Nanoscale View Article Online
Published on 13 August 2014. Downloaded by Yale University Library on 10/07/2015 07:01:14.
PAPER
Cite this: Nanoscale, 2014, 6, 13876
View Journal | View Issue
Room-temperature resonant quantum tunneling transport of macroscopic systems Zhengwei Xiong,a,b,c Xuemin Wang,a,c Dawei Yan,a,c Weidong Wu,*a,c Liping Peng,a,c Weihua Li,a,c Yan Zhao,a,c Xinmin Wang,a,c Xinyou An,a,c Tingting Xiao,d Zhiqiang Zhan,a,c Zhuo Wanga,c and Xiangrong Chen*b A self-assembled quantum dots array (QDA) is a low dimensional electron system applied to various quantum devices. This QDA, if embedded in a single crystal matrix, could be advantageous for quantum information science and technology. However, the quantum tunneling effect has been difficult to observe around room temperature thus far, because it occurs in a microcosmic and low temperature condition. Herein, we show a designed a quasi-periodic Ni QDA embedded in a single crystal BaTiO3 matrix and demonstrate novel quantum resonant tunneling transport properties around room-temperature according to theoretical calculation and experiments. The quantum tunneling process could be effectively
Received 17th July 2014, Accepted 11th August 2014 DOI: 10.1039/c4nr04056b www.rsc.org/nanoscale
modulated by changing the Ni QDA concentration. The major reason was that an applied weak electric field (∼102 V cm−1) could be enhanced by three orders of magnitude (∼105 V cm−1) between the Ni QDA because of the higher permittivity of BaTiO3 and the ‘hot spots’ of the Ni QDA. Compared with the pure BaTiO3 films, the samples with embedded Ni QDA displayed a stepped conductivity and temperature (σ–T curves) construction.
Introduction In the last two decades, quantum dot systems have displayed rich effects, not only for the quantum confinement and resonant structure, but also for the special spectrum of energy levels. In comparison with quantum well structures and quantum wires, quantum dot structures are so small that even a single electron inflow or outflow will dramatically change the transport properties, attributable to the exchange of charge energy and their special energy band configuration.1 Therefore, the electron tunneling effect of quantum dots was the primary focus in recent years for both theory and experiments.2,3 As far as we know, the size of metal quantum dot must be quite small (sub-10 nm), due to high electron density, large effective mass and short phase coherence length (compared with those of semiconductors). Thus, several researchers had to deal with random metal quantum dots rather than an ordered system.4 In our previous work, the shape of Ni nanocrystals (NCs) displayed a truncated triangle outline.5,6 Others preferred to
a Science and Technology on Plasma Physics Laboratory, Research Center of Laser Fusion, China Academy of Engineering Physics, P.O. Box 919-987-7, Mianyang 621900, China. E-mail: [email protected] b College of Physical Science and Technology, Sichuan University, Chengdu 610064, China. E-mail: [email protected] c Research Center of Laser Fusion, CAEP, P.O. Box 919-983, Mianyang 621900, China d Department of Applied Physics, Chongqing University, Chongqing 401331, China
13876 | Nanoscale, 2014, 6, 13876–13881
prepare self-assembled quantum dots and obtain novel quantum tunneling properties.7,8 However, the quantum resonant tunneling effect (QRT) is difficult to observe for these abovementioned systems. For studying QRT, the quantum dot is often called an “artificial atom” and the performance concerning the electron transport has to be implemented in a microcosmic and low temperature condition,9–11 which is not convenient for experimental operations. For the purpose of manipulation, it is important to design a special system in which quantum electronic transport can be observed at around room temperature. Herein, we have fabricated a system that consists of a multilayered stack of BaTiO3 (BTO) matrix layers and Ni NCs containing layers (Ni QDA/BTO films), forming a quasi-periodic superlattice, as shown in Fig. 1a. The BTO matrix can keep the NCs in a metallic state and form a metal–semiconductor Schottky junction. In these systems, the electronic energy band structure has been calculated, and the conductivity–temperature (σ–T ) and current–voltage (I–V) relationships were investigated. The calculated results were in accordance with the experiments.
Model design The quasi-periodic structure and corresponding energy bands are shown in Fig. 1b and c, respectively. For better understanding, we first consider a single Ni-metal quantum dot system
This journal is © The Royal Society of Chemistry 2014
View Article Online
Published on 13 August 2014. Downloaded by Yale University Library on 10/07/2015 07:01:14.
Nanoscale
Paper
Fig. 1 (a) Schematic diagram of Ni QDA/BTO films. One deposition period involves a number of pulses on the Ni target in ultra-high vacuum, followed by the epitaxial growth of BTO matrix. (b) Planar view of (a). (c) Energy band structure of (b) with an applied electronic field Ee. (d) A single Ni quantum dot embedded in BaTiO3. (e) Calculated subband width and space (n = 1, 2, 3, …), the inset is an expanded view. The dots in (c) indicate the electron bands. Efs and Efm represent the Fermi level of semiconductor and metal, respectively.
(Fig. 1d). In this system, a semiconductor BTO matrix covers the two metal electrodes and Ni-metal quantum dot, producing three Schottky junctions (one is the Ni-BTO and the other two are the metal electrodes-BTO). On the basis of semiconductor theory, the depletion layer width d can be written as follows: d¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ε0 εr V 0 eN
ð1Þ
where ε0 and εr is the dielectric constant of vacuum and BTO, respectively, V0 is the contact potential, e is the electron charge, and N is the carrier density. In our previous work, the epitaxial BTO matrix with embedded NCs exhibited a cubic phase at room temperature.12 For paraelectric BTO, the permittivity gradually decreases with an increase in temperature.13–15 From those references, εr can be deduced about 843 (at 300 K) ∼120 (at 668 K). For a Schottky junction, the barrier height ΦB is the energy difference between the metal Fermi level and the semiconductor conduction band; i.e., the difference between the metal work function Wm and the semiconductor electron affinity χs.16 Here, Wm = 5.11 eV for Ni and χs = 4.15 eV for BTO,17,18 ΦB is inferred to be 0.96 eV, and V0 is 0.96 V. Based on the literature,19 the carrier density N is temporarily set as 1012–1014 cm−3. The depletion layer width can be approxi-
This journal is © The Royal Society of Chemistry 2014
mately obtained and the values are more than 1 μm in the range of 300–668 K. These layers are much larger than the distance between the electrode and Ni QDA. Hence, there are few carries in the gray area, as shown in Fig. 1d. In this case, a potential barrier is constituted with two Schottky barriers: electrode-BTO and Ni QDA-BTO. The electrons can only be transported from one electrode to Ni QDA, and then to another electrode though quantum tunneling effect under a suitable applied electronic field. We expand the single Ni quantum dot system of electrode-BTO-Ni-BTO-electrode to the Ni QDA system of electrode-(BTO-Ni-BTO)n-electrode, as shown in Fig. 1b. For these systems, the gap between the n Ni QDA is less than 10 nm,5,6 which indicates that electrons are very lacking in the blue area of Fig. 1b and that the Ni QDAs are surrounded by a depletion area. Therefore, a periodic barrierwell structure is formed. In parallel to the direction of the applied electronic field, this periodic structure can be simplified to ten parallel one-dimensional quantum barrier-well structures (Fig. 1c). The electronic bands and their transport properties can be analyzed using the superlattice theory. The quasi-periodic structure composed of alternating, ultrathin layers of Ni QDA and BTO constitutes many subbands in such a barrier-well system. The quantum subband widths and their spaces can be calculated using the Kronig–Penny model.20 In the case of a superlattice, Bloch wave functions should be used instead of free electron wave functions. In a periodic potential U(x), it can be obtained by d2 u du 2 2mUðxÞ 2 k uðxÞ ¼ 0 þ 2ik α þ 2 h dx2 dx
ð2Þ
where α = (2mE/ħ2)1/2, E is the subband energy; m = ħ2/(∂2E/∂k2) is the effective electron mass of Ni,21 wave vector k = πn/d (n = 1, 2, 3, …), and d is period of the superlattice (≈16 nm).5,6 Taking into account their derivatives and simplifying at the successive boundaries of the superlattice potential, the subband widths and spaces can be deduced. The calculated results are shown in Fig. 1e. Associated with the theory of Wannier–Stark ladder, the subband energy can be expressed as follows: E ¼ E0 þ ndeEeff
ð3Þ
where E0 is the energy of ground state and Eeff is the effective local electric field. It can be found that with the increase in temperature, the permittivity of cubic BTO decreases, the Eeff decreases, and then the subband energy decreases. The inclining tendency of energy bands are mitigated, which makes the upgrade of subbands on one side (Fig. 1c); thus, the moved subbands and temperature are tied up. Contrasted with Fig. 1e, we can confirm the relative position of neighbouring subbands in the different temperature regions. Because the slope of the inclining subbands becomes smaller with higher temperature, the relative positions of all subbands change. When two subbands are in alignment in the neighbouring wells i.e. Ei ≈ Ei+1, the QRT occurs. For a small metallic particle with complex dielectric function ε(ω) embedded in a matrix with a real dielectric constant
Nanoscale, 2014, 6, 13876–13881 | 13877
View Article Online
Paper
Nanoscale
εm, many studies have been reported in the past years. For example, considering the particles as spherical, the polarizability can be present
Published on 13 August 2014. Downloaded by Yale University Library on 10/07/2015 07:01:14.
αðωÞ ¼ 4πR3
εðωÞ εm εðωÞ þ 2εm
ð4Þ
supposing a plane external electromagnetic wave with a wavelength much larger than the radius of the particle λ ≫ R.22 The effective local electric field (Eeff ) of the particle can be expressed as follows:20 Eeff ¼
3V εm E e 3V αðωÞ
ð5Þ
where V is the particle volume and Ee is the applied electric field (Ee = 2 × 102 V cm−1). Changing the shapes to ellipsoid, the polarizability of the particles can be rewritten as follows: αðωÞ ¼ V
εðωÞ εm εm þ Ai ½εðωÞ εm
ð6Þ
where V = 4πabc/3, a, b, c are the three radii, and Ai is defined as the length ratio between two axes.23 For various shapes of the nanoparticles, Eeff can be approximately given by Eeff ¼
3 εm Ee εðωÞ εm 3 εm þ Ai ½εðωÞ εm
ð7Þ
parameters are shown elsewhere.28 The deposition processes involved several pulses on the Ni target in ultrahigh-vacuum, followed by the epitaxial growth of BTO layers. Before the deposition, the substrate was in situ annealed three hours at 973 K in order to remove surface contamination. After the completion of Ni NC/BTO growth cycle, the film was annealed about 20 min at 923 K in an oxygen atmosphere at 10 Pa, and this procedure was alternated ten times. For the sake of measuring the electrical properties of the films, two square Au electrodes of 50 × 30 × 0.3 mm3 in volume were deposited by dc magnetron sputtering through a shadow mask. Their leakage current behavior was characterized by a Keithley meter. There were four samples (Sample 1, 2, 3, 4), corresponding to 100, 300, 600 and 800 pulses on the Ni target, respectively. As a reference, the pure BTO was also fabricated.
Results and discussion In situ RHEED monitoring According to the above-mentioned deductions, the Ni QDA/ BTO structure, as shown in Fig. 1a, was fabricated. The deposition process of self-assembled Ni NCs embedded in an BTO matrix is shown in Fig. 2. The black frames are the oscillated
In order to calculate the enhanced local electric field, we assumed four types of quantum dots with the same volume, corresponding to I: a spherical Ni NC in air (Ai = 1), II: a spherical Ni NC in BTO, III: an equilateral pentagonal Ni NC (for cross-section) in BTO (Ai ≈ 0.81), and IV: a pentagonal Ni NC in BTO at a particular acute angle as shown in ref. 6 (Ai ≈ 0.10). The linear refractive index and extinction coefficient of bulk Ni were used to calculate the permittivity.24 Selecting ε(300 nm) = 8.8325,26 and εm(300 nm) = 843 at room temperature,13 εair = 1, and the calculated Eeff are 2.84 × 102 (I), 5.19 × 103 (II), 6.33 × 104 (III) and 1.26 × 105 V cm−1 (IV), according to eqn (7). It is obvious that the Eeff of a single spherical quantum dot has almost no changes relative to the applied electric field; however, embedding the dots in a dielectric matrix enhances the Eeff, and the smaller keen-edged angle results in a stronger Eeff (∼105 V cm−1). Because the local field strength predominates, the emission current is much higher at the tip of Ni NCs than around the edges. These tips with the strongest electric field enhancement have often been referred as ‘hot spots’,27 which can strengthen the quantum tunneling current. Due to the ‘hot spots’, coupling the irregular Ni NCs in BTO matrix provides a great possibility for quantum tunneling behavior around room temperature.
Experimental section The Ni QDA/BTO films were fabricated on a SrTiO3 (001) substrate with the in situ monitoring of reflection high-energy electron diffraction (RHEED). Note that the key experimental
13878 | Nanoscale, 2014, 6, 13876–13881
Fig. 2 (a) RHEED intensity oscillation variations of one Ni NC/BTO growth cycle. RHEED patterns were collected at different times: (b) 500 s for BTO deposited on STO substrate, (c) 670 s and (d) 720 s for Ni NCs deposited on BTO layer, (e) 750 s, (f) 800 s and (g) 1320 s for BTO deposited on Ni NCs layer.
This journal is © The Royal Society of Chemistry 2014
View Article Online
Published on 13 August 2014. Downloaded by Yale University Library on 10/07/2015 07:01:14.
Nanoscale
Paper
signal derived from the change targets. At the optimal temperature of 923 K, the intensity variation of RHEED diffraction patterns is shown in Fig. 2a, which presents that the growth process includes two parts: the self-organization of Ni NCs and the layer-by-layer epitaxial BTO growth. By tracking the relative “streakiness” of the diffraction pattern, it is possible to qualitatively study the evolution of the atomic scale roughness.29 The first BTO layer was deposited on a SrTiO3 (001) substrate. As shown in Fig. 2b, the striking streak of RHEED patterns indicates a flat surface of BTO. Interestingly, the streaky patterns of BTO disappeared gradually with the increasing Ni pulses, whereas the spots of Ni became dominant in Fig. 2c and d. In addition, owing to the large lattice mismatch between BTO and Ni, it results in an overall decrease in RHEED intensity. Thus, it was considered as the formation of three-dimensional (3D) islands of Ni NCs on BTO surface. The surface-lattice parameter, which is proportional to the inverse of the distance between the different diffraction spots or streaks, can be directly measured from the RHEED patterns.30 We estimated the lattice constant of Ni (0.354 nm) and BTO (0.399 nm), approaching those of the bulk metal Ni (0.352 nm) and BTO (0.40 nm) in a cubic structure.31,32 Therefore, it is demonstrated that the deposited Ni and BTO represent NCs and a cubic phase, respectively. The next layer BTO was deposited after accomplishing the Ni NCs. The obvious oscillations with RHEED intensity indicate that the BTO recovers a two-dimensional (2D) epitaxial layer (Fig. 2a). The characteristic diffraction streaks of BTO grown on Ni NCs recover slowly in Fig. 2e–g. This transient behavior of the overall RHEED intensity and patterns represents the fact that the growth mode is changing from the 2D layer-by-layer to 3D islands. Thus, the BTO layers still leveled off the irregular growth fronts and achieved a flat surface for the subsequent strained NCs layer, although the self-assembled NCs created a geometrically irregular surface for BTO deposition. These two growth modes could be performed alternately in a perfect way, through which the NCs would be embedded in BTO. Conductivity–temperature measurements It is well known that semiconductors have a strong temperature–resistivity behavior, which is governed by the Arrhenius equation: σ ¼ σ 0 expðΔE=kB TÞ
ð8Þ
where σ is the electrical conductivity, σ0 a pre-exponential factor, T the absolute temperature, kB the Boltzmann constant, and ΔE the material’s activation energy. Using this relation, the logarithm of electrical conductivity versus the reciprocal of temperature was plotted for all samples. The activation energy, which is the difference between the energy of the conduction band edge and the trap (ΔE = Ec − Et), can be calculated from the slope of the Ln(σ) versus 1000 T−1 plot. From Fig. 3a, the values for pure BTO thin film are about 0.15 (ΔE1) and 0.23 eV (ΔE2), indicating that the film contains shallow traps near the conduction band edge. The shallow traps with activation
This journal is © The Royal Society of Chemistry 2014
Fig. 3 (a) Natural logarithm (Ln) of the conductivity of the pure BTO versus the inverse of temperature, ΔE1 and ΔE2 were estimated according to eqn (8). The inset shows the calculated carrier density N inverse of temperature (using a mobility of 0.1 cm2 V s−1).34 (b) Current–temperature curves of the samples. (c) Ln(σ) versus 1000 T−1 for sample 1, the colored lines and dots correspond to the changes of subbands in (d), where the black dots indicate the other electron bands, and the dashed lines are used to conveniently contrast the relative position of two subbands.
energy of 0.20 eV have previously been reported in epitaxial BTO thin films.33 In that case, the conductivity was attributed to the weakly localized electrons induced by formation of oxygen vacancies in the lattice. Note that the oxide fabricated by the PLD method inevitably contains some oxygen vacancies. One transition point around T = 410 K was observed, in good agreement with the Curie temperature of BTO.14 There is a discrepancy between the pure BTO and the Ni QDA/BTO films. The former usually exists in a tetragonal phase and transitions to a cubic phase over the Curie temperature; however, the latter BTO shows a cubic structure. Because the layer of BTO is comparable with its critical thickness (∼10 nm), the BTO lattice tends to match the cubic STO substrate, and the compressive stress originating from the embedded Ni QDA decreases the lattice constant in the c-orientation.12 From the inset of Fig. 3a, the carrier density lies in the range from 1012 to 1014 cm−3, which agrees well with the theoretical speculation above. Compared with the pure BTO films, the samples with embedded Ni QDA display a stepped σ–T construction (Fig. 3b). In order to understand the changes of subbands during the heating process, Sample 1 (d ≈ 16 nm) was used as an example (Fig. 3c). The relative position of subbands in the different temperature regions marked different stages and are shown in Fig. 3d. For the (1) stage, the primary contribution to conductivity is the interaction between the fourth and fifth subband. A great part of two wider subbands (n = 5 and 4) overlap reciprocally, which is a wider area due to the larger n relative to the (2)–(6) stages, indicating that the currents remains almost invariable. Continuing to heat to some extent, the excited current begins to decrease as the positions of
Nanoscale, 2014, 6, 13876–13881 | 13879
View Article Online
Published on 13 August 2014. Downloaded by Yale University Library on 10/07/2015 07:01:14.
Paper
Fig. 4 (a) Characteristics of the samples, (b) an expanded view of Sample 2. The dark area is a buffer, indicating that the conduction mechanism has changed.
subbands dislocate between the fourth and fifth subband for the (2) stage. Furthermore, elevating temperature upgrades the lower subbands and yields a gradual approach for the third and fourth subband, beginning to increase the current slowly for the (3) stage. While the third and fourth subband holds on a line, the QRT occurs. At this time, the current is sharply increasing at the (4) stage. As the two subbands (n = 4 and n = 3) completely overlap, the current reaches a maximum at the (5) stage. Overlapping between the lower subbands (n = 3 and n = 2) is present in the (6) stage, indicating that the second QRT occurs. With an increase in temperature, the n, subband widths and spaces become smaller. In our system, the electron transport from higher to lower subbands is a novel sequential QRT. The alternate switching of conductivity is a consequence of competition between the temperature and the positions of subbands. The qualification of Ei ≈ Ei+1 changes of QRT from satisfaction to dissatisfaction urge the observation of stepped σ–T construction. By the same approach, the electron transport of other three samples (Samples 2, 3 and 4) can be revealed. Relative to Sample 1 and 2, an additional plateau in the ranges from 433 to 543 K is existed in Sample 3 and 4. In addition, the tunneling currents with the higher Ni QDA concentration in the various stages are larger (Fig. 4a). With the decrease of spaces between the Ni NCs dependent on the higher concentration, two aspects of reactions are produced. On the one hand, the subband density increases rapidly, i.e. more opportunities for the occurrence of QRT. On the other hand, by applying an electric field to the samples, the space between the inclining subbands is obviously shortened, i.e. the width of the BTO barrier is reduced, indicating an easier way to the quantum tunneling. It can be concluded that embedding more Ni QDA can effectively modulate the subband structure, and further impact electron transport; moreover, more systematic studies will be carried out in the future. Here, most contributions are the observation of QRT around room temperature in a macroscopic condition. This will provide great convenience for manipulation in experimental researches and future applications. Room temperature voltage–current measurements The existence of quantum tunneling is validated by the I–V characteristics at room temperature in Fig. 4. It is shown that the values of emission currents for Ni QDA/BTO films are
13880 | Nanoscale, 2014, 6, 13876–13881
Nanoscale
larger by two orders in magnitude than those of the pure BTO films with typical value of resistivity (∼108 Ω m).35 The pure BTO film shows a linear I–V curve, whereas Ni NCs/BTO films exhibit nonlinear behavior over ∼32 V. A buffer, shown in the dark area of Fig. 4, arises after embedding Ni QDA. Then, the current under the bias over ∼45 V is rapidly reinforced with higher Ni NC concentration. This transformation is an indication of quantum tunneling. The different slopes with different Ni NC concentrations demonstrate that the leakage in Ni QDA/BTO films is dominated by different quantum tunneling mechanisms. Note that the tunneling current can be described by J ¼ J s expðqV=E00 Þ ð9Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where E00 ¼ eh=4π N D =mε0 ε is the energy for tunneling, Js is the saturation current, ND is the donor concentration and m* is the effective mass.36 The energy for tunneling E00 of 0.37, 0.35, 0.31 and 0.25 eV was found for the four samples (Fig. 4b), respectively. This reveals that the occurrence of quantum tunneling becomes easier with the increase of Ni NC concentration. The quantum tunneling process can be effectively modulated by introducing resonant artificial interface states and tuning the Ni QDA concentration.
Conclusions In summary, we have designed a quasi-periodic quantum dots array of Ni NCs embedded in a dielectric matrix of BaTiO3, in which the growths of 2D layer-by-layer for BaTiO3 and 3D islands for Ni NCs were performed alternately. A novel resonant quantum tunneling was observed around room temperature, for which the formation mechanism was elaborately explained according to the theoretical calculation. Our innovation was that applying a relative smaller electric field (2 × 10−2 V cm−1), a much larger Eeff (∼10−5 V cm−1) could be generated compared with that of a single quantum dot. The above-mentioned results open a new door for the resonant quantum tunneling in a macroscopic condition, which brings great convenience for manipulation in experiments and future applications.
Acknowledgements The authors would like to thank the support by the National Natural Science Foundation of China (Grant No. 11174214 and 11204192), and the NSAF (Grant No. U1430117).
Notes and references 1 S. Karmakar, S. Kumar, P. Marzo, E. Primiceri, R. Di Corato, R. Rinaldi, P. G. Cozzi, A. P. Bramanti and G. Maruccio, Nanoscale, 2012, 4, 2311–2316. 2 S. Csonka, I. Weymann and G. Zarand, Nanoscale, 2012, 4, 3635–3639.
This journal is © The Royal Society of Chemistry 2014
View Article Online
Published on 13 August 2014. Downloaded by Yale University Library on 10/07/2015 07:01:14.
Nanoscale
3 H. Zhao, Z. Fan, H. Liang, G. S. Selopal, B. A. Gonfa, L. Jin, A. Soudi, D. Cui, F. Enrichi, M. M. Natile, I. Concina, D. Ma, A. O. Govorov, F. Rosei and A. Vomiero, Nanoscale, 2014, 6, 7004–7011. 4 C. W. Beenakker, Rev. Mod. Phys., 1997, 69, 731. 5 F. Ge, X. Wang, Y. Li, L. Cao, H. Zhang, H. Wang and W. Wu, J. Nanopart. Res., 2011, 13, 6447–6453. 6 F. Ge, Y. Ma, X. Wang, L. Chen, S. Han, H. Zhang, H. Wang and Y. Tang, J. Wuhan Univ. Technol.-Mater. Sci. Ed., 2011, 26, 897–901. 7 V. Arima, M. Iurlo, L. Zoli, S. Kumar, M. Piacenza, F. Della Sala, F. Matino, G. Maruccio, R. Rinaldi, F. Paolucci, M. Marcaccio, P. G. Cozzi and A. P. Bramanti, Nanoscale, 2012, 4, 813–823. 8 C.-W. Jiang, I. C. Ni, S.-D. Tzeng, C.-S. Wu and W. Kuo, Nanoscale, 2014, 6, 5887–5893. 9 C.-C. Lin and J.-G. Hwu, Nanoscale, 2013, 5, 8090–8097. 10 D. Stoffler, H. v. Lohneysen and R. Hoffmann, Nanoscale, 2011, 3, 3391–3394. 11 M. Yokota, S. Yoshida, Y. Mera, O. Takeuchi, H. Oigawa and H. Shigekawa, Nanoscale, 2013, 5, 9170–9175. 12 S. Yoshida, Y. Terada, R. Oshima, O. Takeuchi and H. Shigekawa, Nanoscale, 2012, 4, 757–761. 13 H. Chang, C. Gao, I. Takeuchi, Y. Yoo, J. Wang, P. Schultz, X.-D. Xiang, R. Sharma, M. Downes and T. Venkatesan, Appl. Phys. Lett., 1998, 72, 2185–2187. 14 B. Hoerman, G. Ford, L. Kaufmann and B. Wessels, Appl. Phys. Lett., 1998, 73, 2248–2250. 15 S. Roberts, Phys. Rev., 1947, 71, 890. 16 J. Robertson and C. Chen, Appl. Phys. Lett., 1999, 74, 1168– 1170. 17 J. Scott, Ferroelectr. Rev., 1998, 1, 1–129. 18 A. Hartmann, R. Lamb, J. Scott, P. Johnston, M. El Bouanani, C. Chen and J. Robertson, J. Korean Phys. Soc., 1998, 32, S1329–S1331.
This journal is © The Royal Society of Chemistry 2014
Paper
19 S. Gilbert, L. Wills, B. Wessels, J. Schindler, J. Thomas and C. Kannewurf, J. Appl. Phys., 1996, 80, 969–977. 20 C. Kittel and P. McEuen, Introduction to solid state physics, Wiley, New York, 1976. 21 W. Nolting, W. Borgiel, V. Dose and T. Fauster, Phys. Rev. B: Condens. Matter, 1989, 40, 5015. 22 C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles, John Wiley & Sons, 2008. 23 U. Kreibig and M. Vollmer, Optical properties of metal clusters, Springer-Verlag, 1995. 24 P. Johnson and R. Christy, Phys. Rev. B: Solid State, 1974, 9, 5056. 25 Z. Xiong, X. Chen, X. Wang, L. Peng, D. Yan, H. Lei, Y. Fu, J. Wu, Z. Li and X. An, Appl. Surf. Sci., 2013, 268, 524–528. 26 P. B. Johnson and R.-W. Christy, Phys. Rev. B: Solid State, 1972, 6, 4370. 27 Y. Lin, X. Q. Liu, T. Wang, C. Chen, H. Wu, L. Liao and C. Liu, Nanotechnology, 2013, 24, 125705. 28 Z. Xiong, W. Sun, X. Wang, F. Jiang and W. Wu, J. Alloys Compd., 2012, 513, 300–303. 29 C. Friesen and C. Thompson, Phys. Rev. Lett., 2004, 93, 056104. 30 K. Godo, J. Chang, H. Makino, T. Takai, T. Hanada, T. Yao, T. Sasao and T. Goto, J. Appl. Phys., 2002, 92, 5490–5493. 31 M. Yousuf, P. C. Sahu, H. Jajoo, S. Rajagopalan and K. G. Rajan, J. Phys. F: Met. Phys., 1986, 16, 373. 32 K. Hellwege and A. Hellwege, Landolt-Bornstein, New Ser., Group III, 1981, 3. 33 L. Pintilie, Ferroelectrics-Phys. Effects, 2011, 101. 34 A. M. J. H. Seuter, Philips Res. Rep. Suppl., 1974, 3, 1. 35 W. Heywang, J. Mater. Sci., 1971, 6, 1214–1224. 36 W. Lü, X. Wang, Z. Liu, S. Dhar, A. Annadi, K. Gopinadhan, A. R. Barman, H. Su and T. Venkatesan, Appl. Phys. Lett., 2011, 99, 172103.
Nanoscale, 2014, 6, 13876–13881 | 13881
Published on 13 August 2014. Downloaded by Yale University Library on 10/07/2015 07:01:14.
PAPER
Cite this: Nanoscale, 2014, 6, 13876
View Journal | View Issue
Room-temperature resonant quantum tunneling transport of macroscopic systems Zhengwei Xiong,a,b,c Xuemin Wang,a,c Dawei Yan,a,c Weidong Wu,*a,c Liping Peng,a,c Weihua Li,a,c Yan Zhao,a,c Xinmin Wang,a,c Xinyou An,a,c Tingting Xiao,d Zhiqiang Zhan,a,c Zhuo Wanga,c and Xiangrong Chen*b A self-assembled quantum dots array (QDA) is a low dimensional electron system applied to various quantum devices. This QDA, if embedded in a single crystal matrix, could be advantageous for quantum information science and technology. However, the quantum tunneling effect has been difficult to observe around room temperature thus far, because it occurs in a microcosmic and low temperature condition. Herein, we show a designed a quasi-periodic Ni QDA embedded in a single crystal BaTiO3 matrix and demonstrate novel quantum resonant tunneling transport properties around room-temperature according to theoretical calculation and experiments. The quantum tunneling process could be effectively
Received 17th July 2014, Accepted 11th August 2014 DOI: 10.1039/c4nr04056b www.rsc.org/nanoscale
modulated by changing the Ni QDA concentration. The major reason was that an applied weak electric field (∼102 V cm−1) could be enhanced by three orders of magnitude (∼105 V cm−1) between the Ni QDA because of the higher permittivity of BaTiO3 and the ‘hot spots’ of the Ni QDA. Compared with the pure BaTiO3 films, the samples with embedded Ni QDA displayed a stepped conductivity and temperature (σ–T curves) construction.
Introduction In the last two decades, quantum dot systems have displayed rich effects, not only for the quantum confinement and resonant structure, but also for the special spectrum of energy levels. In comparison with quantum well structures and quantum wires, quantum dot structures are so small that even a single electron inflow or outflow will dramatically change the transport properties, attributable to the exchange of charge energy and their special energy band configuration.1 Therefore, the electron tunneling effect of quantum dots was the primary focus in recent years for both theory and experiments.2,3 As far as we know, the size of metal quantum dot must be quite small (sub-10 nm), due to high electron density, large effective mass and short phase coherence length (compared with those of semiconductors). Thus, several researchers had to deal with random metal quantum dots rather than an ordered system.4 In our previous work, the shape of Ni nanocrystals (NCs) displayed a truncated triangle outline.5,6 Others preferred to
a Science and Technology on Plasma Physics Laboratory, Research Center of Laser Fusion, China Academy of Engineering Physics, P.O. Box 919-987-7, Mianyang 621900, China. E-mail: [email protected] b College of Physical Science and Technology, Sichuan University, Chengdu 610064, China. E-mail: [email protected] c Research Center of Laser Fusion, CAEP, P.O. Box 919-983, Mianyang 621900, China d Department of Applied Physics, Chongqing University, Chongqing 401331, China
13876 | Nanoscale, 2014, 6, 13876–13881
prepare self-assembled quantum dots and obtain novel quantum tunneling properties.7,8 However, the quantum resonant tunneling effect (QRT) is difficult to observe for these abovementioned systems. For studying QRT, the quantum dot is often called an “artificial atom” and the performance concerning the electron transport has to be implemented in a microcosmic and low temperature condition,9–11 which is not convenient for experimental operations. For the purpose of manipulation, it is important to design a special system in which quantum electronic transport can be observed at around room temperature. Herein, we have fabricated a system that consists of a multilayered stack of BaTiO3 (BTO) matrix layers and Ni NCs containing layers (Ni QDA/BTO films), forming a quasi-periodic superlattice, as shown in Fig. 1a. The BTO matrix can keep the NCs in a metallic state and form a metal–semiconductor Schottky junction. In these systems, the electronic energy band structure has been calculated, and the conductivity–temperature (σ–T ) and current–voltage (I–V) relationships were investigated. The calculated results were in accordance with the experiments.
Model design The quasi-periodic structure and corresponding energy bands are shown in Fig. 1b and c, respectively. For better understanding, we first consider a single Ni-metal quantum dot system
This journal is © The Royal Society of Chemistry 2014
View Article Online
Published on 13 August 2014. Downloaded by Yale University Library on 10/07/2015 07:01:14.
Nanoscale
Paper
Fig. 1 (a) Schematic diagram of Ni QDA/BTO films. One deposition period involves a number of pulses on the Ni target in ultra-high vacuum, followed by the epitaxial growth of BTO matrix. (b) Planar view of (a). (c) Energy band structure of (b) with an applied electronic field Ee. (d) A single Ni quantum dot embedded in BaTiO3. (e) Calculated subband width and space (n = 1, 2, 3, …), the inset is an expanded view. The dots in (c) indicate the electron bands. Efs and Efm represent the Fermi level of semiconductor and metal, respectively.
(Fig. 1d). In this system, a semiconductor BTO matrix covers the two metal electrodes and Ni-metal quantum dot, producing three Schottky junctions (one is the Ni-BTO and the other two are the metal electrodes-BTO). On the basis of semiconductor theory, the depletion layer width d can be written as follows: d¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ε0 εr V 0 eN
ð1Þ
where ε0 and εr is the dielectric constant of vacuum and BTO, respectively, V0 is the contact potential, e is the electron charge, and N is the carrier density. In our previous work, the epitaxial BTO matrix with embedded NCs exhibited a cubic phase at room temperature.12 For paraelectric BTO, the permittivity gradually decreases with an increase in temperature.13–15 From those references, εr can be deduced about 843 (at 300 K) ∼120 (at 668 K). For a Schottky junction, the barrier height ΦB is the energy difference between the metal Fermi level and the semiconductor conduction band; i.e., the difference between the metal work function Wm and the semiconductor electron affinity χs.16 Here, Wm = 5.11 eV for Ni and χs = 4.15 eV for BTO,17,18 ΦB is inferred to be 0.96 eV, and V0 is 0.96 V. Based on the literature,19 the carrier density N is temporarily set as 1012–1014 cm−3. The depletion layer width can be approxi-
This journal is © The Royal Society of Chemistry 2014
mately obtained and the values are more than 1 μm in the range of 300–668 K. These layers are much larger than the distance between the electrode and Ni QDA. Hence, there are few carries in the gray area, as shown in Fig. 1d. In this case, a potential barrier is constituted with two Schottky barriers: electrode-BTO and Ni QDA-BTO. The electrons can only be transported from one electrode to Ni QDA, and then to another electrode though quantum tunneling effect under a suitable applied electronic field. We expand the single Ni quantum dot system of electrode-BTO-Ni-BTO-electrode to the Ni QDA system of electrode-(BTO-Ni-BTO)n-electrode, as shown in Fig. 1b. For these systems, the gap between the n Ni QDA is less than 10 nm,5,6 which indicates that electrons are very lacking in the blue area of Fig. 1b and that the Ni QDAs are surrounded by a depletion area. Therefore, a periodic barrierwell structure is formed. In parallel to the direction of the applied electronic field, this periodic structure can be simplified to ten parallel one-dimensional quantum barrier-well structures (Fig. 1c). The electronic bands and their transport properties can be analyzed using the superlattice theory. The quasi-periodic structure composed of alternating, ultrathin layers of Ni QDA and BTO constitutes many subbands in such a barrier-well system. The quantum subband widths and their spaces can be calculated using the Kronig–Penny model.20 In the case of a superlattice, Bloch wave functions should be used instead of free electron wave functions. In a periodic potential U(x), it can be obtained by d2 u du 2 2mUðxÞ 2 k uðxÞ ¼ 0 þ 2ik α þ 2 h dx2 dx
ð2Þ
where α = (2mE/ħ2)1/2, E is the subband energy; m = ħ2/(∂2E/∂k2) is the effective electron mass of Ni,21 wave vector k = πn/d (n = 1, 2, 3, …), and d is period of the superlattice (≈16 nm).5,6 Taking into account their derivatives and simplifying at the successive boundaries of the superlattice potential, the subband widths and spaces can be deduced. The calculated results are shown in Fig. 1e. Associated with the theory of Wannier–Stark ladder, the subband energy can be expressed as follows: E ¼ E0 þ ndeEeff
ð3Þ
where E0 is the energy of ground state and Eeff is the effective local electric field. It can be found that with the increase in temperature, the permittivity of cubic BTO decreases, the Eeff decreases, and then the subband energy decreases. The inclining tendency of energy bands are mitigated, which makes the upgrade of subbands on one side (Fig. 1c); thus, the moved subbands and temperature are tied up. Contrasted with Fig. 1e, we can confirm the relative position of neighbouring subbands in the different temperature regions. Because the slope of the inclining subbands becomes smaller with higher temperature, the relative positions of all subbands change. When two subbands are in alignment in the neighbouring wells i.e. Ei ≈ Ei+1, the QRT occurs. For a small metallic particle with complex dielectric function ε(ω) embedded in a matrix with a real dielectric constant
Nanoscale, 2014, 6, 13876–13881 | 13877
View Article Online
Paper
Nanoscale
εm, many studies have been reported in the past years. For example, considering the particles as spherical, the polarizability can be present
Published on 13 August 2014. Downloaded by Yale University Library on 10/07/2015 07:01:14.
αðωÞ ¼ 4πR3
εðωÞ εm εðωÞ þ 2εm
ð4Þ
supposing a plane external electromagnetic wave with a wavelength much larger than the radius of the particle λ ≫ R.22 The effective local electric field (Eeff ) of the particle can be expressed as follows:20 Eeff ¼
3V εm E e 3V αðωÞ
ð5Þ
where V is the particle volume and Ee is the applied electric field (Ee = 2 × 102 V cm−1). Changing the shapes to ellipsoid, the polarizability of the particles can be rewritten as follows: αðωÞ ¼ V
εðωÞ εm εm þ Ai ½εðωÞ εm
ð6Þ
where V = 4πabc/3, a, b, c are the three radii, and Ai is defined as the length ratio between two axes.23 For various shapes of the nanoparticles, Eeff can be approximately given by Eeff ¼
3 εm Ee εðωÞ εm 3 εm þ Ai ½εðωÞ εm
ð7Þ
parameters are shown elsewhere.28 The deposition processes involved several pulses on the Ni target in ultrahigh-vacuum, followed by the epitaxial growth of BTO layers. Before the deposition, the substrate was in situ annealed three hours at 973 K in order to remove surface contamination. After the completion of Ni NC/BTO growth cycle, the film was annealed about 20 min at 923 K in an oxygen atmosphere at 10 Pa, and this procedure was alternated ten times. For the sake of measuring the electrical properties of the films, two square Au electrodes of 50 × 30 × 0.3 mm3 in volume were deposited by dc magnetron sputtering through a shadow mask. Their leakage current behavior was characterized by a Keithley meter. There were four samples (Sample 1, 2, 3, 4), corresponding to 100, 300, 600 and 800 pulses on the Ni target, respectively. As a reference, the pure BTO was also fabricated.
Results and discussion In situ RHEED monitoring According to the above-mentioned deductions, the Ni QDA/ BTO structure, as shown in Fig. 1a, was fabricated. The deposition process of self-assembled Ni NCs embedded in an BTO matrix is shown in Fig. 2. The black frames are the oscillated
In order to calculate the enhanced local electric field, we assumed four types of quantum dots with the same volume, corresponding to I: a spherical Ni NC in air (Ai = 1), II: a spherical Ni NC in BTO, III: an equilateral pentagonal Ni NC (for cross-section) in BTO (Ai ≈ 0.81), and IV: a pentagonal Ni NC in BTO at a particular acute angle as shown in ref. 6 (Ai ≈ 0.10). The linear refractive index and extinction coefficient of bulk Ni were used to calculate the permittivity.24 Selecting ε(300 nm) = 8.8325,26 and εm(300 nm) = 843 at room temperature,13 εair = 1, and the calculated Eeff are 2.84 × 102 (I), 5.19 × 103 (II), 6.33 × 104 (III) and 1.26 × 105 V cm−1 (IV), according to eqn (7). It is obvious that the Eeff of a single spherical quantum dot has almost no changes relative to the applied electric field; however, embedding the dots in a dielectric matrix enhances the Eeff, and the smaller keen-edged angle results in a stronger Eeff (∼105 V cm−1). Because the local field strength predominates, the emission current is much higher at the tip of Ni NCs than around the edges. These tips with the strongest electric field enhancement have often been referred as ‘hot spots’,27 which can strengthen the quantum tunneling current. Due to the ‘hot spots’, coupling the irregular Ni NCs in BTO matrix provides a great possibility for quantum tunneling behavior around room temperature.
Experimental section The Ni QDA/BTO films were fabricated on a SrTiO3 (001) substrate with the in situ monitoring of reflection high-energy electron diffraction (RHEED). Note that the key experimental
13878 | Nanoscale, 2014, 6, 13876–13881
Fig. 2 (a) RHEED intensity oscillation variations of one Ni NC/BTO growth cycle. RHEED patterns were collected at different times: (b) 500 s for BTO deposited on STO substrate, (c) 670 s and (d) 720 s for Ni NCs deposited on BTO layer, (e) 750 s, (f) 800 s and (g) 1320 s for BTO deposited on Ni NCs layer.
This journal is © The Royal Society of Chemistry 2014
View Article Online
Published on 13 August 2014. Downloaded by Yale University Library on 10/07/2015 07:01:14.
Nanoscale
Paper
signal derived from the change targets. At the optimal temperature of 923 K, the intensity variation of RHEED diffraction patterns is shown in Fig. 2a, which presents that the growth process includes two parts: the self-organization of Ni NCs and the layer-by-layer epitaxial BTO growth. By tracking the relative “streakiness” of the diffraction pattern, it is possible to qualitatively study the evolution of the atomic scale roughness.29 The first BTO layer was deposited on a SrTiO3 (001) substrate. As shown in Fig. 2b, the striking streak of RHEED patterns indicates a flat surface of BTO. Interestingly, the streaky patterns of BTO disappeared gradually with the increasing Ni pulses, whereas the spots of Ni became dominant in Fig. 2c and d. In addition, owing to the large lattice mismatch between BTO and Ni, it results in an overall decrease in RHEED intensity. Thus, it was considered as the formation of three-dimensional (3D) islands of Ni NCs on BTO surface. The surface-lattice parameter, which is proportional to the inverse of the distance between the different diffraction spots or streaks, can be directly measured from the RHEED patterns.30 We estimated the lattice constant of Ni (0.354 nm) and BTO (0.399 nm), approaching those of the bulk metal Ni (0.352 nm) and BTO (0.40 nm) in a cubic structure.31,32 Therefore, it is demonstrated that the deposited Ni and BTO represent NCs and a cubic phase, respectively. The next layer BTO was deposited after accomplishing the Ni NCs. The obvious oscillations with RHEED intensity indicate that the BTO recovers a two-dimensional (2D) epitaxial layer (Fig. 2a). The characteristic diffraction streaks of BTO grown on Ni NCs recover slowly in Fig. 2e–g. This transient behavior of the overall RHEED intensity and patterns represents the fact that the growth mode is changing from the 2D layer-by-layer to 3D islands. Thus, the BTO layers still leveled off the irregular growth fronts and achieved a flat surface for the subsequent strained NCs layer, although the self-assembled NCs created a geometrically irregular surface for BTO deposition. These two growth modes could be performed alternately in a perfect way, through which the NCs would be embedded in BTO. Conductivity–temperature measurements It is well known that semiconductors have a strong temperature–resistivity behavior, which is governed by the Arrhenius equation: σ ¼ σ 0 expðΔE=kB TÞ
ð8Þ
where σ is the electrical conductivity, σ0 a pre-exponential factor, T the absolute temperature, kB the Boltzmann constant, and ΔE the material’s activation energy. Using this relation, the logarithm of electrical conductivity versus the reciprocal of temperature was plotted for all samples. The activation energy, which is the difference between the energy of the conduction band edge and the trap (ΔE = Ec − Et), can be calculated from the slope of the Ln(σ) versus 1000 T−1 plot. From Fig. 3a, the values for pure BTO thin film are about 0.15 (ΔE1) and 0.23 eV (ΔE2), indicating that the film contains shallow traps near the conduction band edge. The shallow traps with activation
This journal is © The Royal Society of Chemistry 2014
Fig. 3 (a) Natural logarithm (Ln) of the conductivity of the pure BTO versus the inverse of temperature, ΔE1 and ΔE2 were estimated according to eqn (8). The inset shows the calculated carrier density N inverse of temperature (using a mobility of 0.1 cm2 V s−1).34 (b) Current–temperature curves of the samples. (c) Ln(σ) versus 1000 T−1 for sample 1, the colored lines and dots correspond to the changes of subbands in (d), where the black dots indicate the other electron bands, and the dashed lines are used to conveniently contrast the relative position of two subbands.
energy of 0.20 eV have previously been reported in epitaxial BTO thin films.33 In that case, the conductivity was attributed to the weakly localized electrons induced by formation of oxygen vacancies in the lattice. Note that the oxide fabricated by the PLD method inevitably contains some oxygen vacancies. One transition point around T = 410 K was observed, in good agreement with the Curie temperature of BTO.14 There is a discrepancy between the pure BTO and the Ni QDA/BTO films. The former usually exists in a tetragonal phase and transitions to a cubic phase over the Curie temperature; however, the latter BTO shows a cubic structure. Because the layer of BTO is comparable with its critical thickness (∼10 nm), the BTO lattice tends to match the cubic STO substrate, and the compressive stress originating from the embedded Ni QDA decreases the lattice constant in the c-orientation.12 From the inset of Fig. 3a, the carrier density lies in the range from 1012 to 1014 cm−3, which agrees well with the theoretical speculation above. Compared with the pure BTO films, the samples with embedded Ni QDA display a stepped σ–T construction (Fig. 3b). In order to understand the changes of subbands during the heating process, Sample 1 (d ≈ 16 nm) was used as an example (Fig. 3c). The relative position of subbands in the different temperature regions marked different stages and are shown in Fig. 3d. For the (1) stage, the primary contribution to conductivity is the interaction between the fourth and fifth subband. A great part of two wider subbands (n = 5 and 4) overlap reciprocally, which is a wider area due to the larger n relative to the (2)–(6) stages, indicating that the currents remains almost invariable. Continuing to heat to some extent, the excited current begins to decrease as the positions of
Nanoscale, 2014, 6, 13876–13881 | 13879
View Article Online
Published on 13 August 2014. Downloaded by Yale University Library on 10/07/2015 07:01:14.
Paper
Fig. 4 (a) Characteristics of the samples, (b) an expanded view of Sample 2. The dark area is a buffer, indicating that the conduction mechanism has changed.
subbands dislocate between the fourth and fifth subband for the (2) stage. Furthermore, elevating temperature upgrades the lower subbands and yields a gradual approach for the third and fourth subband, beginning to increase the current slowly for the (3) stage. While the third and fourth subband holds on a line, the QRT occurs. At this time, the current is sharply increasing at the (4) stage. As the two subbands (n = 4 and n = 3) completely overlap, the current reaches a maximum at the (5) stage. Overlapping between the lower subbands (n = 3 and n = 2) is present in the (6) stage, indicating that the second QRT occurs. With an increase in temperature, the n, subband widths and spaces become smaller. In our system, the electron transport from higher to lower subbands is a novel sequential QRT. The alternate switching of conductivity is a consequence of competition between the temperature and the positions of subbands. The qualification of Ei ≈ Ei+1 changes of QRT from satisfaction to dissatisfaction urge the observation of stepped σ–T construction. By the same approach, the electron transport of other three samples (Samples 2, 3 and 4) can be revealed. Relative to Sample 1 and 2, an additional plateau in the ranges from 433 to 543 K is existed in Sample 3 and 4. In addition, the tunneling currents with the higher Ni QDA concentration in the various stages are larger (Fig. 4a). With the decrease of spaces between the Ni NCs dependent on the higher concentration, two aspects of reactions are produced. On the one hand, the subband density increases rapidly, i.e. more opportunities for the occurrence of QRT. On the other hand, by applying an electric field to the samples, the space between the inclining subbands is obviously shortened, i.e. the width of the BTO barrier is reduced, indicating an easier way to the quantum tunneling. It can be concluded that embedding more Ni QDA can effectively modulate the subband structure, and further impact electron transport; moreover, more systematic studies will be carried out in the future. Here, most contributions are the observation of QRT around room temperature in a macroscopic condition. This will provide great convenience for manipulation in experimental researches and future applications. Room temperature voltage–current measurements The existence of quantum tunneling is validated by the I–V characteristics at room temperature in Fig. 4. It is shown that the values of emission currents for Ni QDA/BTO films are
13880 | Nanoscale, 2014, 6, 13876–13881
Nanoscale
larger by two orders in magnitude than those of the pure BTO films with typical value of resistivity (∼108 Ω m).35 The pure BTO film shows a linear I–V curve, whereas Ni NCs/BTO films exhibit nonlinear behavior over ∼32 V. A buffer, shown in the dark area of Fig. 4, arises after embedding Ni QDA. Then, the current under the bias over ∼45 V is rapidly reinforced with higher Ni NC concentration. This transformation is an indication of quantum tunneling. The different slopes with different Ni NC concentrations demonstrate that the leakage in Ni QDA/BTO films is dominated by different quantum tunneling mechanisms. Note that the tunneling current can be described by J ¼ J s expðqV=E00 Þ ð9Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where E00 ¼ eh=4π N D =mε0 ε is the energy for tunneling, Js is the saturation current, ND is the donor concentration and m* is the effective mass.36 The energy for tunneling E00 of 0.37, 0.35, 0.31 and 0.25 eV was found for the four samples (Fig. 4b), respectively. This reveals that the occurrence of quantum tunneling becomes easier with the increase of Ni NC concentration. The quantum tunneling process can be effectively modulated by introducing resonant artificial interface states and tuning the Ni QDA concentration.
Conclusions In summary, we have designed a quasi-periodic quantum dots array of Ni NCs embedded in a dielectric matrix of BaTiO3, in which the growths of 2D layer-by-layer for BaTiO3 and 3D islands for Ni NCs were performed alternately. A novel resonant quantum tunneling was observed around room temperature, for which the formation mechanism was elaborately explained according to the theoretical calculation. Our innovation was that applying a relative smaller electric field (2 × 10−2 V cm−1), a much larger Eeff (∼10−5 V cm−1) could be generated compared with that of a single quantum dot. The above-mentioned results open a new door for the resonant quantum tunneling in a macroscopic condition, which brings great convenience for manipulation in experiments and future applications.
Acknowledgements The authors would like to thank the support by the National Natural Science Foundation of China (Grant No. 11174214 and 11204192), and the NSAF (Grant No. U1430117).
Notes and references 1 S. Karmakar, S. Kumar, P. Marzo, E. Primiceri, R. Di Corato, R. Rinaldi, P. G. Cozzi, A. P. Bramanti and G. Maruccio, Nanoscale, 2012, 4, 2311–2316. 2 S. Csonka, I. Weymann and G. Zarand, Nanoscale, 2012, 4, 3635–3639.
This journal is © The Royal Society of Chemistry 2014
View Article Online
Published on 13 August 2014. Downloaded by Yale University Library on 10/07/2015 07:01:14.
Nanoscale
3 H. Zhao, Z. Fan, H. Liang, G. S. Selopal, B. A. Gonfa, L. Jin, A. Soudi, D. Cui, F. Enrichi, M. M. Natile, I. Concina, D. Ma, A. O. Govorov, F. Rosei and A. Vomiero, Nanoscale, 2014, 6, 7004–7011. 4 C. W. Beenakker, Rev. Mod. Phys., 1997, 69, 731. 5 F. Ge, X. Wang, Y. Li, L. Cao, H. Zhang, H. Wang and W. Wu, J. Nanopart. Res., 2011, 13, 6447–6453. 6 F. Ge, Y. Ma, X. Wang, L. Chen, S. Han, H. Zhang, H. Wang and Y. Tang, J. Wuhan Univ. Technol.-Mater. Sci. Ed., 2011, 26, 897–901. 7 V. Arima, M. Iurlo, L. Zoli, S. Kumar, M. Piacenza, F. Della Sala, F. Matino, G. Maruccio, R. Rinaldi, F. Paolucci, M. Marcaccio, P. G. Cozzi and A. P. Bramanti, Nanoscale, 2012, 4, 813–823. 8 C.-W. Jiang, I. C. Ni, S.-D. Tzeng, C.-S. Wu and W. Kuo, Nanoscale, 2014, 6, 5887–5893. 9 C.-C. Lin and J.-G. Hwu, Nanoscale, 2013, 5, 8090–8097. 10 D. Stoffler, H. v. Lohneysen and R. Hoffmann, Nanoscale, 2011, 3, 3391–3394. 11 M. Yokota, S. Yoshida, Y. Mera, O. Takeuchi, H. Oigawa and H. Shigekawa, Nanoscale, 2013, 5, 9170–9175. 12 S. Yoshida, Y. Terada, R. Oshima, O. Takeuchi and H. Shigekawa, Nanoscale, 2012, 4, 757–761. 13 H. Chang, C. Gao, I. Takeuchi, Y. Yoo, J. Wang, P. Schultz, X.-D. Xiang, R. Sharma, M. Downes and T. Venkatesan, Appl. Phys. Lett., 1998, 72, 2185–2187. 14 B. Hoerman, G. Ford, L. Kaufmann and B. Wessels, Appl. Phys. Lett., 1998, 73, 2248–2250. 15 S. Roberts, Phys. Rev., 1947, 71, 890. 16 J. Robertson and C. Chen, Appl. Phys. Lett., 1999, 74, 1168– 1170. 17 J. Scott, Ferroelectr. Rev., 1998, 1, 1–129. 18 A. Hartmann, R. Lamb, J. Scott, P. Johnston, M. El Bouanani, C. Chen and J. Robertson, J. Korean Phys. Soc., 1998, 32, S1329–S1331.
This journal is © The Royal Society of Chemistry 2014
Paper
19 S. Gilbert, L. Wills, B. Wessels, J. Schindler, J. Thomas and C. Kannewurf, J. Appl. Phys., 1996, 80, 969–977. 20 C. Kittel and P. McEuen, Introduction to solid state physics, Wiley, New York, 1976. 21 W. Nolting, W. Borgiel, V. Dose and T. Fauster, Phys. Rev. B: Condens. Matter, 1989, 40, 5015. 22 C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles, John Wiley & Sons, 2008. 23 U. Kreibig and M. Vollmer, Optical properties of metal clusters, Springer-Verlag, 1995. 24 P. Johnson and R. Christy, Phys. Rev. B: Solid State, 1974, 9, 5056. 25 Z. Xiong, X. Chen, X. Wang, L. Peng, D. Yan, H. Lei, Y. Fu, J. Wu, Z. Li and X. An, Appl. Surf. Sci., 2013, 268, 524–528. 26 P. B. Johnson and R.-W. Christy, Phys. Rev. B: Solid State, 1972, 6, 4370. 27 Y. Lin, X. Q. Liu, T. Wang, C. Chen, H. Wu, L. Liao and C. Liu, Nanotechnology, 2013, 24, 125705. 28 Z. Xiong, W. Sun, X. Wang, F. Jiang and W. Wu, J. Alloys Compd., 2012, 513, 300–303. 29 C. Friesen and C. Thompson, Phys. Rev. Lett., 2004, 93, 056104. 30 K. Godo, J. Chang, H. Makino, T. Takai, T. Hanada, T. Yao, T. Sasao and T. Goto, J. Appl. Phys., 2002, 92, 5490–5493. 31 M. Yousuf, P. C. Sahu, H. Jajoo, S. Rajagopalan and K. G. Rajan, J. Phys. F: Met. Phys., 1986, 16, 373. 32 K. Hellwege and A. Hellwege, Landolt-Bornstein, New Ser., Group III, 1981, 3. 33 L. Pintilie, Ferroelectrics-Phys. Effects, 2011, 101. 34 A. M. J. H. Seuter, Philips Res. Rep. Suppl., 1974, 3, 1. 35 W. Heywang, J. Mater. Sci., 1971, 6, 1214–1224. 36 W. Lü, X. Wang, Z. Liu, S. Dhar, A. Annadi, K. Gopinadhan, A. R. Barman, H. Su and T. Venkatesan, Appl. Phys. Lett., 2011, 99, 172103.
Nanoscale, 2014, 6, 13876–13881 | 13881
