Optimization of Random Telegraph Noise Characteristics in Memristor for True Random Number Generator

Memristor devices can be utilized for various computing applications, and stochastic computing is one of them. The intrinsic stochastic characteristics of the memristor cause unpredictable current fluctuations by the capture and emission of electrons in a trap site. Herein, a true random number generator (TRNG) using the random telegraph noise (RTN) of the memristor as an entropy source is proposed. TiOx/Al2O3 memristors are fabricated, and the capture time probability of the RTN characteristics is modulated to 50% with varying read‐voltage and device conductance state. In addition, the TRNG operations with the RTN current signals as entropy sources are experimentally demonstrated with a customized breadboard, and the randomness is verified with the National Institute of Standards and Technology (NIST) tests.


Introduction
The internet of things (IoT), which is a system where edge devices are directly connected and communicated, is no longer a future story but has expanded its area to most areas of human life including smart home appliances and self-driving cars thanks to the recent advancement of wireless communication technologies. [1][2][3][4][5] It is expected that billions of devices are connected all over the world and there are a couple of connected devices per person in average. [6] Accordingly, the number of communications between each device has drastically increased and the importance of IoT security has become critical against potential attacks or any kind of information leaks. Since software-based security protocols and encryption algorithms are relatively prone to physical attacks with high computing power or machine-learning algorithm, hardware security technologies have been investigated with fundamental cryptographic primitives. [7][8][9][10] Among them, a hardwarebased true random number generator (TRNG) is a system that can generate random bits and can be used for key cryptography, digital signatures, and ciphers, and has been demonstrated by means of intrinsic stochastic processes. [11][12][13][14][15][16][17] It is necessary for the generation of unpredictable encryption keys to ensure information security and strong encryption; therefore, the entropy source is one of the most important factors to realize a TRNG.
Memristor realized by a metal-insulator-metal structure is one of the most emerging nonvolatile memories thanks to the advantages of low-power operation, metal-insulator-metal structure, and fast-switching operation and has been utilized not only for stand-alone memory device but also for various computing applications including analogue computing for neuromorphic system, and stochastic computing such as physical unclonable function. [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] TRNG is also one of these applications and several studies have employed random telegraph noise (RTN) in a memristor device as an entropy source for TRNG. [36][37][38][39][40][41][42][43][44][45][46] RTN is an intrinsic randomness characteristic of electronic devices and is mainly caused by the capture and emission of electrons in a trap site. [47][48][49][50][51][52] This phenomenon generates random and unpredictable stochastic fluctuations with respect to time, resulting in read current instability due to sudden sharp fluctuations. [53][54][55] Although this behavior usually interrupts the accurate operations of computing applications where a read current should be stable, it can be used as an entropy source for a TRNG because these sharp current fluctuations occur randomly. To use the RTN as a stable random entropy source, the capture/emission time ratio can be de-biased with the help of additional circuitries such as a toggle flip-flop or adjusted to 50% with device engineering including bias modulation. [44,45] In this study, we demonstrate a TRNG using two-level RTN current characteristics of TiO x /Al 2 O 3 memristors. First, the programming characteristics of the device are presented and the current fluctuation characteristics according to the device state are verified regarding both cycle-to-cycle and device-to-device variations. Subsequently, the capture time probability is investigated according to the read bias condition and device state. With the help of the randomness of the RTN characteristics as the entropy source, a TRNG circuit is experimentally constructed on a breadboard and its randomness is verified by National Institute of Standards and Technology (NIST) randomness test.

Results and Discussions
2.1. Switching Properties and RTN Characteristics Depending on Device State Figure 1a shows the top-view optical image and cross-sectional view transmission electron microscopy (TEM) image of the memristor having an active area of 2.5 Â 2.5 μm 2 . The device has Ti/Pt metal stack for both top electrode (TE) and bottom electrode (BE), and TiO x /Al 2 O 3 stack as switching layer. The detailed fabrication method is described in Experimental Section. The electrical current-voltage (I-V )-switching characteristics of the fabricated 30 devices are plotted in Figure 1b. First, the forming process of the memristive devices was conducted with a positive-voltage sweep to 4 V. Then, a positive-voltage sweep was performed to 1.1 V for a set operation, while a reset operation was performed through a negative-voltage sweep to À1.5 V. To examine the RTN characteristics of the device, sampling frequencies ranging from 100 Hz to 100 kHz were tested after a reset operation and transient characteristics were measured at the read voltage of 0.1 V as shown in Figure 1c (see Figure S1, Supporting Information for additional frequencies). The RTN characteristics were not correctly recorded at a sampling frequency below 1 kHz, and discrete two-level RTN current signals could be obtained at 5 kHz or higher. This is because actual RTN signals can be distorted when sampling frequency is too low compared with capture time (τ c ), and emission time (τ e ). [56,57] In contrast, RTN characteristics could be adequately extracted when sampling rate exceeds τ c and τ e , and 10 kHz was determined as sampling frequency for all the measurement of transient characteristics to verify RTN signals. Figure 1d shows the normalized current fluctuation (ΔI/I) of the RTN signals according to the device conductance over 20 cycles in 10 devices in average to confirm the statistical tendency of RTN signals depending on the device state. The set-reset process was repeated in each device, and the read operation was performed at 0.1 V for 10 s in every cycle at room temperature. Apparently, there is an appreciable change in the magnitude of conductance by the RTN effect at a low-conductance level. A large ΔI/I over several cycles implies that RTN signals can be detected more easily and reliably thanks to enough current difference between RTN signals by the capture and emission of electrons in a dominant trap. The current fluctuation by the RTN effects can be observed more easily at low-conductance state (LCS) since the device conduction is limited by the tunneling gap. In contrast, ΔI/I becomes small with a narrower distribution at a high-conductance level (HCS), which implies that RTN signals are less likely to occur because the device current flows through a conductive filament in the switching layer. Figure 1e shows the transient characteristics of read current at sampling frequency of 10 kHz for 4 s when the device conductance is 1 mS, where the current fluctuation by the RTN effect cannot be found. Therefore, it is determined to investigate the RTN characteristics at the device conductance below 0.2 mS to obtain RTN signals stably over time.
The multistate programming characteristics were verified using write-and-verification algorithm with incremental-steppulse programming (ISPP) scheme as shown in Figure 2a.
The amplitudes of a set pulse and reset pulse started at 0.5 and À0.7 V, respectively, and incremented with a step of 0.05 V after the state verification at the read voltage of 0.1 V. For both the set and reset operations, the pulse width was set to 10 μs. There are three target states within the device state window: HCS (0.02 -0.04 mS), median-conductance state (MCS, 0.09 -0.11 mS), and LCS (0.18 -0.20 mS), and the programming steps were finished when the device state reached a target-conductance value. Here, the maximum number of iterations was set 500 for the device programming. It is confirmed that the device state can be tuned according to the target value by the write-and-verification scheme within the maximum number of pulses (<20 pulses per each tuning operation) thanks to the gradual switching characteristics, which is utilized to investigate the dependency of capture time probability on the device state. In addition, the write-and-verification algorithm is verified regarding both the cycle-to-cycle (C2C) and device-to-device (D2D) variations. Figure 2b,c shows the programmed conductance level of 1000 cycles and 100 devices, respectively, by using the median value of each region as the target value and 0.01 mS as the tolerance conductance, which confirms that accurate programming can be conducted in each region. The probability plot of current fluctuation (ΔI) was measured at sampling frequency of 10 kHz for 2 s over 20 cycles in 25 devices (a total 500 points per each state) and plotted in Figure 2d. It is confirmed that the RTN occurs stably for both C2C and D2D variabilities, and ΔI is smaller in a lower-conductance state because the gap distance in the ruptured filament becomes thicker as the device conductance is decreased. It is also observed that ΔI is log-normally distributed due to the normal variations of the tunneling gap which can exponentially modulate a trap-assisted tunneling current. It is believed that charge transport is dominated by trap-assisted tunneling at oxygen vacancies when oxide-based memristor is at LCS, so the RTN signals can be mostly determined by the current contribution of a singledominant oxygen vacancy, resulting in two-level RTN signals. The ΔI/I dependency on the device state is also verified as shown in Figure 2e and LCS has a larger ΔI/I in average, which will be helpful to distinguish two-level RTN signals and generate 1 and 0 bit in a TRNG.
In addition, the read-voltage effect on the capture time probability is analyzed according to the device state. The capture time probability is defined as the ratio of capture time to total time and extracted by a customized MATLAB code. A positive voltage was applied to the BE, and the read voltage was varied from 0.01 to 0.25 V, and RTN characteristics were measured according to the device state. The distinguishing cases are plotted for LCS, MCS, and HCS as shown in Figure 3a-c, respectively, and the average capture time probability for 30 devices is summarized as a function of the read-voltage and device state in Figure 3d. Our device tends to have one strong filament formed in the switching layer rather than multiple weak filaments according to our previous report, [58] resulting in the fact that most of the devices have twolevel RTN signals. Even if some devices have multilevel RTN characteristics, the TRNG circuit can be digitally operated as long as a single-dominant trap has a significant effect than other, which will be discussed later. Each condition was tested for 5 times to obtain the effect of the read cycle (see Figure S2, Supporting Information), resulting in a total 150 points per each condition. It is observed that the capture time probability, which is the time at which the trap is empty, is decreased as increasing the read voltage regardless of the device state. Especially, the  Figure 3d, which statistically confirms that the capture time probability can be modulated according to the read voltage although it has variations on some levels. This implies that electrons at the BE could be captured in the trap by a strong electric field. If the energy level of the trap (E T ) is higher than the Fermi level (E F ) when the voltage is low, it is difficult for electrons to be captured in the trap. However, as the read voltage is increased, E T approaches E F , and the reduced E T -E F increases the probability that electrons can be captured in the trap, which can reduce the capture time probability. Moreover, the capture time probability is also decreased at a higher-conductance state with the same read voltage. This is because the residual filament in the switching layer is thicker when the device conductance is higher, which reduces the distance between the trap and the top of residual filament.
The trap causing RTN exists in the Al 2 O 3 layer because the filament is ruptured in the switching layer. The longer the residual filament is, the higher the capture probability of electrons in the trap is. Therefore, it is hard to observe the RTN characteristics www.advancedsciencenews.com www.advintellsyst.com when the device conductance is high, and the capture time probability is also reduced.
To verify this behavior, the effective trap energy in the switching layer depending on the read voltage and the device state was extracted with regard to the Fermi level by the RTN characteristics for each state using the Shockley-Read-Hall statistics. [59][60][61][62][63] Although this method reflects tunneling process since the capture cross section, which is the effective area of a trap including tunneling effect and activated process, is considered, these results might be the rough estimations since trapassisted tunneling process is not fully considered. Therefore, they are utilized not to extract accurate positions but for reference to understand the effect of the bias condition and device state on the RTN characteristics qualitatively. The average trap energy for 30 devices is extracted from each state and plotted as a function of the read voltage as shown in Figure 4a, which confirms that the effective trap energy is decreased with a higher read voltage. This is because the effective trap energy can be modulated depending on the bias conditions and reduced with a higher read voltage considering the downward band bending near the TE. [64,65] The reduced effective trap energy by the applied voltage increases the capture probability of electrons in the trap, reducing the capture time probability as a result. Figure 4b shows the statistical distributions of effective trap energy at the read voltage of 0.08 V according to the conductance state. The extracted average effective trap energy from 30 devices is À3.79, À17.9, and À42.7 meV for LCS, MCS, and HCS, respectively, which confirms that the capture time probability can be also adjusted by the device state. This is because the residual filament is modulated depending on the device state and the trap location is changed accordingly. Since the residual filament in the switching layer is lengthened at HCS with a small tunneling gap, a dominant trap is highly likely to be placed near the TE, which means that the effective trap energy at HCS is more affected by the read voltage. In contrast, the filament is partially ruptured at LCS with a large tunneling gap and a trap tends to be placed far from the TE; therefore, the effective trap energy at LCS is less affected by the read voltage and decreased due to the downward band bending near the TE. These imply that the effective trap energy can be adjusted by both the read-voltage and device state, and the capture time probability can be also modulated accordingly. The capture time probability is expected to 50% since the effective trap energy is modulated close to 0 at LCS under the read voltage of 0.08 V as shown in Figure 3d. In short, the device conductance and the read voltage can determine the effective trap energy; therefore, the capture time probability can be modulated by both of them and tuned to 50% in both directions for a TRNG. In addition, a larger ΔI/I can be obtained at a lower-conductance state, which is required to have clear two-level RTN signals. Therefore, LCS at 0.08 V of the read voltage, where the average capture time probability converged to 50%, is determined to use the RTN characteristics as an entropy source of a TRNG circuit. www.advancedsciencenews.com www.advintellsyst.com Figure 5a shows the TRNG circuit using the RTN characteristics of the memristor as a random entropy source. When the read voltage is applied to the TE of the memristor, the current flows the first an op-amp which is used as an inverting amplifier, where the RTN current signals are amplified and converted into voltage at node 1. R1 is set 1 MΩ to make the voltage fluctuation (ΔV ) at node 1 near 1 V, which is smaller than supply voltage (V dd ), so that the next-stage circuit can accept ΔV as input fluctuation. Then, a DC-blocking capacitor C is placed between two op-amps to use a common ground as reference voltage in a comparator. Thanks to the DC-blocking capacitor, the offset value of the node 1 V becomes close to ground, and high-and low-level voltage signals become positive and negative, respectively, at node 2. This makes the comparator have the common ground as the reference voltage. To optimize C and R2 values, the spice simulations are conducted with various resistancecapacitance (RC) values (see Figure S3, Supporting Information). When the RC value is small, an RC time constant is too short to  www.advancedsciencenews.com www.advintellsyst.com maintain high-and low-level voltage signals, and the node 3 voltage is mostly grounded due to the high impedance of capacitor. In contrast, the DC component of the fluctuated voltage signals is not clearly removed when the RC value is large due to a long RC time constant. It is confirmed that a proper RC value is required to keep two-level voltage signals as well as remove a DC component, and 220 μF and 10 kΩ are determined as C and R2, respectively. The second op-amp acts as a comparator and generates output signals by comparing the node 2 voltage and the common ground. The digital output signals V dd and 0 are generated at node 3 when the node 2 voltage is positive and negative, respectively. Finally, a D flip-flop samples the node 3 voltage signals according to the clock (CLK) to generate a random bit at node 4. The output of the D flip-flop is determined as the value of node 3 voltage at the rising edge of CLK. The frequency of the CLK is slower than that of the RTN current signals to compensate the randomness and generate random bit strings at a constant rate. Figure 5b shows the schematic view of the TRNG testing system. The read voltage is biased to the memristor by semiconductor parameter analyzer (Keysight B1500) and the TRNG circuit is configured through a probe station and breadboard (see Figure S4, Supporting Information, for more detailed discussions regarding experimental setup).

TRNG Circuit and Performance
The experimentally measured node voltage characteristics are presented in Figure 5c-e. The RTN current signals are inverting amplified in a form of voltage at node 1, and their DC component is removed at node 2. The digital output signals are generated through the comparator with the common-ground reference, and the random bit is generated through the D flip-flop at the rising edge of the CLK. Here, the CLK frequency needs to be set closely related to the capture and emission time because the randomness of TRNG can be varied depending on the CLK frequency. If the sampling frequency is too faster than the capture and emission time, the randomness can be significantly degraded because the TRNG circuit would generate an identical bit stream (see Figure S5, Supporting Information). [66] In average, the capture and emission time in our devices is extracted as 71.5 and 69.2 ms, respectively, so the CLK frequency is set 10 Hz. It is confirmed that the percentage of 0 and 1 among 60 000 bits generated by the TRNG circuit is 49.97% and 50.03%, respectively, which implies that the TRNG circuit can generate random bit strings unbiasedly. In addition, it is also confirmed that the TRNG can be digitally operated even with multilevel RTN signals as long as a dominant trap has the greatest impact on the device conduction than other traps since the comparator can generate digital outputs based on 0 V (see Figure S6, Supporting Information). Finally, NIST randomness tests are conducted to check the randomness of the generated bit strings from the TRNG circuit, and the results are summarized in Table 1. There is a p-value as an indicator of the results of the NIST randomness test. A p-value means the probability that a perfect random number generator would generate a less random sequence than the tested sequence is, and it is considered random if it is greater than 0.01. [67] The generated random number data set successfully passed all the 16 NIST tests. Especially, the monobit test (the frequency test) implies if the probability of 0 and 1 converges to 50% or not, and its p-value is 0.085 for this study, indicating that sufficiently random bit sequences are generated.

Conclusion
In this study, we proposed the TRNG circuit using the RTN current signals of the TiO x /Al 2 O 3 memristor as entropy sources. The multilevel switching characteristics were verified with ISPP algorithm, and the state-dependent RTN characteristics were investigated with different read-voltage conditions. The RTN current signals were optimized with both the device conductance and read voltage to have 50% of capture or emission time probability, and its behaviors were discussed with the trap locations. Subsequently, the TRNG circuit was constructed on a breadboard and its behaviors were experimentally demonstrated. The circuit operation was verified by measuring transient characteristics of each node. Thanks to the sampling operations of the D flip-flop at the rising edge of CLK signals, random bit strings could be stably generated at a constant rate and passed all the NIST randomness tests. We believe our results can provide a framework for future study to utilize the RTN characteristics of memristors for stochastic computing applications such as physically unclonable functions and TRNGs.

Experimental Section
Device Fabrication: The 60 nm thick Pt was first deposited using e-beam evaporation to form the BE on the Si/SiO 2 substrate in 4 inch wafer. Subsequently, 3 nm thick Al 2 O 3 and 32 nm thick TiO x layers were deposited using atomic layer deposition and DC reactive sputtering as the switching material and buffer layer, respectively. Finally, a 60 nm thick Pt layer was deposited by e-beam evaporation to form the TE. Both TEs and BEs were patterned by a UV photolithography and liftoff process with the single cell size 2.5 Â 2.5 μm 2 .
Electrical Characterization and NIST Randomness Test: All the electrical characteristics of the memristor were measured using a source measure

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.