Thermoelectric Potential of Bi and Bi 1 x Sb x Nanowire Arrays

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1 Thermoelectric Potential of Bi and Bi 1 x Sb x Nanowire Arrays M. S. Dresselhaus a,b, Y.-M. Lin a, O. Rabin c, S. B. Cronin b, M. R. Black a, and J. Y. Ying d a Dept. of Electrical Engineering and Computer Science b Dept. of Physics, c Dept. of Chemistry d Dept. of Chemical Engineering Massachusetts Institute of Technology, Cambridge, MA , USA. ABSTRACT The potential of Bi and Bi 1 x Sb x nanowire arrays for thermoelectric applications is discussed. The advantages of bismuth as a low dimensional thermoelectric material are enumerated and the role of modeling is emphasized. The advantages of using the Sb concentration as well as the wire diameter as materials parameters for optimizing the thermoelectric performance of these nanowires are discussed, with particular emphasis given to the development of a high performance p-type nanowire thermoelectric material. INTRODUCTION Bismuth provides a very attractive model system for thermoelectric applications because of the very large anisotropy of the three ellipsoidal constant energy surfaces for electrons, and the very light effective masses and high carrier mobilities that can be observed with these electron carriers. Since bismuth is a semimetal with a very small band overlap energy, the fabrication of nanowires of sufficiently small diameters provides an opportunity to make bismuth into a semiconductor and to exploit the highly desirable electronic properties of its anisotropic constant energy surfaces for new categories of applications [1, 2]. In addition, bulk bismuth has charge carriers with very long mean free paths associated with its high mobility for electronic transport, and heavy mass ions which are highly effective for scattering phonons, thereby making bismuth a very attractive material for thermoelectric applications. Bismuth can also be alloyed isoelectronically with antimony to yield a high mobility alloy with reduced thermal conductivity, thereby giving much greater flexibility in tailoring the properties of bismuth-related nanowires for specific thermoelectric applications [1]. As a bulk material, semimetallic Bi has a relatively low Seebeck coefficient S because of the approximate cancellation between the contributions to S from the electron ( ) and hole (+) carriers. It was early recognized that bulk Bi could however be a good thermoelectric material, if the hole carriers could somehow be removed. It was further found that the addition of Sb could make Bi into a semiconductor for a narrow range of Sb concentrations (between 7 and 22% Sb), and for such semiconducting Bi 1 x Sb x alloys, relatively high ZT values should be achievable when properly doped and oriented. Low dimensionality, however, offers a more fundamental opportunity to overcome the problem of the low Seebeck coefficient found in 3D bulk bismuth. As the quantum well (or

2 Arb. unit (22) (12) (11) (24) θ (degree) Figure 1: (a)cross-sectional view of the cylindrical channels of 65 nm average diameter of an anodic alumina template, shown as a transmission electron microscope (TEM) image. The template has been mostly filled with bismuth, and the TEM image was taken after the top and bottom sides of the sample had been ion milled with 6 KV Ar ions [3]. (b) X-ray diffraction pattern for anodic alumina/bi nanowire composites. The average wire diameter of the Bi nanowires for this sample is about 52 nm. The insert shows the selected area electron diffraction pattern taken from the same sample. The two experimental results indicate that the Bi nanowires are highly crystalline and possess a preferred growth orientation [4]. wire) width decreases, the band edge for the lowest subband in the conduction band rises above that for the highest subband in the valence band, thereby inducing a semimetalsemiconductor transition. If the 2D (or 1D) bismuth system is then doped to the optimum doping level, a large enhancement in Z 2D T (and even a greater enhancement in Z 1D T ) should be possible as the quantum well (or wire) width is decreased [1]. Although significant effort has been given to preparing bismuth quantum wells, it has been difficult to find suitable barrier materials that are compatible with the bismuth from a materials science standpoint. This difficulty has hindered the development of bismuth-related quantum well superlattice systems. On the other hand, for bismuth nanowires it has been easy to find a compatible material using the alumina template approach, described below. Another reason why bismuth is an attractive model system for studying the potential of low dimensional structures for thermoelectric applications is because of the ability to carry out detailed model calculations with low dimensional bismuth nanostructures. Firstly, the electronic structure of bulk bismuth is well understood, so that model calculations can be carried out readily. Using these models, it has been straight forward to predict the wire diameter below which Bi nanowires become semiconducting [2]. This value turns out to be on the order of 4 5 nm at 77 K, depending on the crystalline orientation of the nanowires. These diameters are relatively large and can readily be fabricated in the laboratory by presently available synthesis methods. PREPARATION OF Bi NANOWIRES Arrays of hexagonally-packed parallel bismuth nanowires, 7 11 nm in diameter and

3 25 65 µm in length, have been prepared [see Fig. 1(a)] [3]. These nanowires are embedded in a dielectric matrix of anodic alumina, which, because of its array of parallel nano-channels, is used as a template for preparing Bi nanowires, as shown in Fig. 1(a). Fortunately, the bismuth can be confined to these nanochannels, and the bismuth does not diffuse into the anodic alumina matrix itself, so that from an electronics standpoint, the alumina provides a suitably high energy gap (3.2 ev) barrier for bismuth or Bi 1 x Sb x alloy nanowires. When prepared by the pressure injection method, the Bi nanowires are highly oriented with a common crystallographic direction along the wire axis, as shown in Fig. 1(b). Since the band structure of Bi is highly anisotropic, the transport properties of Bi nanowires are expected to be dependent on the crystallographic orientation along the wire axis. For the range of wire diameters of interest to thermoelectric applications, the growth direction of the bismuth and Bi 1 x Sb x nanowires is along a direction perpendicular to the (12) lattice planes. In addition, structural analysis shows that the crystal structure of bulk Bi is maintained in the nanowires, indicating that many properties of bulk Bi may be utilized in modeling the behavior of Bi nanowires [1]. Furthermore, the crystal structure of the Bi 1 x Sb x nanowires is also the same for the range of x of interest in these studies. MODEL CALCULATIONS To model the electronic structure, we assume, as a first approximation, the simplest possible model for an ideal 1D quantum wire, where the carriers are confined inside a cylindrical potential well, bounded by a barrier of infinite potential height. Due to the small electron effective mass components of Bi, the quantum confinement effects in Bi nanowires are more prominent than for wires from other materials with the same diameter. This means that quantum effects associated with 1D nanowires can be observed for relatively larger diameter nanowires in bismuth and in Bi 1 x Sb x alloys than for other materials [1]. Model calculations have been used to predict the wire diameter where the semimetalsemiconductor transition occurs as a function of crystallographic orientation and temperature [2]. Results for such a calculation are shown in Fig. 2 for Bi quantum wires oriented along the [112] growth direction, and the calculations predict that the semimetalsemiconductor transition occurs at a nanowire diameter of 49 nm at 77 K. Shown in this diagram is the wire diameter dependence of the band edges for the L-point electron pocket A and for the (B,C) pockets. The ellipsoid of electron pocket A has the major axis lying on the plane spanned by the trigonal axis and the wire axis, while the pockets B and C are the electron ellipsoids at the other two L points. In Fig. 2 it is seen that the L(B,C) electrons constitute the lowest lying electron subband. The corresponding wire diameter dependences of the energy of the highest subband for the T -point holes and for the two types of L-point holes are also shown in Fig. 2. Experimental confirmation of the predictions of these calculations comes from the two-terminal temperature-dependent resistance measurements made on nanowire arrays with diameter ranging from 7 11 nm prepared by a vapor phase injection method [1, 5]. These measurements show a dramatic change in the temperature dependence of the resistance (resistivity) for nanowires with diameters below 48 nm, consistent with the calculated temperature-dependent resistivity based on the model used to calculate the diameter dependent band edge energies of Fig. 2 [4]. Measurements of the transport properties of these arrays of Bi nanowires have also been carried out for wires of different diameters as a function of magnetic field, showing ballistic transport at low temperature [6]. Good agreement between the various tempera-

4 1 8 6 L e (A) L e (B,C) T holes Energy (mev) nm L holes = 38 E gl = Wire diameter (nm) Figure 2: The band edge energies at 77 K of Bi quantum wires oriented along the [1 12] growth direction, showing the energies of the highest energy subbands for the T -point and L-point hole carrier pockets, and the lowest energy subbands for the L-point electron pockets (A, B and C). The zero of energy refers to the conduction band edge in bulk Bi. As the wire diameter d W decreases, the conduction subband edges move up in energy, while the valence subband edges move down. At d c = 49 nm, the lowest conduction subband edge formed by the L(B, C) electrons is predicted to cross the highest T -point valence subband edge, and a semimetal-semiconductor transition is predicted to occur [4]. ture and magnetic field dependent transport measurements and the modeling calculations has been achieved, thereby validating the use of bismuth nanowires as a model system. ALLOYING BISMUTH WITH ANTIMONY As mentioned above, alloying provides another useful parameter for controlling the properties of bismuth-related nanowires. The same basic synthesis methods used for preparing bismuth nanowires can also be used to prepare Bi 1 x Sb x nanowires. The motivation for considering Sb alloying of Bi comes from Fig. 2, where it is seen that the L-point bandgap of bismuth increases dramatically as the Bi wire diameter decreases in the semiconductor regime. This observation implies that bismuth becomes less attractive as a thermoelectric material with decreasing wire diameter because the highly anisotropic electron Fermi surfaces of bulk bismuth become less anisotropic as the L-point bandgap increases. The dependence of the T -point and L-point band edges on Sb concentration, shown in Fig. 3(a), suggests that the addition of Sb to Bi provides an additional degree of control of the electronic structure which might allow semiconducting nanowires with greater Fermi surface anisotropy to be fabricated. In this context we have extended our modeling calculations to the case of Bi 1 x Sb x nanowires, considering the antimony concentration to be another controllable variable, which in addition to the nanowire diameter could be used to optimize the thermoelectric properties of quantum nanowire arrays [8]. Before discussing the effect of Sb alloying on the band edge energies of bismuth nanowires, it is instructive to review the location of the electron and hole carrier pockets in Sb (see Fig. 4) because of the relevance of these carrier pockets on the electronic structure of Bi 1 x Sb x alloys in the concentration range x that is interesting to thermoelectric

5 (a) (b) Figure 3: (a) Schematic diagram for the energy bands near the Fermi level for Bi 1 x Sb x bulk alloys as a function of x at low T ( 77 K) [7]. The numerical values on the x axis refer to the Sb concentration. Regions where the alloy is a semimetal (SM), a direct gap semiconductor, and an indirect gap semiconductor are indicated, where SC denotes the semiconducting phase. (b) Phase diagram of the corresponding electronic band structure of Bi 1 x Sb x nanowires, showing the regions of d W and x where the nanowires are expected to be semimetallic or to be semiconducting (both direct gap and indirect gap regions). The bold horizontal arrow in the center points to the condition where the highest lying subband edges for the 1 hole pockets (about the T point, the 3 L points and the 6 H points in the Brillouin zone) are all accidentally degenerate in energy [8]. Figure 4: Location of the three L-point electron carrier pockets and the six H-point hole carrier pockets of Sb in the rhombohedral Brillouin zone. The high symmetry directions of this rhombohedral Brillouin zone are also indicated.

6 applications. From Fig. 4 we see that the crystal structures for Sb and Bi are similar and that the electron pockets for Sb are at the L points, as in Bi. However, the holes in Sb are located in 6 pockets at the H points in the Brillouin zone, and these hole pockets are approximated by ellipsoids of revolution. The constant energy surfaces specifying the carrier pockets in antimony are less anisotropic and enclose much larger volume in k-space, as compared to bismuth. In the range of Sb concentration x of interest to thermoelectric applications, the carrier concentrations for the Bi 1 x Sb x nanowires are similar to that for the corresponding Bi nanowires, the electron carriers are also located at the L points, and the hole carriers are located at either the T point, the three L points, or the six H points, or at a combination of these points, depending on the Sb concentration x and on the nanowire diameter. As was mentioned above, the flexibility in using Sb concentration x as a control variable is especially attractive for making p-type nanowires for thermoelectric applications, since the ZT values of pure Bi nanowires of a given diameter (e.g., d W 1 nm) are much more favorable for n-type than for p-type Bi nanowires [1, 4]. For practical thermoelectric devices, however, both n-type and p-type legs are needed. Since Sb is isoelectronic with Bi and has the same A15 crystal structure, bulk Bi 1 x Sb x alloys yield a high carrier mobility material, but with electronic properties that can be varied considerably as the Sb concentration is varied [see Fig. 3(a)]. Of particular interest here is the low Sb concentration range (below x =.7) where the bulk material is semimetallic, the regions from.7 < x <.9 and.16 < x <.22 where bulk Bi 1 x Sb x is an indirect gap semiconductor, and the region.9 < x <.16 where bulk Bi 1 x Sb x is a direct gap semiconductor [7]. Our calculations for the electronic structure for the Bi 1 x Sb x nanowires based on the simplest model calculations [see Fig. 3(b)] [8] show that variation of the wire diameter leads to another important degree of freedom in the control of the electronic structure, showing regions where, depending on the nanowire diameter and Sb alloy concentration, the nanowires are predicted to be semimetallic, a direct gap semiconductor, or an indirect gap semiconductor. The calculations of Fig. 3(b) show how variation of the nanowire diameter can be used to change the electronic structure of Bi 1 x Sb x alloys quite dramatically. Of particular interest in this diagram for the Bi 1 x Sb x nanowires is the point at x =.13 and a wire diameter of 6 nm, where the L-point, T - point and H-point hole subband edges are all degenerate with one another. It is predicted that for a system where all 1 hole subband edges are degenerate in energy, the density of states for holes can be especially high, leading to a substantial enhancement in the expected Seebeck coefficient, thereby leading to an increased ZT [8]. Calculated results for the predicted ZT for both n-type and p-type Bi 1 x Sb x nanowires as a function of Sb concentration x and wire diameter d W are shown in Fig. 5. These results predict that a ZT value of 1.2 should be achievable for both n-type and p-type nanowires of 4 nm diameter and an Sb concentration of x.13. However, by going to smaller diameter nanowires, even higher ZT values should be achievable. The results of Fig. 5 suggest that, in general, ZT for Bi 1 x Sb x nanowires is larger than for Bi nanowires of a given diameter. Experiments on Bi 1 x Sb x nanowires up to x =.15 show that good crystallinity and mobility values are maintained for 4 nm wires [9]. Further experimental work is, however, needed to see whether the crystallinity and mobility can be maintained for the smaller nanowire diameters (below 1 nm) needed to achieve the predicted large enhancements in ZT. The feasibility of demonstrating interesting transport properties in Bi 1 x Sb x nanowires is supported by the preservation of a high degree of crystallinity upon Sb alloying of the Bi nanowires (see Fig. 6). In this figure a comparison is made between the X-ray diffraction patterns of 4 nm diameter Bi nanowires with Bi.85 Sb.15 alloy nanowires of

7 Wire Diameter (nm) Antimony Content (at%) Wire Diameter (nm) Antimony Content (at%) (a) (b) Figure 5: (a) Contour plot of optimal ZT values (optimized for ZT by placement of the Fermi level) for n-type Bi 1 x Sb x nanowires vs. wire diameter and antimony concentration. (b) Contour plot of optimal ZT values for p-type Bi 1 x Sb x nanowires vs. wire diameter and antimony concentration[8]. The transport calculations to obtain ZT are based on the energy band structure for the nanowires shown in Fig. 4(b) [8]. similar diameters and similar Bi nanowires doped with.15 at.%te. The ability to dope the nanowires is conveniently accomplished by Te doping which moves the Fermi level up to increase the electron carrier concentration. This figure confirms that such additions of Sb or Te do not disturb the good crystallinity of the nanowires, nor does the addition of Sb or Te change the basic crystal structure, nor the preferred nanowire growth direction [9], as mentioned above. Temperature dependent resistance R(T ) measurements show that R(T ) depends on the Sb concentration in a reproducible, non-monotonic manner [9] and these results are shown in Fig. 7. Here we see that the general functional form of R(T )/R(27K) does not change much as x in Bi 1 x Sb x is varied, but the magnitude of R(T ) first decreases rapidly with increasing x from to.5 and then R(T ) increases slowly as x increases from.5 to.15 [1]. This non-monotonic dependence of R(T )/R(27K) on x has been explained in considerable detail by the model calculations of the Bi 1 x Sb x system in terms of the dependence of the carrier concentrations and of the different mixes of carrier types as a function of x and T [9, 1], thus giving confidence in our ability to make predictions on the use of antimony concentrations x to achieve the desired thermoelectric performance for n-type and p-type devices based on Bi 1 x Sb x nanowires of various x values, diameters, and temperature ranges of operation. Low temperature (4 K) measurements on Bi 1 x Sb x nanowire arrays (for x.1) show a maximum in the magnetoresistance as a function of magnetic field, indicating that Sb doping does not disturb the long carrier mean free paths characteristic of transport in Bi nanowires [1]. Optical absorption measurements (see Fig. 8) [11, 12] have been carried out on Bi filled alumina template samples where quantum confinement effects can also be seen. In these experiments the Bi nanowire diameters are much smaller than the wavelength of light, so that analysis is needed to extract the frequency-dependent dielectric function [ɛ 1 (ω) + iɛ 2 (ω)] for the bismuth nanowires from optical reflectivity and transmission mea-

8 (12) Intensity (Arbitary units) (11) (c) 15 at% Sb (b).15 at% Te (22) (24) (a) undoped Bi θ ( o ) Figure 6: The XRD patterns for 4-nm nanowires arrays with different compositions. The XRD peaks of these nanowire arrays are assigned to the peaks of the Bi standard, showing that the lattice structure of Bi nanowires is not affected by the addition of Te (<.15 at%) to dope nanowires n-type or the addition of Sb (< 15 at%) which is isoelectronic to Bi. The intensity distributions of the peaks also indicate Sb and Te alloyed or doped nanowires possess a preferred crystal orientation along the wire axis that is perpendicular to the (12) lattice plane. 2.5 R(T)/R(27 K) Bi 5% Sb 1% Sb 15% Sb 1 1 Temperature (K) Figure 7: Measured temperature dependence of the resistance normalized to the resistance at 27 K of 4-nm Bi 1 x Sb x alloy nanowires of various Sb concentrations ( x.15)[9]. Of particular interest is the strong non-monotonic dependence of the curves on Sb concentration, providing a stringent test of the model calculations.

9 2 6 ε (1/λ) ~ ε (1/λ) wavenumber (cm ) wavenumber (cm ) Figure 8: The dielectric function ɛ 1 (ω) + iɛ 2 (ω) of Bi nanowires with different diameters obtained from analysis of reflectivity measurements, showing that the ɛ 2 peak moves to higher energies and the intensity increases as the diameter decreases[11]. The numbers in the figure insets indicate the nanowire diameter in nm. surements on the alumina template with and without the bismuth nanowires. The optical properties for the Bi nanowires are found using effective medium theory, the Kramers Kronig relations, and Maxwell s equations [11, 12]. Figure 8 shows a large sharp feature near 1 cm 1 which moves to higher frequencies as the nanowire diameter decreases. Additional peaks in the optical reflectivity are seen when the template is removed and the optical measurements are done on free-standing Bi nanowires, consistent with an assignment of at least some of the structures in the IR spectra to inter-subband transitions [13]. The geometry of the nanowire structures could also be advantageous for certain thermoelectric applications, such as thermal management of integrated circuits with small feature sizes. Progress along this direction has been aided by the success in growing Bi nanowire arrays in an alumina template that is prepared on a silicon substrate, thereby allowing for integration between thermoelectric nanowire arrays and semiconducting electronics [14, 15]. By growing the alumina template on a silicon wafer covered by a Ti electrode, arrays of Bi nanowires have been synthesized by an electrochemical process, demonstrating enhanced mechanical rigidity and reduced brittleness. Thermoelectric applications of devices based on these structures are under consideration. CONCLUSIONS Bismuth nanowires are a quasi one-dimensional material that has considerable potential for thermoelectric applications. Alloying Bi with Sb introduces another degree of freedom to the system that seems to offer significant advantages for thermoelectric applications, especially for p-type thermoelectric materials. The good agreement between experiment and theory supports the use of the Bi 1 x Sb x system as a model system for the study of thermoelectricity in 1D systems.

10 ACKNOWLEDGMENTS The authors gratefully acknowledge the helpful discussions with Dr. G. Dresselhaus, Prof. Jean-Paul Issi, Dr. Joseph Heremans, Ted Harman, Prof. Gang Chen, and Prof. P. Hagelstein. They are also thankful to many other colleagues for their assistance with the preparation of this article. The authors are grateful for support for this work by the U.S. Navy Contract #N K-24, the MURI program subcontract PO #25-G-7A114-1 through UCLA, DARPA contract #N , and by NSF grant DMR REFERENCES [1] M. S. Dresselhaus, Yu-Ming Lin, T. Koga, S. B. Cronin, O. Rabin, M. R. Black, and G. Dresselhaus. In Semiconductors and Semimetals: Recent Trends in Thermoelectric Materials Research III, edited by T. M. Tritt, pages 1 121, Academic Press, San Diego, CA, 21. Chapter 1. [2] Y. M. Lin, X. Sun, and M. S. Dresselhaus, Phys. Rev. B 62, (2). [3] Z. Zhang, J. Y. Ying, and M. S. Dresselhaus, J. Mater. Res. 13, (1998). [4] Yu-Ming Lin. Fabrication, Characterization and Theoretical Modeling of Te-doped Bi nanowire Systems for Thermoelectric Applications. Master s thesis, Massachusetts Institute of Technology, May 2. Department of Electrical Engineering and Computer Science. [5] J. Heremans, C. M. Thrush, Yu-Ming Lin, S. Cronin, Z. Zhang, M. S. Dresselhaus, and J. F. Mansfield, Phys. Rev. B 61, (2). [6] Y.-M. Lin, S. B. Cronin, J. Y. Ying, M. S. Dresselhaus, and J. P. Heremans, Appl. Phys. Lett. 76, (2). [7] B. Lenoir, M. Cassart, J. P. Michenaud, H. Scherrer, and S. Scherrer, J. Phys. Chem. Solids 57, (1996). [8] O. Rabin, Yu-Ming Lin, and M. S. Dresselhaus, Appl. Phys. Lett. 79, (21). [9] Yu-Ming Lin, S. B. Cronin, O. Rabin, Jackie Y. Ying, and M. S. Dresselhaus, Appl. Phys. Lett. 79, (21). [1] Yu-Ming Lin, S. B. Cronin, O. Rabin, Jackie Y. Ying, and M. S. Dresselhaus. In Thermoelectric Materials 21 - Research and Applications: MRS Symposium Proceedings, Boston, December 21, edited by G. S. Nolas, D. C. Johnson, and D. G. Mandrus, page G1.6, Materials Research Society Press, Pittsburgh, PA, 22. [11] M. R. Black, Y.-M. Lin, S. B. Cronin, Oded Rabin, and M. S. Dresselhaus. In Anisotropic Nanoparticles: Synthesis, Characterization and Applications: MRS Symposium Proceedings, Boston, December 2, edited by S. Stranick, P. C. Searson, L. A. Lyon, and C. Keating, pages C4321 C4327, Materials Research Society Press, Pittsburgh, PA, 21. [12] M. R. Black, M. Padi, S. B. Cronin, Y.-M. Lin, O. Rabin, T. McClure, G. Dresselhaus, P. L. Hagelstein, and M. S. Dresselhaus, Appl. Phys. Lett. 77, (2).

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