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Influences on the nonlinearity of ferroelectric synapses for neuromorphic computing

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Abstract and Figures

Hafnium oxide based ferroelectric FETs (FeFETs) have been demonstrated as a viable memory implementation of synapses for neuromorphic computing and deep learning [1]. For a neuromorphic implementation the synaptic memory is mandatory to retain a multitude of addressable conductance states in order to resemble the weight function. In FeFETs this is realized by remnant polarization state levels resulting in modulated drain current. To address the different states (weight increase/decrease), three different types of signal sequences have been utilized. Firstly, varying the number of pulses, secondly, varying the pulse width, and thirdly, varying the pulse height [2]. One important figure of merit is the nonlinearity of the weight increase/decrease. Here, we present the modulation capability of the nonlinearity for Si- and Zr-doped HfO2 FeFETs. We demonstrate that the nonlinearity decreases with increasing read gate voltage in depression, whereas it increases in potentiation. Furthermore, for the studied pulse sequences, the influence of pulse width and amplitude is discussed. Additionally, influences from the device integration, such as interface layer material and spacer oxide, as well as the ferroelectric layer dopant, were investigated. Finally, the trends of different device parameters are depicted in terms of future scalability.
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© Fraunhofer IPMS
M. Lederer I13.08.2019 I slide 1
Influences on the nonlinearity of
HfO2based ferroelectric synapses
(FeFETs) for neuromorphic
computing
13.08.2019
M. Lederer, T. Kämpfe, T. Ali, Y. Gao, K. Seidel
© Fraunhofer IPMS
M. Lederer I13.08.2019 I slide 2
Ferroelectric Fieldeffect Transistor (FeFET)
SiO2
Si
S D
TiN
a-Si
HSO
SiO2
Pr
Pr
Orthorhombic (Pca21)
Ferroelectricity in HfO2
Gate-First
ΔVT= 1-1.2 V
±5V, < 100 ns
104endurance
10y retention
Stabilized by Dopants, Stress, …
FeFET Gate Stack
28nm Proof of Concept
J. Müller et al., VLSI (2012)
-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
0.00
0.25
0.50
0.75
1.00
I
D
[µA]
VG [V]
-3 -2 -1 0123
-40
-30
-20
-10
0
10
20
30
40
Polarization [µC/cm²]
E [MV/cm]
HSO 10nm
© Fraunhofer IPMS
M. Lederer I13.08.2019 I slide 3
Neuromorphic Computing
Conductance of crossbar array represent weight matrix
Level-based representation
Most efficient for fully connected layers
X1
X2
X3
X4
Xn
A1
A2
A3
An
Weight
matrix
Pre-
neuron
layer
Post-
neuron
layer
V1
V3
V4
Vn
I1I2I3In
Multilevel
memory
Dot-product engine
© Fraunhofer IPMS
M. Lederer I13.08.2019 I slide 4
-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
0.00
0.25
0.50
0.75
1.00
I
D
[µA]
VG [V]
0 5 10 15 20 25 30 35 40 45 50 55 60 65
0.0
0.2
0.4
0.6
0.8
1.0
Potentiation
Depression
Nonlinearity Fit
V
G = 0.8 V
Current [µA]
Pulse Number
Non-Linearity Coefficient
Seq. 1 Seq. 3
Seq. 2
Signal Shape
M. Jerry et al., IEDM (2017)
,=1.726
+ 0.162
Ip,d= B 1 exp PD
A+ C
2. Nonlinearity Coefficient:
P := Pulse Number
D := Start Pulse Number
1. Nonlinearity Fit:
Potentation
(LTP):
Seq. 3: 150ns
W: 50 µm, L: 25 µm
-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
0.00
0.25
0.50
0.75
1.00
I
D
[µA]
VG [V]
2.5V -3V
4V -4.5V
Depression
(LTD):
© Fraunhofer IPMS
M. Lederer I13.08.2019 I slide 5
Influence of the Gate Voltage
Depression:Potentation:
Seq. 3
Nonlinearity is strongly dependent on gate voltage
0 5 10 15 20 25 30
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Current [µΑ]
Pulse Number
VG [V]:
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
0 5 10 15 20 25 30
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Current [µΑ]
Pulse Number
VG [V]:
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
0.0
0.1
0.2
0.3
0.4
0.5
Nonlinearity Coefficient
Gate Voltage [V]
Potentiation
Depression
© Fraunhofer IPMS
M. Lederer I13.08.2019 I slide 6
0 5 10 15 20 25 30
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Current [µΑ]
Pulse Number
V
G [V]:
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
0 5 10 15 20 25 30
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Current [µΑ]
Pulse Number
V
G [V]:
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
Influence of the Gate Voltage
Seq. 3
Variance strongly dependent on gate voltage
Relative and absolute variance show maximum at different gate voltages
Potentation:
 
Depression:
-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
-6x10-7
-4x10-7
-2x10-7
0
2x10-7
4x10-7
6x10-7
150ns Pot.
150ns Dep.
VG [V]
Iend - Istart [A]
10-4
10-3
10-2
10-1
100
101
102
103
104
150ns Pot.
150ns Dep.
Iend / Istart
 
© Fraunhofer IPMS
M. Lederer I13.08.2019 I slide 7
Sequence 1 3: Nonlinearity
Sequence 3 shows lowest nonlinearity
Seq. 1
Seq. 3
Seq. 2
-0.2 0.0 0.2 0.4 0.6 0.8 1.0
0.00
0.25
0.50
0.75
1.00
1.25
Nonlinearity Coefficient
Gate Voltage [V]
LTP: Seq. 1
Seq. 2
Seq. 3
LTD: Seq. 1
Seq. 2
Seq. 3
W: 25 µm,
L: 25 µm
VG= 0.8V
W: 25 µm, L: 25 µm
© Fraunhofer IPMS
M. Lederer I13.08.2019 I slide 8
Sequence 1 3: Variance (Ion/Ioff)
Seq. 2 & 3 less asymmetric
Higher variance for Seq. 2 & 3
Variance can be improved by using more pulses
(Seq. 3)
0246810 12 14 16 18 20 22 24 26 28 30 32
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
Current [µA]
Pulse Number
Depression
Seq. 1
Seq. 2
Seq. 3
Seq. 1
Seq. 3
Seq. 2
-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
-1x10
-6
-5x10
-7
0
5x10
-7
1x10
-6
LTP: Seq. 1
Seq. 2
Seq. 3
LTD: Seq. 1
Seq. 2
Seq. 3
V
G
[V]
I
end
- I
start
[A]
-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
10
-4
10
-3
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
LTP: Seq. 1
Seq. 2
Seq. 3
LTD: Seq. 1
Seq. 2
Seq. 3
Iend / Istart
VG [V]
W: 25 µm,
L: 25 µm
VG= 0.8V
W: 25 µm,
L: 25 µm
© Fraunhofer IPMS
M. Lederer I13.08.2019 I slide 9
Sequence 1 3: Area Scaling
Seq. 1 shows a very rapid increase in nonlinearity with area scaling
Seq. 2 and 3 show slower increase, could be used for smaller devices
Origin lies in domain structure and nucleation limited switching
Seq. 1 Seq. 3
Seq. 2
Signal Shape
100 1000
0.00
0.05
0.10
0.15
0.20
0.25
Seq. 2 LTD
Seq. 3 LTD
Nonlinearity Coefficient
Area [µm²]
100 1000
10
-2
10
-1
10
0
Area [µm²]
Seq. 1 LTD
Seq. 2 LTD
Seq. 3 LTD
I
end
/ I
start
0200 400 600 800 1000 1200 1400
0
1
2
3
4 Seq. 1 LTD
Seq. 2 LTD
Seq. 3 LTD
Nonlinearity Coefficient
Area [µm²]
© Fraunhofer IPMS
M. Lederer I13.08.2019 I slide 10
Sequence 1 3: Possible Adjustments for Area Scaling
Adjusting signal shape for smaller devices improves nonlinearity
Seq. 1 Seq. 3
Seq. 2
100 1000
0.0
0.1
0.2
0.3
0.4
0.5
0.6 3/-3.5 LTD
3.5/-4 LTD
Nonlinearity Coefficient
Area [µm²]
100 1000
0
2
4
6
8
10
12 3.5/-4.5 V
50ns LTD
100ns LTD
150ns LTD
3/-4 V
100ns LTD
Nonlinearity Coefficient
Area [µm²]
100 1000
0.00
0.05
0.10
0.15
0.20
0.25
0.30 50ns Dep.
100ns Dep.
150ns Dep.
Nonlinearity Coefficient
Area [µm²]
© Fraunhofer IPMS
M. Lederer I13.08.2019 I slide 11
FeFET SiO2 vs SiON
SiON: Lower voltages necessary to switch fully Increase in nonlinearity
SiO2
Si
SD
TiN
a-Si
HSO
SiO2
SiO2
Si
SD
TiN
a-Si
HSO
SiON
0-1 -2 -3 -4 -5 -6 -7 -8
0.1
0.3
0.5
0.7
0.9
1.1
1.3
Lower
ER
SiON
SiO2
VT (V)
Erase Pulse Amplitude (V)
PG State Low (V
T
)
High (V
T
)
ER State
No FE
Switching
Low Voltage FE Switching
T. Ali et al., TED (2018)
Seq. 2
0.0 0.2 0.4 0.6 0.8
-1x10
-6
-8x10
-7
-6x10
-7
-4x10
-7
-2x10
-7
0
2x10
-7
4x10
-7
6x10
-7
8x10
-7
1x10
-6
SiO
2
: LTP
LTD
SiON:
LPT
LTD
SiO
2
: LTP
LTD
SiON:
LPT
LTD
V
G
[V]
I
end
- I
start
[A]
10
-4
10
-3
10
-2
10
-1
10
0
10
1
10
2
10
3
I
end
/ I
start
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0.0
0.5
1.0
1.5
2.0
Nonlinearity Coefficient
VG [V]
10nm:
300 µm2 LTP
300 µm2 LTD
5nm: 300 µm2 LTP
300 µm2 LTD
W: 20 µm, L: 10 µm
© Fraunhofer IPMS
M. Lederer I13.08.2019 I slide 12
FeFET HSO vs HZO
Lower Variance due to larger MW (FeFET Comparison) not reaching saturation current
More Subloop Behaviour Lower nonlinearity coefficient
SiO2
Si
SD
TiN
a-Si
HSO
SiON
SiO2
Si
SD
TiN
a-Si
HZO
SiON
-3 -2 -1 0123
-40
-30
-20
-10
0
10
20
30
40
Polarization [µC/cm²]
E [MV/cm]
HZO 10nm
HSO 10nm
Seq. 2
-0.2 0.0 0.2 0.4 0.6 0.8
0.0
0.5
1.0
1.5
2.0
2.5
Nonlinearity Coefficient
VG [V]
HZO:
300 µm2 LTP
300 µm2 LTD
HSO:
300 µm2 LTP
300 µm2 LTD
0.0 0.2 0.4 0.6 0.8
-1x10-6
-5x10-7
0
5x10-7
1x10-6
HSO: LTP
LTD
HZO: LPT
LTD
HSO: LTP
LTD
HZO: LPT
LTD
VG [V]
Iend - Istart [A]
10-3
10-2
10-1
100
101
102
103
Iend / Istart
W: 20 µm, L: 10 µm
© Fraunhofer IPMS
M. Lederer I13.08.2019 I slide 13
FeFET thickness influence
Thinner film results in an increased electrical field Compressed / steeper behaviour with VG
SiO2
Si
SD
TiN
a-Si
HZO
SiON
SiO2
Si
SD
TiN
a-Si
HZO
SiON
Seq. 2
0.2 0.4 0.6 0.8 1.0 1.2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
I
D
[µA]
V
G
[V]
10 nm
5 nm
-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
-6x10
-7
-4x10
-7
-2x10
-7
0
2x10
-7
4x10
-7
6x10
-7
10 nm: 5 nm:
LTP LPT
LTD LTD
10 nm:
LTP
LTD
5 nm:
LPT
LTD
VG [V]
Iend - Istart [A]
10
-3
10
-2
10
-1
10
0
10
1
10
2
10
3
Iend / Istart
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0.0
0.5
1.0
1.5
2.0
Nonlinearity Coefficient
VG [V]
10nm:
300 µm
2
LTP
300 µm
2
LTD
5nm: 300 µm
2
LTP
300 µm
2
LTD
W: 20 µm, L: 10 µm
W: 20 µm, L: 10 µm
W: 20 µm,
L: 10 µm
© Fraunhofer IPMS
M. Lederer I13.08.2019 I slide 14
Conclusion & Outlook
Nonlinearity and variance can be tuned by signal shape and gate
voltage
Trade-off between variance and nonlinearity
Scaling of area without strong increase in nonlinearity possible for
sequence 2 and 3
100 1000
0.0
0.1
0.2
0.3
0.4
0.5
0.6 3/-3.5 LTD
3.5/-4 LTD
Nonlinearity Coefficient
Area [µm²]
-0.2 0.0 0.2 0.4 0.6 0.8 1.0
0.00
0.25
0.50
0.75
1.00
1.25
Nonlinearity Coefficient
Gate Voltage [V]
LTP: Seq. 1
Seq. 2
Seq. 3
LTD: Seq. 1
Seq. 2
Seq. 3
-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
0.00
0.25
0.50
0.75
1.00
I
D
[µA]
VG [V]
SiO2
Si
S D
TiN
a-Si
HSO
SiO2
0200 400 600 800 1000 1200 1400
0
1
2
3
4 Seq. 1 LTD
Seq. 2 LTD
Seq. 3 LTD
Nonlinearity Coefficient
Area [µm²]
© Fraunhofer IPMS
M. Lederer I13.08.2019 I slide 15
Acknowledgements
We received funding within the ECSEL Joint Undertaking
project TEMPO in collaboration with the European Union's
H2020 Framework Program (H2020/2014-2020) and National
Authorities, under grant agreement number 783176.
© Fraunhofer IPMS
M. Lederer I13.08.2019 I slide 16
Sequence 1: Pulse Amplitude
Amplitude reduction:
Decrease of nonlinearity in potentation
Reduced assymetry of the variance
Decrease in absolute variance
Seq. 1
Amplitude Variation (100ns)
0.0 0.5 1.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Nonlinearity Coefficient
V
G
[V]
3.5V/-4.5V:
100ns LTP
100ns LTD
3V/-4V:
100ns LTP
100ns LTD
-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
-5x10-7
-4x10-7
-3x10-7
-2x10-7
-1x10-7
0
1x10-7
2x10-7
3x10-7
4x10-7
5x10-7
LTP: 3.5V
3V
LTD: -4.5V
-4V
LTP: 3.5V
3V
LTD: -3.5V
-4V
VG [V]
Iend - Istart [A]
10-2
10-1
100
101
102
Iend / Istart
© Fraunhofer IPMS
M. Lederer I13.08.2019 I slide 17
Sequence 1: Pulse Width
Strong effect on depression
Moving to lower VG
Converging at ~0.5
No clear/strong influence on potentation
Seq. 1
Width Variation (3.5V/-4.5V)
0.0 0.5 1.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Nonlinearity Coefficient
V
G
[V]
3.5V/-4.5V:
LTP: 50ns
100ns
150ns
LTD: 50ns
100ns
150ns
-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
-5x10-7
-4x10-7
-3x10-7
-2x10-7
-1x10-7
0
1x10-7
2x10-7
3x10-7
4x10-7
5x10-7 LTP: 50ns
100ns
150ns
LTD: 50ns
100ns
150ns
VG [V]
Iend - Istart [A]
10-2
10-1
100
101
102
LTP: 50ns
100ns
150ns
LTD: 50ns
100ns
150ns
Iend / Istart
© Fraunhofer IPMS
M. Lederer I13.08.2019 I slide 18
Sequence 2: Pulse Amplitude
Trade-off between nonlinearity and variance
Seq. 2
0.0 0.5 1.0
0.00
0.25
0.50
0.75
1.00
Nonlinearity Coefficient
V
G
[V]
Potentation:
3V
3.5V
Depression:
3.5V
4V
-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
-1x10-6
-5x10-7
0
5x10-7
1x10-6
LTP: 3V
3.5V
LTD: -3.5V
-4V
LTP: 3V
3.5V
LTD: -3.5V
-4V
VG [V]
Iend - Istart [A]
10-4
10-3
10-2
10-1
100
101
102
103
Iend / Istart
© Fraunhofer IPMS
M. Lederer I13.08.2019 I slide 19
Sequence 3: Pulse Width
Longer pulses increase slope of nonlinearity
Absolute variance reaches maximum for 100ns
Variance improvements with higher number
of pulses
Seq. 3
0.0 0.5 1.0
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
Nonlinearity Coefficient
VG [V]
Potentation:
50ns
100ns
150ns
Depression:
50ns
100ns
150ns
-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
-4x10-7
-3x10-7
-2x10-7
-1x10-7
0
1x10-7
2x10-7
3x10-7
4x10-7 LTP: 50ns
100ns
150ns
LTD 50ns
100ns
150ns
VG [V]
Iend - Istart [A]
10-3
10-2
10-1
100
101
102
103
LTP: 50ns
100ns
150ns
LTD: 50ns
100ns
150ns
Iend / Istart
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