High-temperature characterization of the thermoelectric properties of chalcogenide Ge_{2}Sb_{2}Te_{5} (GST) is critical for phase change memory devices, which utilize self-heating to quickly switch between amorphous and crystalline states and experience significant thermoelectric effects. In this work, the electrical resistivity and Seebeck coefficient are measured simultaneously as a function of temperature, from room temperature to 600 °C, on 50 nm and 200 nm GST thin films deposited on silicon dioxide. Multiple heating and cooling cycles with increasingly maximum temperature allow temperature-dependent characterization of the material at each crystalline state; this is in contrast to continuous measurements which return the combined effects of the temperature dependence and changes in the material. The results show p-type conduction (S > 0), linear S(T), and a positive Thomson coefficient (dS/dT) up to melting temperature. The results also reveal an interesting linearity between dS/dT and the conduction activation energy for mixed amorphous-*fcc* GST, which can be used to estimate one parameter from the other. A percolation model, together with effective medium theory, is adopted to correlate the conductivity of the material with average grain sizes obtained from XRD measurements. XRD diffraction measurements show plane-dependent thermal expansion for the cubic and hexagonal phases.

## I. INTRODUCTION

Ge_{2}Sb_{2}Te_{5} (GST) has been the most studied phase-change material for phase change memory (PCM) devices. The atomic structure of this chalcogenide material is very stable in crystalline phases, and it presents an electrical resistivity that is 5–6 orders of magnitude lower compared to the resistivity of the material in the amorphous phase. The face centered cubic (*fcc*) phase of the material and the hexagonal (*hcp*) phase are characterized by very high conductivities due to high carrier density.^{1,2} Thermoelectric transport—the coupling of electronic and thermal transport—plays an important role in the operation of PCM devices due to high current densities and temperature gradients^{3–8} and has been observed as asymmetric amorphization of GST line cells and polarity dependent operation of PCM cells in general.^{3} However, data on thermal conductivity and Seebeck coefficient of phase-change materials are still limited. In this work, we report the evolution of the Seebeck coefficient S(T) and the electrical resistance R(T) characteristics of GST as the material is progressively changed from amorphous to crystalline *fcc* and then to crystalline *hcp*. The Seebeck coefficient of a material represents the open circuit voltage generated across a temperature gradient along a sample, which can be approximated as $S=dV0/d\Delta T$ for small temperature gradients.^{9,10}

## II. EXPERIMENTAL SETUP AND MEASUREMENT PROCEDURE

The electrical resistivity and Seebeck coefficient of GST are measured simultaneously using GST thin films with tungsten bottom contacts. A 1 *μ*m thick silicon dioxide (SiO_{2}) layer is grown on a low doped p-type Si substrate. 300 nm deep trenches of the 2 mm × 2 mm area are opened into SiO_{2} by optical lithography and reactive ion etching (RIE). Tungsten is then deposited by physical vapor deposition (PVD), and the contacts are formed using second optical lithography and RIE steps. Bottom tungsten contacts were found to provide better adhesion and contact to the GST films, and the misalignment arising from the two lithography steps is not important for these large-scale structures. Thin GST films are deposited by elemental co-sputtering of Ge, Sb, and Te and capped by a 10 nm layer of SiO_{2} to prevent evaporation and oxidation (Fig. 1). GST has been found to form good Ohmic contacts with most metals.^{11}

The measurement setup used for simultaneous S(T) and R(T) measurements up to high temperatures was described in detail in Ref. 12. The bottom metal contacts are probed with tungsten probes through the soft GST film and are connected to an HP 4145B semiconductor parameter analyzer. A distance of 20 mm between the two contacts is sufficient to achieve a temperature difference of ΔT ∼ 10 °C. The measurements were performed in an enclosed chamber under low vacuum (8 × 10^{4} kPa) with nitrogen flow to minimize the oxidation of the chuck and probe tips. Two K-type thermocouples clamped very close to the contacts for each GST sample were used to monitor the temperature on both sides of the sample. The brass-alloy chuck is ∼10 mm thick, providing a good thermal inertia and linear temperature profile on the surface between the probe locations. Two resistive heaters inserted in the chuck are used to set the temperature gradient (Fig. 2). In order to reach very high temperatures (∼800 °C), an inductive heater coil positioned below the setup is used to generate a high frequency alternating magnetic field that results in heating of the chuck through contact with steel surrounding plates. The temperature gradient can also be controlled with the inductive heater by moving the coil from one side to another. The surrounding steel plates form an oven-like enclosure for heat confinement and heating of the probes and probe arms to reduce the probe cooling effect.

When a temperature gradient is set across the sample at a given stabilized temperature, the I-V characteristics obtained with the semiconductor parameter analyzer simultaneously provide the Seebeck voltage, which is the x-axis intercept of the line, and the resistance between the two contacts, which is the slope of the line (Fig. 3).

In the experiments, the maximum temperature difference recorded between the probe arm and the surface of the chuck does not exceed 150 °C at a chuck temperature of ∼600 °C. The probe needles (Cascade Microtech PTT-24/4–25 tungsten needles) are ∼20 mm long, and its tip diameter is 2.5 *μ*m. An approximated geometry of a GST sample with electrical contact (2D cylindrically symmetric tungsten probe tip on sample tungsten bottom contact) is simulated in COMSOL to estimate the effect of the cooling by the probe arms via a 10 *μ*m diameter tungsten contact on the surface of the GST film (Fig. 1). A worst-case scenario is simulated by setting the temperature of the top surface of a 1 *μ*m thick tungsten contact on the sample surface at 200 °C, with the bottom surface temperature of the sample (surface of the chuck) at 400 °C. The simulations show that outside the small area where the probe tips come into contact (10 *μ*m diameter), the temperature of the sample surface is the same as the chuck temperature (Fig. 4).

GST behaves like a p-type semiconductor,^{13} and the conductivity $\sigma \u2009$ can be expressed as

where *e* is the elementary charge, *p* is the carrier density, and *μ _{p}* is the low field hole mobility. Both the carrier density and the mobility are temperature dependent.

The measured resistance of the sample is scaled to resistivity using the resistivity value of the sample measured at room temperature using the van der Pauw (vdP) method^{14} and assuming that the geometry factor does not change with temperature. The resistivity of a square shaped GST thin film sample with known film thickness, from the same wafer, is measured at room temperature using four probes to contact the film surface [Fig. 5(a)]. According to the vdP technique, the resistivity of the sample is given by

where *t* is the thickness of the film, R_{14,23} = V_{14}/I_{23}, and R_{12,43} = V_{12}/I_{43}, and the values of the coefficient *f* are tabulated for arbitrary values of the resistance ratio R_{14,23}/R_{12,43}.^{14}

The measured resistivity of the 100 nm thick *fcc-*GST film in a square shape [configuration in Fig. 5(a)], at room temperature, previously heated up to 200 °C, is 504 ± 3 mΩ·cm (assuming a 5% error on the film thickness).

A second sample from the same wafer, with 4 inline metal contacts, as shown in Fig. 5(b), is also heated up to 200 °C, with the same heating rate (∼5 °C/min), to measure the R(T) characteristic during heating and cooling back to room temperature. The resistance between the two inner contacts on the surface of the sample is given by

The results obtained from the 2 previous measurements are used to determine the resistivity value of the film at 200 °C

This procedure is repeated for a second anneal temperature (300 °C) and the R(T) characteristic obtained while heating matches the R(T) obtained during the previous cooling from 200 °C (Fig. 6). The obtained resistivities at 200 °C and 300 °C are 75 mΩ·cm and 11 mΩ·cm, respectively.

The measured R(T) characteristics for different samples are then scaled to resistivity (Fig. 7) using the resistivity value at 200 °C, which assumes the same geometry factor measured at room temperature.

The sign of the Seebeck coefficient indicates the majority carrier type (S > 0 for p-type conduction). The configuration shown in Fig. 5(c) is used for simultaneous R(T) and S(T) measurements of two different samples during the same run. The temperature difference ΔT = T_{hot} − T_{cold} is the temperature difference between the two probe locations, which is varied between −10 °C and +10 °C at given stable average temperatures T_{AVG}=(T_{hot} + T_{cold})/2.

## III. RESULTS AND DISCUSSION

### A. Continuous R(T) measurements

Continuously increasing temperature measurements of R(T) were performed on 50 nm, 100 nm, and 200 nm (target thicknesses) GST thin films up to the melting temperature and scaled to resistivity ρ(T) using the room-temperature value after anneal at 200 °C as described above (Fig. 7). During these measurements, the temperature was increased at a constant rate of 5 °C/min. The two transitions, from amorphous to *fcc* (∼155 °C) and from *fcc* to *hcp* (∼365 °C), correspond to the turning points in the curves. The as-deposited amorphous films have a room-temperature resistivity of ∼8.7 × 10^{2} Ω·cm, in agreement with reported values of 8 × 10^{2} to 9 × 10^{2} Ω·cm.^{4} The films typically start breaking up and become discontinuous after melting (∼600 °C). The resistivity of the 100 nm GST film in the *hcp* phase is calculated to be slightly higher than that of the 50 nm and 200 nm films after the second transition phase which can be attributed to variations in film thicknesses. The drop in resistivity at ∼585 °C as shown in Fig. 7 (inset) indicates the melting of the film. The liquid resistivity of 1.14 mΩ·cm observed after this point is also in agreement with previously reported values for GST.^{6,15} A film thickness reduction of ∼5% due to material density changes after the first transition has been reported^{16} but is not taken into account in our calculations of resistivity.

The R(T) curves of the as-deposited amorphous GST films show a drop in resistivity of more than five orders of magnitude as the material transitions from amorphous to *fcc* and *hcp* crystalline phases. In GST devices, this ratio is only approximately four orders of magnitude.^{15} This difference is attributed to the melt-quench amorphization process in small-scale devices through electrical pulses, which leads to lower atomic disorder and hence lower amorphous resistivity to start with, compared to as-deposited amorphous films.

### B. Simultaneous S(T) and R(T) measurements

In order to characterize the temperature-dependent resistance R(T) and Seebeck coefficient S(T) of the material at each crystalline state as the material progressively changes from amorphous to crystalline, measurements during multiple heating and cooling cycles with increasingly maximum temperature were performed (Figs. 8 and 9). The R(T) and S(T) characteristics were obtained simultaneously from 2-point I-V measurements performed on 2 samples [Fig. 5(c)] using a parameter analyzer. Due to the required thermal gradient, and for practical experiment times, the measurements are performed in 10 °C increments from 40 °C up to 300 °C, in 20 °C increments above 300 °C, and in 50 °C increments for the last measurement (up to 540 °C). The final temperature was set to 180 °C for the first cycle and was increased by 20 °C for each subsequent cycle.

The R(T) and S(T) results obtained simultaneously for 50 nm and 200 nm GST films are shown in Figs. 8 and 9. The R(T) characteristics show the expected exponential decrease in the resistance with increasing temperature, within each crystalline state, as the material progressively crystallizes from amorphous to *fcc* and from *fcc* to *hcp*.^{17,18} The conductivity of the film below the glass transition (∼100 °C)^{19} follows an Arrhenius dependence (Fig. 8 insets)

where *E* is the conduction activation energy, *k* is the Boltzmann constant, *T* is the absolute temperature, and *σ*_{0} is defined as the minimum metallic conductivity.^{20} In the amorphous phase, the activation energy *E* corresponds to the energy for sub-band hopping mechanism which does not occur in *fcc* and *hcp*-GST based on UV/visible/NIR band gap measurements.^{21} The activation energy for conduction obtained for the amorphous phase from the first cycle, *E * = 0.417 eV, is in agreement with reported values,^{22} and it decreases as the material crystallizes in the following cycles of increasingly maximum temperatures. Given the large carrier concentration in GST,^{23,24} the overall decrease in the resistance from one annealing cycle to another is expected to be mostly due to the increase in mobility with crystallization. After the *fcc* to *hcp* transition (last four R(T) curves), the material shows a metallic behavior with the resistance increasing with temperature due to mobility degradation, in agreement with previous reports.^{5,16,25}

Once the material starts crystallizing, and for each state (corresponding to the material annealed at the previous cycle maximum temperature), the Seebeck coefficient increases linearly with temperature until further crystallization occurs beyond the previous anneal temperature. Linear fits of these regions of S(T) curves, with fixed zero intercept (0 mV/K at 0 K, Fig. 10), result in very small relative standard deviation errors on the slopes (0.6–3.7%).

The observed linear dependence of the Seebeck coefficient with temperature is consistent with the Boltzmann approximation transport model for degenerate semiconductors, which results in^{26–28}

where *k _{B}* is the Boltzmann constant,

*h*is the Plank constant,

*e*is the elementary charge,

*p*is the carrier density, m

_{p}* is the carrier effective mass, and

*T*is the absolute temperature.

Figure 11(a) shows the conductivity activation energy and dS(T)/dT as a function of anneal temperature for the 50 nm and 200 nm films. The derivative dS/dT, ∝ m_{p}*/*p*^{2/3}, shows a linear dependence on the conductivity activation energy for the amorphous-*fcc* mixed phase, where this energy is positive [Fig. 11(b)]. dS/dT is closely related to the electrical conductivity, *e*^{2}*pτ _{p}*/m

_{p}*, where τ

_{p}is the carrier relaxation time. Decoupling the relative changes in the carrier concentration, effective mass, and relaxation time as the material crystallizes would require Hall measurements. The linear dependence of dS/dT with

*E*, together with the linear S(T) with S = 0 V/K at 0 K, can still be used to empirically estimate one transport parameter from the other. A few low-temperature measurements of conductivity (to obtain the activation energy) can be used to determine dS/dT, and hence, S(T) or a single measurement of Seebeck coefficient can be used to determine the conductivity activation energy

*E*. The different slopes of dS/dT vs.

*E*for the 50 nm and 200 nm films may be due to a mismatch of the activation energies for the two thicknesses since the anneal temperature may not result in the same crystallinity state [Fig. 11(a)].

The positive Seebeck coefficient obtained for the GST films confirms the p-type conduction of the material up to the maximum measured temperature of ∼800 K. The S(T) decrease with temperature for the amorphous phase, as well as the increase with temperature for the stable *hcp* phase, is in agreement with previous reports.^{5,6} For the *fcc* phase, however, these multiple stepped measurements show that the Seebeck coefficient also increases with temperature for each crystalline state, up to the maximum temperature reached in the previous cycle. The decrease in S(T) with temperature observed for amorphous GST and *fcc*-GST after certain temperature is therefore due to crystallization rather than bipolar conduction which explains the S(T) turn-around in stable semiconductors as they approach the intrinsic regime. A positive or negative slope in S(T) determines the direction of asymmetry of the thermal profile (Thomson effect) that has been observed in phase-change memory devices and has important implications related to power and reliability of the devices. The positive S(T) slope we observe for the crystalline material (both *fcc* and *hcp*) is consistent with observations of asymmetric amorphization of PCM line cells toward the higher potential terminal.^{3,29,30}

### C. Average grain size from XRD measurements

Room temperature XRD measurements on pre-annealed samples and *in-situ* XRD measurements (at stabilized temperatures during anneal)^{31} were performed to correlate R(T) and S(T) with grain sizes in mixed-phase GST. Figure 12 shows the evolution of XRD patterns with temperature for an as-fabricated amorphous 100 nm GST film as the chuck temperature was increased from room temperature to 585 °C in 100 °C steps and decreased back to room temperature. The peaks in the pattern of the amorphous sample are repeated in all patterns, suggesting that these originate from the silicon substrate and sample holder. The *fcc* phase of the sample at 200 °C and 300 °C is identified by the peaks at 25.5°, 29.4°, 42.4°, and at 52.6°, while the *hcp* phase exhibits different peaks at the angles 21.4°, 25.7°, 28.9°, 40.1°, 42.8°, 48.5°, and 52.9° corresponding to different planes, similar to what has been previously observed.^{32–36} After cooling down the sample to room temperature, a new pattern is acquired, and it shows a small shift to the right in all *hcp* peaks, which is due to the thermal expansion of the material at high temperatures.^{37} From these results, the highest increase in the *hcp* planes spacing at 400 °C is 1.45% for the (004) direction.

The average grain size at different temperatures was obtained from the XRD patterns using Scherrer's equation^{38,39} which relates the full-width-half-max (FWHM) *β* to the grain size (*gs)*^{40}

where *λ* is the X-ray wavelength and *θ* is the diffraction angle. XRD measurements have been previously reported for *hcp*-GST annealed up to 330 °C, and the average grain size was found to be 40.3 nm.^{41}

The data for average grain size versus temperature were interpolated with a third order polynomial fit to correlate XRD grain size results with R(T) and S(T) measurements obtained after different anneal temperatures (Fig. 13). Grain sizes calculated from impedance spectroscopy (IS) measurements by Huang *et al.*, assuming a brick model,^{42} fall in the same range but show a significantly different trend with the anneal temperature (downward curvature, square symbols in Fig. 13).

### D. Percolation model

Since the increase in average grain size in *fcc*-GST is only from ∼18 nm to ∼30 nm, the drastic change in conductivity observed at the amorphous to *fcc* transition is likely due to percolation paths that form in the material as both the number of grains and the grain size increase. The electrical conductivity of an inhomogeneous material formed by two materials with different conductivities was described in the late 1800s by Rayleigh^{43} and Wiener^{44} and then formulated into the effective-medium theory by Bruggeman^{45} for various shapes and by Landauer^{46} for spheres of conductivity *σ*_{c} embedded in a material of conductivity *σ*_{a}. The model was adopted recently for mixed phase amorphous-crystalline chalcogenides such as GST.^{47} In this work, we model the mixed phase amorphous-*fcc* GST as spheres of fully crystalline *fcc*-GST embedded in amorphous GST and use the average grain sizes obtained from XRD measurements as the diameter of the spheres. The conductivity of the mixed material in this case is given by^{45–48}

with

where *σ _{c}* is the conductivity of the crystalline spheres,

*σ*is the conductivity of the amorphous matrix, and

_{a}*f*is the crystallinity fraction of the material (fraction of the crystalline volume to the total volume of the sample). Using

*σ*and

_{c}*σ*obtained from our R(T) measurements (σ = 1/ρ,

_{a}*ρ*= 494 Ω·cm, and

_{a}*ρ*= 0.01 Ω·cm, explained below), the calculated mixed phase resistivity of GST (Fig. 14) shows a sharp drop of ∼3 orders of magnitude at the percolation threshold of 33% crystalline fraction.

_{c}Solving Eq. (8) for *f* yields

which can be written in terms of the resistances assuming a constant geometry factor *C*, *σ=C*/*R* as

where *R*, *R _{a}*, and

*R*are the resistances of the mixed phase, the amorphous phase, and the fully crystalline

_{c}*fcc*GST, respectively.

The resistance of the mixed phase material at each crystallinity fraction *f* follows an Arrhenius dependence:

where *R*_{0} and *E* are the pre-factor and conduction activation energy of the mixed material. The parameters for amorphous GST *R*_{a0} and *E*_{a} are obtained from the first R(T) measurement on the amorphous film (Fig. 8)

The resistance of fully crystalline *fcc-*GST is assumed to be constant with temperature (E = 0 eV) since the activation energy is observed to change from positive values for the mixed amorphous-*fcc* phase to negative values for the mixed *fcc-hcp* phase (see dashed lines in Fig. 8, insets). This constant resistance value for fully crystalline *fcc*-GST is taken as the resistance at the second transition temperature (the zero of the second derivative of the R(T) 'envelope' formed by the last data point from each cycle)

The different parameters, *R*_{a0}, E_{a}, and R_{c0}, are given in Table I for the 50 nm and 200 nm thick films and are used to calculate the crystallinity fraction *f* of the sample as a function of temperature from Eq. (10).

. | 50 nm thin film . | 200 nm thin film . |
---|---|---|

R_{a0} (Ω) | 77.05 | 56.99 |

E_{a} (meV) | 419.8 | 376.7 |

R_{c0} (Ω) | 3558 | 1104 |

. | 50 nm thin film . | 200 nm thin film . |
---|---|---|

R_{a0} (Ω) | 77.05 | 56.99 |

E_{a} (meV) | 419.8 | 376.7 |

R_{c0} (Ω) | 3558 | 1104 |

Figure 15(a) shows the calculated crystallinity fraction *f* along with the corresponding experimental S(T) slopes of the mixed-phase material as a function of anneal temperature for the 50 nm and 200 nm thick films. The crystallinity fraction of the 200 nm thin film is slightly higher than that of the 50 nm film. Figure 15(b) also shows the experimental dS/dT *(*∝ *m/p ^{2/3})* and room-temperature conductivity σ

_{RT}

*(*∝

*mτ/p)*versus calculated crystalline fraction

*f*for the 50 nm and 200 nm thin film samples. These relations can now be used to estimate S(T) and σ(T) for a given amorphous-

*fcc*mixed phase material from a single, room-temperature value of the conductivity. σ

_{RT}can be used to determine

*f*and the corresponding dS/dT and hence S(T), which can then be used to determine the conduction activation energy

*E*(Fig. 11) to obtain the full σ(T).

Since the model for conductivity we have used assumes spherical crystals in an amorphous matrix and *f* is proportional to *(gs)*^{3} times the number of the grains in the sample, it is interesting to look at the relationship between *f* and *(gs)*^{3} obtained from XRD (Fig. 16), which appears to show three distinct regions for crystallization:

180 °C < T < 220 °C: the crystallinity of the sample increases rapidly with slow grain growth (Δf/Δ

*gs*^{3}= 1.1 × 10^{−4}nm^{−3}), suggesting that nucleation in the material is dominant.220 °C < T < 300 °C:

*f*changes linearly with*(gs)*^{3}at a lower rate compared to the previous region (Δf/Δ*gs*^{3}=5.1 × 10^{−5}nm^{−3}), suggesting that the number of crystals is approximately constant and the increase in crystallinity is mainly related to the growth of the crystals.300 °C < T < 320 °C: the crystallinity again increases rapidly with a small increase in grain size (Δf/Δ

*gs*^{3}=1.1 × 10^{−4}nm^{−3}), implying that the critical size of the crystals is reached and the increase in crystallinity is mainly due to crystallization of the remaining gaps between the crystals.

## IV. SUMMARY

Simultaneous measurements of the temperature dependent electrical resistance and Seebeck coefficient of GST (Ge_{2}Sb_{2}Te_{5}) thin films were performed up to 540 °C. Repeated measurements to increasingly maximum temperatures allow characterization of the properties of each state (in contrast to continuous measurements which show the convoluted effects of the temperature dependence of the transport parameters and material crystallization during heating, as also shown here up to melting temperature). The measured resistance was scaled to resistivity using the 4 point room-temperature resistivity measurement performed on a sample of the same film. The R(T) characteristics measured at different crystalline states follow an Arrhenius dependence with a decreasing activation energy as the material crystallizes. The S(T) results show p-type conduction until melting temperature and linear S(T) characteristics for each state above glass transition temperature, in agreement with the degenerate semiconductor transport model. The measurements also show that both the mixed amorphous-*fcc* and the mixed *fcc*–*hcp* phases exhibit a constant positive Thomson coefficient (dS/dT). A linear relationship between the slope of S(T) characteristics and the activation energy of the Arrhenius conduction for the GST material is also observed for the mixed amorphous-*fcc* phase. This observation can be useful to estimate the temperature-dependent conductivity or Seebeck coefficient of GST from a single measurement of the Seebeck coefficient or a few conductivity measurements at low temperature points (to obtain the conduction activation energy). *In-situ* XRD measurements on a 100 nm thin GST film sample showed the plane-dependent thermal expansion of the *hcp* phase, with a maximum thermal expansion observed for the (004) plane.

A percolation model of conducting spheres in a lower conductivity matrix (which predicts the sharp drop observed in the resistance with a relatively small change in the grain size, at a critical crystalline density threshold) was applied to the measured data to relate the electrical transport parameters and the crystalline grain sizes obtained from XRD measurements. The R(T) results of mixed phase amorphous-*fcc* are then expressed in terms of the amorphous and fully crystalline *fcc* temperature-dependent resistance values using the effective-medium theory to obtain the temperature dependent crystallinity fraction of the material.

This study focused on the properties of GST up to the second phase transition (*fcc*–*hcp*), which is the more technologically relevant range as phase-change memory devices do not experience the slow *fcc*–*hcp* transition during switching. A similar percolation and effective medium theory model can however be applied to the mixed *fcc*–*hcp* phase after the second transition for a fuller understanding of the crystallization dynamics and transport properties in chalcogenide glasses.

## ACKNOWLEDGMENTS

The GST films were deposited at IBM T.J. Watson Research Center and characterized at UConn. This work was partially supported by the U.S. National Science Foundation through Award Nos. ECCS 0925973 and ECCS 1150960. The characterization and analysis efforts of L.A. were supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award No. DE-SC005038. L.A. also acknowledges a graduate fellowship from the Graduate Assistance in Areas of National Need (GAANN). F.D. and K.C. acknowledge graduate fellowships from the Republic of Turkey Ministry of National Education. A.C. was supported through an NSF GRFP fellowship. The authors would also like to thank Simone Raoux, Norma Sosa, and Matthew BrightSky for their contributions to sample fabrication at the IBM T.J. Watson Research Center.