We measure heterogeneous power dissipation in phase change memory (PCM) films of 11 and 22 nm thin Ge_{2}Sb_{2}Te_{5} (GST) by scanning Joule expansion microscopy (SJEM), with sub-50 nm spatial and ∼0.2 K temperature resolution. The heterogeneous Joule and Peltier effects are explained using a finite element analysis (FEA) model with a mixture of hexagonal close-packed and face-centered cubic GST phases. Transfer length method measurements and effective media theory calculations yield the GST resistivity, GST-TiW contact resistivity, and crystal fraction of the GST films at different annealing temperatures. Further comparison of SJEM measurements and FEA modeling also predicts the thermopower of thin GST films. These measurements of nanometer-scale Joule, thermoelectric, and interface effects in PCM films could lead to energy-efficient designs of highly scaled PCM technology.

## I. INTRODUCTION

Phase change memory^{1} (PCM) is a non-volatile memory technology with potential for fast (sub-nanosecond)^{2} and low power (femtojoule)^{3,4} operation. PCM has potential to replace DRAM and Flash memory in future electronics.^{5} Data in chalcogenide based PCM, such as Ge_{2}Sb_{2}Te_{5} (GST), are stored by the large ratio (>10^{3}) in electrical resistance between amorphous and crystalline states of the material. Reversible switching between phases is typically driven by Joule heating; however, Peltier,^{6} Seebeck,^{7} and Thomson^{8} effects have been observed to contribute to phase change.^{9} Previous studies have shown that the thermopower for bulk and thin film face-centered cubic (fcc) GST is large (200–400 *μ*V K^{−1}).^{7,10–13} Higher temperature annealing forms hexagonal close-packed (hcp) GST^{14} which reduces the GST thermopower (15–50 *μ*V K^{−1}).^{7,10,11,13} Few studies have examined the effect of amorphous, fcc, and hcp phases on electrical^{15,16} or thermoelectric^{7,12} properties of thin GST films, which are important for device scaling. Electrical contacts and thermal interfaces to GST are also important for heat generation and thermal confinement of GST devices.^{17–20} Recent work has measured the role of interfaces^{17} and thermoelectric effects^{6,8,12} in GST devices. These studies are essential, since electrical and thermal interfaces could reduce PCM programming power^{17,18} by 20%–30%, and thermoelectric effects may reduce power consumption^{9} an additional 20%–40% depending on the thermopower of thin GST films. However, little is known of electrical properties, interface resistances, thermopower, and heat generation in sub-25 nm thin GST films.

In this study, we measured the nanometer-scale temperature distribution and properties of lateral PCM devices with 11 and 22 nm thin GST. Transfer length method (TLM) measurements on devices with varying channel lengths yielded the GST electrical resistivity *ρ _{GST}* and GST-TiW contact resistivity

*ρ*for each sample. Effective media theory (EMT)

_{C}^{7,21}calculations yielded the crystal fraction of amorphous, fcc, and hcp GST for the 11 and 22 nm thin GST samples annealed at 150, 200, and 250 °C. Nanometer-scale thermometry with sub-50 nm spatial and ∼0.2 K temperature resolution was accomplished by scanning Joule expansion microscopy (SJEM),

^{12,22–25,35}an atomic force microscopy (AFM) based technique. The SJEM technique is modified for simultaneous and direct observation of Joule and Peltier effects on working PCM devices. We observe

*uniform*heating for mixed amorphous and fcc GST thin films, and laterally

*heterogeneous*Joule and thermoelectric effects in mixed fcc and hcp GST thin films. Increasing the annealing temperature increases the hcp GST crystal fraction and the heterogenous Joule heating and Peltier heating and cooling between fcc and hcp GST. We develop a two and three dimensional (2D and 3D) finite element analysis (FEA) model to understand SJEM results. The 3D FEA model predicts the observed heterogeneous heating and estimates the hcp GST grain size. Comparing SJEM measurements with the 2D FEA model predicts

*ρ*and

_{GST}*ρ*, which are in good agreement with values obtained from TLM measurements. The good agreement between TLM measurements and FEA fitting of SJEM measurements to predict the properties of the sub-25 nm thin GST films indicates both methods are accurate for measuring device properties. SJEM measurements and modeling also yield the first measurements of the thermopower of sub-25 nm thin GST films.

_{C}## II. MEASUREMENTS

### A. Device fabrication and SJEM measurements

Figure 1(a) shows the lateral GST device. A 300 nm SiO_{2}/Si wafer was diced into ∼1.5 × 1.5 cm^{2} samples, and GST with thickness *t _{GST}* = 11 or 22 nm was sputtered onto the samples at 5 mT in an Ar environment at a rate of 2.5 nm min

^{−1}. The samples were annealed at a temperature

*T*= 150, 200, or 250 °C for 10 min in a N

_{A}_{2}environment, with a heating and cooling rate of ∼30 °C min

^{−1}. The supplement describes

*in-situ*two probe measurements of the sample resistance while annealing.

^{26}After annealing, lateral GST devices with channel length

*L*= 2 to 12

*μ*m were fabricated by photolithography patterning and sputtering of 10 nm TiW (10/90% weight) and 30–60 nm Au. The Au reduces the electrode sheet resistance. Fabrication was completed by spin coating 60–200 nm of poly(methyl methacrylate) (PMMA) on the samples. The PMMA serves a dual purpose: it protects the devices from oxidation, and amplifies thermo-mechanical expansions of the PCM device during operation.

^{12}

Figure 1(a) shows a schematic of the SJEM experiment. A sinusoidal waveform at frequency *ω** **=** *43 kHz and bias amplitude *V* drives the device and generates resistive heating within the device. The periodic resistive heating of the device locally increases the temperature of the surrounding PMMA, SiO_{2}, and Si substrate. The resulting thermo-mechanical expansions of the sample were measured by the AFM laser, photodiode, and cantilever in contact with the surface. A lock-in amplifier at the first or second harmonic, 1*ω* or 2*ω*, with a low-pass filter bandwidth of 3–27 Hz recorded the peak-to-peak (twice the amplitude) surface expansion Δ*h* down to ∼2–3 pm. The measurement spatial resolution was ∼50 nm and temperature resolution was ∼0.2 K.^{12,22} SJEM can resolve current crowding and Peltier effects due to current flow between the GST and TiW as the current transfer length *L _{T}* = 0.4–1.2

*μ*m between the GST-TiW (the distance over which 1/

*e*of the current is transferred between the two materials) is greater than the spatial resolution.

^{12}

A FEA model was used to interpret the SJEM measurements by predicting the thermo-mechanical surface expansion and corresponding GST temperature rise. The model simulates Joule and thermoelectric effects in the GST device using modified heat diffusion and Poisson equations.^{27,28} To simulate the SJEM measurements, the predicted temperature field was coupled with a thermo-mechanical model. The Fourier transform of the equations yielded the frequency response of the predicted Δ*h* and Δ*T*.^{12} The supplement contains additional information on the model.^{26}

Figure 1(b) shows the measured surface expansion Δ*h* overlaid on the topography of a 7.5 *μ*m channel length and 22 nm thin GST device annealed at 250 °C. The device was biased with *V _{DS}* = 8.9 V. Subtracting the voltage drop across the electrodes and probes from

*V*yields the device bias amplitude

*V*. The GST peak-to-peak temperature rise Δ

_{DS}*T*is proportional to Δ

*h*and is related using FEA modeling.

^{12,22,25}The measured Δ

*h*is non-uniform across the device, indicating heterogeneous lateral heating, electric field, and resistivity distribution due to the presence of mixed fcc and hcp GST.

Figure 2 shows how SJEM can measure both Joule and Peltier effects. Figure 2(a) shows a simple diagram of the lateral GST devices, where hole flow into (from) the contacts locally heats (cools) the device.^{12,22,29} The schematic shows both time and frequency domain diagrams of the technique. We distinguish the time dependent device bias *V _{DS}*(

*t*) from the frequency domain zero and first harmonic device bias by

*V*

_{DS,}_{0}

_{ω}and

*V*

_{DS,}_{1}

_{ω}, where

*V*

_{DS,}_{1}

_{ω}is a complex number. We distinguish the time dependent temperature rise

*T*from the zero, first, and second harmonic temperature rise by

*T*

_{0}

_{ω},

*T*

_{1}

_{ω}, and

*T*

_{2}

_{ω}, where

*T*

_{1}

_{ω}and

*T*

_{2}

_{ω}are complex numbers. The first and second harmonic peak-to-peak temperature rise are given by Δ

*T*

_{1}

_{ω}= 2|

*T*

_{1}

_{ω}| and Δ

*T*

_{2}

_{ω}= 2|

*T*

_{2}

_{ω}|. For SJEM measurements, the peak-to-peak device temperature rise Δ

*T*is proportional to the measured peak-to-peak sample surface thermo-mechanical expansion Δ

*h*.

Figure 2(b) shows the temperature distribution for a bipolar waveform, defined as *V _{DS}*(

*t*) =

*V*

_{DS,}_{1}

_{ω}sin(2π

*ωt*) where time is given by

*t*. Joule heating is evident as the large temperature rise across the device and is independent of the carrier flow direction. The Peltier effect is evident at the contacts as the small change in

*T*with carrier flow direction.

^{12,22}Joule heating is proportional to

*V*

_{DS}^{2}and Peltier effects are proportional to

*V*. Joule heating occurs at the zero and second harmonic 2

_{DS}*ω*, and Peltier effects occur at the first harmonic 1

*ω*for a device subject to a bipolar waveform. Therefore, Δ

*T*

_{2}

_{ω}is due to Joule heating, and Δ

*T*

_{1}

_{ω}is due to Peltier effects. Figure 2(c) shows the frequency domain Δ

*T*

_{1}

_{ω}and Δ

*T*

_{2}

_{ω}from Fig. 2(b). Joule heating is evident in Fig. 2(c) as the large Δ

*T*

_{2}

_{ω}across the channel. Peltier effects are evident as the small Δ

*T*

_{1}

_{ω}at the contacts. Thus, SJEM provides independant measurements of Joule and Peltier effects.

^{35}We note

*T*

_{1}

_{ω}experiences a 180° phase shift between the contacts as Peltier heating or cooling of the contacts depends on the bias polarity, or carrier flow direction.

^{12,22}

### B. GST properties

TLM measurements were used to obtain device and contact resistance for each sample. The lateral GST devices have a device width *W* = 245 *μ*m and source-drain spacing *L* = 2–12 *μ*m. The sheet and contact resistance of each sample was calculated from simple linear regression of the measured resistance of more than 10 devices per sample. The GST resistivity, GST-TiW contact resistivity, and current transfer length were calculated from the sheet and contact resistance.^{12,22,30} The supplement shows the TLM measurements and analysis.^{26}

Figure 3(a) shows the GST resistivity and GST-TiW contact resistivity from TLM measurements on all the samples. The measured GST resistivity *ρ _{GST}* continuously decreases with increasing annealing temperature. The measured GST-TiW contact resistivity

*ρ*also decreases with annealing temperature until

_{C}*T*= 250 °C. The contact resistance for the samples annealed at 250 °C is a few ohms, near our TLM measurement resolution, and we are unable to determine if

_{A}*ρ*is lower than the values shown in Fig. 3(a) from TLM measurements. The measured contact resistance of the 22 nm thin GST sample annealed at 200 °C is also near the measurement resolution.

_{C}EMT^{21} was applied to calculate the crystal fraction *x _{f}* of the GST phases

^{7}of each sample. The

*in-situ*annealing resistance measurements

^{26}show a large (∼10

^{3}–10

^{4}Ω) change in sample resistance at ∼160 °C indicating the majority of GST quickly changes from amorphous to fcc GST.

^{31,32}The sample resistance continuously decreases with increased annealing temperature indicating a gradual transition from fcc to hcp GST.

^{14}Samples annealed above 160 °C have little amorphous phase present and are assumed to be a binary mixture of fcc and hcp GST. Samples annealed below 160 °C have significant amorphous phase and are assumed to be a binary mixture of amorphous and fcc GST. The application of EMT is further described in the supplement.

^{26}

Figure 3(b) shows the calculated crystal fraction for amorphous, fcc, and hcp GST for each sample. The crystal fraction of amorphous, fcc, and hcp GST is given by *x _{amr}*,

*x*, and

_{fcc}*x*. The majority of samples are dominated by fcc GST; except the two samples annealed at 250 °C have a significant fraction of hcp GST. We are unable to explain the observed trends in the calculated crystal fraction with GST thickness. Previous work has shown the amorphous to fcc phase transition temperature does not significantly change with film thickness and the fcc to hcp transition temperature decreases with decreasing film thickness.

_{hcp}^{32}Therefore, we expect similar

*x*for samples annealed at 150 °C and higher

_{f}*x*for the thinner samples annealed at higher temperatures, contrary to our observations. Interfaces dominate the growth kinetics of thin film GST,

_{hcp}^{31}and further work is required to understand the growth of thin GST films on SiO

_{2}.

## III. RESULTS AND DISCUSSION

### A. SJEM measurements of uniform GST devices

Figure 4 shows the measured and predicted Δ*h* for 2.2 *μ*m channel length and 22 nm thin GST device annealed at 200 °C. The device is biased with amplitude *V _{DS}* = 0.9, 1.2, and 1.5 V. The measured Δ

*h*was uniform in the

*y*-direction indicating uniform lateral heating, electric field, and resistivity distribution. Comparison of measurements and predictions of the surface expansion and temperature distribution in the device yields the GST properties.

^{12}Measurements are an average of 18 line scans with deviation smaller than the markers.

Figure 4 shows measurements and predictions of Joule heating, current crowding, and Peltier effects. Figure 4(a) shows the measured and predicted Δ*h*_{2}_{ω}, due to Joule heating. Joule heating occurs in the GST channel and at the GST-TiW contacts due to finite *ρ _{GST}* and

*ρ*.

_{C}^{12,22}Fitting the measured and predicted Δ

*h*predicts

_{2}_{ω}*ρ*= 4.8 ± 0.3 × 10

_{GST}^{−5}Ω m and

*ρ*= 1.1 ± 0.3 × 10

_{C}^{−11}Ω m

^{2}for the 2.2

*μ*m channel length and 22 nm thin GST device annealed at 200 °C, similar to TLM measurements. Figure 4(b) shows the predicted Δ

*T*

_{2}

_{ω}from Fig. 4(a). The predicted Δ

*T*

_{2}

_{ω}is larger than our previous measurements for thin GST films.

^{12}Figure 4(c) shows the measured and predicted Δ

*h*

_{1}

_{ω}, due to Peltier effects. Peltier heating and cooling occurs at the GST-TiW contact due to their difference in thermopower.

^{12,22,29}Fitting the measured and predicted Δ

*h*yields

_{1}_{ω}*S*= 110 ± 10

_{GST}*μ*V K

^{−1}for the device with a calculated composition of 69 ± 1% fcc and 31 ± 1% hcp GST. Fitting measurements and predictions for

*ρ*,

_{GST}*ρ*, and

_{C}*S*yields a coefficient of determination

_{GST}*R*

^{2 }= 0.68 between FEA predictions and SJEM measurements. The fitting error was determined by fitting each measured line scan to FEA predictions. Although the coefficient of determination is low for fitting FEA predictions to SJEM measurements, the predicted GST properties are in agreement with TLM measurements, indicating the FEA model accurately predicts the GST properties and device temperature rise. A small spike in Δ

*h*

_{1}

_{ω}is observed at

*x*= 0

*μ*m, due to the presence of a small grain of hcp GST in the predominately fcc GST sample. The difference in

*S*between fcc and hcp GST causes local Peltier effects in the channel, explored further below, and was not included in 2D FEA simulations. Figure 4(d) shows the predicted Δ

_{GST}*T*

_{1}

_{ω}from Fig. 4(c). At the contact, Peltier heating and cooling cause a 1.6 and 3 K change in temperature, Δ

*T*

_{1}

_{ω}, compared to the Joule heating induced temperature rise, Δ

*T*

_{2}

_{ω}, of 7 and 18 K for

*V*= 0.9 and 1.5 V. Peltier effects were ∼23% and ∼17% of the contact temperature change for

_{DS}*V*= 0.9 and 1.5 V. A constant surface expansion of ∼2–3 pm is recorded across the device for 1

_{DS}*ω*and 2

*ω*based measurements when no bias is applied, with no correlation to the device topography. Therefore, the large Δ

*h*observed when a bias is applied to the device is due to Joule heating and Peltier effects.

### B. Measurements of heterogeneous Joule and thermoelectric effects

Figure 5 shows the measured heterogeneous surface expansion for three 11 nm thin GST devices with channel lengths 2.5, 3.2, and 2.5 *μ*m annealed at 150, 200, and 250 °C. Figures 5(a)–5(c) show the measured Δ*h*_{2}_{ω,Norm} which is the measured Δ*h*_{2}_{ω} normalized by the average channel Δ*h*_{2}_{ω}. The measured Δ*h*_{2}_{ω,Norm} is an indicator of local GST Joule heating. Figures 5(d)–5(f) show the measured Δ*h*_{1}_{ω,Norm} which is the measured Δ*h*_{1}_{ω} normalized by the average contact Δ*h*_{1}_{ω}. Figures 5(g)–5(i) show the measured phase of the first harmonic expansion *Θ*_{1}_{ω}. The measured Δ*h*_{1}_{ω,Norm} and *Θ*_{1}_{ω} are indicators of local GST Peltier effects. The devices annealed at 150, 200, and 250 °C were driven by a device bias *V _{DS}* = 4.8, 2.6, and 1.0 V. The device annealed at 150 °C exhibited the largest Peltier effects at the GST-TiW contacts due to the large difference in the mixed amorphous and fcc GST and TiW contact thermopower.

Figures 5(a)–5(c) show the normalized second harmonic expansion for the three devices. The measured Δ*h*_{2}_{ω,Norm} is proportional to Δ*T*_{2}_{ω} and is an indicator of local GST Joule heating. Figures 5(a)–5(c) show the heterogeneity of Δ*h*_{2}_{ω,Norm} increases with annealing temperature. We attribute the lateral heterogeneous Joule heating of our devices to the presence of large grains of hcp GST in a matrix of fcc GST. The presence of hcp grains in a matrix of fcc GST would create a non-uniform resistivity distribution causing heterogeneous lateral Joule heating. The device in Fig. 5(a) has a low hcp phase crystal fraction and experiences uniform Joule heating, and the device in Fig. 5(c) is composed of ∼48% hcp GST and experiences heterogeneous Joule heating. The measured Δ*h*_{2}_{ω,Norm} deviates ∼45% across the channel in Fig. 5(c), or the Joule heating induced temperature rise varies ±45% across the channel. The supplement further describes heterogeneous lateral Joule heating including a similar but smaller trend for the 22 nm thin GST samples.^{26}

Figures 5(d)–5(f) show the normalized first harmonic expansion for the three devices. The measured Δ*h*_{1}_{ω,Norm} is proportional to Δ*T*_{1}_{ω} and is an indicator of local Peltier effects due to lateral changes in material thermopower. Figure 5(d) shows Δ*h*_{1}_{ω,Norm} for a device which experiences uniform Peltier effects at the contacts and no Peltier effects in the channel, indicating the channel has uniform thermopower. Figures 5(e) and 5(f) show Δ*h*_{1}_{ω,Norm} for two devices with significant hcp GST crystal fraction and show significant Δ*h*_{1}_{ω,Norm} measured in the channel. The presence of both fcc and hcp GST in the channel causes local Peltier heating and cooling due to the large difference in fcc and hcp GST thermopower (150–300 *μ*V K^{−1}).^{7,10,13} Large spikes are evident in Δ*h*_{1}_{ω,Norm} for these two devices in the channel and at the contacts. The heterogeneous resistivity distribution forms preferential current pathways, locally increasing the current density and locally enhancing thermoelectric effects.^{22} However, the average Δ*h*_{1}_{ω} is the largest in Fig. 5(d) due to the large difference in amorphous-fcc GST and TiW thermopower (200–400 *μ*V K^{−1}).^{7,10,13}

Figures 5(g)–5(i) show the measured phase of the first harmonic expansion for the three devices. SJEM measures the first harmonic expansion amplitude Δ*h*_{1}_{ω} and phase *Θ*_{1}_{ω}. The measured Δ*h*_{1}_{ω} indicates the magnitude of Peltier heating and cooling. The measured *Θ*_{1}_{ω} indicates if the sample experiences local Peltier heating or cooling with bias polarity. A 180° shift in *Θ*_{1}_{ω} is observed between Peltier heated and cooled locations. Figure 5(d) shows measurable Δ*h*_{1}_{ω} at the contacts indicating Peltier effects at the contacts. Figure 5(g) shows a 180° shift in Θ_{1}_{ω} between the contacts indicating one contact experiences Peltier heating while the other contact experiences Peltier cooling. Therefore, Peltier heating and cooling can be discerned by combination of measureable Δ*h*_{1}_{ω} and 180° shifts in *Θ*_{1}_{ω}. The devices in Figs. 5(h) and 5(i) show similar behavior to Fig. 5(g), but additional peaks in Δ*h*_{1}_{ω} and 180° shifts in *Θ*_{1}_{ω} are observed in the channel corresponding to intra-GST Peltier heating and cooling, due to the presence of fcc and hcp GST.

We hypothesize why uniform lateral heating is observed in amorphous-fcc GST devices and heterogeneous lateral heating is observed in fcc-hcp GST devices. We attribute the difference in heating due to the different growth mechanisms of fcc and hcp GST which develop different grain structure. Previous work has shown fcc GST grows from amorphous GST as small grains (<10 nm) or 20–30 nm diameter columns at a GST-SiO_{2} surface.^{31,33} Previous work has also shown that fcc GST grows as a uniform lateral plane from amorphous GST at a free GST surface.^{31} Our samples have both a GST-SiO_{2} and free GST surface. The growth of a uniform lateral plane of fcc GST would result in uniform heating for amorphous-fcc samples. Also, a device composed of small (<30 nm) grains of fcc GST would exhibit homogeneous properties at the 50-nm scale, and SJEM measurements of the device would also observe uniform heating. Previous work has shown fcc GST gradually transforms into hcp GST with increasing annealing temperature.^{14} We observe heterogeneous lateral heating of our fcc-hcp GST devices indicating the hcp grains increase to a size greater than the measurement spatial resolution. The observation of Peltier heating and cooling in the GST channel indicates Peltier effects between fcc and hcp GST with different thermopowers. We conclude the uniform lateral heating of amorphous-fcc GST devices is due to the planar or small grain size growth of fcc GST, and the heterogeneous lateral heating of fcc-hcp GST devices is due to the gradual growth of large hcp grains from fcc GST.

### C. Predictions of heterogeneous Joule and thermoelectric effects

Figure 6 shows the measured and predicted surface thermo-mechanical expansion for a measured and simulated 22 nm thick GST device. The measured device has a channel length of 7.5 *μ*m and was annealed at 250 °C. The simulated device has a channel length of 8 *μ*m. We do not expect a match between measurements and predictions as the exact phase distribution of the measured device is unknown. The supplement describes the development of the FEA model used to simulate a mixed phase GST device.^{26}

Figure 6(a) shows the simulated phase distribution of the GST channel. Cylinders with 400 nm diameter and 22 nm thick hcp GST were randomly placed in a matrix of fcc GST. Additional hcp GST was added at several locations to reduce meshing and computation intensity. The measured and simulated devices are composed of 70 ± 3% and 67% hcp GST. The simulated fcc and hcp GST properties were *ρ _{GST}* = 2 × 10

^{−4}and 3.3 × 10

^{−5}and

*S*= 200 and 15

_{GST}*μ*V K

^{−1}.

Figures 6(b)–6(g) show the measured and predicted surface expansion for the two devices. Figures 6(b) and 6(c) show measured and simulated heterogeneous Δ*h*_{2}_{ω}, indicating non-uniform Joule heating and resistivity distribution. The heterogeneous resistivity distribution is due to the presence of large and randomly mixed hcp GST grains in the device. Figures 6(d)–6(g) show measured and simulated spikes in Δ*h*_{1}_{ω} and 180° shifts in *θ*_{1}_{ω} indicating local Peltier effects. The Peltier effects observed at the GST-TiW contact are due to the difference in thermopower between the GST and TiW. The Peltier effects observed in the GST channel are due to the difference in thermopower between fcc and hcp GST. The simulation only considers Joule and Peltier effects in a lateral GST device due to a random mixture of large hcp and fcc GST grains with no interface resistance between the grains, and the simulation predicts the measured heterogeneous heating behavior well. Therefore, the majority of heterogeneous Joule heating in the devices is attributed to the finite resistivity of the large fcc and hcp grains.

We estimate the hcp GST grain size from Figures 6(a), 6(d), and 6(e). The same method is used to calculate the average hcp GST grain length *l _{hcp}* from Figs. 6(d) and 6(e), and the accuracy of the method is verified by comparing the calculated

*l*from Figs. 6(a) and 6(e). We calculate

_{hcp}*l*= 0.8

_{hcp}*μ*m for the simulation from Fig. 6(a) by dividing the volume of hcp GST by the number of hcp grains and assuming the hcp GST is composed of uniform diameter cylinders which are 22 nm thick. The supplement describes the calculation of

*l*using Figs. 6(d) and 6(e),

_{hcp}^{26}briefly described here. Figures 6(d) and 6(e) are used to calculate

*l*by estimating the average distance between Δ

_{hcp}*h*

_{1}

_{ω}peaks, which correspond to changes in GST phase. We calculate

*l*= 1.1

_{hcp}*μ*m for the device shown in Fig. 6(e), close to the

*l*= 0.8

_{hcp}*μ*m from Fig. 6(a). We expect our method of calculating

*l*from peaks in Δ

_{hcp}*h*

_{1}

_{ω}to overestimate

*l*as not every fcc-hcp interface experiences significant Peltier effects. We calculate

_{hcp}*l*= 0.7

_{hcp}*μ*m for the device shown in Fig. 6(c) which is a 22 nm thick GST sample annealed at 250 °C.

### D. GST properties from SJEM measurements

Figure 7 shows the measured and predicted surface expansion for a 3.2 *μ*m channel length and 11 nm thin GST device annealed at 200 °C. The measured Δ*h* was heterogeneous in the *y*-direction due to the non-uniform fcc and hcp phase distribution, discussed above. Matching 2D FEA predictions and SJEM measurements predicted the effective device properties. Measurements are an average of 18 line scans with deviations smaller than the markers.

Figure 7(a) shows the measured and predicted second harmonic expansion for the device at *V _{DS}* = 1.5, 2.2, and 2.6 V. Fitting the measured and predicted Δ

*h*

_{2}

_{ω}predicts

*ρ*= 5.5 ± 0.4 × 10

_{GST}^{−5}Ω m and

*ρ*= 3.3 ± 0.5 × 10

_{C}^{−10}Ω m

^{2}, similar to TLM measurements. The supplement details the discrepancy between the measured and predicted Δ

*h*

_{2}

_{ω}at the contacts due to error in simulating the thick PMMA coating of this device.

^{26}

Figure 7(b) shows the measured and predicted first harmonic expansion for the device at *V _{DS}* = 2.6 V. The other biases are not shown for clarity, but all bias conditions are used when fitting measurements and predictions. Fitting the measured and predicted Δ

*h*

_{1}

_{ω}predicts

*S*= 72 ± 10

_{GST}*μ*V K

^{−1}for the device with a calculated composition of 72 ± 1% fcc and 28 ± 1% hcp GST. Fitting measurements and predictions for

*ρ*,

_{GST}*ρ*, and

_{C}*S*yields

_{GST}*R*

^{2 }= 0.65. Figure 7(b) shows additional measured Δ

*h*

_{1}

_{ω}peaks in the channel due to Peltier effects between fcc and hcp GST. The observed Peltier effects are accompanied by changes in Δ

*h*

_{2}

_{ω}, or local Joule heating. The local change in Joule and Peltier effects indicates current is flowing between fcc and hcp GST due to their different resistivities and thermopowers. Heterogeneous heating of GST was not included in the 2D FEA model.

We observe an increase in the heterogeneity of the measured expansion as the GST thickness decreases. Figures 4 and 7 show the measured Δ*h* of two devices with similar channel lengths and annealing temperatures but different GST thickness. The thinner device in Fig. 7 shows increased heterogeneous heating compared to the device in Fig. 4. We observe an increase in lateral heterogeneous heating for all the 11 nm thin devices compared to similar 22 nm thin devices, which is detailed in the supplement.^{26} Further study into the growth mechanisms of thin film GST^{7,31,32} is required to understand the GST grain structure which causes the increased heterogeneous heating with decreasing GST thickness.

Figure 8(a) shows the predicted GST resistivity and GST-TiW contact resistivity from fitting FEA predictions to SJEM measurements of Δ*h*_{2}_{ω} for all the measured devices. A minimum of 3 devices were measured per sample. The predicted *ρ _{GST}* in Fig. 8(a) is similar to the TLM measurements shown in Fig. 3(d). However, FEA fitting of SJEM measurements predicts lower

*ρ*values than TLM measurements. The contact resistance of the 11 nm thin GST devices annealed at 250 °C and the 22 nm thin GST devices annealed at 200 and 250 °C were near the TLM measurement resolution. Therefore, TLM measurements yielded inaccurate measurements of

_{C}*ρ*for these samples. However, we observed noticeable contact heating in our Δ

_{C}*h*

_{2}

_{ω}measurements for similar devices, allowing the FEA model to predict

*ρ*for these devices. Figure 8(a) shows that FEA fitting of SJEM measurements predicts lower

_{C}*ρ*values for these samples than TLM measurements. FEA fitting of SJEM measurements is unable to predict

_{C}*ρ*< 2 × 10

_{C}^{−11}Ω

*μ*m

^{2}as no significant contact heating was observed for these devices. Adjusting the device geometry can increase the

*ρ*resolution of TLM or FEA fitting of SJEM measurements.

_{C}Figure 8(b) shows the predicted GST thermopower from fitting FEA predictions to SJEM measurements of Δ*h*_{1}_{ω} for all the measured devices. The GST thermopower continuously decreases with increasing annealing temperature as amorphous, fcc, and hcp GST have decreasing thermopowers. EMT was applied to calculate *S _{GST}* from the calculated GST crystal fractions shown in Fig. 3(b).

^{7,34}The supplement details the application of EMT.

^{26}We calculate slightly lower

*S*when applying EMT than the predicted

_{GST}*S*from FEA fitting of SJEM measurements. A large discrepancy is observed between the two methods for the 11 nm thin GST sample annealed at 150 °C, and the supplement further discusses this discrepancy.

_{GST}^{26}The agreement between EMT calculations and FEA fitting of SJEM measurements indicates EMT can accurately describe the behavior of thin film GST, and the electrical and thermoelectric properties of 11–22 nm thin GST films behave like a uniform and random mixture of bulk GST phases.

^{21,34}

## IV. CONCLUSION

In conclusion, we measured the nanometer–scale temperature distribution and properties of lateral PCM devices with 11 and 22 nm thin GST, after annealing at 150, 200, and 250 °C. A modified SJEM technique enabled direct measurements of heterogeneous Joule and Peltier effects in thin GST films with sub-50 nm spatial and ∼0.2 K temperature resolution. The GST resistivity, GST-TiW contact resistivity, and crystal fraction of each phase were estimated from TLM measurements^{12} and EMT calculations.^{7,21} We observe uniform heating for mixed amorphous and fcc GST and heterogeneous Joule and Peltier effects in mixed fcc and hcp GST thin films. A 3D FEA model predicts the observed heterogeneous Joule heating and Peltier effects between fcc and hcp GST and estimates the hcp grain size. Increasing the annealing temperature increases the hcp crystal fraction, increasing heterogeneous Joule and Peltier effects. Comparing SJEM measurements with a 2D FEA model predicts *ρ _{GST}*,

*ρ*, and

_{C}*S*of the sub-25 nm thin GST films. The estimated

_{GST}*S*matches well with calculations using EMT. The large measured thermopower of GST for the low annealing temperature (

_{GST}*T*= 150 °C) could reduce the energy consumption by >50% in highly scaled PCM devices due to Peltier heating, compared to scenarios which only utilize Joule heating.

_{A}^{9}However, higher annealing temperatures increase hcp GST crystalline fraction, which decreases GST thermopower and the predicted reduction in PCM energy consumption. Knowledge of nanometer-scale Joule, thermoelectric, and interface effects in GST devices should enable improvements in energy efficient designs of future PCM technology.

## ACKNOWLEDGMENTS

The authors gratefully acknowledge support by the National Science Foundation (NSF) Grant No. ECCS 10-02026, and by the Materials Structures and Devices (MSD) Focus Center, under the Focus Center Research Program (FCRP), a Semiconductor Research Corporation entity.

## References

*in-situ*annealing resistance measurements, TLM measurements, EMT calculations, FEA model information, hetergenous sample heating trends, and hcp grain size calculations.