NANO LETTERS
Anomalous Band Gap Evolution from Band Inversion in Pb1-xSnxTe Nanocrystals
2009 Vol. 9, No. 4 1583-1587
Indika U. Arachchige† and Mercouri G. Kanatzidis*,†,‡ Department of Chemistry, Northwestern UniVersity, EVanston, Illinois 60208, and Material Science DiVision, Argonne National Laboratory, Argonne, Illinois 60439 Received December 14, 2008; Revised Manuscript Received February 17, 2009
ABSTRACT We report the synthesis of a series of narrowly disperse Pb1-xSnxTe nanocrystals by employing a colloidal synthetic strategy. As synthesized nanocrystals are solid solutions with cubic NaCl-type structure and exhibit band energy gaps in the mid-IR region. We show that these ternary nanocrystals display qualitatively the same anomalous trend in band gaps as a function of x that is attributed to the band inversion phenomenon of the corresponding bulk materials; however unlike the bulk the band gap does not vanish at any Sn concentration but achieves a minimum of 0.28 eV for x ) 0.67.
Ternary Pb1-xSnxTe alloys are narrow band gap semiconductors of the so-called IV-VI family with cubic rock salt crystal structure. They exhibit an anomalous trend in their optoelectronic properties as a function of Sn concentration (x), which is not found in the corresponding II-VI semiconductors such as the Cd1-xHgxTe. The energy gaps in the Cd1-xHgxTe materials evolve naturally as a linear function of Hg concentration (x), and lie between the band gaps (Eg) of the end-members CdTe (1.5 eV) and HgTe (0 eV).1,2 In contrast, the Pb1-xSnxTe materials exhibit narrower energy gaps than their end members, PbTe (0.29 eV3) and SnTe (0.18 eV4) and show an anomalous dependence of band energies with Sn concentration.5,6 These observations are understood by the so-called band inversion model, proposed by Dimmock et al. in which the valence and the conduction bands are inverted (in SnTe) from those of PbTe.5 Accordingly, the energy gap of Pb1-xSnxTe materials initially decreases with increasing Sn concentration (x) and vanishes for an intermediate alloy composition (valence and conduction band cross over point, Eg ) 0). With further increase in Sn fraction (x), the energy gap starts to increase as the character of the band edge states is inverted up to the SnTe value (Figure 1A). Experimental investigations indicate that the Sn concentration (x) at which the band gap becomes zero varies from x ∼ 0.32 to x ∼ 0.65 as the temperature increases from 4 to 300 K, respectively.6,7 This unique band structure behavior of Pb1-xSnxTe is used as an advantage when * Corresponding author,
[email protected]. † Northwestern University. ‡ Argonne National Laboratory. 10.1021/nl8037757 CCC: $40.75 Published on Web 03/24/2009
2009 American Chemical Society
designing IR photodetectors, laser diodes, and thermophotovoltaic energy converters.8,9 Nanocrystals display unique size-tunable physicochemical properties that are distinct from their bulk counterparts.10,11 Specifically, in nanocrystalline semiconductors, the sizetunable optical and electronic properties are observed because of the quantization of the energy levels.12-14 So far, the preponderance of research has been focused on the simple binary semiconductor nanocrystals such as Cd, Zn, and Pb chalcogenides. Reports on more complex ternary and quaternary nanomaterials are rare and include nanocrystals prepared by molecular beam or vapor deposition,15 solvothermal techniques,16 colloidal17,18 and inverse micellar19 synthetic strategies, and intentional doping of binary nanocrystals.20,21 These more complex nanomaterials exhibit novel physicochemical properties, which are not observed in the simpler binary materials. According to the band inversion model described above, Pb1-xSnxTe alloys with some intermediate compositions exhibit zero energy gaps and have metallic properties. However, it is very difficult to precisely determine the band edge structure of the intermediate compositions near and beyond the band inversion region, since only high carrier concentration samples can be obtained due to deviation from stoichiometry. On the other hand, nanocrystals of Pb1-xSnxTe would not have high carrier concentrations and can serve as ideal samples to determine the band edge structure near and beyond the inversion region. Hence, our goal for this work was to prepare a series of nanocrystalline Pb1-xSnxTe over a wide range of x values and determine if and how the band inversion expressed itself as a function of x and whether the
Figure 1. Schematic representation of the band energy diagram of the Pb1-xSnxTe system where x ) 0.67 at 300 K for (A) bulk materials and (B) the nanocrystals showing the nature of band inversion.
energy gap did indeed vanish or not. We show here, that Pb1-xSnxTe nanocrystals exhibit qualitatively the same anomalous nonlinear trend in band gap dependence with Sn concentration; however the band gap achieves only a minimum of 0.28 eV at x ∼ 0.67 but does not vanish at any Sn concentration. Furthermore, the energy gaps of nanocrystalline Pb1-xSnxTe are significantly blue-shifted as a result of quantum confinement, making the entire series of nanocrystalline Pb1-xSnxTe narrow gap semiconductors. A series of Pb1-xSnxTe nanocrystals with approximately 7.5 nm in size was prepared by reacting a mixture of lead oleate and bis[bis(trimethylsilyl)amino]tin(II) with elemental Te dissolved in TOP at 150 °C (Supporting Information). Attempts to prepare larger nanocrystals (10-20 nm) by increasing the reaction time (3-5 min) led to the formation of highly anisotropic nanocrystals with irregular shapes. Hence, the reaction time was fixed at 1.5 min to ensure the formation of narrowly disperse nanocrystals with nearly spherical geometry. All compositions make highly stable colloidal suspensions in common nonpolar organic solvents. We observed that the amount of Sn incorporated into PbTe lattice is low if the nanocrystals were prepared only in octadecene. Hence, oleylamine was used as a stabilizer to incorporate a higher amount of Sn into the PbTe nanocrystals. Since primary amines form strong complexes with Sn2+ ions, we presume that the elemental Sn fraction incorporated into PbTe is stabilized by the amine ligands. 1584
Figure 2. (A) Powder X-ray diffraction patterns of the (a) Pb0.86Sn0.14Te, (b) Pb0.8Sn0.2Te, (c) Pb0.5Sn0.5Te, (d) Pb0.33Sn0.67Te, (e) Pb0.2Sn0.8Te, and (f) Pb0.14Sn0.86Te nanocrystals. The ICDDPDF overlays of cubic PbTe (PDF # 08-0028) is shown as vertical lines. (B) A plot showing the change in lattice parameter with the nominal atomic composition of Pb1-xSnxTe nanocrystals.
Pb1-xSnxTe nanocrystals obtained from this route are highly crystalline and retain the cubic NaCl-type structure of PbTe (Figure 2A). The powder diffraction patterns are shifted to larger 2θ angles confirming the incorporation of Sn into the PbTe lattice. The lattice parameters lie between those of SnTe and PbTe and decrease systematically from higher to lower Sn concentrations (Vegard’s law is generally obeyed) implying a solid solution behavior (Figure 2B). The average crystallite size calculated based on the line broadening of the Bragg reflections was in the range of 4.4-5.1 nm for all compositions.22 Additionally, we did not observe any impurity peaks that correspond to binary SnTe or elemental Pb, Sn, or Te. Energy dispersive spectroscopy under scanning electron microscopy (SEM) and transmission electron microscopy (TEM) examination was used to investigate the elemental composition of Pb1-xSnxTe nanocrystals, and the results are listed in the Table 1. In general, both TEM/EDS and SEM/ EDS (EDS, energy dispersive spectroscopy) analyses suggest that as-prepared nanocrystals have atomic compositions that are close to the expected compositions. The use of stoichiometric amounts of Pb, Sn, and Te (i.e., 1:1:2 ratio for PbSnTe2) precursors led to the formation of nanocrystals that Nano Lett., Vol. 9, No. 4, 2009
Table 1. Comparison of Nominal x Values, Elemental Compositions, Average Crystallite Sizes, Lattice Parameters, and Optical Band Gaps of Pb1-xSnxTe Nanoparticles nominal composition
elemental compositiona
crystallite size (nm)
Pb0.86Sn0.14Te Pb0.81(0.031Sn0.19(0.031Te 5.1 ( 0.2 Pb0.8Sn0.2Te Pb0.78(0.026Sn0.22(0.026Te 4.6 ( 0.2 Pb0.5Sn0.5Te Pb0.55(0.03Sn0.45(0.03Te 5.0 ( 0.2 Pb0.33Sn0.67Te Pb0.31(0.031Sn0.69(0.031Te 4.4 ( 0.2 Pb0.2Sn0.8Te Pb0.17 ( 0.021Sn0.83 ( 0.021Te 4.8 ( 0.2 Pb0.14Sn0.86Te Pb0.13 ( 0.025Sn0.87 ( 0.025Te 4.6 ( 0.2 a Composition from five individual measurements in SEM/EDS and TEM/EDS.
lattice parameter (Å)
band gap (eV)
6.439(2) 6.423(2) 6.382(2) 6.365(2) 6.357(2) 6.334(2)
0.63 0.55 0.47 0.28 0.53 0.61
Figure 3. TEM images of the (a) Pb0.86Sn0.14Te, (b) Pb0.8Sn0.2Te, (c) Pb0.5Sn0.5Te, (d) Pb0.33Sn0.67Te, (e) Pb0.2Sn0.8Te, (f) Pb0.14Sn0.86Te, (g) SnTe, and (h) PbTe nanocrystals. (i) HRTEM image of Pb0.33Sn0.67Te nanocrystal in panel d. Insets in (c) and (d) show the selected area electron diffraction pattern from a 200 nm2 area of nanocrystals. The diffraction rings are indexable to a cubic NaCl-type lattice.
are deficient in Sn and Te. Hence excess Sn (3-5 times) and Te (4-5 times) precursors were used to achieve the expected atomic composition. TEM images of Pb1-xSnxTe nanocrystals without any size selective processing are shown in Figure 3a-f. The asprepared nanocrystals are approximately spherical in shape, and the average particle size is in the range of 6.0-8.7 nm for all compositions. Nevertheless, the crystallite size determinations using the Scherrer formula yield values that are slightly smaller than the particle size calculated based on TEM. This can be attributed to the presence of an amorphous shell around nanoparticles which can be clearly seen in the high-resolution TEM image (Figure 3i). In Nano Lett., Vol. 9, No. 4, 2009
general, Pb0.86Sn0.14Te and Pb0.14Sn0.86Te compositions form fairly monodisperse, aggregate-free, spherical nanoparticles that are similar in size and shape to the binary SnTe and PbTe nanocrystals (Figure 3, panels g and h).24,25 Interestingly, the nanocrystals with 1:1 (Pb:Sn) composition, i.e., Pb0.5Sn0.5Te, exhibit spherical to oval geometries and are relatively polydisperse compared to the nanocrystals of other compositions. We presume that the anisotropic growth of nanocrystals is due to the difference in reactivity/binding affinity of Pb and Sn precursors, i.e., Pb2+ coordinated with oleic acid ligands and the Sn2+ coordinated with amine ligands. When a large excess of lead oleate is present in the reaction mixture compared to the amount of Sn precursor 1585
Figure 4. (a) STEM image of Pb0.8Sn0.2Te nanocrystal acquired in the TEM and the (b) corresponding EDS spectrum showing the presence of the expected elements in a single nanoparticle. STEM/EDS elemental maps of (c) Pb, (d) Sn, and (e) Te created based on the EDS spectrum.
Figure 5. [A] Mid-IR absorption spectra of the (a) Pb0.86Sn0.14Te (red), (b) Pb0.8Sn0.2Te (brown), (c) Pb0.5Sn0.5Te (olive), (d) Pb0.33Sn0.67Te (blue), (e) Pb0.2Sn0.8Te (purple), and (f) Pb0.14Sn0.86Te (cyan) nanocrystals. The dotted lines indicate the band gap estimated from absorption band onsets. The sharp absorption peaks at 0.33 and 0.36 eV correspond to symmetric and asymmetric vibrational mode of C-H bonds of the residual surfactant molecules. A broad absorption hump at 0.45-0.3 eV corresponds to O-H vibrational modes of residual oleic acid ligands. [B] A plot demonstrating the variation of band energies with the mole fraction of Sn (x) in Pb1-xSnxTe alloys (squares) and nanocrystals (triangles) at 300 K. The data points for Pb1-xSnxTe alloys were obtained from Dimmock et al.
(i.e., Pb0.86Sn0.14Te) the resulting Pb-rich nanocrystals are primarily passivated by oleic acid ligands. This results in the formation of narrowly disperse nanocrystals that are closer in size and shape to binary PbTe nanoparticles. Similarly, when a large excess of the Sn precursor is present in the reaction mixture (i.e., Pb0.14Sn0.86Te) resulting nanocrystals are primarily passivated by amine ligands and particles that are similar in size and shape to binary SnTe nanocrystals are formed. However, when the effective concentrations of Pb and Sn precursors are closer to each other (i.e., Pb0.5Sn0.5Te), the resulting nanocrystals are passivated by both oleic acid and amine ligands. Hence, the shape evolution 1586
of nanocrystals depends on the binding affinities of oleic acids and amine ligands. We assume that oleic acid and the amines can change the surface energy of certain crystal faces relative to the others. Hence it could tightly bind to one crystallographic phase while the other faces are weakly passivated by acid/amine ligands. This results in a faster growth for certain crystal phases compared to the others, which could ultimately lead to the formation of anisotropic nanocrystals. Consequently, particles tend to grow into anisotropic shapes with increasing Pb (for Sn-rich phases) and Sn (for Pb-rich phases) precursors. Despite the differences in atomic composition, selected area electron diffracNano Lett., Vol. 9, No. 4, 2009
tion patterns collected from an area of Pb0.5Sn0.5Te and Pb0.33Sn0.67Te nanocrystals (Figure 3, panels c and d insets) show the main diffraction rings correspond to the cubic NaCl structure type. The structural homogeneity of Pb1-xSnxTe nanocrystals was confirmed by recording EDS spectral images in scanning transmission electron microscopy (STEM) mode using a 1 nm scanning probe and EDS microanalysis. STEM image, EDS spectrum, and the corresponding elemental maps recorded from a single Pb0.8Sn0.2Te nanoparticle are shown in Figure 4. EDS spectra show the peaks of Pb, Sn, and Te in a single nanoparticle. Elementals maps generated based on the EDS spectra show that Sn is evenly distributed in the entire PbTe lattice confirming the solid solution behavior. Similar results were obtained from nanocrystals of other compositions which supports the view that nanoparticles obtained from this route are homogeneous solid solutions and not a phase-separated collection of PbTe and SnTe nanocrystals. Pb1-xSnxTe nanocrystals exhibit well-defined band gaps in the mid-IR region (Figure 5a-f). The band gap onset values estimated based on the absorption spectra are in the range of 0.28-0.65 eV.25 The lowest energy gap of 0.28 eV was observed for the Pb0.33Sn0.67Te nanoparticles, and the band gap increases with increasing Pb concentration (for Pbrich phases) and Sn concentration (for Sn-rich phases). The binary PbTe and SnTe nanoparticles with similar particle size to Pb1-xSnxTe (∼7.5 nm) exhibit band gaps that are slightly larger than Pb1-xSnxTe nanocrystals (PbTe ) 0.68 eV and SnTe ) 0. 65 eV). Since the nanoparticles made by this route have nearly the same morphology and particle size, the variation of the band gap energies can be correlated to the Sn concentration (x). Accordingly, these observations are consistent with the band inversion model, where a decrease in energy gap with increasing Sn (for Pb-rich phases) or increasing Pb (for Sn-rich phases) is observed.5 As a result of expected quantum confinement effect in the nanocrystals, the band gap energies are significantly blue-shifted compared to those of the bulk materials. Furthermore, the bulk Pb0.35Sn0.65Te alloy which is metallic with Eg ) 0 at 300 K has now become a narrow gap semiconductor with a Eg ∼ 0.28 eV as a result of quantum confinement on the nanometer scale. In conclusion, the full series of Pb1-xSnxTe nanocrystals can be synthesized with a straightforward low-temperature colloidal synthetic route. The nanoparticles are solid solutions with the cubic rock salt structure and are nearly spherical in shape with absorption band energies in the mid-IR region. The anomalous band inversion occurring in the bulk semiconductors persists in the nanocrystalline state with the important difference that the nanocrystals fail to achieve a band gap ∼0 eV state. Since we did not observe metallic behavior (zero energy gap) in this series of nanocrystals, it appears the Pb1-xSnxTe nanocrystals obey the band inversion model, but at the cross over point of x ) 0.67 there is a huge “avoided crossing” as a result of quantum confinement (Figure 1b). Hence, band structure calculations that take into
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account the quantum confinement effect are needed to further investigate the band edge structure of the Pb1-xSnxTe nanocrystals. The solution stability, processability, and the ability to tune the band energies by changing the atomic ratio of Pb1-xSnxTe would be helpful when designing nanocrystals for thin film preparation and device applications. Hence, we are currently investigating the use of these ternary nanoparticles for thin film transistors as well as ordered lithographic patterning to make nanoparticle arrays for sensing, and thermoelectric applications. Acknowledgment. This work was supported by the Office of Naval Research. The electron microscopy work was performed in the Electron Probe Instrumentation Center (EPIC) facility of NUANCE Center (supported by NSFNSEC, NSF-MRSEC, Keck Foundation, the State of Illinois) at Northwestern University. Supporting Information Available: Detailed experimental procedures for the synthesis of PbTe, SnTe, and Pb1-xSnxTe nanocrystals, characterization techniques, and sample preparation methods. This material is available free of charge via the Internet at http://pubs.acs.org. References (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25)
Finkman, E.; Nemirovsky, Y. J. Appl. Phys. 1979, 50, 4356–4361. Finkman, E.; Schacham, S. E. J. Appl. Phys. 1984, 56, 2896–2900. Esaki, L.; Stiles, P. J. Phy. ReV. Lett. 1966, 24, 1108–1113. West, A. R. Basic Solid State Chemistry, 2nd ed.; John Wiley & Sons Ltd.: New York, 1999. Dimmock, J. O.; Melngailis, I.; Strauss, A. J. Phy. ReV. Lett. 1966, 16, 1193–1196. Abramof, E.; Ferreira, S. O.; Rappl, P. H. O.; Closs, H.; Bandeira, I. N. J. Appl. Phys. 1997, 82, 2405–2410. Jovovic, V.; Thiagarajan, S. J.; Heremans, J. P.; Komissarova, T.; Khokhlov, D.; Nicorici, A. J. Appl. Phys. 2008, 103, 053710-1053710-7. Preier, H. Appl. Phys. 1979, 20, 189–206. Chaudhri, T. K. Int. J. Energy. Res. 1998, 16, 481–487. Alivisatos, A. P. Science 1996, 271, 933–937. Murray, C. B.; Kagan, C. R.; Bawendi, M. G. Annu. ReV. Mater. Sci. 2000, 30, 545–610. Steigerwald, M. I.; Brus, L. E. Acc. Chem. Res. 1993, 23, 183–188. Wang, Y.; Herron, N. J. Phys. Chem. 1991, 95, 525–532. Trindale, T. O.; O’Brien, P.; Pickett, N. L. Chem. Mater. 2001, 13, 3843–3858. Peng, H.; Schoen, D. T.; Meister, S.; Zhang, X. F.; Cui, Y. J. Am. Chem. Soc. 2007, 129, 34–35. Hu, J.; Lu, Q.; Tang, K.; Qian, Y. T.; Lu, Q.; Tang, K.; Zhou, G.; Liu, X. Chem. Commun. 1999, 1093–1094. Wang, D.; Zheng, W.; Hao, C.; Li, Y. Chem. Commun. 2008, 25, 2556–2558. Arachchige, I. U.; Wu, J.; Dravid, V. P.; Kanatzidis, M. G. AdV. Mater. 2008, 20, 3638–3642. Karkamkar, A. J.; Kanatzidis, M. G. J. Am. Chem. Soc. 2006, 128, 6002–6003. Erwin, S. C.; Zu, L.; Haftel, M. I.; Efros, A. L.; Kennedy, T. A.; Norris, D. J. Nature 2005, 436, 91–94. Norris, D. J.; Efros, A. L.; Erwin, S. C. Science 2008, 319, 1776– 1779. Borchert, H.; Shevchenko, E. V.; Robert, A.; Mekis, I.; Kornowski, A.; Grubel, G.; Weller, H. Langmuir 2005, 21, 1931–1936. Kovalenko, M. V.; Heiss, W.; Schevchenko, E. V.; Lee, J.-S.; Schwinghammer, H.; Alivasatos, A. P.; Talapin, D. V. J. Am. Chem. Soc. 2007, 129, 11354–11355. Urban, J. J.; Talapin, D. V.; Shevchenko, E. V.; Murray, C. B. J. Am. Chem. Soc. 2006, 128, 3248–3255. Tandon, S. P.; Gupta, J. P. Phys. Status Solidi 1970, 38, 363–367.
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