When the GB is located in the channel of the n-type MOSFET, the acceptor type trap forms an energy barrier when electrons are trapped as shown in Fig. 3. The GB-induced potential barrier directly suppresses current flow. Consequently, it causes the V_e ascend⁵. Thus, it is shown that the variations of the conduction characteristics are caused mainly by the number of WBCs located in the channel³. The V_e is defined by the constant current method, which determines the V_e as the V_g the value for I_D = 10^−seven A/µm¹⁵.

Statistical analysis of transfer characteristics

Figure 4 shows the drain current (I_D) as a function of the gate voltage (V_g) curves of 4000 samples each ADG 1T-DRAM single layer and ADG 1T-DRAM 3D stacked with a g_Cut of 30 nm under drain voltage = 0.5 V Histograms of (a) the V_es (b) the sub-threshold oscillates (SSs) (c) the on-currents (I_ons), and (d) off currents (I_stoppeds) obtained from simulations for 4000 samples with the proposed GB model, for single-layer 1T-DRAM ADGs and proposed 3D stacked 1T-DRAM ADGs are taken from Fig. 4.

The I_D–V_g 4000 sample curves of single layer ADG 1 T-DRAMs and 3D stacked ADG 1 T-DRAMs. The parameters retained are L_mg= 70nm, L_CG= 50nm, J_beef= 3nm, J_body= 12 nm, and J_spacer= 30nm.

In Fig. 5a, the averages of the extracts V_es of single-layer 1T-DRAM ADGs and stacked 3D 1T-DRAM ADGs are 1.002 V and 0.956 V, respectively. The SDs for the V_es are 15.9 mV and 6.5 mV respectively. The RSDs are 1.58% and 0.68% respectively. The RSD is the SD divided by the mean and multiplied by 100. In other words, a large RSD indicates that the SD is large compared to the mean and has a large dispersion. Since the RSD is expressed as a percentage, it is a merit coefficient that can be used to compare the distribution of data sets with different units of measurement. The I_D are higher in stacked 3D 1T-DRAM ADGs due to multi-layer structure, resulting in lower V_e. The RSDs of V_es are 1.58% for single-layer 1T-DRAM ADGs and 0.68% for stacked 3D 1T-DRAM ADGs. Since the RSD of single-layer 1T-DRAM ADGs is about twice the RSD of stacked 3D 1T-DRAM ADGs. Therefore, the 3-D structure has better reliability for the V_e variations due to GB.

Histograms of (a) the V_ec(b) the SSs (vs) the I_onthe sand (D) the I_stopped s obtained from the proposed 4,000 samples of 1 single-layer T-DRAM and 3-D stacked 1 T-DRAM with the proposed GB distribution.

Figure 5b shows the distribution of SSs. The average of SSs of single-layer 1T-DRAM ADGs and stacked 3D 1T-DRAM ADGs have similar values, 115.0 mv/dec and 114.2 mv/dec, respectively. Single-layer 1T-DRAM ADGs have SS ranging from 110 mv/dec to 140 mv/dec, as can be seen. However, in the case of 3D stacked 1T ADG DRAMs, it can be seen that most SSs are distributed between 112 mv/dec and 117 mv/dec, respectively. This phenomenon occurs because they have 3D stacked structures that complement the fluctuation in current characteristics caused by GBs. This phenomenon is called the averaging effect. In the case of single-layer 1T-DRAM ADG, it is greatly affected by the GBs of a channel region. However, even if one layer is significantly affected by GBs, the current and memory performance variation due to GBs is small in stacked 3D 1T-DRAM ADG because the performance degradation is shared with the other two layers. . This is a phenomenon similar to the decrease in the variation of the work function when the granularity of the metal grid decreases^16.17. Therefore, the RSD of SSs of stacked 3D 1T-DRAM ADGs is more than 9 times smaller than single-layer 1T-DRAM ADGs, which can be considered excellent in the reliability of transfer characteristics.

Figure 5c shows the distribution of I_ons. The average I_ons single-layer 1T-DRAM ADGs and stacked 3D 1T-DRAM ADGs are 1.87×10^–4 A/µm and 5.74×10⁻⁴ A/µm, respectively. The average I_ons of 3D-stacked 1T-DRAM ADGs, which are multi-channel structures, is about three times larger than single-layer 1T-DRAM ADGs. A stocking I_on is a long-standing weakness of poly-Si transistors, but it can be solved by using a 3D stacked structure. Moreover, the DS of I_ons are 1.45×10⁻⁵ A/µm and 2.49×10⁻⁵ A/µm, respectively. For SD, the dispersion of stacked 3D 1T-DRAM ADGs seems larger, but for RSD, which reflects the actual dispersion, the RSD of single-layer 1T-DRAM ADGs is 7.75%, and the Le RSD of stacked 3D 1T-DRAM ADGs is 4.34%, respectively. In conclusion, 3D stacked 1T-DRAM has excellent transfer characteristics, such as greater I_on and more minor variation.

Figure 5d shows the distribution of I_stopped s. The average of I_stopped s of stacked 3D 1T-DRAM ADGs is 1.6 times larger than single-layer 1T-DRAM ADGs. The I_stopped s is the parameter with the most pronounced averaging effect. As mentioned above, thanks to the averaging effect, the RSD of the I_stopped of 3-D stacked ADG 1T-DRAM is 3% due to 3-D structure. On the other hand, the transfer curves of single-layer 1T-DRAM ADGs exhibit large variances, which results in an RSD of 130.7%, as shown in Fig. 4. The factor of merit (FOM) of transfer characteristics and memory performance are summarized in Table 4.

Statistical analysis of memory performance

The histograms of (a) detection margins (SM) and (b) RTs from simulations of 4000 samples with the proposed GB model, for the proposed single-layer 1T-DRAM ADGs and stacked 1T-DRAM ADGs in 3D, are shown in Figure 6a. In Figure 6a, the averages of the SMs of single-layer ADG 1T-DRAM and 3D stacked ADG 1T-DRAM are 5.72 µA/µm and 17.4 µA/µm, SDs are 1.44 µA/µm and 2.54 µA/µm, and RSDs are 25.2% and 14.6%, respectively. The SD of SMs in stacked 3D 1T-DRAM ADGs is larger than that of monolayers, but the RSD is the opposite. Also, in the case of single-layer 1T-DRAM ADGs, depending on the GB distribution, some samples get poor SMs below 3 µA/µm which is the reference value¹⁸. On the other hand, all samples of the 3D stacked 1T ADG DRAMs have an SM greater than 3 µA/µm.

Histograms of (a) SMs and (b) the RTs obtained from the proposed 4,000 samples of 1 single-layer T-DRAM and 1 stacked 3D T-DRAM with the proposed GB distribution.

As shown in Fig. 6b, the average RTs of single-layer 1T-DRAM ADGs and stacked 3D 1T-DRAM ADGs are 212 ms and 200 ms, respectively, which show similar values. However, as shown in Figure 6b, the SDs of the RTs are 116 ms and 82 ms and the RSDs of the RTs are 54.7% and 41%. This indicates that 3D stacked 1T-DRAM ADGs have smaller RT gaps. Additionally, in single-layer 1T-DRAM ADGs, 6.2% of samples are insufficient for RT to meet 64ms, which is the International Roadmap for Devices and Systems (IRDS) memory criteria (> 64ms)¹⁹. However, in the case of 3D-stacked 1T-DRAM ADGs, all samples have an RT greater than 60 ms, as shown in Fig. 6b. In terms of RT, stacked 3D 1T-DRAM ADGs are more reliable than single-layer 1T-DRAM ADGs. The memory performance FOM is summarized in Table 4.

Therefore, when considering the SDs and RSDs of transfer characteristics and memory performance, the stacked 3D 1T-DRAM ADGs showed excellent performance not only of transfer characteristics but also of memory performance. . In addition, they also show strong immunity to the impact of GB, especially on retention in the context of memory performance. Thus, our offered stacked 3D 1T-DRAM ADGs can be excellent devices in terms of reliability. The performance comparison of conventional 1T-1C DRAMs, capacitorless DRAMs, and 3D stacked asymmetric double-gate 1T-DRAM is summarized in more detail in the Supplementary Information.