Based on the theoretical analysis in the previous section, it is expected that the synaptic behavior of the IGZO TFT in two operating regions can be achieved due to the trap states in its defective oxide (e.g. SiO2), thus the Syn-TFT. The fabrication process of the Syn-TFT is given in following “Materials and fabrication process of the Syn-TFT”27. In addition, to verify memory, experimental results of the static and pulsed characteristics of the fabricated Syn-TFT with the IGZO channel layer are described in the following “Selection of the gate read-voltage to determine the operating region” and “Pulsed characteristics of the Syn-TFT”, respectively. For the static characteristics of “Selection of the gate read-voltage to determine the operating region”, the operating region is determined depending on the level of the \({\text{V}}_{\text{GS}}^{ \, {\text{read}}}\) relative to the VT. In “Pulsed characteristics of the Syn-TFT”, the synaptic behavior, such as the weight updates, is analyzed in terms of the drw for two operating regions. Here, the experimental framework is performed with a standard semiconductor analyzer, called Keithley™ 4200A. As another observation of the weight updates characteristics, the weight linearity can be analyzed for two operational regimes. In order to check this, the plots of \(\Delta\overline{{\text{w} }_{\text{G}}}\) versus \(\overline{{\text{w} }_{\text{G}}}\) are shown in the following “Weight linearity of the Syn-TFT”.
In addition, when an array composed of Syn-TFTs is used as an analog accelerator (AA), the performances (e.g. a classification accuracy (CA)) of the AA are expected to be different depending on the operating region. For this, the comparison of the CA as a training result for a classification task is presented in “Analog accelerator based on the Syn-TFT array”. Here, the CA is checked with the AA simulation based on the weight updates monitored with the fabricated Syn-TFT, using a resistive memory simulator, called CrossSim™34,35,36,37.
Materials and fabrication process of the Syn-TFT
The fabrication process of the Syn-TFT is as follows. On the glass wafer, RF-sputtering is performed for Molybdenum (Mo) deposition for the gate electrode, assuming that the work-function of Mo is 5 eV27. This is followed by wet etching to pattern the gate electrode. And then, SiO2 are layered with plasma enhanced chemical vapor deposition (PECVD). The total film thickness of 350 nm is used as the gate insulator where the defects (e.g. trap states) can be given due to a low temperature process. The channel layer of the Syn-TFT is a 50 nm-thick IGZO deposited with RF-sputtering, using an IGZO ceramic target, subsequently patterned by RIE. In the sputter deposition, the oxygen-gas partial pressure against Ar (i.e. O2/(O2 + Ar)) is 15% to realize Syn-TFT structure, in which each was annealed at 250 ℃. Then an etch-stop layer is formed using SiOx to protect the IGZO channel layer. This is followed by dry etching to define source and drain electrode, respectively. For the final metallization, 150 nm-thick Mo is deposited with a RF sputtering, and patterned with a wet etching. Finally, the device is passivated with a 200 nm-thick SiNx/SiOx, which followed by another thermal annealing at 250 ℃ for all the samples.
Selection of the gate read-voltage to determine the operating region
In order to check the characteristics of the weight updates depending on the operating region (i.e. the above-threshold and sub-threshold regions), it is needed to select a proper \({\text{V}}_{\text{GS}}^{ \, {\text{read}}}\). For this, the static characteristics of the fabricated Syn-TFT need to be firstly monitored for the conditions of both \({\text{V}}_{\text{GS}}^{ \, {\text{read}}} > \, {\text{V}}_{\text{T}}\) and \({\text{V}}_{\text{GS}}^{ \, {\text{read}}} \, {<} \, {\text{V}}_{\text{T}}\). Figure 3a,b show the transfer characteristics at the two extreme states (i.e. the FF and FD) for each operational region of the fabricated Syn-TFT, respectively. As can be seen, the \({\text{V}}_{\text{GS}}^{ \, {\text{read}}}\) in the above-threshold and sub-threshold regimes are set as 3.5 V and 1.8 V, respectively. Note that, for the case of \({\text{V}}_{\text{GS}}^{ \, {\text{read}}}\) in the above-threshold regime, since the \({\text{V}}_{\text{GS}}^{ \, {\text{read}}}\) can get into the sub-threshold regime for the shift of the VT with applying multiple positive programming pulses, a proper \({\text{V}}_{\text{GS}}^{ \, {\text{read}}}\) needs to be chosen satisfying with the condition, i.e. \({\text{V}}_{\text{GS}}^{ \, {\text{read}}}\) > VTO + \(\Delta{\text{V}}_{\text{T}}^{ \, {\text{fd}}}\). For the FF state (i.e. VT = VTO) with the \({\text{V}}_{\text{GS}}^{ \, {\text{read}}}\) determined in two operating regions, the \({\text{I}}_{\text{O}}^{\text{ ff}}({\text{above}})\) and \({\text{I}}_{\text{O}}^{\text{ ff}}({\text{sub}})\) at VGS = \({\text{V}}_{\text{GS}}^{ \, {\text{read}}}\) are approximately 100 nA and 3.5 nA, respectively. From this state, after positive programming pulses of 100 cycles are applied to the gate terminal, the IO in two operational regions at VGS = \({\text{V}}_{\text{GS}}^{ \, {\text{read}}}\) arrive at the FD state with \(\Delta{\text{V}}_{\text{T}}\) = \(\Delta{\text{V}}_{\text{T}}^{ \, {\text{fd}}}\) due to multiple electron trapping (see Fig. 1c), resulting in \({\text{I}}_{\text{O}}^{\text{ fd}}({\text{above}})\) = 51 nA and \({\text{I}}_{\text{O}}^{\text{ fd}}({\text{sub}})\) = 0.06 nA, respectively. Here, it is found that the ratio between the \({\text{I}}_{\text{O}}^{ \, {\text{ff}}}({\text{sub}})\) and \({\text{I}}_{\text{O}}^{\text{ fd}}({\text{sub}})\) is larger compared to the ratio between \({\text{I}}_{\text{O}}^{ \, {\text{ff}}}({\text{above}})\) and \({\text{I}}_{\text{O}}^{\text{ fd}}({\text{above}})\), as shown in Fig. 3a,b. This is because the sub-threshold current is dependent on the exponential function, which can be explained with Eqs. (4) to (7). On the other hand, for the case of the above-threshold regime, the current equation is a linear function (see Eq. 2), thus a relatively small ratio between the \({\text{I}}_{\text{O}}^{ \, {\text{ff}}}\) and \({\text{I}}_{\text{O}}^{ \, {\text{fd}}}\). Note that it is found that the \(\Delta{\text{V}}_{\text{T}}^{ \, {\text{fd}}}\) of two operating regions, such as the \(\Delta{\text{V}}_{\text{T}}^{ \, {\text{fd}}}\) of the above-threshold regime (i.e. \(\Delta{\text{V}}_{\text{T}}^{ \, {\text{fd}}}\)(above) = 0.46 V) and \(\Delta{\text{V}}_{\text{T}}^{ \, {\text{fd}}}\) of the sub-threshold regime (i.e. \(\Delta{\text{V}}_{\text{T}}^{ \, {\text{fd}}}\)(sub) = 0.58 V), are to be different each other. This can be explained with a sensitivity (s). And the s can be represented, as follows38,
$$\text{s } \, \equiv \, \frac{\Delta{\text{n}}_{\text{e}}}{{\text{n}}_{\text{e}}^{ \, {\text{read}}}},$$
(21)
where the \(\Delta{\text{n}}_{\text{e}}\) is the negative charge density trapped or de-trapped from the defective gate oxide and \({\text{n}}_{\text{e}}^{ \, {\text{read}}}\) is the negative charge density in the In–Ga–Zn–O film at \({\text{V}}_{\text{GS}} \, = \, {\text{V}}_{\text{GS}}^{ \, {\text{read}}}\). Here, since the \({\text{n}}_{\text{e}}^{ \, {\text{read}}}\) of the sub-threshold regime is smaller compared to the \({\text{n}}_{\text{e}}^{ \, {\text{read}}}\) of the above-threshold regime and the \(\Delta{\text{n}}_{\text{e}}\) of the sub- threshold regime can be bigger than the \(\Delta{\text{n}}_{\text{e}}\) of the above-threshold regime, the s of the sub-threshold regime can be larger compared to the s of the above-threshold regime, thus \(\Delta{\text{V}}_{\text{T}}^{ \, {\text{fd}}}\)(sub) > \(\Delta{\text{V}}_{\text{T}}^{ \, {\text{fd}}}\)(above).
Measured drain current (IO) as a function of the gate voltage (VGS) for the Syn-TFT at the extreme cases [e.g. the full facilitation (FF) and full depression (FD)] for VI = 0.1 V, where the gate read voltage (\({\text{V}}_{\text{GS}}^{\text{ read}}\)) is set as (a) \({\text{V}}_{\text{GS}}^{\text{ read}}\text{ } > \, {\text{V}}_{\text{T0}}\) in the above-threshold regime and (b) \({\text{V}}_{\text{GS}}^{\text{ read}}\text{ } < \, {\text{V}}_{\text{T0}}\) in the sub-threshold regime, respectively. In addition, error bars of 10% are indicated for the IO at the FF and FD, respectively.
Based on the selected \({\text{V}}_{\text{GS}}^{ \, {\text{read}}}\) in respective operating regions, the detailed synaptic processes (i.e. the synaptic depression and facilitation) need to be monitored to verify the characteristics of the weight updates. Therefore, both the detailed pulse-specification and respective pulsed characteristics of the fabricated Syn-TFT are explained in the following section.
Pulsed characteristics of the Syn-TFT
Based on the analysis with respect to the static characteristics of the fabricated Syn-TFT to select the appropriate \({\text{V}}_{\text{GS}}^{ \, {\text{read}}}\) for each operational region, the pulsed characteristics of the device need to be monitored. Figure 4a,b show the pulse-specification for the synaptic depression and facilitation in respective operating regions. For the above-threshold regime, the \({\text{V}}_{\text{GS}}^{ \, {\text{prog}}}\) for the synaptic depression and facilitation is 8.5 V and −6.5 V, respectively, maintaining \({\text{V}}_{\text{GS}}^{ \, {\text{read}}}\) = 3.5 V, as seen in Fig. 4a. For the case of the sub-threshold regime (see Fig. 4b), the \({\text{V}}_{\text{GS}}^{ \, {\text{prog}}}\) is set as 6.8 V and −8.2 V for the synaptic depression and facilitation at \({\text{V}}_{\text{GS}}^{ \, {\text{read}}}\) = 1.8 V, respectively. Note that the pulse height (i.e. the difference between the \({\text{V}}_{\text{GS}}^{ \, {\text{prog}}}\) and \({\text{V}}_{\text{GS}}^{ \, {\text{read}}}\)) depending on the synaptic process is commonly given for both operating regions, such as 5 V for the synaptic depression and −10 V for the synaptic facilitation. In addition, the pulse width in two operating regions is commonly set as 3.08 s in the synaptic depression and 37.76 s in the synaptic facilitation, respectively. Other specifications of the programming pulses are common for two operating regions, as follows, the number of cycles and duty cycle for each synaptic process are 100 cycles and 50%, respectively.
Waveform of the positive/negative programming pulses for the synaptic processes (e.g. a synaptic depression and facilitation) of (a) the above-threshold regime and (b) sub-threshold regime, respectively. The output current of (c) the above-threshold regime and (d) sub-threshold regime for the synaptic processes of the Syn-TFT based on the programming pulses, respectively. Here, programming pulses of 100 cycles for respective synaptic process are applied to the gate terminal. The normalized synaptic weight (\(\overline{{\text{w} }_{\text{G}}}\)) versus the number of the programming pulses for (e) the above-threshold regime and (f) sub-threshold regime, respectively. Here, the dynamic ratio (drw) of each operating region can be calculated with the \(\overline{{\text{w} }_{\text{G}}}\) of two extreme states. The calculated static-power consumption (\({\text{P}}_{\text{static}}^{\text{ read}}\)) at the \({\text{V}}_{\text{GS}}^{\text{ read}}\) for the synaptic processes of (g) the above-threshold regime and (h) sub-threshold regime, respectively, indicating the maximum static power consumption (\({\text{P}}_{\text{static}}^{\text{ read}}\)(max)).
With the waveform condition of these programming pulses as seen in Fig. 4a,b, the dynamics of the IO needs to be firstly monitored for the synaptic depression and facilitation. Figure 4c,d describe the IO varied for the synaptic processes in two operational regimes. As can be seen, it is found that the IO is gradually decreased with a series of positive programming pulses for the synaptic depression. It is because the \(\Delta{\text{V}}_{\text{T}}\) is increased by electrons trapped into the gate oxide (see Fig. 1c), thus the increase of the VT. This can be explained with Eqs. (2) and (3). After 100 cycles of positive programming pulses for the synaptic depression, the IO arrives at the FD with \(\Delta{\text{V}}_{\text{T}}^{ \, {\text{fd}}}\)(above) = 0.46 V and \(\Delta{\text{V}}_{\text{T}}^{ \, {\text{fd}}}\)(sub) = 0.58 V, respectively. As a result, the \({\text{I}}_{\text{O}}^{\text{ fd}}({\text{above}})\) and \({\text{I}}_{\text{O}}^{\text{ fd}}({\text{sub}})\) are approximately 41 nA and 0.06 nA in terms of the IO, respectively, as indicated in Fig. 4c,d. During the synaptic facilitation, it is shown that the IO is gradually increased with applying negative programming pulses because the \(\Delta{\text{V}}_{\text{T}}\) is reduced by electrons de-trapped out of the gate oxide (see Fig. 1d), resulting in the recovery of the VT. This can also be explained with Eqs. (2) and (3). And the IO is almost back to the \({\text{I}}_{\text{O}}^{ \, {\text{ff}}}({\text{above}})\) of 91 nA and \({\text{I}}_{\text{O}}^{ \, {\text{ff}}}({\text{sub}})\) of 2.8 nA, respectively, which corresponds to the FF (see Fig. 4c,d).
Based on the IO as mentioned earlier, the characteristics of weight updates can be checked and monitored. Figure 4e,f show the behavior of the \(\overline{{\text{w} }_{\text{G}}}\) for the synaptic depression and facilitation in two operating regions. During the synaptic depression, it is shown that the trend of the \(\overline{{\text{w} }_{\text{G}}}\) decays with applying positive programming pulses due to the increased \(\Delta{\text{V}}_{\text{T}}\), which results in the decrease of the IO. Its decay can also be explained with Eqs. (12) and (13). At the FD, the \(\overline{{\text{w} }_{\text{G}}}\) in two operational regimes finally approaches at \(\overline{{\text{w} }_{\text{G}}^{ \, {\text{fd}}}}\)(above) = 0.45 and \(\overline{{\text{w} }_{\text{G}}^{ \, {\text{fd}}}}\)(sub) = 0.021, respectively. This is because the IO arrives at the FD state, which is consistent with Eq. (15). After positive programming pulses continued for 100 cycles, it is found that the \(\overline{{\text{w} }_{\text{G}}}\) is facilitated with a series of negative programming pulses, approaching the \(\overline{{\text{w} }_{\text{G}}^{ \, {\text{ff}}}}\)(above) \(\cong\) 1 and \(\overline{{\text{w} }_{\text{G}}^{ \, {\text{ff}}}}\)(sub) \(\cong\) 1, respectively. It is because of the gradual decrease of the \(\Delta{\text{V}}_{\text{T}}\), resulting in the increase of the IO, which can also be explained with Eqs. (12) and (13). In addition, it is found to be a linear increase of the \(\overline{{\text{w} }_{\text{G}}}\) for the synaptic facilitation. This can specifically be explained with both the IO relative to the ΔVT and the ΔVT as a function of the number of programming pulses described in Fig. S2 of Supplementary Information.
With both the extracted \(\overline{{\text{w} }_{\text{G}}^{ \, {\text{fd}}}}\) and \(\overline{{\text{w} }_{\text{G}}^{ \, {\text{ff}}}}\), the drw can be calculated as approximately 2.2 in the above-threshold and 47 in the sub-threshold regime, respectively, using Eq. (16). As expected, the drw(sub) is much bigger compared to the drw(above). This is because the exponential function of the sub-threshold regime (see Eq. 18) can be more sensitive compared to the rational function of the above-threshold regime (see Eq. 17) as the \(\Delta{\text{V}}_{\text{T}}^{ \, {\text{fd}}}\) for each operating region is comparable (see Fig. 3). Accordingly, for the sub-threshold regime, it is verified that the drw is much larger compared to the above-threshold regime. Note that, since drw(sub) > drw(above) with the same pulse width for each synaptic process with respect to two operating regions, it can be considered that the speed of weight updates in the sub-threshold regime is faster compared to the above-threshold regime.
Additionally, as another observation of the pulsed characteristics, the \({\text{P}}_{\text{static}}^{ \, {\text{read}}}\) can be estimated during the synaptic processes for two operational regimes, as seen in Fig. 4g,h. It is found that the \({\text{P}}_{\text{static}}^{ \, {\text{read}}}\) in each operating region decays for the synaptic depression since the IO is reduced with applying positive programming pulses, which can be explained with Eq. (19). After the synaptic depression, with applying a series of negative programming pulses, it is shown that the \({\text{P}}_{\text{static}}^{ \, {\text{read}}}\) is gradually increased for the synaptic facilitation due to the gradual increase of the IO, which is consistent with Eq. (19). Afterward, at the FF, the \({\text{P}}_{\text{static}}^{ \, {\text{read}}}\) finally arrives at the \({\text{P}}_{\text{static}}^{ \, {\text{read}}}\)(max) of 9.1 nW in the above-threshold regime and 0.28 nW in the sub-threshold regime, respectively, which can be calculated with Eq. (20). As can be seen, the \({\text{P}}_{\text{static}}^{ \, {\text{read}}}\)(max) in the sub-threshold regime is found to be about two orders of magnitude smaller than that in the above-threshold regime since the operating current in the sub-threshold regime is much lower compared to the above-threshold regime, as indicated in Fig. 3a,b.
Weight linearity of the Syn-TFT
As another observation for the characteristics of weight updates (e.g. the drw), the weight linearity can be checked for two operating regions, using the plots of \(\Delta\overline{{\text{w} }_{\text{G}}}\) versus \(\overline{{\text{w} }_{\text{G}}}\) based on the extracted data in Fig. 4e,f. Here, the \(\Delta\overline{{\text{w} }_{\text{G}}}\) is represented as a difference between the \(\overline{{\text{w} }_{\text{G}}^{ \, {\text{n}}}}\) and \(\overline{{\text{w} }_{\text{G}}^{ \, {\text{n-1}}}}\) where the \(\overline{{\text{w} }_{\text{G}}^{ \, {\text{n}}}}\) is the \(\overline{{\text{w} }_{\text{G}}}\) after applying the nth programming pulses and \(\overline{{\text{w} }_{\text{G}}^{ \, {\text{n-1}}}}\) is the \(\overline{{\text{w} }_{\text{G}}}\) before applying the nth programming pulse. Figure 5 describes the weight updates of the Syn-TFT with a color map of the cumulative distribution function (CDF) for the synaptic depression and facilitation of those operating regions, respectively, applying the noise components (e.g. the noise power spectral density (NPSD)). Here, the CDF distribution presents a probabilistic variation of the \(\Delta\overline{{\text{w} }_{\text{G}}}\) with respect to a synaptic state. In addition, with the plots of \(\Delta\overline{{\text{w} }_{\text{G}}}\) versus \(\overline{{\text{w} }_{\text{G}}}\), the linear range in the weight update is estimated with 30% variation of the \(\Delta\overline{{\text{w} }_{\text{G}}}\). As indicated in Fig. 5a,b, it is shown that the linear range of the weight for the synaptic depression (i.e. \({\mathcal{L}}_{d}\)) in the above-threshold and sub-threshold regimes is 0.615 and 0.562, respectively. Moreover, the linear range of the weight for the synaptic facilitation (i.e. \({\mathcal{L}}_{f}\)) is found to be 0.637 in the above-threshold regime and 0.966 in the sub-threshold regime, respectively (see Fig. 5c,d). With both the extracted \({\mathcal{L}}_{d}\) and \({\mathcal{L}}_{f}\), the arithmetic mean with respect to the linear range of the weight (i.e. \({\mathcal{L}}_{\text{avg}}=({\mathcal{L}}_{d}+{\mathcal{L}}_{f}) / 2\)) for total synaptic processes can be calculated as 0.626 in the above-threshold regime and 0.764 in the sub-threshold regime, thus a good linearity with a wider linear range of the weight in the sub-threshold regime. This can be because a large drw as a ratio between the \(\overline{{\text{w} }_{\text{G}}^{ \, {\text{fd}}}}\) and \(\overline{{\text{w} }_{\text{G}}^{ \, {\text{ff}}}}\) leads to the wide linear range of the weight. In addition, this result is consistent with a linear increase of \(\overline{{\text{w} }_{\text{G}}}\) for the synaptic facilitation in the sub-threshold regime, as shown in Fig. 4f. Note that the physical interpretation with respect to the weight linearity is specifically explained with IO versus \(\Delta\) VT and \(\Delta\) VT versus time (t) plots for two operating regions in Supplementary Information (see Fig. S1a–d in Section S1).
Plots of \(\Delta\overline{{\text{w} }_{\text{G}}}\) versus \(\overline{{\text{w} }_{\text{G}}}\) of (a) the above-threshold regime and (b) sub-threshold regime for the synaptic depression, respectively. In addition, for the synaptic facilitation, plots of \(\Delta\overline{{\text{w} }_{\text{G}}}\) versus \(\overline{{\text{w} }_{\text{G}}}\) of (c) the above-threshold regime and (d) sub-threshold regime, respectively. For these plots, weight updates of respective operational regime of the Syn-TFT are used and those show the cumulative distribution function (CDF) of the probabilistic variation for the \(\Delta\overline{{\text{w} }_{\text{G}}}\). Here, the \({\mathcal{L}}_{d}\) and \({\mathcal{L}}_{f}\) are the linear range of the weight for the synaptic depression and facilitation, respectively. Note that 100 cycles of the programming pulses are applied to the Syn-TFT for the synaptic depression and facilitation of two operating regions, respectively.
Therefore, it is verified that the weight linearity in the sub-threshold regime can be better compared to the above-threshold regime for overall synaptic processes (e.g. the synaptic depression and facilitation), achieving the wide linear range of the weight.
Analog accelerator based on the Syn-TFT Array
As shown in the previous sections, for the device level, the drw(sub) is found to be larger compared to the drw(above), showing a relatively lower power consumption. And it is also found that the linear range of the weight in the sub-threshold regime is wider compared to the above-threshold regime. These results are summarized in Table 1 for two operating regions.
With these results indicated in Table 1, it can be expected that performances, such as the CA, of the AA based on the Syn-TFT array are to be different in those operating regions at the array level. To check this, the CA as a result of the classification task needs to be monitored. Note that handwritten digits in the Modified National Institute of Standards and Technology database (MNIST) are used for the classification task of the AA, as shown in Fig. 6a. To evaluate the performance of the AA based on the Syn-TFT array for an artificial neural network (ANN), the 60,000 training examples and 10,000 test examples are also used (see Fig. 6b)35. In addition, the network size, which can be calculated as the product of the size of each layer in the ANN (e.g. the input, hidden, and output layers), is 784 × 300 × 10 for the MNIST classification. Note that, in order to resolve the effects of the drw and linearity on the AA performance with respect to two operating regions, the effect of the signal-to-noise ratio (SNR) is intentionally kept the same for each operating region. So, the SNR is equally set in the simulation while considering noise components with 10% of signal for two cases39. As a result of the classification task with this AA, the CA is estimated in Fig. 7 for two operating regions, which is tested for 40 epochs. As can be seen, the CA of the sub-threshold regime is found to be bigger compared to the above-threshold regime at each epoch, resulting in the maximum value of 87.51%. This can be explained with the drw and \({\mathcal{L}}_{\text{avg}}\) for two operating regions. For the case of the drw, it is found that the sub-threshold regime is larger than that of the above-threshold regime, as shown in Table 1. Moreover, the \({\mathcal{L}}_{\text{avg}}\) of the sub-threshold regime is found to be wider compared to the above-threshold regime (see Table 1), thus a relatively good weight linearity in the sub-threshold regime. Here, since the SNR, which is proportional to the CA, is intentionally set the same for both two operating regions, it is expected that other parameters, such as the dynamic ratio and weight linearity, would mainly determine the CA. Note that the comparison related to efficiency metrics between proposed Syn-TFT and existing similar synaptic devices is shown in Supplementary Information (see Section S3)40,41,42,43.
(a) Examples of handwritten digits in the MNIST (Modified National Institute of Standards and Technology database) to be classified with an analog accelerator. Here, 28 × 28 grayscale images in the MNIST are used for the training. (b) Schematic of an artificial neural network (ANN) with three layers as a simple multi-layer perceptron (MLP) structure. Here, the In is nth neuron in an input layer, Hm is mth neuron in a hidden layer, and Ok is kth neuron in an output layer.
Classification accuracy (CA) of the analog accelerator (AA) based on the Syn-TFT array versus training epochs for the above-threshold regime and sub-threshold regime, respectively. Here, the classification task is performed with the CrossSim™ and tested for the MNIST.
Consequently, these results indicate that the Syn-TFT operated in the sub-threshold regime can achieve a relatively large drw(sub) while showing a relatively wide linear range of the weight. With these results of the device level, when the Syn-TFT array is used as the AA, it is also found that the CA of the sub-threshold regime is larger than that of the above-threshold due to those advantages at the device level of the Syn-TFT operated in the sub-threshold region. Therefore, it is believed that the selection of the sub-threshold regime in the Syn-TFT is essential for a high performance of the ANN while achieving a large drw and good weight linearity.