電子物理系
博
士 論 文
半導體奈米結構電性傳輸
與奈米元件接點電阻之研究
Electrical Transport of Semiconducting Nanostructures
and Impact of Nanocontact on Nanoelectronics
研 究 生：林彥甫
指導教授：簡紋濱 教授
中 華 民 國 九十九 年 七 月
2
研 究 生：林彥甫 Student：Yen-Fu Lin
指導教授：簡紋濱 Advisor：Prof. Wen-Bin Jian
國 立 交 通 大 學
電 子 物 理 系
博 士 論 文
A Dissertation
Submitted to Department of Electrophysics College of Science
National Chiao Tung University in partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy
in Electrophysics
July 2010
Hsinchu, Taiwan, Republic of China
i
半導體奈米結構電性傳輸與奈米元件接點電阻之研究
學生: 林彥甫 指導教授: 簡紋濱 教授
國立交通大學電子物理系博士班
摘要
過去數十年間，藉由物理與化學的方法各式各樣半導體奈米線被成功的製 造。透過由上而下或由下而上的組裝方法，這些半導體奈米線已被廣泛地應用 於研究單電子電晶體、場效電晶體或光電元件等領域中。但在大多數的研究中 由於奈米電子元件多具有兩點(Two-probe)的電極結構，因此透過該兩點電極結 構，系統性地徹底掌握本質奈米線電性傳輸特性是一項相當重要的研究議題。 在過去的文獻中雖然有許多半導體奈米線電性的研究被報導，但對於所量測到 的電性傳輸行為究竟是本質奈米線所主導或由於接點電阻所造成的效應並沒 有一個深入的探討。本篇論文將透過兩點電極結構深入研究接點電阻在半導體 奈米線元件中所扮演的角色，並探求本質氧化鋅(ZnO)、磷化銦(InP)、磷化鎵 (GaP)半導體奈米線與聚苯胺(polyaniline)奈米纖維的傳輸特性。 本實驗主要分成三大部分，在第一部分的研究裡，我們利用氧化鋅(ZnO) 奈米線製造出多組具有兩點電極的奈米線元件，並系統性地研究接點電阻在奈 米元件中的影響。我們發現依據與溫度相依的電流-電壓關係曲線圖與電阻的 分析，兩點氧化鋅奈米線元件可區分成雙邊歐姆接觸(two Ohmic)、單邊蕭特 基接觸(one Schottky)與背對背蕭特基接觸(back-to-back Schottky)等三種類型。ii
發現由接點電阻所主導的背對背蕭特基奈米電子元件，其溫度與電阻關係曲線 圖可藉由Mott 變程跳躍傳輸模型(variable range hopping) 1/
0 exp(( / ) )p R∝ T T 來 加以說明。在接點電阻所主導的樣品中，Mott 變程跳躍傳輸模型的指數函數 p 值，隨著室溫接點電阻率的上升逐漸由2 上升到 4，意味著變程跳躍傳輸模型 在接點系統中，由低維度擴展至高維度的變程跳躍傳輸機制。更進一步地，藉 由了解接點電阻在奈米線元件中所扮演的角色，我們可以成功地探究本質氧化 鋅(ZnO)、磷化銦(InP)與磷化鎵(GaP)半導體奈米線電性傳輸特性。 由於了解到接點電阻在奈米線元件中所具有的影響。因此，第二部分的研 究裡，我們針對磷化銦(InP)奈米線元件進行研究，探求接點電阻與本質奈米 線電阻所主導的電子元件在光與氣體的環境中其反應是否具有差異化。實驗過 程中，我們採用標準電子束微影的方式製作出多組磷化銦(InP)奈米線電子元 件，藉由分析其變溫電阻變化曲線圖，我們可以成功地將樣品區分為奈米線所 主導(nanowire-dominated)與接點電阻所主導(contact-dominated)的兩類型元件。 在本質奈米線所主導的磷化銦(InP)電子元件中，其高、低溫部分的溫度-電阻 關係圖分別可以使用熱活化傳輸理論與三維變程式跳躍傳輸理論來加以說明。 更進一步地，將磷化銦奈米線電子元件曝照於光與氧氣的環境下，我們發現無 論是奈米線或接點電阻所主導的奈米元件皆具有曝照前/後電阻的變化。令人 訝異的是接點電阻所主導的奈米線電子元件無論在曝照光或氣體的反應下皆 具有較高的電阻變化率出現。 第三部分的研究中，我們探討有機半導體奈米材料-聚苯胺(polyaniline)奈 米纖維的電性傳輸性質。實驗中，藉由介面聚合的化學方法，聚苯胺(polyaniline) 奈米纖維成功的被合成。在酸、鹼溶液的摻雜(doping)與去摻雜(dedoping)化學 反應中，我們發現聚苯胺奈米纖維之薄膜樣品，其與溫度相依的電阻皆依循著
iii 1/2 lnR∝( )T − 關係式變化。另一方面，為了探究單根聚苯胺(polyaniline)奈米纖 維本質電性傳輸機制，我們首次利用介電泳動法成功地製作出多組具單根纖維 之 奈 米 元 件 。 透 過 系 統 化 的 分 析 與 研 究 ， 其 電 性 傳 輸 實 驗 結 果 可 用 charge-energy-limited-tunneling 理論來加定量說明之。
iv
Electrical Transport of Semiconducting Nanostructures
and Impact of Nanoocntact on Nanoelectronics
Student: Yen-Fu Lin Advisor: Prof. Wen-Bin Jian
Institute of Electrophysics
National Chiao Tung University
Abstract
Various semiconductor nanowires have been synthesized by using either physical or chemical growth methods in the past decades. These nanowires applied to single electron transistors, field-effect transistors, optoelectronics, and nanoelectronics through top-down or bottom-up assembling approaches has been immediately demonstrated. Because of most nanoscale electronics having two-probe configuration as the source and drain electrodes, identification and determination of intrinsic electrical properties of nanowires and the contribution of nanocontact through a systematic procedure of this two-probe approach become very important. Although a lot of two-probe nanoelectronics and applications have been demonstrated in previous reports, the electrical properties bringing either from the nanocontacts or from the nanowires have not been uncovered clear yet. In this work, a two-probe technique was adopted to explore electrical properties of ZnO, InP, GaP nanowires and polyaniline nanofibers.
v
fabricate two-probe nanodevices and to survey the impact of nanocontact on nanowire based nanoelectronics. According to temperature behaviors of current-voltage curves and resistances, the devices could be grouped into three types, including two Ohmic contacts, one Ohmic and one Schottky contacts, and two back-to-back Schottky contacts. The nanocontact could be treated as disordered system and be explained by Mott variable range hopping model for electrons of the form 1/
0
exp(( / ) )p
R∝ T T . The exponential parameters of Mott variable range hopping theory rises from 2 to 4 with an increase of specific contact resistivity at room temperature, implying a change from one- to three-dimensional hopping. Moreover, after understanding how to distinguish the nanowire- and contact-dominated nanodevices, we demonstrate that the two-probe measurement can be applied to the exploration of the intrinsic properties of semiconductor nanowires. This two-probe measurement approach also works on highly resistive nanowires without an Ohmic contact issue. By using this method, electron transport behaviors, resistivity, and carrier concentrations of ZnO, InP, and GaP semiconductor nanowires have been investigated.
The interface problems in nanowire-based electronics play important roles due to the reason that the reduced contact area in nanoelectronics multiplies enormously the contribution of electrical contact properties. The second portion is to illustrate the sensitivity difference in response to light and oxygen gas between the nanowire- and contact-dominated InP nanowire devices. By using a standard electron-beam lithography technique, two-probe InP nanowire devices were fabricated. Although the InP were picked up from the same source sample and the dimensions of the nanowires and nanodevices were also kept the same, the room-temperature resistance of these devices varied considerably. It was conjectured the difference of room-temperature comes from the contribution of
vi
contact resistance. According to the temperature behaviors, the nanowire devices can be categorized into nanowire- and contact-dominated ones. The temperature dependent resistances follow the thermally activated and three-dimensional Mott variable range hopping transport at high and low temperatures, respectively. Both nanowire- and contact-dominated devices were exposed to light and oxygen gas to see any difference. In comparison with the nanowire-dominated devices, the contact-dominated InP nanowire devices always exhibit a much higher ratio of resistance changes in response to either light or oxygen gas exposures.
The last portion of this work is to study the electrical transport of polyaniline nanofibers. Polyaniline nanofibers were synthesized by using polymerization at the interface of immiscible solvents. They exhibit a uniform nanoscale morphology rather than agglomeration with granular structures as that produced via conventional chemical oxidation. The as-synthesized polyaniline nanofibers are doped (dedoped) with an HCl acid (NH3 base) and their temperature behaviors of
resistances all follow an exponential function with an exponent of T-1/2. To achieve the measurement of conduction mechanism in a single nanofiber, the dielectrophoresis technique is implemented to position nanofibers on top of and across two Ti/Au electrodes patterned by electron-beam with a nanogap of 100-200 nm. Their temperature behaviors and electric field dependences are unveiled and the experimental results agree well with the theoretical model of charge-energy-limited-tunneling. Through fitting to this transport model, the size of conductive grain, the separation distance between two-grains, and the charging energy per grain in a single polyaniline nanofiber are estimated to be about 5 nm, 3 nm, and 78 meV, respectively. This nanotechnological approach has been applied to determination of mesoscopic charge transport in the polyaniline conducting polymer.
vii
致謝
民國九十二年暑假，我進入了蔡志申老師(時任東海大學物理系 助理教授)所主持的表面 磁學實驗室，’’研究所的推薦徵選入學’’是我進入蔡老師實驗室最單純不過的理由了，當時我 沒有遠大的抱負，亦沒有對深入了解物理有任何期許，但這卻是讓我栽入固態物理實驗領域 直至今日重要的一步。在蔡老師實驗室的時間雖然不長，卻讓我深刻學習到做實驗物理學重 要的精神。 很幸運地，民國九十四年夏天，我進入交通大學電子物理系碩士班就讀，延續大學時代 的所學，我選擇進入由簡紋濱老師所領導的實驗室，在過去的五個年頭中，由碩士班逕升至 博士班，我特別誠摯地感謝簡紋濱老師的指導，簡老師細心的教導使我得以一窺奈米領域的 深奧，不時的討論並指導我正確的方向，使我在這些年中獲益匪淺。簡老師對學問的嚴謹更 是我輩學習的典範。 感謝教導我微影製程技術的王敬平學長，與真空技術與工程繪圖概念的歐逸青，您們不 厭其煩的技術傳承，是我往後五年實驗過程中最重要的基石。此外，謝謝同ㄧ時段與我共同 打拼的廖泰慶與楊肇嘉同學。感謝我第一屆指導的學弟們：陳建翔、邱奕正、洪祥智、傅聖 凱與邱紹謙，感謝您們包容我當時對於學術的無知，在與您們知識共同成長的過程中確實令 我學習到不少。同時也要謝謝過去五年共事過的學弟、妹們：趙宏基、郭融學、侯朝振、吳 俊吉、陳怡然、張育偉、張家弘、許文澤、鄭淞芳、曾祥一、紀彥羽、謝文佳、洪子昌、陳 姿涵、宋竹芸、莊維倫、陳昶廷、張加欣、李雅琪、林光華、范戊靖、王聖璁與楊明洵，由 於您們的參與，無論是學術上的討論或是言不及義的閒扯，都讓單調的實驗室生活變得絢麗 多彩。同時也祝福今年與我一同畢業的碩士班學弟、妹們：謝文佳、洪子昌、陳姿涵、宋竹 芸與莊維倫，祝福您們各個都有好身體、好工作與好歸宿。 感謝交大電物系朱仲夏老師、許世英老師、鄭舜仁老師、中興物理系郭華丞老師與清大 物理系陳正中老師，百忙之中抽空參與學生口試，並對學生論文的批評與指教，著實令學生 受益匪淺。 感謝一路相伴的依萍，我依舊有許多事情還需繼續努力，希望共同創造更美好的未來； 最後，謹以此文獻給我的家人，爸、媽、姐姐與妹妹，您們的健康、平安與快樂是我前進重 要的動力。 中華民國九十九年七月二十五日viii
Contents
摘要 ... i Abstract ... iv 致謝 ... vii Contents ... viii List of Figures ... x 1 Introduction ... 1 1.1 Overview ... 1 1.2 Outline of Work ... 3 References ... 4 2 Theoretical Models ... 7 2.1 Thermionic-emission Theory ... 72.2 Thermal Activated Transport ... 10
2.3 Mott Variable Range Hopping ... 12
2.4 Charge Energy Limited Tunneling... 14
References ... 15
3 Utilize Two-Probe Configuration Measurements to Survey the Impact of Nanocontact on Nanodevices and Transport Properties in Semiconductor Nanowires ... 17
3.1 Introduction ... 17
3.2 Experimental Method ... 19
3.3 Results and Discussion ... 20
3.3.1 The Impact of Nanocontact on Nanodevices ... 21
ix
References ... 39
4 Enhanced Photoresponse and Gas Sensing of InP Nanowire Device ... 42
4.1 Introduction ... 42
4.2 Experimental Method ... 43
4.3 Results and Discussion ... 44
References ... 52
5 Nano Approach Investigation of Conduction Mechanism of Polyaniline Nanofibers ... 55
5.1 Introduction ... 55
5.2 Experimental Method ... 56
5.3 Results and Discussion ... 59
References ... 67
x
List of Figures
Figure 3.1: (a) A schematic diagram of a single NW device. Typically, the
separation distance between the two contact electrodes is about ~1 μm. (b) FE-SEM image of a typical nanowire device with pre-fabricated micron electro-pads and alignment marks. An image of the indicated rectangular area is given in (c). The enlarged area displays a close view of a single ZnO NW device. 21
Figure 3.2: (a) I-V curves of a Type I ZnO NW device with a RT resistance of ~15
kΩ. The inset introduces a model of circuit diagram for Type I devices. (b) I/T2 as a function of inverse temperature at various bias voltages. (c) Resistance as a function of temperature revealing electron transport in the Type I device. ... 23
Figure 3.3: (a) I-V curves of a Type II ZnO NW device with a RT resistance of ~50
kΩ. The inset introduces a model of circuit diagram for Type II devices. (b) I/T2 as a function of inverse temperature at various bias voltages. (c) ln(I/(1-exp(-qV/kT))) as a function of voltage. (d) Resistance as a function of temperature revealing electron transport in this Type II device. The dashed and solid lines are best fittings (see text) of Equations 4 and 5, respectively. ... 25
Figure 3.4: (a) I-V curves of a Type III ZnO NW device with a RT resistance of
~1.5 MΩ. The inset introduces a model of circuit diagram for Type III devices. (b)
I/T2 as a function of inverse temperature at various bias voltages. (c) Resistance as a function of temperature revealing electron transport in this Type III device (red circles) and in another Type III device having a RT resistance of ~128 MΩ (black squares). The dashed and solid lines are best fittings (see text) of Equations 4 and 5, respectively. ... 27
xi
our as-fabricated ZnO NW devices of Type I, II, and III, marking as blue circles, black triangles, and red squares, respectively. The figure is approximately separated into Regions A, B, and C according to the exponent parameters of our devices. (b) Three different nanocontact models corresponding to the ZnO NW devices belonging to Regions A, B, and C of Figure (a). ... 29
Figure 3.6: The fitting exponent parameters p as a function of RT contact
resistivity for NW devices. The fitting exponent parameter as a function of T0 shows in the inset. ... 31
Figure 3.7: (a) Schematic diagram of a two-probe ZnO NW device with a typical
SEM image shown in the inset. Temperature-dependent resistance of (b) two- and (c) four-probe ZnO NW devices. A schematic diagram of a four-probe device is drawn in the inset of Fig. (c). Solid and dashed lines delineate the best fits to the mathematical forms of thermally activated transport and Mott-VRH, respectively. After fitting to Mott-VRH (dashed lines), the exponents, p's, of ZnO-1, ZnO-2, ZnO-3, and ZnO-4 devices are estimated to be 4, 2, 4, and 4, respectively. ... 35
Figure 3.8: (a) Resistance as a function of inverse temperature for two-probe InP
NW devices with a typical SEM image shown in the inset. The solid and dashed lines delineate the best fits to mathematical equations of thermally activated transport and Mott-VRH, respectively. After fitting to Mott-VRH (dashed lines), the exponents, p's, for InP-1, InP-2, and InP-3 are estimated to be 4, 2.4, and 4, respectively. ... 37
Figure 3.9: I-V curves, taken at room temperature, from six different GaP NW
devices. The inset shows temperature-dependent resistance of GaP-5 device. The solid line in the inset demonstrates the best fit to the thermally activated transport equation. ... 39
xii
and a red curve fitted according to a Gaussian function, shown in the inset. The average diameter and the standard deviation of nanowires are evaluated to be about 21.4 and 13.5 nm, respectively. (b) FE-SEM image of a single InP NW embedded in two Ti/Au electrodes. A cartoon schematic for our two-probe InP NW device is illustrated in the inset. ... 45
Figure 4.2: (a) I-V curves of a typical InP NW device with a RT resistance of ~ 22
MΩ. (b) Resistance as a function of inverse temperature for two-probe InP NW devices. The solid and dashed lines delineate the best fits to the mathematical equations of thermally activated transport and Mott-VRH, respectively. The inset shows the transition temperature as a function of RT resistance for InP NW devices. ... 48
Figure 4.3: (a) The sensitivity of light exposure for contact and NW-dominated
two-probe InP NW devices. (b) The response ratio (ΔR / R0) as a function of RT
resistance for two-probe InP NW devices. ... 50
Figure 4.4: (a) The sensitivity of oxygen exposure for contact- and NW-dominated
two-probe InP NW devices. (b) The response ratio (ΔR / R0) as a function of RT
resistance for two-probe InP NW devices. ... 52
Figure 5.1: A schematic illustration of polyaniline nanofibers synthesis in a
rapidly-mixed reaction. ... 58
Figure 5.2: Schematic diagrams outlining the fabrication procedure of (a)
polyaniline nanofiber thin-film device and (b) nanoscale nanodevices. ... 59
Figure 5.3: (a) FE-SEM image of as-synthesized polyaniline nanofibers with the
corresponding size distribution and a red curve fitted according to a Gaussian function, shown in the inset. The average diameter and the standard deviation of nanofibers are evaluated to be about 45.0 and 19.3 nm, respectively. (b) I-V behaviors and (c) R-T of dedoped, as-synthesized, and doped nanofiber thin films.
xiii
(d) SEM image of a polyaniline nanofiber device. (e) The change of I-V curves of a polyaniline nanofiber device at room temperature after electron-beam exposure. (f) The room-temperature resistance of the nanoscale devices as a function of the electron-beam exposing time. ... 61
Figure 5.4: (a) Resistance as a function of inverse temperature for two-probe
polyaniline nanofiber thin-film devices (L01 and L02) and nanofiber devices (S01-S06). The solid lines represent the best fitting to data in accordance with the charge-energy-limited tunneling theory (More information is given in Section 2.4). The fitting exponent, p, as function of room-temperature resistance for polyaniline thin-film and nanofiber devices shows in the inset. The average value and standard deviation of the exponent parameter p’s are 2.08 and 0.275, respectively. (b) Room-temperature as a function of L / A for all nanofiber devices. The solid line gives the best linear least square fitting to data. ... 64
Figure 5.5: (a) dV / dI vs 1/ E curves at different temperatures for S06 device. The
dashed and the dotted line represent the limiting behavior at zero temperature and the threshold electrical field at different temperature. The data in the form of dV / dI vs E-1/2 curves also draw in the inset, for comparison. (b) A schematic diagram to model the polyaniline nanofiber. The solid line represents individual polyaniline chains. The spheres imply metallic regions of emeraldine salt (ES) form that is surrounded by insulating regions of emeraldine base (EB) form. The average diameter, d, and the separation, s, of the conducting region are marked in (b). ... 67
1
Chapter 1
Introduction
1.1 Overview
‘’It is a nano world, let’s make it a better place’’ [1]-there is a lot of truth in this cheerful slogan. Actually, if the scientific community ever needed to be convinced that nanotechnology was real, D. M. Eigler and E. K. Schweizer (They were working at IBM’s Almaden Research Center in San Jose, California, United States) provided the evident indication in the 5 April 1990 issue of Nature [2]. They achieved a milestone in humankind’s ability to build small structures by utilizing an ultra-high vacuum scanning tunneling microscope in liquid helium environment (~ 4 K). This ability was demonstrated to be able to move and position individual atoms on a metal surface with atomic-scale precision. In possibly the most well-known image in the history of nanotechnology, they wrote down the letters ‘’IBM’’ with 35 xenon atoms on a smooth nickel surface. After this pioneering feat done, the field, nano world, was created.
Various structures of matter having dimensions of the order of a billionth of a meter manipulated and investigated by nanotechnology were preformed. In the past two decades, the diversity of inorganic structures with nanoscale sizes such
2
as nanowires (NWs) [3, 4], nanocrystals [5, 6], nanotubes [3, 7] and nanobelts [8] have been synthesized by using either chemical or physical strategy and give a great deal of opportunities for the assembly of nanoscale devices and arrays by the bottom-up approach. Organic materials with nanoscale structures have also been made [9]. Due to high surface-to-volume ratio, these nanoscale structures represent novel and / or enhanced functions crucial to many fields of technology. Hence, preliminary field-effect transistors [10], single electron transistors [11], light-emitting diodes [12], photo-detectors [13], chemical sensors [14], and logic gates [15] have been demonstrated immediately.
In a bulk material, electrons are free to move in the solid, so their energy spectrum is almost continuous and the density of electron state per unit energy increases as the square-root of energy. In contrast, from three-dimensional bulk system down to a one-dimensional nanostructure, electrons feel confined gradually and the continuous energy spectrum will become discrete and the energy gap will increase. Undoubtedly, in this situation, the fundamental problems in quantum mechanics, tunneling, phase interference and weak localization effects, play an important role in nanostructure materials, should be taken account of. For example, the electron-electron interactions in one-dimensional metals exhibit dramatically different behavior from three-dimensional metals, in which electrons form a Fermi liquid [16]. Because the electrostatic charging energy is inversely proportional to the grain size of material, the Coulomb blockage effect cannot be neglected in nanostructure materials and dominate the electron transport behavior [11]. Besides, as the dimensions are reduced to a length smaller than the electron’s mean free path, the electronic transport becomes ballistic and the quantized conductance is observed [17].
3
technique of the electron-beam lithography and focused-ion-beam deposition for two- [18, 19] or four- [20, 21] electrode fabrication has been used recently. The scanning probe microscopy for making contacts to these nanostructures is also adopted to address current-voltage characteristics studies [22, 23]. The nano world is already upon us. It cannot be questioned and refused. If we enter it with a positive attitude, it could help decorate and improve our life in the near future.
1.2 Outline of Work
The first portion of this work is presented in chapter 3. According to temperature dependence of resistance and current-voltage characteristic in two-probe ZnO NW devices, contact- and nanowire-dominated devices can be distinguished. A disorder system that occurs between metal-semiconductor interfaces is proposed to explain the transport behaviors of the contact-dominated devices. Besides, we demonstrate that two-probe electrical measurement can also be applied to the exploration on the intrinsic properties of nanowire. This two-probe measurement approach works on highly resistive nanowires without Ohmic contact issue, as well. By employing this method, the electrical resistivity and carrier concentration of ZnO, InP and GaP NWs have been investigated.
The second portion of this work is illustrated in chapter 4. We fabricate a series of two-probe InP NW devices. These NWs fabricated nanodevices are picked up from the same source intentionally. Based on the result in chapter 3, contact or NW-dominated InP devices can be separated each other. In the past it is believed that the electronic and optoelectronic properties of nanodevices are mainly governed by intrinsic NWs. Here contact- and NW-dominated nanodevices are used to expose to light (green laser) and gas (oxygen) to identify the influence of contact effect.
4
The third portion of this work is given in chapter 5. Besides inorganic nanostructure materials surveyed, PANI nanofibers have also been fabricated two-probe nanodevices and studied the intrinsic transport properties. The dielectrophoresis technique is adopted to facilitate to move and position nanofibers onto a nanogap. To shine the electron-beam on contact area, the organic/metal contact resistance is reduced in order to probe the intrinsic electrical properties of a single PANI nanofiber. Through deliberately discussions, the charge energy limited tunneling theory can be used to describe the transport properties of PANI nanofibers.
In chapter 2, we sketch theoretical models that can be applied to our work. Thermionic-emission theory, thermal activated transport, Mott variable range hopping and charge energy limited tunneling are followed to introduce briefly. Experimental results as well as discussions are presented in chapter 3 ~ 5 and the conclusions are summarized in chapter 6.
References
[1] A. Nordmann, Nano Researchers Facing Choices 10, 13 (2007)
[2] D. M. Eigler and E. K. Schweizer, Nature 344, 524 (1990)
[3] J. Hu, T. W. Odom and C. M. Lieber, Acc. Chem. Res. 32, 435 (1999)
[4] Y. Cui, X. Duan, J. Hu and C. M. Lieber, J. Phys. Chem. B 104, 5213 (2000) [5] C. B. Murray, C. R. Kagan and M. G. Bawendi, Science 270, 1335 (1995) [6] A. L. Gast and W. B. Russel, Phys. Today, 24 (1998)
5
[7] S. Iijima, Nature 354, 56 (1991)
[8] Z. W. Pan, Z. R. Dai and Z. L. Wang, Science 291, 1947 (2001)
[9] J. Huang, S. Virji, B. H. Weiller and R. B. Kaner, J. Am. Chem. Soc. 125, 314 (2005)
[10] S. J. Tans, A. R. M. Verschueren and C. Dekker, Nature 393, 49 (1998)
[11] D. L. Klein, R. Roth, A. K. L. Lim, A. P. Alivisatos and P. L. McEuen, Nature 389, 699 (1997)
[12] Y. Cui and C. M. Lieber, Science 291, 851 (2001)
[13] H. Kind, H. Yan, B. Messer, M. Law and P. Yang, Adv. Mater. 14, 158 (2002) [14] Y. Cui, Q. Wei, H. Park and C. M. Lieber, Science 293, 1289 (2001)
[15] V. Derycke, R. Martel, J. Appenzeller and P. Avouris, Nano Lett. 1, 453 (2001) [16] M. Bockrath, D. H. Cobden, J. Lu, A. G. Rinzler, R. E. Smalley, L. Balents and P. L. McEuen, Nature 397, 598 (1999)
[17] H. Ohnishi, Y. Kondo and K. Takayanagi, Nature 395, 780 (1998)
[18] B. Wei, R. Spolenak, P. K. Redlich, M. Rühle and E. Arzt, Appl. Phys. Lett. 74, 3149 (1999)
[19] Y. F. Lin and W. B. Jian, Nano Lett. 8, 3146 (2008)
6 Nature 382, 54 (1996)
[21] S. P. Chiu, Y. H. Lin and J. J. Lin, Nanotechology 20, 015203 (2009) [22] H. Dai, E. W. Wong and C. M. Lieber, Science 272, 523 (1996)
7
Chapter 2
Theoretical Models
Since semiconductor devices had to make contact with the outside world, the interface between metal and semiconductor had become vital. The metal-semiconductor junction formed either a rectifying or an Ohmic contact. In the beginning the metal-semiconductor junction theory will be illustrated in Section 2.1. The electrical transport theories about thermal activated transport (Section 2.2), Mott-variable range hopping (Section 2.3), charge energy limited tunneling (Section 2.4) are also introduced in the following paragraphs, since they could be well-applied to account for our experimental data.
2.1 Thermionic-emission Theory
The current transport in a metal-semiconductor (M-S) junction is due mainly to majority carriers as opposed to minority carriers in a p-n junction. When a metal makes contact with a semiconductor, a barrier is formed at M-S interface. This barrier is responsible for controlling the electrical properties. In 1942, Bethe proposed the thermionic-emission theory to accurately describe the electrical behaviors in M-S interface [1, 2]. In the below subsection, we will consider a metal makes contact with an n-type semiconductor and discuss the total current density.
8
The sum of current density J from the semiconductor to the metal JS→M
and from the metal to the semiconductor JM→S can be given as the following form * 2 2 3 * 2 4 exp exp
exp exp 1 exp
S M M S a B B B B a a B B B B J J J eV em k e T h k T k T eV eV e A T k T nk T k T π φ φ → → = + ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ =⎜ ⎟ ⎜− ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎡ ⎛ ⎞⎤ ⎡ ⎛ ⎞⎤ ⎡ ⎛ ⎞⎤ =⎢ ⎜− ⎟⎥ ⎢⋅ ⎜ ⎟⎥ ⎢⋅ − ⎜− ⎟⎥ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (2.1)
Eq. (2.1) can be written in a usual diode form as
exp a 1 exp a ST B B eV eV J J nk T k T ⎡ ⎤ ⎛ ⎞ ⎛ ⎞ = ⎜ ⎟⎢ − ⎜− ⎟⎥ ⎝ ⎠⎣ ⎝ ⎠⎦ (2.2) , where * 2exp B ST B e J A T k T φ ⎡ ⎛ ⎞⎤ ≡⎢ ⎜− ⎟⎥ ⎝ ⎠ ⎣ ⎦ (2.3)
e, m*, n, kB, h,
φ
B and Va are charge, effective mass of semiconductor material,ideality factor, the Boltzmann constant, the Planck constant, effective Schottky barrier height and applied bias, respectively. The effective Schottky barrier height,
B
φ
, is a function of applied bias which will decrease with an increase of the electric field. The parameter, A* is called the effective Richardson constant for thermionicemission. The current-voltage characteristic of metal-semiconductor junction can be presented by a diode-like form such as a p-n junction, as shown in Eq. (2.2). In the forward bias (apply a positive voltage to the metal with respect to the semiconductor) the effective Schottky barrier is reduced and electrons can easily flow from the semiconductor into the metal. In contrast, in the reverse bias the
9
effective barrier height arise and electrons are limited to get a saturation current density, JST.
From Eq. (2.2) we could notice that ideality factor is an important parameter to determine whether this metal-semiconductor junction is a good diode or not. For an ideal mteal-semiconductor diode, the ideality factory, n, always keeps at unit. As values of Va is greater than 3 kBT / e, Eq. (2.2) can be represented in the simpler
form exp a ST B eV J J nk T ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ (2.4)
so that a plot of ln J versus Va in the forward direction could give a straight line and
the ideality factory could be extracted from the slop. Actually, we always measure the total current, I, rather than the current density, J. This is because that the determination of the current density necessitates an accurate measurement of the contact area, A. Hence, the advantage of retaining the more exact form of Eq. (2.4) is that a plot of
ln
⎣
⎡
I
/ 1 exp
(
−
(
−
eV k T
a/
B)
)
⎤
⎦
versus Va will give a straight linefor all values of Va, not only for the region Va < 3 kBT / e but also for negative value
as well. The saturation current and the ideality factor could be drawn out from the intercept and slope in the plot of
ln
⎣
⎡
I
/ 1 exp
(
−
(
−
eV k T
a/
B)
)
⎤
⎦
versus Va,respectively.
As a general rule, the contact resistance, RC, is inversely relative to the contact
area, A, as C C R A ρ = (2.5)
10
impact of contact resistance becomes more and more important to contribute enormously to the total resistance, especially in nanoscale metal-semiconductor devices. In order to comprehend the equivalent contact resistance in metal-semiconductor interface, we consider furthermore the differential form of Eq. (2.2). M-S contact results in the zero-bias specific contact resistivity of the form
1 * 0 exp a B B C a B V k e J V A Te k T φ ρ − = ⎛ ∂ ⎞ ⎛ ⎞ ⎛ ⎞ =⎜ ⎟ =⎜ ⎟ ⎜ ⎟ ∂ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ (2.6)
As shown in Eq. (2.6), the zero-bias specific contact resistivity will decrease rapidly as the effective Schottky barrier height decrease. The lower the barrier is, the smaller the contact resistance is. On the other hand, if the semiconductor has a higher doping concentration (Nd), the tunneling carriers will dominate the transport
behavior, so Eq. (2.6) can then replace to be written as exp B C d N φ ρ ∝ ⎛⎜⎜ ⎞⎟⎟ ⎝ ⎠ (2.7)
which shows that the strong carrier concentration dependence of contact resistivity is observed.
2.2 Thermal Activated Transport
Using the Boltzmann approximation, the thermal equilibrium electron concentration in non-degenerated semiconductors can be defined as [3]
exp C F C B E E n N k T ⎛ − ⎞ = ⎜− ⎟ ⎝ ⎠ (2.8)
, where NC, EC and EF are the effective density of states in the conduction band, the
bottom edge of the conduction band and intrinsic Fermi level, respectively. We consider the total charge density in complete ionization condition. The net charge
11
density of semiconductor in thermal equilibrium should keep to be zero, indicating the total negative charges (electrons, n, and ionized acceptors, NA−) must be equal to the total positive charges (holes, p, and ionized donors, ND+). Hence, the charge
neutrality condition is expressed as
n N+ A− = +p ND+ (2.9) Consider the case of n-type semiconductor, where donor impurities with the carrier concentration ND (cm-3) are added into the material, the net charge equation can be
re-written as
D D
n= +p N+ ≈N+ (2.10) We apply Eq. (2.10) to Eq. (2.8), and then assume that ND >NA(Compensated
n-type material), the electron concentration can be approximated by
(
)
exp 2 ⎛ − ⎞ ⎛ − ⎞ ≈⎜ ⎟ ⎜− ⎟ ⎝ ⎠ ⎝ ⎠ C D D A C A B E E N N n N N k T (2.11), where EA = EC – ED is an activation energy.
On the other hand, consider an external field applied E to semiconductor, the electric force will accelerate free electrons to create the current, called a drift current, Jdrift. This drift current for n-type semiconductor can be given as
1 drift n J e nEμ E ρ = (2.12) , where
μ
n and ρ are the electron mobility and resistivity, respectively. Assume that the electron mobility is a weak temperature dependent parameter. Therefore, substitution of Eq. (2.11) into Eq. (2.12), the resistivity of n-type semiconductor,ρ, becomes 0exp ρ ρ= ⎛⎜ ⎞⎟ ⎝ ⎠ A B E k T (2.13)
12
, where
ρ
0 is a constant. The mathematical formula of Eq. (2.13) is called thethermal activated transport for semiconductor carriers. The thermal activated transport dominates the carriers behavior in semiconductors at sufficiently high temperatures.
2.3 Mott Variable Range Hopping
Mott first proposed in 1968 that the most frequent hopping process would not be a nearest state at low temperature and expected a temperature dependent resistance behavior which is called Mott variable range hopping (Mott-VRH) [4]. Mott variable range hopping transport is a model describing low temperature conduction in strongly disordered systems with localized states. The argument of this transport theory shows simply in the below.
We consider that at a temperature T the electron will normally hop to a site at a distance smaller than a hopping distance R. The hopping distances, R, is a function of temperature and increases with the decreasing temperature. Within a range R of a given site, the density of states per unit energy range near the Fermi energy is 3 4 ( ) 3 R g EF π (2.14) , where g(EF) is the density of states near the Fermi level and is assumed to be a
constant in this model. Thus for the hopping process through a distance R with the lowest activation energy, the energy E will be the reciprocal of Eq. (2.14) and is given as 3 1 4 ( ) 3 F E R g E π = (2.15)
13
activation energy state E and the largest hopping distance R. The hopping probability can be shown as
exp 2 exp ξ ⎛ ⎞ ⎛ ⎞ ∝ ⎜− ⎟⋅ ⎜− ⎟ ⎝ ⎠ ⎝ B ⎠ R E P k T (2.16)
, where ξ is the localization length. The hopping distance is much longer than the localization length at low temperatures. In order to take the maximum value of the hopping distance R, the first order of the differentiation of Eq. (2.16) to R will be considered exp 2 exp ξ ⎡ ⎛− ⎞⋅ ⎛− ⎞⎤ ⎢ ⎜ ⎟ ⎜ ⎟⎥ ⎝ ⎠ ⎝ ⎠ ⎣ B ⎦ d R E dR k T (2.17)
The optimum value of R is
1/4 9 8 B ( F) R k Tg E ξ π ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ (2.18) Because the resistivity, ρ , is inversely proportional to the hopping probability, so that we substitute for R into Eq. (2.16) to get the conductivity form
1/4 0 exp T T ρ ∝ ⎡⎢⎛⎜ ⎞⎟ ⎤⎥ ⎝ ⎠ ⎢ ⎥ ⎣ ⎦ (2.19) , where 0 31 ( ) B F T k ξ g E ∝ (2.20)
Eq. (2.19) is called three dimensional Mott variable range hopping to describe the non-neighboring hopping process at low temperature. As a general rule, the Mott variable range hopping could be extended to a general formula as
1/ 0 exp p T T ρ∝ ⎡⎢⎛⎜ ⎞⎟ ⎤⎥ ⎝ ⎠ ⎢ ⎥ ⎣ ⎦ (2.21)
14
disordered system, respectively. For other methods of deriving this equation (Eq. (2.21)), giving somewhat different value of T0, please refer to Mott and Davis’s [5]
or Shklovskii and Efors’ s theory [6].
2.4 Charge Energy Limited Tunneling
The transport model of charge energy limited tunneling (CELT) is proposed in 1973 by P. Sheng and his co-worker for granular metals in which the conduction is supposed to proceed from tunneling between small conducting grains embedded in a insulating matrix [7, 8]. They predicted the temperature dependence of the low-field resistance, 1/2 0 exp⎛⎛ ⎞ ⎞ = ⎜⎜⎜ ⎟ ⎟⎟ ⎝ ⎠ ⎝ ⎠ low T R R T (2.22)
, where Rlow and T0 are constants. This equation can be attributed to a relationship C
s E× = constant, where s and EC is the separation of neighboring metal grains and
the charging energy, respectively. In Sheng model the charging energy, EC, is an
energy required to create a positive-negative charged pair to move an electron between two neutral conducting grains and is inversely proportional to the average diameter of the conducting grains, d (i.e. s / d = constant). In this regime (low-electric field) the voltage difference between neighboring granular metals is much smaller than kBT / e. Thermal activation is therefore the main mechanism
responsible for charge generation. On the other hand, as the magnitude of electric-field is increased, an additional mechanism, field-induced tunneling, becomes more and more important and the charge carriers gradually deviates from the thermal equilibrium value. The field-induced tunneling mechanism can be written as
15 0 exp⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ high E R R E (2.23)
, where Rhigh is a constant. E0 high field approach.
In this model, the charging energy plays an important role. The generated carriers in a granular system are thermally assisted in the low-field regime and a field-induced in the high-field regime. Besides, tunneling only occurs between nearest neighboring grain.
References
[1] E. H. Rhoderick and R. H. Williams, Metal-Semiconductor Contacts, 2nd;
Clarendon press, Oxford (1988)
[2] D. A. Neamen, Semiconductor Physics and Devices: Basic Principle, 3th;
McGraw-Hill, New York (2003)
[3] S. M. Sze, K. K. Ng, Physics of Semiconductor Devices; John Wiley & Sons: Edison, New York (2005)
[4] S. N. Mott, Conduction in Non-Crystalline Materials; Clarendon Press; Oxford (1993)
[5] N. F. Mott and E. A. Davis, Electronic Processes in Non-Crystalline
Materialsls; Clarendon Press; Oxford (1979)
[6] B. I. Shklovskii and A. L. Efros, Electronic Properties of Doped
Semiconductor; Cardona (1984)
16
17
Chapter 3
Utilize Two-Probe Configuration
Measurements to Survey the Impact of
Nanocontact on Nanodevices and
Transport Properties in
Semiconductor Nanowires
3.1 Introduction
Semiconductor nanowires (NWs) [1-3], nanocrystals [4, 6] and carbon nanotubes [7, 8], synthesized using either chemical or physical manners in the past decade, give us many opportunities for the assembly of nanoscale devices and arrays by the bottom-up approach. On account of high surface-to-volume ratio, these nanoscale materials represent novel and / or enhanced functions crucial to many fields of technology. Moreover, preliminary electronic and optoelectronic devices, such as field effect transistors (FETs) and light emitting diodes (LEDs) by utilizing nano
18
scale materials have also been perceptive and demonstrated successively [9, 10]. However, in order to exploit these to accomplish the high-dimensional, vertical integrated and multifunctional circuits in the near future, the contact problem in the nanoscale devices, plays the most important role, should be overcome, in particular, the most nanodevices possessing a two-probe configuration as the source and drain electrodes. Additionally, to identify and determine intrinsic properties of NWs also is a pivotal issue to touch the target of nanotechnology application.
An ideal interface between a nanowire and a metal contact in nanodevices is often assumed in many previous reporters. Actually, this is barely the case in reality due to the contact resistance. Recently it has been pointed out that the contact resistance should be taken into account when probing electrical transport in nanomaterials. Bachtold et al. applied four-probe electric measurements to carbon nanotubes and found the contact resistance could be reduced by six orders of magnitudes after electron beam exposure [11]. Hwang et al. discovered that the contact resistance is reduced as the Ti layer thickness, that is in the Ti/Au electrodes contacting on GaN NWs, is increased [12]. Zhang et al. proposed a model to describe contact-dominated behaviors at low field regime and to extract intrinsic nanowire resistivity at high field regime [13]. Furthermore, in order to eliminate a possible contamination layer formed between metal-semiconductor interfaces in nanoscale devices and to fabricate a good Ohmic contact to get the electrical properties in NWs, a rapid thermal annealing [14] or local current-induced Joule heating [15] were adopted.
In this work, a series of two-probe NW devices were fabricated to explore the current-voltage (I-V) characteristics and temperature dependence resistance. According to temperature behaviors of resistances, contact- and NW-dominated devices can be distinguished each other. In Section 3.3.1 only ZnO NW devices
19
were utilized to reveal the impact of nanocontact and a disordered contact picture between the nanowires and Ti/Au electrodes was proposed. In Section 3.3.2 ZnO, InP and GaP NW devices were investigated in determination of the intrinsic temperature dependent resistance.
3.2 Experimental
Method
ZnO NWs were synthesized by a thermal evaporation (vapor transport) on quartz substrates with gold nanoparticles as catalysts to control the NW diameter [16]. InP and GaP NWs were synthesized by self-seeded, solution-liquid-solid growth [17]. NWs were analyzed by using a field-emission scanning electron microscope (FE-SEM, JEOL JSM-7000F). ZnO NWs are ~40 nm in diameter and 5-10 μm in length, whereas InP and GaP NWs are 2-5 μm in length and ~20 and ~30 nm in diameter, respectively. Prior to the electron-beam (e-beam) lithography process, micrometer-scale Ti/Au electrodes, current leads and alignment marks were photo-lithographically generated on a Si wafer (heavy doped p-type Si wafer), capped with a 400-nm thick SiO2 layer, in order to prevent from current leakages
through the substrate. In each experiment, the stocked ZnO, InP, or GaP NWs were dispersed on a pre-patterned substrate. FE-SEM was employed to locate the position of NWs. A standard e-beam lithography technique was used to pattern Ti/Au (40/150-nm thickness) current leads and to contact the NWs. The as-fabricated two-probe NW devices were annealed at 400 oC in a high vacuum for 1 min in order to improve the contact.
All of as-fabricated two-probe NW devices were then placed into a crystat (Variable Temperature Insert Cryostat, CRYO Industries of America Inc.) for acquiring their temperature dependence of I-V measurements. These electrical characterizations were carried out with a current and voltage resolution of 10 pA
20
and 1 mV, respectively. The temperature dependent resistances reported in this article were measured in a temperature range between 300 and 77 K. Besides, it should be noticed that the resistance at a given temperature was extracted from the regime around the zero bias voltage.
3.3 Results
and
Discussion
A schematic diagram of our two-probe configuration NW devices is represented in Fig. 3.1 (a). The separation distance of ~ 1 μm between two e-beam lithography electrodes is kept the same for all of our nanodevices. FE-SEM image of a typical NW device is given in Fig. 3.1 (b) and the high-resolution FE-SEM image of the indicated rectangular area is depicted in Fig. 3.1 (c). The alignment marks are utilized for the e-beam lithography to determine the position of our randomly dispersed nanowires. In the below discussion, we will use the same configuration of nanodevices to investigate the impact of nanocontact (Section 3.3.1) and the transport behaviors of semiconductor nanowire (Section 3.3.2).
21
Figure 3.1: (a) A schematic diagram of a single NW device. Typically, the
separation distance between the two contact electrodes is about ~1 μm. (b) FE-SEM image of a typical nanowire device with pre-fabricated micron electro-pads and alignment marks. An image of the indicated rectangular area is given in (c). The enlarged area displays a close view of a single ZnO NW device.
3.3.1 The Impact of Nanocontact on Nanodevices
In this work, more than thirty two-probe ZnO NW devices were fabricated to determine the intrinsic resistance of ZnO NWs and to explore the influence of nanocontact on nanodevices by analyzing their corresponding I-V characteristics and electron transport. It is emphasized that all of ZnO NWs used to fabricate nanodevices is detached from the same source sample. Even though this reason, we still observed a distinct RT (room-temperature) resistance of our ZnO NW devices. Hence, according to their RT (room-temperature) resistances and I-V curves, the devices were grouped into three different types. Fig. 3.2 (a) presents the first type, Type I, ZnO NW device with characteristics of a lower RT resistance, a linear I-V
22
demeanor in low voltage range, and a symmetrically downward bending feature in
I-V curves. The low RT resistance and linear I-V dependence imply that both of the
two nanocontacts are Ohmic type. Moreover, the temperature behavior of current at various bias voltage is analyzed with regard to the thermionic-emission theory (see Section 2.1) and shown in Fig. 3.2 (b) but we did not find any concordance. The result of inconsistence with Schottky contact supports the Ohmic type contacts for Type I devices as well. The circuit diagram of Type I devices with two Ohmic nanocontacts (indicated as circles) and one ZnO NWs (a resistance symbol) is given in the inset of Fig. 3.2 (a). Since both the two nanocontacts are Ohmic type, the device resistance could mainly come from the intrinsic ZnO NW resistance. On the other hand, the zero-voltage resistances as a function of temperature are displayed in Fig. 3.2 (c). The electron transport behavior can be well apprehended in agreement with the thermally activated transport (see Section 2.2) of electrons in ZnO NWs. The intrinsic ZnO NW resistance unveils thermally activated transport of conduction through the NW which conforms to our four-terminal measurements [18] and other groups’ results [19, 20]. Since the conduction through the nanowire has been unambiguously investigated in Type I devices, the other devices having higher RT resistances could give electrical properties at nanocontact.
23
Figure 3.2: (a) I-V curves of a Type I ZnO NW device with a RT resistance of ~15
kΩ. The inset introduces a model of circuit diagram for Type I devices. (b) I/T2 as a function of inverse temperature at various bias voltages. (c) Resistance as a function of temperature revealing electron transport in the Type I device.
A rectifying behavior on I-V curves, especially at low temperatures, has been unambiguously obtained and presented in Fig. 3.3 (a). We notice that the non-symmetrical I-V curves of the Type II NW device could only originate from one and only one Schottky nanocontact with the other one of Ohmic type. A circuit diagram model is offered in the inset of Fig. 3.3 (a) to depict the Schottky nanocontact, the ZnO NW, and the Ohmic nanocontact from left to right. The analyses in accordance with thermionic-emission theory (see Section 2.1) are given in Fig. 3.3 (b) and (c). For Type II devices, we observed linear dependence between ln(I/T2) and 1/T with a slope indicating the effective Schottky barrier in the Schottky nanocontact. At a high bias voltage, the slope tends to zero which denotes
24
the vanishing of effective Schottky barrier
φ
B when the bias approaches the break down voltage. Moreover, the I-V curve in a wide voltage range introducing in Fig 3.3(c) fits precisely with thermionic-emission theory both in forward and reverse bias voltages. Intriguingly and surprisingly, the ideality factor estimated from our fitting is very close to the ideal value of 1. Alternatively, the RT resistance of Type II devices ranges from near the upper bound RT resistance of Type I devices to that of Type III devices as will be acquainted in the next paragraphs. The temperature dependence of resistance R(T) in Fig 3.3 (d) indicates that the electron transport behavior cannot be solely interpreted by the thermally activated transport in ZnO NW. In addition, We found that electron transport in these Type II devices departs from thermal activated transport and starts to reconcile with thermionic-emission and VRH conduction. We noticed that the fittings with either Schottky contact or VRH conduction do not make a significant difference at temperatures above 100 K. These results suggest that electrical properties, including I-V curves and zero-voltage resistances, mostly arise from the single Schottky nanocontact in the Type II NW devices.25
Figure 3.3: (a) I-V curves of a Type II ZnO NW device with a RT resistance of ~50
kΩ. The inset introduces a model of circuit diagram for Type II devices. (b) I/T2 as a function of inverse temperature at various bias voltages. (c) ln(I/(1-exp(-qV/kT))) as a function of voltage. (d) Resistance as a function of temperature revealing electron transport in this Type II device. The dashed and solid lines are best fittings (see text) of Equations 4 and 5, respectively.
Typical characteristics of the last type, the Type III ZnO NW devices with analyses through thermionic-emission theory are given in Fig. 3.4. First of all, the
I-V curves in Fig. 3.4 (a) reveal symmetrical and an upward bending feature, and
the data can be fitted well with thermionic-emission theory in reverse bias voltage. The linear dependence of ln(I/T2) and 1/T at various bias voltage appears
26
prominently in Fig 3.4 (b) that supports our idea of Schottky contacts for Type III devices. Since no forward bias I-V reliance of a Schottky diode is spotted and the currents in both positive and negative voltages agree well with the reverse-bias thermionic-emission theory (see Fig. 3.4 (a) and (b)), we propose a model of two back-to-back Schottky contacts, which is commonly addressed to explain nonlinear
I-V curves of semiconductor NW devices [21, 22], in the inset of Fig. 3.4 (a) to
demonstrate the Type III devices. As for zero-voltage resistance, we obtained several different temperature dependent behaviors. Two typical sets of resistance data are presented in Fig. 3.4 (c) with the best fittings of dashed and solid lines following Schottky contact and VRH conduction, respectively. In this case, we found that the data points vary from the ideal Schottky contact form at temperatures below 200 K. Including the information of high RT resistances for Type III devices as well as the best fitting in accordance with VRH conduction form, we propose that a deteriorated contact between the Ti electrode and the ZnO NW forms due to a non-crystalline interface layer or titanium oxides. Owing to a diminished nanocontact area, a poor specific contact resistivity results in a high contact resistance and dominates electrical properties of the Type III NW devices.
27
Figure 3.4: (a) I-V curves of a Type III ZnO NW device with a RT resistance of
~1.5 MΩ. The inset introduces a model of circuit diagram for Type III devices. (b)
I/T2 as a function of inverse temperature at various bias voltages. (c) Resistance as a function of temperature revealing electron transport in this Type III device (red circles) and in another Type III device having a RT resistance of ~128 MΩ (black squares). The dashed and solid lines are best fittings (see text) of Equations 4 and 5, respectively.
In order to discuss electron transport in ZnO NW devices and to fit their temperature dependent resistance, we adopted VRH conduction and included the exponent parameter p of 1 for thermally activated transport. The estimated exponent parameters as a function of device RT resistance are given in Fig. 3.5 (a). An unambiguous trend of a rising exponent parameter with an increase of RT resistance has been detected that signals worsened electrical properties in the nanocontacts. Moreover, the graph can be approximately separated into Regions A,
28
B, and C with an exponent parameter of about 1, 2, and bigger than 3, respectively. We discerned that all Type I ZnO NW devices are gathering in Region A indicating two Ohmic contacts on the individual ZnO NW. It is noted that the Type I devices have RT resistances lower than 100 kΩ. In addition, Type II devices distribute in Region B and unveil one-dimensional VRH conduction in one and only one nanocontact on the ZnO NW. Unlike Type I and II devices, Type III devices, having RT resistances higher than 100 kΩ, spread over Region B and C that connotes two- and three-dimensional VRH conduction in both nanocontacts of a NW device. In Fig. 3.5 (b) we provide three nanocontact models to elaborate our thoughts. Since a direct Ti metal contacting on ZnO should be attributed to Ohmic contacts as inferred from experiments of bulk systems [23], we propose a direct contacting model for nanocontacts of ZnO NW devices in Region A. Otherwise, the RT resistance is greater for devices in Regions B and C, we argue that titanium oxide form in the nanocontacts due to poor vacuum conditions during thermal evaporation. For NW devices in Region B, we believe that the oxide layer is thin enough for electrons to transport as one-dimensional VRH conduction. When the oxide layer is thick, the conduction channels mix to form two- and three-dimensional VRH conduction such as the proposed nanocontact model for devices in Region C.
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Figure 3.5: (a) The fitting exponent parameters p as a function of RT resistance for
our as-fabricated ZnO NW devices of Type I, II, and III, marking as blue circles, black triangles, and red squares, respectively. The figure is approximately separated into Regions A, B, and C according to the exponent parameters of our devices. (b) Three different nanocontact models corresponding to the ZnO NW devices belonging to Regions A, B, and C of Figure (a).
In the above discussion, we have learned that the interface problems in nanowire-based electronics play important roles due to the reason that the reduced contact area in nanoelectronics multiplies enormously the contribution of electrical contact properties. In the interfacial nanocontact system, electron transport follows Mott variable range hopping theory of the form 1/
0
exp(( / ) )
∝ p
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specific contact resistivity of an interfacial nanocontact system is further considered according to the form ρC = ×R A , where R and AC C represent RT
resistance and contact area of nanodevices, respectively. The fitting exponent parameters, p, as a function of nanodevices contact resistivity at room temperature are given in Fig. 3.6. It should be emphasized that many two-probe nanodevices of different systems of semiconductor nanowires (The intrinsic electrical properties of these nanodevices will be illustrated in Sec. 3.3.2.) are used to extract the exponent parameters. A straightforward trend of a rising exponent parameter with an increase of specific contact resistance can be seen. The exponential parameter, p, rises from 2 to 4 with an increase of specific contact resistivity, as shown in Fig. 3.6, indicating a change from one- to three-dimensional hopping condition. Besides, a universal trend (i.e. the dashed line) is marked in Fig. 3.6, implying the nanocontact system seems to exhibit a general behavior of electron transport, even in these nanodevices fabricated by disparate nanowires. Moreover, the fitting exponent parameters as a function of T0 also depict in the inset of Fig. 3.6. Since
the fitting parameter, T0, is proportional inversely to the localization length in
disorder system (see Eq. (2.20)), the increasing T0 suggests strongly a reduction of
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Figure 3.6: The fitting exponent parameters p as a function of RT contact
resistivity for NW devices. The fitting exponent parameter as a function of T0 shows in the inset.
3.3.2 Transport Behaviors in Semiconductor
Nanonanowires
It is already learned in Section 3.3.1 that with the shrinkage of nanocontact area on nanodevices, the contact resistance will contribute extremely to the total resistance of the two-probe NW devices. In the below discussion, we have made the best efforts in facilitating the Ohmic contact so that the contact resistance can be neglected. Here, ZnO, InP, and GaP NW devices were investigated in determination of the intrinsic temperature dependent resistance.
Fig. 3.7 (a) displays a schematic diagram of a two-probe ZnO NW measurement system and the inset is a typical FE-SEM image of a ZnO NW device.
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The scheme demonstrates that the NW was buried under the leads (electrodes) and contacted with a Ti metal, having a contact area of ~1×0.04 μm2. The separation distance between two probes is a constant of ~1 μm. The targeted NWs were selected from the same source sample. Since these NWs have the same diameter and length, they should exhibit the same resistance. Fig. 3.7 (b) presents data collected from three two-probe devices in which the NWs were detached from the same source sample. It was observed that not only the room-temperature resistances on the three devices, ZnO-1, ZnO-2, and ZnO-3, are largely different (up to four orders of magnitudes), but their temperature behaviors are also disparate. According to above-mentioned assumption, that is, NWs of the same sample source should have defect concentration and resistances in the same order of magnitude, we propose that the higher resistance from ZnO-1 and ZnO-2 devices could be due to the nanocontact. This conjecture has been confirmed by current-voltage measurements which exhibit a nonlinear, non-Ohmic behavior [24]. As reported in previous section, the nanocontact can be treated as a disordered system and the electron transport in nanocontact follows a theory of Mott-VRH (More theoretical and experimental detail could be referred to Section 2.2 and Section 3.3.1, respectively) 1/ 0 0 ( )= exp⎛⎜⎜⎛ ⎞⎜ ⎟ ⎞⎟⎟ ⎝ ⎠ ⎝ ⎠ p T R T R T (3.1)
where R and T are resistance and temperature, T0 is a constant, R0 is a weak
temperature-dependent constant, and p is the exponent parameter. The dashed lines give the best fits to data in Fig. 3.7 (b) to derive the exponent p of 2 and 4 for ZnO-2 and ZnO-1 devices, respectively. The increase of room-temperature resistance as well as disorder in the nanocontact can raise the exponent parameter p from 2 to 4 and the nanocontact-constrained electron system from one- to
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three-dimensional Mott-VRH.
On the other hand, if a device, such as ZnO-3, holds the lowest room-temperature resistance, it implies that the intrinsically electrical property of the NW and the temperature-dependent resistivity may follow a thermally activated transport equation ( )= 0exp⎛⎜ ⎞⎟ ⎝ ⎠ A B E R T R k T (3.2)
where R0 is a constant, kB is the Boltzmann constant, and EA is the activation energy.
The solid line in Fig. 3.7 (b) presents the best fit to the data of ZnO-3 device according to the thermally activated transport equation. The room-temperature resistance of ZnO-3 device is 16.8 kΩ and the length and diameter of the NW are 1 μm and 40 nm, respectively, resulting in a resistivity of ~0.002 Ω cm. Assuming that the electron mobility is 50 cm2 V-1 s-1 [25], we can estimate the carrier concentration to be 1019 cm-3 at room temperature. At temperatures lower than 140 K, it is amazing to see that the temperature-dependent resistance deviates from the theoretically predicted values. Since a random distribution of native defects and a disorder are introduced, the electron transport in ZnO NWs, having a low carrier concentration, should follow Mott-VRH at very low temperatures. The resistance of ZnO-3 device agrees well with the three-dimensional Mott-VRH theory (the dashed line, p = 4) at temperatures lower than 140 K. To verify this conjecture, we adopted a four-probe measurement method (see Fig. 3.7 (c)) and confirmed that the intrinsic NW transport follows the three-dimensional Mott-VRH theory described in Eq. (3.1) with the exponent parameter p = 4. This result is in consistent with a determination reported recently [20]. As a consequence, the two-probe measurement with two Ohmic contacts and low resistance can be employed in acquiring carrier concentration and electron transport properties in ZnO NWs.
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Furthermore, the source sample of ZnO-4 is different from that of ZnO-3 and the room-temperature resistivity and carrier concentration of ZnO-4 were evaluated to be 17 Ω cm and 1016 cm-3, respectively. The carrier concentration of ZnO-4 NW is about three orders of magnitude lower than that of ZnO-3 NW. It should be pointed out that the ZnO NWs picked up from different source samples can exhibit extraordinarily discrepant resistivities and carrier concentrations, even though they are synthesized by the same growth method. The change in carrier concentrations among NWs picked up from different source samples is expected to come from varied concentrations of structure defects such as oxygen vacancies and Zn interstitials.
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Figure 3.7: (a) Schematic diagram of a two-probe ZnO NW device with a typical
SEM image shown in the inset. Temperature-dependent resistance of (b) two- and (c) four-probe ZnO NW devices. A schematic diagram of a four-probe device is drawn in the inset of Fig. (c). Solid and dashed lines delineate the best fits to the mathematical forms of thermally activated transport and Mott-VRH, respectively. After fitting to Mott-VRH (dashed lines), the exponents, p's, of ZnO-1, ZnO-2, ZnO-3, and ZnO-4 devices are estimated to be 4, 2, 4, and 4, respectively.
To extend the application of this two-probe measurement method to other semiconductor NWs, InP NW devices were fabricated through a solution-based growth15 and a typical SEM image is presented in the inset of Fig. 3.8. InP NWs, like ZnO NWs, are natively n-type doped with a relatively low carrier concentration, which have been proved by the back gate effect (not shown in this
