Phase Change Memory (PCM) Devices
Optical Storage (e.g., DVD) Electrical Storage (XPoint)A Die
The architecture
1
2015
By optical pulse:
By electrical pulse: Often refer to Joule heating
How to Operate the PCM Devices?2
Here, we focus on carrier dynamics upon optical
excitations.
Recrystallization time – several to 100 nanoseconds
Amorphization time – can be as short as picoseconds
Time Scale of the Carrier Dynamics
10-15 10-12 10-9
e-e coupling
e-ph coupling
Intraband relaxation
[s]
Auger process
Radiative
recombination
Interband transition
atto femto pico nano
3
Two Recent Examples
1. Order-to-disorder transition and carrier
multiplication [Bang, Sun, et al., PRL117, 126402
(2016) ]
2. Order-to-order transition in Peierls-distorted
solids [Chen, Li, Bang, et al., PRL120, 185701
(2018) ].
4
Example 1: Order to Disorder Transition
The flagship PCM material is GST (Ge2Sb2Te5), which exists in
a metastable NaCl phase [known as a distorted rocksalt (RS)],
with about 20% randomly distributed cation vacancies
Our simulation cell: 87-atom supercell (21 Ge, 18 Sb,
48 Te, and 9 cation vacancies)
5
6
Before we entered the field, no first-principles
modeling of GST phase transition as it yielded
null result (needs a too high temperature or
requires an unrealistic simulation time)
Rather, people study melt quenching at
~3000K, assuming the physical properties of
the amorphous phase is the same as the melt.
AIMD at Fixed Occupation (fo) 7
Li, et al., PRL107, 015501 (2011)
Ge-Te s antibondingSb-Te p bonding
Light absorption will affect the elements differently!
VBM
T < Tmelting
9% Excitation
24 ps
Time Evolution of Atomic Structure8
Li, et al., PRL107, 015501 (2011)
Ultrafast
amorphization
at a temperature
(700 K)
considerably
below melting
point (~1000K).
fo-AIMD vs. High-Temperature Melt Quench9
Pair correlation
function (PCF)
shows unexpectedly
intermediate range
order
Mean square
displacement (MSD)
also substantially
smaller than melt
A non-thermal
phase change !PRL107, 015501 (2011)
10
DFT (Hohenberg-Kohn): Expectation value of operator 𝑂 is
a unique functional of ground-state electron density 𝑛0(𝒓).
TDDFT (Runge-Gross): One-to-one correspondence
between density 𝑛(𝒓, 𝑡) and its time-dependent potential
𝑉(𝒓, 𝑡). HOWEVER, this is only true for a specified initial
many-body state Ψ0.
Often, TDDFT refers to density-density response function
within linear response theory, not time-evolving states.
Time-Dependent Density Functional Theory (TDDFT)
Molecular Dynamics (MD)
TDDFT-MD: real-time ab-initio MD coupled with TDDFT
• (Ehrenfest dynamics) Electron is time-evolved quantum
mechanically, but ion is classically
Meng, Kaxiras, J. Chem. Phys. 129, 054110 (2008)
ab initio MD
• Born-Oppenheimer approximation → time-independent
electronic ground state at each atomic configuration
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Two Competing Carrier-Relaxation Mechanisms
Phonon emission (PE):
(a) potential energy
surface (PES) drops
vertically. (c) PE
reduces excited
carrier density.
Carrier multiplication
(CM): (b) PES moves
horizontally. (d) CM
increases excited
carrier density.12
Bang, et al., PRL117, 126402 (2016)
el
hole
Excitation-Induced Disorder
Energy of excitation (relative to the size of band gap), i.e., low
energy (LEE) and high energy (HEE), can be crucial to structural
evolution after excitation (1 ps thereafter): LEE has little effect,
whereas HEE causes severe disorder leading to amorphization.
Ge SbTe
V
LEE HEE 13
Bang, et al., PRL117, 126402 (2016)
Analysis: Time-Resolved Disorder
Degree of disorder measured
by # of wrong bonds and % of
disordered cations (Ge and Sb)
Disorder of LEE increases,
consistent with increased ionic
temperature (𝑇𝑖𝑜𝑛), but not of
HEE as 𝑇𝑖𝑜𝑛(HEE) ≈ 𝑇𝑖𝑜𝑛(GS)
Rule out e-ph coupling as the
relaxation mechanism for HEE.
Preheating T and TGS = 670 K
14
Bang, et al., PRL117, 126402 (2016)
= ground state
Carrier Multiplication Accounts for the Difference
els.
holes
Carrier occupation approaches the Fermi-Dirac distribution in 1 ps.
HEE shows an increasing in
carrier density, while LEE
shows a decrease
15Bang, et al., PRL117, 126402 (2016)
Continuation of TDDFT-MD with fo-AIMD
TD
DF
T-M
D
Pronounced 𝑇𝑖𝑜𝑛 spike at 1 ps for HEE but not for LEE.
DF
T-M
D a
fter
TD
DF
T-M
D
16
When Is fo-AIMD Reasonable for GST?
Ground-state PES
HEE PES
LEE PES
The PES for LEE is close to,
and will relax towards, the
ground state, so fo-AIMD is a
reasonable approximation
The PES for HEE is drastically
different from the ground
state due to carrier
multiplication, so fo-AIMD is
not a good approximation
Shallower PES is responsible for the larger disorder seen for HEE.
17
Bang, et al., PRL117, 126402 (2016)
Electric Field: the More Accurate Approach
Excited-carrier density is given by
∆𝜌 ∝
𝑖,𝑗
𝜓𝑖 𝝐 ∙ℏ𝑖𝛻 𝜓𝑗
2
𝛿 휀𝑖 − 휀𝑗 − ℏ𝜔 𝜓𝑖2 − 𝜓𝑗
2
where 𝝐 is the electric field
Using silicon as an
example (an indirect-gap
semiconductor), we
obtain good agreement
with experiment
18
Lian, Zhang, Meng, PRB94, 184310 (2016)
It suggests that for GST LEE should dominate over HEE.
Example 2: Order-to-Order Transition
GeTe is a special case of the GST PCM materials. It is
stabilized in a ferroelectric r-phase:
L = Long bond, S = Short bond; L = Low angle, H = High angle
cubic (c)-phase
Rhombohedral (r)-phase
LL
HS
192-atom simulation supercell
19
Chen, Li, et al., PRL120, 185701 (2018)
By fs x-ray diffraction, Matsubara [PRL117, 135501 (2016)]
proposed a rattling model for the excited state of the r-phase
where, while Te maintains at the original position, Ge rattles
between 6 equivalent off-center positions
In contrast, ultrafast electron diffraction [ACS Nano 9, 6728
(2015)] suggested that Te is not fixed in the original position,
but exhibits a displacive motion along [001], followed by a shear
lattice deformation to result in a real rocksalt c-phase
fo-AIMD study by Kolobov [JPCC118, 10248 (2014)], on the other
hand, suggested a model in which the short and long bonds in r-
GeTe are randomly distributed as a result of the excitation, so
the structure effectively becomes an averaged “pseudocubic”.
Dispute: A “Cubic” Phase upon Excitation? 20
Coherent Displacements under Illumination
(a) Occupation of partial
density of states (5% excitation)
(b) Potential energy surfaces
(PESs) of the ground and
excited states: bistability!
(c) Charge density changes
(color contour) and atomic
forces (red arrows) as results
of the excitation
Momentumless light causes
directional coherent motion of
the atoms.
21
PRL120, 185701 (2018)
Time Evolution of Average Key Quantities
(a) Directional forces
(b) Bondlength
(c) Bond angle
(d) Ion temperature 𝑇𝑖𝑜𝑛
𝑇𝑚 – melting point
𝑇𝑟−𝑐 – Curie temperature for
(thermally-driven)
ferroelectric transition
Is the transition thermally driven,
since 𝑇𝑖𝑜𝑛(80 fs) is close to 𝑇𝑟−𝑐?
(5% excitation)
22
PRL120, 185701 (2018)
No! The r-c Transition Is Entirely Non-ThermalGround-state MD
Kinetic energy does not always reflect system thermal motion
Noticeably, 𝑇𝑖𝑜𝑛 << 𝑇𝑟−𝑐 → transition is not thermally driven.23
Throughout Transition, No Structural Randomization
24
Chen, Li, et al., PRL120, 185701 (2018)
By fs x-ray diffraction, Matsubara [PRL117, 135501 (2016)]
proposed a rattling model for the excited state of the r-phase
where, while Te maintains at the original position, Ge rattles
between 6 equivalent off-center positions ꓫ
In contrast, ultrafast electron diffraction [ACS Nano 9, 6728
(2015)] suggested that Te is not fixed in the original position, but
exhibits a displacive motion along [001], followed by a shear
lattice deformation to result in a real cubic (c) rocksalt phase √
fo-AIMD study by Kolobov [JPCC118, 10248 (2014)], on the other
hand, suggested a model in which the short and long bonds in r-
GeTe are randomly distributed as a result of the excitation, so
the structure effectively becomes an averaged “pseudocubic”. ꓫ
Dispute of a “Cubic” Phase upon Excitation 25
Non-thermal phase changes, not only
those in phase change memory (PCM)
applications, is a fruitful research area for
TDDFT-MD.
Take Home Message26