Abstract
This chapter reviews the results of silver nanometer-sized contacts (Ag NCs). To realize fabrication, atomistic observation, and mechanical and electrical measurement of Ag NCs, an in situ method where a contact-retract test of atomic force microscopy and a current feedback function of scanning tunnelling microscopy have been combined with high-resolution transmission electron microscopy (HRTEM). By inserting these functions inside HRTEM, it has been enabled to observe atomistic structures, which can be formed at the final stage of a rapture process, and to measure a change of properties correlated to structural dynamics.
Keywords
- Silver nanometer-sized contacts
- atomic force microscopy
- conductance quantization
- Young's modulus
1. Introduction
Currently, miniaturisation of electronics has continued, and it started the device development at atomistic and molecular scale.[1] Devices included into this electronic circuit are nanometer-sized contacts (NCs), atomic-sized wires (ASWs), single molecular junctions (SMJs), and so on.[2] (Figure 1) SMJ is a system of a single molecule sandwiched by a pair of nanometer-sized metallic electrodes. SMJs enable single electronic operation, high-density integration, and electric power saving.[3-7] To engineer SMJs, we need to reveal structure of device configuration that includes interfaces between molecules and electrodes and mechanical and electrical properties. Metallic NCs and ASWs are fundamental materials that have potentials for device applications themselves as well as key factors of application for SMJs[8].
1.1. Electrical Property of NCs
Research in metallic NCs at 1988 by van Wees et al. started with conductance quantization in a point contact of two-dimensional electronic gas (2DEG) formed at interface of semiconductors. [9] When a negative bias is applied between gate electrodes placed on semiconductors, a depletion layer is formed in 2DEG under the electrodes. At a gap of this depletion layer, in which electrons cannot exist, a point contact of 2DEG forms. Energy of electrons passing through the contact is written as below, wherein W is the width of point contact.
Here, the first term is the kinetic energy along x direction, and the second term is the discrete energy level due to confinement along y direction. With
Here,
In early stage of metallic NCs, niobium (Nb) and nickel (Ni) NCs were researched. Just before the rapture of these NCs in tensile deformation process, the conductance of several
After the electrical conductance of NCs for other metallic species was researched, construable conductance of quantization was limited for monovalent metals, which are better suited for free electron approximation, such as Au[19, 20], silver (Ag) [19, 21-26], copper (Cu)[11, 19, 21, 27-35], and Na[18, 36, 37]. For the other metallic NCs, such as Nb[12, 13, 15, 21, 38], Ni[11, 14, 17, 22, 39-41], platinum (Pt) [11, 12, 17, 22, 28, 42-51], aluminium (Al), [13, 15, 28, 52, 53], paradium (Pd) [31, 44, 47, 49, 54, 55], iridium (Ir) [44, 46, 54], rhodium (Rh) [44, 54], zinc (Zn) [56, 57], and cobalt (Co)[47], the measured conductance is not construable for integer multiples of
1.2. Structure of NCs
To fabricate metallic NCs, mechanically controllable break junction (MCBJ) method [12, 38] and STM method [58]were mainly used. In these methods, however, one cannot observe the structure of NCs. Therefore, for quantization-type NCs, it is expected that the minimum cross-sectional area of NC, which shows the integer multiples of
Here,
1.3. Mechanical property of NCs
Gimzewski et al. researched elastic and plastic deformation of NCs [62], but they could not discuss the mechanical properties of NCs by hitherto known MCBJ and STM methods. After that, Agraït et al. introduced the secondary STM tip on the backside of first tip to measure the displacement, and they also measured the conductance and force variation at the same time.[63] In 1996, Rubio et al. introduced an AFM cantilever to measure the force acting on NCs instead of STM tip.[64] The force value varied in a sawtooth pattern corresponding to the staircase pattern of conductance (Figure 7). It is supposed that the repetition of elastic and plastic regions appears in deformation process of Au NCs. In addition, force-displacement curve gives a spring constant of NCs.
In 2001, Kizuka et al. observed the deformation process of Au NCs using HRTEM-based
1.4. Deformation of NCs
Sørensen et al. suggested three slip modes for deformation of NCs [69] (Figure 8). The tensile deformation axis is perpendicular to {111}. Deformation occurs with slipping on one, two, or three {111}, which are tilted from the tensile deformation axis (Figure 8).
To actually observe the deformation of NCs, two
As Kizuka et al. further improved the
The observed Au ASW has up to 10 atoms in length with an average interatomic distance of 0.27 nm (Figure 10). In tensile deformation process of ASWs, as tensile stress is concentrated on the contact region, interatomic distances of Au ASWs become longer up to 0.30 nm. At the same time, conductance of Au ASWs was measured. Resultant conductance greatly decreases when the number of atoms that is constructing ASWs exceed 4. Moreover, the force acting on the contact was measured. The tensile strength of this ASW was estimated to be from 8 to 17 GPa. This value is several times larger than that of Au NCs and much larger than bulk Au. At elastic deformation regions of stress-strain curves, Young’s modulus of Au ASWs was estimated to be from 47 to 116 GPa. This value is remarkably comparable with that of single crystal Au.
The NCs and ASWs of other materials than Au have been also observed. The conductance quantization-type NCs, such as Au, Ag[26, 75] and Cu [34] ASWs, were also observed. On the other hand, those of anti-quantization-type NCs, such as Pt [47, 51], Pd[47, 76], Ir[66], and Co [47]ASWs, were also observed.
As described above, the problems in the research in metallic NCs commonly exist until now, among many materials as unrevealed below: 1) corresponding relationships between structure and electrical property of NCs, 2) phenomenon and mechanisms in the disappearance of conductance quantization, and 3) mechanical property of NCs. Especially, as research in NCs has been concentrated on Au, the structural dynamics of NCs is uncertain. Even some of the metallic NCs are already researched, only the structures that appeared in tensile deformation process have been observed. Therefore, the stable structure and electrical conductivity of the NCs are not yet revealed.
To guide the general rule of the phenomenon that appears in the metallic NCs, it is necessary to examine structural dynamics, electrical conductivity and mechanical properties, clarify the correspondence relationship between the structure and properties directly. The method used to observe structures and properties at the same time, which can analyse the correspondence, is limited
The purpose of this research is to clarify Ag NCs as a quantized metal using
2. In situ HRTEM
2.1. Experimental – In situ HRTEM -
In the observation of NCs, we used combined HRTEM with functions of STM and AFM (Figure 11) [61]. One can insert two specimen holders into the sample room of this microscopy. Each holder can be driven by a course mechanical goniometer that has ±1 mm with submicron resolution and a fine piezo that has picometer scale. That is, we can move the sample to make a contact or a deformation with atomistic level using eight degrees of freedom.
When we measured the force acting on a contact, we attached a silicon cantilever used in AFM on one of the specimen holders. This cantilever was covered with metallic film that is 20-40 nm thick. The other one was mechanically polished and Ar-ion milled metallic thin plate.
HRTEM images were recorded with television camera. We applied bias voltages between samples. The current through the contact was measured by two-terminal method. The current signal was amplified 105 times and was then converted into voltage signal. Forces that are acting on a cantilever along deflection and torsion directions were detected using optical lever method used in AFM. When a laser is irradiated on the backside of cantilever, reflection angle of the laser varies with the cantilever deflection. We detected it as variation in relative strength of incident laser beam into quadrant photo-diode. These values were also amplified in the circuit. We recorded voltage signals corresponding to voltage, current, deflection, and torsion per 480 s, then we analysed these signals and observed images with time synchronizations.
Firstly, we set up two samples in a distance of 10 nm using course-moved mechanical goniometer with low magnification observation. After that, we made a contact using piezo drives. Then, we applied bias voltages of 13 mV and repeated to make a contact and tensile deformation. Each atomistic structure of NCs only appeared during several milliseconds in deformation process. This time is often shorter than the time resolution of the system of image recording for TEM (~17 ms / 1 frame). To observe specific structure longer, we used current to piezo drive feedback system.
3. Structure, conductance, and mechanical properties
3.1. Observation of tensile deformation process
In this section, we show the tensile deformation process of Ag NCs. Figure 12 is a time-sequence series of high-resolution images of the thinning process of Ag NC. The thinning was caused by the cantilever tip retraction from the plate with a speed of approximately 0.3 nm/s; the tip-plate distance was not controlled by the conductance feedback circuit in this observation. The tip and plate are observed with dark contrast in the upper and the lower regions of each frame, respectively. The NC is located at the centre of each image. The minimum cross section of the contacts is located in the middle of each frame between the tip and the plate in the vacuum. On the surfaces of both the tip and the plate, neither contamination nor an oxide layer is observed throughout Figs. 12(a)–12(f). The (111) lattice fringes with a 0.24 nm spacing are observed on the tip, the plate, and at their contact; the NC has a crystalline structure. The width of the minimum cross section in Fig. 12(a) is 2.2 nm. The width decreases as retraction proceeds, as shown in Figs. 12(b)–12(e). After this thinning, the width of the NC reaches 0.58 nm in Fig. 12(e), and finally, the NC breaks, as shown in Fig. 12(f).
Figure 13 is the time variation in strain, minimum cross-sectional area, current, current density, force, and stress of the Ag NC during the tip-plate retraction process shown in Fig. 12 as function of time. The time in Fig. 13 corresponds to the observation time in Fig. 12. As the tip-plate distance increases gradually, the minimum cross-sectional width decreases, as shown in Fig. 12(a) and 12(b). During this thinning process, rapid decreases in current and force are simultaneously observed. This shows that the thinning of the NC proceeds intermittently during tip retraction. Thus, slips occurred at these rapid decreases after elastic elongation, as indicated by the arrows above the force curve in Fig. 13. To calculate the current density and the stress of the NC, we assumed that the minimum cross section of the contact was circular. The minimum cross-sectional area was calculated using the observed width. In the time region from 0 to approximately 2.0 s, the stress increases as the cross-sectional area decreases.
The force at fracture is approximately 2 nN, which is similar to the values for Au single-atom contacts (approximately 1.5 nN).[64] The stress reaches approximately 3 GPa before fracture, which is 1/3 of the fracture strength previously observed for Au single-atom contacts(approximately 8 GPa)[61] and comparable to yield stress for Au NCs (1.7–4.2 GPa).[63] This shows that the critical shear stress of the Ag NC increases as the NC becomes thinner. The variation in stress against strain is represented in Fig. 14. A sawtooth curve, consisting of cycles of gradually increasing stress followed by a successive rapid decrease in stress is seen in Fig. 14. The regions of gradually increasing stress correspond to elastic elongation of the NC. The rapid decreases in the strain-stress curve correspond to slip events, due to the structural relaxation of accumulated strain during elastic elongation. From the slope in each elastic elongation region, the plotted Young’s modulus of the NC was estimated. Figure 15 shows the Young’s modulus plotted against the minimum cross-sectional width. The slope changes at a width of approximately 1 nm.
3.2. Conductance histogram
Figure 16 shows the conductance of Ag NCs during the simple retraction of the tip. The histogram of the conductance values is integer multiples of
Figure 18 shows high-resolution images of Ag contacts during conductance feedback control with an assigned value of
The contrast in Fig. 18 is weaker than that of Au NCs because the electron-scattering intensity of Ag atoms is lower than that of Au atoms.[61] Figures 19(a)–19(c) show the conductance of and the force acting on the Ag contacts presented in Figs. 18(a)–18(c) during the conductance feedback control, respectively. The observed conductance values converged to be assigned a value of
Figure 20 shows conductance histograms of the Ag contacts, along with their minimum cross-sectional width during feedback control with assigned values of conductance of 1, 2, and
3.3. Mechanical properties of Ag NCs during thinning
The sawtooth curve was observed in the stress-strain relationship that is up to a strain of 0.25, as presented in Fig. 14. Thus, the tensile deformation of the NC initially proceeded through cycles of elastic elongation and subsequent slip up to this strain. The tensile stress at which the slips occurred was 0.5–0.6 GPa in the strain region of 0–0.25 in Fig. 3. The critical shear stress was calculated from the stress and the angle between the tensile and slip directions. The value calculated was 0.07 GPa, comparable to 1/10 of the theoretical shear stress (0.77 GPa) and the critical shear stress of Ag whiskers on {111} in <110> (0.71 GPa).[78] Thus, the slips in this strain region are inferred to be dislocation-mediated slips. After this slip process, a rapid increase in stress followed by a decrease is seen at a strain of 0.25. During the decrease, a sawtooth shape was observed: slip events continued after the rapid increase. The maximum stress in this region increased to 2 GPa. This stress corresponds to a critical shear stress of 0.2 GPa, comparable to 1/3 of the theoretical shear stress and whisker shear stress. It was also noted that for smaller contacts having widths of less than 1 nm, the slope of the Young’s modulus-width relationship increased, and the modulus reached 10 GPa, as shown in Fig. 4. Thus, it is found that the elastic property of the NCs changes when their width decreases to less than 1 nm. These results reveal that a different type of deformation occurred for the smaller contacts. A molecular dynamics simulation by Sørensen et al. showed that in Au NCs, the crossover from a dislocation-mediated slip to a homogeneous slip occurs when their width decreases to less than 1.5±0.3 nm.[69] In the present observation, the minimum cross-sectional width of the Ag NCs was 1.5 nm when the critical shear stress was 0.2 GPa. Therefore, it is inferred that the deformation mechanism changes from dislocation-mediated slip to homogeneous slip when the width decreases to less than 1.5 nm. That is, changes, such as increase in the Young's modulus of nanoscaled materials, are caused by a simplification of deformation system to a direct atomistic materials mechanics rather than a slip system of macroscaled materials. In such cases, mechanical properties of the materials are subject to modulation by the size effect.
3.4. Stable contact with a certain conductance
When the feedback value was assigned to be
3.5. Structures of Ag NCs exhibiting a conductance of 1 G0
During the feedback control with an assigned conductance of
In the present study, in addition to simple tensile deformation, we introduced a conductance feedback system into
4. Current-voltage characteristics measurement
In this section, we show the current-voltage characteristics measurement of Ag NCs. Figure 21 is high-resolution images of the thinning process of Ag NC in a timeline. The NC is located at the centre of each image. The upper and the lower dark regions are the tip and the plate. The other brighter region is the vacuum. The continuous (111) lattice fringes of Ag (0.24 nm) are observed in the tip, the plate, and their contact region. It shows that the NC is a single crystalline structure. The width of the minimum cross section of the NC decreased from 6 atoms to 1 atom, and finally, the contact broke. Although the width of the contact region in Figs. 21(c) and 21(d) is the same, the contrast of the constricted region became brighter, implying that the thickness decreased. Figure 22 shows the high-resolution images and line profile of the constricted region of Figs. 21(d)–21(f). The intensity is classified into some levels; the intensities of the number of atom in thickness and the noise level in the vacuum. In Figs. 21(d) and 21(e), two and one large peaks are observed, indicating that their widths are 2 atoms and 1 atom, respectively. On the other hand, only the noise level is observed in the intensity in Fig. 21(f); the two tips are separated in the vacuum. From similar analysis, we constructed models of the atomic configurations of the Ag NC in Fig. 21, as shown in Fig. 22.
Figure 24 is the time-variation of the width, bias voltage, current, conductance, force, and stress during the thinning process of the Ag NC shown in Fig. 21, as a function of time. As the NC becomes thinner, the amplitude of the current and the conductance decrease stepwise. Similarly, the tensile force acting on the NC also decreases stepwise. The magnitude of the stress, which is calculated by dividing the force by the minimum cross-sectional area, is 1–6 GPa at times a–d and increases to 14 GPa before fracture at time e. Figure 25 shows the I–V curves measured for the NC presented in Fig. 21. The zero-bias conductance was estimated from the gradient of each curve to be
here,
4.1. Non-linearity of conductance and scattering of electrons in the Ag NC
The HRTEM images (shown in Fig. 21) were averaged over the time of 2 frames (over a period 67 ms,), which is similar to one cycle of alternating bias voltage that is 50 ms (Fig. 24). Thus, one of the I–V curves was corresponding to the averaged image over the 1 period. We confirmed that no discernible changes in image were observed between the 2-frame images used for averaging in the television system. We also noted that there was no identified hysteresis in any of the I–V curves, and no change was observed between the successive increases and decreases in voltage. Under these conditions, the variation in the non-linear parameter was observed. Therefore, even though a small invisible structural change might occur and affect each I–V curve, the variation in the non-linear parameter was observed, which we discuss next. As shown in Fig. 26,
If we applied the bias voltage over 240 mV, the NCs of 5 nm size became unstable owing to electromigration; electron scattering increases enough to cause the atom migrations.[35] Such scattering contributes to the broadening of peaks in the conductance histograms of Ag NCs.[77]
As described above, electron scattering increases with decreasing contact width. During this thinning, the current density increased from 6 TA/m2 (at time a) to 10 TA/m2 (at time d). This current density was calculated by dividing the current value by the minimum cross-sectional area. On the other hand, when the contact transforms to the ASW,
4.2. Metal-specific differences
As shown in Fig. 26,
5. Conclusions
In this study, we focused on Ag NCs and investigated the atomic arrangement, electrical conductivity and mechanical properties. In addition to the simple tensile deformation, particularly to observe the Ag NCs representing the certain conductance value of the quantized conductance, feedback circuit was introduced into in situ electron microscopy. At the same time, the measured stress and force acting on the NCs were estimated. The observed image and the stress-strain relationship gave us the elastic constant such as Young's modulus. It was found that to reduce the contact width below 1 nm, Young’s modulus should be increased. From the value of the critical shear stress of Ag NCs, it is suggested that deformation mechanism changes to isotropic slip from a dislocation slip when the contact width decreases below 1.5 nm.
From the observation using a conductance feedback circuit, several types of NCs structures with different widths were found to contribute to a peak, which correspond to the quantization level in the conductance histograms. In particular, when conductance is controlled to
As a result of I-V measurement of Ag NCs, non-linearity of the conductance increase when the width of the contacts reduces. When NCs deformed ASWs, this trend changes; non-linear components became positive. Changes of the conductance in non-linear parameters of Ag NCs are similar to that of Au and different from that of Pt. This corresponds to the characteristics of the valence electron configuration of the elements.
As described above, in this study, I examined the structure and properties of Ag NCs using
Acknowledgments
This work was partly supported by Japan Society for the Promotion of Science Fellows (No. 221479).
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