanowires focused on electrical resistivity, whereas the knowledge of heat transport suffers from the lack of information. As

the goal to study conductive nanowires, we built a system for thermodynamic and transport properties measurements, based on a so-called “self-heating 3ω method”. By using this method, we measured the electrical resistivity, thermal conductivity and specific heat of a single sagging nickel nanowire at the same time.

(b) (a)

Figure 1.1 (a) Below a certain wire diameter, a semimetal-to-semiconductor transition occurs in Bi-nanowire. (b) Measured temperature dependence of the resistance ratio R(T)/R(300) of Bi-nanowire of various diameter.

Chapter 2

Theorem

Introduction

This chapter descripts properties for transports behavior, magnetism, and thermoelectricity. Section 2.1 focuses on transport properties of electrons and phonons, which include (A) Kinetic theory of ideal particles and (B) Thermal conductivity of metals. [32-34]

Section 2.2 gives a common description to magnetism about magnetic materials. Section 2.3 will introduce the thermoelectricity for thermoelectric materials, which include bulk and low-dimensional materials. Mainly, this section will talk about the two important effect, they are Seebeck, and Peltier effect and the definition of favor thermaoelectric parameter: figure-of-merit ZT.

2.1 Thermal conduction

Thermal energy can be transmitted through materials via electrical carriers (electrons or holes), phonons (lattice waves), electromagnetic waves, spin waves, or other excitations. Normally, the total thermal conductivity is the summation of carriers, phonons, and the other components representing various excitations:

e ph α

κ = κ + κ +

∑

κ , (2.1) where α denotes other excitations. The thermal conductivities of solids vary dramatically in different materials. This is caused by differences of lattice structure, defects or dislocations of lattice, anharmonic of the lattice vibration, grain sizes for polycrystalline samples and carrier concentrations. All of these differences will take effects to interactions between the carriers and the phonons and etch other, interactions between magnetic ions and the lattice waves, etc. These effects make the thermal conductivity an interesting area of study both experimentally and theoretically. In metals, the major thermal energy carriers are electrical carriers (electrons and holes), while in insulators lattice waves are the dominant heat transporter.

2.1.1

Kinetic theory of ideal particles

To consider a general case, in a thermal nonequilibrium system with ideal particles, the thermal conductivity coefficient κ of gas is defined with respect to the steady-state flow of heat with a temperature gradient:

Q= −κ⋅∇ , T (2.2)

where κ, Q, and T are thermal conductivity, heat flow rate, and absolute temperature respectively.

A particle moves in the presented temperature gradient with velocity υ, we assume that the heat capacity of this particle is c, its energy must change at a rate of

E c

t υ T

∂ _{= − ⋅∇}

∂ . (2.3)

The average distance of particles collect with one another is υτ, where τ is the

relaxation time. The average total heat flow rate per unit area summing over all particles is therefore

2

1 3

Q= −ncτ υ υ⋅ ∇ = −T ncτυ ∇ . (2.4) T

The brackets in Eq. (2.4) represent an average over all particles. To Combine Eq. (2.2) and (2.4), we have

2

1 1

3nc 3C l

κ = τυ = υ , (2.5)

where C=nc is the total heat capacity and l=υτ is the particle mean free path (mfp).

In solids the same derivation can be made for various excitations (electrons, phonons, etc.). In general, the thermal conductivity is the contributions from all components, the total κ can be

1 (

3 C le e e Cp p pl α Cα α αl )

κ = υ + υ +

∑

υ , (2.6)

good phenomenological description of the thermal conductivity, and it is practically very useful for order of magnitude estimates.

Like most of the nonequilibrium transport parameters, thermal conductivity cannot be solved exactly. Calculations are usually based on a combination of perturbation theory and the Boltzmann equation, which are the bases for analyzing the microscopic processes that govern the heat conduction by carriers and lattice waves.

2.1.2

Thermal conductivity of metals

Most metals are solids with crystal structure where the ions occupy translational equivalent positions to form 3-dimensional lattice structure in the crystal. Thermal energy could be transported via lattice vibration in crystal structure when a temperature gradient is imposed on the structure. In metals, the heat conduction associated with the vibrations of the lattice called phonon thermal conductivity, κp. Meanwhile, the periodic arrays of ions construct a condition, in which the free electrons could transport freely in the lattice structure. These electrons are responsible not just for the transport of charge but also for the transport of heat. Their contribution to the thermal conductivity is referred to as the electronic thermal conductivity κe. In discussions of the heat transport in metals, one makes an implicit and essential assumption that the electrons and phonons are independent entities. They are described by their respective unperturbed wave functions, and any kind of interaction between the charge carriers and lattice vibrations enters the theory subsequently in the form of transitions between the unperturbed states. This suggests that one can express the overall thermal conductivity of metals as consisting of two

independent terms, the phonon contribution and the electronic contribution:

e p

κ κ κ= + . (2.24)

These two electrons and phonons are certainly the main heat carrying entities.

In fact, in metals such as gold, silver, copper, and aluminum, the heat current associated with the flow of electrons by far exceeds a small contribution due to the flow of phonons. Thus, for practical purposes, the thermal conductivity can be taken as that due to the charge carriers. For high impurity metals the electronic term is less dominant, and one has to take into account the phonon contribution in order to properly assess the heat conducting potential of such materials. It is known that there are some other possible excitations in the structure of metals, such as spin waves, that may, under certain circumstances, contribute a small additional term to the thermal conductivity. For simplification, we shall not consider these small and often conjectured contributions. In the following selections, the transport of electrons and phonons would be discussed, respectively. Table 2.1 presents thermal and electrical conductivities of familiar metals together with their Lorenz ratio, all referring to a temperature of 273 K.

Electronic thermal conduction

For the free electron theory in solids, we consider each electron as an ideal particle. These particles move in a periodic potential produced by the ions and other electrons without interaction, and then regards the deviation from the periodicity due to the vibrations of the lattice as a perturbation. The values of the electron wave vector k depend on the periodicity and the size of the crystal. The electron energy

depends on the form of the potential and is a continuous function of

k

E k in a

Brillouin zone, but it is discontinuous at the zone boundaries. According to Fermi-Dirac distribution, the equilibrium distribution function of electrons in the state 0 k f k is given by 0 1 exp( ) 1 k F k B f E E k T = ₋ + , (2.7)

where EF and kB are the Fermi energy and Boltzmann’s constant, respectively. For Boltzmann’s equation, in the presence of an electrical field E and a temperature

gradient∇ , the steady state that represents a balance between the effects of the T

scattering processes, the external field and temperature gradient. The expressions for the current density J and the heat錯誤! 尚未定義書籤。 Q are

k k

J =

∫

e f dkυ (2.8)

and

( _{k F}) _{k k}

Q=

∫

E −E υ f dk. (2.9)

Here we define an integral function Kn as

0 2 _{( )( )}n k n k k F k f K k k E E E υ τ ∂ = − − ∂

∫

dk . (2.10)

Thus Eqs (2.8) and (2.9) can be written as [34] 2 0 eff e J e K E K T T 1 = − ∇ (2.11) and 1 1 eff Q eK E K T T 2 = − ∇ , (2.12)

respectively. As J =0, the electronic thermal conductivity can be simplified as

2 1 2 0 0 1 e J K Q K T K T κ = ⎛ ⎞ = − = _⎜ − ∇ _{⎝ ⎠}⎟. (2.13)

And from Eq. (2.11), the electrical conductivity σ can be derived as

2 0

e K

σ = . (2.14)

Since is approximately a delta function at the Fermi surface with width kBT,

Kn can be evaluated by expansion. Therefore we observe

k k E f ∂ ∂ /0 2 2 2 2 2 ₃ 2 ( ) B F F k T k T K E O e E π _σ ⎛ ⎞ = _{+ ⎜} ⎝ ⎠ B ⎟ , (2.15) and 2 2 1 0 B F K k T O K E ⎛ ⎞ ≈ ⎜ ⎝ ⎠⎟ . (2.16)

Thus Eqs. 2.13 can be derived into the Wiedemann-Franz law with the standard Lorentz number L0 as 2 2 8 0 ₃ 2 2.45 10 / e kB L T e κ π σ − = = = × _WiΩ _{K .} 2 _(2.17)

From this free electron gas model, the Lorenz number is totally a calculation of physics constants. This implied that pure metals should have the same electronic thermal conductivity to electrical conductivity ratio, and this ratio is proportional to the absolute temperature. Furthermore, for strong degenerate electron gases, Eq. (2.17) is independent of the scattering mechanism and the band structure for the

electrons as long as the scatterings are elastic. The Wiedemann-Franz law is generally well obeyed at high-temperatures. However, the law fails at low- and intermediate-temperature due to the enhanced inelastic scattering of the charge carriers. Over a wide temperature range, scattering of electrons by phonons is a major factor for determining the electrical and electronic thermal conductivities. The resistance due to this type of scattering is called the ideal resistance. The ideal electrical and electronic thermal resistances can be approximately written as

5 5 1 _D i i D T A J T θ ρ σ θ ⎛ ⎞ _⎛ = _{= ⎜ ⎟ ⎜} ⎝ ⎠ ⎝ ⎠ ⎞ ⎟ (2.18) and

(

)

(

)

5 2 2 7 5 2 2 0 5 1 3 1 1 2 D D F D i i D D D J T k A T W J L T T q T J T θ θ θ κ θ π π θ ⎧ ⎫ ⎛ ⎞ _{⎛ ⎞⎪} ⎛ ⎞ _{⎛ ⎞ ⎪} = = _{⎜ ⎟ ⎜ ⎟⎨} + _{⎜ ⎟ ⎜ ⎟} − _⎬ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎪_⎩ ⎝ ⎠ ⎪_⎭, (2.19) where

(

)

2 0 1 D T n x D n x x e J T _e θ θ ⎛ _{⎞ =} ⎜ ⎟ ⎝ ⎠

∫

₋ dx , (2.20)

( )

( )

2 6 2 2 * 2 2 3 4 D c B D F F q G A e m n k k π θ υ ′ = , (2.21)

θD is the Debye temperature for phonons, kF is the electron wave number at the Fermi surface, qD is the phonon Debye wave number, G′ is the constant representing the strength of the electron-phonon interaction, nc is the number of unit cells per unit volume, and υF is the electron velocity at the Fermi surface. By combining Eqs. (2.18) and (2.21), at high temperature (T>>θD), as the electron-phonon interaction under consideration, the electronic thermal conductivity is

4 i D AT ρ θ = , (2.22)

0 0 4 i i D A W L L T

ρ

θ

= = . (2.23)

At low temperature (T<<θD), the electronic thermal conductivity is 5 124.4 i D T A

ρ

θ

⎛ ⎞ = _{⎜ ⎟} ⎝ ⎠ , (2.24)

and thermal resistivity is

3 2 2 0 3 124.4 F i D D k A T W L T

θ

π

q ⎛ ⎞ ⎛ ⎞ = _{⎜ ⎟ ⎜ ⎟} ⎝ ⎠ ⎝ ⎠ . (2.25)

In addition to the electron-phonon interaction, the electron-defect interaction contributes to the electrical resistivity and electronic thermal resistivity. According to Matthiessen’s rule, the resistivity ρ and the electronic thermal resistivity We is

0 1 i ρ ρ ρ σ = = + (2.26) and 0 1 e e W W κ Wi = = + , (2.27)

where ρ0 and W0 are the residual electrical resistivity and electronic thermal resistivity, respectively, due to the electrons scattered by impurities and defects. At very low temperature, the electronic thermal conductivity

0 0 0 1 e L T W κ ρ ≈ = . (2.28)

is linear dependence of temperature. The Wiedemann-Franz law hold at very high and very low temperature as shows in Figure 2.1. In alloys or metals with a high concentration of defects, electron-defect and electron-phonon interaction only become comparable at high-temperatures. In this case, there is no maximum in the κe, versus, T curve, and κe will approach the high-temperature constant monotonically as T increases. Both cases are illustrated in Figure 2.2, which shows the low temperature thermal conductivity of silver [34].

Figure 2.1 Temperature dependence of normalized Lorenze number for monovalent metals.

Figure 2.2 Thermal conductivity of very low and high residual resistivity silver, showing the influence of the residual resistivity on the low-temperature thermal conductivity.

Lattice thermal conduction

Lattice thermal conduction is the dominant thermal conduction mechanism in nonmetals, if not the only one. In solids, lattice vibrations are an essential feature of all crystalline material, atoms vibrate about their equilibrium positions. Even in some semiconductors and alloys, it dominates a wide temperature range. The vibrations of atoms are not independent of each other, but are rather strongly coupled with neighboring atoms. The crystal lattice vibration can be characterized by the normal modes, or standing waves. The quanta of the crystal vibration field are referred to as ‘‘phonons’’, a kind of ideal particle. Phonon dispersion curves for solids normally consist of acoustic and optical branches. Schematic phonon dispersion curves for monatomic and diatomic lattices are shown in Figure 2.3.

Figure 2.3 Schematic phonon dispersion curves for a given direction of q of (a) monatomic lattice and (b) diatomic lattice. The lattice parameter is denoted a0.

The low-frequency acoustic branches correspond to atoms in a unit cell moving in same phase, whereas the high-frequency optical branches represent atoms in a unit cell moving in opposite phases. In the presence of a temperature gradient, the thermal energy is considered as propagating by means of wave packets consisting of various normal modes, or phonons. So, from this point of view, we could treat transport of lattice vibration as interaction of particles, collision of phonons. There are two collision-process, they are the Normal and Umklapp processes. As the N

process (K1+K2=K3) occur, where the K1, K2, and K3 are the momentum of three collision phonons, the phonon flux is unchanged in momentum on collision. Therefore there is no thermal resistance in this kind of elastic collision. The other one is U process, the important three-phonon processes that cause thermal resistivity are of the form K1+K2=K3+G, where G is a reciprocal lattice vector. As temperature higher than Debye temperature (θD), all phonon collisions will then be U processes, with the attendant high momentum change in the collision. In this regime we can estimate the thermal resistivity without particular distinction between N and U processes. At high temperature the lattice thermal resistivity is linear dependence of temperature. [32]

2.2 Magnetism

Paramagnetism

The orientations of magnetic moments in paramagnetic materials are random and they are independent to each other. We could consider the total magnetic moment of a paramagnetic material as an atom or ion in free space. The magnetization should proportion to the external applied field, and obey the Curie law [1, 2]. Paramagnets do not retain any magnetization in the absence of an externally applied magnetic field, because thermal motion causes the spins to become randomly oriented. Thus the total magnetization will drop to zero when the applied field is removed. Even in the presence of the field there is only a small induced magnetization because only a small fraction of the spins will be oriented by the field. Paramagnetic materials possess a quite small positive magnetic susceptibility (χ), which is less than 10-5, normally.

Ferromagnetism

It is well known that ferromagnets expose to a magnetic field they retain the magnetization even the field is removed. Ferromagnet was used for any material that could exhibit spontaneous magnetization: a net magnetic moment in the absence of an external magnetic field. In particular, a material is "ferromagnetic" in this narrower sense only if all of its magnetic ions add a positive contribution to the net magnetization. If some of the magnetic ions subtract from the net magnetization, then the material is "ferrimagnetic". If the ions anti-align completely so as to have zero

net magnetization, despite the magnetic ordering, then it is an antiferromagnet. All of these alignment effects only occur at temperatures below a certain critical temperature, called the Curie temperature for ferromagnets and ferrimagnets or the Néel temperaturefor antiferromagnets. The most common way to represent the magnetic properties of a ferromagnetic material is by a plot of magnetization M against H, as shows in Figure 2.4 [32].

2.3 Thermoelectricity

In the three decades from 1821 to 1851, the basic effects were discovered and understood macroscopically, and their applicability to thermometry, power generation, and refrigeration was recognized. The sole lasting contribution in the next 80 years was Altenkirch's derivation of thermoelectric efficiency in 1911. Then in the late 1930s, there began 20 years of progress (figure 2.6) that lead to a microscopic understanding of thermoelectricity and the development of today's materials [35].

The topic of thermal-electric energy conversion phenomena were studied over two century. The thermoelectric effect provides a means by which thermal energy can be converted into electricity can be used for heat pumping or Power generation. Especially, the solid state cooling and power generation devices which based on thermoelectric effects have been investigated since the Seebeck and Peltier effect were discovered [36, 37].

Figure 2.5 Progress in the figure of merit of thermoelectric materials at room temperature.

Seebeck effect

The Seebeck effect was first presented by Thomas Johann Seebeck in 1821. This phenomenon related with the generation of a voltage along a conductor when it is subjected to a temperature gradient. Chemical potential cause carriers (electrons or holes) diffuse from the hot side to the cold side, creating an internal electric field that opposes further diffusion. The Seebeck coefficient is defined as the voltage generated per degree of temperature difference between two ends (figure 2.7a).

V S T δ δ = − , (2.30)

Peltier effect

The Peltier effect is the reverse of the Seebeck effect and observed in 1834 by Jean Peltier. The Peltier effect describes a phenomenon that carriers carry heat when they flow through a conductor. The heat current IQ is proportional to the current I

and the proportionality constant Π is called the Peltier coefficient (figure 2.7b).

Q I = Π •I, (2.31) TH TC A B V 1 2 (a) _A B I 1 2 (b)

Figure 2.6 Definition of the thermaoelectric effects. The conductors A and B are joined at junctions 1 and 2. (a) If these junctions are at different temperature, a Seebeck voltage appears across an opening in one of the conductor. (b) If a current is passed, there is Peltier cooling at one junction and Peltier heating at the other.

A thermoelectric EMF is created in the presence of a temperature difference between two different materials. This usually causes a continuous current to flow in the conductors. The voltage is on the order of hundred and several microvolts per degree in semiconductor and metal, respectively. As two materials are joined together, there will be an excess or deficiency in the energy at the junction. The energy difference make the junction either absorb or emit heat, causing heating or cooling. The Seebeck and the Peltier coefficients are related through the Kelvin relation Π=ST, where T is the absolute temperature. A commercial thermoelectric device is shown in Figure 2.8a, which made of many pairs of p–n legs. P-type and n-type semiconductor elements are welded in the top and bottom sides, such that a current flows through all the elements in series, while the energy they carry leaves the cold or hot side in parallel. The thermoelectric power generator and cooler work in reverse, which shown in Figure 2.8b and 2.8c, respectively. For example, in a power generator the hot side has a higher temperature, electrons and holes are driven to the cold side through diffusion and flow through an external load to do useful work.

N P N P N P N P

(a)

(b)

Loading

(c)

Figure 2.7 (a) The actual commercial thermaoelectric device. (b) and (c) are the cooler and power generator, respectively.

The heat energy to electrical power conversion efficiency for a given thermocouple varies with the resistance of the load. Ioffe (1957) showed that the highest efficiency is given by

0.5 0.5 ( ) (1 ) / (1 ) H C H C H T T ZT T T T ZT η= − + + + , (2.32)

where T is taken to be equal to (TH+TC)/2, and the quantity Z, which is known as the

figure of merit of the thermocouple. The performance of thermoelectric device depends on the figure of merit (ZT) of the material, given by

2

S ZT σ T

κ

= , (2.33)

where S, T, σ and κ are the Seebeck coefficient, absolute temperature, electrical

conductivity and thermal conductivity, respectively. From an intuitional view, the reason that the electrical conductivity σ enters Z is due to Joule heating. The thermal conductivity κ appears in the denominator of Z because, in thermoelectric coolers or

power generators, the thermoelectric elements also act as the thermal insulation between the hot and the cold sides. The main research issue in thermoelectric materials is to increase power factor (mutilation of Sσ) and decrease thermal conductivity (κ) to cause a large figure of merit.

In the recent two decades, environment-protection concepts lead to renewed activity in the science and technology of alternative energy. The directly usage of solar energy is an important issue. There are two accepted proposes for develop the solid-state energy converter, they are photonic-electric and thermal-electric effects.

The thermal-electric effect related phenomena were observed and studied for a long time. Closely related cooling and power generation mechanisms, thermomagnetic effects and themionic emission, are less well established but may soon have their day.

In bulk materials, the quantities S, σ and κ are inter-related, so that the figure of merit, ZT, is difficult to increase in conventional 3D crystalline systems. For a long time, materials with ZT ~1 were accepted limit of ZT. But the new variable of size gives rise to differences in the density of electronic states, allowing new opportunities to vary S, σ and κ independently. The common picture of dimensional-dependent band structure is shown in figure 2.5. As the dimension decreases from 3D crystalline solids to 2D (quantum wells) to 1D (quantum wires) and finally to OD (quantum dots), new physical phenomena are introduced and new opportunities to vary S, σ and κ independently.

Figure 2.8 Electronic density of states for (a) bulk 3D crystal, (b) 2D quantum well, (c) 1D nanowire and (d) OD quantum dot.

There are three generic approaches have been proposed to date for low-dimensional materials, which described in ref.4. (1) quantum-confinement effects

[38]: to enhance density of states near the Fermi energy. Using such effects, a ZT of 0.9 at 300 K and 2.0 at 550 K, using estimated thermal-conductivity values, has been reported [39] in PbSe0.98Te0.02/ PbTe quantum-dot structures. (2)

phonon-blocking-electron-transmitting superlattices: These structures utilize the acoustic mismatch between the superlattice components to reduce κL[40-42], thereby potentially eliminating alloy scattering of carriers. (3) thermionic effects in heterostructures. [43] Furthermore, they also report a ZT at 300 K of ~2.4 in p-type Bi2Te3/Sb2Te3 superlattices and a ZT ~1.4 in n-type Bi2Te3/Bi2Te2.83Se0.17

superlattices.

The low-dimensional materials seem owing a lot of different behavior from bulk materials. This gives us the motivation to investigate on electronic and thermodynamic behavior for understanding the fundamentals in nano-physics. In the recent two decades, environment-protection concepts lead to renewed activity in the science and technology of alternative energy. The directly usage of solar energy is an important issue. There are two accepted proposes for develop the solid-state energy converter, they are photonic-electric and thermal-electric effects.

The thermal-electric effect related phenomena were observed and studied for a long time. Closely related cooling and power generation mechanisms, thermomagnetic effects and themionic emission, are less well established but may soon have their day.

Chapter 3

Experimental facilities and measurement methods

Introduction

This chapter introduce equipments for study the samples. Section A of 3.1 gives a bright description of X-ray diffraction (XRD) technique for characterizing the lattice structure of nanowires by the x-ray powder diffraction method. Section B of 3.1 gives the description of Scanning electron microscope (SEM) for determining and observing the geometry dimensions and morphology of samples, respectively. Section C of 3.1 talks about the sample temperature control system.

The last decays have seen significant developments in thin-film thermal conductivity measurement techniques. However, the characterization of the thermal conductivity of a nanowire remains a challenging task. Usually, thermal conductivity measurements are difficult to make with relatively high accuracy, certainly better than within 5%. Sections of 3.2 descript the methods for us to study the electronic and thermal conductivity. Section A of 3.2 introduces the four-probe method for resistivity measurement. Section B and C of 3.2 gives the detail description for Self-heating 3ω method and Construction of measurement system & sample holder, respectively.

3.1

Introduction to experimental equipments

3.1.1

X-ray diffraction (XRD)

X-ray diffraction (XRD) is a non-destructive technique that reveals detailed information about the crystallographic structure of natural and manufactured materials. It’s now a common technique for the study of crystal structures and atomic spacing. When a monochromatic X-ray beam with wavelength λ is projected onto a crystalline material at an angle θ, diffraction occurs only when the distance traveled by the rays reflected from planes differs by a complete number n of wavelengths when conditions satisfy Bragg's Law (nλ=2d sin θ). This law relates the wavelength of electromagnetic radiation to the diffraction angle and the lattice spacing in a crystalline sample. Conversion of the diffraction peaks to d-spacing allows identification of materials. By varying the angle, the Bragg's Law conditions are satisfied by different d-spacings in polycrystalline materials. Based on the principle of X-ray diffraction, a wealth of structural, physical and chemical information about the material investigated can be obtained. A host of application techniques for various material classes is available, each revealing its own specific details of the sample studied.

The specific wavelengths are characteristic of the target material (Cu, Fe, Mo, Cr). The geometry of an X-ray diffractometer is such that the sample rotates in the path of the collimated X-ray beam at an angle θ while the X-ray detector is mounted on an arm to collect the diffracted X-rays and rotates at an angle of 2θ. The instrument used to maintain the angle and rotate the sample is termed a goniometer. X-ray powder diffraction is the method used for the identification of unknown crystalline materials. In our results, the XRD is performed by the PANalytical X'Pert PRO analysis system.

3.1.2

Scanning electron microscope (SEM)

The scanning electron microscope (SEM) is a type of electron microscope that images the sample surface by scanning it with a high-energy beam of electrons in a raster scan pattern. The electrons interact with the atoms that make up the sample producing signals that contain information about the sample's surface topography, composition and other properties such as electrical conductivity.

The types of signals produced by an SEM include secondary electrons, characteristic x-rays, specimen current and transmitted electrons. These types of signal all require specialized detectors for their detection that are not usually all present on a single machine. The signals result from interactions of the electron beam with atoms at or near the surface of the sample. In the most common or standard detection mode, secondary electron imaging or SEI, the SEM can produce very high-resolution images of a sample surface, revealing details about 1 to 5 nm in size. Due to the way these images are created, SEM micrographs have a very large depth of field yielding a characteristic three-dimensional appearance useful for understanding the surface structure of a sample. This is exemplified by the micrograph of pollen shown to the right. A wide range of magnifications is possible, from about x 25 (about equivalent to that of a powerful hand-lens) to about x 250,000, about 250 times the magnification limit of the best light microscopes. Characteristic X-rays are emitted when the electron beam removes an inner shell electron from the sample, causing a higher energy electron to fill the shell and release energy. These characteristic x-rays are used to identify the composition and measure the abundance of elements in the sample. The morphology and geometry dimensions of our samples are determined with models Hitachi S-4200 FESEM and Horeba EX-220 energy dispersion spectroscopy.

3.1.3

Magnetic Property Measurement System (MPMS)

The Quantum Design MPMS provides solutions for a unique class of sensitive magnetic measurements in key areas such as high-temperature superconductivity, biochemistry, and magnetic recording media. The modular MPMS design integrates a Superconducting Quantum Interference Device (SQUID) detection system, a precision temperature control unit residing in the bore of a high-field superconducting magnet, and a sophisticated computer operating system. Powerful software controls measurements, making data collection and analysis quick and easy.

3.1.4

Physical Property Measurement System (PPMS)

The Quantum Design PPMS represents a unique concept in laboratory equipment: an open architecture, variable temperature-field system, designed to perform a variety of automated measurements. Use the PPMS with options designed for it or easily adapt it to your own experiments. Sample environment controls include fields up to ± 5 Tesla and temperature range of 1.8 - 400 K. Its advanced expandable design combines many features in one instrument to make the PPMS the most versatile system of its kind.

3.1.5 Cryostat

system

The construction for temperature control system include three main parts, the OXFORD Heliox series 3He refrigerator, sample holder, and control device. The figure below represents a schematic of the. The 3He refrigerator insert can be treated like any sample rod for a variable temperature insert. Once loaded, the insert is cooled from 300K down around 70K using exchange gas. The 3He gas contained in a small dump sitting on top of the insert is then condensed at around 1.5K. Once the

3_{He pot has reached a stable temperature and condensation is completed, the}

adsorption pump will start to cool the 3He pot and experimental set-up to below 300 mK. The condensation and the cool down time typically require less than 1 hour. Meanwhile, a homemade sample holder (Figure 3.1) was mounted together with the commercial heater on the 3He pot. The minimum temperature of this construction is 0.4 K, and in our experience, the temperature of sample can keep at this temperature over 4 hours. Furthermore, the whole temperature control instruments were monitored by a computer through the interface GPIB.

Radiation Shielding Sample chip

Sample mounting bas Copper base

Figure 3.1 The sketch of the homemade sample holder with copper base and two layer shields.

3.2

Electronic property measurement methods

3.2.1 Four-probe

method

If you wanted to determine the high precise of a resistance, you would probably connect its two leads up to an Ohmmeter and read off the value. This could be a problem, if the resistance you are trying to measure is very small. A voltage source may damage your sample due to the high passing current. Do you know how much current should we use to measure resistance? For this reason, one often determines the resistance of a sample by passing through it a known current I, measuring the resulting voltage drop ΔV, and performing the division to get R = ΔV/I. This might be a direct current, or it might be an alternating current. The constant-current circuit allows us to determine the sample resistance with a very small current eliminating the possibility of damage to the sample, especially for an ultra fine wire.

We now turn to the other issue, the problem of lead resistance. The sample resistance might be so low that the resistance of the leads running to the sample might be significant by comparison. A related problem is that of contact resistance. Somehow we must connect leads between our sample and the external circuit, and this involves making "contact" to the sample. Contacts are notorious sources of resistance. The situation is illustrated as Figure 3.2a. Let the two contacts to the sample be represented by equivalent resistances RC1 and RC2. The measured voltage

drop V = I (RC1 + RS + RC2). How do we know what fraction of the voltage drop V

is due to R and how much is due to the contacts? Fact is we have no way of knowing, because we measure their series combination. This is especially a problem if RS is much smaller than RC1 and RC2. Consequently, the resistance of the leads

include to the reading.

The four-probe method is the most common way to separate out the resistivity of conducting materials. This can be seen by looking at the equivalent circuit, shown in the Figure 3.2b. Two of the probes are used for applied current source and the other two probes are used to measure voltage. By separating the current contacts from the voltage contacts we are able to distinguish the sample resistance from that of the contacts and connecting wires. If the voltmeter has an infinite input impedance, no current will flow through the voltage contacts, and the measured voltage drop V is across the portion of the sample that is between the two voltage contacts. Even if R is much smaller than RC1 and RC2, the measured voltage drop is still V = I R.

(a)

Figure 3.2 The sketch for the conditions of leads connection from sample to instruments and the effective circuits. Inset (a) is the 2-probe method. Inset (b) is the 4-probe method.

(b)

GR V

R

C1

R

C2

R

S

R

C3

R

C4 V

R

C3

R

C4

R

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S V