The ZTC point is the gate voltage at which current variation
due to temperature changes is minimized [28,31],
serving as a critical reference point that reduces the temperature
sensitivity of the device and ensures stable performance
even at high temperatures. Previous studies applied
the ZTC concept to analyze the current-voltage characteristics
of 1T-DRAM under temperature variations and
confirmed that memory operation at the ZTC point remained
stable despite temperature changes [20]. These
studies demonstrated that the ZTC point serves as a crucial
reference for ensuring reliable operation even at high
temperatures. In this study, the ZTC concept is utilized to
minimize drain current fluctuations in 1T-DRAM depending
on device parameters and to ensure stable operation
even in high-temperature environments (300 K-400 K).
Fig. 2 shows the drain current characteristics as a function
of gate voltage under various temperature conditions
(300 K-400 K) and WF1, which are shown in both linear
and log scales. In Fig. 2(a), the shift of the ZTC point with
changes in WF1 can be observed. At the ZTC point, the current is hardly affected by temperature variations. However,
before and after the ZTC point, the current characteristics
vary with temperature changes [26]. Before the
ZTC point, as the temperature increases, the carrier concentration
rises due to thermal generation effects, resulting
in a higher drain current value. In contrast, beyond
the ZTC point, as the temperature rises, the increase in
phonon scattering decreases carrier mobility, resulting in
a reversal phenomenon where the current reduces. The reversal
phenomenon can cause instability in memory operation
within a specific range, potentially degrading data
retention performance at high temperatures.
In Fig. 2(a), as the ZTC point shifts to the right, the
threshold voltage also shifts to the right, resulting in the
device operating at a higher operation point. In contrast,
as the ZTC point shifts to the left, the threshold voltage also shifts to the left, lowering the operation point. The
shift of the ZTC point alters the operating voltage range of
the device, and this change directly impacts memory performance
in practical environments. However, even if the
ZTC point shifts, the device can operate stably at this point
without being significantly affected by temperature variations.
Therefore, the location of the ZTC point serves as a
critical design factor with respect to the device’s memory
operation efficiency and stability.
Fig. 2(b) shows the changes observed in the off-current
state. The off-current refers to the drain current flowing
when the gate voltage is 0 V, and its value increases as the
WF1 value decreases. This is because the energy barrier is
lowered, allowing charges to leak more easily, which can
significantly affect the retention time of the memory along
with a reduction in the threshold voltage. Therefore, it is
essential to optimize the WF1 value by considering the
off-current variations induced by temperature changes.
Fig. 3 shows the impact of WF1 and body doping concentration
variations on the ZTC point. As the WF1 value
increases, the ZTC point generally rises. Notably, when
WF1 is above 4.8 eV, the ZTC point remains almost identical
for body doping concentrations of $1x10^{16} cm^{-3}$ and
$1x10^{17} cm^{-3}$. This phenomenon occurs because a high
WF1 value compensates for the variations in mobility and
threshold voltage caused by temperature changes, thereby
stabilizing the position of the ZTC point [33]. However,
when the body doping concentration increases to $1x10^{18}
cm^{-3}$, the ZTC point tends to rise. At high body doping
concentrations, the electric field within the channel is intensified, resulting in a significant reduction in mobility.
To compensate for this, the threshold voltage increases,
thereby causing the ZTC point to rise. When the
WF1 value is below 4.8 eV, the compensation between the
temperature-dependent effects of mobility and threshold
voltage is insufficient, resulting in the ZTC point not remaining
consistent.
In Fig. 2, the temperature range of 300 K to 400 K
was analyzed to investigate the transfer characteristics under
varying thermal conditions. In contrast, the measurements
in Fig. 4 were conducted for memory characteristic
analysis, with the high-temperature condition set to 358
K (= 85℃), a commonly referenced evaluation point in
evaluations of DRAM retention characteristics.
Fig. 4(a) shows the voltage range of 0.9 V to 1.4 V,
which represents the gate voltage ($R_{-vg1}$) in the read state,
and this range was set to evaluate memory performance under various gate voltage conditions of the 1T-DRAM.
The memory characteristics were analyzed using the 1TDRAM
when WF1 was 4.7 eV and the body doping concentration
was $1 x 10^{17} cm^{-3}$. DRAM memory operating
voltage conditions are presented in Table 2. The program
(write “1”) phase utilizes the band-to-band tunneling
(BTBT) phenomenon. In this phenomenon, electronhole
pairs are generated between the conduction band and
the valence band when a high electric field is induced by
the gate voltage [27]. During this phase, the concentration
of holes formed through BTBT is a critical factor in determining
the sensing margin. In the “1” state, numerous
holes are generated through BTBT and accumulate in the
body region under gate 2, maintaining a high current. In
contrast, in the “0” state, BTBT occurs very limitedly, resulting
in a lower hole concentration and maintaining a
low current. The difference in drain current between the
read “1” state and the read “0” state is referred to as the
sensing margin, which serves as a critical metric for evaluating
memory performance. The sensing margin at a gate
voltage of 1.1 V was 12.549 mA, confirming that the memory
operates normally (T =300 K). Additionally, the drain
current variations were observed under the given temperatures
(300 K, 358 K) as a function of the gate voltage
($R_{-vg1}$) in the read state. The sensing margin varies depending
on temperature and gate voltage conditions, and
a reversal in current values between the read “1” and read
“0” states can be observed at 300 K and 358 K within a
specific voltage range.
Fig. 4(b) shows the drain current variations of the read
“1” and “0” states as a function of gate voltage ($R_{-vg1}$) at
temperatures of 300 K and 358 K. The arrows in the figure
are used to highlight the current values within the specified
voltage range and display an enlarged graph, clearly
illustrating the differences in memory operation characteristics
with respect to temperature. In the region where the gate voltage ($R_{-vg1}$) is at or below 0.9 V, it can be observed
that the read “0” value at 358 K is nearly identical
to the read “1” value at 300 K. However, in the region
where the gate voltage ($R_{-vg1}$) is above 1.4 V, the read
“0” value at 300 K is greater than the read “1” value at
358 K. This phenomenon occurs due to variations in drain
current caused by temperature changes. This reversal phenomenon,
where the read “0” value is greater than the read
“1” value, is a cause of reduced stability in memory operation
within specific regions. Therefore, it is crucial to define
the optimal range of gate voltage ($R_{-vg1}$) to maximize
the stability of the memory device.
The sensing margin and reversal phenomenon observed
in Fig. 4 are further analyzed through the electron density
and mobility distributions shown in Fig. 5. Fig. 5 shows
the variations in electron density and mobility during the
read operation in the 1T-DRAM, clearly presenting the
differences in physical phenomena before and after the
ZTC point (= 1:15 V).
Fig. 5(a) shows the electron density distribution in the
region before the ZTC point, comparing the read “1” state
at 300 K and the read “0” state at 358 K when the gate
voltage ($R_{-vg1}$) in the read state is 0.9 V. In the read “1”
state, the electron density within the channel remains uniform,
whereas in the read “0” state, the electron density
significantly increases inside the channel due to thermal
generation effects, leading to a higher current value and
causing a reversal phenomenon where it exceeds the read
“1” value.
Fig. 5(b) shows the electron density distribution comparing
the read “1” and read “0” states at 358 K when the
gate voltage ($R_{-vg1}$) in the read state is 1.1 V. In this region,
the electron density within the channel is higher in
the read “1” state than in the read “0” state, indicating that
no reversal phenomenon occurs and the device remains in
a normal state.
Fig. 5(c) shows the electron mobility distribution for the
read “1” state at 358 K and the read “0” state at 300 K
when the gate voltage in the read state is 1.4 V. In the read
“0” state, the electron mobility density is higher than in
the read “1” state, resulting in a larger current value and
causing a reversal phenomenon. The reversal phenomenon
demonstrates the differences in physical phenomena, such
as thermal generation effects and changes in electron mobility,
before and after the ZTC point, providing valuable
insights for evaluating the stability and performance of
memory devices.
The gate voltages ($R_{-vg1}$) used in Figs. 6 and 7 are summarized in Table 3. These values were determined based on the ZTC point of each parameter condition. The measurements in Figs. 6 and 7 were conducted using these optimal read voltages.
Fig. 6(a) and (b) show how the drain current changes over time at temperatures of 300 K and 358 K, respectively, when the WF1 value and body doping concentration are varied. The data state of the 1T-DRAM utilizes the characteristic that the hole concentration is high in the read “1” state and low in the read “0” state. The read operation was performed at the ZTC point, and it was confirmed that “1” and “0” are clearly distinguishable.
Fig. 6(c) shows the changes in sensing margin depending on WF1 and body doping concentration. The sensing margin increases with the rise in WF1 and reaches its peak value at WF1 = 4.9 eV. However, when WF1 increases to 5.0 eV or higher, the electric field weakens. This reduction in the electric field causes a decrease in the BTBT phenomenon. As a result, the hole generation rate drops, which reduces the current difference between the read “1” and “0” states and lowers the sensing margin.
The body doping concentration is a key parameter related to the body characteristics of 1T-DRAM, serving a crucial role in controlling hole generation. At low doping concentrations, the depletion region widens, and the electric field weakens, potentially limiting hole generation through the BTBT phenomenon. As a result, the sensing margin is reduced. This makes it difficult to reliably distinguish between data states. At higher doping concentrations, the depletion region becomes narrower, and the electric field intensifies, enhancing the BTBT phenomenon and increasing the sensing margin. Consequently, by optimally setting WF1 and body doping concentration, the sensing margin and data stability can be maximized.
Fig. 7(a), (b), and (c) show the data retention characteristics of the 1T-DRAM as a function of WF1 values and demonstrate the impact of the asymmetric double-gate structure's design characteristics on data retention time. The depletion region formed between gate 1 and gate 2 in this structure suppresses hole recombination and effectively retains holes, enhancing data stability.
In Fig. 7(a), the read “1” state current of the 1T-DRAM with a WF1 of 4.6 eV declines sharply after around 30 ms. This is attributed to the reduction of the depletion region at lower WF1 values, which is insufficient to inhibit hole recombination. Therefore, holes cannot be retained for a prolonged period, which results in shorter data retention time and makes it difficult to reliably distinguish data states. As the WF1 value increases, the depletion region expands. This expansion effectively suppresses hole recombination. As a result, the current in the read “1” state remains stable for approximately 70 ms in Fig. 7(b), improving the distinction and stability of data states.
In Fig. 7(c), the WF1 value significantly increases, leading to the sufficient formation of the depletion region. This depletion region strongly suppresses the recombination of holes and electrons, allowing the current in the read “1” state to remain stable for approximately 330 ms. All preceding results were obtained using the ZTC point as the operating voltage condition for the read operation, confirming a clear distinction between the read “1” and “0” states. Furthermore, retention characteristics were successfully achieved under these conditions.
Fig. 8 shows the variation in retention time of the 1T-DRAM as a function of WF1. As the WF1 value increases, a tendency for longer retention time can be observed. This is because a higher WF1 value strengthens the electric field formed by gate 1, which increases the generation of holes. The generated holes are suppressed from recombining due to the depletion region and are stably retained in the body region beneath gate 2. At WF1 = 4.6 eV, the retention time is short at approximately 30 ms, while it increases steadily as the WF1 value rises. At WF1 = 5.1 eV, the retention time reaches approximately 550 ms, and this further improves data retention characteristics. However, if the WF1 value becomes excessively high, the sensing margin may decrease, and this makes it more difficult to distinguish data states.
Transfer characteristics of the 1T-DRAM with variation of temperature (300 K, 318 K, 328 K, 338 K, 348 K, 358 K, 380 K, 400 K). (a) linear scale, (b) log scale
Zero temperature coefficient (ZTC) point as a function of body doping concentration for different work function (WF1) values.
(a) Memory characteristics of the 1T-DRAM with variation of read gate voltage ($R_{-vg1}$), (b) drain current at “1” and “0” states as a function of gate voltage in read operation
Electron density distribution in 1T-DRAM during read operations: (a) 0.9 V at 300 K for read “1” and 0.9 V at 358 K read “0” states, (b) 1.1 V at 358 K for read “1” and read “0” states. Electron mobility distribution in 1T-DRAM during read operations: (c) 1.4 V at 358 K for read “1” and 1.4 V at 300 K for read “0” states.
Memory characteristics of the 1T-DRAM with variation of (a) work function (WF1) values (4.6 eV–5.1 eV), (b) body doping concentrations ($10^{16} cm^{-3}–10^{18} cm^{-3}$). (c) Sensing margin of the 1T-DRAM as a function of work function (WF1) for body doping concentrations.
Retention characteristics of the 1T-DRAM at 300 K and 358 K under different work function (WF1) values: (a) WF1 = 4.6 eV, (b) 4.7 eV, and (c) 5.0 eV
Retention time of the 1T-DRAM with different work functions (WF1) at 358 K.
Bias conditions for memory of the 1T-DRAM
Optimal read gate voltages ($R_{-vg1}$) for different work functions (WF1) and body doping conditions.