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Formation of HgTe NanodisksEmbedded in PbTe Matrix byPrecipitation Phenomena

Man-Jong Lee*, and Choong-Un Kim*

Materials Science and Engineering Program, The UniVersity of Texas at Arlington,

P.O. Box 19031, Arlington, Texas 76019

Received August 9, 2003; Revised Manuscript Received October 3, 2003

ABSTRACT

We report findings related to the HgTe nanodots fabricated from the precipitation phenomenon in the HgTe PbTe quasi-binary system. With

homogeneous nucleation and growth of HgTe phase, a well defined nanostructure is obtained, where the nanodots are three-dimensionally

dispersed within the PbTe matrix. The nanodots prefer to take disk shape to relax a strong strain energy that resulted from the formation ofdisordered HgTe phase. With this facile and effective technique, the nanodots with various morphologies can be realized within any form of

matrix, such as powder, bulk, or thin film, providing a new way to tailor the properties of the nanodots.

With the emerging importance of semiconductor nanodots,both in fundamental studies of material properties1,2 and inpractical application to advanced devices,3,4 the search forfabrication methods has intensified in the past few years.While such efforts have resulted in the successful develop-ment of several new techniques, such as the self-assemblyprocess in epitaxial films via Stranski-Krastanow (S-K)growth mode,5,6 they have limited applicability, due mainly

to their rigorous processing requirements. Recently, weintroduced a new process that can produce high-densitynanodots in any form of another semiconductor matrix.7,8

This technique takes advantage of the precipitation phenom-enon in quasi-binary semiconductor systems and producesthree-dimensionally distributed nanodots by inducing ho-mogeneous nucleation and growth of the target phase. Ourinitial attempt using the HgTe-PbTe quasi-binary systemshows that the technique is extremely effective in producingHgTe nanodots embedded within a PbTe matrix withexcellent interfaces. More importantly, nanodot structureswith various morphologies can be made with the simplevariation of thermal treatment conditions. This, the control

of dot morphology, should provide a way to tailor theproperties of the dots and add to the benefits of the technique.This paper suggests a mechanism responsible for the forma-tion of disk-shaped HgTe nanodots along with evidencesupporting the conclusions that (1) the shape change fromsphere to disk is a result of strain energy relaxation and (2)

the large strain energy observed is due to the formation andgrowth of disordered HgTe embryos during precipitation.

For the present study, the solid solution of PbTe and HgTe,where mole percent of HgTe is 2.5 (PbTe-2.5 HgTe), ismade by mixing and melting pure PbTe and HgTe in a quartzampule.9 Following the solid solution heat treatment at theeutectic temperature to obtain supersaturation, where the solidsolubility of HgTe is the maximum (5 mol %), the alloy is

air-quenched to room temperature in order to maintain single-phase solid solutions. The alloy is then aged at a temperature(300-400 C) for up to 300 h to induce homogeneousnucleation and growth of HgTe nanocrystallites. Conven-tional transmission electron microscopy (CTEM) is used forthe analysis of the size, shape, and orientation of nanopre-cipitates using diffraction patterns and bright field imaging.High-resolution transmission electron microscopy (HRTEM)observation is carried out at 250 kV with a Philips EM430SuperTwin HRTEM. For Raman spectroscopy, alloys arecleaved to expose 001 of the cast ingot. Raman shift ofcharacteristic frequencies in the range of 50 to 300 cm-1 ischaracterized to detect both LO and TO phonon frequenciesof nanocrystalline HgTe. For comparison, Raman spectros-copy is also done on pure HgTe ingots made following asimilar melting process. The Raman study is conducted atroom temperature using the Ar laser (514.5 nm) as a source.The spectrometer has a resolution of 0.17 cm-1 in full widthhalf-maximum (fwhm).

Figure 1, a series of TEM images taken at three differentaging times at 300 C, evidences the morphological evolutionof HgTe nanodots produced in PbTe solid solution containing2.5 mole percent of HgTe (hereafter PbTe-2.5 HgTe). The

* Corresponding authors. Kim: e-mail choongun@uta.edu. Lee: e-mailmanjonglee@add.re.kr

Present address; Technology Department, Agency for Defense Develop-ment, Yousung P.O. Box 35, Daejon, Korea.

NANO

LETTERS

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CTEM micrograph shown in Figure 1a is taken after 10 minof aging and represents the embryo stage of the HgTe phase.

Due to the large strain field contrast, the exact size of theHgTe phase is unclear, but it is believed to be substantiallysmaller than it appears in this micrograph. Little variationin the shape of the contrast with the electron beam tilt angleindicates that the majority of the HgTe nanodots shown herehave a spherical shape. When the alloy is further aged, theHgTe turns into a thin nanodisk without any significantchange in density. Such a change can be seen in Figure 1b,a CTEM micrograph taken at the 100 zone axis after 300h of aging at 300 C. Notice the presence of three sets ofthin disks aligned along the 100 directions. Observationsat various aging times suggest that the transition to disk shapeis completed within an hour of aging at 300 C, as evidenced

in Figure 1c. This HRTEM micrograph represents thenanostructure of the alloy after 5 h of aging and shows aHgTe nanodisk aligned parallel to the 100 beam direction.The nanostructure of the samples aged for 1 h has essentiallythe same disk formation but with more interference fromthe strain field. As shown in Figure 1d, a HRTEM micro-graph of the alloy after 300 h of aging, the HgTe nanodiskis exceptionally stable and persists without coarsening.

The HgTe nanodots formed by the precipitation techniqueare extremely small and have coherent interfaces with thePbTe matrix. Notice that the size of the disk shown in Figure

1c is only 4-5 nm in diameter and is less than 1 nm thick.Less than 1 nm thickness is especially noteworthy becauseit is close to the unit cell size of the equilibrium HgTe phase.In addition to electron diffraction analysis, several features

shown in Figure 1 suggest that HgTe has a coherent interfacewith PbTe and aligns to the PbTe matrix with a cube-cuberelationship, i.e., {100}HgTe//{100}PbTe and [100]HgTe//[100]PbTe.The very first evidence that the lattice between HgTe andPbTe is connected can be seen in the HRTEM micrographshown in Figure 1c. It can be seen that the PbTe lattice runsacross the HgTe phase without any sign of discontinuity ormisfit dislocation. The second indication is the presence oflattice strain, observable as a dark contrast encompassingthe sphere and disk under TEM. For example, the HRTEMmicrograph in Figure 1c shows an area of dark contrast(marked with arrows) extending from the face of the HgTedisk toward the PbTe matrix. The contrast is due to the lattice

distortion in PbTe and evidences the presence of the strainfield. Note also that no apparent contrast exists near the diskedge, meaning that the initially existed strain field is locallyrelaxed. When the lattice spacing is measured at variouslocations in and near the disk (a-c), it is determined thatthe strain is the result of the larger HgTe lattice fitting intothe smaller PbTe matrix. The lattice spacing in PbTe awayfrom the disk (a) is measured to be 6.46 , which is closeto the lattice constant of the equilibrium PbTe phase, 6.462. On the other hand, lattice spacing measured across thethickness direction of the disk is 7.23 at the disk center(b) and 6.74 at the edge (c), indicating that the HgTe latticeis significantly larger compared with the lattice constant of

the equilibrium HgTe phase, 6.456 .The formation of a disk observed in this study is

attributable to change in the internal free energy state. SinceHgTe nanodots, having a considerable lattice mismatch, formcoherently within the PbTe matrix, strain energy plays acritical role in determining the shape of the nanodots. Agraphical representation of the lattice strain affecting theshape of the HgTe phase is shown in Figure 2. When thePbTe-2.5 HgTe alloys quenched from the supersaturatedstate are heated to elevated aging temperature, the alloysbecome unstable with respect to the equilibrium state and

Figure 1. TEM images of nanostructures formed from the agingtreatment of PbTe-2.5 HgTe alloys at 300 C. (a) A CTEM brightfield image of the initial stage nanostructure, aged for 10 min,showing the formation of spherical HgTe embryos. (b) CTEMimage of a nanostructure, aged for up to 300 h, where three typesof aligned HgTe nanodisks are shown; 1 denotes a nanodisk alignedperpendicular to the beam direction, 2 and 3 indicate nanodisksaligned parallel to the beam direction. (c) HRTEM image of anHgTe nanodisk aligned parallel to the beam direction which wasaged for 5 h. (d) A HRTEM image aged for up to 300 h where allthree alignments are shown.

Figure 2. Schematic illustrations of the nucleation and growth andthe shape evolution mechanism of HgTe nanodots.

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thus are at the condition of the compositional instability. Sucha compositional instability leads to the nucleation of HgTephase, which is shown in Figure 2a. At the nucleation stage,HgTe embryos are small in size and induce a smallhydrostatic compression field to both HgTe and PbTe dueto volume difference. Since the total strain energy is smallerthan the interfacial energy, the spherical shape is preferred.

As the embryo with a larger lattice volume grows (Figure2b), however, strain energy from hydrostatic compressionincreases more rapidly than the interfacial energy. The HgTesphere becomes unstable when it approaches the critical sizewhere strain energy overwhelms the interfacial energy(Figure 2c). At this state, a shape change should occur tominimize the overall system energy. In this case, HgTe phaseprefers to grow in the elastically soft direction (Figure 2d),thereby reducing the strain energy. In cubic alloys, thisdirection is determined by the elastic anisotropy factor,() (C11 - C12 - 2C44)/C44).10 The of HgTe is estimatedto be negative, meaning that the soft direction is 001. Asa consequence, the strained HgTe spheres grow to disks by

aligning along the three sets of the 001 directions for strainrelaxation, resulting in a well-defined nanostructure compris-ing three-dimensionally distributed HgTe nanodisks, asshown in Figure 1d.

While the shape change mechanism can be understoodthrough strain energy considerations, initially, it is not clearhow such a large strain energy could result from the HgTephase formation because the lattice constant of equilibriumHgTe (zinc blende) is similar to that of PbTe (rock salt). Infact, the difference in the lattice constants of the equilibriumphases is only 0.01%. It is unlikely that such a smalldifference could result in the extensive strain field observedunder TEM and drive the shape change from a sphere to a

disk. As evidenced in the HRTEM image analysis, the latticeof HgTe embryos is considerably larger than that of the PbTematrix and the equilibrium HgTe phase. This suggests thatthe HgTe sphere and disk are not in an equilibrium state butrather in a disordered state. As graphically illustrated inFigure 3, the disordered structure of zinc blende is diamondcubic, that is, Hg and Te are randomly located in the zincblende structure. A simple consideration of the atomicpacking factor can show that the unit cell volume of thedisordered structure can be substantially larger than that ofthe ordered structure. The packing density of the diamond

structure is 0.34, while it is 0.52 for HgTe in the zinc blendestructure. With less dense packing in the diamond structure,

it is probable that the disordered HgTe phase has a largervolume than the ordered phase.More direct observation supporting the possibility that

HgTe forms in a disordered structure is obtained from Ramanscattering characterization. Raman scattering measures thevibrational states of a crystal lattice that are sensitive tocrystal order or disorder.11 According to van de Walle etal.,12 in binary alloys the phonon density of states (DOS)changes with the extent of disorder and accompanyingvolume change. This is because the strength of the atomicbonds is weaker in the disordered structure. Figure 4compares the Raman spectra of well-annealed polycrystallineHgTe (Figure 4a) and PbTe-2.5 HgTe aged at 300 C for

1 h. The two major Raman frequency shifts, TO phonon shift,TO(), and LO phonon shift, LO(), in the well-annealedzinc blende HgTe, are located at 118.5 and 134.9 cm-1,which agree well with those of single crystalline HgTe.13

Contrarily, the Raman shifts in HgTe nanodots (Figure 4b)occur at considerably lower frequencies. The Raman shiftoccurring at lower frequencies indicates that the atomic bondsare weaker due to structural disorder and larger unit cellvolume.

Considering the fact that, in this system, diffusion rate isextremely slow compared to its driving force, the formationof the disordered HgTe precipitate phase is not a surprisingresult. With rapid cooling after the solid-solution heat

treatment, a large thermodynamic driving force for precipita-tion builds up in the alloy. Since precipitation is induced ata temperature where its kinetics is slow, the number of HgTeembryos explodes. While these conditions allow the forma-tion of a large number of extremely small embryos, theymay not provide sufficient time for the formation of anordered structure. Furthermore, with slow diffusion kinetics,the disordered structure persists for an extended period. Whilethe results are not presented here, characterization of HgTenanodots after longer aging time than what is used in thisstudy provided an evidence of the ordering in HgTe disks.

Figure 3. Schematic illustrations of a disordered lattice (a) andan ordered lattice (b) of zinc blende HgTe structure.

Figure 4. The difference of Raman spectra of well-annealedpolycrystalline bulk HgTe (a) and HgTe nanodots within PbTe (b).

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When alloys are aged beyond 300 h at 300 C, it is foundthat the strain contrast gradually disappears and that the disksgrow thicker. This shape transition is possible only whenthe disorder-order transition reduces the HgTe unit cellvolume and further relaxes strain energy in the nanodisks.

It is expected that the HgTe nanodots, regardless of theirshape, would be subjected to a strong quantum confinementby the PbTe matrix and thereby exhibit significantly differentelectrical and optical properties from bulk HgTe. As the

band-gap energy of PbTe (0.31 eV for Eg,dir(L6V+

- L6c-

)) issignificantly higher than that of bulk HgTe (-0.14 eV forEg,dir(8V - 6c)), charge carriers in an HgTe dot are likelyto be confined within the dot. Furthermore, with a bulk HgTeexciton Bohr radius of 39.3 nm (calculated from the availabledata in ref 13), which is more than three times larger thanthe dots, the carriers may loose their dimensional freedomand have higher kinetic energy than those in the bulk. Whilecharacterizations of the dot properties are still ongoing, theresult from our optical absorption study is noteworthy in thisrespect: it suggests a strong connection between the dotformation and the absorption properties. When the as-quenched alloys were characterized using FTIR (Fourier

transform infrared) spectroscopy, it was found that absorptionoccurred at IR energy of 0.31 eV and higher, which is thesame as bulk PbTe. However, an additional IR absorptionpeak was found below, but near, 0.31 eV when the alloyswere aged. We believe that the additional absorption wasdue to HgTe nanodots, not only because they were absentin single-phase PbTe-2.5 HgTe alloys but also because thepeak location and intensity changes with aging time. Due tothe complexity of dot structure (order and disorder, and alsoshape evolution), the exact mechanism of absorption isdifficult to understand, but deserves further study.

In summary, this study demonstrates the effectiveness ofthe precipitation technique in producing three-dimensionallydistributed HgTe nanodisks having crystallographic align-ment with semiconducting PbTe. In addition, this study

provides insights on the mechanism behind the shapeevolution of nanodots produced by the precipitation phe-nomena. It is found that the strain energy plays a pivotalrole in determining the equilibrium shape of nanodots. Inthe present case, it is determined that the formation of adisordered HgTe embryo produces a large strain field, whichis responsible for the shape evolution from a sphere to adisk. The various nanodot structures, differing in shape anddegree of order, may provide unique properties needed for

advanced applications. Furthermore, with the versatility inthe choice of material system and the ability to producenanodots in any form, such as powder, bulk, or thin film,this technique can enable various new classes of materialsand devices.

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