We model electrical conductivity in metastable amorphous Ge2Sb2Te5 (GST) using independent contributions from temperature and electric field to simulate phase change memory devices and ovonic threshold switches. 3D, 2D-rotational, and 2D finite element simulations of pillar cells capture threshold switching and show filamentary conduction in the on-state. The model can be tuned to capture switching fields from ∼5 to 40 MV/m at room temperature using the temperature dependent electrical conductivity measured for metastable amorphous GST; lower and higher fields are obtainable using different temperature dependent electrical conductivities. We use a 2D fixed out-of-plane-depth simulation to simulate an ovonic threshold switch in series with a Ge2Sb2Te5 phase change memory cell to emulate a crossbar memory element. The simulation reproduces the pre-switching current and voltage characteristics found experimentally for the switch + memory cell, the isolated switch, and the isolated memory cell.

Phase change memory (PCM) is a non-volatile memory that stores information as the conductive crystalline or resistive amorphous phase of a material. The crystalline-to-amorphous phase transition is controllable and reversible, with PCM attaining 103× faster write times and 104× better endurance than flash memory.2 PCM is CMOS back-end-of-line compatible, allowing memory integration on-chip with CMOS circuitry to eliminate latency from off-chip memory access.3 PCM can be implemented as a crossbar array, allowing high device density (4F2) in multiple memory layers for efficient neuromorphic computing.4 Crossbars consist of perpendicular word and bit lines with memory elements sandwiched between these lines at the cross-points (Fig. 1). Each word or bit line is connected to Vdd or ground through a transistor, and cross-points can be randomly accessed by activating their corresponding word and bit lines. Non-selected devices can form undesirable current sneak paths between selected and non-selected lines; hence, access devices with non-linear current–voltage (IV) characteristics, high Ion/Ioff ratios (Ion/Ioff  ∼ 106 for a 1000 × 1000 device array), and high drive capabilities to write (Iwrite ∼ MA/cm2) are needed at each cross-point.5 Ovonic threshold switches (OTSs) made from amorphous chalcogenides are one such access device.

FIG. 1.

A schematic illustration of a cross-point cell with an ovonic threshold switch in series with a phase change memory element. The shown cell structure is used for 2D analysis to compare modeling results to the experimental results in Ref. 1.

FIG. 1.

A schematic illustration of a cross-point cell with an ovonic threshold switch in series with a phase change memory element. The shown cell structure is used for 2D analysis to compare modeling results to the experimental results in Ref. 1.

Close modal

Amorphous chalcogenides are highly resistive under low electric fields and exhibit “threshold switching” to a highly conductive on-state at a threshold voltage (Vth). Once switched, these materials remain in the on-state while a minimum holding current or voltage (Ihold or Vhold) is maintained (Fig. 2).6 Crystallization dynamics of these materials determine whether they are more suitable for an OTS or a PCM device. PCM materials include various stoichiometries of Ag–In–Sb–Te and Ge–Sb–Te, with typical crystallization times on the order of 10 ns.7 OTS materials remain in their amorphous phase during normal operation and are often characterized by the number of switching cycles they withstand before failure (through, e.g., material damage or crystallization): >600 for GeTe6,8 >108 for AsTeGeSiN,9 and unknown for As-doped Se–Ge–Si, a material used in a commercial OTS + PCM crossbar array.10 

FIG. 2.

(a) 3D and (b) 2D-rotational OTS geometries used in this work. T = 300 K is used as the initial condition and as the boundary condition at the top and bottom of the TiN contacts. (c) When a 3 V/60 ns triangular pulse is applied at Vapp, the device (i) is highly resistive until Vswitch∼ 1.75 V, (ii) switches on at ∼10 ps, (iii) and (iv) remains on until the voltage and current drop below Vhold∼ 0.4 V and Ihold ∼ 0.25 mA, and (v) returns to the high resistance off-state. Symmetric switching behavior is observed when a negative ramped pulse is applied. The 2D-rotational and 3D simulations give similar results, as expected for rotationally symmetric filamentary switching. The inset in (c) is the first quadrant in a logarithmic scale.

FIG. 2.

(a) 3D and (b) 2D-rotational OTS geometries used in this work. T = 300 K is used as the initial condition and as the boundary condition at the top and bottom of the TiN contacts. (c) When a 3 V/60 ns triangular pulse is applied at Vapp, the device (i) is highly resistive until Vswitch∼ 1.75 V, (ii) switches on at ∼10 ps, (iii) and (iv) remains on until the voltage and current drop below Vhold∼ 0.4 V and Ihold ∼ 0.25 mA, and (v) returns to the high resistance off-state. Symmetric switching behavior is observed when a negative ramped pulse is applied. The 2D-rotational and 3D simulations give similar results, as expected for rotationally symmetric filamentary switching. The inset in (c) is the first quadrant in a logarithmic scale.

Close modal

There is still debate on the mechanism(s) underlying threshold switching despite many studies investigating this phenomenon.1,6,11–19Vth scales linearly with device thickness, suggesting a field-based mechanism at a threshold Eth.15 Theoretical arguments and the presence of crystalline filaments in failed devices suggest that on-state conduction is filamentary.12,15

Current–field (IE) measurements on amorphous chalcogenides typically show an ohmic regime at low E, an intermediate regime where ln(I)E or E12, and a high field regime where I increases at a super-exponential rate with E.20 Reference 20 reviews conduction mechanisms in amorphous materials and shows that multiple mechanisms can fit measured data through the tuning of parameters, which are otherwise difficult to validate (e.g., trap-to-trap distance, effective carrier mass, and carrier mobility). Models for these mechanisms have been proposed, which define carrier concentrations (n) and mobilities (μ) as functions of E and temperature (T) such that all three IE regimes are captured with an electrical conductivity σ=qnμ, but such techniques are computationally expensive in addition to relying on multiple unknown fitting parameters. Reference 13 proposes a field-based switching model where carrier concentrations rapidly increase once trap states near the Fermi band are filled and fits the model to amorphous (a-) Ge2Sb2Te5 (GST) measurements. References 18 and 19 propose a field-assisted thermal model based on multiple trap barrier lowering and fit the model to a-GeTe and doped a-GST measurements. References 14 and 21 ascribe switching to crystalline filaments, which form under high E and fit the model to a-GST using relaxation oscillations. They suggest that these filaments become unstable at low E in OTS materials but remain stable in PCM materials.

Here, we model conductivity in a-GST as the sum of T and E dependent terms (σa = σT + σE). This model does not require a computationally expensive evaluation of the (density of states × Fermi function) integral at every (T, E) combination where conductivity is needed; hence, it is appropriate for transient finite element simulations with dynamic T and E. While this model trades accuracy for ease of computation, simulations show that it (i) can be tuned to fit a wide range of switching fields, (ii) captures the appropriate changes in threshold switching as we systematically vary ambient conditions, geometries, and the rise and fall times of applied pulses, and (iii) can reproduce the behavior of a series PCM + OTS device when used with a finite element phase change model.22–25 

We use a-GST material parameters as in Refs. 23 and 25 to simulate an OTS material. References 26–29 present a comprehensive development and analysis of material parameters for a-GST, c-GST, SiO2, and TiN. A concise summary of all parameters can be found in Ref. 30. Of particular interest to this work is σa, which we model as in Ref. 26 and cap at σmax = σT(930 K) (Fig. 3),

(1)

which is equivalent to assuming that free carriers are excited to a band edge via independent thermal and electrical processes,

(2)

where nT and nE are carriers excited via thermal or electrical processes and μ is the free carrier mobility.

FIG. 3.

(a) T and E dependent contributions to electrical conductivity in (1); the temperature is uncertain for T > Tmelt. (b) Conductivity-field behavior using the model in this work (metastable a-GST) and the model in Ref. 19 (drifted, doped a-GST) at various temperatures. We use Eswitch (300 K) = 25.01 MV/m in this work and Eswitch (300 K) = 155 MV/m for the curves in Ref. 19. Spheres in (b) show thermal contribution to conductivity at each temperature using the model in this paper.

FIG. 3.

(a) T and E dependent contributions to electrical conductivity in (1); the temperature is uncertain for T > Tmelt. (b) Conductivity-field behavior using the model in this work (metastable a-GST) and the model in Ref. 19 (drifted, doped a-GST) at various temperatures. We use Eswitch (300 K) = 25.01 MV/m in this work and Eswitch (300 K) = 155 MV/m for the curves in Ref. 19. Spheres in (b) show thermal contribution to conductivity at each temperature using the model in this paper.

Close modal

We fit σT to low-E measurements of metastable a-GST wires31 and molten GST thin films,32 as described in Ref. 33 [Fig. 3(a)]. Measurements of liquid GST show a semiconductor-to-metal transition near 930 K,34 with σ becoming practically independent of T. We, therefore, limit σa(T, E) to σT(930 K) = 4.1 × 105−1 m−1), which is in line with the highest conductivities measured in molten GST34–36 [Fig. 3(a)].

σE is assumed to be an exponential that contributes 1% of σT(300 K) at zero field and 10% of σT(Tmelt) at Eth,

(3)

where C1 = 2.42 × 10−7 m/V is chosen such that σE(Eth) = σT(Tmelt)× 10%. We use Eth = 56 MV/m, the breakdown field measured in as-deposited a-GST,37 and Tmelt = 858 K32 [Fig. 3(a)].

We include σE curves at various temperatures calculated using the models in this work (for metastable a-GST) and the models in Ref. 19 (for drifted, doped a-GST) for comparison [Fig. 3(b)]. σT dominates at low fields, while σE begins to dominate at higher and higher fields with increasing T.

We couple heat transfer and current continuity physics to simulate transient device operation, including temperature dependent thermoelectric effects,38 

(4)
(5)

where dm is the mass density, cp is the specific heat, t is the time, k is the thermal conductivity, V is the electric potential, J is the current density, S is the Seebeck coefficient, and qH accounts for the latent heat of phase change. We use temperature dependent parameters for a-GST, crystalline GST (c-GST), TiN, and SiO2 as in Refs. 23 and 25, including interfacial thermoelectric effects and thermal conductance. The interfacial electro-thermal phenomenon is expected to impact device behavior by increasing joule heating39 and confining heat in the active layer40 during switching (OTS) or read/write/erase (PCM) operations. Our model does not capture additional effects on interfacial electrical conductance (from, e.g., barrier lowering or tunneling).

We model the phase change as

(6)

where CD is a two-vector whose magnitude (CD) corresponds to phase (CD = 0 or 1 for the amorphous or crystalline phase) and whose orientation (θCD) corresponds to grain orientation (tan(θCD) = CD2/CD1), capturing nucleation, growth, and grain boundary melting.23,25 We solve for (6) in PCM devices but not in OTS devices, which we assume do not crystallize in our simulations.

We first simulate switching in 3D and 2D-rotational geometries by applying a 3 V/60 ns triangular pulse [Figs. 2(a) and 2(b)]. Results show filamentary switching with current confined to the central portion of the device [Figs. 4(a)4(j)], with practically identical IV characteristics for 3D and 2D-rotational simulations [Fig. 2(c)]. 3D simulations show some instability of the filament location [slightly off-center in Figs. 4(d) and 4(i)] and filament migration over time.

FIG. 4.

(a)–(e) x–y and (f)–(j) x–z temperature cut planes while switching the 3D OTS in Fig. 2(a) illustrate filamentary on-state conduction. (k) Current and (l) device voltage transients resulting from the applied Vapp used to generate the I–V in Fig. 2(c). Superscripts “−” and “+” in (a)–(j) refer to the time steps (1 ns increments) before and after events (tswitch, tpeak, and thold) labeled on the x axis in (l) [Fig. 2(a): RLoad = 1 kΩ, hOTS = 50 nm, rOTS = 100 nm, and Vapp = 5 V/60 ns triangular pulse].

FIG. 4.

(a)–(e) x–y and (f)–(j) x–z temperature cut planes while switching the 3D OTS in Fig. 2(a) illustrate filamentary on-state conduction. (k) Current and (l) device voltage transients resulting from the applied Vapp used to generate the I–V in Fig. 2(c). Superscripts “−” and “+” in (a)–(j) refer to the time steps (1 ns increments) before and after events (tswitch, tpeak, and thold) labeled on the x axis in (l) [Fig. 2(a): RLoad = 1 kΩ, hOTS = 50 nm, rOTS = 100 nm, and Vapp = 5 V/60 ns triangular pulse].

Close modal

We next evaluate the impact of σE by simulating switching with σE = 0 [Fig. 5(a)] and compare the results with σE defined as in (3) [Fig. 5(b)]. Vswitch and Iswitch are the values at which VDevice begins to decrease. Threshold switching occurs even with σE = 0 due to thermal runaway. However, defining σE as in (3) gives a switching field (Eswitch = Vswitch/hOTS) that is smaller and less dependent on hOTS [Fig. 5(c)]. Some hOTS dependence is still observed due to changing thermal conditions.

FIG. 5.

The switching voltage increases with hOTS both (a) without and (b) with field dependent conductivity. Including field dependent conductivity reduces the switching field's (c) magnitude and (d) sensitivity to hOTS. [Fig. 2(b): RLoad = 5 kΩ, hOTS = 25–100 nm, rOTS = 100 nm, and Vapp = 5 V/5 s triangular pulse].

FIG. 5.

The switching voltage increases with hOTS both (a) without and (b) with field dependent conductivity. Including field dependent conductivity reduces the switching field's (c) magnitude and (d) sensitivity to hOTS. [Fig. 2(b): RLoad = 5 kΩ, hOTS = 25–100 nm, rOTS = 100 nm, and Vapp = 5 V/5 s triangular pulse].

Close modal

Reference 37 reports switching fields from 8.1 MV/m (as-deposited a-Ge15Sb85) to 94 MV/m (as-deposited 4 nm thick a-Sb). We examine the tunability of our model by varying Eth in (3) from 5.6 to 560 MV/m (Fig. 6). Results show Eswitch varying from 5 to 42.5 MV/m. Eswitch = 25.01 MV/m when Eth = 56 MV/m, similar to the Eswitch = 28.75 MV/m measured in Ref. 13 for melt-quenched a-GST. σE becomes negligible compared to σT when Eth > 200 MV/m even for high fields: the σT used in this work precludes Eswitch > 42.5 MV/m; a reduced σT is required for higher switching fields. Iswitch decreases by ∼100× as Vswitch increases, resulting in a decrease in switching power (Pswitch) from ∼100 to 20 μW [Fig. 6(b)].

FIG. 6.

(a) The switching current (voltage) decreases (increases) and (b) the switching power decreases with increasing Eth in (3). The device switches thermally before the field contribution becomes significant for Eth> 1 × 108 V/m. As a result, further increases to Eth result in the same switching characteristics [Fig. 2(b): RLoad = 5 kΩ, hOTS = 100 nm, rOTS = 100 nm, and Vapp = 5 V/5 s triangular pulse].

FIG. 6.

(a) The switching current (voltage) decreases (increases) and (b) the switching power decreases with increasing Eth in (3). The device switches thermally before the field contribution becomes significant for Eth> 1 × 108 V/m. As a result, further increases to Eth result in the same switching characteristics [Fig. 2(b): RLoad = 5 kΩ, hOTS = 100 nm, rOTS = 100 nm, and Vapp = 5 V/5 s triangular pulse].

Close modal

Vswitch has been shown to decrease with increasing ambient temperature (Tambient), while the temperature behavior of Iswitch and Pswitch is less clear.19 We simulate switching while varying Tambient [the initial temperature and the fixed top and bottom TiN boundary temperatures, Fig. 2(b)] from 300 to 400 K (Fig. 7). Vswitch decreases as expected [Fig. 7(a)]. Iswitch at first decreases and then increases with increasing Tambient, while Pswitch monotonously decreases in the Tambient range simulated but is beginning to flatten with increasing T by 400 K.

FIG. 7.

The (a) voltage, (b) current, and (c) power required to switch as the ambient temperature changes. Vswitch decreases monotonically, but Iswitch and Pswitch have more complex relationships with Tambient. [Fig. 2(b): RLoad = 5 kΩ, hOTS = rOTS = 100 nm, and Vapp = 5 V/5 s triangular pulse]. Experimental switching characteristics for melt-quenched GST mushroom cells with 50 nm heater contacts19 included for reference.

FIG. 7.

The (a) voltage, (b) current, and (c) power required to switch as the ambient temperature changes. Vswitch decreases monotonically, but Iswitch and Pswitch have more complex relationships with Tambient. [Fig. 2(b): RLoad = 5 kΩ, hOTS = rOTS = 100 nm, and Vapp = 5 V/5 s triangular pulse]. Experimental switching characteristics for melt-quenched GST mushroom cells with 50 nm heater contacts19 included for reference.

Close modal

Next, we systematically vary rOTS, hOTS, and the rise time (τrise) of Vapp in the geometry shown in Fig. 2(b) (Fig. 8). Results agree with expected OTS behavior: Vswitch approximately doubles as hOTS doubles;6Vswitch decreases with increasing τrise, approaching a minimum value;16Ihold and Vhold are only weakly dependent on hOTS;15 and switching characteristics are only weakly dependent on rOTS due to filamentary conduction in the on-state.

FIG. 8.

Switching characteristics of OTS devices with varying radii (rows), ramp times (columns), and heights (colors). The simulated holding currents and voltages are weakly dependent on hOTS, but the switching voltage doubles as hOTS doubles [geometry in Fig. 2(b)].

FIG. 8.

Switching characteristics of OTS devices with varying radii (rows), ramp times (columns), and heights (colors). The simulated holding currents and voltages are weakly dependent on hOTS, but the switching voltage doubles as hOTS doubles [geometry in Fig. 2(b)].

Close modal

Finally, we simulate reset of an initially polycrystalline PCM cell using a series OTS as an access device (OTS + PCM, Fig. 1), followed by a subsequent pulse to switch on the OTS with the now-reset PCM, based on devices fabricated and characterized in Ref. 1. We use a 2D, 45 nm fixed out-of-plane-depth simulation instead of a 2D-rotational simulation to more appropriately model phase change dynamics in the PCM with (6). We use a 500 nm out-of-plane depth in the bit line to account for its large thermal mass (Fig. 1) and set Tambient = 300 K as the initial temperature everywhere and as a fixed constraint on the TiN word and bit line external boundaries. We begin with a polycrystalline set PCM device and then reset the device with a 5 V/5 ns square pulse (1 ns rise and fall times) at Vapp followed by 1 μs for thermalization [starting at Fig. 1 and ending at Fig. 9(a); an animation of this reset is available in the supplementary material]. We then sweep Vapp from 0 to 2.5 V over 50 ns to characterize the OTS + reset PCM. We also simulate an isolated OTS and an isolated reset PCM in the same way by replacing the PCM or OTS, respectively, with TiN [Figs. 9(c) and 9(d)]. We plot the IV characteristics before switching, dividing currents and voltages by the isolated OTS Iswitch and Vswitch values in order to compare our results to those presented in Ref. 1 [Fig. 9(d)]. The results are similar, with the OTS limiting the current in the reset PCM until VDevice/VswitchOTS>2 [Fig. 9(d)]: the increased voltage necessary to switch is due to the a-GST in the PCM region corresponding to the reset state. This limits the current during read in a reset cell while allowing high current in a set cell, creating a large read margin. The smaller scaled currents for the PCM and OTS + PCM in our simulation could be due to a difference in the amorphous volume in the reset PCM; the fixed out-of-plane depth in our simulations, which cannot capture filaments smaller than 45 nm in depth and may thus overestimate Iswitch in the OTS; or parameter differences between aGST and the (unreported) OTS material used in Ref. 1.

FIG. 9.

(a) Reset OTS + PCM, (b) isolated OTS, and (c) isolated reset PCM. The PCM region in (a) and (c) contains some nanocrystals formed while quenching after reset, but the device is still in the reset state—there is no crystalline path between the top and bottom contacts. (d) Pre-switching I–V characteristics scaled by Vswitch and Iswitch in the OTS using the model in this work (spheres) and experimental data extracted from Ref. 1 (squares). I–V characteristics from this work show similar switching voltages but lower scaled switching currents. The schematic of the simulation setup is shown in Fig. 1. The OTS + PCM reset animation for this simulation, including the formation of crystals during the post-reset quench, is available in the supplementary material.

FIG. 9.

(a) Reset OTS + PCM, (b) isolated OTS, and (c) isolated reset PCM. The PCM region in (a) and (c) contains some nanocrystals formed while quenching after reset, but the device is still in the reset state—there is no crystalline path between the top and bottom contacts. (d) Pre-switching I–V characteristics scaled by Vswitch and Iswitch in the OTS using the model in this work (spheres) and experimental data extracted from Ref. 1 (squares). I–V characteristics from this work show similar switching voltages but lower scaled switching currents. The schematic of the simulation setup is shown in Fig. 1. The OTS + PCM reset animation for this simulation, including the formation of crystals during the post-reset quench, is available in the supplementary material.

Close modal

The coupling of thermal and electric field contributions to electrical conductivity in amorphous semiconductors is complex, as evidenced by the large number of physical models proposed to explain the same characteristics. Our modeling results show that threshold switching and “snap-back” observed in OTS and PCM devices can be explained through electro-thermal phenomena giving rise to thermal runaway and filamentary conduction and can be modeled efficiently with a finite element framework.

See the supplementary material for a video of crystallinity and temperature dynamics as the OTS + PCM cell is reset [going from Fig. 1 to Fig. 9(a)].

This work was supported by the Air Force Office of Scientific Research (AFOSR) MURI under Award No. FA9550-14-1-0351. The authors would like to thank Ilya Karpov of Intel Corporation, Martin Salinga of RWTH Aachen University, Abu Sebastian of IBM Zurich, and Geoffrey Burr of IBM Almaden for valuable discussions.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

1.
D.
Kau
,
S.
Tang
,
I. V.
Karpov
,
R.
Dodge
,
B.
Klehn
,
J. A.
Kalb
,
J.
Strand
,
A.
Diaz
,
N.
Leung
,
J.
Wu
,
S.
Lee
,
T.
Langtry
,
K. W.
Chang
,
C.
Papagianni
,
J.
Lee
,
J.
Hirst
,
S.
Erra
,
E.
Flores
,
N.
Righos
 et al., “
A stackable cross point phase change memory
,” in
Technical Digest—International Electron Devices Meeting
(
IEDM
,
2009
), pp.
1
4
.
2.
F.
Xia
,
J.
Xiong
, and
N.-H.
Sun
, “
A survey of phase change memory systems
,”
J. Comput. Sci. Technol.
30
(
1
),
121
144
(
2015
).
3.
H.-S. P.
Wong
,
S.
Raoux
,
S.
Kim
,
J.
Liang
,
J. P.
Reifenberg
,
B.
Rajendran
,
M.
Asheghi
, and
K. E.
Goodson
, “
Phase change memory
,”
Proc. IEEE
98
(
12
),
2201
2227
(
2010
).
4.
A.
Chen
, “
Memory selector devices and crossbar array design: A modeling based assessment
,”
J. Chromatogr. Sci.
16
(
4
),
1186
1200
(
2017
).
5.
G. W.
Burr
,
R. S.
Shenoy
,
K.
Virwani
,
P.
Narayanan
,
A.
Padilla
,
B.
Kurdi
, and
H.
Hwang
, “
Access devices for 3D crosspoint memory
,”
J. Vac. Sci. Technol. B
32
(
4
),
040802
(
2014
).
6.
S. R.
Ovshinsky
, “
Reversible electrical switching phenomena in disordered structures
,”
Phys. Rev. Lett.
21
(
20
),
1450
1453
(
1968
).
7.
T.
Matsunaga
,
J.
Akola
,
S.
Kohara
,
T.
Honma
,
K.
Kobayashi
,
E.
Ikenaga
,
R. O.
Jones
,
N.
Yamada
,
M.
Takata
, and
R.
Kojima
, “
From local structure to nanosecond recrystallization dynamics in AgInSbTe phase-change materials
,”
Nat. Mater.
10
(
2
),
129
134
(
2011
).
8.
M.
Anbarasu
,
M.
Wimmer
,
G.
Bruns
,
M.
Salinga
, and
M.
Wuttig
, “
Nanosecond threshold switching of GeTe6 cells and their potential as selector devices
,”
Appl. Phys. Lett.
100
(
14
),
143505
(
2012
).
9.
M. J.
Lee
,
D.
Lee
,
H.
Kim
,
H. S.
Choi
,
J. B.
Park
,
H. G.
Kim
,
Y. K.
Cha
,
U. I.
Chung
,
I. K.
Yoo
, and
K.
Kim
, “
Highly-scalable threshold switching select device based on chaclogenide glasses for 3D nanoscaled memory arrays
,” in
Technical Digest—International Electron Devices Meeting, December
(
IEDM
,
2012
), pp.
10
13
.
10.
J.
Choe
, see https://www.techinsights.com/about-techinsights/overview/blog/intel-3D-xpoint-memory-die-removed-from-intel-optane-pcm/ for “Intel 3D XPoint Memory Die Removed from Intel Optane™ PCM (Phase Change Memory),” Tech Insights, 2017; accessed 10 December 2018.
11.
R. W.
Pryor
and
H. K.
Henisch
, “
Nature of the on-state in chalcogenide glass threshold switches
,”
J. Non. Cryst. Solids
7
(
2
),
181
191
(
1972
).
12.
K. E.
Petersen
, “
On state of amorphous threshold switches
,”
J. Appl. Phys.
47
,
256
(
1976
).
13.
D.
Ielmini
, “
Threshold switching mechanism by high-field energy gain in the hopping transport of chalcogenide glasses
,”
Phys. Rev. B Condens. Matter Mater. Phys.
78
(
3
),
035308
(
2008
).
14.
M.
Nardone
,
V. G.
Karpov
,
D. C. S. S.
Jackson
, and
I. V.
Karpov
, “
A unified model of nucleation switching
,”
Appl. Phys. Lett.
94
(
10
),
10
12
(
2009
).
15.
W.
Czubatyj
and
S. J.
Hudgens
, “
Invited paper: Thin-film ovonic threshold switch: Its operation and application in modern integrated circuits
,”
Electron. Mater. Lett.
8
(
2
),
157
167
(
2012
).
16.
M.
Wimmer
and
M.
Salinga
, “
The gradual nature of threshold switching
,”
New J. Phys.
16
,
113044
(
2014
).
17.
A.
Athmanathan
,
D.
Krebs
,
A.
Sebastian
,
M.
Le Gallo
,
H.
Pozidis
, and
E.
Eleftheriou
, “
A finite-element thermoelectric model for phase-change memory devices
,” in
International Conference on Simulation of Semiconductor Processes and Devices (SISPAD), October 2015
(
IEEE
,
2015
), pp.
289
292
.
18.
M.
Le Gallo
,
M.
Kaes
,
A.
Sebastian
, and
D.
Krebs
, “
Subthreshold electrical transport in amorphous phase-change materials
,”
New J. Phys.
17
(
9
),
093035
(
2015
).
19.
M.
Le Gallo
,
A.
Athmanathan
,
D.
Krebs
, and
A.
Sebastian
, “
Evidence for thermally assisted threshold switching behavior in nanoscale phase-change memory cells
,”
J. Appl. Phys.
119
(
2
),
025704
(
2016
).
20.
M.
Nardone
,
M.
Simon
,
I. V.
Karpov
, and
V. G.
Karpov
, “
Electrical conduction in chalcogenide glasses of phase change memory
,”
J. Appl. Phys.
112
(
7
),
071101
(
2012
).
21.
I. V.
Karpov
,
M.
Mitra
,
D.
Kau
,
G.
Spadini
,
Y. A.
Kryukov
, and
V. G.
Karpov
, “
Evidence of field induced nucleation in phase change memory
,”
Appl. Phys. Lett.
92
(
17
),
173501
(
2008
).
22.
Z.
Woods
and
A.
Gokirmak
, “
Modeling of phase-change memory: Nucleation, growth, and amorphization dynamics during set and reset: Part I—Effective media approximation
,”
IEEE Trans. Electron Devices
64
(
11
),
4466
4471
(
2017
).
23.
Z.
Woods
,
J.
Scoggin
,
A.
Cywar
,
L.
Adnane
, and
A.
Gokirmak
, “
Modeling of phase-change memory: Nucleation, growth, and amorphization dynamics during set and reset: Part II—Discrete grains
,”
IEEE Trans. Electron Devices
64
(
11
),
4472
4478
(
2017
).
24.
J.
Scoggin
,
R. S.
Khan
,
H.
Silva
, and
A.
Gokirmak
, “
Modeling and impacts of the latent heat of phase change and specific heat for phase change materials
,”
Appl. Phys. Lett.
112
(
19
),
193502
(
2018
).
25.
J.
Scoggin
,
Z.
Woods
,
H.
Silva
, and
A.
Gokirmak
, “
Modeling heterogeneous melting in phase change memory devices
,”
Appl. Phys. Lett.
114
(
4
),
043502
(
2019
).
26.
A.
Faraclas
,
N.
Williams
,
A.
Gokirmak
, and
H.
Silva
, “
Modeling of set and reset operations of phase-change memory cells
,”
IEEE Electron Device Lett.
32
(
12
),
1737
1739
(
2011
).
27.
A.
Faraclas
,
G.
Bakan
,
H.
Adnane
,
F.
Dirisaglik
,
N. E.
Williams
,
A.
Gokirmak
,
H.
Silva
,
L.
Adnane
,
F.
Dirisaglik
,
N. E.
Williams
,
A.
Gokirmak
, and
H.
Silva
, “
Modeling of thermoelectric effects in phase change memory cells
,”
IEEE Trans. Electron Devices
61
(
2
),
372
378
(
2014
).
28.
N.
Kan’an
,
A.
Faraclas
,
N.
Williams
,
H.
Silva
, and
A.
Gokirmak
, “
Computational analysis of rupture-oxide phase-change memory cells
,”
IEEE Trans. Electron Devices
60
(
5
),
1649
1655
(
2013
).
29.
A.
Cywar
,
J.
Li
,
C.
Lam
, and
H.
Silva
, “
The impact of heater-recess and load matching in phase change memory mushroom cells
,”
Nanotechnology
23
(
22
),
225201
(
2012
).
30.
J.
Scoggin
, “Modeling and finite element simulations of phase change memory materials and devices,” Ph.D. dissertation (University of Connecticut, 2019).
31.
F.
Dirisaglik
,
G.
Bakan
,
Z.
Jurado
,
S.
Muneer
,
M.
Akbulut
,
J.
Rarey
,
L.
Sullivan
,
M.
Wennberg
,
A.
King
,
L.
Zhang
,
R.
Nowak
,
C.
Lam
,
H.
Silva
,
A.
Gokirmak
 et al., “
High speed, high temperature electrical characterization of phase change materials: Metastable phases, crystallization dynamics, and resistance drift
,”
Nanoscale
7
(
40
),
16630
16625
(
2015
).
32.
L.
Adnane
,
N.
Williams
,
H.
Silva
, and
A.
Gokirmak
, “
High temperature setup for measurements of Seebeck coefficient and electrical resistivity of thin films using inductive heating
,”
Rev. Sci. Instrum.
86
(
10
),
105119
(
2015
).
33.
S.
Muneer
,
J.
Scoggin
,
F.
Dirisaglik
,
L.
Adnane
,
A.
Cywar
,
G.
Bakan
,
K.
Cil
,
C.
Lam
,
H.
Silva
, and
A.
Gokirmak
, “
Activation energy of metastable amorphous Ge2Sb2Te5 from room temperature to melt
,”
AIP Adv.
8
(
6
),
065314
(
2018
).
34.
R.
Endo
,
S.
Maeda
,
Y.
Jinnai
,
R.
Lan
,
M.
Kuwahara
,
Y.
Kobayashi
, and
M.
Susa
, “
Electric resistivity measurements of Sb2Te3 and Ge2Sb2Te5 melts using four-terminal method
,”
Jpn. J. Appl. Phys.
49
(
6
),
5802
(
2010
).
35.
T.
Kato
and
K.
Tanaka
, “
Electronic properties of amorphous and crystalline Ge2Sb2Te5 films
,”
Jpn. J. Appl. Phys.
44
(
10
),
7340
7344
(
2005
).
36.
K.
Cil
,
F.
Dirisaglik
, and
L.
Adnane
, “Electrical resistivity of liquid Ge2Sb2Te5 based on thin-film and nanoscale device measurements,” in IEEE Transactions on Electron Devices (IEEE, 2013).
37.
D.
Krebs
,
S.
Raoux
,
C. T.
Rettner
,
G. W.
Burr
,
M.
Salinga
, and
M.
Wuttig
, “
Threshold field of phase change memory materials measured using phase change bridge devices
,”
Appl. Phys. Lett.
95
(
8
),
082101
(
2009
).
38.
G.
Bakan
,
N.
Khan
,
H.
Silva
, and
A.
Gokirmak
, “
High-temperature thermoelectric transport at small scales: Thermal generation, transport and recombination of minority carriers
,”
Sci. Rep.
3
(
1
),
2724
(
2013
).
39.
S.
Shindo
,
Y.
Sutou
,
J.
Koike
,
Y.
Saito
, and
Y. H.
Song
, “
Contact resistivity of amorphous and crystalline GeCu2Te3 to W electrode for phase change random access memory
,”
Mater. Sci. Semicond. Process.
47
(
8
),
1
6
(
2016
).
40.
C. M.
Neumann
,
K. L.
Okabe
,
E.
Yalon
,
R. W.
Grady
,
H. S. P.
Wong
, and
E.
Pop
, “
Engineering thermal and electrical interface properties of phase change memory with monolayer MoS2
,”
Appl. Phys. Lett.
114
(
8
),
082103
(
2019
).

Supplementary Material