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

11

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