RELATED APPLICATIONS 
       [0001]    This application claims the benefit of provisional patent application serial number 61/447,459, filed Feb. 28, 2011, the disclosure of which is hereby incorporated herein by reference in its entirety. 
     
    
     GOVERNMENT SUPPORT 
       [0002]    This invention was made with government funds under contract number AR0000033 awarded by ARPA-E. The U.S. Government may have rights in this invention. 
     
    
     FIELD OF THE DISCLOSURE 
       [0003]    The present disclosure relates to thermoelectric materials. 
       BACKGROUND 
       [0004]    In recent years, an increasing concern of global energy usage and its impact on the environment, in particular global warming, has resulted in extensive research into novel technologies of generating electrical power. 
         [0005]    Thermoelectric power generators have emerged as a promising alternative green technology due to their distinct advantages. In general, thermoelectric power generators offer a potential application in the direct conversion of waste-heat energy into electrical power irrespective of the cost of the thermal energy input. 
         [0006]    A thermoelectric device can be used as a thermoelectric power generator or a thermoelectric cooler. Applications of these devices range from, for example, electronic thermal management and solid state refrigeration to power generation from waste heat sources. A thermoelectric generator is a solid state device that provides direct energy conversion from thermal energy (heat) due to a temperature gradient into electrical energy based on a so-called “Seebeck effect.” The thermoelectric power cycle, with charge carriers (electrons) serving as the working fluid, follows the fundamental laws of thermodynamics and intimately resembles the power cycle of a conventional heat engine. Thermoelectric power generators offer several distinct advantages over other technologies including, for example, high reliability, small footprint but with potential scaling to meet large area applications, lightweight, flexibility, and non-position dependency. 
         [0007]    A major challenge of thermoelectric devices is their relatively low conversion efficiency, which is typically ˜5%. This has been a major cause in restricting their use in electrical power generation and thermal management to specialized fields where space and reliability are a premium. 
         [0008]    The figure-of-merit (ZT) of a thermoelectric material is a dimensionless unit that is used to compare the efficiencies of various materials. ZT is determined by three physical parameters: the thermopower α (also known as a Seebeck coefficient), electrical conductivity σ, and thermal conductivity k=k e +k ph , where the k e  and k ph  are thermal conductivities of electrons and phonons, respectively; and absolute temperature T: 
         [0000]    
       
         
           
             ZT 
             = 
             
               
                 
                   
                     α 
                     2 
                   
                    
                   σ 
                 
                 
                   ( 
                   
                     
                       k 
                       e 
                     
                     + 
                     
                       k 
                       ph 
                     
                   
                   ) 
                 
               
                
               
                 T 
                 . 
               
             
           
         
       
     
         [0009]    Maximum ZT in bulk thermoelectric materials is governed by the intrinsic properties of the material system. Most candidates require low thermal conductivity as the driving force for enhanced ZT because of the inverse relationship between the Seebeck coefficient and electrical conductivity. This interdependence and coupling between the Seebeck coefficient and the electrical conductivity makes it difficult to increase ZT&gt;1, despite nearly five decades of research. Increasing this value to 2.0 or higher will disrupt existing technologies and will ultimately enable more widespread use of thermoelectric systems. 
         [0010]    In L. D. Hicks and M. S. Dresselhaus,  Effect of quantum - well structures on the thermoelectric figure of merit, Phys. Rev. B , Vol. 47, No. 19, 12727-12731 (May 15, 1993), Hicks and Dresselhaus pioneered the concept of quantum confined structures that could significantly increase ZT by independently optimizing the Seebeck coefficient and electrical conductivity. Since then, numerous research groups have adopted nano-structured approaches to increase ZT and have ultimately determined that the enhancement resulted from reduced thermal conductivity from phonon scattering at the interfaces. In J. P. Heremans, V. Jovovic, E. S. Toberer, A. Saramat, K. Kurosaki, A. Charoenphakdee, S. Yamanaka, and G. J. Snyder,  Enhancement of Thermoelectric Efficiency in PbTe by Distortion of the Electronic Density of States, Science , Vol. 321, 554-557 (Jul. 25, 2008), Heremans showed a significant improvement in the Seebeck coefficient by distortion of the electronic density of states through the use of impurity levels. 
         [0011]    An alternative approach recently investigated to enhance thermoelectric performance using nano-structured materials is hot carrier transport via thermionic emission. The design criteria require a potential barrier of several k B T (where k is Boltzman constant, and T is temperature) to selectively transport high-energy “hot” carriers. The distribution of hot carriers at energy greater than the barrier height with respect to the Fermi level defines the Seebeck coefficient and the integral of this distribution defines the conductivity. Enhancement of the Seebeck coefficient has been observed by hot carrier transport for several material systems. This enhancement will be offset to some extent by a decrease in the electrical conductivity since fewer carriers are participating in transport. Thus, the overall impact on ZT will be highly dependent on the material system. 
         [0012]    There is a need for a nano-structured thermoelectric material formed in a material system that maximizes, or at least significantly improves, ZT through hot carrier transport via thermonic emission. 
       SUMMARY 
       [0013]    Embodiments of a thin-film heterostructure thermoelectric material and methods of fabrication thereof are disclosed. In general, the thermoelectric material is formed in a Group IIa and IV-VI materials system. The thermoelectric material includes an epitaxial heterostructure and exhibits high heat pumping and figure-of-merit performance in terms of Seebeck coefficient, electrical conductivity, and thermal conductivity over broad temperature ranges through appropriate engineering and judicious optimization of the epitaxial heterostructure. 
         [0014]    The epitaxial heterostructure forms one or more potential barriers that assist carrier heat transport by thermonic emission. More specifically, in one embodiment, the epitaxial heterostructure formed in a Group IIa and IV-VI materials system and includes a first well layer, a barrier layer on a surface of the first well layer, and a second well layer on a surface of the barrier layer opposite the first well layer, where at least one of the first well layer, the barrier layer, and the second well layer includes a Group IIa and IV-VI material. A bandgap of the barrier layer is greater than a bandgap of each of the first and second well layers. 
         [0015]    In another embodiment, the epitaxial heterostructure includes multiple barrier layers separated by multiple well layers. A bandgap of each well layer is less than a bandgap of all adjacent barrier layers in the epitaxial heterostructure. The well layers and the barrier layers in the epitaxial heterostructure are all formed in a Group IIa and IV-VI materials system. 
         [0016]    In one embodiment, each of the multiple barrier layers includes one or more layers of a first material in a Group IIa and IV-VI materials system and each of the multiple well layers includes one or more layers of a second material in the Group IIa and IV-VI materials system, where a bandgap of each barrier layer is greater than a bandgap of all adjacent well layers in the epitaxial heterostructure. 
         [0017]    In one particular embodiment, each barrier layer includes one or more layers of Pb (1-x-y) Sr x Sn y Se (0&lt;x&lt;1; 0&lt;y&lt;1) material, and each well layer includes one or more layers of Pb (1-a-b) Sr a Sn b Se (0&lt;a&lt;1; 0&lt;b&lt;1) material, where a bandgap of the Pb (1-x-y) Sr x Sn y Se (0&lt;x&lt;1; 0&lt;y&lt;1) material is greater than a bandgap of the Pb (1-a-b) Sr a Sn b Se (0&lt;a&lt;1; 0&lt;b&lt;1) material. 
         [0018]    In another embodiment, at least one of the multiple barrier layers in the epitaxial heterostructure is a short period superlattice. The superlattice includes a number of superlattice barrier layers separated by superlattice well layers, where an effective bandgap of the superlattice is greater than a bandgap of all adjacent well layers in the epitaxial heterostructure. In one particular embodiment, the superlattice barrier layers are Pb (1-x-y) Sr x Sn y Se (0&lt;x&lt;1; 0&lt;y&lt;1) material layers, and the superlattice well layers are Pb (1-x′-y′) Sr x′ Sn y′ Se (0&lt;x′&lt;1; 0&lt;y′&lt;1) material layers, where a bandgap of each Pb (1-x-y) Sr x Sn y Se material layer is greater than a bandgap of all adjacent Pb (1-x′-y′) Sr x′ Sn y′ Se material layers. A period thickness of the superlattice is less than a tunneling probability length at a given operating temperature in order to scatter phonons at interfaces between superlattice barrier layers and superlattice well layers in the superlattice. Furthermore, in another embodiment, thicknesses of the superlattice barrier layers and the superlattice well layers in the superlattice are varied to create an energy grading across the superlattice to increase cross-plane effective carrier density transport. 
         [0019]    In yet another embodiment, at least one of the well layers in the epitaxial heterostructure is a short period superlattice. The superlattice includes a number of superlattice barrier layers separated by superlattice well layers, where an effective bandgap of the superlattice is less than a bandgap of all adjacent barrier layers in the epitaxial heterostructure. In one particular embodiment, the superlattice well layers are Pb (1-a-b) Sr a Sn b Se (0&lt;a&lt;1; 0&lt;b&lt;1) material layers, and the superlattice barrier layers are Pb (1-a′-b′) Sr a′ Sn b′ Se (0&lt;a′&lt;1; 0&lt;b′&lt;1) material layers, where a bandgap of each Pb (1-a′-b′) Sr a′ Sn b′ Se material layer is greater than a bandgap of all adjacent Pb (1-a-b) Sr a Sn b Se material layers. A period thickness of the superlattice is less than a tunneling probability length at a given operating temperature in order to scatter phonons at interfaces between the superlattice barrier layers and the superlattice well layers in the superlattice. Furthermore, in another embodiment, thicknesses of the superlattice barrier layers and the superlattice well layers in the superlattice are varied to create an energy grading across the superlattice to increase cross-plane effective carrier density transport. 
         [0020]    In yet another embodiment, at least one of the barrier layers in the epitaxial heterostructure is a short period superlattice and at least one of the well layers in the epitaxial heterostructure is a short period superlattice. 
         [0021]    Those skilled in the art will appreciate the scope of the present disclosure and realize additional aspects thereof after reading the following detailed description of the preferred embodiments in association with the accompanying drawing figures. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWING FIGURES 
         [0022]    The accompanying drawing figures incorporated in and forming a part of this specification illustrate several aspects of the disclosure, and together with the description serve to explain the principles of the disclosure. 
           [0023]      FIG. 1  illustrates a thin-film thermoelectric material having an epitaxial heterostructure including a well layer and a barrier layer according to one embodiment of the present disclosure; 
           [0024]      FIG. 2  illustrates a thin-film thermoelectric material having an epitaxial heterostructure including multiple barrier layers separated by well layers according to another embodiment of the present disclosure; 
           [0025]      FIG. 3  illustrates an embodiment of a barrier layer for the thermoelectric material of  FIGS. 1 and 2  where the barrier layer includes a short period superlattice according to one embodiment of the present disclosure; 
           [0026]      FIG. 4  illustrates an embodiment of a barrier layer for the thermoelectric material of  FIGS. 1 and 2  where the barrier layer includes a short period superlattice according to another embodiment of the present disclosure; 
           [0027]      FIG. 5  is an energy band diagram for a barrier layer and adjacent well layers according to one embodiment of the present disclosure; 
           [0028]      FIG. 6  is an energy band diagram for a barrier layer and adjacent well layers according to one exemplary embodiment where the barrier layer is formed by a short period superlattice that creates an increasing energy grading to increase cross-plane effective carrier density transport; 
           [0029]      FIG. 7  illustrates an embodiment of a well layer for the thermoelectric material of  FIGS. 1 and 2  where the well layer includes a short period superlattice according to one embodiment of the present disclosure; 
           [0030]      FIG. 8  illustrates an embodiment of a well layer for the thermoelectric material of  FIGS. 1 and 2  where the well layer includes a short period superlattice according to another embodiment of the present disclosure; 
           [0031]      FIG. 9  is an energy band diagram for a barrier layer and adjacent well layers according to one exemplary embodiment where the well layers are formed by short period superlattices that create increasing energy gradings to increase cross-plane effective carrier density transport; and 
           [0032]      FIG. 10  is an energy band diagram for a barrier layer and adjacent well layers according to one exemplary embodiment where the barrier layer and the well layers are formed by short period superlattices that create increasing energy gradings to increase cross-plane effective carrier density transport. 
       
    
    
     DETAILED DESCRIPTION 
       [0033]    The embodiments set forth below represent the necessary information to enable those skilled in the art to practice the embodiments and illustrate the best mode of practicing the embodiments. Upon reading the following description in light of the accompanying drawing figures, those skilled in the art will understand the concepts of the disclosure and will recognize applications of these concepts not particularly addressed herein. It should be understood that these concepts and applications fall within the scope of the disclosure and the accompanying claims. 
         [0034]    The generation of high heat pumping capacity and high conversion efficiency from semiconductor thin-film thermoelectrics is very attractive owing to the compact and efficient properties of these devices. Applications of these devices range from, for example, electronic semiconductor chip cooling, solid state refrigeration, to power generation from waste heat sources. There have been many advances in thin-film thermoelectrics over the past few years, with many researchers concentrating on device fabrication, device physics, and systems applications. 
         [0035]      FIG. 1  illustrates a thin-film thermoelectric material  10  (hereinafter “thermoelectric material  10 ”) according to one embodiment of the present disclosure. In general, the thermoelectric material  10  is formed in a Group IIa and IV-VI materials system. As used herein, the “Group IIa and IV-VI materials system” is a system of Group IIa materials, Group IV-VI materials, and Group IIa and IV-VI materials. In one preferred embodiment, the Group IIa and IV-VI materials system is defined as Pb (1-x-y) Sr x Sn y Se (0&lt;x&lt;1; 0&lt;y&lt;1) materials, where x and y denote the relative mole fraction of the atomic species. In contrast, a Group IIa material is a material that includes only Group IIa elements (e.g., Strontium), a Group IV-VI material is a material that includes only Group IV and Group VI elements (e.g., PbSe), and Group IIa and IV-VI materials are materials that include Group IIa, IV, and VI elements (e.g., PbSrSe). 
         [0036]    As illustrated, the thermoelectric material  10  includes a heterostructure  12  formed in the Group IIa and IV-VI materials system. The heterostructure  12  includes a well layer  14 , a barrier layer  16  on a surface of the well layer  14 , and another well layer  18  on a surface of the barrier layer  16  opposite the well layer  14 . The well layer  14 , the barrier layer  16 , and the well layer  18  are formed in the Group IIa and IV-VI materials system, and at least one, and potentially all, of the well layer  14 , the barrier layer  16 , and the well layer  18  includes a Group IIa and IV-VI material. Notably, the well layers  14  and  18  may or may not be formed of the same low bandgap material. The heterostructure  12  may be formed using any suitable epitaxial growth process. 
         [0037]    In general, a bandgap of the barrier layer  16  is greater than bandgaps of the well layers  14  and  18 , which are referred to herein as adjacent well layers of the barrier layer  16 . It should be noted that, when referring to the well layers  14  and  18  and the barrier layer  16 , a “high bandgap” material of the barrier layer  16  is a material in the Group IIa and IV-VI materials system having a bandgap that is greater than a bandgap of a “low bandgap” material in the Group IIa and IV-VI materials system of the adjacent well layers  14  and  18 . Likewise, the “low bandgap” material of the well layers  14  and  18  is a material in the Group IIa and IV-VI materials system having a bandgap that is less than a bandgap of the “high bandgap” material in the Group IIa and IV-VI materials system of the adjacent barrier layer  16 . 
         [0038]    In one embodiment, the well layer  14  is formed by one or more layers of the same low bandgap material in the Group IIa and IV-VI materials system. The barrier layer  16  is formed by one or more layers of the same high bandgap material in the Group IIa and IV-VI materials system. Lastly, the well layer  18  is formed by one or more layers of the same low bandgap material in the Group IIa and IV-VI materials system. Again, the low bandgap material used for the well layer  14  may be the same as or different than the low bandgap material used for the well layer  18 . 
         [0039]    As described below in detail, in another embodiment, the barrier layer  16  is a short period superlattice having a number of alternating high bandgap and low bandgap layers formed in the Group IIa and IV-VI materials system that together provide a desired effective, or combined, bandgap for the barrier layer  16 . Note that, when referring to the superlattice, “high bandgap” material layers are material layers formed in the Group IIa and IV-VI materials system having bandgaps that are greater than adjacent “low bandgap” material layers in the superlattice, and the “low bandgap” material layers are material layers formed in the Group IIa and IV-VI materials system having bandgaps that are less than bandgaps of adjacent “high bandgap” material layers in the superlattice. A period thickness of the superlattice is less than a tunneling probability length at a given operating temperature in order to scatter phonons at interfaces between the alternating high bandgap and low bandgap material layers in the superlattice. Furthermore, as also discussed below, thicknesses of the high bandgap and low bandgap material layers in the superlattice may be varied to create an energy grading across the superlattice to increase cross-plane effective carrier density transport. 
         [0040]    Like the barrier layer  16 , the well layer  14  may be a short period superlattice having a number of alternating high bandgap and low bandgap material layers formed in the Group IIa and IV-VI materials system that together provide a desired effective bandgap for the well layer  14 . Again note that, when referring to the superlattice, “high bandgap” material layers are material layers formed in the Group IIa and IV-VI materials system having bandgaps that are greater than bandgaps of adjacent “low bandgap” material layers in the superlattice, and the “low bandgap” material layers are material layers formed in the Group IIa and IV-VI materials system having bandgaps that are less than bandgaps of adjacent “high bandgap” material layers in the superlattice. A period thickness of the superlattice is less than a tunneling probability length at a given operating temperature in order to scatter phonons at interfaces between the alternating high bandgap and low bandgap material layers in the superlattice. Furthermore, as also discussed below, thicknesses of the high bandgap and low bandgap material layers in the superlattice may be varied to create an energy grading across the well layer  14  to increase cross-plane effective carrier density transport. In a similar manner, the well layer  18  may be a short period superlattice. Note that, depending on the particular implementation, the well layer  14 , the barrier layer  16 , and/or the well layer  18  may be implemented as a superlattice. 
         [0041]    In one preferred embodiment, the barrier layer  16  is or at least includes a high bandgap Pb (1-x-y) Sr x Sn y Se (0&lt;x&lt;1; 0&lt;y&lt;1) material, where x and y denote the relative mole fraction of the atomic species, and the well layers  14  and  18  are or include a low bandgap Pb (1-a-b) Sr a Sn b Se (0&lt;a&lt;1; 0&lt;b&lt;1) material, where a and b denote the relative mole fraction of the atomic species. The bandgap of the high bandgap Pb (1-x-y) Sr x Sn y Se material of the barrier layer  16  is greater than the bandgap of the low bandgap Pb (1-a-b) Sr a Sn b Se material of the adjacent well layers  14  and  18 . 
         [0042]    The high bandgap Pb (1-x-y) Sr x Sn y Se (0&lt;x&lt;1; 0&lt;y&lt;1) material is a semiconductor material and is doped either n-type or p-type. In one embodiment, a doping concentration of the high bandgap Pb (1-x-y) Sr x Sn y Se (0&lt;x&lt;1; 0&lt;y&lt;1) material is in the range of and including 1×10 17  and 5×10 19  dopants per cubic centimeters (cm 3 ) and has a bandgap of E g1 . In another embodiment, the doping concentration of the high bandgap Pb (1-x-y) Sr x Sn y Se (0&lt;x&lt;1; 0&lt;y&lt;1) material is in the range of and including 1×10 18  and 1×10 19  dopants per cm 3  and has a bandgap of E g1 . Similarly, the low bandgap Pb (1-a-b)Sr   a Sn b Se (0&lt;a&lt;1; 0&lt;b&lt;1) material is a semiconductor material and is doped either n-type or p-type. In one embodiment, a doping concentration of the low bandgap Pb (1-a-b) Sr a Sn b Se (0&lt;a&lt;1; 0&lt;b&lt;1) material is in the range of and including 1×10 17  and 5×10 19  dopants per cm 3  and has a bandgap E g2  that is less than E g1 . In another embodiment, the doping concentration of the low bandgap Pb (1-a-b) Sr a Sn b Se (0&lt;a&lt;1; 0&lt;b&lt;1) material is in the range of and including 1×10 18  and 1×10 19  dopants per cm 3  and has a bandgap of E g2  that is less than E g1 . 
         [0043]    In one embodiment, the barrier layer  16  is formed by one or more layers of the same high bandgap Pb (1-x-y) Sr x Sn y Se (0&lt;x&lt;1; 0&lt;y&lt;1) material. In another embodiment, the barrier layer  16  is comprised of a film of varying stoichiometry to engineer the conduction and valence band profiles. More specifically, the barrier layer  16  may include multiple layers of alternating high bandgap Pb (1-x-y) Sr x Sn y Se (0&lt;x&lt;1; 0&lt;y&lt;1) material and low bandgap Pb (1-x′-y′) Sr x′ Sn y′ Se (0&lt;x′&lt;1; 0&lt;y′&lt;1) material forming a short period superlattice, as described below in detail. 
         [0044]    Similarly, in one embodiment, the well layer  14  is formed by one or more layers of the same low bandgap Pb (1-a-b) Sr a Sn b Se (0&lt;a&lt;1; 0&lt;b&lt;1) material. In another embodiment, the well layer  14  is comprised of a film of varying stoichiometry to engineer the conduction and valence band profiles. More specifically, the well layer  14  may include multiple layers of alternating low bandgap Pb (1-a-b) Sr a Sn b Se (0&lt;a&lt;1; 0&lt;b&lt;1) material and high bandgap Pb (1-a′-b′) Sr a′ Sn b′ Se (0&lt;a′&lt;1; 0&lt;b′&lt;1) material forming a short period superlattice, as described below in detail. Likewise, in one embodiment, the well layer  18  is formed by one or more layers of the same low bandgap Pb (1-a-b) Sr a Sn b Se (0&lt;a&lt;1; 0&lt;b&lt;1) material. In another embodiment, the well layer  18  is comprised of a film of varying stoichiometry to engineer the conduction and valence band profiles. More specifically, the well layer  18  may include multiple layers of alternating low bandgap Pb (1-a-b) Sr a Sn b Se (0&lt;a&lt;1; 0&lt;b&lt;1) material and high bandgap Pb (1-a′-b′) Sr a′ Sn b′ Se (0&lt;a′&lt;1; 0&lt;b′&lt;1) material forming a short period superlattice, as described below in detail. 
         [0045]    The heterostructure  12  formed in the Group IIa and IV-VI materials system provides improved figure-of-merit (ZT) values over similar heterostructures formed in conventional material systems. This is due to both increasing the Seebeck coefficient and decreasing the thermal conductivity. Depending on the material system compared to, the heterostructure  12  provides a 2× to 10× improvement in the ZT value and possibly more. Note that while Pb (1-x-y) Sr x Sn y Se (0&lt;x&lt;1; 0&lt;y&lt;1) and Pb (1-a-b) Sr a Sn b Se (0&lt;a&lt;1; 0&lt;b&lt;1) materials are referred to above, other materials in the Group IIa and IV-VI materials system may be used for the well and barrier layers  14  through  18  in the heterostructure  12 . For example, in one alternative embodiment, the barrier layer  16  is or includes PbSrSe, and the well layers  14  and  18  are or include PbSe. In another embodiment, barrier layer  16  is or includes PbSe and the well layers  14  and  18  are or include PbSnSe. In all embodiments, a thickness of the barrier layer  16  must be larger than the tunneling probability length at a given operating temperature. The tunneling probability length is defined as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
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         [0000]    where L tunnel  is the minimum thickness, m* is the effective mass of the barrier material, q is the electron charge (1.6×10 −19  C), Φ is the barrier height in volts (V), k B  is Boltzmann&#39;s constant, T is temperature in Kelvin, and h is Planck&#39;s constant. 
         [0046]    Lead-chalcogenide materials, such as Pb (1-x-y) Sr x Sn y Se (0&lt;x&lt;1; 0&lt;y&lt;1) and Pb (1-a-b) Sr a Sn b Se (0&lt;a&lt;1; 0&lt;b&lt;1) have intrinsically low thermal conductivity, high carrier n and p-type mobility, and a wide bandgap tuning range, compared to other material systems. Further, Group IV-VI materials crystallize in the rock-salt structure, in contrast to tetrahedrally-coordinated Group IV semiconductors like diamond, silicon, germanium and the Group III-V (GaAs, InAs, AlAs, GaP, etc.) or Group II-VI semiconductors (CdTe, ZnTe, etc.). As a result, many physical and electronic properties of the Group IIa and IV-VI materials system described herein differ from that of the tetrahedrally-bonded semiconductors. Also, the lead-salt compounds are mechanically much softer than their tetrahedrally-bonded counterparts resulting in higher tolerance to lattice strain and thermal expansion mismatch. 
         [0047]      FIG. 2  illustrates the thermoelectric material  10  according to another embodiment of the present disclosure. In this embodiment, rather than having one barrier layer  16 , the heterostructure  12  includes a number of barrier layers  16 - 1  through  16 -N separated by corresponding well layers  14 - 1  through  14 -N. The heterostructure  12  is terminated at both ends by well layers, namely, the well layer  14 - 1  and the well layer  18 . The number (N) is an integer greater than or equal to 1. For example, the number (N) may be an integer in a range of and including 1 to 1000, but is not limited thereto. The heterostructure  12  of  FIG. 2  increases the Seebeck coefficient through thermonic emission, and decreases the thermal conductivity through interface scattering at the interfaces between the well layers  14 - 1  through  14 -N and  18  and the adjacent barrier layers  16 - 1  through  16 -N. 
         [0048]    As discussed above with respect to the barrier layer  16 , the barrier layers  16 - 1  through  16 -N are or include a high bandgap material in the Group IIa and IV-VI materials system. In one embodiment, each of the barrier layers  16 - 1  through  16 -N is formed by one or more layers of the same high bandgap Pb (1-x-y) Sr x Sn y Se (0&lt;x&lt;1; 0&lt;y&lt;1) material. In another embodiment, at least one of the barrier layers  16 - 1  through  16 -N, and potentially all of the barrier layers  16 - 1  through  16 -N, is comprised of a film of varying stoichiometry to engineer the conduction and valence band profiles. More specifically, at least one of the barrier layers  16 - 1  through  16 -N may be a short period superlattice including multiple layers of alternating high bandgap Pb (1-x-y) Sr x Sn y Se (0&lt;x&lt;1; 0&lt;y&lt;1) material and low bandgap Pb (1-x′-y′) Sr x′ Sn y′ Se (0&lt;x′&lt;1; 0&lt;y′&lt;1) material, as described below in detail. 
         [0049]    Similarly, in one embodiment, the well layers  14 - 1  through  14 -N are or include a low bandgap material in the Group IIa and IV-VI materials system. In one embodiment, each of the well layers  14 - 1  through  14 -N is formed by one or more layers of the same low bandgap Pb (1-a-b) Sr a Sn b Se (0&lt;a&lt;1; 0&lt;b&lt;1) material. In another embodiment, at least one of the well layers  14 - 1  through  14 -N, and potentially all of the well layers  14 - 1  through  14 -N, is comprised of a film of varying stoichiometry to engineer the conduction and valence band profiles. More specifically, at least one of the well layers  14 - 1  through  14 -N may be a superlattice including multiple layers of alternating low bandgap Pb (1-a-b) Sr a Sn b Se (0&lt;a&lt;1; 0&lt;b&lt;1) material and high bandgap Pb (1-a′-b′) Sr a′ Sn b′ Se (0&lt;a′&lt;1; 0&lt;b′&lt;1) material, as described below in detail. 
         [0050]      FIG. 3  illustrates one of the barrier layers  16 - 1  through  16 -N of  FIG. 2  (hereinafter referred to as barrier layer  16 -X), where the barrier layer  16 -X is a short period superlattice  20  according to one embodiment of the present disclosure. Note that this discussion is equally applicable to the barrier layer  16  of  FIG. 1 . For convenience, the superlattice  20  is referred to herein as a barrier superlattice  20 . The barrier superlattice  20  includes a number of superlattice (SL) barrier layers  22 - 1  through  22 -N separated by superlattice (SL) well layers  24 - 1  through  24 -(N− 1 ). The superlattice barrier layers  22 - 1  through  22 -N are high bandgap material layers formed in the Group IIa and IV-VI materials system and having a bandgap E g,SLB . Preferably, the superlattice barrier layers  22 - 1  through  22 -N are high bandgap Pb (1-x-y) Sr x Sn y Se (0&lt;x&lt;1; 0&lt;y&lt;1) material layers. The superlattice barrier layers  22 - 1  through  22 -N may all be the same high bandgap material or two or more of the superlattice barrier layers  22 - 1  through  22 -N may be different high bandgap materials in the Group IIa and IV-VI materials system. 
         [0051]    The superlattice well layers  24 - 1  through  24 -(N− 1 ) are low bandgap material layers formed in the Group IIa and IV-VI materials system and having a bandgap E g,SLW , where E g,SLW &lt;E g,SLB . Preferably, the superlattice well layers  24 - 1  through  24 -(N− 1 ) are low bandgap Pb (1-x′-y′) Sr x′ Sn y′ Se (0&lt;x′&lt;1; 0&lt;y′&lt;1) material layers. The superlattice well layers  24 - 1  through  24 -(N− 1 ) may all be the same low bandgap material or two or more of the superlattice well layers  24 - 1  through  24 -(N− 1 ) may be different low bandgap materials in the Group IIa and IV-VI materials system. An effective, or combined, bandgap of the superlattice barrier layers  22 - 1  through  22 -N and the superlattice well layers  24 - 1  through  24 -(N−1) is the bandgap of the barrier layer  16 -X, which as discussed above is greater than the bandgap of all adjacent well layer(s) in the heterostructure  12  for the thermoelectric material  10 . 
         [0052]    It should be noted that when referring to the barrier superlattice  20 , the “high bandgap” material layers forming the superlattice barrier layers  22 - 1  through  22 -N are material layers having bandgaps that are greater than bandgaps of the “low bandgap” material layers forming the adjacent superlattice well layers  24 - 1  through  24 -(N−1). Likewise, the “high bandgap” material layers forming the superlattice well layers  24 - 1  through  24 -(N−1) are material layers having bandgaps that are less than bandgaps of the “high bandgap” material layers forming the adjacent superlattice barrier layers  22 - 1  through  22 -N. 
         [0053]    In the barrier superlattice  20  of  FIG. 3 , a superlattice period thickness  26  of the barrier superlattice  20  is less than the tunneling probability length at a given operating temperature. Further, the superlattice barrier layers  22 - 1  through  22 -N and the superlattice well layers  24 - 1  through  24 -(N−1) are all of the same thickness such that the bandgaps of the superlattice barrier layers  22 - 1  through  22 -N and the bandgaps of the superlattice well layers  24 - 1  through  24 -(N−1) are constant over distance. The barrier superlattice  20  reduces thermal conductivity by phonon scattering at the interfaces between the superlattice barrier layers  22 - 1  through  22 -N and the adjacent superlattice well layers  24 - 1  through  24 -(N−1). 
         [0054]    It should be noted that since the barrier superlattice  20  is the structure of the barrier layer  16 -X, the barrier superlattice  20  is preferably terminated on both ends by superlattice barrier layers, namely, superlattice barrier layers  22 - 1  and  22 -N. However, the barrier superlattice  20  is not limited thereto. For instance, the barrier superlattice  20  may alternatively be terminated by superlattice well layers or terminated at one end by a superlattice barrier layer and the other end by a superlattice well layer. If terminated by a superlattice well layer, the superlattice well layer preferably has a bandgap that is greater than a bandgap of the adjacent well layer in the heterostructure  12  of the thermoelectric material  10 . 
         [0055]      FIG. 4  illustrates the barrier superlattice  20  according to another embodiment of the present disclosure. The barrier superlattice  20  of  FIG. 4  is similar to that of  FIG. 3 . However, in this embodiment, the barrier superlattice  20  includes superlattice well layers  24 - 1  through  24 - 4  and superlattice barrier layers  22 - 1  through  22 - 4  arranged as shown where thicknesses of the superlattice barrier layers  22 - 1  through  22 - 4  and thicknesses of the superlattice well layers  24 - 1  through  24 - 4  are varied to create an energy grading across the barrier layer  16 -X to increase cross-plane effective carrier density transport. More specifically, the superlattice period thickness  26  is less than the tunneling probability length at a given operating temperature. As the thicknesses of the superlattice barrier layers  22 - 1  through  22 - 4  increase, the bandgap of the barrier superlattice  20  also increases. 
         [0056]    In this example, the thicknesses of the superlattice barrier layers  22 - 1  through  22 - 4  linearly increase from one end of the barrier superlattice  20  to the other end of the barrier superlattice  20 . As a result, the bandgap of the barrier superlattice  20  linearly increases in the same manner. Note that while the thicknesses of the superlattice barrier layers  22 - 1  through  22 - 4  and the superlattice well layers  24 - 1  through  24 - 4  are varied to provide a linear increase in the bandgap of the barrier superlattice  20  in the direction of carrier flow in this example, the thicknesses of the superlattice barrier layers  22 - 1  through  22 - 4  and the superlattice well layers  24 - 1  through  24 - 4  may be varied to increase the bandgap of the barrier superlattice  20  in any desired linear or non-linear manner (e.g., exponentially, step-wise, or the like). 
         [0057]      FIG. 5  is an energy band diagram for one of the barrier layers  16 -X and the two adjacent well layers (referred to as well layers  14 -X and  14 -Y) of the heterostructure  12  of  FIG. 2  according to one embodiment of the present disclosure. In this embodiment, the barrier layer  16 -X is formed of one or more layers of the same high bandgap material in the Group IIa and IV-VI materials system or is a superlattice according to  FIG. 3 . As a result, the bandgap of the barrier layer  16 -X (E g,BARRIER ) is constant across the thickness of the barrier layer  16 -X. This energy band diagram is equally applicable to one embodiment of the heterostructure  12  of  FIG. 1 . 
         [0058]    The well layers  14 -X and  14 -Y correspond to bandgap E g,WELL , and the barrier layer  16 -X corresponds to bandgap E g,BARRIER . An effective barrier height or potential (Φ) at each interface between the barrier layer  16 -X and the adjacent well layers  14 -X and  14 -Y is defined as the difference between the bandgap of the barrier layer  16 -X (E g,BARRIER ) and the bandgap of the well layers  14 -X and  14 -Y (E g,WELL ) and can be adjusted by altering the alloy composition or the doping profile in the well and/or barrier layers  14 -X,  14 -Y, and  16 -X. The barrier height (Φ 1 ) is chosen to promote one directional lateral carrier transport over the potential barrier. Preferably, the Fermi energy level with respect to the barrier layer conduction band is within 0.5 k B T to 1 k B T and is set by adjusting the alloy composition and doping level. In one non-limiting example, the well layers  14 -X and  14 -Y are formed of PbSe and the barrier layer  16 -X is formed of Pb 0.92 Sr 0.08 Se. In this exemplary diagram, the barrier height (Φ 1 ) is constant with increasing distance. Typical barrier heights vary between 0.005 and 0.3 electron volts (eV) depending on the temperature of operation. 
         [0059]      FIG. 6  is an energy band diagram for one of the barrier layers  16 -X and the two adjacent well layers  14 -X and  14 -Y of the heterostructure  12  of  FIG. 2  according to another embodiment of the present disclosure. In this embodiment, the barrier layer  16 -X is a superlattice according to  FIG. 4 . As a result, the bandgap of the barrier layer  16 -X (E g,BARRIER ) increases across the thickness of the barrier layer  16 -X in the desired direction of carrier flow. 
         [0060]    The well layers  14 -X and  14 -Y correspond to bandgap E g,WELL , and the barrier layer  16 -X corresponds to bandgap E g,BARRIER  that varies with distance across the barrier layer  16 -X. More specifically, the bandgap of the barrier layer  16 -X (E g,BARRIER ) increases in the desired direction of carrier flow. As a result, an effective barrier height or potential (Φ 1 ) at a first interface between the barrier layer  16 -X and the adjacent well layer  14 -X in the direction of carrier flow is less than an effective barrier height or potential (Φ 2 ) at a second interface between the barrier layer  16 -X and the adjacent well layer  14 -X in the direction of carrier flow. The barrier heights (Φ 1  and Φ 2 ) are chosen to promote lateral carrier transport over the potential barrier in the desired direction of carrier flow while discouraging lateral carrier transport over the potential barrier in the direction opposite to the desired direction of carrier flow. In one non-limiting example, the barrier layer  16 -X may be formed of Pb 1-x Sr x Se with x varying from 8% to 13% across the barrier layer  16 -X (Pb decreases accordingly as well). 
         [0061]      FIGS. 7 and 8  are similar to  FIGS. 3 and 4  and illustrate superlattice embodiments of one of the well layers  14 - 1  through  14 -N. More specifically,  FIG. 7  illustrates one of the well layers  14 - 1  through  14 -N of  FIG. 2  (hereinafter referred to as well layer  14 -X), where the well layer  14 -X is a short period superlattice  28  according to one embodiment of the present disclosure. Note that this discussion is equally applicable to the well layer  14  or  18  of  FIG. 1 . For convenience, the superlattice  28  is referred to herein as a well superlattice  28 . The well superlattice  28  includes a number of superlattice (SL) well layers  30 - 1  through  30 -N separated by superlattice (SL) barrier layers  32 - 1  through  32 -(N−1). The superlattice well layers  30 - 1  through  30 -N are low bandgap material layers formed in the Group IIa and IV-VI materials system and having a bandgap E g,SLW . Preferably, the superlattice well layers  30 - 1  through  30 -N are low bandgap Pb (1-a-b) Sr a Sn b Se (0&lt;a&lt;1; 0&lt;b&lt;1) material layers. The superlattice well layers  30 - 1  through  30 -N may all be the same low bandgap material or two or more of the superlattice well layers  30 - 1  through  30 -N may be different low bandgap materials in the Group IIa and IV-VI materials system. 
         [0062]    The superlattice barrier layers  32 - 1  through  32 -(N−1) are high bandgap material layers formed in the Group IIa and IV-VI materials system and having a bandgap E g,SLB , where E g,SLW &lt;E g,SLB . Preferably, the superlattice barrier layers  32 - 1  through  32 -(N−1) are high bandgap Pb (1-a′-b′) Sr a′ Sn b′ Se (0&lt;a′&lt;1; 0&lt;b′&lt;1) material layers. The superlattice barrier layers  32 - 1  through  32 -(N−1) may all be the same high bandgap material or two or more of the superlattice barrier layers  32 - 1  through  32 -(N−1) may be different high bandgap materials in the Group IIa and IV-VI materials system. An effective, or combined, bandgap of the superlattice well layers  30 - 1  through  30 -N and the superlattice barrier layers  32 - 1  through  32 -(N−1) is the bandgap of the well layer  14 -X, which as discussed above is less than the bandgap of all adjacent barrier layer(s) in the heterostructure  12  for the thermoelectric material  10 . 
         [0063]    It should be noted that when referring to the well superlattice  28 , the “high bandgap” material layers forming the superlattice barrier layers  32 - 1  through  32 -(N−1) are material layers having bandgaps that are greater than bandgaps of the “low bandgap” material layers forming the adjacent superlattice well layers  30 - 1  through  30 -N. Likewise, the “high bandgap” material layers forming the superlattice well layers  30 - 1  through  30 -N are material layers having bandgaps that are less than bandgaps of the “high bandgap” material layers forming the adjacent superlattice barrier layers  32 - 1  through  32 -(N−1). 
         [0064]    In the well superlattice  28  of  FIG. 7 , a superlattice period thickness  34  of the well superlattice  28  is less than the tunneling probability length at a given operating temperature. Further, the superlattice well layers  30 - 1  through  30 -N and the superlattice barrier layers  32 - 1  through  32 -(N−1) are all of the same thickness such that the bandgaps of the superlattice barrier layers  32 - 1  through  32 -(N−1) and the bandgaps of the superlattice well layers  30 - 1  through  30 -N are constant over distance. The well superlattice  28  reduces thermal conductivity by phonon scattering at the interfaces between the superlattice well layers  30 - 1  through  30 -N and the adjacent superlattice barrier layers  32 - 1  through  32 -(N−1). 
         [0065]    It should be noted that since the well superlattice  28  is the structure of the well layer  14 -X, the well superlattice  28  is preferably terminated on both ends by superlattice well layers, namely, superlattice well layers  30 - 1  and  30 -N. However, the well superlattice  28  is not limited thereto. For instance, the well superlattice  28  may alternatively be terminated by superlattice barrier layers or terminated at one end by a superlattice barrier layer and the other end by a superlattice well layer. If terminated by a superlattice barrier layer, the superlattice barrier layer preferably has a bandgap that is less than a bandgap of the adjacent barrier layer in the heterostructure  12  of the thermoelectric material  10 . 
         [0066]      FIG. 8  illustrates the well superlattice  28  according to another embodiment of the present disclosure. The well superlattice  28  is similar to that of  FIG. 7 . However, in this embodiment, thicknesses of the superlattice barrier layers  32 - 1  through  32 - 4  and thicknesses of the superlattice well layers  30 - 1  through  30 - 4  are varied to create an energy grading across the well layer  14 -X to increase cross-plane effective carrier density transport. More specifically, the superlattice period thickness  34  is less than the tunneling probability length at a given operating temperature. As the thicknesses of the superlattice barrier layers  32 - 1  through  32 - 4  increase, the bandgap of the well superlattice  28  also increases. 
         [0067]    In this example, the thicknesses of the superlattice barrier layers  32 - 1  through  32 - 4  linearly increase from one end of the well superlattice  28  to the other end of the well superlattice  28 . As a result, the bandgap of the well superlattice  28  linearly increases in the same manner. Note that while the thicknesses of the superlattice barrier layers  32 - 1  through  32 - 4  and the superlattice well layers  30 - 1  through  30 - 4  are varied to provide a linear increase in the bandgap of the well superlattice  28  in the direction of carrier flow in this example, the thicknesses of the superlattice barrier layers  32 - 1  through  32 - 4  and the superlattice well layers  30 - 1  through  30 - 3  may be varied to increase the bandgap of the well superlattice  28  in any desired linear or non-linear manner (e.g., exponentially, step-wise, or the like). 
         [0068]      FIG. 9  is an energy band diagram for one of the well layers  14 -X and the two adjacent barrier layers  16 -X and  16 -Y of the heterostructure  12  of  FIG. 2  according to another embodiment of the present disclosure. In this embodiment, the well layer  14 -X is a superlattice according to  FIG. 8 . As a result, the bandgap of the well layer  14 -X (E g,WELL ) increases across the thickness of the well layer  14 -X in the desired direction of carrier flow. 
         [0069]    The barrier layers  16 -X and  16 -Y correspond to bandgap E g,BARRIER , and the well layer  14 -X corresponds to bandgap E g,WELL  that varies with distance across the well layer  14 -X. More specifically, the bandgap of the well layer  14 -X (E g,WELL ) increases in the desired direction of carrier flow. As a result, an effective barrier height or potential (Φ 1 ) at a first interface between the well layer  14 -X and the adjacent barrier layer  16 -X in the direction of carrier flow is greater than an effective barrier height or potential (Φ 2 ) at a second interface between the well layer  14 -X and the adjacent barrier layer  16 -Y in the direction of carrier flow. The barrier heights (Φ 1  and Φ 2 ) are chosen to promote lateral carrier transport over the potential barrier in the desired direction of carrier flow while discouraging lateral carrier transport over the potential barrier in the direction opposite to the desired direction of carrier flow. 
         [0070]      FIG. 10  is an energy band diagram of a series of adjacent well and barrier layers  14  and  16  in the heterostructure  12  of  FIG. 2  according to yet another embodiment of the present disclosure. In this embodiment, both the barrier layers  16  and the well layers  14  are formed as superlattices as described above with respect to  FIGS. 4 and 8 , respectively. Again, the barrier heights are chosen to promote lateral carrier transport over the potential barrier in the desired direction of carrier flow while discouraging lateral carrier transport over the potential barrier in the direction opposite to the desired direction of carrier flow. 
         [0071]    While the embodiments of the thermoelectric material  10  described herein have numerous advantages, some non-limiting examples are:
       1. Embodiments that use PbSe-based materials:
           a. have intrinsically low thermal conductivity compared to other material systems that is stable throughout a wide range of doping from n-type to p-type materials,   b. have near equal band conduction and valence band offsets-n-type and p-type material have similar transport properties, and   c. are mechanically much softer than Group III-V, Group II-VI, and Group IV bonded counterparts resulting in higher tolerance to lattice strain and thermal expansion mismatch;   
           2. Heterostructure design to increase carrier transport. The hot carrier transport increases the ZT compared to bulk materials;   3. Embodiments where well and/or barrier layers  14  and  16  are constructed from short period superlattices to reduce thermal conductivity by phonon scattering at the interfaces; and   4. Embodiments having highly doped well and/or barrier layers reduce thermal conductivity through electron-phonon scattering mechanisms.       
 
         [0079]    While the foregoing written description of the invention enables one of ordinary skill to make and use what is considered presently to be the best mode thereof, those of ordinary skill will understand and appreciate the existence of variations, combinations, and equivalents of the specific embodiment, method, and examples herein. The invention should therefore not be limited by the above described embodiment, method, and examples, but by all embodiments and methods within the scope and spirit of the invention as claimed. 
         [0080]    Those skilled in the art will recognize improvements and modifications to the preferred embodiments of the present disclosure. All such improvements and modifications are considered within the scope of the concepts disclosed herein and the claims that follow.
Embodiments of a thin-film heterostructure thermoelectric material and methods of fabrication thereof are disclosed. In general, the thermoelectric material is formed in a Group IIa and IV-VI materials system. The thermoelectric material includes an epitaxial heterostructure and exhibits high heat pumping and figure-of-merit performance in terms of Seebeck coefficient, electrical conductivity, and thermal conductivity over broad temperature ranges through appropriate engineering and judicious optimization of the epitaxial heterostructure.