Quantum Dot Superlattice Thermoelectric Materials and Devices. T. C. Harman, P. J. Taylor, M. P. Walsh, and B. E. LaForge. Supplementary Material

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1 Quantum Dot Superlattice Thermoelectric Materials and Devices T. C. Harman, P. J. Taylor, M. P. Walsh, and B. E. LaForge Supplementary Material Some Properties of Ternary Materials In Table I (see printed version), the measured Seebeck coefficient, Hall carrier concentration and Hall carrier mobility (the latter two properties calculated from van der Pauw measurements), and the calculated materials TE figure of merit are displayed for two typical PbSeTe QDSL samples (the lattice thermal conductivity calculated from the n-qdsl B device test data is discussed). Typical PbSe 0.98 Te 0.02 /PbTe sample n-qdsl B consisted of 8005 periods, each period approximately 13.0 nm thick, leading to a film thickness of mm, with an equivalent alloy composition (EAC) of PbSe 0.13 Te The equivalent alloy composition, x, where x is defined in the ternary alloy expression PbSe x Te 1-x, is 0.98 for the dot layer part of the films. Data on bulk samples of PbSe indicate that the Seebeck coefficient of PbSe follows the same curve as PbTe and both may be described by an empirical Seebeck coefficient, S, vs carrier concentration, n, relationship (S1,S2). The Seebeck coefficients (S1,S2) of the n-type PbSe 0.98 Te 0.02 /PbTe QDSL samples are much greater than the values calculated from the S vs n relationship for high mobility PbTe or PbSe at 300 K. It is seen from Table 1 (see printed version) and Ref. 1 (see printed version) that for sample n-qdsl B, the Seebeck coefficient is 75% higher than measured for bulk or homogeneous film n-type PbTe or PbSe for a given carrier concentration. In Table S1, we have summarized various experimental measurements that have been obtained for the p-type samples. The large increases in Seebeck coefficient and ZT (relative to PbTe) in both n-type and p-type samples are

2 attributed to multiple factors such as the lowering of the lattice thermal conductivity below the values of the homogeneous pseudobinary PbSe x Te 1-x alloys, due to the enormous number density of interfaces between dissimilar materials considering the presence of many PbSe 0.98 Te 0.02 QD s embedded in a PbTe matrix, superimposed on a 2-dimensional superlattice/wetting layer structure. Also, excess Te relative to the stoichiometric composition (S3), appears to result in a more favorable carrier scattering mechanism which also enhances the Seebeck coefficient. The Pb-chalcogenides are not line compounds (S4) so that slight excesses of Pb/Sn or chalcogenide occur even at the relatively low growth temperatures used in MBE. A slight Te excess makes the material chalcogenide-rich. Since MBE is a non-equilibrium growth method, excess chalcogenide beyond the solid solubility limit can be incorporated in the growing material. Even at the growth temperature of K, PbTe and PbSe have some solid solubility (S4). At significantly higher growth temperatures than K, most of the excess Te is re-evaporated and power factors, i.e. S 2 /ρ, are reduced. At significantly lower growth temperatures than K, the carrier mobility is adversely effected and an enhanced power factor is not observed. A Pb-chalcogenide flux ratio of approximately 7 is used, rather than the standard flux ratio of 10. We have found that the lower flux ratio yields an enhanced power factor effect for the K growth temperatures. Excess Te makes the growing surface chalcogenide-rich which allows the Bi atoms to incorporate on the Pb/Sn sublattice and act predominantly as donor impurities. The presence of PbSe 0.98 Te 0.02 quantum dots embedded in a PbTe matrix is believed to result in some partial confinement (S5) of electrons in the QD s and increased power factors. 2

3 Some Properties of Quaternary Materials Quaternary PbSnSeTe QDSL structures, having comparable Seebeck coefficient values to the PbSeTe/PbTe QDSL structures have been grown (S1,S2) but the quaternary materials can be designed to have lower energy gaps and reduced lattice thermal conductivities, thus higher ZT values are anticipated. In order to calculate the desired compositions of the QD Pb 1-x Sn x Se y Te 1-y layers embedded in PbTe matrices grown on BaF 2 (111) substrates by MBE, we used the following relationships (S6) for energy gap, Eg (ev) and lattice constant a o (Å) in terms of x,y, and T, Eg (ev) = T 0.05y 0.52x 0.37xy (Eq. S1) and a (Å) = y x xy (Eq. S2) where T is the temperature in degrees Kelvin. Figure S1 shows the Eg and lattice constant versus mole fraction SnSe for the QD/wetting layer component (PbSnSeTe) of the QD materials we are growing. Also, the Eg and lattice constant of the PbTe matrix layer component is indicated in Fig. S1. With Quaternary QDSL materials, we expect to gain three ways as follows: 300 K Eg can be reduced by half, which is believed to be near optimum (S7); the band offsets are increased; and finally the thermal conductivity is expected to be lower. In Table S1, we have summarized various experimental measurements that have been obtained for the p- type ternary QDSL samples. The large Seebeck coefficient and ZT (relative to bulk PbTe and PbSeTe alloys) enhancement found in n-type QDSL films may occur in p-type films, based on recent unpublished (S8) results. Some Growth Results 3

4 The MBE growth of films of both ternary and quaternary QDSL structures was carried out in an Applied Epi 2-inch Gen II MBE growth chamber. The growth rate was 0.98 µm/hr for n-qdsl B but growth rates above 2 µm/hr have been used. The beam equivalent pressures (BEP) of the PbTe, PbSe, and SnSe fluxes were used to calculate the overall composition of alloy films. The BEPs used were the average of measured values before, during, and after growth of each film by placing an ion gauge at the substrate position in the MBE system. The mole fraction, x, of SnSe in the dot layer was calculated by using the relationship x =BEP SnSe /(BEP SnSe + BEP PbSe ) (Eq. S3) where the subscript denotes the BEP of the material being measured. The measured average fluxes, along with the calculated compositions of SnSe, are shown in Table SII. For growth run n-qua A for example, the dot composition is calculated to be (PbSe 0.98 Te 0.02 ) 0.84 (SnSe) Comparing with the generic composition, Pb 1-x Sn x Se y Te 1-y, the values x = and y = are obtained. Thus, from Eq. S2 we calculate Eg (ev) = 120 mev at 300 K for n- Qua A. In order to find the overall composition of the equivalent homogenized quaternary (EHQ) structure, we introduce the formula (PbTe) 1-y' (Pb 1-x Sn x Se y Te 1-y ) y' as the mean PbSnSeTe composition of the structure, i.e. the composition of the material if it was totally homogenized. In order to introduce some systematic variations into the experiments, we decided to preset the mole fraction of PbSnSeTe as y' = 0.13 using y = CCPbSnSeTe/(CCPbSnSeTe + CCPbTe) (Eq. S4) for the mean PbSnSeTe overall alloy composition. CC is the timing count that is programmed into the computer prior to the growth run for the Pb 0.84 Sn 0.16 Se Te part of the deposition and for the PbTe part of the deposition, i.e. the computer counts for each particular shutter arrangement. Although 4

5 approximately fixed for a particular growth run, the dot physical size and areal number density can also be changed systematically by varying the amount of Pb 0.84 Sn 0.16 Se Te and PbTe in each layer. The temperature of the effusion cells are adjusted until the growth rates (GR) are approximately the same for the matrix and dot material (determined in separate calibration growth runs), i.e. GR PbSnSeTe = GR PbTe. This condition allows for precise control of the composition of the dot material and the matrix material by simply adjusting the relative deposition times. For convenience, the nominal composition of the equivalent homogeneous quaternary (EHQ) alloy is given approximately by Eq. S4. For example, during CC PbSnSeTe, the PbSe and SnSe shutters covering the PbSe and SnSe effusion cells are open while the PbTe shutter covering the PbTe effusion cell is closed and vice versa for CC PbTe. The Te and Bi 2 Te 3 shutters are kept open throughout the growth runs for these QDSL structures. The Te is supplied to ensure the desired stoichiometry is maintained. The Bi 2 Te 3 is used as the source of the Bi n-type dopant and Tl 2 Se is used as the source of the Tl p-type dopant. The average beam equivalent fluxes for PbTe, SnSe and PbSe as well as the mean PbSnSeTe composition of the QDSL films are given in Tables S2 and S3. For example, knowing the deposition times and Eq. (S4), we calculate the mean PbSnSeTe composition of n-qua A as (PbTe) 0.87 (Pb 0.84 Sn 0.16 Se Te ) 0.13, which can also be written as Pb Sn Se Te for the EHQ alloy of the QDSL structure. Some thermoelectric properties of the first quaternary QDSL PbSnSeTe materials are given in Table S1. The Seebeck coefficient, electrical resistivity, and thermal conductivity (of n-qdsl B in Table 1(see printed version)) are measured values, whereas the lattice thermal conductivity is calculated using the Weidemann-Franz law to be 3.3 mw/cm-k. 5

6 The EHQ alloy composition for the overall structure of n-qua A is Pb Sn Se Te We use this EHQ to calculate the lattice constant as Å from Eq. (S2). Also, we have measured the position of the (444) Bragg reflection of n-qua A using x-ray diffraction (XRD). We used this XRD result to obtain our independent measurement of the lattice constant of the EHQ alloy as Å. The agreement between the two methods is excellent. The period of the quaternary QDSL samples was calculated from the growth variables and is given in Table S3. The period was also determined to be 165Å from the XRD (444) satellite peaks for n-qua A, which is in good agreement with the growth variable method. The number of periods was 251 and 2258 for growth runs n-qua A and n-qua B, respectively. Note that our PbTe matrix or spacer layer and (PbSeTe or PbSeSnTe) dot layer thicknesses are significantly smaller than those used by Kang et al. (S9-S10), for thin films of the PbEuTe(spacer layer)/pbse(dot layer) self-assembled QDSL system. Some Factors Needed for High ZT QDSL Materials at 300 K A lattice constant mismatch in Pb-chalcogenides is necessary to provide the strain required for the Stranski-Krastanov growth mode to occur and quantum dot structures to be formed (S10). Lattice constant mismatch between the matrix and dot material should be approximately 5% for the Pb-chalcogenide materials. The dot material used for the QDSL structures has a smaller lattice constant than the matrix material. The difference in the lattice constant between PbTe, i.e Å, and the QDSL layer Pb 0.84 Sn 0.16 Se Te 0.017, (i.e Å for sample n-qua A) is 5.4%. To the best of our knowledge, only the Pb-salt materials have both desirable QD formation characteristics and high static dielectric constants. High static dielectric constants are believed advantageous in low temperature TE 6

7 materials for the suppression of ionized impurity scattering. Hence, relatively high carrier mobilities at high carrier concentrations can occur in both the matrix and dot layers. Thus, electrical resistivities are unusually low at the optimal carrier concentration for high ZT. It is also advantageous to have a material with multiple energy-band pockets for the electrons and holes. The PbSnSeTe materials have four pockets for both electrons and holes, which yields a higher density-of-states effective mass than materials having single pockets. The high effective masses lead to relatively high Seebeck coefficients for a given carrier concentration. These factors contribute to the QDSL PbSnSeTe materials having 300 K TE power factors comparable to bulk (Bi,Sb) 2 (Se,Te) 3 alloys. It is well known that, in general, binary compounds have higher lattice thermal conductivities than pseudobinary, e.g. PbSeTe, and pseudoternary, e.g. PbSnSeTe alloys. The work on homogeneous bulk PbSeTe pseudobinary alloys (S11-S12) has established that the lattice thermal conductivity of these alloys at 300 K decreases a factor of 2.0 to 2.5 as x is decreased to 0.5. Recently, evidence was added that the lattice thermal conductivity (S13) of Pb 1-x Sn x Te pseudobinary alloys behaves like the PbSeTe alloys, i.e. a very low value for x = 0.5. This behavior indicates that the PbSnSeTe quaternary alloys may have even lower lattice thermal conductivity values than either PbSeTe or PbSnTe alloys. Recent work (S14) indicates the potential for extremely low lattice thermal conductivity values for in-plane QDSL materials due to the phase change of materials at interfaces and the effect of the QDs on the phonon group velocity at interfaces. A factor of approximately two reduction in the in-plane lattice thermal conductivity over in-plane quantum wells was predicted in the 10 to 15 % volume fraction range of dots. We estimate that the volume fraction of the MBE grown QDSL samples are in the 10 to 13 % volume fraction range of 7

8 dots. A large elastic constant mismatch at the interfaces between the QDs and the matrix layer contributes to the reduction of the lattice thermal conductivity at 300 K. The total bandgap offset between the matrix and dots may be increased from 50 mev to 192 mev in quaternary alloys and this increased bandgap offset may enhance carrier confinement within the dots. For temperatures in the vicinity of 300 K and below, it seems reasonable (S14- S16) that lattice thermal conductivities for the equivalent quaternary QDSL structures may reach values lower than 3.3 mw/cm-k, due to the combination of alloy and interface phonon scattering in more optimized structures. The physical mechanisms responsible for the enhancement of the Seebeck coefficient are believed to be more nearly optimized carrier scattering mechanisms and quantum effects (S1,S17,S18) but other mechanisms may play a role, such as strain induced shifts of the QD energy levels. QD strain effects may also assist with phonon scattering. Comparison of the luminescence photon energy with that of bulk PbSe shows the strong influence of carrier confinement (S19) in PbEuSeTe QDSL structures. Some confinement of electrons in n-type and holes in p-type in PbSnSeTe QDSL structures would be expected in view of these results. The optimized engineered structure has the potential to yield still higher values for the Seebeck coefficient and lower values of lattice thermal conductivity than indicated in Table 1 (see printed version). It is believed that ZTs comparable to n-type values may be possible for p-type QDSL structures because of the similarity of the conduction and valence bands in PbSnSeTe materials and early experimental results for p-type QDSL structures (S8). References and Notes: 1. T. C. Harman, P. J. Taylor, D. L. Spears, M. P. Walsh, J. Electron. Mater. Lett. 29, L1 (2000). 8

9 2. T. C. Harman, P. J. Taylor, D. L. Spears, M. P. Walsh, in the 18 th Int. Conf. on Thermoelectrics: ICT Symposium Proc., Baltimore, p. 280, Institute of Electrical and Electronics Engineers, Inc., Piscataway, NJ, T. C. Harman, P. J. Taylor, D. L. Spears, M. P. Walsh, J. Electron. Mater. Lett. 28, L1 (1999). 4. T. C. Harman, J. Nonmetals 1, 183 (1973). 5. M. S. Dresselhaus, Ch. 1, Recent Trends in Thermoelectric Materials Research III, Semiconductors and Semimetals, Vol. 71, Vol. Ed. T.W. Tritt, Series Eds. R. K. Willardson and E. R. Weber, Academic Press, London (2001) p A. I. Tkachuk, O. N. Tsarenko, Inorganic Materials 37, 224 (2001). 7. H. J. Goldsmid, Proc. of 18 th Int. Conf. on Thermoelectrics, Baltimore, MD, (1999) p T. C. Harman, D.L. Spears, D.R. Calawa, S.H. Groves, M.P. Walsh, Proc. XVI Intl. Conf. on Thermoelectrics, Dresden, Germany, (1997). 9. H. H. Kang et al., Mat ls. Sci. & Eng. B80, 104 (2001). 10. G. Springholz, V. Holy, M. Pinczolits, G. Bauer, Science 282, 734(1998). 11. A. F. Ioffe, Doklady Akademie Nauk SSSR 106, 981(1956). 12. E. D. Devyatkova, V. V. Tikhonov, Sov. Phys.-Solid State 7, 1427(1965). 13. M. Orihashi, Y. Noda, L-D. Chen, T. Goto, T. Hirai, J. Phys. Chem. Solids 61, 919 (2000). 14. A. Khitun, K. L. Wang, G. Chen, Nanotechnology 11, 327 (2000) and references therein. 9

10 15. G. A. Slack, Solid State Phys. 34, 1 (1979).(see Table XVII). 16. H. Beyer et al., Mat. Res. Symp., 626, (2001). 17. L, D. Hicks, T. C. Harman, X. Sun, M. S. Dresselhaus, Phys. Rev. B52, R10493 (1996). 18. D. A. Broido, T. L. Reinecke, Appl. Phys. Lett. 70, 2834 (1997). 19. M. Aigle et al., Phys. Stat. Sol. (b) 224, 223 (2001). 20. This work was sponsored by the Department of the Navy and the Defense Advanced Research Projects Agency (DARPA) under AF Contract No. F C The opinions, interpretations, conclusions and recommendations are those of the authors and are not necessarily endorsed by the United States Government. SUPPLEMENTAL TABLE S1 300-K thermoelectric properties of Tl-Doped (p-type) PbSe 0.98 Te 0.02 /PbTe Samples Grown by MBE, and Bi-doped quaternary PbSnSeTe/PbTe QDSL samples. Sample No. Seebeck Coefficient (µv/k) ZT* Carrier Concentration (cm -3 ) Carrier Mobility (cm 2 /V-s) p-qdsl A x p-qdsl B x n-qua A x n-qua B x *These ZT values are based on lattice thermal conductivity values calculated from the device test data. 10

11 TABLE S2 The estimated mean composition (or mole fraction of SnSe) and Eg of the QD part of the Pb 1-x Sn x Se y Te 1-y /PbTe QDSL samples as determined by the BEP method, i.e. Eq. S3. Run Number BEP SnSe (10-6 Torr) BEP PbSe (10-6 Torr) Approx. Mean SnSe Composition (Eq.S3), Estimated Energy Gap (ev) x n-qua A n-qua B TABLE S3 The approximate composition and period of the mean equivalent quaternary QDSL n-qua A and n-qua B samples as determined by the BEP/computer count method, i.e. Eqs. S3 and S4. Run Number BEP PbTe (10-6 Torr) Approx. Composition (Eg.5), y' Period (Å) n-qua A n-qua B FIGURE CAPTION Figure S1. The energy gap and the lattice constant versus mole fraction SnSe for the dot component of the quaternary QDSL materials is displayed. Also, the energy gap and lattice constant for the matrix component of the QDSL is indicated. 11

12 350 P bt e Matrix P bt e Matrix 6.5 E nergy G ap (mev ) Quaternary Dot A lloy a = 0.117x Quaternary Dot A lloy E g = 889x a L attic e C ons tant (ÅA ) x, S ns e Mole F rac tion