Supplementary material
Thermal
dispersion
and
secondary
crystallization of phase change memory
cells
Y. F. Deng1,2, Z. Li1,2,a), J. H. Peng1,2, C. Liu1,2, X. S. Miao1,2
1
Wuhan National Laboratory for Optoelectronics, Huazhong University of Science
and Technology, Wuhan 430074, China
2
School of Optics and Electronic Engineering, Huazhong University of Science and
Technology, Wuhan 430074, China
_________________
a)
Electronic mail: lizhen@mail.hust.edu.cn
Section S1
Testing system
The PCRAM testing system contains Keithley 4200-SCS semiconductor
characterization system with embedded-in pulse generator module ， Tektronix
DPO70604 digital scope and Cascade S300 probe station. The embedded-in pulse
generator board serves to produce a programmed pulse sequence. SMUs
(Source-Measure Unit) of semiconductor characterization system measure I-V curve
and resistance of the cells.
Section S2
Phase change module
The phase change module is based on the rate of amorphous volume change (va),
which is negative at crystallization and positive at amorphization.1 The ratio of
amorphization (Ca) in time domain is obtained by1,2
Ca  Ca 0   va dt ,
(1)
and
  PV

n nVa
 SaVg  , T  Tm
 
 Vm



(2)
va   T  Tm
，
, T  Tm

d
 hCa gst
Ska


where Ca0 is the initial amorphous ratio of each pulse, Pn is the nucleation probability
per unit time, Vn is the volume of a nucleus, Va is the amorphous volume, Vm is the
volume of a monomer, Sa is the total area of amorphous-crystal interfaces, Vg is the
growth velocity of small crystallites, Tm is the melting point, ∆h is the latent heat of
solid- to-liquid transition, dgst is the thickness of phase change layer, S is the bottom
contact area and ka is the thermal conductivity of amorphous state.
Section S3
Table and figures
TABLE SI. Physical parameters of the model.
Symbol Rc0 Ra0
Unit
kΩ
Value
3
kΩ
∆h
dgst
Tm
Ea1
Ea2
J/cm3 nm
K
eV
eV W/K-m W/K-m
850 418.9
75
889 2.19 2.3
kc
0.5
ka
0.2
Figure S1. The sketch of cell temperature and the temperature Tan.
Figure S2. (a) The waveforms of pulse sequence used in simulation. (b) The threshold
voltage of set and reset operation at different pulse interval.
Figure S3. The simulated R-V curves for the measurement of the threshold voltage of
set operation at different pulse interval (a)-(c), and the temperature Tan (d). Inset: The
waveforms of pulse sequences used in simulation.
Figure S4. The simulated R-V curves for the measurement of the threshold voltage of
reset operation at different pulse interval (a)-(c), and the temperature Tan (d). Inset:
The waveforms of pulse sequences used in simulation.
References
1
K. Sonoda, A. Sakai, M. Moniwa, K. Ishikawa, O. Tsuchiya, and Y. Inoue, IEEE
Trans. Electron Devices 55, 1672 (2008).
2
C. Peng, L. Cheng, and M. Mansuripur, J. Appl. Phys. 82, 4183 (1997).