Mimicking Neurotransmitter Release in Chemical Synapses via

Mar 4, 2017 - Abstract Image. Neurotransmitter release in chemical synapses is fundamental to diverse brain functions such as motor action, learning, ...
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Mimicking Neurotransmitter Release in Chemical Synapses via Hysteresis Engineering in MoS2 Transistors Andrew J. Arnold,†,⊥ Ali Razavieh,‡ Joseph R. Nasr,§,⊥ Daniel S. Schulman,∥,⊥ Chad M. Eichfeld,⊥ and Saptarshi Das*,§,⊥ †

Department of Electrical Engineering, §Engineering Science and Mechanics, ∥Materials Science and Engineering, and ⊥Materials Research Institute, Pennsylvania State University, University Park, Pennsylvania 16802, United States ‡ GLOBALFOUNDRIES, Albany NanoTech Complex, Albany, New York 12203, United States ABSTRACT: Neurotransmitter release in chemical synapses is fundamental to diverse brain functions such as motor action, learning, cognition, emotion, perception, and consciousness. Moreover, improper functioning or abnormal release of neurotransmitter is associated with numerous neurological disorders such as epilepsy, sclerosis, schizophrenia, Alzheimer’s disease, and Parkinson’s disease. We have utilized hysteresis engineering in a back-gated MoS2 field effect transistor (FET) in order to mimic such neurotransmitter release dynamics in chemical synapses. All three essential features, i.e., quantal, stochastic, and excitatory or inhibitory nature of neurotransmitter release, were accurately captured in our experimental demonstration. We also mimicked an important phenomenon called longterm potentiation (LTP), which forms the basis of human memory. Finally, we demonstrated how to engineer the LTP time by operating the MoS2 FET in different regimes. Our findings could provide a critical component toward the design of next-generation smart and intelligent human-like machines and human−machine interfaces. KEYWORDS: chemical synapse, neurotransmitter release, long-term potentiation, MoS2 field effect transistor, gate hysteresis The first step toward achieving the above-mentioned objective is to understand the intricate information-processing strategy adopted by the human brain. Massive, parallel, and connected networks of neurons carrying the information encoded in electrical impulses, better known as action potentials, process the information “on the go”, i.e., during the transmission of the information from one neuron to another.2−4 The signal transmission primarily takes place at synapses, where a signal-carrying neuron communicates with the targeted neuron or a specialized cell. In chemical synapses the electrical signal is transduced into a chemical signal through the release of neurotransmitters, which are at the core of decision making.5,6 Neurotransmitters have three characteristic features: quantal release, stochastic or probabilistic release, and excitatory or inhibitory release.7,8 A combination of these three features determines the immediate action as well as long-term adjustment in the cellular and molecular machinery of the postsynaptic neuron via changes in postsynaptic current (PSC)

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ecent advancements in imaging techniques have revealed many interesting and important details regarding information processing inside the mammalian nervous systems, which must be accurately accounted for in solid-state devices in order to develop more realistic and efficient human-like machines and human−machine interfaces.1 Such artificial machines can also help scientists and physicians to simulate and understand various brain diseases and disorders. The goal of neuromorphic engineering and the human brain project is understanding the minute details of how the brain manages billions of information processing units connected via trillions of synapses, then mimicking those activities through solid-state nanoelectronic devices, circuits, and architectures with the ultimate objective to create robust computational and design platforms that can facilitate learning and development, short-term and long-term plasticity, and adapt to evolutionary changes. This would also lead to the design of artificial sensory (audio, vision, motion) systems, systems to study the growth and advancement of diseases and disorders and possible effects of drugs, and autonomous and intelligent robots that will eventually simplify complex surgical procedure. © 2017 American Chemical Society

Received: January 6, 2017 Accepted: March 4, 2017 Published: March 4, 2017 3110

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ACS Nano or membrane potential (MP).9−11 These neurotransmitters control diverse brain functions such as motor action, learning ability, memory formation, perception, and concentration. Neurotransmitters are also associated with human emotions, behaviors, judgement, and mental and physiological conditions. Therefore, a solid-state device that can accurately replicate the neurotransmitter release and its consequences in a chemical synapse could hold the key to develop intelligent machines that thrive on the intricate correlation between memory and logic. Moreover, such devices can also guide neuroscientists in simulating, understanding, and eventually curing numerous neurological diseases and disorders such as epilepsy, sclerosis, schizophrenia, Alzheimer’s disease, and Parkinson’s disease, which are directly related to abnormal release and/or improper functioning of the neurotransmitters.12 From the above discussion it evident that information gathered by various sensory organs of the human body are transduced into electrical impulses, which are then processed by an elaborate and intricate network of neurons through the release of neurotransmitters within the human brain.13 The ultimate results of the neural information processing is twofold: a short-term action such as muscle movement or chemical secretion, and a long-term change in neural connectivity, which forms the basis for learning.14 We relate short-term brain functions to logic operations of a computer and long-term changes in neural connectivity to memory storage by a computer. This is done intentionally so that we can associate two different mechanisms with different time constants in order to emulate both short-term and long-term plasticity of the human brain.15,16 The time constant for logic operation is primarily controlled by the transit time of electrons (holes) from the source terminal to the drain terminal of our MoS2 field effect transistor (FET) and depends on the mobility of MoS2 flakes used as the semiconducting channel material, whereas the time constant for memory retention is determined by the charging and discharging of traps in the gate oxide. In computers, logic transistors are never used for memory storage and vice versa. However, human behavior is circumstantial and based on previous experience; that is, human logic is strongly correlated and intertwined with human memory and learning. Therefore, use of a single transistor capable of both logic and memory operation is better suited to mimic the release of neurotransmitters and hence human behavior. Numerous methods have been developed to mimic synaptic transmission and neuronal behavior in artificial devices for computing purposes using both transistors and other devices. Early efforts used very large scale integrated (VLSI) analog silicon complementary metal-oxide-semiconductor (CMOS) circuits.17,18 This method has the advantage of using conventional scalable silicon wafer processing techniques, but each synapse requires an analog circuit with multiple transistors, adding to the complexity of the system. Memristors are an alternative to analog circuits, which change their resistance based on the previous current through the device. Hybrid Systems comprised of memristor cross bar arrays integrated with Si CMOS have been utilized for neuromorphic computing.19−21 These systems have the advantage that each synapse can be modeled by a single memristor. Lowdimensional materials have also been investigated for use in neuromorphic computing systems due to their scalability. The 1T phase of MoS2 nanosheets has been shown to have memristive behavior, which could be used for neuromorphic applications.22,23 Memristors based on MoS2 grain boundaries

have shown gate-tunable set voltages, allowing further control over synaptic effects.24 In addition, organic core−sheath nanowires with ionic gating gel have been shown to mimic synaptic behavior with ultralow energy consumption rivaling that of biological synapses.25 Transistor-based synapses have also been explored with channel materials made from carbon nanotubes,26 black phosphorus,27 and graphene.28 Although artificial synaptic transmission has been realized in the recent past, there exists no report of a device that accurately mimics the typical behaviors of neurotransmitters. In this article, we employ hysteresis engineering in a MoS2 FET in order to mimic the three essential features of neurotransmitter release dynamics in a chemical synapse as mentioned above. In principle, we are utilizing nonideal effects such as the shift in threshold voltage under extensive electric stress and slow response of interface charge and trap states to achieve our objective. We also provide an experimental framework to capture the long-term potentiation (LTP) phenomenon in the human brain, which is considered as the basis of human memory and learning. Finally, we demonstrate how different operating regimes of a MoS2 FET can be used to engineer the LTP time. The choice of MoS2 is motivated by the recent interest in two-dimensional layered semiconductors as promising candidates for future solid-state devices owing to their atomically thin body nature that allows for aggressive scaling and excellent electrostatic control.29

RESULTS AND DISCUSSION Figures 1a and 1b show the optical image and the device schematic of the MoS2 FET sought to replicate neurotransmitter dynamics in a chemical synapse. The device fabrication is described in the Methods/Experiment section. Figure 1c shows the output characteristic of the device for

Figure 1. Back-gated MoS2 field effect transistor. (a) Optical image and (b) schematic drawing. (c) Transfer characteristics at different source to drain biases (VDS). The drain-induced barrier lowering (DIBL) is relatively small, which indicates excellent electrostatic gate control. The inset shows the trans-conductance (gm) as a function of VGS. The electron mobility extracted from the plateau of gm versus VGS plot was found to be 20 cm2/(V s). (d) Output characteristics of the same device for different back gate voltages showing decent current saturation. The channel length and channel width of the device were ∼200 nm and ∼6 μm, respectively. The thickness of the MoS2 flake was 2 nm. 3111

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adsorption of gas molecules on the surface of MoS2. According to them, at large negative gate voltages (OFF state) the MoS2 channel is depleted of electrons, which facilitates the release of electrons that are trapped by the adsorbed H2O and O2 molecules. This reduces carrier depletion in the channel (i.e., makes the channel more n-type), leading to the negative shift of VTH‑FW. In contrast, at large positive voltages electrons are trapped by the adsorbed H2O and O2 molecules from the MoS2 channel, which increases the carrier depletion (i.e., makes it more p-type), leading to the positive shift of VTH‑BW. As expected, the magnitude of the threshold shift is determined by the strength of the applied gate bias (VPP). According to Cho et al.,33 the number of adsorbates can also increase (decrease) with increasing stress duration (TS) as observed in our MoS2 FETs shown in Figure 2b. Figure 2c shows a schematic representation of the proposed electron-trapping−detrapping mechanism by adsorbed molecules on the surface of the MoS2 channel. Guo et al.34 and Park et al.,35 however, suggested electron trapping at the interface between SiO2 and MoS2 to be responsible for hysteresis observed in their MoS2 FETs. These interface trap states originate from the dangling Si−O bonds at the surface. Electrons trapped in these interface states follow a Fermi−Dirac distribution, with the Fermi level being determined by the equilibrium Fermi level of the MoS2 channel. As shown schematically in Figure 2d, negative gate voltage releases electrons from the trap states into the MoS2 channel (i.e., makes it more n-type), whereas positive gate bias depletes electrons from the MoS2 channel (i.e., makes it more p-type). This give rise to the observed shift in VTH, which is consistent with the earlier discussion. Note that the band movement inside the MoS2 channel in the ON state of the device operation is much weaker (owing to large channel capacitance) compared to the OFF state (where the channel capacitance is essentially negligible). Therefore, under this picture, the magnitude of the VTH shift is expected to be larger for negative gate bias stress compared to positive gate bias stress. Finally, a third picture was invoked by Shu et al.,36 based on their observation that gate voltage hysteresis exists even in suspended MoS2 FETs measured under high-vacuum conditions. In such devices the origin of electron traps cannot be attributed to the MoS2/SiO2 interface or to the gas adsorption/ desorption effect. It has to originate from defects in the MoS2 itself. Moreover, they also demonstrated that FETs based on thinner MoS2 have a larger hysteresis compared to FETs based on thicker MoS2, which suggests that the origin of this effect is more related to the surface than to the bulk. Nevertheless, whatever the origin of the hysteresis in MoS2 FETs, our focus in this article is to engineer the same in order to mimic the neurotransmitter release dynamics in chemical synapses within the human brain. In particular, we utilize the change in source to drain current of a back-gated MoS2 FET owing to the change in threshold voltage introduced by different stress duration, magnitude, and polarity to respectively capture the quantal, stochastic, and excitatory or inhibitory nature of neurotransmitter release. Synapses are elemental to information propagation in the central nervous system (CNS). These are structures where the plasma membrane of the signal-carrying neuron (presynaptic neuron) comes in close proximity to the plasma membrane of the target neuron (postsynaptic neuron), as shown in Figure 3a. In most neurons the presynaptic sites are located on an axon, whereas the postsynaptic sites are located either on a dendrite or on the cell body (soma). Such axo-dendritic synapses are

various back gate overdrive voltages, which clearly suggests enhancement mode operation. Minor Schottky barrier effects are visible in the linear section of the characteristics, which is consistent with our earlier findings that Ni contacts result in ∼100−150 meV Schottky barrier heights.30 Figure 1d shows the transfer characteristics for different drain biases. The electron mobility, extracted from the peak trans-conductance value (gm), was found to be ∼20 cm2/(V s), which is similar to mobility values reported in the literature.31 Although channel lengths are relatively short, lack of drain-induced barrier lowering (DIBL) indicates good electrostatics and overall a highly reliable device in terms of electrical behavior. Figure 2 shows the hysteresis behavior of the same MoS2 FET under different stressing conditions. Figure 2a shows the

Figure 2. Hysteresis engineering and origin of hysteresis in MoS2 FETs. (a) Hysteresis in the transfer characteristics for different peak-to-peak back gate sweep voltage (VP). (b) Hysteresis as a function of the voltage sweep time (TS). (c) Hysteresis in MoS2 FETs due to the electron trapping (OFF state) and detrapping (ON state) mechanism between adsorbed water or oxygen molecules and the exposed MoS2 surface. (d) Hysteresis in MoS2 FETs due to trapped states at the MoS2/SiO2 interface. The filling of trapped states is governed by Fermi−Dirac statistics with the Fermi level given by the equilibrium Fermi level of the MoS2 channel. (e) Hysteresis in MoS2 FETs due to intrinsic defects.

transfer characteristics for three different peak-to-peak back gate sweep voltages (VP). Note that the forward sweep (negative to positive) makes the threshold voltage (VTH‑FW) more negative (shifts toward the left), indicating electron capture by the MoS2 channel, whereas backward sweep (positive to negative) makes the threshold voltage (VTH‑BW) more positive (shifts toward the right), indicating the release of these trapped electrons. Earlier studies on hysteresis of MoS2 FETs have indicated different possible origins for these electron trapping and detrapping mechanism. Li et al.32 suggested 3112

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Figure 3. Description of a biological synapse. (a) Different parts of a neuron with a zoomed-in view of the synapse. (b) Neurotransmitter release in response to action potential (AP) at the presynaptic neuron. The postsynaptic current (PSC), which is determined by the number of neurotransmitters released via vesicle exocytosis, is proportional to the firing frequency of the presynaptic AP.

prevalent in the mammalian nervous system.37 However, axoaxonic, dendro-dendritic, somato-dendritic, dendro-somatic, and somato-somatic synapses also exist in various parts of the CNS. The adult human brain is estimated to contain ∼1014 synapses. The signal transmission in chemical synapses is mediated by endogenous messenger chemicals, better known as neurotransmitters. Neurotransmitters are contained in synaptic vesicles that cluster near the cell membrane in the axon terminal of the presynaptic neuron. Once the action potential propagates along the presynaptic axon and reaches the axon terminal, voltage-gated calcium (Ca) channels are activated and allow the influx of Ca+2 ions into the presynaptic terminal. This triggers (through extensive molecular machinery) the fusion of the synaptic vesicle with the plasma membrane, resulting in the release of neurotransmitters in the synaptic cleft, as shown in Figure 3b. These released neurotransmitters bind with the receptor molecules on the postsynaptic cell membrane and trigger further molecular machinery that ultimately changes the membrane potential of the postsynaptic neuron and generates postsynaptic current.13 In order to realize the transduction function for the proposed neurotransmitters, we mimicked the presynaptic action potential in chemical synapses through gate voltage pulse and the postsynaptic current induced by the neurotransmitter release through the change in source to drain current (ΔIDS) in our MoS2 FETs. The details and characteristic features of neurotransmitter release are then encoded using the amplitude, frequency, and polarity of the gate voltage pulses as described below. The release of neurotransmitters is quantal in nature.8 Each synaptic vesicle inside the presynaptic neuron is similar in size and carries almost an equal number of neurotransmitters; for example, each synaptic vesicle inside a motor neuron holds approximately 10 000 molecules of the neurotransmitter acetylcholine. Exocytosis of a single vesicle, thus, results in miniature postsynaptic current (MPSC), which is the smallest amount of stimulation that one neuron can send to another neuron. 8 The summation of MPSC is known as the postsynaptic current. Note that PSC is an integer multiple of MPSC. Whenever PSC reaches a threshold value, an action potential is generated in the postsynaptic neuron. PSC is directly proportional to the number of vesicles and hence the total number of neurotransmitters released in the synaptic cleft.

The number of synaptic vesicles released depends on the strength of the action potential that arrives at the presynaptic terminal. Since the amplitude of action potential is constant, its strength is determined by the frequency of firing, as shown in Figure 3b. Clearly, a higher frequency of action potential stimulates the fusion of a larger number of synaptic vesicles and hence the release of more neurotransmitters. The PSC is given by eq 1, where nT is the number of neurotransmitters contained in each synaptic vesicle and f(nAP) is the number of vesicles released in response to nAP, the number of action potentials arriving at the presynaptic terminal. The exact functional dependence of f(nAP) on nAP is unknown. However, one could rightly assume that f(nAP) will increase with increasing nAP and finally saturate at a maximum value, which corresponds to the total number of vesicles present in the presynaptic terminal. As we will discuss in Figures 4 and 5, the above-mentioned aspect of neurotransmitter release can be accurately captured by applying voltage pulse trains comprised of variable numbers of individual pulses to the back gate of our MoS2 FETs. PSC ∝ n Tf (nAP)

(1)

The release of neurotransmitters is inherently stochastic in nature and is generally associated with a release probability (pr).38 The stochasticity suggests that for a given action potential there is a finite likelihood of vesicle exocytosis and hence neurotransmitter release. Moreover such stochasticity shows significant diversity among different synapses and often changes over time and also due to physiological conditions.39,40 In fact individual synapses can regulate their neurotransmitter release probability dynamically through local feedback over short time scales as well as through long-term synaptic plasticity.41 The cellular and molecular mechanism responsible for this stochastic nature is still under investigation. It is also not well understood why such stochasticity exists in the first place. However, the stochastic nature plays an essential role in signal propagation through neuronal networks and, therefore, needs to be captured in solid-state devices seeking to mimic synaptic transmission. As we will show, the release probability of synaptic transmission can be correlated with the amplitude of the voltage pulse applied to the back gate electrode in our MoS2 FETs. In order to capture the stochastic nature of neurotransmitter release, eq 1 should be modified into eq 2. 3113

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PSC ∝ pr n Tf (nAP)

(2)

Finally neurotransmitters can be excitatory or inhibitory in nature. Excitatory neurotransmitters increase the PSC, whereas inhibitory neurotransmitters decrease the PSC. For example, glutamate is an excitatory neurotransmitter that is found in fast excitatory synapses throughout the human brain.42−44 Glutamate is also found in modifiable synapses that are thought to be the main memory-storage elements in the brain. Note that excessive glutamate release can cause excitotoxicity and lead to chronic diseases including stroke and epilepsy.45 Similarly, GABA is an inhibitory neurotransmitter that is found in fast inhibitory synapses in the CNS. Many sedative drugs act by enhancing the effects of GABA.46 Other neurotransmitters include acetylcholine, dopamine, serotonin, and norepinephrine. However, despite the wide variety of neurotransmitters, synapses essentially convey only two types of signals, i.e., excitatory and inhibitory, within the neuronal network. A single neuron typically receives thousands of excitatory and inhibitory signals every second. This bipolar nature of synaptic transmission is captured in our MoS2 FETs through the polarity of the back gate voltage pulse. Figures 4a and 4b, respectively, show the input gate voltage pulse sequences used to mimic the excitatory and inhibitory synaptic transmissions in our MoS2 FET. As evident from these figures, each pulse sequence consists of seven pulse trains, and each pulse train consists of a certain number of individual pulses. These individual pulses have a duration of tP = 10 ms and are 50 ms apart, as shown in the zoomed-in insets. Each pulse train is separated from its adjacent pulse train by 40 s. The amplitudes of each individual pulse within a given pulse sequence are constant. However, the amplitudes differ between pulse sequences. In fact, as shown in Figure 4, the amplitudes were varied from 10 to 60 V in steps of 10 V (marked by different colors) for both negative and positive polarities. These pulse sequences were applied to the back gate of our MoS2

Figure 4. Artificial synapse based on a MoS2 FET. (a) Positive and (b) negative pulse sequences applied to the back gate of our MoS2 FET in order to mimic synaptic transmissions. A pulse sequence consists of several pulse trains containing a variable number of individual pulses. Individual pulses within a given pulse train have a duration of 10 ms and are 50 ms apart, as shown in the zoomed-in insets. Each pulse train was separated from its adjacent pulse train by 40 s. The amplitudes of the pulse sequences were varied from 10 to 60 V in steps of 10 V. (c and d) Corresponding source to drain currents (IDS) in the MoS2 FET in response to the applied pulse sequences in (a) and (b), respectively. Positive pulses stimulate inhibitory neurotransmission, whereas negative pulses stimulate excitatory neurotransmission.

Figure 5. Mimicking neurotransmitter release. (a) Excitatory postsynaptic current (EPSC) and (b) inhibitory postsynaptic current (IPSC) as a function of the number of gate voltage pulses (which is equivalent to the number of action potentials in biological synapses: nAP) mimicking the quantal nature of neurotransmitter release. (c) EPSC and (d) IPSC as a function of amplitude of gate voltage pulses mimic the stochastic nature of neurotransmitter release. (d and e) Release probabilities for excitatory and inhibitory neurotransmission, respectively. Circles are experimental data and dotted lines are fittings obtained from the numerical model described in the text with fitting parameters τC (charging time constant) = 110 ms and VA (activation voltage for traps) = 20 V. 3114

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ACS Nano FET. Figures 4c and 4d show the corresponding source to drain currents (IDS). Note that the MoS2 FET was always restored to its initial condition before applying the pulse sequence of a particular amplitude. This was done to make a fair and errorfree comparison between the changes in the device current (ΔIDS) as a function of the pulse number (frequency) and pulse amplitude. As seen in these figures, negative gate pulses increase IDS (i.e., positive ΔIDS) and hence can be used to stimulate excitatory neurotransmitter release, whereas positive gate pulses decrease IDS (i.e., negative ΔIDS) and hence can be used to stimulate inhibitory neurotransmitter release. Please note that the gate voltages used in our MoS2 FETs to replicate neurotransmitter release dynamics are rather high. This is due to the fact that our MoS2 devices were fabricated on highly doped silicon wafers with a 90 nm layer of SiO2 used as a back gate oxide. The required gate voltages can be scaled significantly by increasing the gate oxide capacitance by using thinner oxide layers (tOX) or high-k dielectric (εOX) material such as ALD-deposited Al2O3 or HfO2. In order to explain the transient response of the MoS2 FET of Figures 4c and 4d, we invoke a simple physics-based model that includes the dynamics of the charge trapping and detrapping mechanism. The steady-state ON current of a MoS2 FET is given by eq 3, where μn is the electron mobility in MoS2, COX is the capacitance of the back gate oxide (COX = εOX/tOX = 3.4 × 10−4 F/m2, where εOX is the dielectric constant and tOX is the thickness of the back gate oxide), W and L are, respectively, MoS2 channel width and channel length, VGS is the applied gate voltage, VTH is the threshold voltage, and VDS is the source to drain voltage. The threshold voltage of an FET is given by eq 4, where QIT is the number of interface trapped charges and VTH0 is the unperturbed steady-state threshold voltage, i.e., VTH for QIT = 0. However, when back gate pulses are applied to the MoS2 FET for a short duration of time, interface trap states are charged in accordance with eq 5, where τC is the time constant for trapping and QM is the charge corresponding to the maximum number of interface trap states that can be excited by a voltage pulse of magnitude VP. The reader should remember from our discussion in Figure 2d that the occupancy of trap states depends on the magnitude of the applied gate voltage. QM is given by standard Boltzmann factor with VA as the activation voltage for the interface traps as described in eq 6. Note that the positive (negative) sign in the expression for QM stands for the positive (negative) amplitude of the gate voltage pulse. τC and VA will be used as fitting parameters for our experimental findings. IDS = μn COX

W (VGS − VTH)VDS L

VTH = VTH0 + dQ IT(t ) dt

=

Change in the device current (ΔIDS) in response to a pulse train (containing N individual pulses) applied to the back gate of our MoS2 FET will, therefore, be given by eq 7. In this equation, tT is the total time within a pulse train during which the back gate voltage was applied to the MoS2 FET, i.e., tT = NtP. Note that the appearance of ΔIDS as spikes in Figure 4c and d is due to the fact that even for the largest N = 50, tT = 500 ms, which is much smaller compared to the spacing between the consecutive pulse trains (40 s). Once a given pulse train is switched OFF, the device starts to restore back to its initial condition (i.e., VTH = VTH0) and the trapped charges begin to discharge. As we will demonstrate and discuss later, the discharging time constant (τD) is orders of magnitude higher than the charging time constant (τC), i.e., τD ≫ τC. This explains the gradual decay of IDS in the quiet period of a given pulse sequence. This will also form the basis for mimicking a phenomena called long-term potentiation using our MoS2 FET. Note that LTP is responsible for memory formation in the mammalian nervous system. PSC = ΔIDS ∝ −ΔVTH ∝ −Q IT(t T) ⎛ t ⎞⎤ ⎛ |V | ⎞ ⎡ = ∓γ exp⎜ P ⎟×⎢1 − exp⎜ − T ⎟⎥ ⎝ VA ⎠ ⎢⎣ ⎝ τC ⎠⎥⎦

We define the excitatory postsynaptic current (EPSC) as the change in source to drain current, i.e., ΔIDS for pulse sequences with negative amplitudes, and the inhibitory postsynaptic current (IPSC) as the change in source to drain current, i.e., ΔIDS for pulse sequences with positive amplitudes. We also correlate the number of individual pulses (N) within a pulse train to the number of action potentials (nAP) arriving at the biological synapses. Figures 5a and 5b, respectively, show how artificial EPSC and IPSC change as a function of the strength of the artificial action potential (N = nAP) for different pulse amplitudes (VP). The color codes correspond to Figure 4. The dotted lines are a fit to the experimental data using eq 7. The only parameters used to fit the curves are τC = 110 ms and VA = 20 V. As seen in these figures, both EPSC and IPSC increase initially with increasing nAP and ultimately saturate for higher nAP for any given pulse amplitude. The saturation in EPSC and IPSC is a direct consequence of the fact that the maximum number of trap states and hence trap charges that can be induced by a particular amplitude of gate voltage is constant. When the number of pulses is less, the total charging time tT = NtP is not sufficient to charge all the traps activated by the gate voltage pulse. However, as the number of pulses increases, the activated traps are allowed to be completely charged. This results in a constant maximum shift in the threshold voltage and hence saturation in EPSC and IPSC. Note that this feature of our artificial synapse based on MoS2 FET accurately mimics the release of neurotransmitter in response to an action potential with different frequencies of firing (nAP), as shown in Figure 3b. Similarly, Figures 5c and 5d, respectively, show EPSC and IPSC as a function of the amplitude of the gate voltage pulse (VP) for a single pulse (blue circles) and for a pulse train consisting of five pulses (black circles). The corresponding dotted lines represent fitting using eq 7 with the same parameters used to fit Figures 5a and 5b. We correlate the amplitude dependence of EPSC and IPSC to the probability of vesicle exocytosis (pr) in order to capture the stochastic nature of neurotransmitter release during synaptic transmission.

(3)

Q IT COX

Q M − Q IT(t ) τC

(4)

;

⎡ ⎛ t ⎞⎤ Q IT(t ) = Q M⎢1 − exp⎜ − ⎟⎥ ⎢⎣ ⎝ τC ⎠⎥⎦

⎛ |V | ⎞ Q M = ±Q 0 exp⎜ P ⎟ ⎝ VA ⎠

(7)

(5)

(6) 3115

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ACS Nano Figures 5e and 5f, respectively, capture the release probability for excitatory and inhibitory neurotransmission. Mathematically, we are correlating pr with the exponential function involving VP, but normalized to VM, where VM is the maximum amplitude of the gate voltage pulse. Equation 8 describes the various correlation factors. Note that we are assuming a constant nT, which is a very realistic assumption in the context of biological synapses. It is worthwhile mentioning that we have not considered multineurotransmitter release or co-release of neurotransmitter from a given chemical synapse.47,48 Instead, our model assumes that the control of neural firing (feedback) is achieved by a separate population of inhibitory interneurons. This is indeed true for networks with fast synaptic transmission, which can be assumed to sum linearly.49 As such, we have not introduced any frequency modulation of EPSP or IPSP. However, our future studies will focus on recurrent neural networks with slow, nonlinear transmission or a single population of neurons where co-release of neurotransmitter may be a general mechanism of providing negative feedback to neural firing.

Figure 6. Long-term potentiation (LTP). (a) Decay of EPSC obtained by applying single gate voltage pulse of −60 V in amplitude and 50 ms in duration. Dotted line represents an exponential fit with discharge time constant τD = 6000 s. (b) Extracted long-term potentiation time (τLTP) as a function of both pulse height and frequency. Similar to biological synapses, the extracted τLTP values range from a few minutes to several hours.

d[I(t )] I (t ) ; =− dt τD

PSC ∝ n Tpr f (nAP) PSC = ΔIDS ⎡ ⎛ |V | ⎞⎤⎡ ⎛ |V | − |VM| ⎞⎤ = ⎢γ exp⎜ M ⎟⎥⎢exp⎜ P ⎟⎥ ⎢⎣ VA ⎠⎥⎦ ⎝ VA ⎠⎥⎦⎢⎣ ⎝

IF = I0 + EPSC

⎛ EPSC ⎞ τLTP = τD ln⎜1 + ⎟ I0 ⎠ ⎝

⎡ ⎛ | V | − | V | ⎞⎤ M pr = ⎢exp⎜ P ⎟⎥ ; ⎢⎣ ⎝ VA ⎠⎥⎦

⎡ ⎛ Nt ⎞⎤ f (nAP) = ⎢1 − exp⎜ − P ⎟⎥ ⎢⎣ ⎝ τC ⎠⎥⎦

(9)

⎛ τ ⎞ I0 = (I0 + EPSC) exp⎜ − LTP ⎟; ⎝ τD ⎠

⎡ ⎛ Nt ⎞⎤ × ⎢1 − exp⎜ − P ⎟⎥ ⎢⎣ ⎝ τC ⎠⎥⎦

⎡ ⎛ | V | ⎞⎤ n T = ⎢γ exp⎜ M ⎟⎥ ; ⎢⎣ ⎝ VA ⎠⎥⎦

⎛ t ⎞ I(t ) = IF exp⎜ − ⎟ ; ⎝ τD ⎠

(10)

The long-term potentiation time (τLTP) can be extended to almost a day by exploiting the subthreshold characteristics of the MoS2 FET as shown in Figure 7. Figure 7a shows the transient response of the MoS2 FET to pulse sequences with amplitudes (VP − VB) of −10, −20, −30, and −40 V, when the device is biased in the OFF state by applying a constant back gate voltage of VB = −20 V. Figures 7b and 7c show, respectively, the artificial EPSC as a function of frequency (nAP) and amplitude (VP) of the presynaptic input. The characteristic features remained the same as in the case of ON state operation. However, note that the EPSC axes are in natural logarithmic scale. This can be explained from the fact that in the subthreshold regime of device operation (VGS < VTH) the current depends exponentially on the threshold voltage, as given by eq 11, unlike the linear dependence observed in the ON state given by eq 3. Therefore, any change in VTH will manifest in an exponential change in IDS and hence in the EPSC. Since EPSCs are orders of magnitude higher than the steady-state current in the OFF state of the device operation, the extracted τLTP is improved significantly, as shown in Figure 7d.

(8)

One of the most remarkable features of synapses is their ability to strengthen or weaken over time owing to their own signaling activity or activity in another signaling pathway. This phenomenon is called synaptic plasticity, and it has profound importance in memory formation and learning.50 In excitatory synapses, a long-lasting increase in signal transmission is called long-term potentiation, whereas a similar effect in inhibitory synapses is called long-term depression (LTD). LTP can be mimicked in our MoS2 FETs by utilizing the finite discharge time of the interface-trapped charges introduced by the transient gate voltage pulses. Figure 6a shows the decay of EPSC obtained by applying a single gate voltage pulse of −60 V in amplitude and 50 ms in duration. By using a simpleexponential fit, governed by eq 9, a decay time constant (τD) of 6000 s was extracted from the experimental data. Note that in eq 9, IF is the total device current following the excitatory presynaptic input, whereas I0 is the steady-state device current. Obviously, IF is the sum of steady-state current and excitatory postsynaptic current. The latter is dependent on the amplitude and frequency of the excitatory input and is given by eq 8. We define the LTP time (τLTP) in our artificial synapse as the time required to restore the MoS2 transistor back to its steady-state condition. As such, τLTP is given by eq 10. Figure 6b demonstrates the extracted τLTP as a function of both pulse height and frequency. Similar to biological synapses, the extracted τLTP values range from a few minutes to several hours.

⎡ m(VGS − VTH) ⎤ IDS = IOFF exp⎢ ⎥ kBT ⎦ ⎣

(11)

CONCLUSION In this paper we employed hysteresis engineering in MoS2 FETs in order to mimic biological synapses through a solidstate device. We demonstrated that by changing the frequency, amplitude, and polarity of gate voltage pulses, one can accurately capture the quantal, stochastic, and excitatory or 3116

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ACKNOWLEDGMENTS This work was partially supported by Air Force Office of Scientific Research (AFOSR) Grant Number FA9550-17-10018, through the Young Investigator Program. The authors would also like to acknowledge the technical staff members at the Material Research Institute at Penn State University. REFERENCES (1) Brooks, R. A. Intelligence Without Representation. Artificial intelligence 1991, 47, 139−159. (2) Bean, B. P. The Action Potential in Mammalian Central Neurons. Nat. Rev. Neurosci. 2007, 8, 451−465. (3) Burnstock, G. Physiology and Pathophysiology of Purinergic Neurotransmission. Physiol. Rev. 2007, 87, 659−797. (4) Kandel, E. R., Schwartz, J. H., Jessell, T. M., Siegelbaum, S. A., Hudspeth, A. Principles of Neural Science; McGraw-Hill: New York, 2000. (5) Fonnum, F. Glutamate: A Neurotransmitter in Mammalian Brain. J. Neurochem. 1984, 42, 1−11. (6) Lodish, H., Berk, A., Zipursky, S. L., Matsudaira, P., Baltimore, D., Darnell, J. Molecular Cell Biology; W. H. Freeman: New York, 2000. (7) Sudhof, T. C. The Synaptic Vesicle Cycle. Annu. Rev. Neurosci. 2004, 27, 509. (8) Del Castillo, J.; Katz, B. Quantal Components of the End-plate Potential. J. Physiol. 1954, 124, 560−573. (9) Fatt, P.; Katz, B. Spontaneous Subthreshold Activity at Motor Nerve Endings. J. Physiol. 1952, 117, 109. (10) Cooke, S.; Bliss, T. Plasticity in the Human Central Nervous System. Brain 2006, 129, 1659−1673. (11) Bliss, T. V.; Collingridge, G. L. A Synaptic Model of Memory: Long-term Potentiation in the Hippocampus. Nature 1993, 361, 31− 39. (12) Yang, J.-L.; Sykora, P.; Wilson, D. M.; Mattson, M. P.; Bohr, V. A. The Excitatory Neurotransmitter Glutamate Stimulates DNA Repair to Increase Neuronal Resiliency. Mech. Ageing Dev. 2011, 132, 405−411. (13) Striedter, G. F. Neurobiology: A Functional Approach; Oxford University Press, 2015. (14) Gerstner, W., Kistler, W. M., Naud, R., Paninski, L. Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition; Cambridge University Press, 2014. (15) Nestler, E. J. Molecular Basis of Long-term Plasticity Underlying Addiction. Nat. Rev. Neurosci. 2001, 2, 119−128. (16) Zucker, R. S.; Regehr, W. G. Short-term Synaptic Plasticity. Annu. Rev. Physiol. 2002, 64, 355−405. (17) Mead, C. Neuromorphic Electronic Systems. Proc. IEEE 1990, 78, 1629−1636. (18) Douglas, R.; Mahowald, M.; Mead, C. Neuromorphic Analogue VLSI. Annu. Rev. Neurosci. 1995, 18, 255−281. (19) Jo, S. H.; Chang, T.; Ebong, I.; Bhadviya, B. B.; Mazumder, P.; Lu, W. Nanoscale Memristor Device As Synapse in Neuromorphic Systems. Nano Lett. 2010, 10, 1297−1301. (20) Wang, Z.; Joshi, S.; Savel’ev, S. E.; Jiang, H.; Midya, R.; Lin, P.; Hu, M.; Ge, N.; Strachan, J. P.; Li, Z.; et al. Memristors with Diffusive Dynamics As Synaptic Emulators for Neuromorphic Computing. Nat. Mater. 2017, 16, 101−108. (21) Kim, K.-H.; Gaba, S.; Wheeler, D.; Cruz-Albrecht, J. M.; Hussain, T.; Srinivasa, N.; Lu, W. A Functional Hybrid Memristor Crossbar-array/CMOS System for Data Storage and Neuromorphic Applications. Nano Lett. 2011, 12, 389−395. (22) Cheng, P.; Sun, K.; Hu, Y. H. Mechanically Induced Reverse Phase Transformation of MoS2 from Stable 2H to Metastable 1T and Its Memristive Behavior. RSC Adv. 2016, 6, 65691−65697. (23) Cheng, P.; Sun, K.; Hu, Y. H. Memristive Behavior and Ideal Memristor of 1T Phase MoS2 Nanosheets. Nano Lett. 2015, 16, 572− 576. (24) Sangwan, V. K.; Jariwala, D.; Kim, I. S.; Chen, K-S.; Marks, T. J.; Lauhon, L. J.; Hersamem, M. C. Gate-Tunable Memristive

Figure 7. Engineering LTP through OFF state operation of MoS2 FET. (a) Transient response of the MoS2 FET to pulse sequences (presynaptic inputs) with different amplitudes. The device is biased in the OFF state by applying a constant back gate voltage of VB = −20 V. EPSC response in natural logarithmic scale as a function of (b) frequency (nAP) and (c) amplitude (VP) of the presynaptic input. (d) Extracted long-term potentiation time (τLTP). A significant improvement is observed compared to the ON state operation.

inhibitory nature of neurotransmitter release in chemical synapses. We also discussed a possible way to replicate and engineer long-term potentiation in the human brain, which forms the basis for learning and memory.

METHODS/EXPERIMENT For device fabrication, MoS2 flakes were transferred onto a p+2 silicon substrate with a 90 nm thermally grown oxide (SiO2) using standard micromechanical exfoliation with high-quality dicing tape. The p+2 silicon substrate and the SiO2 layer serve as the global back gate and the gate dielectric, respectively. Prior to device fabrication, the exfoliated MoS2 flakes were annealed for 3 h in argon at 250 °C. Source and drain (S/D) contacts are defined using electron-beam lithography followed by electron-beam evaporation of metal contacts. Ni (120 nm) was used as the contact metal. Channel length and width for the device were 200 nm and 2 μm, respectively, and the flake thickness was 2 nm, which is equivalent to about three monolayers.

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] or [email protected]. ORCID

Daniel S. Schulman: 0000-0002-0751-0578 Saptarshi Das: 0000-0002-0188-945X Author Contributions

A.J.A., A.R., and S.D. designed and conceived the idea. A.J.A., A.R., and D.S.S. performed the experiments. A.J.A., A.R., D.S.S., J.R.N., and C.M.E. helped with device fabrication. A.J.A., A.R., and S.D. analyzed the data and wrote the manuscript. Notes

The authors declare no competing financial interest. 3117

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