﻿ 多电平闪存信道下阈值电压高效检测算法
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 应用科技  2019, Vol. 46 Issue (5): 57-62  DOI: 10.11991/yykj.201901015 0

### 引用本文

FAN Zhengqin, HAN Guojun. High-efficiency detection algorithm for threshold voltage in multi-level cell NAND flash memory[J]. Applied Science and Technology, 2019, 46(5): 57-62. DOI: 10.11991/yykj.201901015.

### 文章历史

High-efficiency detection algorithm for threshold voltage in multi-level cell NAND flash memory
FAN Zhengqin , HAN Guojun
School of Information Engineering, Guangdong University of Technology, Guangzhou 510000, China
Abstract: Aiming at reducing read latency caused by read operation in high-density NAND flash memory threshold-voltage detection, an improved low-latency read-retry mechanism is proposed. Specifically, according to the distribution characteristics of the raw bit error rate in the voltage overlap region, the scheme introduces the idea of trichotomy to gradually reduce the range of threshold-voltage detection. Furthermore, only one read operation needs to be updated each time the range of voltage detection is narrowed. Simulation results exhibit that the proposed mechanism of the paper, which well ensures the data-storage reliability, significantly reduces the read latency through comparison with traditional read-retry mechanism.
Keywords: threshold-voltage detection    NAND flash memory    read-retry mechanism    raw bit error rate    voltage overlap region    read voltage optimization    read latency    data storage

1 阈值电压检测 1.1 系统模型

1）擦除操作：数据写入单元前必须要先擦除。擦除状态的阈值电压服从高斯分布。擦除状态的阈值电压概率密度函数如下：

 ${p_{\rm{e}}}\left( x \right) = \frac{1}{{{\sigma _{\rm{e}}}\sqrt {2{\text{π}}} }}{{\rm{e}}^{ - \frac{{\left( {x - {\mu _{\rm{e}}}} \right)}}{{2\sigma _e^2}}}}$

2）编程操作：ISPP技术应用于写入数据。擦除状态的阈值电压服从均匀分布。第 $k$ 个编程状态的阈值电压概率密度函数如下：

 $p_{\rm{p}}^k(x) = \left\{ \begin{array}{l} \dfrac{1}{{\Delta {V_{\rm{pp}}}}},\;\;\; \;V_{\rm{p}}^k \leqslant x \leqslant V_{\rm{p}}^k + \Delta {V_{\rm{pp}}} \\ 0,\;\;\;{\text{其他}} \end{array} \right.$

3）单元间干扰（cell-to-cell interference, CCI）：相邻单元间干扰是由于寄生电容耦合效应引起的，会使阈值电压向右偏移。

 $F = \sum {\Delta V_t^k} {\gamma ^k}$

4）持久性噪声（retention noise）：持久性噪声是由于氧化层电荷泄露引起的，会使阈值电压向左偏移。持久性噪声服从高斯分布，概率密度函数建模如下：

 ${p_{\rm{r}}}\left( x \right) = \frac{1}{{{\sigma _{\rm{r}}}\sqrt {2{\text{π}}} }}{{\rm{e}}^{ - \frac{{\left( {x - {\mu _{\rm{r}}}} \right)}}{{2\sigma _r^2}}}}$

 ${\mu _{\rm{r}}} = (x - {x_0}) \cdot \left[ {{A_t}{{(P)}^{{\alpha _i}}} + {B_t}{{(P)}^{{\alpha _o}}}} \right] \cdot \log \left( {1 + T} \right)$

1.2 读电压优化

 ${T_{{\rm{read}}}} = \sum\limits_{i = 1}^N {\left( {T_{{\rm{ECC}}}^i + {T_{{\rm{flash}}}}} \right)}$ (5)

Step0 初始化： ${V_1} = {V_{\rm{s}}}$

${V_2} = {V_1} - \varDelta$

读操作，计算 ${N_{{\rm{ERR}}}}\left( {{V_1}} \right)$ ${N_{{\rm{ERR}}}}\left( {{V_2}} \right)$

Step1 While ${N_{{\rm{ERR}}}}\left( {{V_2}} \right) \leqslant {N_{{\rm{ERR}}}}\left( {{V_1}} \right)$ do

While ${N_{{\rm{ERR}}}}\left( {{V_2}} \right) \leqslant {N_{{\rm{ERR}}}}\left( {{V_1}} \right)$ do

更新： ${V_1} = {V_2}$

${N_{{\rm{ERR}}}}({V_1}) = {N_{{\rm{ERR}}}}\left( {{V_2}} \right)$

${V_2} = {V_1} - \varDelta$

读操作，计算 ${N_{{\rm{ERR}}}}\left( {{V_2}} \right)$

End

Step2 ${V_{{\rm{opt}}}} = {V_1}$

2 优化方案

Step0 初始化： ${V_l} = {V_{\rm{e}}} + {{\left( {{V_{\rm{s}}} - {V_{\rm{e}}}} \right)}/3}$

${V_r} = {V_l} + {{\left( {{V_{\rm{s}}} - {V_{\rm{e}}}} \right)}/3}$

$n = 2$

读操作，计算 ${N_{{\rm{ERR}}}}\left( {{V_l}} \right)$ ${N_{{\rm{ERR}}}}\left( {{V_r}} \right)$

Step1 判断 $\left| {{V_{\rm{s}}} - {V_{\rm{e}}}} \right|$ 是否小于 $\varDelta$ 。若是，转Step7；若否， $n = n + 1$ ，转Step2；

Step2 判断 ${N_{{\rm{ERR}}}}\left( {{V_l}} \right)$ 是否小于 ${N_{{\rm{ERR}}}}\left( {{V_r}} \right)$ 。若是，转Step3；若否，转Step4；

Step3 更新： ${V_{\rm{s}}} = {V_r}$

${V_{\min }} = {V_l}$

${V_{{\rm{mid}}}} = {{\left( {{V_{\rm{e}}} + {V_{\rm{s}}}} \right)}/2}$

判断 ${V_{\min }}$ 是否大于 ${V_{{\rm{mid}}}}$ 。若否，转Step5；若是，转Step6；

Step4 更新： ${V_{\rm{e}}} = {V_l}$

${V_{\min }} = {V_r}$

${V_{{\rm{mid}}}} = {{\left( {{V_{\rm{e}}} + {V_{\rm{s}}}} \right)}/2}$

判断 ${V_{\min }}$ 是否大于 ${V_{{\rm{mid}}}}$ 。若否，转Step5；若是，转Step6；

Step5 更新： ${V_l} = {V_{\min }}$

${V_r} = {{\left( {{V_l} + {V_{\rm{s}}}} \right)}/2}$

Step6 更新： ${V_r} = {V_{\min }}$

${V_l} = {{\left( {{V_r} + {V_e}} \right)}/2}$

读操作，计算 ${N_{{\rm{ERR}}}}\left( {{V_l}} \right)$ ，转Step1；

Step7 判断 ${N_{{\rm{ERR}}}}\left( {{V_l}} \right)$ 是否小于 ${N_{{\rm{ERR}}}}\left( {{V_r}} \right)$ 。若是， ${V_{{\rm{opt}}}} = {V_l}$ ；若否， ${V_{{\rm{opt}}}} = {V_r}$

3 仿真结果

3.1 多噪声信道下原始误码率仿真

3.2 高精度信道检测误码率比较

3.3 高精度信道检测时延比较