Charge confinement and thermal transport processes in modulation-doped epitaxial crystals lacking lattice interfaces

Heterogeneous nanosystems offer a robust potential for manipulating various functional material properties, beyond those possible from their individual constituent materials. We demonstrate the formation of a class of materials with a homogeneous lattice but spatially heterogeneous electrical functionality; specifically, we develop epitaxial modulation-doped thin films in which the spatial separation of electronic charge densities is achieved without perturbing the parent crystal's compositional or structural homogeneity. Unlike the previous realizations of modulation doping in crystals, our materials demonstrate periodic layering of spatially segregated, varying electronically donor-doped regions in a single compositionally and structurally homogenous single-crystalline lattice. We demonstrate the formation of “modulation-doped epitaxial crystals” (MoDECs) using alternating layers of doped cadmium oxide, and the ability to spatially confine regions of variable carrier concentration via low potential-energy barriers in a spatially homogeneous, epitaxial crystal with a chemically and structurally homogenous lattice (i.e., no chemical or structural lattice interfaces). The low potential energy that confines electrons within the doped layers coupled with the crystalline nature of the MoDECs and lack of lattice interfaces presents a platform to study the electron thermal boundary resistances at low-energy electronic barriers. We find that the electron interfacial density does not impede thermal conductivity, despite evidence that the doped layers retain their carrier concentrations. Thus, the negligible thermal boundary resistances at the electronic interfaces result in the thermal conductivities of the MoDECs being related to only a series resistance sum of the thermal resistances of each of the individual layers, with no thermal resistances from the electronic boundaries that maintain charge separation. This is in stark contrast with other nanoscale multilayer materials, where thermal boundary resistances at the internal material interfaces reduce the thermal conductivity of the multilayer compared to that of the parent materials. The ability to modulation dope epitaxially grown films with no structural heterogeneity in the lattice will further enable unique platforms for mid-IR photonics, such as hyperbolic metamaterials, optical filters with spatially discrete optical absorption, or energy harvesting based on charge injection across modulation-doped interfaces.

Figure 1

(a) $2\theta -\omega$ scan of the (002) peak of the CdO MoDEC on sapphire. (b) Rocking curves of the (002) CdO peaks for both single species films and layered MoDECs. There is little to negligible difference in crystallinity between the MoDECs and the CdO films, indicating the MoDECs are single crystalline. (c) ADF STEM of a similar MoDEC sample on c-sapphire, which shows no lattice distortion between layers further confirming the highly crystalline quality of these materials. Doping initiates roughly within the center of the 20-nm long vertical white bar, and the high magnification image (right) taken from the black inset exhibits no lattice distortions across this interface region. Taken together, the XRD and TEM characterizations suggest that the MoDECs are crystallographically indistinguishable from the homogeneous reference films, and the doping and varying modulation periods of the doped layers have negligible impact on the lattice of the films.

Figure 2

(a) Conductivity vs interfacial density of MoDECs, as measured by Hall measurements. Conductivity scales with overall concentration of carriers. (b) Finite-element simulations of Poisson's equation for a five-layer CdO MoDEC, showing carriers are well confined to the more highly doped layers. (c) Thermal conductivity of all three MoDEC sample series. The thermal conductivities of all MoDECs lie in-between the thermal conductivities of the single species control films.

Figure 3

(a) Thermal resistance model for a MoDEC. The total thermal resistance of a MoDEC sample ($R_{\mathrm{total}}$) is the sum of the resistances of each layer and the thermal boundary resistances at the interfaces. (b) The blue line is the calculated thermal conductivity of a MoDEC with a concentration of Y:CdO going from 0 to 100% calculated via Eq. (2) (where the dotted lines represent the uncertainty of this calculation), assuming $R_{\mathrm{int}}=0$. The black squares are the average thermal conductivities of the three different MoDEC series. The red circles are the thermal resistance of single species CdO films with a comparable carrier concentration as the corresponding MoDEC. The agreement confirms that the electronic interfaces offer negligible thermal resistance.