The origin of massive nonlinearity in mixed-Ionic-Electronic-Conduction (MIEC)-based access devices, as revealed by numerical device simulation,

The origin of massive nonlinearity in Mixed-Ionic-Electronic-Conduction
(MIEC)–based Access Devices, as revealed by numerical device simulation
A. Padilla, G. W. Burr, R. S. Shenoy, K. V. Raman§ , D. Bethune, R. M. Shelby, C. T. Rettner, J. Mohammad,
K. Virwani, P. Narayanan, A. K. Deb§ , R. K. Pandey† , M. Bajaj† , K. V. R. M. Murali† , B. N. Kurdi and K. Gopalakrishnan‡
IBM Research – Almaden, 650 Harry Road, San Jose, CA 95120 (‡ IBM T. J. Watson Research Center, Yorktown Heights, NY 10598)
(§ IBM India Research Labs, Bangalore KA, India 560045)
(† IBM SRDC India, Bangalore KA, India 560045)
Tel: (408) 927–1512, Fax: (408) 927–2100, E-mail: [email protected]
Abstract
Numerical modeling is used to explain the origin of the large
ON/OFF ratios, ultra-low leakage, and high ON current densities
exhibited by BEOL-friendly Access Devices (AD) based on Cucontaining MIEC materials [1-5]. Motion of large populations of
copper ions and vacancies leads to exponential increases in hole
current, with a turn-ON voltage that depends on material bandgap.
Device simulations match experimental observations as a function
of temperature, electrode aspect-ratio, thickness, and device CD.
Keywords: Access device, MIEC, NVM, PCM, RRAM, MRAM
Introduction
Mixed-Ionic-Electronic-Conduction (MIEC)-based ADs [1–5]
exhibit ideal characteristics for 3D-stacking of large crosspoint
arrays of any resistive nonvolatile memory (NVM) in the BEOL,
including bipolar diode-like characteristics (Fig.1), large ON/OFF
ratios, high voltage margin Vm (for which leakage stays below 10
nA), ultra-low leakage (< 10 pA), and high ON current densities.
Although dependent on total electrode area [1,2,4], the Vm of any
given MIEC device structure is mostly independent of the size of
the gap between the two electrodes, dgap (Fig. 2). In addition,
transient response is markedly faster for points higher up the I–V
curve (Fig. 3), with turn-on times varying from >1µsec (for I 1µA) to 15nsec for I >100µA[4].
The operation of MIEC devices has been qualitatively attributed
to the modulation of electronic current by the motion of Cuions [1,5]. In this work, we quantify this theory using Sentaurus TCAD. Adapting features for tracking mobile H+ ions [6],
we perform 2–D numerical device simulations of Cu-based MIEC
semiconductors containing large concentrations of mobile positive
+
Cu+ ions and negative V−
Cu vacancies. Cu ions are allowed to invacancies
do not interact
teract with conduction electrons, yet V−
Cu
with holes. The simulator self-consistently solves the continuity
and Poisson equations, along with ionization-recombination kinetics (Fig. 4) and a ‘Unified Contact’ Schottky model [7] at each
ion-blocking metal electrode. While 1–D models have been developed (Fig.5), none have incorporated Schottky interfaces, minority
carriers, and electron-ion recombination simultaneously.
Modeling MIEC ADs
In the absence of ions, a metal-semiconductor-metal (MSM)
structure is simply two Schottky diodes connected back-to-back.
As bias increases, current originally limited by the reverse-biased
diode increases due to minority-carrier diffusion. However, unlike
MIEC ADs, turn-on voltages Vm are large and depend strongly on
dgap (Fig.6).
In such a p-type MSM structure, a metal work-function very
close to the valence band should imply large current flow even at
low bias voltages. The large number of mobile positive ions in Cucontaining MIEC materials (Fig. 7) interact with conduction-band
electrons and change this behavior markedly (Fig. 8). At zero bias
(Fig.9(a)), mobile ions settle into a U-shaped distribution with large
electric fields at each interface, maintaining a dynamic equilibrium
between electrostatic ion drift towards, and ion diffusion away
from, each interface [8]. This ion accumulation results in narrow
depletion widths and residual electron tunneling at each interface,
yet strong suppression of holes and hole current.
At low bias, holes are injected from the positively-biased electrode (Fig. 9(b)), eventually resulting in significant hole diffusion
current (with a characteristic SS of ∼85 mV/dec) as the device
transitions out of the OFF-state dominated by electron current.
Copper ions move away from (and vacancies move towards) the
positive electrode, where current is limited at high bias by hole
tunneling. Hall-effect measurements performed on MIEC-based
materials (Fig. 8, inset) confirm hole-dominated currents at large
carrier densities. This behavior is consistent with a suppressed interaction between V−
Cu vacancies and holes (large energy barrier),
unlike the interaction between Cu+ ions and electrons.
Role of Electrode Gap
Within a device with a large electrode-gap dgap , a distinct
−
‘quasi-neutral’ region where [Cu+ ] ∼ [VCu
] separates the regions
of extreme ion aggregation at each interface. This allows the device characteristics to be independent of dgap until these interfacial
regions begin to interfere with each other, leading to a decrease
in the voltage margin Vm (at 10nA) (Fig. 10). Filaments are not
modeled here, but may also form across a narrow dgap . While simulated trends of Vm do show an increase as devices are scaled in CD
(Fig.10), the trend is not as strong as that seen experimentally[2].
Device Asymmetry and Transient Response
Simulated IV characteristics become asymmetric for devices
with highly asymmetric electrode areas, such as conductive-AFM
measurements of blanket films (Fig. 11), and show an increase in
leakage current as temperature increases. Transient simulations
of the MIEC AD response (Fig. 12) show rapid response at high
bias and high current, with a slower response at low bias and low
current, similar to experiments (Fig. 3). However, the modeled
interplay — between fast ion migration that turns on the device,
and the slower interaction between ions and electrons that allows
hole current to dominate (Fig. 13) — does not exhibit the same
vast dynamic range in response speeds (from ∼25ns to ∼100ms)
observed experimentally, suggesting that further model refinement,
possibly involving interfacial Cu+ reduction, will be necessary.
Finally, by carefully tuning simulation mesh against TEM images,
precise matching of IV characteristics can be obtained (Fig.14).
Conclusions
A commercial device simulator was adapted to explain the
large ON/OFF ratios, ultra-low leakage, and high ON current densities offered by BEOL-friendly Access Devices (AD) based on
Cu-containing Mixed-Ionic-Electronic-Conduction (MIEC) materials [1-5]. Ultra-low leakage at low bias is due to residual electron tunneling, with hole current suppressed by a central ‘quasineutral’ region. Device turn-on occurs as hole injection from the
positively-biased electrode increases sharply, driven by motion of
large populations of copper ions and vacancies. Simulated trends
in turn-on voltage Vm vs. dgap and CD, transient response, temperature dependence, and highly asymmetric device geometries all
match experimental observations.
References
[1] K. Gopalakrishnan et. al., VLSI Tech. Symp., 19.4 (2010).
[2] R. S. Shenoy et. al., VLSI Tech. Symp., 5B.1 (2011).
[3] G. W. Burr et. al., VLSI Tech. Symp., T5.4 (2012).
[4] K. Virwani et. al., IEDM Tech. Digest, 2.7 (2012).
[5] G. W. Burr et. al., VLSI Tech. Symp., T6.4 (2013).
[6] Sentaurus TCAD, www.synopsys.com (2012).
[7] M. Ieong et. al., IEDM Tech. Digest, 733 (1998).
[8] J. Maier, in Prog. Solid St. Chem. 23 171 (1995).
100uA
Normalized
(300ns)
1uA
100nA
10nA
Vm~1.53V
1nA
100pA
DC IV
10pA
1pA
-1.5
-1.0
-0.5
0
0.5
1.0
Blanket
80%
Bridges
tip
MIEC
Diode-in-via
BEC
oxide
Si wafer
C-AFM
40%
tip
TEC
SiN
1.5
MIEC
BEC
100
oxide
Si wafer
1000
VBL
MIEC
100nm
Isat ~ 50uA
VWL
3uA
1uA
Fig. 4 Sentaurus TCAD[6] is
used to model drift, diffusion,
100nA
and two rate-equation inter10ns
100ns
1us
10us
100us
1ms
Time
actions between mobile copFig. 3 Larger applied voltages with higher per ions (Cu+ ), atoms (Cu0 ),
saturation currents lead to faster turn-on of mobile vacancies (V − ), and
Cu
MIEC access devices.
electrons.
dgap [nm]
300nA
Fig. 2 Measured turn-on voltages depend
strongly on device CD[2] (not shown), but
are insensitive to the gap between electrodes (dgap ) down to very small thicknesses.
Fig. 1
Access Devices (ADs) based
on Cu-containing Mixed-Ionic-ElectronicConduction (MIEC) materials exhibit bipolar diode-like characteristics with ultra-low
leakage and large ON/OFF ratios[1-5].
VBL
10uA
C-AFM
60%
10
Voltage [V]
30uA
C rent
Curr
Voltage Margin
Current [uA]
Higher
100%
pulsed IV
10uA
1e21
Ignores…
Results:
1D Model
predicts
linear dc
IV curves
Gil et al.
Solid State
Ionics 179
(2008)
• MSM structure
• mobile acceptors &
holes OR
• mobile donors &
electrons
• minority carriers 1D Model
• Schottky/ohmic predicts
nature of contacts various dc
IV curves
Strukov et al.
small 5, No. 9
(2009)
• MSM structure
• mobile ions,
electrons, holes
• fixed acceptors
• bulk-limited
transport, with ohmic
contacts
t t for
f electrons
l t
• electron-ion
recombination
kinetics
• Schottky nature
of contacts
13 Table:
1nA
100
150
1fA
100nm
Voltage
1e-21
-8
-6
-4
-2
2f , 2r = 1.86e-9
1 86e-9 e -0.1955/kBT , 1e3 cm-3 s-1
[V]
0
2
4
6
(b)
1
V+ 30um
measurements
I20um Van der Pauw
1e17
1 A
1uA
Hall-effect
Van der Pauw
MIEC
V-
1e16 dgap= 300nm
1e15
10nA
dgap= 40nm
cylinder
simulation
1e14
100pA
cylinder
simulation
Current
1nA
10nA
100nA
1uA
10uA
dggapp= 40nm
CD = 40nm
1nA
100pA
Electron
current
Fig. 7 Important parameters in our nu10pA
2D BoR
merical model for MIEC ADs include
Voltage [V]
1pA
-1.5
-1
-0.5
0
0.5
1
1.5
bandgap Eg , the large number of copper atoms (Cu0 ) contributing mobile Fig. 8 Simulated IV curve for a cylindrical MIEC
−
ions (Cu+ ) and vacancies (VCu
), and AD. As bias increases, electron-dominated current
the associated interaction rates (Fig.4). gives way to holes, matching Hall–effect measurements (inset).
(e)
(d)
8
Fig. 6
While a simulated MSM
structure without ions has an MIEClike IV, currents are too low and ONtransition voltages are large and depend strongly on dgap .
1D (Metal-MIEC-Metal) Models have been proposed previously.
1e18
100nA
1f , 1r = 3e-9 , 6e2 cm-3 s-1
dgap =
TEC=BEC
= 50nm
I+
1e19
10uA
[Cu0] = 1e21 cm-3
 = 4.05
4 05 eV
V
200
Hole carrier density [cm-3]
1e20
100uA
cylinder simulation
“Body-of-rotation”
simulation
(c)
1
Electron quasi-Fermi level
0.5
0.5
0
0
-0.5
Valence band
-1
-0.5
Hole quasi-Fermi level
-1
-1.5
15
Electrons
V=0V
V
0V
-20
-15
Cu+
V=0.4V ((10pA)
p )
Holes
V=0.8V (5nA)
Y position [nm]
-10
-5
0
5
10
15
20 -20
-15
-10
-5
0
5
1e22
1e20
1e18
1e16
1e14
1e12
1e10
1e8
1e6
1e4
100
10
TEC: 0.000V
0 000V
15
20 -20 BEC: 0.400V
-15
-10
-5
0
5
10
TEC: 0.000V
0 000V
15
V=1.5V (160uA)
V=1.2V (17uA)
20 -20 BEC: 0.800V
-15
-10
-5
0
5
10
TEC 0.000V
TEC:
0 000V
20 -20 BEC: 1.200V
-15
15
-10
-5
0
5
10
15
Occ
cupancie
es [cm-3]
VCu-
1e22
1e20
1e18
1e16
1e14
1e12
1e10
1e8
1e6
1e4
100
-1.5
15
Cu0
Electron E
Energy [eeV]
Ele
ectron En
nergy [eV
V]
dgap [nm]
5
1e-18
Fig. 5
1D Metal-MIEC-Metal
models proposed previously —
none combine Schottky interfaces,
minority carriers, and electron-ion
recombination.
(a)
Conduction band
Occupa
ancies [cm-3]
10
0
DCu+ = DVCu- = 8e-4 cm2/s
M = 5.375 eV
15
1pA
1D Model
predicts
memristor
IV curves
Eg = 1.4 eV
30 Flatband
25 Voltage [V]
20
C rrentt
Cur
Models…
Currren
nt
Reference:
Arribart et al. • p
p-type
yp semiconductor • minorityy carriers
ElectroChimica • mobile Cu+ & holes
• Schottky/ohmic
Acta 24 (1978) • Fixed acceptors
nature of contacts
• Cu+ reduction at
cathode
20
TEC: 0.000V
BEC: 1.500V
TEC: 0.000V
BEC: 0.000V
200
1.8
dgap [nm]
1.6
1.4
1.2
1
0.8
0.6
2D BoR
0.4
CD [nm]
“Body-of-rotation”
simulation
0.2
0
0
50
dgap= 80nm
CD = 80nm
100
150
200
2.0V
250
300
Fig. 10 Variation in simulated voltage
margin as thickness (dgap ) and
diameter (CD)
vary
around
the CD = 40nm,
dgap = 40nm
cylinder shown
in Fig.8.
Fig. 3 limits
100uA
Simula
ated curre
ent
10uA
150oC
1 2V
1.2V
10uA
1.0V
1uA
10nA
0 8V
0.8V
1nA
10ns
100ns
1us
10us
Time
100us
1e22
1e20
1e18
1e16
1e14
1e12
1 10
1e10
1e8
1e6
1e4
100
Occ
cupancies [cm
m-3]
100nA
1
0.5
0
-0.5
-1
-1.5
1ms
Fig. 12 Transient simulations of MIEC AD response
show that the ion migration needed to turn on an MIEC
AD occurs slowly at low bias and current, yet rapidly at
high bias and current, although not with the same wide
dynamic range observed in experiments (Fig. 3). Transient data at higher temperature is likely to be faster, accommodated by adjusting the rate constants in Figs.4 & 7
with the appropriate energy barriers.
((a))
Silver
paint
MIEC
TiN
Oxide
120oC
60oC
100nA
30oC
MIEC
1uA
180oC
10nA
120oC
90oC
60oC
30oC
150oC
1nA
100pA
20 mm / 40 nm
10nA Asymmetry: 500,000x
-0.6
06
10uA
100nA
1uA
1
A
90oC
-0.4
04
-0.2
02
0
10pA
1pA
4 um / 25 nm
Asymmetry:
160x
-0.8
0 8 -0.6
0 6 -0.4
0 4 -0.2
02
02
0.2
AFM tip voltage [V]
0
0 2 0.4
0.2
0 4 0.6
06
Voltage (Small electrode) [V]
Fig. 11 (a) Conductive-AFM measurements of blanket films show highly asymmetric IV
characteristics because of the large asymmetry in electrode areas, and noise floor increases
with temperature. These features can be (b) qualitatively matched in simulation.
((c))
Conduction band
Current
Electron quasi-Fermi
quasi Fermi level
Cu0
Holes
10uA
V l
Valence
band
b d
Cu+
(pulses)
100uA
Hole quasi-Fermi level
1e22
1 20
1e20
1e18
1e16
1e14
1e12
1e10
1e8
1 6
1e6
1e4
100 Y position [nm]
-40
-30
-20
Simullated cu
urrent
150
curre
ent
2
100
AFM
50
Energy [eV]
0
Occupa
ancies [cm-3]
Volta
age Margin (at 100nA) [V
V]
Fig. 9 At zero bias (a), the large number of mobile positive ions settle into a U-shaped distribution with large electric fields at each interface, maintaining dynamic
equilibrium between electrostatic ion drift towards, and ion diffusion away from, each interface. This ion accumulation results in narrow depletion widths and residual
electron tunneling at each interface, yet strong suppression of holes and hole current. As bias increases (b,c,d), holes are injected from the positively-biased electrode
(TEC, at left), the hole barrier presented by the valence band shrinks, and hole current increases exponentially. Copper ions move away from (and vacancies move towards)
the TEC, where current is limited at high bias by hole tunneling. At high bias (e), Cu0 , the lattice copper sites that can contribute ions, are depleted at the TEC side and
over-saturated at the BEC side, possibly initiating damage of the material.
C AFM TIP
C-AFM
180oC
Simulated
1uA
VCu-
20ns
1ns Electrons
Total Current
100nA
10nA
Experiment
p
1nA
(b)
100pA
(d)
10ns
1us
Y position [nm]
-10
0
10
20
30
40 -40
-30
-20
-10
0
Simulated
(DC)
MIEC
Electron
current
10pA
10
20
30
40
Fig. 13 After a voltage ramp to 1.0V (a, 1ns), hole occupancy remains suppressed by the large Cu+ population
diffusing slowly away from the positive (left) interface (b,
10ns). After 20ns (c), this ion population has departed,
flattening the bands and allowing some hole injection. By
1us (d), the slow interaction between Cu+ and electrons
has suppressed electron current, allowing hole current to
dominate.
Voltage
1pA
-1 5
-1.5
-1
-0 5
-0.5
0
05
0.5
1
15
1.5
Fig. 14 By carefully tuning the simulation mesh
against TEM images for dimensions and the slight
recess into the bottom electrode, precise matching of IV characteristics can be obtained, including
ultra-low leakage currents, voltage turn-ON values,
and >7 orders of magnitude in ON–OFF ratio.