In the present context of fabless manufacturing, semiconductor device models play a critical role in emulating the fabricated device in any application. The traditional compact model development required a vast pool of experimental/simulation data to be manually fitted and optimized with various parameters1-4. In addition, these models have to be periodically updated with newer device physics, which often requires developing the same model from scratch. Recently, machine learning (ML) tools have gained popularity in various scenarios5-9. Also, ML has immense potential to improve the development of any compact model of any semiconductor device10,11. In this regard, we have derived the data-driven models from many experimental observations. Owing to its support for a broader range of regression methods, one can use these ML techniques to develop device models supporting multiple hierarchies. These will further cater to the requirement of the tailored device model suitable for specific circuit or device simulations.
As the memristor fabrication technologies have not yet been standardized, their theoretical models may not take account of the various challenges associated with the fabrication of memristors, namely, variability in terms of terminal contacts, packaging, process parameter variations, measuring equipment accuracy, etc., which are usually ignored in the physics-based analytical modeling approach. Thus, one should prefer a data-driven modeling approach adopting the experimentally characterized data on fabricated devices to incorporate all the practical issues associated with the memristors in the compact model.
Among the various structures of metal-oxide memristors, e.g., nanorods12-15, nanobelts16-19, nanofibers20-22, nanowires23-27, etc., nanofiber memristors are suitable for the development of advanced and novel electronic and optoelectronic devices28. A large variety of metal oxides, such as TiO229, SnO2, HfO2, CeO2, etc., have been well studied for memristive applications. Even though Sn (owing to multiple oxidation states) has a large oxide family (SnO2, Sn2O3, Sn3O4, SnO), applications of SnO2 in memristors are primarily limited due to the high conductance of conventional SnO2 thin film. Previous reports on artificial synapse based on a gate tunable, a 2 nm thick 2D SnO2 memristor gave an ROFF : RON ratio of ∼10, operating within ±15 V30. SnO2 is a well-known n-type semiconductor with superior electron mobility, whose high surface-to-volume ratio of 1D nanofiber SnO2 form offers significant deep-level traps. This enhances the memory window, response time, set voltage, and current level of a memristor. To the best of the authors’ knowledge, the 1D SnO2 memristor has not been reported yet. Furthermore, its data-driven model will open new promising avenues for novel and complex applications.
This article has experimentally demonstrated a 1D SnO2 nanofiber-based memristor on a p-type Si substrate for the first time. With the help of the electrospinning technique, a SnO2 nanofiber with an average diameter of 759.2 nm was deposited. Silver (Ag) and aluminum (Al) were employed in the fabricated memristor as the top and bottom electrodes, respectively. The electrospunned n-type SnO2 nanofiber was used as the active layer of the fabricated memristor. The proposed device exhibits a very high ROFF : RON of ∼104 (ION : IOFF of ∼105) with an excellent activation slope of 10 mV/dec, low set voltage of ∼1.14 V, and good repeatability. The device operation has been explained with the help of device physics. Eventually, a compact data-driven model in conjunction with ML-based techniques of the fabricated memristor was also presented. Different algorithms such as polynomial regression, support vector regression, K nearest neighbors (KNN), and artificial neural network (ANN) were employed to model the experimental data of the fabricated device. Finally, the proposed two models adopting ANN techniques were observed to provide the best compact models based on R2 and mean absolute percentage error (MAPE). Elaborated flowcharts, ANN architectures, data modeling, and model validation were also presented in detail in the manuscript.
Fig. 1. Complete schematic indicating synthesis and device fabrication of the 1D-SnO2 nanofiber-based memristor. |
RESULTS AND DISCUSSION
Materials characterizations
Fig. 2a depicts the X-ray diffraction (XRD) pattern of the pristine SnO2 nanofibers. A tetragonal rutile structure was confirmed by the attained characteristic peaks with planes (110), (101), (200), (111), (210), (211), (220), (002), (310), (112), (301), (202), and (321) at appropriate diffraction angles31. The obtained results corroborate with standard literature (JCPDS-41-1445). Fig. 2b illustrates the X-ray photoelectron spectroscopy (XPS) survey spectra of synthesized SnO2 nanofibers, wherein Sn 4d, Sn 3d, O 1s, Sn 3p3, and Sn 3p1 were observed at appropriate binding energies (BEs). Fig. 2c depicts the deconvoluted core-level fitted XPS spectra of Sn 3d with two doublet peaks, i.e., Sn 3d3/2 and Sn 3d5/2 ascribed to ∼495.3 and ∼486.88 eV BEs, respectively. Fig. 2d shows the deconvoluted XPS spectra of O 1s with two prominent peaks corresponding to the lattice (OL), oxygen vacancies (OV), and adsorbed oxygen species (OA) observed at ∼530.7, ∼532.28 eV, and ∼533.08 eV, respectively. Referring to the core-level spectra of O 1s, the estimated lattice oxygen, vacancy oxygen, and chemically adsorbed oxygen are 80.2%, 14.5%, and 5.2%, respectively. Obviously, chemically adsorbed oxygen is less than the available oxygen vacancies, so vacancies do play an important role in the memristive action. These results indicate that the amount of adsorbed oxygen is increased by the introduction of SnO2 nanofibers. Surface-adsorbed oxygen tends to form more active sites, thereby increasing the traps supporting the memristive action. Fig. 2e features the HR-SEM image of the deposited nanofiber in top view on the fabricated device. The mesh will contain several vacant spaces (Fig. 2e), and multiple nanofibers overlaid on each other. The statistical distribution of the measured diameter of the synthesized SnO2 nanofibers is illustrated in Fig. 2e (inset). Calculation suggests that an average diameter of 762.3 nm is achieved with mean = 1.24, median 1.245, and SD = 0.09. The roughness of the electrospun nanofiber shown in Fig. 2f was measured employing the scanning tunneling microscope (STM). The area can be measured at 200 × 200 nm2, and the roughness (in terms of the measured tip currents) is 30 nA-68 nA. The process was repeated to cover the 2 × 2 μm2 area, and the roughness average (R.A.) is found to be 1.8 nA.
Fig. 2. a, XRD spectrum for pristine SnO2 nanofiber. b, High-resolution XPS survey spectrum of pristine SnO2 nanofiber. c, High-resolution core-level fitted XPS spectra for the elements Sn 3d. d, High-resolution core-level fitted XPS spectra for the elements O 1s. e, High-resolution FE-SEM images of SnO2 nanofibers in top view with the statistical distribution of the diameter of the nanofiber (in set) with mean = 1.24, median 1.245 and SD = 0.09. f, Surface roughness of the SnO2 nanofiber deposited on the Al-coated Si wafer. FE-SEM, field emission scanning electron microscopy; SD standard deviation; XPS, X-ray photoelectron spectroscopy; XRD, X-ray diffraction. |
Electrical characterizations
Fig. 3a shows the schematic of the proposed device fabricated on the p-type Si wafer. Al (∼70 nm) was deposited adopting the thermal evaporation technique. For the synthesized SnO2 nanofiber, experimental measurements indicated an average thickness of 762 nm for the individual nanofibers. For the complete nanofiber mesh, the measured thickness was approximately 9.4 μm. However, the mesh contains several vacant spaces (Fig. 2e), and multiple nanofibers overlaid on each other. As a consequence, the bulk nanofiber achieves higher thickness. However, for the memristive action in SnO2 nanofiber, a metal-semiconductor-metal structure was employed, in which the active SnO2 layer was covered on top with an Ag electrode. During the top electrode deposition via the thermal evaporation technique, metal ions were easily migrated/diffused/transported through the porous SnO2-based nanofiber mesh and reached closer to the bottom electrode. As a result, when the metal-semiconductor-metal structure was formed, the thickness of the active layer will be significantly less than that of the bulk SnO2 nanofiber structure. Evidently, the measured average thickness of individual nanofibers in the active layer of the fabricated memristor is 762 nm, which is extremely less than the overall thickness of the SnO2 nanofiber mesh. Fig. 3b shows the current-voltage (I-V) characteristics in a linear scale obtained with the adoption of a probe station and a Keithley 2450 source meter. An external bias voltage sweeping between ±2 V was applied between the electrodes. The measured threshold voltage of the proposed SnO2 nanofiber-based memristor is ∼1.14 V, with a saturation current of 0.14 mA. The fabricated device exhibits the signature hysteresis of the memristor. I-V characteristics in the logarithmic scale in Fig. 3c indicate that initially, the memristor operates in a high resistance state (HRS) when a low DC voltage sweep was applied (0 V to 1.14 V), voltage ranged from 1.14 V to 1.145 V, the measured current showed a sharp increase from 3.35 ⨯ 10−7 A (0.335 μA) to 2.76 ⨯ 10−5 A (27.6 μA), demonstrating a switching from the OFF state to the low resistance state (LRS) or the ON state. The OFF/ON transformation process could be deemed a “writing” process in digital storage32, 33, 34, 35. The current level could be maintained at LRS regardless of applying another positive voltage sweep from 0 to 2 V, a negative voltage sweep from 0 to −2 V, or even removing the power supply, which served as a “reading” process in digital storage. However, the current declined steadily from −0.55 V to −0.33 V when the device underwent a negative sweep from 0 to −2 V, indicating from the LRS to HRS. This transition represented that the stored information could be readily erased. Notably, the nanofiber-based device could realize the ON/OFF transformation by switching the positive or negative applied voltage. When applying the bias, the fabricated device begins to conduct electricity by forming a conductive filament. The current response shows that the conduction mechanism started at 0.86 V, and the subsequent switching occurs at 1.14 V and 1.62 V, respectively. These multiple switching characteristics can be beneficial for applications that require multiple saturation current levels. The availability of multiple oxidation states of Sn can be the probable reason for this phenomenon. The activation slope of the fabricated device is 10 mV/dec with ROFF : RON of ∼104 (ION : IOFF∼105), which is clearly visible in Fig. 3c. The pattern is repeated for the consecutive 100-cycle I-V characteristics in Fig. 3d, where the interval of the 4th cycle data for proper observation was displayed. For the 1st cycle, switching happens at 1.62 V, and switching happens for the 100th cycle at 0.92 V. The SET voltage VSET of the consecutive cycles (like for the 4th, 8th, and so on) decreases with the presence of the localized ions, and beyond that, it remains almost the same. The I-V response for 100 consecutive cycles shows very stable switching from a high resistance state (HRS) to low resistance state (LRS) and vice versa. The multiple switching characteristics are also present in these plots. HRS signifies the data writing, LRS denotes the data memorization or holding the data, and the breakdown voltage VBR represents the data erase, all of these three symbols characterize the properties of the memristor. The variation of VBR for 100 consecutive cycles from −0.61 V to −0.33 V is also visible in Fig. 3d. Fig. 3e depicts the current HRS of the fabricated memristor and LRS currents for 1000 consecutive cycles. The result indicates that ROFF : RON of ∼104 (ION : IOFF of ∼105) does not alter significantly with the cycle number (except for the first cycle). The average current values of HRS and LRS are ∼1 nA and 0.1 mA, respectively. Fig. 3f depicts the statistical variation in measured VSET for 30 switching cycles, which confirms the stability of the device. The mean value of VSET is approximately 1.24 V.
Fig. 3. a, Schematic of the fabricated 1D SnO2 nanofiber-based memristor. b, Measured I-V characteristics of the fabricated memristor in linear at room temperature. c, Measured I-V characteristics of the fabricated memristor in logarithmic scales at room temperature. d, I-V characteristics in logarithmic scale for 100 consecutive cycles. e, Variation of RON and ROFF for 1000 consecutive switching cycles with a variation of ION and IOFF for 1000 consecutive switching cycles inset. f, The statistical distribution of the VSET for 30 switching cycles. |
Conduction mechanism
The conduction mechanism of the fabricated memristor can be explained with the adoption of the schematic of the nanofiber shown in Fig. 4a. The conductive network comprised of nanofibers plays a vital role in the memristive action as more conductive paths would promote exciting hopping of electron carriers. Meanwhile, SnO2 nanofibers can also provide direct pathways for charge transport36. With the help of oxygen vacancies, nanofibers can thus provide direct pathways for charge Ag+ ions to transport with the applied positive bias. Overlap of the n-type of SnO2 nanofibers can promote exciting electron carriers through the hopping mechanism. The migration of Ag+ ions is a vertical migration. As depicted in the field emission scanning electron microscopy (FE-SEM) image in Fig. 4a (inset) of the fabricated nanofibers, there exist finite gaps between the synthesized nanofibers. When the top electrode is deposited via thermal evaporation, metal ions are also deposited on the bottom nanofiber layer owing to its porous structure. Therefore, the actual metal-semiconductor-metal structure exhibiting the signature memristive characteristics consists of a monolayer or few layers of SnO2 nanofibers. Thus, during the forming process, the Ag+ ions migrate vertically along the nanofiber, and a conduction bridge is formed at the appropriate bias level. The energy band diagram and the ultraviolet photoelectron spectroscopy (UPS) spectra along with UV-Vis absorption spectra and Tauc plot (inset) of synthesized SnO2 nanofiber are shown in Fig. 4b inset. A UV-Vis absorption study was conducted to estimate the bandgap, and then the Tauc plot shown in Fig. 4b inset was adopted to estimate the bandgap of the synthesized SnO2 nanofiber, which was measured to be ∼2.25 eV. From the UPS study, the Fermi edge (EF) of 1.36 eV and Ehomo of 1.57 eV are derived, and the work function (Φ) is calculated to be 4.63 eV. With this information, we have drawn the energy band diagram of the SnO2.
VWhere, hν represents the energy of the He-I source (i.e., 21.22 eV) and Ecut-off is the binding energy at the higher energy end of the spectrum, i.e., 15.23 eV. The work function of the SnO2 nanofiber was then calculated to be 4.63 eV, and the work function value of Ag adopted from the literature is 4.7 eV37. The vacuum levels of SnO2 and Ag in standalone/bulk conditions are of the equal values, which are represented in Fig. 4c. However, a Schottky barrier will form between the semiconductor (SnO2) and the metal electrode (Ag), leading to the band bending at the interface shown in Fig. 4d. This bending will also contribute to a bending of the vacuum level. The 0.1 eV difference in the work function of SnO2 and Ag helps the device to start the conduction mechanism at a lower voltage (i.e., 0.66 V). The I-V characteristics Fig. 3c indicate that the conduction bridge was completely formed around 1.14 V. Beyond 1.14 V, the current increases sharply.
Fig. 4. a, Schematic diagram of conduction mechanism of SnO2 nanofibers with high-resolution FE-SEM images of the SnO2 nanofiber in the top view (in set). b, Measured UPS spectra of synthesized 1D SnO2 with UV-Vis absorption spectra with Tauc plot in the inset. c-d, Band structure of the fabricated memristor before contact and after contact. Results of UPS survey spectra of the active material were incorporated to draw the E-B diagram of the fabricated memristor. FE-SEM, field emission scanning electron microscopy; UPS, ultraviolet photoelectron spectroscopy. |
DATA-DRIVEN MODELING
The data preprocessing was carried out based on two features. We measured current I and sequential order number of measurement cycles (out of a total of 100 cycles, corresponding to 1.6 ⨯ 105 data points) as functions of the applied bias V, the independent variable. The sequential order number of the measurement cycles was correlated to the endurance of the fabricated devices. The external bias voltage was swept from 0 V → + 2 V → − 2 V → 0 V. The created datasets were split into two parts: (a) upsweep data and (b) downsweep data. Two different ANN models based on voltage sweeping were developed for each data set, i.e., upsweep and downsweep. However, it should be noted that the different normalization processes applied for the type I model for preprocessing the data in both sweeps are different. In the type I model, the ANN was trained using normalized voltage and normalized cycle number as input features and normalized current as output, keeping the measured current completely hidden. Thus, the output variable in the type I model will be the normalized current on a linear scale.
In the type II model, raw voltage and cycle numbers were adopted as the input features. Meanwhile, the logarithmic transformation was applied to the current, which was used as the output feature for the training of the ANN algorithm. This was conducted to increase the efficacy of the derived model to capture important features of the fabricated memristor in the lower range of the measured current. Fig. 5 shows the algorithmic flowchart for the ANN-based modeling.
Fig. 5. The flow chart indicating the various steps involved in the development of two data-driven models of the memristor. |
The ANN architecture used for each of the models is shown in Fig. 6. For type I ANN and type II ANN, the output layer has only one node corresponding to the desired output by the proposed model. Additionally, all hidden layers have been scaled down by a factor of 20 so as to enhance interpretability. The rectified linear unit (ReLU) activation function in the input and hidden layers and a linear activation function in the output layer have been adopted, which is common in ANN regressions. The loss function for the model is a mean squared error (MSE), and the optimizer used is Adam. The optimization algorithm computes the gradient of the loss function' and adapts learning rate of each weight during training. To prevent overfitting, an early stopping callback function was implemented with a minimum improvement parameter of 0.0005 for type I, and 0.005 for type II and patience (indicates the wait time for the minimum improvement prior to the stop of training) of 50 epochs.
Fig. 6. ANN architecture with the input layer, hidden layers have been downsized by a factor of 20 for the above image. a, Type I Upsweep. b, Type I downsweep. c, Type II upsweep. d, Type II downsweep. ANN, artificial neural network. |
Additionally, we activated the “restore best weights” option in the early stopping callback. This option enables us to store the best model found during training. The model was trained with a batch size of 10 and 150 epochs.
In the ANN models, a 72 : 18 : 10 train-test-validation split was adopted, as shown in Table 1.
Table 1. Data splitting among train-test-validation. |
| Dataset | Train | Validation | Test |
|---|---|---|---|
| Size (in %) | 72 | 18 | 10 |
It is worthy to be noted that the standardization in the case of the type I model shown in Fig. 7 was achieved by scaling the dataset to unit variance and with zero means. Similarly, in the type II model, the ANN algorithm was trained using the original voltage cycle numbers, and the output that the model would be predicting is the current represented on a 10-base logarithmic. In the type II model, as shown in Fig. 8, the logarithmic transformation was applied to the device current values before the ANN algorithm training to increase the efficacy of the derived model, so as to capture important features of the fabricated memristor in the lower range of current. This was especially conducted to achieve the key features like the set voltage, abrupt jump in the measure device current, etc., which is common in fabricated memristors while switching from HRS to LRS. The logarithmic transformation was categorically chosen to exploit its steeper slope for lower values of current (I), leading to enhanced disparities between the low values of I. Another ANN model has also been trained using untransformed data (raw voltage and cycle numbers as model inputs with current as the model output), which led to a model incapable of exhibiting key features of the memristor, as mentioned earlier. However, with the application of logarithmic transformation on the measured data, the created dataset also exhibited a relatively smaller rescaling for the larger values of I. This led to an underprediction of measured values of I via the ANN model. Such type I model fits the entire data with equal weightage, which leads to better performance in metrics like R2 and MSE.
Fig. 7. Comparative I-V response for experimental and Type I ANN modeling. a, Measured current I vs. applied voltage V. b, Model output I vs. V with R2 = 0.9984, MSE = 4.6802 ⨯ 10−11 MAPE = 25.4675. c, Model output on the log10 scale. d-h, Single-cycle comparisons (Blue is for measured data, and Red is the predicted data) for arbitrarily chosen cycle numbers 5, 15, 45, 65 and 95. MAPE, mean absolute percentage error; MSE, mean squared error. |
Fig. 8. Comparative I-V response for experimental and Type II ANN modeling. a, Measured I vs. applied voltage V on the log10 scale. b, Model output I vs. V on the log10 scale; R2 = 0.9818, MSE = 0.0386, MAPE = 0.0175. c-h, Single-cycle comparisons-(blue is for the measured data, and red is the predicted data) for arbitrarily chosen cycle numbers 5, 15, 25, 45, 65 and 95. ANN, artificial neural network; MAPE, mean absolute percentage error; MSE, mean squared error. |
However, allotting higher priority to lower values of I, as shown in the type II model, is very important for observing key characteristics of the memristor. This behavior of the type II model contributes to its better performance in the metric MAPE. A flow chart indicating the various steps of the development of the two data-driven models of the memristor is shown in Fig. 5. Measurement on the various fitting parameters of both models was also conducted. For the type I model, the measured values of R2 score, mean squared error (MSE), and MAPE were 0.9985, 4.2711 × 10−11, and 25.4675, respectively. Similarly, the R2 score, MSE, and MAPE values for the type II model were found to be 0.9818, 0.0386 and 0.0175, respectively.
In the data-driven modeling of memristors, the coefficient of determination or R2 serves as an important metric to evaluate the performance of the model. R2 is adopted for measuring the proportion of the variance in the dependent variable (memristor behavior in this case) explained by the independent variables (features used in the model). A high R2 value indicates that the model can accurately capture the relationship between the variables, which is crucial for accurately predicting the behavior of memristors. Therefore, R2 can help researchers determine how effective their data-driven modeling techniques are in capturing the behavior of memristors and improving their design.
On the other hand, MAPE is an essential metric in the data-driven modeling of memristors since it measures the percentage of the average absolute error between the measured and predicted values of memristor behavior. MAPE helps to quantify the accuracy of the predictions made by the model. It is particularly useful when dealing with datasets where a small error percentage can significantly impact the overall performance of the model. Therefore, MAPE can provide insights into the accuracy and precision of the data-driven model and help researchers identify improvement areas. To find out if our proposed models work well, the models were benchmarked with three other ML models on the 2 metrics—R2 and MAPE.
The five models taken for comparative analysis are as follows:
1)Polynomial regression (with hybrid modeling, i.e., with separate models for high voltage and low voltage where the memristor behaves differently)
2)Support vector regression
3)K nearest neighbors
4)Type I ANN model
5)Type II ANN model
Type II ANN model exhibited the best MAPE score, indicating that it is the best model shown in Table 2. Although the KNN model had the best R2 score and a decent MAPE score, it has the drawback that it can't be used to predict output for voltage and cycle values not covered by the range of our training data. As such, the type I ANN model, with the second-best R2 score, is the best one, as seen in Table 2.
Table 2. Performance evaluation of the different ML-based models for the fabricated nanofiber-based memristor. |
| Empty Cell | Polynomial regression (with hybrid modeling) | SVR | KNN (K = 5) | Type I ANN | Type II ANN |
|---|---|---|---|---|---|
| R2 | 0.9815 | 0.9860 | 0.9997 | 0.9985 | 0.9818 |
| MAPE | 33.0819 | 158.9226 | 0.1257 | 25.4675 | 0.0175 |
ANN, artificial neural network; KNN, K nearest neighbors; MAPE, mean absolute percentage error; ML, machine learning; SVR, support vector regression. |
The best way to validate the model is to test it with the measured data of the new SnO2 nanofiber-based memristors fabricated with the adoption of the same process recipe. We have thoroughly checked all 100 cycle data with the modeled data to justify the proposed ANN model's validation. The reliability of type I and type II models was also checked with the same cycle number experimental data of the newly fabricated device. Fig. 9 a-d shows that the model works well with the same fabricated devices. It can be observed that the nonlinearity of the device, the threshold voltage, and the trend of high- and low-resistive paths also followed perfectly with respect to cycle number. As it has been noticed that the threshold voltage decreases with the increasing number of cycles, this exact nature was observed in the new devices as well.
Fig. 9. a-b, The model output (pink) and the experimental output (black) of random cycle data of a newly fabricated device type I ANN for cycle 10 and cycle 40. c-d, The model output (pink) and the experimental output (black) of random cycle data of a newly fabricated device type II ANN for cycle 20 and cycle 81. ANN, artificial neural network. |
This work was also compared with the recently reported fabricated nanofiber-based memristor in terms of active material, a top and bottom electrode, switching window, fabrication technique, and modeling in Table 3. To the best of the authors’ knowledge, very few reports are found to provide the best performance and cover data-driven modeling.
Table 3. Performance evaluation of the fabricated nanofiber-based memristor. |
| Year | Active material | TE | BE | Switching window | Technique | Modeling | Ref. |
|---|---|---|---|---|---|---|---|
| 2013 | Nb2O5 | DL C | Pt | 2 × 104 | Electrospinning | Thermodynamic model | 38 |
| 2019 | CuO | Al | Cu | 50 | Spin-coating | NA | 39 |
| 2020 | fMWCNT s-TiO2 | Ag | FT O | > 10 | Electrospinning | Space charge limited current model | 40 |
| 2022 | LiF | Al | ITO | 104 | Electrophoretic-induced self-assembly deposition | Space charge limited current model | 21 |
| 2023 | Sericin | Ag | W | > 100 | Electrospinning | NA | 41 |
| 2023 | TiO2 | SnS/TiO2 | Ti | 102 | Hydrothermal | Physics based | 42 |
| 2023 | SnO2 nanofiber | Ag | Al | 105 | Electrospinning | Data-driven modeling | This work |
APPLICATION OF THE DATA-DRIVEN MODEL
When the memristors are connected in the topologies shown in Fig. 10, the outputs X and Y yield the AND and OR functionalities with a caveat. When both A and B are logic high (logic state 1 or logic level VDD), nodes X and Y will eventually reach 1 through the charges pumped into the load capacitor CL from the VDD power supplies at A and B. Similarly, when both A and B are at a logic low value (logic state 0 or logic level Gnd), nodes X and Y will eventually reach 0, as CL will discharge through the memristors, irrespective of whether the memristors are in their HRS or LRS. Unlike the typical MOS technology, when one of the inputs is high and the other one low, the robustness of the voltage levels at nodes X and Y will depend on the RLOW/RHIGH ratios given by and .
Fig. 10. a, AND & OR logic implementations using memristors and the b, associated truth tables. |
Fig. 11a shows the ANN type II model of the fabricated SnO2 memristor's I-V characteristics (Fig. 9) plotted on the linear scale between 0 and 2 V variation corresponding to Gnd and VDD transition. The inverse gradient of the I-V relation in Fig. 11a gives the resistance of the memristor as a function of the applied bias, as predicted by the ANN model. As a benchmarking example, the best-case scenario for the circuit design (Fig. 10) was chosen by selecting the lowest RLOW/RHIGH ratio, which is commensurate with the previous circuit analysis. The ANN model predicted the maximum resistance during the upsweep is and the minimum resistance during the downsweep is , which makes a good approximation for .
Fig. 11. a, The I-V characteristics predicted by the ANN type II model of the fabricated SnO2 memristor on a linear scale between 0 and 2 V sweep. b, The realization of AND and OR logic functionalities using the resistances extracted from the ANN predicted characteristics in a. ANN, artificial neural network. |
The inputs A and B in Fig. 11b are taken as ideal square pulse trains with 50% duty cycle, 2 V (0 to peak) amplitude, and 0.8 μs and 0.4 μs time periods (frequencies of 1.25 and 2.5 MHz, respectively). Under no-load condition (i.e., CL=0), the output signals X and Y are shown to realize a perfect AND and OR logic implemented with the adoption of the fabricated memristors. It is worthy to be noted that such an implementation is far simpler and cheaper than the conventional AND and OR digital ICs available in the market.
CONCLUSION
In conclusion, this article successfully demonstrated the fabrication, characterization, and data-driven modeling of the SnO2 nanofiber-based memristor. The proposed device contributed to a very high ROFF : RON of ∼104 (ION : IOFF of ∼105) with an excellent activation slope of 10 mV/dec, low set voltage of ∼1.14 V, and good repeatability. The switching mechanism is explained by analyzing the derived energy band diagram from the experimental UPS spectra. This article further demonstrates that data-driven modeling uses experimental data of the memristor. With the help of a benchmarking comparison with multiple standard ML algorithms, we have conclusively shown that the type II ANN technique provides the best results based on R2 scores (98%) and MAPE of 0.0175. The proposed model is further validated with the measured characteristics of new memristor devices fabricated with the adoption of the same fabrication recipes, and the predictions of the proposed data-driven model is in good agreement with the measured characteristics. Furthermore, the realization of the AND and OR logic using just two memristors provide the same functionality of equivalent CMOS AND and OR logic gate ICs available in the market at a much simpler and cheaper process.
METHODS
Materials and instruments
Polyacrylonitrile (PAN, molecular weight ∼150,000), dimethyl formamide (DMF), and tin chloride (SnCl4·5H2O) were procured from Sigma Aldrich. Deionized water from a Merck Millipore system (resistivity ∼18.2 MΩ cm) was utilized for the whole experiment. Without further purification, the chemicals procured were employed to synthesize pristine SnO2 nanofibers with the adoption of the electrospinning technique. The FE-SEM images were obtained using an FEI, LoVac Apreo electron microscope. LoVac X'pert PRO XRD was utilized to know the structural characterization of SnO2 nanofibers. A Thermo thermo Scientific scientific K-α XPS instrument was employed to identify the chemical composition and oxidation states of SnO2 nanofibers. All the electrical characterizations related to memristive properties were performed with the adoption of a Keithley 2450 source meter and a probe station.
Synthesis of SnO2 nanofibers
SnO2 nanofibers were synthesized by adopting the electrospinning technique. In brief, PAN (10 wt.%) and SnCl4·5H2O (4 wt.%) were added to DMF solvent, and then, the mixture was stirred for 4 h at room temperature at the stirring speed of 750 rpm to attain the homogeneous viscous solution that was ready for electrospinning. The electrospinning setup utilized to synthesize nanofibers comprised a high-voltage supply, syringe, needle, and grounded collector. SnO2 nanofibers were electrospun on a fixed target with a single side-masked Si wafer coated with Al at room temperature. The fixed target plate with Al-coated Si wafer was placed at a distance of 10 cm away from the tip of a 24-gauge needle. Furthermore, continuous deposition of SnO2 nanofibers was conducted on the target for 30 min at 20 kV applied voltage between the needle and the grounded collector with a constant flow rate of 10 μL/min to achieve a considerable amount of nanofibers on the masked Si wafer. After removal of the mask from the device, the attained SnO2 nanofibers were annealed at 600 °C for 1 h with the adoption of a box furnace to eliminate the polymer and unwanted residues in the resultant nanofibers.
Device fabrication
The memristor was fabricated on a <100> p-type Silicon substrate. At first, the Si wafer was thoroughly cleaned using isopropyl alcohol and acetone and then dried at 100 °C for 20 min in a high-temperature oven. Subsequently, utilizing the thermal evaporation technique, Al was deposited on Si employing a mask that protects the bottom electrodes from electrospinning. Next, SnO2 nanofibers were deposited on the Al-coated Si wafer. After annealing at 600 °C for 1 h, Ag contacts were made with the adoption of silver paste. The bottom contact was taken from the Al layer, and the top contact was taken from Ag. The fabricated device was dried in a hot air oven at 100 °C for 30 min. The complete schematic for the synthesis and device fabrication of the SnO2 nanofiber-based memristor is illustrated in Fig. 1.
MISCELLANEA
Declaration of competing interest The authors declare no competing interests.
