Exploring the design space for resistive nonvolatile memory crossbar arrays with mixed-Ionic-Electronic-Conduction (MIEC)-based access devices,

Exploring the Design Space for Resistive Nonvolatile Memory Crossbar Arrays
with Mixed Ionic-Electronic-Conduction (MIEC)–based Access Devices
P. Narayanan, G. W. Burr, R. S. Shenoy, S. Stephens, K. Virwani, A. Padilla, B. Kurdi, and K. Gopalakrishnan‡
IBM Research – Almaden, 650 Harry Road, San Jose, CA 95120 (‡ IBM T. J. Watson Research Center, Yorktown Heights, NY 10598)
Tel: (408) 927–2920, Fax: (408) 927–2100, E-mail: [email protected]
Abstract
Using circuit-level SPICE simulations, we explore the design
constraints on crossbar arrays composed of a nonvolatile memory
(NVM) (+1R) and a highly nonlinear Access Device (AD) enabled
by Cu-containing Mixed Ionic-Electronic Conduction (MIEC) materials [1-5]. Such ADs must maintain ultra-low leakage through
a large number of unselected and partially selected 1AD+1R cells,
while delivering high currents to the few cells selected for either
read or write. We show that power consumption during write, not
read margin, is the most stringent constraint for large 1AD+1R
crossbar arrays, with NVM switching voltage VN V M and selector
voltage margin Vm being much more critical than write current. We
show that scaled MIEC devices (Vm ∼ 1.54V [4]) can support 1Mb
arrays for VN V M up to 1.2V. Stacking two MIEC devices enables
VN V M ∼ 2.4V . A 20% improvement in Vm can either enable a 4×
increase in array size or counteract a 5× increase in interconnect
line resistance.
Keywords: Access device, MIEC, crossbar array, NVM selectors
Introduction
MIEC-based ADs [1–5] exhibit ideal characteristics for 3Dstacking of large crossbar arrays of any resistive 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.
Even with such attractive characteristics, however, the design of a
large crossbar array of 1AD+1R devices (Fig. 2) — within which
writes and reads must be reliable yet leakage through non-selected
devices low — requires careful choice of selected & unselected
wordline (VW & VR ) and bitline (VB & VC ) voltages. We quantify
the design-space enabled by scaled MIEC-based ADs (Vm ∼ 1.54V
[4]) in terms of achievable array size, excess required power during
write, and read margin.
Simulation framework
We assume an NVM device that transitions between an ohmic
Low Resistance State (LRS) and a High Resistance State (HRS)
exhibiting Poole-Frenkel (PF) conduction (Fig. 3). The equivalent
circuit for the MIEC AD (Fig. 3, inset) is carefully fit to experimental data (Fig. 1). Before each SPICE simulation, the inner
voltages VC , VR (Fig.4(b)) are chosen for an aggregate unselected
leakage of 10uA (e.g., for a 1Mb array, 10pA/device). As outer
voltages VB , VW are swept apart, the voltage across the worst-case
selected 1AD+1R device(s) (Fig. 4(a)) increases. After the simulation completes, the NVM switching event (Fig. 5) identifies the
external voltages (VB , VW ) required for a successful write. Default
NVM, MIEC AD, and array parameters are shown in Table.1. Total
required power is examined just before and just after switching for
both the LRS-to-HRS and HRS-to-LRS transitions.
Design space for NVM write
In our approach, only voltage choices which trigger a successful write are even considered. A design point becomes unfavorable when the total applied power becomes much larger than the
base 1AD+1R write power. For instance, even a 10% increase in
VHRS causes applied power to increase by two orders of magnitude
(Fig. 6). This extra applied voltage at the far-edge selected device
(Fig. 4(a)) exponentially increases leakage in nearby half-selected
devices (Fig.4(b)). The resulting larger voltage drops in the wiring
then exacerbate voltage stress at near-edge half-selected devices.
While this positive feedback effect is roughly the same for the
worst-case (all LRS) and for random stored data patterns, it can be
suppressed by the high resistance of the HRS state (Fig. 6, inset).
Like VHRS , there is a VLRS threshold, beyond which write power
grows dramatically. However, the array design is quite robust to
increases in switching currents IHRS , ILRS (Fig.6).
Fig.7 shows that small increases in VHRS dramatically reduce
achievable array size. When the design works (blue region at left),
almost all the externally applied power reaches the selected device,
opening up opportunities for parallel writes; when the design fails,
almost all external power is dissipated in half-selected 1AD+1R
devices. Figs. 8 and 9 show that, similar to NVM voltage VHRS ,
maintaining a sufficiently large AD voltage margin Vm is critical to
successful array design. Degradations in AD slope S lead to excess
power (Fig.8), yet can be offset by Vm improvements (Fig.9).
For a given NVM, improvements in either the slope S or the
voltage margin Vm of the MIEC-based AD can enable significant
increases in the achievable array size (Fig. 10), or can be used to
accommodate the increases in line resistances expected at scaled
technology nodes (Fig. 11). Fig. 12 shows the achievable array
size for both the scaled MIEC AD (Vm ∼ 1.54V) and a stacked
combination of two MIEC ADs. The larger voltage margin far outweighs the degradation in AD slope and series resistance, allowing
a stacked MIEC diode to support 1Mb arrays for NVM switching
voltages as large as 2.4V. Note that large SPICE simulations are
enabled by modeling all unselected 1AD+1R device pairs with a
single aggregate device (Fig.13).
Design space for NVM read
Read margin is the change in voltage across a peripheral load
resistor RLOAD (Fig.13) when the selected device moves between
the HRS and LRS states. The applied read voltage is determined
based on avoiding a disturb (Fig. 13(A)) on the near-edge cell, the
two reads are performed with a true V/2 scheme and data patterns
shown in Fig.13(B,C)) (other schemes/patterns showed similar performance, not shown). The load resistance is chosen to increase
read margin (Fig. 14, inset) without excessive RC timing issues.
While read margin degrades with lower read voltage/disturb condition (Fig. 14), and higher interconnect resistance (Fig. 15, inset),
NVM resistance contrast has the most significant impact (Fig. 15).
Read margin does depend upon AD parameters (Fig.16), but write
power considerations are clearly far more stringent (Figs.8,9).
Conclusions
We have explored the design of 1AD+1R crossbar arrays using highly nonlinear Access Devices (AD) based on Mixed IonicElectronic Conduction (MIEC) [1-5]. Circuit-level SPICE simulations were used to show that achievable array size and excess
required power during write depends strongly on careful matching between the turn-on voltage Vm of the AD and the switching
voltage VN V M of the NVM. This implies that research in this field
should be directed towards NVMs with lower VN V M (and ADs
with higher Vm ), as opposed to decreases in raw NVM switching
current. Scaled MIEC devices (Vm ∼ 1.54V [4]) are shown to
support VN V M up to 1.2V (for 1Mb arrays), and two stacked MIEC
devices enable VN V M ∼ 2.4V .
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] ITRS 2011 Interconnect tables (www.itrs.net).
Partially (WL) Selected Cells
DC IV
10pA
1pA
-1.5
-1.0
-0.5
0
0.5
1.0
1.5
Voltage [V]
VR
SET Switching
RESET Switching
Holding V during SET
Read Disturb Voltage
Resistance States
PF HRS @ 0.1V
NVM “SET” snapback
Current
1uA
LRS
HRS
Selected
device
Half-selected
Half
selected
devices
10nA
Un-selected
devices
100pA
1pA
0.5
1.0
1.5
2.0
Vh
VDIS
RLRS , RHRS
RHRS−P F
1.2V, 3µA
0.8V, 30µA
0.5V
0.25×VHRS
26.67kΩ, 400kΩ
10MΩ
1.89Mb
1.57Mb
1.26Mb
5mW
1Mb
% Change
in VHRS
784Kb
576Kb
6 b
400Kb
256Kb
56 b
-50%
50%
from nominal
VHRS=1.2V
-30%
30%
-10%
10%
+10%
10%
+30%
30%
+50%
50%
VB
drop
across
wiring
+
Voltage drop
across NVM
VR
VC
VW
S
Rs
IN F
Fig. 4 Total applied voltage at switching is a) NVM voltage VN V M + AD
voltage + wiring IR-drop, identified by
b) sweeping select-lines VW and VB
at fixed unselect bias (and leakage).
VHRS ((1.2V))
VLRS (0.8V)
ILRS (30uA)
1
IHRS (3uA)
0.1
-50%
-30%
-10%
+10%
+30%
+50%
% Change in Individual Parameters
+50%
Vm (1.54V)
+40%
Fig. 6 Switching
voltages
(VHRS , VLRS )
are much more
critical to low
power 1AD+1R
crossbar design
than
switching
currents
(IHRS , ILRS ).
Inset: impact of
data patterns.
≥10mW
% Change in S
from nominal
+30% S = 85mV/dec
S (85mV/dec)
1
+20%
+10%
0
5mW
-10%
10%
Rs (2850Ω)
-20%
-30%
30%
0.1
1mW
b)
10
1.54V
85mV/dec
2850Ω
3pA
Vm
10
Pow
wer [m
milli-W
Watts]
≥10mW
Array size
…+
(VLRS , ILRS)
Fig. 5 Cell currents vs. total applied voltage Array Size
N ×M
1Mb (1024×1024)
for the HRS-to-LRS (“SET”) operation on a Interconnect R/cell[6]
Rint
2.215Ω
64×64 array, exhibiting NVM transition.
Table. 1 Default simulation parameters.
2.25Mb
V(selected NVM)
Vh
Fig. 3 Generic NVM model for SPICE, with
switching between an ohmic LRS and an HRS
exhibiting Poole-Frenkel conduction. Inset
shows equivalent circuit for SPICE modeling
of the bipolar, highly non-linear MIEC AD.
VHRS , IHRS
VLRS , ILRS
Voltage Margin
Turn-on Slope
V lt
Voltage
[V] Series Resistance
2.5
3.0
3.5 Noise Floor
RHRS-PF
(VHRS , IHRS)
Fig. 1 Scaled MIEC access deVR
vices exhibit voltage margins Vm
(at 10nA) of ∼1.54V, ON-OFF conVC
VC
VC
VB
trast in excess of 107 and ultra-low
(M-1) Unselect Columns (Bitlines)
leakage at low bias [1-5], suitable Fig. 2 Crossbar array with selected, parfor large arrays with many unse- tially (WL) selected, partially (BL) selected devices.
lected, and unselected 1AD+1R cells.
100uA
(VHRS , IHRS)
 RHRS
INF
Log I
VR
Total Voltage to Switch NVM
Voltage drop
across AD
Log I
100pA
Vm~1.53V
1.53V
Slope
S ~ 85mV/dec
a)
I(selected NVM)
(VLRS , ILRS)
Pow
wer [m
milli-W
Watts]
10nA
Rseries
Partially (BL) Seleccted Cells
Currrent [uA]
(300ns)
1uA
100nA
((N-1) Unse
elect Rowss (Wordline
es)
pulsed IV
10uA
1nA
Selected Cell
VW
100uA
% Change in Vm
-40%
-50%
-30%
-10%
+10%
+30%
+50%
from nominal
-50%
50%
-50%
1mW
Vm = 1.54V
+10%
Vm
Vm (1.54V)
S  60mV/dec
1
+20% Vm
0.1
10
Power [milli-W
Watts]
Pow
wer [m
milli-W
Watts]
10
+10%
Vm (1.54V)
(1 54V)
1
1Mb
b 1.57Mb
b 2.25Mb
22 b
3
3.14Mb
b
16Mb
4Mb
1Mb
256Kb
S  60mV/dec
+20% Vm
01
0.1
2 6 b
256Kb
Vm
Ma
aximu
um Arrray S
Size
-30%
-10%
+10%
+30% +50%
Fig. 7 Write power vs. VHRS and array size: small
% Change in Individual Parameters
changes in VHRS dramatically reduce achievable ar- Fig. 8 Voltage margin V (at 10nA) is the most Fig. 9 Write power as a function of voltage margin Vm
m
and AD slope S.
ray size.
critical AD parameter in 1AD+1R crossbar Design.
(Vm 3.08V, S 170mV/dec)
64Kb
Full SPICE model
16Kb
Approximate,
iterative model
4Kb
0.72
4Mb
b
Stacked
MIEC
MIEC
(Vm 1.54V, S 85mV/dec)
0.96
1.20
1.44
1.68
1.92
2.16
2.40
NVM Switching Voltage [V]
(2.215 Ω/cell)
Change in Line Resistance
Fig. 12 Maximum achievable array size vs. VN V M . For two
Fig. 10 Any improvement in AD parameters
Fig. 11 Alternatively, improved AD parameters stacked MIEC ADs, V improvement outweighs degradation
m
permits significantly larger size arrays.
can be used to accommodate the higher line resis- in turn-on slope and series resistance. A simple model, iterating
tances of scaled technology nodes.
out from the selected device, is close to SPICE in accuracy.
Partially (WL) Selected Cells
Selected Cell
HRS
HRS
VR
B. Read HRS
C. Read LRS
LRS
HRS
LRS
LRS
LRS
LRS
HRS
HRS
VC
RLOAD
VREAD
VB = -V
VA/2
Fig. 13 One aggregate 1AD+1R can
model the combined leakage of all unselected crosspoints; read operation adds
RLOAD at array periphery. Insets show
assumed patterns of stored data.
150
RHRS (400kΩ)
-50%
RLRS (26.67kΩ)
180
160
140
120
100
80
60
50
0
6X
180
VDIS (0.3V)
200
100
5X
[mV]
HRS
Partiallyy (BL) Sele
ected Cellss
HRS
Re
ead M
Marg
gin [m
mV]
250
A. Worst-case
Read Disturb
4X
Rea
ad Marrgin [m
mV]
VW =
VA/2
3X
Rea
ad Ma
argin
Array Size
2X
1X
% Change in
Individual Parameters
-30%
-10%
+10%
+30%
+50%
Fig. 14 Sensitivity of read margin to
VDIS , RHRS and RLRS . Inset: Read
margin is maximized when RLOAD approaches RHRS−P
F . Default value of
√
RLOAD = RLRS RHRS ∼ 103kΩ.
40
15X
12X
9X
6X
3X 1.5X
S
(85mV/dec)
160
140
Vm
(1.54V)
120
100
Resistance Contrast
80
-50%
% Change in
Individual Parameters
Fig. 15 Read margin deteriorates sig-30%
-10%
+10% +30% +50%
nificantly with loss of resistance contrast Fig. 16 The impact of V and S changes
m
(LRS resistance approaches ohmic HRS), on read margin is significantly less critiand (inset) decreases linearly as intercon- cal than their write power impact (Fig.8).
nect resistance increases.