Multilevel HfO₂-based RRAM devices for low-power neuromorphic networks

In recent years, artificial intelligence (AI) has achieved excellent performance in tasks such as machine translation, face recognition, and speech recognition which are now essential applications for big data analysis in cloud computing. To carry out these machine learning tasks, deep neural networks (DNNs) are massively trained in software by using very large datasets.¹ In particular, the emergence of specifically-designed computing machines, such as the graphics processing unit (GPU)² and the tensor processing unit (TPU),³ capable of significantly speeding up the network training, enabled DNNs to outperform the human ability in classifying images⁴ or playing Go.⁵ However, the training of DNNs generally requires an extensive amount of time and energy, mostly contributed by the intensive data transfer from the memory to the processing unit, where the feedforward propagation, the backpropagation, and the weight update are executed. To improve the energy efficiency of these networks, the development of novel processing schemes, such as analog memory and physical computing in non-von Neumann architectures, is currently under scrutiny.⁶ 

Among the novel concepts to accelerate neural networks, the emerging memory technologies such as phase-change memory (PCM) and resistive-switching random access memory (RRAM) have attracted strong interest. The main advantage of emerging memory is the ability to compute by physical laws such as Ohm’s law and Kirchhoff’s laws to enable matrix-vector multiplication (MVM) with a significant reduction in energy and area.⁷ Also, RRAM and PCM elements offer the opportunity to store multiple states^8–10 which is essential to achieve synaptic weights with analog behavior enabling scalable synaptic arrays with high accuracy in the learning phase.¹¹ Achieving analog precision and low variation, however, imposes in-depth investigations from the viewpoint of device materials able to offer large resistance window, high cycling endurance, high device yield, and low forming voltages.¹¹ 

There have been several hardware and software demonstrations of neural networks implemented with memory-based synapses in recent years. A small-scale experimental implementation of a single layer perceptron network capable of image classification via supervised learning¹² was achieved using a 12 × 12 crossbar array with 30 Al₂O₃/TiO_2−x RRAM devices as synaptic connections and a small dataset of 3 × 3 binary images.¹³ Moving from small-scale to medium-scale implementations, a hardware accelerator based on 165 000 PCM synapses was proposed in Ref. 14 by achieving an inference accuracy of about 83% in image classification on the well-known Modified National Institute of Standards and Technology (MNIST) handwritten digit dataset¹² because of the asymmetry and nonlinearity of PCM conductance response. A higher inference accuracy of about 92% was obtained using Ta/HfO₂/Pt RRAM devices into an 8 kbit synaptic array although the power consumption was not optimized due to the high current operation in RRAM devices.¹⁵ In addition to classification of images from MNIST dataset, recognition of grayscale faces was also investigated at a hardware level by a 1024 TaO_x/HfAl_yO_x RRAM cell array capable of achieving accuracy performance very close to standard computing systems.¹⁶ Binarized neural networks have also been implemented with RRAM synapses.^17,18 Overall, a hardware demonstration capable of combining high recognition accuracy, analog weight storage, and low-power operation is still missing.

In this work, we report the hardware implementation of a 2-layer perceptron neural network in a 4 kbit array of HfO₂-based RRAM devices with one-transistor/one-resistor (1T1R) structure capable of multilevel operation. We first investigated three different HfO₂-based RRAM materials, namely, amorphous HfO₂, polycrystalline HfO₂, and Al-doped amorphous HfO₂ in terms of I-V characteristics, forming voltage, resistance window, and variability. Based on this preliminary comparison, Al-doped amorphous HfO₂ RRAM technology was selected for the implementation of synaptic weights mainly thanks to its lower variability. A novel multilevel programming approach enabled to program a weight array with 5-level accuracy achieving an inference accuracy above 80% for the MNIST test dataset. Finally, networks with improved size, decreasing variability and increasing number of levels, were calculated to support inference machine development with the best tradeoff between good accuracy and low-power consumption for edge computing applications.

HfO₂ is a typical material for CMOS, RRAM, and FeRAM devices thanks to the well consolidated know-how on deposition and control of the chemical and structural property for high-k gate dielectric applications. The properties of the HfO₂ layer in RRAM devices, however, are significantly different from CMOS gate dielectric, in terms of leakage current and breakdown voltage. For instance, the HfO₂ layer should display a relatively large leakage current in the pristine state, thus enabling a relatively low breakdown voltage, which enables a low-voltage forming taking place in the RRAM device.¹⁹ In addition, the requirements for analog synapses are different from those needed in binary memory devices. As a result, choosing the most proper RRAM technology for dedicated inference machines requires a cross-layer characterization that spans from the structural properties of the materials to their fundamental electrical behavior.

To enable a detailed characterization of HfO₂-based RRAM devices, we compared various process flows in terms of structural, forming and switching characteristics. Providing a tight control of the device-to-device uniformity and low operating current/voltages is in fact a key challenge for developing inference machines with high accuracy and low operating energy. In particular, the deposition of the dielectric material in the RRAM stack is found to heavily affect the conduction properties of the RRAM cell, with several implications on characteristic parameters such as the resistance ratio between high resistance state (HRS) and low resistance state (LRS), the forming voltage, and the set/reset voltages.²⁰ In this work, we compare three deposition recipes of HfO₂ material, leading to different microstructure and composition, namely, amorphous hafnium oxide (a-HfO), a poly-crystalline hafnium oxide (p-HfO), and an Al-doped amorphous hafnium oxide (HfAlO).

Figure 1 shows the TEM cross section of the three HfO₂ layers deposited on silicon, namely, (a) p-HfO, (b) a-HfO, and (c) HfAlO. All the HfO₂-based dielectric layers were deposited by the atomic layer deposition (ALD) process by using a batch ALD furnace and a halide precursor.²¹ By varying the temperature of the deposition process, we could control the microstructure of the device, namely, the HfO₂ film deposited at 300 °C appeared p-HfO with a monoclinic phase, while the HfO₂ film was deposited in the a-HfO at 150 °C. The HfAlO layer was grown at 300 °C with an Al content of about 10%. Note the presence of a crystalline texture in p-HfO, while a-HfO and HfAlO layers show an amorphous structure. The interfacial SiO₂ layer of less than 1 nm between the Si substrate and the HfO₂ layer can be seen for all deposition processes. The grain boundaries in p-HfO have been shown to serve as preferential leakage paths as a result of the higher defect concentration compared to the bulk of the crystalline grain.^22,23 On the other hand, electrical conduction for a-HfO and HfAlO mainly takes place via uniformly distributed random percolation paths with a relatively high concentration of defects.

Figure 2 shows a STEM-EDX image of the one-transistor/one-resistor (1T1R) structure of area 890 × 965 nm² that was adopted as the synaptic element in this work. The transistor was integrated in the front end [Fig. 2(a)] with 0.24 µm BiCMOS process technology based on 3 metal layers with gate width W = 1.14 µm and gate length L = 0.24 µm. The transistor allowed us to tune the compliance current I_C during the set transition, thus enabling a tight control of the LRS conductance for analog weight storage.²⁴ The HfO₂-based RRAM device consisting of a metal-insulator-metal (MIM) stack of area 600 × 600 nm² was deposited in the back end on top of metal 2 M2 [Fig. 2(b)]. The RRAM was connected to the drain terminal of the select transistor with minimum interconnect length to minimize the parasitic resistance and capacitance. The top and bottom electrodes consist of TiN layers with a thickness of 150 nm deposited by magnetron PVD sputtering (a sheet resistance of 10–50 Ω/sq) and a 7 nm Ti scavenging layer between the top electrode and the HfO₂ layer, the latter having a thickness of 8 nm except where noted.

Importantly, we observed in HfO₂ RRAM devices that the scavenging layer is oxidized into a Ti_xN_yO_y layer after the sintering process at 400 °C in forming gas, as already shown in Ref. 21. Note that this process was also observed in TiN/Ti/HfO_x/TiN RRAM devices used in Refs. 25 and 26.

To assess the integration capabilities of the different materials, we have investigated the yield from the point of view of both the process and the forming operation. The yield is reported in Table I for the various RRAM materials with the 1T1R structure. The process yield was evaluated as the percentage of cells with a read current I_read < 1 µA before forming, thus displaying a sufficiently high resistance in the pristine state. The forming yield was instead evaluated as the percentage of devices with I_read > 18 µA after the forming operation. This minimum read current was observed to correspond to a functional device capable of switching between the HRS and LRS with a sufficient resistance window. RRAM devices with p-HfO microstructure showed relatively low yield after the fabrication process, which might be due to the presence of anomalous grain boundary with large metallic segregation, thus leading to electrical shorts before forming. On the other hand, a-HfO and HfAlO processes showed excellent yield both after fabrication and forming operation; thus, they appear as promising candidates for integrated RRAM synapses to develop inference machines.

Figure 3 shows the measured quasistatic I-V curves of (a) p-HfO, (b) a-HfO, and (c) HfAlO RRAM devices. The characteristics include the forming operation, the first reset transition after forming, and the first set transition after the first reset. The experiments were carried out on individual 1T1R devices with the array by using a Keithley 4200-SCS semiconductor parameter analyzer operated within a Cascade PA200 semiautomatic probe station. A voltage from 0 to 5 V was applied to the top electrode during the forming operation with a fixed gate voltage of 1.5 V, corresponding to an I_C of about 30 µA at the maximum top electrode voltage. During the reset process, the voltage at the source terminal was increased from 0 to 2.5 V with a gate voltage of 2.8 V, which was large enough to minimize the transistor resistance with respect to the LRS resistance. Finally, during the set procedure, the voltage at the top electrode was increased from 0 to 2 V with a gate voltage of 1.6 V, corresponding to an I_C around 35 µA at the maximum applied voltage. A sweep rate of 1 V/s was used for all the quasistatic operations in Fig. 3.

The I-V curves show typical RRAM behaviors in Fig. 3, such as the abrupt forming step at about 4 V, the noisy reset transition, and the low-voltage set process. The latter is particularly beneficial for proper control of the LRS resistance in analog synaptic application. In fact, a large set voltage might lead to an unwanted overshoot which results in a poor control of the LRS resistance.²⁷ Low set voltage is therefore an essential property to enable tight control of the LRS conductance and synaptic update in training algorithms such as the backpropagation technique.¹⁴ 

To statistically evaluate the switching behavior of the three RRAM technologies, a pulse mode scheme was applied on 100 1T1R devices integrated in 4 kbit test vehicles by using a pulse width of 10 µs. Figure 4 shows (a) the cumulative distribution of the measured forming voltage, (b) first reset voltage, and (c) first set voltage for the various HfO₂ devices. The forming voltage is defined as the voltage for which the read current measured at V_read = 0.2 V exceeds 18 µA after the applied pulse, where the voltage was incrementally updated by 0.1 V at every attempt, starting from 0.2 V. The set voltage was defined in a similar way, except that set transition was applied after forming and reset. The reset voltage was defined as the first voltage causing the read current to drop below the verify level of 5 µA.

The results in Fig. 4 show that p-HfO displays the lowest forming voltage compared to other technologies; however, the set and reset voltages show larger values and relatively large spread with respect to a-HfO and HfAlO. Such a large device-to-device variability in p-HfO devices prevents an accurate analog programming of the RRAM elements for inference application.

Another crucial property of the RRAM devices is the endurance performance, which was assessed for 1000 consecutive reset/set cycles by using a reset pulse amplitude of 1.8 V and a set pulse amplitude of 1.2 V. The resistance ratio of the RRAM elements was evaluated at V_read = 0.2 V. Figure 5 shows the average read current at V_read as a function of the number of cycles for (a) p-HfO, (b) a-HfO, and (c) HfAlO RRAM. The cell-to-cell variability is shown by using the dispersion coefficient, defined as σ/μ. Both LRS and HRS current decrease with the number of cycles for p-HfO devices, which also leads to a drop of the resistance ratio, mainly caused by the increase in the LRS variability with increasing number of cycles. The degradation of the LRS conductance and the higher cell-to-cell variability in the array might be attributed to the grain boundaries conduction mechanism in the p-HfO structure.²⁸ For instance, thermally activated diffusion of the defects from the grain boundary might lead to the gradual loss of conductance in Fig. 5(a). On the other hand, a-HfO shows a smaller variability, a larger resistance ratio, and a smaller degradation of the LRS conductance. Finally, the doping by Al atoms in the HfO₂ layer supports the endurance properties with minimum LRS drop and small variability. These results suggest that Al doping stabilizes the HfO₂ matrix by hindering oxygen-vacancies relaxation without severe changes of the switching parameters.²⁸ The LRS variability in HfAlO is almost suppressed compared with p-HfO and a-HfO, providing an approximately constant resistance ratio of about 10. Due to the large resistance ratio, robust cycling, and limited variability, HfAlO seems a promising material for RRAM-based neuromorphic synapses.

Figure 6 shows a systematic study of the variability for (a) p-HfO, (b) a-HfO, and (c) HfAlO RRAM. In the figure, the standard deviation σ for cycle-to-cycle (C2C) and device-to-device (D2D) distributions is shown for both LRS and HRS as a function of the median device resistance μ. Variability data were collected for a subset of 1000 1T1R devices integrated in the 4 kbit test vehicle and for 1000 cycles. The steep increase in variability from LRS to HRS can be understood by the contributions of Poisson variation of the defect number^29,30 and the shape variation of the filamentary path within HfAlO.³¹ Although the spread σ shows a similar behavior for all three RRAM technologies, HfAlO exhibits the largest resistance ratio between the LRS and HRS regions, in line with the results of Fig. 5. Also, note that HfAlO displays a better endurance compared with p-HfO and a-HfO counterparts since, based on the variability characteristics shown in Fig. 6, it is easier to control the conductance for HfAlO devices, which is in addition to the fact that its resistance window is larger. As reported in Ref. 28, once a desired conductance level is achieved, HfAlO devices show less instability during cycling. These results confirm the lower variability and large window induced by Al doping and amorphous structure. In the following, this RRAM technology will be considered for the implementation of artificial synapses in inference machines.

To explore the ability to store analog weights in RRAM synapses, we selected HfAlO RRAM as the best technology from the previous study, thanks to the improved resistance window, yield, endurance, and variability. The multilevel storage in HfAlO RRAM devices was studied for a 4 kbit array with 1T1R structures, which is schematically shown in Fig. 7. In addition to the memory and select transistor elements, the array also comprises (i) bit line (BL) and word line (WL) address decoders to access the single 1T1R cells, (ii) the BL voltage selection block and source line (SL) voltage selection block that provide the voltages to activate forming/set/reset operations into RRAM devices, and (iii) a direct memory access (DMA) interface connected with the BL decoder that provides the readout current to selected devices.³² 

The key point making HfAlO RRAM suitable for neuromorphic applications is its ability to store multiple resistive states thanks to its limited resistance variability. In particular, HfAlO RRAM enables to program up to 5 resistance states to implement synaptic weights of the neural network. The first level, which is called L₁, corresponds to the HRS and was achieved by a programming scheme under incremental step pulse with verify algorithm (ISPVA) approach consisting of the application of sequential reset pulses with increasing amplitude from 0 to 3 V at source terminal of cell selectors with grounded drain, gate terminal biased at 2.7 V, and a threshold current I_th = 5 µA [Fig. 8(a)]. On the other hand, the other 4 programmable levels correspond to different LRS (L₂-L₅) and were achieved via a multilevel application of ISPVA strategy (M-ISPVA) schematically described in Fig. 8(b). Here, a sequence of voltage pulses with increasing amplitude from 0 to 3 V is applied to the drain of the transistor with grounded source and gate biased by a variable voltage V_G in the range 1 V–1.6 V to obtain increasing I_C and thus decreasing LRS.²⁴ In addition, whereas a threshold current of 5 µA was set for L₁, current targets of 15 µA, 30 µA, 45 µA, and 60 µA were used in the M-ISPVA programming scheme to achieve L₂, L₃, L₄, and L₅ levels, respectively. Note that each sequential voltage pulse applied to source/drain to achieve HRS/LRS is followed by a read pulse to check that the current target set for each level is reached. To test the efficiency of the M-ISPVA approach, resistance levels in HfAlO RRAM were compared with LRS experimental data collected by HfO₂ RRAM cells [Fig. 8(c)] evidencing a similar behavior with slope close to 1 of the relative variability of resistance for increasing average resistance.³¹ 

Note that the ISPVA and M-ISPVA techniques do not specifically require linearity and symmetry of weight update, which are instead key requirements for backpropagation techniques of on-line training.^11,14 For off-line training, the essential feature of memory devices is the ability to store multilevel weights which can be programmed at time zero as a code to perform pattern recognition during the system lifetime. This is the main criterion for selecting the most suitable memory device as the synaptic element in the neural network.

As shown in Fig. 9(a), the 2-layer neural network designed into the 4 kbit RRAM array consists of 197 input neurons, 20 hidden neurons, and 10 output neurons. The network was first trained in simulation on the well-known MNIST dataset of handwritten digits by a supervised learning approach based on the backpropagation rule.¹² According to this scheme, the signal emitted by input neurons in response to image submission is forward propagated through all network layers leading to generation of an error signal which is calculated as a difference of effective output signal and expected network response. Sequentially, the error signal calculated at the output stage is backpropagated toward the input layer and exploited to update synaptic weights to make the error signal lower after next image presentations. After repeating this training scheme (forward and backward cycles) with a learning rate parameter of 0.01 for 20 epochs, where each epoch consists of the presentation of the entire training dataset based on 60 000 images, the final weight matrix was used to test the ability of the simulated network to correctly classify 10 000 unseen MNIST images resulting in an inference accuracy of 92%. Note that the array size forced us to use a downscaled version (14 × 14 pixels) of original 28 × 28 MNIST images for both training and inference phases.

To achieve in hardware an inference accuracy close to the one obtained in simulation by using only 5 resistance levels, we applied a random rounding strategy to lower precision of the calculated weight matrix from 64-bit floating point to 5 evenly spaced discrete levels centered around 0. This, however, led to a decrease in inference accuracy at the software level from 92% to 86.5%. Also, since the levels can have both positive and negative signs and device conductance can only be positive, we implemented any synaptic weight as difference of two conductances W_ij = G_ij − G_r, where G_r is a fixed reference conductance corresponding to the intermediate level [Fig. 9(b)]. These steps enabled to map the calculated weight matrix based on 5 levels into the 4 kbit array achieving an experimental weight matrix based on 5 current levels.

Although software simulations were carried out using 5 evenly spaced numerical levels, programming operation at the device level is affected by variability. It is highlighted by the probability density function (PDF) distributions of the 5 current levels measured at V_read = 0.5 V in Fig. 10(a) where their unavoidable broadening due to variability can lead to some overlap between consecutive levels. To test temperature retention of current levels after programming operation, array cells were subjected to an annealing experiment at temperature T = 125 °C for 1 h. As a result, a level shift toward lower currents combined with an additional broadening of PDFs were observed, which resulted in highly overlapping current levels, as shown in Fig. 10(b).

In view of the cell-to-cell variability of resistance in Fig. 10, achieving more than 5 levels might be challenging for our HfAlO RRAM. Therefore, we considered only 5-level synapses in our neural network with a consequent limitation in accuracy of recognition. Achieving more than 5 levels would require to finely tune the ISPVA algorithm parameters, such as step voltage and compliance current, at the expense of time and energy of the multilevel programming. Alternatively, it might be possible to control the cell-to-cell variability by carefully engineering the RRAM materials and stack.

Inference ability of 2-layer neural network implemented at the array level was evaluated testing the experimental weight matrix in simulation via presentation of MNIST test dataset containing 10 000 binary digit images unused during the learning phase. In our application, on pixels within presented image indicate the application of a test voltage V_read, which can vary from 0.1 V to 0.5 V, to corresponding synaptic device, whereas off pixels correspond to zero voltage application. Figure 11(a) shows inference performance as a function of V_read for variable slope of the neuron activation function. Here, maximum inference accuracy η_test obtained before performing the temperature annealing is 82.82%, whereas η_test = 72% was obtained after the experiment, which supports detrimental effect of the bake-induced level broadening on inference capability of the neural network. Results also evidence that best accuracy is achieved by using the maximum read voltage V_read = 0.5 V, which reduces the impact of nonlinearity on programmed current levels, and a sigmoid slope of 2 × 10⁴ V/A in both cases. However, note that increasing the read voltage amplitude during the inference phase also leads to an increase in power consumption since the power dissipated in each synaptic element is given by $P=VreadIread≈Vread2/R$⁠. This indicates that there is an inherent tradeoff in our synaptic array between inference accuracy and energy efficiency.

Figures 11(b) and 11(c) show the confusion matrices capturing ability of neural network to associate each digit from 0 to 9 with corresponding class before and after the annealing experiment, respectively. As expected, low performance suggested by the confusion matrix in Fig. 11(c) further confirms the strongly negative impact of annealing on classification of almost all digits compared with recognition accuracy exhibited by network in Fig. 11(b).

While inference accuracy achieved on MNIST test dataset by our array is still far from software performance, our implementation is competitive with other recently proposed hardware neural networks, especially in terms of energy consumption during the inference phase. To get an estimation of energy consumed by our 4 kbit neural network during inference cycles, we considered (i) the number of operations involved into matrix-vector multiplications at each network layer given by the array size of 4 kbit, (ii) the width of applied read pulses or cycle duration t_p = 12 µs, and (iii) the calculated power dissipated on average per inference cycle at V_read = 0.5 V, which is P ≈ 20 mW, eventually achieving a power efficiency of about 17 GigaOps/s/W. However, note that t_p could be lowered to 10 ns by improvements of array and measurement setup, thus enabling to reach a power efficiency of about 20 TeraOps/s/W, which is four orders of magnitude better than state-of-art CPUs and GPUs.³³ 

Also, while a detailed comparison with other small/medium-scale hardware networks is quite difficult, a good estimate can however be obtained taking into account fundamental parameters such as the number of synaptic devices, the maximum synaptic conductance G_max, and the behavior of conductance response. As first benchmark, a classification accuracy of 82.9% was experimentally demonstrated in Ref. 14 using a 1T1R PCM array with 165 000 2-PCM synapses featured by G_max = 20 µS. Compared to our implementation achieving a similar accuracy, this inference performance obtained in Ref. 14 however required a number of hardware synaptic devices (165 000 syn × 2 PCM/syn) being about 80 times the number of devices within our 4 kbit array which results in a lower energy efficiency. More recently, another hardware neural network including about 8000 synaptic devices was proposed in Ref. 15 by achieving a higher classification accuracy of 91.71% in MNIST classification task. Here, key role for achieving such inference accuracy was first played by high linearity of G-response and high maximum conductance of Ta/HfO₂/Pt RRAM synaptic devices G_max = 400 µS, which is at least twice G_max in our implementation (see Table II). These considerations combined with higher synaptic density and application of variable voltage at the input layer to encode MNIST grayscale images lead to high power consumption to reach high performance. Unlike aforementioned studies, our 4 kbit array is able to realize an inference machine capable of combining a good inference accuracy with low-power operation thanks to the novel M-ISPVA approach whose refinement via material engineering promises a more accurate control of device variability and consequently higher power and classification efficiency.

In this frame, to evaluate the potential of an improved M-ISPVA approach, we calculated inference ability for HfAlO RRAM arrays of size 4 kbit, 8 kbit, and 16 kbit. As shown in Fig. 12, decreasing level variability leads to a higher inference accuracy increasing for larger arrays (red dots). Additionally, the use of more levels (9 levels in this case) allows us to improve network inference ability further, enabling to achieve classification accuracies higher than 90% for arrays of size larger than 4 kbit (blue dots). Finally, to support the calculated results obtained using 9 levels for synaptic weights, Fig. 13 shows the corresponding inference confusion matrices which evidence a significant improvement in terms of network ability to classify all the digits compared to experimental results shown in Fig. 11(b).

This work investigates the RRAM-based synaptic devices for neural networks with improved tradeoff between energy efficiency and classification accuracy. We show that RRAM devices with amorphous HfAlO have superior performance with respect to p-HfO and a-HfO in terms of resistance window, variability, and endurance. 5-level synaptic weights are stored in a 4 kbit array with the 1T1R structure by using a novel multilevel programming scheme. An inference accuracy larger than 80% is demonstrated in a 2-layer neural network with limited operation current thanks to relatively high resistance of the analog LRS synapses. Statistical cell-to-cell variability limits the maximum number of levels because of the overlap between adjacent resistance distributions, hence the maximum accuracy of recognition. Our work shows that the combination of material engineering and algorithm-based weight programming can enable inference machines with scalable circuit area, low-power consumption, and good recognition accuracy which are required for AI tasks in the edge.

This article has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 648635), from the Università degli Studi di Ferrara under the Bando per il finanziamento della ricerca scientifica “Fondo per l’Incentivazione alla Ricerca” (FIR) – 2018, and from the German Research Foundation (DFG) in the frame of the research group Grant No. FOR2093.