Multimode modulated memristors for in-sensor computing system

Zhang Yu-Qi; Wang Jun-Jie; Lü Zi-Yu; Han Su-Ting

doi:10.7498/aps.71.20220226

Abstract

Authors and contacts

FullText HTML

1. 引　言
2. 浅海全波动混响理论
2.1 浅海海底粗糙界面散射
2.2 浅海海底粗糙界面混响
3. 海底反射系数的三参数模型
4. 海底粗糙界面反向散射模型
4.1 角度特性
4.2 强度特性
5. 结　论

References

Cited By

Abstract

To develop future interactive artificial intelligence system, the construction of high-performance human perception system and processing system is vital. In a traditional perceptual and processing system, sensors, memory and processing units are physically separated because of their different functions and manufacture conditions, which results in frequent shuttling and format transformation of data resulting in long time delay and high energy consumption. Inspired by biological sensory nervous system, one has proposed the concept of in-sensor computing system in which the basic unit integrates sensor, storage and computing functions in the same place. In-sensor computing technology can provide a reliable technical scheme for the area of sensory processing. Artificial memristive synapse capable of sensing light, pressure, chemical substances, etc. is one type of ideal device for the application of in-sensor computing system. In this paper, at the device level, recent progress of sensory memristive synapses applied to in-sensor computing systems are reviewed, including visual, olfactory, auditory, tactile and multimode sensation. This review points out the challenge and prospect from the aspects of device, fabrication, integrated circuit system architecture and algorithms, aiming to provide possible research direction for future development of in-sensor computing system.

Keywords:

PACS:

03.67.Dd	(Quantum cryptography and communication security)
03.65.Ud	(Entanglement and quantum nonlocality)
03.67.Hk	(Quantum communication)

Authors and contacts

1.
Institute of Microscale Optoelectronics, Shenzhen University, Shenzhen 518060, China
2.
College of Electronics and Information Engineering, Shenzhen University, Shenzhen 518060, China

Corresponding author: Han Su-Ting, sutinghan@szu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 62122055, 62074104, 61974093).

FullText HTML

1. 引　言

海底作为浅海混响的主要散射源, 浅海海底界面混响是很多学者探究的课题. 浅海混响根据其形成过程可以分为传播和散射两个过程. 入射声传播和散射声传播过程同属信道声传播问题, 研究较为完善. 而散射过程则比较复杂, 散射强度的测量也较难实现, 尤其是小掠射角的反向散射的测量, 所以针对散射的研究相对比较受限. 在混响研究伊始, 各国学者均采用经验的散射模型描述海底对声场的散射作用. 由于其形式较为简单, 运算速度较快, 在主动声纳预报系统中有很大的优势^[1-4], 至今仍被延续使用. 但是该类型的散射模型也存在着很大的局限性, 很难分析海底散射机理. 最初的经验散射模型是借鉴光学理论中提出的半无限自由空间中的Lambert散射定律给出的海底散射模型, 是海底散射强度与平面波掠射角之间的关系. 而在波导环境中, 由于频散效应的存在, 平面波散射理论不再适用于声场处理, 遂采用简正波理论, 避免了频散产生的多途现象. 然而简正模态的掠射角不同于平面波的掠射角, 因此对波导环境中的声散射问题不能够直接采用经验的Lambert散射模型. 近年来, 越来越多的学者开始从海底散射的物理机理着手建立散射模型. 国际上关于物理散射模型的建模方法包括有限元方法^[5]、Kirchhoff近似方法^[6]、微扰近似方法^[7-10]. 国内关于物理散射模型的研究最具代表性的是中国科学院声学研究所的高天赋和尚尔昌. Shang等^[11]在Gao^[12]和Tang^[13]的研究基础上提出了全波动混响理论, 并对该模型进行了一系列的发展. 2001年, Gao等^[14]提出了依据混响数据反演海底反向散射矩阵的方法. Wu等^[15,16]将海底反射模型引入到浅海混响模型中简化了混响衰减特性与海底沉积层参数之间的关系, 为海底地声参数的反演提供了一种新方法.

本文在尚尔昌和吴金荣的研究基础上, 对反向散射模型进行进一步分析. 通过引入海底反射系数的相移参数, 描述海底对声场的散射作用, 分析海底反向散射模型的角度特性和强度特性. 在实际应用允许的误差范围内, 进一步分析海底粗糙界面反向散射模型的角度特性和强度特性, 并与经验散射模型进行对比, 说明两者之间的异同.

2. 浅海全波动混响理论

在浅海波导环境中, 海底粗糙界面是海底混响的主要散射源. 在图1所示的浅海波导环境中, 平坦海底的平均海深为 ${H_0}$ , 任意水平位置 $r$ 的海底粗糙界面相对于平均海深的起伏高度为 $\eta (r)$ , 其量值远小于 ${H_0}$ , 均值为0, 方差为 $\sigma _\eta ^{\rm{2}}$ . 海底粗糙界面对声场的散射强度远小于入射声场的强度, 即满足弱散射的条件. 海底为半无限均匀介质, 其声速、密度和声吸收系数分别为 ${c_b},{\rho _b}\,{\text{和}}\,\alpha _b^{(w)}$ (声吸收系数的单位是 ${{{\rm{dB}}}/{\rm{\lambda }}}$ ). 海面为平坦的自由边界, 不考虑其对声场的散射作用.

$图 1 浅海波导环境\r\nFig. 1. Shallow water waveguide environment.$

图 1 浅海波导环境

Fig. 1. Shallow water waveguide environment.

下载: 全尺寸图片幻灯片

2.1 浅海海底粗糙界面散射

全波动混响理论的基础思想是将海底粗糙界面对声场的散射作用看作是“二次声源”向外辐射声能量, 从而将海底粗糙界面的散射作为“声源”向波导环境中辐射声能量^[11]. 该“声源”的声源强度与入射声强度成正比关系. 在水平均匀的波导环境中, 单位简谐点源入射声场满足波动方程为

${\nabla ^2}{u_{{\rm{w,b}}}}{\rm{(}}{{{R}}_1},{{{R}}_0}{\rm{)}} + k_{{\rm{w,b}}}^{\rm{2}}{u_{{\rm{w,b}}}}{\rm{(}}{{{R}}_1},{{{R}}_0}{\rm{)}} = 4{\rm{{\text π} \delta (}}{{{R}}_1} - {{{R}}_0}{\rm{)}},$

(1)

海底粗糙界面的“二次声源”满足

$\begin{split} & {\left. {\frac{{\partial {u_{\rm{w}}}({ R_1},{ R_0})}}{{\partial z}} - \frac{{\partial {u_{\rm{b}}}({ R_1},{ R_0})}}{{\partial z}}} \right|_{z = {H_0}}}\\ = & V({R_1}){G^{\rm{i}}}({ R_1},{ R_0}), \end{split}$

(2)

$\begin{split} & {\left. {{\rho _{\rm{w}}}{u_{\rm{w}}}({ R_1},{ R_0}) - {\rho _{\rm{b}}}{u_{\rm{b}}}({ R_1},{ R_0})} \right|_{z = {H_0}}}\\ = & p({ R_1}){G^{\rm{i}}}({ R_1},{ R_0}), \end{split}$

(3)

${G^{\rm{i}}}({{{R}}_1},{{{R}}_0}) = \sqrt {\frac{{2{\rm{\pi }}i}}{{{k_{\rm{w}}}r}}} \sum\limits_{m = 1}^M {{\phi _m}({z_0}){\phi _m}{\rm{(}}{H_0}{\rm{)}}{{\rm{e}}^{{\rm{i}}{k_m}r - {\beta _m}r}}} ,$

(4)

$V({{{R}}_1}) = \left(k_{\rm{w}}^{\rm{2}} - \frac{{k_{\rm{b}}^{\rm{2}}}}{\kappa }\right)\eta {\rm{(}}{r_1}{\rm{)}} + \left(1 - \frac{1}{\kappa }\right){\nabla _ \bot } \cdot {\rm{(}}\eta ({r_1}{\rm{)}}{\nabla _ \bot }{\rm{)}},$

(5)

$p{\rm{(}}{{{R}}_1}{\rm{)}} = {\rm{(}}{\rho _{\rm{w}}} - {\rho _{\rm{b}}}{\rm{)}}\eta {\rm{(}}{r_1}{\rm{)}}\frac{\partial }{{\partial z}},$

(6)

${k_{\rm{w}}} = \frac{{2{{\text π}}f}}{{{c_{\rm{H}}}}},\;\;\;\;\;\;{k_{\rm{b}}} = \frac{{2{{\text π}}f}}{{{c_{\rm{b}}}}},\;\;\;\;\;\;\kappa = \frac{{{\rho _{\rm{b}}}}}{{{\rho _{\rm{w}}}}},$

(7)

其中, ${{{R}}_0} = {\rm{(}}{r_{\rm{s}}},{z_0}{\rm{)}}$ , ${{{R}}_1} = ({r_1},{H_0})$ 分别是声源和散射点的空间位置, 两者之间的水平距离差为 $r = |{r_{\rm{s}}} - {r_1}|$ ; $u_{\rm{w}}, u_{\rm{b}}$ 分别是水介质和沉积层介质中“二次源”的辐射声场(下脚标w和b分别代表水介质和沉积层介质); ${k_{{\rm{w,b}}}}$ 是水介质和沉积层介质中的波数, 与声源频率 $f$ 和介质声速有关; ${c_{\rm{H}}} =$ ${c_{\rm{w}}}{\rm{(}}{H_0}{\rm{)}}$ 是海深处的声速, 沉积层介质和水介质的密度比用 $\kappa$ 表示; ${G^{\rm{i}}}{\rm{(}}{{{R}}_1},{{{R}}_0}{\rm{)}}$ 是波导环境中初级声场的格林函数. 根据简正波理论的思想, 在浅海波导环境中, ${G^{\rm{i}}}{\rm{(}}{{{R}}_1},{{{R}}_0}{\rm{)}}$ 可以表示为简正模态 ${\phi _m}({H_0})$ (实际上是 ${\phi _m}(z)$ , $z$ 是接收深度, 在这里的接收深度为海深 ${H_0}$ )叠加的形式, 如(4)式所示, k_m和 ${\beta _m}$ 分别是简正模态本征值的实部和虚部. $V({{{R}}_1})$ 和 $p({{{R}}_1})$ 则分别是质点振速算子和压力算子, 作用到初级声场的格林函数 ${G^{\rm{i}}}{\rm{(}}{{{R}}_1},{{{R}}_0}{\rm{)}}$ , 得到海底粗糙界面的“二次速度源”的声源强度 $V{\rm{(}}{{{R}}_1}{\rm{)}}{G^{\rm{i}}}{\rm{(}}{{{R}}_1},{{{R}}_0}{\rm{)}}$ 和“二次压力源”的声源强度 $p{\rm{(}}{{{R}}_1}{\rm{)}}{G^{\rm{i}}}{\rm{(}}{{{R}}_1},{{{R}}_0}{\rm{)}}$ . 在瑞利参数较小的情况下, Bass给出了(5)式和(6)式的近似表达式. ${\nabla _ \bot }$ 为水平梯度算子,

${\nabla _ \bot } = \frac{\partial }{{\partial r}}.$

(8)

根据格林定理, 水平均匀波导环境中, “二次速度源”在接收点 ${{R}} = {\rm{(}}{r_{\rm{r}}},z{\rm{)}}$ 处的辐射声场可以通过格林函数 $G_{{\rm{w,b}}}^{\rm{V}}{\rm{(}}{{R}},{{{R}}_1}{\rm{)}}$ 给出形式解. 辐射声场的格林函数满足

$\begin{aligned} & {\nabla ^2}G_{\rm{w}}^{\rm{V}}{\rm{(}}{{R}},{{{R}}_1}{\rm{)}} + k_{\rm{w}}^{\rm{2}}G_{\rm{w}}^{\rm{V}}{\rm{(}}{{R}},{{{R}}_1}{\rm{)}} = 0\;\;\;z < {H_0}\\ & {\nabla ^2}G_{\rm{b}}^{\rm{V}}{\rm{(}}{{R}},{{{R}}_1}{\rm{)}} + k_{\rm{b}}^2G_{\rm{b}}^{\rm{V}}{\rm{(}}{{R}},{{{R}}_1}{\rm{)}} = 0\;\;\;z > {H_0} \end{aligned},$

(9)

同时满足边界条件

$\begin{gathered} {\left. {\frac{{\partial G_{\rm{w}}^{\rm{V}}{\rm{(}}{{R}},{{{R}}_1}{\rm{)}}}}{{\partial z}} - \frac{{\partial G_{\rm{b}}^{\rm{V}}{\rm{(}}{{R}},{{{R}}_1}{\rm{)}}}}{{\partial z}}} \right|_{z = {H_0}}} = {\rm{\delta (}}{{R}} - {{{R}}_1}{\rm{)}} \\ {\left. {\rho G_{\rm{w}}^{\rm{V}}{\rm{(}}{{R}},{{{R}}_1}{\rm{)}} - {\rho _{\rm{b}}}G_{\rm{b}}^{\rm{V}}{\rm{(}}{{R}},{{{R}}_1}{\rm{)}}} \right|_{z = {H_0}}} = 0 \\ \end{gathered} .$

(10)

在接收点 “二次速度源”的辐射声场满足形式解,

$u_{\rm{w}}^{\rm{V}}{\rm{(}}{{R}},{{{R}}_1},{{{R}}_0}{\rm{)}} = \int {G_{\rm{w}}^{\rm{V}}{\rm{(}}{{R}},{{{R}}_1}{\rm{)}}V{\rm{(}}{{{R}}_1}{\rm{)}}{G^{\rm{i}}}{\rm{(}}{{{R}}_1},{{{R}}_0}{\rm{)d}}{{{R}}_1}} .$

(11)

“二次压力源”的辐射声场同样有(11)式的形式解,

$u_{\rm{w}}^{\rm{p}}{\rm{(}}{{R}},{{{R}}_1},{{{R}}_0}{\rm{)}} = \int {G_{\rm{w}}^{\rm{p}}{\rm{(}}{{R}},{{{R}}_1}{\rm{)}}p{\rm{(}}{{{R}}_1}{\rm{)}}{G^{\rm{i}}}{\rm{(}}{{{R}}_1},{{{R}}_0}{\rm{)d}}{{{R}}_1}} ,$

(12)

其中, $G_{\rm{w}}^{\rm{p}}{\rm{(}}{{R}},{{{R}}_1}{\rm{)}}$ 是“二次压力源”的辐射声场的格林函数. 根据边界处法向振速与压力之间的关系, 不难得到 $G_{\rm{w}}^{\rm{p}}{\rm{(}}{{R}},{{{R}}_1}{\rm{)}}$ 与 $G_{\rm{w}}^{\rm{V}}{\rm{(}}{{R}},{{{R}}_1}{\rm{)}}$ 满足

$G_{\rm{w}}^{\rm{p}}{\rm{(}}{{R}},{{{R}}_1}{\rm{)}} = - \frac{1}{{{\rho _{\rm{w}}}}}\frac{\partial }{{\partial z}}G_{\rm{w}}^{\rm{V}}{\rm{(}}{{R}},{{{R}}_1}{\rm{)}}.$

(13)

叠加“二次速度源”和“二次压力源”的辐射声场, 得到海底粗糙界面向波导环境中辐射的总声场

${u_{\rm{w}}}{\rm{(}}{{R}},{{{R}}_1},{{{R}}_0}{\rm{)}} = u_{\rm{w}}^{\rm{V}}{\rm{(}}{{R}},{{{R}}_1},{{{R}}_0}{\rm{)}} + u_{\rm{w}}^{\rm{p}}{\rm{(}}{{R}},{{{R}}_1},{{{R}}_0}{\rm{)}}.$

(14)

将(11)—(13)式代入(14)式, 得到海底粗糙界面散射声场的一般形式解

$\begin{split} & {u_{\rm{w}}}( R,{ R_1},{ R_0})\\ = & \int [G_{\rm{w}}^{\rm{V}}( R,{ R_1})V({ R_1})\\ & - \frac{1}{{{\rho _{\rm{w}}}}}\frac{\partial }{{\partial z}}G_{\rm{w}}^{\rm{V}}( R,{ R_1})p({ R_1})]{G^{\rm{i}}}({ R_1},{ R_0}){\rm{d}}{ R_1}. \end{split}$

(15)

实际上, 入射声场的格林函数、散射场的格林函数以及初级声场的格林函数有一致的形式解, 忽略他们之间的差异,

${G^{\rm{i}}}{\rm{(}}{{{R}}_1},{{R}}{\rm{)}} = G_{\rm{w}}^{\rm{V}}{\rm{(}}{{{R}}_1},{{R}}{\rm{)}} = G{\rm{(}}{{{R}}_1},{{R}}{)},$

(16)

所以对(15)式进行简化得到

$\begin{split} & {u_{\rm{w}}}( R,{ R_1},{ R_0})\\ = & \int_S {[G( R,{ R_1})V({ R_1})} \\ & - \frac{1}{{{\rho _{\rm{w}}}}}\frac{{\partial G( R,{ R_1})}}{{\partial z}}p({ R_1})]G({ R_1},{ R_0}){\rm{d}}{ R_1}. \end{split}$

(17)

对于本地混响, 声源和接收均在同一水平位置. 为了方便计算, 通常令其位于过源点的垂直轴线上, 即 ${r_{\rm{s}}} = {r_{\rm{r}}} = 0$ . 将(4)—(6)式代入(17)式, 并通过分部积分法得到简谐点源的海底粗糙界面的反向散射声场, 将其描述为简正模态的叠加形式^[11],

$\begin{split} & {u_{\rm{w}}}(r,z)\\ = & \displaystyle\frac{{2\pi i}}{{{k_{\rm{w}}}r}}\sum\limits_m^M {\sum\limits_n^M {{\phi _m}({z_0}){\phi _m}({H_0})} } \cdot C_{mn}^\eta K_{mn}^\eta ({k_m},{k_n})\\ & \times {\phi _n}({H_0}){\phi _n}(z){{\rm{e}}^{ - ({\beta _m} + {\beta _n})r}} \end{split}$

(18)

其中

$C_{mn}^\eta = k_{\rm{w}}^{\rm{2}} - \frac{{k_{\rm{b}}^2}}{\kappa } + {\rm{(}}1 - \frac{1}{\kappa }{\rm{)}}{k_m}{k_n} + \frac{{1 - \kappa }}{{{\kappa ^2}}}{\gamma _m}{\gamma _n},$

(19)

$K_{mn}^\eta {\rm{(}}{k_m},k{}_n{\rm{)}} = \int {\eta {\rm{(}}r'{\rm{)}}{{\rm{e}}^{{\rm{i(}}{k_m} + {k_n}{\rm{)}}r'}}{\rm{d}}r'} .$

(20)

2.2 浅海海底粗糙界面混响

实际上(18)式是平坦波导环境中海底粗糙界面散射场的稳定解形式. 对于声源脉冲信号s(t), 其功率谱 $F\left( \omega \right)$ 满足Fourie变换

$F{\rm{(}}\omega {\rm{)}} = \int_{ - \infty }^{ + \infty } {s{\rm{(}}t{\rm{)}}{{\rm{e}}^{ - {\rm{i}}\omega t}}{\rm{d}}t},\tag{21a}$

(21a)

$s{\rm{(}}t{\rm{)}} = \frac{1}{{2{\rm{\pi }}}}\int_{ - \infty }^{ + \infty } {F{\rm{(}}\omega {\rm{)}}{{\rm{e}}^{{\rm{i}}\omega t}}{\rm{d}}\omega }.\tag{21b}$

(21b)

根据Fourie变换的性质, 得到入射信号为s(t)的海底散射声场为

$u_{\rm{w}}^{s{\rm{(}}t{\rm{)}}}{\rm{(}}r,z{\rm{)}} = \frac{1}{{2{\rm{\pi }}}}\int_{ - \infty }^{ + \infty } {F{\rm{(}}\omega {\rm{)}}{u_{\rm{w}}}{\rm{(}}r,z{\rm{)}}{{\rm{e}}^{{\rm{i}}\omega t}}{\rm{d}}\omega } .$

(22)

将声源信号的功率谱函数 $F\left( \omega \right)$ 和(18)式代入(22)式, 同时取水平波束在中心频率处的两阶泰勒级数展开, 进而得到脉宽为 $\tau$ 声源信号s(t)的反向散射声场,

$\begin{split} & u_{\rm{w}}^{s(t)}(r,z)\\ = & \frac{{2\pi i}}{{{k_{\rm{w}}}r}}s(t - {t_0})\sum\limits_m^M {\sum\limits_n^M {{\phi _m}({z_0}){\phi _m}({H_0}) } } \\ & \times C_{mn}^\eta K_{mn}^\eta \cdot {\phi _n}({H_0}){\phi _n}(z){{\rm{e}}^{ - ({\beta _m} + {\beta _n})r}} \end{split}$

(23)

其中, t₀是信号的传播时间, 与散射环的水平距离满足 ${t_0} \approx {{2r}/{{c_{\rm{H}}}}}$ .

混响是能够同一时刻被接收、来自各方向散射回波的叠加. 对于海底粗糙界面混响而言, 同一时刻接收到的散射回波来自于宽度为 $\Delta r = {{{c_{\rm{H}}}\tau }/2}$ 的散射圆环, 其内径为 ${r_{{\rm{in}}}} = r - \displaystyle\frac{{{c_{\rm{H}}}\tau }}{4}$ , 外径为 ${r_{{\rm{ex}}}} = r +$ $\displaystyle\frac{{{c_{\rm{H}}}\tau }}{4}$ . 对(23)式计算强度, 并在散射环面积上进行积分得到海底粗糙界面混响平均强度

${I_\eta }{\rm{(}}r,z{\rm{)}} = \int_A {\langle u_{\rm{w}}^{s{\rm{(}}t{\rm{)}}}{\rm{[}}u_{\rm{w}}^{s{\rm{(}}t{\rm{)}}}{\rm{]}}^{*}\rangle } {\rm{d}}A,$

(24)

其中, ${\rm{[}}u_{\rm{w}}^{s{\rm{(}}t{\rm{)}}}{\rm{]}}^*$ 是 $u_{\rm{w}}^{s{\rm{(}}t{\rm{)}}}$ 的复共轭.

假设散射环面积内的海底界面起伏高度满足各向同性的原则, 对(24)式进一步简化为

${I_\eta }{\rm{(}}r,z{\rm{)}} = 2{\rm{\pi }}r\int_{{r_{{\rm{in}}}}}^{{r_{{\rm{ex}}}}} {\langle u_{\rm{w}}^{s{\rm{(}}t{\rm{)}}}{\rm{[}}u_{\rm{w}}^{s{\rm{(}}t{\rm{)}}}{\rm{]}}^{*}\rangle {\rm{d}}r} .$

(25)

将(23)式代入(25)式, 并假设脉宽远小于混响时间t, 将声源强度近似为

${E_0} = {s^2}\left( {t - {t_0}} \right) \cdot \tau .$

(26)

在这里, 只考虑其非相干特性, 得到短脉冲的非相干混响平均强度

$\begin{split} {I_\eta }(r,z) = & {E_0} \cdot {\left(\frac{{2{\text{π}}}}{{{k_{\rm{w}}}r}}\right)^2}\\ & \times {\text{π}} rc\sum\limits_m^M {\sum\limits_n^M {\phi _m^2({z_0})\phi _m^2({H_0}) \cdot S_{mn}^\eta } } \\ & \times \phi _n^2({H_0})\phi _n^2(z){{\rm{e}}^{ - 2({\beta _m} + {\beta _n})r}}, \end{split}$

(27)

$S_{mn}^\eta = {\left[ {C_{mn}^\eta } \right]^2}{S^\eta }\left( {2{k_0}} \right),$

(28)

$\begin{split} & {S^\eta }(2{k_0})\\ = & \int_{{r_{{\rm{in}}}}}^{{r_{{\rm{ex}}}}} {\int_{{r_{{\rm{in}}}}}^{{r_{{\rm{ex}}}}} {\langle \eta (r')\eta (r'')\rangle {{\rm{e}}^{{\rm{i}}({k_m} + {k_n})r' - {\rm{i}}({k_m} + {k_n})r''}}} } \\ & \times {\rm{d}}r''{\rm{d}}r'\; = \;\sigma _\eta ^{\rm{2}}{P^\eta }(2{k_0}), \end{split}$

(29)

其中, ${S^\eta }(2{k_0})$ 是海底界面的粗糙度谱, 与海底沉积层的地声参数无关, 只是声源频率的函数; $S_{mn}^\eta$ 是海底粗糙界面引起的入射模态和散射模态之间的耦合系数, 反映海底粗糙界面的反向散射能力, 由海底界面粗糙度谱和地声参数决定. 定义

$\Theta _{mn}^\eta = \phi _m^2({H_0})S_{mn}^\eta \phi _m^2({H_0})$

(30)

是区别于经验散射模型的物理散射模型. 它结合了波导环境特性和简正波理论的思想, 建立了受格林函数约束的散射模型, 明确了海底地声参数以及海底粗糙界面与海底反向散射的定量关系. 因此, 地声参数的准确度直接影响到海底反向散射函数的精确度. 通常情况下, 很难直接获取大面积的地声数据, 通过反演得到的地声参数又受地声模型的影响较大, 而且反演的未知参数较多, 导致结果存在很大的不确定性. 从反射系数的角度思考, 海底对声场的影响主要体现在海底反射系数. 海底反射系数的三参数模型与海底地声模型无关, 且参数较少, 利用海底反射系数代替地声参数作为输入参数, 能很大程度上简化海底粗糙界面的反向散射模型.

3. 海底反射系数的三参数模型

尚尔昌在1979年提出了海底反射系数的三参数模型^[17], 随后给出了海底小掠射角的反射系数幅值和相移与掠射角之间的量化关系, 该参数与地声模型无关. 海底反射系数的幅值用Q参数表示

$\ln \left| {V\left( \theta \right)} \right| = - Q\theta ,\;\;\theta \to 0,$

(31)

海底反射系数的相移用P参数表示

$\arg \left[ {V\left( \theta \right)} \right] = -{\text{π}} + P/\theta ,$

(32)

$\theta$ 是海底界面处入射声波的掠射角; Q参数反映海底声吸收效果, 体现声能量的衰减; P参数则描述各阶简正模态在海深处的能量, 即控制各阶简正模态的水平波数. 海底反射系数的相移参数P与地声参数之间的转换关系满足^[18,19]

${P^{{\rm{Low}}}} = \frac{{2\kappa }}{{\sqrt {1 - {\upsilon ^{ - 2}}} }},\;\;{\rm{ }}\theta < \theta ^{\rm{*}},$

(33)

${{{P^{{\rm{Crit}}}} = {\text{π}}}/{\theta ^{*}}},\;\;{\rm{ }}\theta \to \theta ^{\rm{*}},$

(34)

其中, $\upsilon = {{{c_{\rm{b}}}}/{{c_{\rm{H}}}}}$ 表示沉积层介质和水介质的声速比; $\kappa$ 是密度比, 如(7)式所示; $\theta ^{*}$ 是临界掠射角.

(33)式和(34)式分别给出了不同海底掠射角时海底反射系数的相移参数的不同形式. ${P^{{\rm{Low}}}}$ 是甚小掠射角处的海底反射系数相移参数, 是海底沉积层和水介质的声速比和密度比的函数; ${P^{Crit}}$ 是临界角附近海底反射系数的相移参数, 是临界角的函数.

海底反射系数的幅值参数Q与地声参数之间的转换关系满足^[18,19]

$Q = 0.036 \cdot \frac{{{\upsilon ^{ - 1}}\kappa }}{{{{\left[ {1 - {\upsilon ^{ - 2}}} \right]}^{3/2}}}} \cdot \alpha _b^{\left( w \right)},$

(35)

其中, $\alpha _b^{\left( w \right)}$ 是海底沉积层的声吸收系数, 单位是 $dB/\lambda$ .

根据Snell折射定律, $\upsilon$ 与临界掠射角之间满足

${\rm{cos(}}\theta ^{*}{\rm{)}} = {{{c_{\rm{H}}}}/{{c_{\rm{b}}}}} = {\upsilon ^{ - 1}}.$

(36)

将(36)式代入(34)式, 临界角附近的海底反射系数的相移参数 ${P^{Crit}}$ 与声速之间满足

$\upsilon = {\rm{co}}{{\rm{s}}^{ - 1}}{\rm{(}}\frac{{\rm{\pi }}}{{{P^{{\rm{Crit}}}}}}{\rm{)}}.$

(37)

联合(37)式和(33)式得到甚小掠射角的海底反射系数的相移参数 ${P^{Low}}$ 与密度之间满足关系式

$\kappa = \frac{{{P^{{\rm{Low}}}}}}{2}\sin \left(\frac{{\text{π}}}{{{P^{{\rm{Crit}}}}}}\right).$

(38)

(37)式和(38)式分别是海底反射系数的参数与等效的均匀半无限海底介质的地声参数之间的转换关系.

4. 海底粗糙界面反向散射模型

常用的经验散射模型如(39)式所示:

${\Theta _E} = {\mu _E}{\sin ^l}\theta {\sin ^k}\varphi ,$

(39)

其中, ${\mu _{\rm{E}}}$ 是经验散射系数, 反映反向散射强度; $\theta$ 是入射掠射角; $\varphi$ 是散射掠射角. 当 $l = k = 1$ , 是经验的Lambert散射模型. 该类型的散射模型是可分离的经验海底反向散射模型, 不可分离的经验散射模型(参见附录)也被用来描述海底反向散射.

(30)式的海底反向散射模型是根据波导环境建立的散射模型, 明确了入射简正模态、散射简正模态以及海底地声参数对反向散射的强度特性和角度特性的影响. 浅海波导环境中简正模态是受格林函数严格约束的稳定解, 与海底沉积层的介质参数和水文环境有关. 在掠射角小于临界角的条件下, 忽略各阶简正模态的水平波数(掠射角)之间的差异, 即 ${k_m} \approx {k_n} \approx {k_{\rm{w}}}$ , 则(19)式可以近似描述为与模态无关的量.

$\begin{split} C_{mn}^\eta = & \left[1 \!- \!\frac{{k_{\rm{b}}^{\rm{2}}}}{{k_{\rm{w}}^2\kappa }} \!+\! \left(1 - \frac{1}{\kappa }\right)\frac{{{k_m}{k_n}}}{{k_{\rm{w}}^2}} + \frac{{1 - \kappa }}{{{\kappa ^2}}}\frac{{{\gamma _m}{\gamma _n}}}{{k_{\rm{w}}^2}}\right]k_{\rm{w}}^2 \\ & \approx \;\left[1 - \frac{{k_{\rm{b}}^{\rm{2}}}}{{k_{\rm{w}}^{\rm{2}}\kappa }} + \left(1 - \frac{1}{\kappa }\right) + \frac{{1 - \kappa }}{{{\kappa ^2}}}\frac{{k_{\rm{w}}^2 - k_{\rm{b}}^{\rm{2}}}}{{k_{\rm{w}}^{\rm{2}}}}\right]k_{\rm{w}}^{\rm{2}} \\ & = \;\left[2 - 2{\kappa ^{ - 1}} + {\kappa ^{ - 2}} - {\left(\kappa \upsilon \right)^{ - 2}}\right]k_{\rm{w}}^2. \end{split}$

(40)

将(37)式和(38)式代入(40)式, 用海底反射系数的相移参数代替地声参数, 得到

$C_{mn}^\eta = k_{\rm{w}}^2 \cdot \varsigma {\rm{(}}P{\rm{)}},$

(41)

其中

$\varsigma {\rm{(}}P{\rm{)}} \approx 2 - \frac{4}{{P{\rm{sin(}}{{\text{π}}/P}{\rm{)}}}} + \frac{4}{{{P^2}}}.$

(42)

在这里忽略 ${P^{Low}}$ 和 ${P^{Crit}}$ 之间的差异, 文献[18]中也说明了这种近似的合理性.

同时, 海底反射系数的相移参数 $P$ 决定了各阶简正模态在海底粗糙界面平均深度处的能量, 即

${\phi _m}({H_0}) = \sqrt {\frac{2}{{{H_0}}}} \sin \left(\frac{{P{\theta _m}}}{2}\right).$

(43)

将(41)式和(43)式代入(30)式得到远距离(小掠射角)条件下的海底反向散射核函数,

${\Theta _P} = \frac{4}{{H_0^2}}S(2{k_0}){[k_w^2 \cdot \varsigma (P)]^2} \cdot {\sin ^2}\left(\frac{{P\theta }}{2}\right){\sin ^2}\left(\frac{{P\varphi }}{2}\right),$

(44)

其中 $\theta = {\theta _m}$ 为入射掠射角, $\varphi = {\theta _n}$ 为散射掠射角.

采用海底反射系数的相移参数 $P$ 描述海底反射系数, 明确了海底对声散射的物理机理, 不同于经验反向散射模型.

4.1 角度特性

在远距离条件下, (44)式表明, 海底反向散射的角度特性受海底反射系数的相移参数 $P$ 的影响, 不同于经验散射模型. 在临界角附近,

$\mathop {\lim }\limits_{\theta \to \theta *} \frac{{P\theta }}{2} = \frac{{\text{π}}}{2}.$

(45)

以 $\displaystyle\frac{{P\theta }}{2}$ 为宗量, 不能对 $\sin \left(\displaystyle\frac{{P\theta }}{2}\right)$ 进行小角度近似, 所以在临界角附近, (44)式所描述的反向散射模型随掠射角并不满足线性变化的关系.

以 ${{P\theta }/2} = 1$ 为分界点, 当 ${{P\theta }/2} < 1$ 时, 为甚小掠射角范围, 小角度近似引起的海底反向散射强度小于3 dB, 在实际应用中可忽略不计; 当 ${{P\theta }/2} > 1$ 时, 为临界角附近, 小角度近似使海底反向散射强度出现大于3 dB的误差, 实际应用中不可忽略. 所以, 在随后的分析中, 对反向散射模型的强度特性和角度特性进行分段处理.

当 ${{P\theta }/2} > 1$ , 即 ${2/P} < \theta < \theta *$ 时, (44)式不能进行小角度近似, 其随角度的变化关系受P参数加权.

$\begin{split}\Theta _P^{Crit} = & \mu _P^{Crit}{\sin ^2}\left(\frac{{P\theta }}{2}\right){\sin ^2}\left(\frac{{P\varphi }}{2}\right) \\ & \propto {\sin ^2}\left(\frac{{P\theta }}{2}\right){\sin ^2}\left(\frac{{P\varphi }}{2}\right),\end{split}$

(46)

其中

$\mu _P^{Crit} = \frac{4}{{H_0^2}}S(2{k_0}){[k_0^2 \cdot \varsigma (P)]^2}.$

(47)

当 ${{P\theta }/2} < 1$ , 即 $\theta < {2/P}$ 时, 对(44)式的角度项进行小角度近似,

$\sin \left(\frac{{P\theta }}{2}\right) \approx \frac{{P\theta }}{2}.$

(48)

将(48)式代入(44)式得到

$\Theta _P^{Low} = \mu _P^{Low} \cdot {\theta ^2}{\varphi ^2} \propto {\theta ^2}{\varphi ^2},$

(49)

其中

$\mu _P^{Low} = \frac{{{P^4}}}{{4H_0^2}}S(2{k_0}){[k_0^2 \cdot \varsigma (P)]^2}.$

(50)

对(39)式的经验散射模型进行小角度近似得到

${\Theta _E} \approx {\mu _E}{\theta ^l}{\varphi ^k} \propto {\theta ^l}{\varphi ^k}.$

(51)

当 $l = k = 2$ 时, 比较(51)式和(49)式具有相同的角度关系. 所以当掠射角 $\theta < {2/P}$ 时, 基于物理散射机理的反向散射模型与 $l = k = 2$ 的可分离经验散射模型具有一致的角度特性.

4.2 强度特性

通过4.1节的分析, 掠射角不同时, 海底反向散射的角度特性不同, 同时也反映了海底反向散射系数的差异.

(47)式指出, 在临界角附近, 海底反向散射系数由海底反射系数的相移参数P、海底界面粗糙度谱, 海深以及声源信号的频率决定. 忽略临界角附近以及甚小掠射角的P参数之间的差异^[18], 则(42)式中等式右边第三项相比前两项为小量, 可以忽略不计. 第二项中采用小角度近似,

${\rm{sin}}\frac{{\text{π}}}{P} \approx \frac{{\text{π}}}{P},$

(52)

使得(42)式中的第二项近似与P参数无关, 所以 $\varsigma (P) \approx 0.73$ . 图2也表明了 $\varsigma (P)$ 随P参数的变化不是很明显. 所以, 在临界角附近的海底反向散射系数近似与海底沉积层介质无关, 只是海底界面粗糙度谱、海深以及声源频率的函数.

$\mu _P^{Crit} \approx \frac{{2.11}}{{H_0^2}}S(2{k_0})k_0^4.$

(53)

$图 2 $\zeta $随P参数的变化\r\nFig. 2. $\zeta $ varied with P parameters near critical angle.$

图 2

$\zeta$

随P参数的变化

Fig. 2.

$\zeta$

varied with P parameters near critical angle.

下载: 全尺寸图片幻灯片

对于甚小掠射角的海底反向散射系数满足(50)式. 结合 $\varsigma (P)$ 近似为常数的结果, (50)式可以近似为与 ${P^4}$ 成正比, 即

$\mu _P^{Low} \approx {0.13}\frac{{{P^4}}}{{H_0^2}}S(2{k_0})k_0^4 \propto {P^4}.$

(54)

图3以第一类海底为例说明了这种近似结果的合理性. 图中给出了甚小掠射角的海底反向散射系数随 $P$ 参数的变化曲线(仿真参数: 海深为50 m, 声源频率为600 Hz, 海底粗糙界面的标准差为 $0.1\;{\rm{m}}$ , 相关尺度为 ${\rm{10}}\;{\rm{m}}$ , 计算得到Goff-Jordan谱^[20]为－32.8 dB)以及对其进行 $P$ 参数的四次方拟合结果, 两者的变化趋势基本一致. 所以, 在甚小掠射角的条件下, 海底反向散射系数与海底反射系数的相移参数 $P$ 密切相关, 即与海底沉积层的声速比和密度比有关, 与声吸收系数无关.

$图 3 海底甚小掠射角反向散射系数对P参数的依赖\r\nFig. 3. Relationship between P and bottom backscattering coefficient at very low grazing angle.$

图 3 海底甚小掠射角反向散射系数对P参数的依赖

Fig. 3. Relationship between P and bottom backscattering coefficient at very low grazing angle.

下载: 全尺寸图片幻灯片

另外, 从混响平均强度的角度分析, 同样说明了这种近似的合理性. 海底界面粗糙度谱函数采用图3的仿真参数, 海底是第一类均匀半无限介质, 声速为 $18{\rm{36}}\;{\rm{m/s}}$ , 密度为 ${\rm{2}}{\rm{.03}}\;{\rm{g/c}}{{\rm{m}}^{\rm{3}}}$ , 声吸收系数为 $0.88\;{\rm{dB/}}\lambda$ , 海深为50 m, 水介质为1500 m/s的等声速剖面的均匀水体. 声源频率为600 Hz, 发射深度为10 m, 接收深度为30 m. 计算水平散射距离从5 km到50 km的混响平均强度衰减曲线. 图4中实线是根据(30)式仿真的非近似混响平均强度衰减曲线; “○”是根据(46)式和(53)式仿真的临界角的近似结果, 与非近似的混响平均强度衰减曲线在13 km以前完全重合; 随着水平距离的增加, 两者相差逐渐增大; “ $\bullet$ ”是根据(49)式和(54)式仿真的甚小掠射角的近似结果, 在20 km以前, 与非近似结果之间的差异随水平距离的增大而减小, 在20 km以后两者基本吻合. 在散射距离较近时, 掠射角相对较大, 临界角附近近似的海底反向散射模型与真实结果更接近; 在散射距离较远时, 掠射角相对较小, 甚小掠射角的近似结果与真实结果更接近.

$图 4 海底反向散射模型的比较\r\nFig. 4. Compare with bottom backscattering model with different approximate.$

图 4 海底反向散射模型的比较

Fig. 4. Compare with bottom backscattering model with different approximate.

下载: 全尺寸图片幻灯片

5. 结　论

在浅海混响平均强度模型中, 经验散射模型在混响特性分析中存在明显的局限性, 而现有的物理散射模型受地声模型的影响较大. 本文以全波动混响理论的物理散射模型为基础, 结合海底反射系数的三参数模型, 将海底反射系数的相移参数等效代替地声参数, 描述海底对声场的散射作用, 简化了海底反向散射模型. 通过理论分析, 明确了海底掠射角以 ${2/P}$ 为分界点, 海底反向散射的角度特性和强度特性对海底反射系数的相移参数存在不同的依赖关系. 在掠射角满足 $\theta < {2/P}$ 时, 海底反向散射的角度特性近似描述为与可分离经验散射模型的角度特性一致, 与 $P$ 参数无关; 而其散射系数则近似描述为与P⁴线性增强. 当海底掠射角满足 ${2/P} < \theta < \theta ^{*}$ 时, 海底反向散射的角度特性是受 $P$ 参数加权的, 即受海底地声参数的影响; 而其散射系数则近似为与 $P$ 参数无关. 所以不同掠射角范围, 海底对反向散射声场的强度特性和角度特性的贡献不同. 掠射角较大时海底对反向散射声场的影响主要体现在其角度特性; 掠射角非常小时, 海底的影响主要体现在其强度特性.

附录A　经验反向散射模型

经验反向散射模型有多种形式, 主要体现在其角度特性之间的差异. 最常用的海底散射模型是可分离的散射模型,

$\Theta = {\mu _{\rm{E}}}{\rm{si}}{{\rm{n}}^l}\theta {\rm{si}}{{\rm{n}}^k}\varphi, \tag{A1}$

(A1)

其中, ${\mu _{\rm{E}}}$ 是海底反向散射系数; $l,k$ 取不同的值对应不同的散射模型. 常见的Lambert散射模型则是(A1)式中 $l = k = 1$ 时的散射模型. 该模型最初是Mackenzie^[1]在处理深海海底混响模型时由光学的散射原理引入, 给出经验的海底反向散射模型, 随后根据实验数据与理论结果对比得到 ${\mu _{\rm{E}}}$ 的分贝值大约在－27 dB左右, 也就是说 ${\mu _{\rm{E}}} \approx {10^{ - 2.7}}$ . 当 $l = 1,k = 0$ 表示散射源强正比于 $\mu {\rm{sin}}\theta$ 的均匀散射; 当 $l = 0,k = 0$ 表示与角度无关的均匀散射; 同时也存在 $l = k = 2$ 的反向散射模型.

在海底界面大尺度不均匀波导环境中, 小掠射角和基尔霍夫近似的条件下的海底散射模型可以表示为

$\Theta = {\mu _{\rm{E}}}{\rm{si}}{{\rm{n}}^l}\left(\frac{{\theta + \varphi }}{2}\right) \;\;l = 0,\frac{1}{2},1,\frac{3}{2},....\tag{A2}$

(A2)

在海底界面小尺度不均匀波导环境中, 小掠射角和基尔霍夫近似的条件下的海底散射模型可以表示为

$\Theta = {\mu _{\rm{E}}}{\rm{si}}{{\rm{n}}^l}\left[{\rm cos}^{- 1}\left(\frac{{{\rm{cos}}\theta + {\rm{cos}}\varphi }}{2}\right)\right]\;\;l = 0,\frac{1}{2},1,\frac{3}{2},....\tag{A3}$

(A3)

另外一种不可分离的散射模型, 同样被用来描述海底反向散射过程

$\Theta = {\mu _{\rm{E}}}\frac{{{\rm{sin}}\theta {\rm{sin}}\varphi }}{{{\rm{sin}}\theta + {\rm{sin}}\varphi }}.\tag{A4}$

(A4)

通常无论是可分离的经验反向散射强度还是不可分离的经验反向散射强度, 它们的共同点在于海底反向散射强度特性与角度特性相互分离, 相互独立.

References

[1]	Lee Y, Lee T W 2019 Acc. Chem. Res. 52 964 Google Scholar
[2]	Zeng M, He Y, Zhang C, Wan Q 2021 Front. Neurosci. 15 690950 Google Scholar
[3]	Wan C, Cai P, Wang M, Qian Y, Huang W, Chen X 2020 Adv. Mater. 32 1902434 Google Scholar
[4]	Zhou F, Chai Y 2020 Nat. Electron. 3 664 Google Scholar
[5]	Wan T, Ma S, Liao F, Fan L, Chai Y 2022 Sci. China Inf. Sci. 65 141401 Google Scholar
[6]	廖付友, 柴扬 2021 物理 50 378 Google Scholar Liao F Y, Chai Y 2021 Physics 50 378 Google Scholar
[7]	Kim Y, Chortos A, Xu W, Liu Y, Oh J Y, Son D, Kang J, Foudeh A M, Zhu C, Lee Y, Niu S, Liu J, Pfattner R, Bao Z, Lee T W 2018 Science 360 998 Google Scholar
[8]	Shi W, Cao J, Zhang Q, Li Y, Xu L 2016 IEEE Internet Things 3 637 Google Scholar
[9]	El-Atab N 2021 Phys. Status Solidi A 219 2100528
[10]	Phong Truong T, Toan Le H, Thi Nguyen T 2020 J. Phys. : Conf. Ser. 1432 012068 Google Scholar
[11]	Li Y, Wang Z, Midya R, Xia Q, Yang J J 2018 J. Phys. D:Appl. Phys. 51 503002 Google Scholar
[12]	Wang Z, Wu H, Burr G W, Hwang C S, Wang K L, Xia Q, Yang J J 2020 Nat. Rev. Mater. 5 173 Google Scholar
[13]	Sebastian A, Le Gallo M, Khaddam-Aljameh R, Eleftheriou E 2020 Nat. Nanotechnol. 15 529 Google Scholar
[14]	Ielmini D, Wong H S P 2018 Nat. Electron. 1 333 Google Scholar
[15]	Wang J, Lv Z, Xing X, Li X, Wang Y, Chen M, Pang G, Qian F, Zhou Y, Han S T 2020 Adv. Funct. Mater. 30 1909114 Google Scholar
[16]	Zidan M A, Strachan J P, Lu W D 2018 Nat. Electron. 1 22 Google Scholar
[17]	Zhang Y, Wang Z, Zhu J, Yang Y, Rao M, Song W, Zhuo Y, Zhang X, Cui M, Shen L, Huang R, Yang J J 2020 Appl. Phys. Rev. 7 011308 Google Scholar
[18]	Sun K, Chen J, Yan X 2020 Adv. Funct. Mater. 31 2006773
[19]	Lv Z, Wang Y, Chen J, Wang J, Zhou Y, Han S T 2020 Chem. Rev. 120 3941 Google Scholar
[20]	李锟, 曹荣荣, 孙毅, 刘森, 李清江, 徐晖 2019 微纳电子与智能制造 1 87 Li K, Cao R, Sun Y, Liu S, Li Q, Xu H 2019 Micro/nano Electronics and Intelligent Manufacturing 1 87
[21]	Ji X, Zhao X, Tan M C, Zhao R 2020 Adv. Intell. Syst. 2 1900118 Google Scholar
[22]	Sun F, Lu Q, Feng S, Zhang T 2021 ACS Nano 15 3875 Google Scholar
[23]	Carrara S 2021 IEEE Sens. J. 21 12370 Google Scholar
[24]	张章, 李超, 韩婷婷, 许傲, 程心, 刘钢, 解光军 2021 电子与信息学报 43 1498 Google Scholar Zhang Z, Li C, Han T T, Xu A, Cheng X, Liu G, Xie G J 2021 Journal of Electronics and Information Technology 43 1498 Google Scholar
[25]	Zhu Y, Zhu Y, Mao H, He Y, Jiang S, Zhu L, Chen C, Wan C, Wan Q 2021 J. Phys. D:Appl. Phys. 55 053002
[26]	Tripathy A, Nine M J, Losic D, Silva F S 2021 Mater. Sci. Eng. R. Rep. 146 100647 Google Scholar
[27]	Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80 Google Scholar
[28]	Zhao M, Gao B, Tang J, Qian H, Wu H 2020 Appl. Phys. Rev. 7 011301 Google Scholar
[29]	Zhang Y, Mao G Q, Zhao X, Li Y, Zhang M, Wu Z, Wu W, Sun H, Guo Y, Wang L, Zhang X, Liu Q, Lv H, Xue K H, Xu G, Miao X, Long S, Liu M 2021 Nat. Commun. 12 7232 Google Scholar
[30]	Kim S J, Kim S B, Jang H W 2021 Science 24 101889
[31]	Tsai S C, Lo H Y, Huang C Y, Wu M C, Tseng Y T, Shen F C, Ho A Y, Chen J Y, Wu W W 2021 Adv. Electron. Mater. 7 2100605 Google Scholar
[32]	Arndt B, Borgatti F, Offi F, Phillips M, Parreira P, Meiners T, Menzel S, Skaja K, Panaccione G, MacLaren D A, Waser R, Dittmann R 2017 Adv. Funct. Mater. 27 1702282 Google Scholar
[33]	Herpers A, Lenser C, Park C, Offi F, Borgatti F, Panaccione G, Menzel S, Waser R, Dittmann R 2014 Adv. Mater. 26 2730 Google Scholar
[34]	Le Gallo M, Sebastian A 2020 J. Phys. D: Appl. Phys. 53 213002 Google Scholar
[35]	Sebastian A, Le Gallo M, Eleftheriou E 2019 J. Phys. D:Appl. Phys. 52 443002 Google Scholar
[36]	Zhang C, Chen Y, Yi M, Zhu Y, Li T, Liu L, Wang L, Xie L, Huang W 2018 Sci. Sin. Inf. 48 115 Google Scholar
[37]	Ho V M, Lee J A, Martin K C 2011 Science 334 623 Google Scholar
[38]	Chen S, Lou Z, Chen D, Shen G 2018 Adv. Mater. 30 1705400 Google Scholar
[39]	Zhou F, Zhou Z, Chen J, Choy T H, Wang J, Zhang N, Lin Z, Yu S, Kang J, Wong H S P, Chai Y 2019 Nat. Nanotechnol. 14 776 Google Scholar
[40]	Zhang L, Yu H, Xiao C, Si J, Xu H, Zhu W, Wang L 2020 Adv. Electron. Mater. 7 2000945
[41]	Wang Y, Gong Y, Yang L, Xiong Z, Lv Z, Xing X, Zhou Y, Zhang B, Su C, Liao Q, Han S T 2021 Adv. Funct. Mater. 31 2100144 Google Scholar
[42]	Yang L, Singh M, Shen S W, Chih K Y, Liu S W, Wu C I, Chu C W, Lin H W 2020 Adv. Funct. Mater. 31 2008259
[43]	Vasileiadis N, Ntinas V, Sirakoulis G C, Dimitrakis P 2021 Materials 14 5223 Google Scholar
[44]	Wang T Y, Meng J L, Li Q X, He Z Y, Zhu H, Ji L, Sun Q Q, Chen L, Zhang D W 2021 Nano Energy 89 106291 Google Scholar
[45]	Li H, Jiang X, Ye W, Zhang H, Zhou L, Zhang F, She D, Zhou Y, Han S T 2019 Nano Energy 65 104000 Google Scholar
[46]	Yang X, Xiong Z, Chen Y, Ren Y, Zhou L, Li H, Zhou Y, Pan F, Han S T 2020 Nano Energy 78 105246 Google Scholar
[47]	Ham S, Choi S, Cho H, Na S I, Wang G 2019 Adv. Funct. Mater. 29 1806646 Google Scholar
[48]	Gao S, Liu G, Yang H, Hu C, Chen Q, Gong G, Xue W, Yi X, Shang J, Li R W 2019 ACS Nano 13 2634 Google Scholar
[49]	Zhao L, Fan Z, Cheng S, Hong L, Li Y, Tian G, Chen D, Hou Z, Qin M, Zeng M, Lu X, Zhou G, Gao X, Liu J M 2019 Adv. Electron. Mater. 6 1900858
[50]	Kumar M, Lim J, Kim S, Seo H 2020 ACS Nano 14 14108 Google Scholar
[51]	Ma F, Zhu Y, Xu Z, Liu Y, Zheng X, Ju S, Li Q, Ni Z, Hu H, Chai Y, Wu C, Kim T W, Li F 2020 Adv. Funct. Mater. 30 1908901 Google Scholar
[52]	Wu Z, Lu J, Shi T, Zhao X, Zhang X, Yang Y, Wu F, Li Y, Liu Q, Liu M 2020 Adv. Mater. 32 2004398 Google Scholar
[53]	Lin Y, Wang Z, Zhang X, Zeng T, Bai L, Kang Z, Wang C, Zhao X, Xu H, Liu Y 2020 NPG Asia Mater. 12 64 Google Scholar
[54]	Huang W, Hang P, Wang Y, Wang K, Han S, Chen Z, Peng W, Zhu Y, Xu M, Zhang Y, Fang Y, Yu X, Yang D, Pi X 2020 Nano Energy 73 104790 Google Scholar
[55]	John R A, Acharya J, Zhu C, Surendran A, Bose S K, Chaturvedi A, Tiwari N, Gao Y, He Y, Zhang K K, Xu M, Leong W L, Liu Z, Basu A, Mathews N 2020 Nat. Commun. 11 3211 Google Scholar
[56]	Shan X, Zhao C, Wang X, Wang Z, Fu S, Lin Y, Zeng T, Zhao X, Xu H, Zhang X, Liu Y 2021 Adv. Sci. 9 2104632
[57]	Liu Y, Wu L, Liu Q, Liu L, Ke S, Peng Z, Shi T, Yuan X, Huang H, Li J, Ye C, Chu P K, Wang J, Yu X F 2021 Adv. Funct. Mater. 32 2110900
[58]	Hu G, An H, Xi J, Lu J, Hua Q, Peng Z 2021 Nano Energy 89 106282 Google Scholar
[59]	Kumar M, Lim J, Seo H 2021 Nano Energy 89 106471 Google Scholar
[60]	Wang S, Wang C Y, Wang P, Wang C, Li Z A, Pan C, Dai Y, Gao A, Liu C, Liu J, Yang H, Liu X, Cheng B, Chen K, Wang Z, Watanabe K, Taniguchi T, Liang S J, Miao F 2021 Natl. Sci. Rev. 8 nwaa172 Google Scholar
[61]	Zhang C, Ye W B, Zhou K, Chen H Y, Yang J Q, Ding G, Chen X, Zhou Y, Zhou L, Li F, Han S T 2019 Adv. Funct. Mater. 29 1808783 Google Scholar
[62]	Kumar M, Singh R, Kang H, Kim S, Seo H 2020 Nano Energy 73 104756 Google Scholar
[63]	Zhang X, Zhuo Y, Luo Q, Wu Z, Midya R, Wang Z, Song W, Wang R, Upadhyay N K, Fang Y, Kiani F, Rao M, Yang Y, Xia Q, Liu Q, Liu M, Yang J J 2020 Nat. Commun. 11 51 Google Scholar
[64]	Tan H, Tao Q, Pande I, Majumdar S, Liu F, Zhou Y, Persson P O A, Rosen J, van Dijken S 2020 Nat. Commun. 11 1369 Google Scholar
[65]	Kim S H, Baek G W, Yoon J, Seo S, Park J, Hahm D, Chang J H, Seong D, Seo H, Oh S, Kim K, Jung H, Oh Y, Baac H W, Alimkhanuly B, Bae W K, Lee S, Lee M, Kwak J, Park J H, Son D 2021 Adv. Mater. 33 2104690 Google Scholar
[66]	Xia Q, Qin Y, Zheng A, Qiu P, Zhang X 2021 Adv. Mater. Interfaces 8 2101068 Google Scholar
[67]	Kumar M, Park J Y, Seo H 2021 Small Methods 5 2100566 Google Scholar
[68]	Wang D, Wang L, Ran W, Zhao S, Yin R, Yan Y, Jiang K, Lou Z, Shen G 2020 Nano Energy 76 105109 Google Scholar
[69]	Shulaker M M, Hills G, Park R S, Howe R T, Saraswat K, Wong H S P, Mitra S 2017 Nature 547 74 Google Scholar
[70]	Vidiš M, Plecenik T, Moško M, Tomašec S, Roch T, Satrapinskyy L, Grančič B, Plecenik A 2019 Appl. Phys. Lett. 115 093504 Google Scholar
[71]	Lee D, Yun M J, Kim K H, Kim S, Kim H D 2021 ACS Sens. 6 4217 Google Scholar
[72]	Ban C, Min X, Xu J, Xiu F, Nie Y, Hu Y, Zhang H, Eginligil M, Liu J, Zhang W, Huang W 2021 Adv. Mater. Technol. 6 2100366 Google Scholar
[73]	Wang T, Huang H M, Wang X X, Guo X 2021 InfoMat. 3 804 Google Scholar
[74]	Gao Z, Chen S, Li R, Lou Z, Han W, Jiang K, Qu F, Shen G 2021 Nano Energy 86 106078 Google Scholar
[75]	Lu Q, Sun F, Dai Y, Wang Y, Liu L, Wang Z, Wang S, Zhang T 2021 Nano Res. 15 423
[76]	Vanarse A, Osseiran A, Rassau A 2016 Front. Neurosci. 10 115
[77]	Wang L, Wang Z, Lin J, Yang J, Xie L, Yi M, Li W, Ling H, Ou C, Huang W 2016 Sci. Rep. 6 35273 Google Scholar
[78]	Sun L, Zhang Y, Hwang G, Jiang J, Kim D, Eshete Y A, Zhao R, Yang H 2018 Nano Lett. 18 3229 Google Scholar
[79]	Wang W, Pedretti G, Milo V, Carboni R, Calderoni A, Ramaswamy N, Spinelli A S, Ielmini D 2018 Sci. Adv. 4 eaat4752 Google Scholar
[80]	Rahman M A, Walia S, Naznee S, Taha M, Nirantar S, Rahman F, Bhaskaran M, Sriram S 2020 Adv. Intell. Syst. 2 2000094 Google Scholar
[81]	Tan H, Zhou Y, Tao Q, Rosen J, van Dijken S 2021 Nat. Commun. 12 1120 Google Scholar
[82]	Mennel L, Symonowicz J, Wachter S, Polyushkin D K, Molina-Mendoza A J, Mueller T 2020 Nature 579 62 Google Scholar
[83]	Mohamad Hadis N S, Abd Manaf A, Ngalim S H, Herman S H 2017 Sens. Bio-Sens. Res. 14 21 Google Scholar
[84]	Pawar A V, Kanapally S S, Kadam K D, Patil S L, Dongle V S, Jadhav S A, Kim S, Dongale T D 2019 J. Mater. Sci. : Mater. Electron. 30 11383 Google Scholar
[85]	Abdul Hadi S, Humood K M, Abi Jaoude M, Abunahla H, Shehhi H F A, Mohammad B 2019 Sci. Rep. 9 9983 Google Scholar
[86]	Song Y G, Suh J M, Park J Y, Kim J E, Chun S Y, Kwon J U, Lee H, Jang H W, Kim S, Kang C Y, Yoon J H 2021 Adv. Sci. 9 2103484

Cited By

期刊类型引用(2)

1.	赵宁，江英华，周贤韬. 基于单光子的高效量子安全直接通信方案. 物理学报. 2022(15): 36-41 . 百度学术
2.	张晨涛，石小涛，朱文新，朱金龙，郝向英，金锐博. 利用域排列算法设计铌酸锂晶体实现3μm中红外波段频域纯态单光子源. 物理学报. 2022(20): 81-87 . 百度学术

其他类型引用(1)

图 1 (a) 传统的感知处理系统架构; (b) 人体五感示意图; (c) 感存算一体化系统架构; (d) 低级感官处理功能; (e) 用于神经网络计算的可重构响应度的感存算一体单元阵列; (f)感存算一体化技术的应用领域

Figure 1. (a) Traditional architecture of sensing and processing; (b) schematic of human sensory system; (c) in-sensor computing architecture; (d) low-level sensory processing functions; (e) in-sensor computing units with reconfigurable responsivity for neural network computing; (f) application fields of in-sensor computing technology.

DownLoad: Full-Size Img PowerPoint

图 2 (a) 两端忆阻器示意图; (b) 数字型忆阻器的典型电压-电流曲线; (c) 模拟型忆阻器的典型电压-电流曲线; (d) 忆阻器常见机理; (e) 数字型和模拟型忆阻器的应用

Figure 2. (a) Schematic of a two-terminal memristor; (b) typical I-V curve of digital memristor; (c) typical I-V curve of analog memristor; (d) three main mechanisms of memristors; (e) application of analog and digital memristor.

DownLoad: Full-Size Img PowerPoint

图 3 (a) 人类视觉系统示意图; (b)突触、神经元和制备的忆阻器示意图; (c)大脑STP和LTP行为的示意图; (d) 人工突触在红光和紫外光刺激下电流响应对比图^[42]; (e) 可见光/紫外光调控突触可塑性示意图; (f) 人工突触在可见光脉冲刺激下的电流响应; (g) 人工突触在紫外光脉冲刺激下的电流响应; (h) 可见光调控的突触STDP功能模拟; (i) 基于忆阻器阵列的视觉感存算一体系统低级处理和高级处理功能示意图^[56]

Figure 3. (a) Schematic of the human visual system; (b) schematic diagrams of the synapse, neuron, and two-terminal memristor; (c) schematic diagram of STP and LTP behavior; (d) comparison of current response of artificial synapses under red light and ultraviolet light^[42]; (e) diagram of synaptic plasticity regulated by visible/ultraviolet light; (f) current response of artificial synapses stimulated by visible light pulses; (g) current response of artificial synapses stimulated by ultraviolet light pulses; (h) simulation of synaptic STDP function regulated by visible light; (i) schematic diagram of low-level and high-level processing functions of visual in-sensor computing system based on memristor array^[56].

DownLoad: Full-Size Img PowerPoint

图 4 (a) 生物触觉感知系统示意图; (b) 压力传感器和Nafion忆阻器集成的人工触觉感知系统; (c) 触觉系统在不同按压力度下的电流响应图; (d) 对采集到的数据进行K邻近分类网络算法处理^[61]; (e) 集成触觉传感器和HfO₂基忆阻器的触觉感觉神经; (f) “SOS”和“TEAM”莫斯电码信号刺激人工触觉神经元的电流响应^[66]; (g) MXene传感器、ADC-LED电路、光电忆阻器构成的神经系统; (h) 光调控的突触PPF模拟^[64]

Figure 4. (a) Schematic illustration of the biological haptic perception system; (b) artificial haptic perception system consisting of pressure sensor and Nafion-based memristor; (c) current response of tactile system at different pressing magnitudes; (d) schematic of processing by K-nearest neighbors algorithm^[61]; (e) tactile sensory nerve consisting of haptic sensor and HfO₂-based memristor; (f) current response of artificial tactile neuron under “SOS” and “TEAM” Morse code signals stimulus^[66]; (g) artificial afferent nerve system integrating MXene sensor, ADC-LED circuit and optoelectronic memristor; (h) simulation of photo-tunable synaptic PPF behavior^[64].

DownLoad: Full-Size Img PowerPoint

图 5 (a) 生物嗅觉感知系统示意图; (b) 人工嗅觉推理系统原理图; (c) W/WO₃/PEDOT:PSS/Pt忆阻器在脉冲下刺激下的电流相应; (d) 所用忆阻器突触真实和理想的电导调制曲线^[73]; (e) 气敏忆阻器机理示意图; (f) SnO₂气敏忆阻器对不同浓度一氧化氮气体的电流响应; (g) 由Ta₂O₅, HfO₂和SnO₂忆阻器组成的气体感知阵列^[71]

Figure 5. (a) Schematic of biological olfactory system; (b) schematic of artificial olfactory inference system; (c) current response of memristor with W/WO₃/PEDOT:PSS/Pt structure under pulse stimulus; (d) experimental and ideal conductance modulation curves of the memristive synapse^[73]; (e) schematic of the gas sensing mechanism; (f) current response of SnO₂ based gas-sensing memristor depending on NO gas concentration; (g) schematic diagram of the gas-sensing array consisting of Ta₂O₅, HfO₂, and SnO₂-based memristors^[71].

DownLoad: Full-Size Img PowerPoint

图 6 (a)柔性MXene-ZnO忆阻器示意图; (b)器件在不同紫外光照强度下的I-V曲线; (c) MXene-ZnO忆阻器受光和湿度调控的电流分布图; (d) 应用光和电脉冲实现突触LTP和LTD行为的模拟; (e) 基于光和湿度调控的忆阻器突触搭建的神经网络示意图^[41]; (f) 多模脉冲感知处理系统工作流程图^[81]

Figure 6. (a) Schematic structure of the flexible MXene-ZnO-based memristive device; (b) I-V curves of device under UV irradiance with different intensities; (c) current profile of MXene-ZnO memristor regulated by light and humidity; (d) simulation of synaptic LTP and LTD behaviors by UV light and electrical pulses; (e) schematic of neural network based on MXene-ZnO-based memristive synapses^[41]; (f) operational diagram of the multimode spiking perception and processing system^[81].

DownLoad: Full-Size Img PowerPoint

表 1 应用于感存算一体化系统的忆阻器的性能比较

Table 1. Performance comparison of memristors applied to in-sensor computing systems.

	忆阻器结构	响应类型	阻变机理	开启/关闭电压/V	开关比	PSC	STP	LTP	具体实现功能	文献
视觉	Ag/CH₃NH₃PbI₃ (OHP)/ITO	—	碘空位导电细丝	0.32/–0.52	1×10⁴	√	√	√	数字识别分类	[47]
	Ni/Al₂O₃/Au	UV	金属导电细丝	1.7/–1.6	1×10²	—	—	—	图像记忆	[38]
	Pd/MoO_x/ITO	UV	界面效应	–2.13	40	√	√	√	图像预处理	[39]
	Ag nanowire/TiO₂	visible light (vis)	界面效应	—	—	√	√	√	广角感知、处理存储	[50]
	glass/ITO/ZnO/PbS/ZnO/Al	UV/infrared ray (IR)	氧空位导电细丝	—	—	√	√	√	数字识别分类	[45]
	ITO/Nb:SrTiO₃	vis	界面效应	—	—	√	√	√	自适应光电突触	[48]
	ITO/PEDOT:PSS/CuSCN/CsPbBr₃ PNs/Au	UV	界面效应	—	—	√	√	√	回溯记忆功能的图像记忆	[51]
	ITO/SnO₂/CsPbCl₃/TAPC/TAPC:MoO₃/MoO₃/Ag/MoO₃	UV/red light	界面效应	—	—	√	√	√	双模式图像检测记忆	[42]
	RGO/GO-NCQD/graphene	UV	氧空位导电细丝	—	—	√	√	√	图像识别	[53]
	ITO/CsPbBr₂I/P₃HT/Ag	vis/NIR	卤素空位导电细丝	0.4/–0.4	> 10	√	√	√	图像预处理	[46]
	ITO/PCBM/MAPbI₃:Si NCs/Spiro-OMeTAD/Au	UV/NIR/vis	界面效应	—	—	√	√	—	图像预处理	[54]
	Au/Ag-TiO₂/FTO	vis/UV	表面等离子体共振效应/金属导电细丝	3.4/–1.8	1×10³	√	√	√	图像预处理及识别	[56]
	Ag/Cu₃P/ITO	λ = 660 nm	金属导电细丝	—	1×10⁴	√	√	√	回溯记忆功能的图像记忆	[57]
	Ni/p-NiO/n-ZnO/Ni	UV	界面效应	—	—	√	—	—	图像记忆	[40]
	ITO/MXene-ZnO/Al	UV	氧空位导电细丝	-0.5/1.2	1×10⁴	√	—	√	图像预处理及数字识别分类	[41]
	ITO/ZnO/Ag	白光	金属导电细丝	2/–2	—	√	√	√	人脸识别	[44]
	NiO/TiO₂/FTO	UV	界面效应	—	> 10	√	√	√	识别分类图像	[59]
触觉	Au/Nafion/ITO	压力	质子迁移	—	—	√	√	—	手写字母识别	[61]
	NiO/ZnO/ITO/PET	应变	界面效应	—	—	√	√	√	外部应变的时空信息处理	[62]
	Si/NbO_x/TiN	压力	晶体NbO₂通道	V_TH = 2.05 VV_H = 1.53 V	—	—	—	—	将压力模拟信号转换为动态振荡频率	[63]
	ITO/ZnO/NSTO	压力	界面效应	—	1×10⁴	√	√	—	识别和记忆手写字母和单词	[64]
	Al/TiO₂/Al	压力	氧空位导电细丝	—	14.2	√	—	√	压力实时感知、学习/推理、反馈可视化图像	[65]
	Pt/HfO₂/TiN	压力	氧空位导电细丝	0.9–1.1/–1	> 100	√	—	√	触觉记忆学习	[66]
	ZnO/PVA基忆阻器	压力	界面效应	V_TH = 3.25 V	1 × 10³	√	√	√	识别压力分布, 触觉可视化	[68]
嗅觉	Pd/W/WO₃/Pd	乙醇、甲烷、乙烯、一氧化碳	氧空位导电细丝	—	—	√	—	√	气体识别	[73]
嗅觉	Ti/rGO-CS/Au	H₂S	界面效应	—	—	√	√	—	气体识别	[75]

DownLoad: CSV

[1]	Lee Y, Lee T W 2019 Acc. Chem. Res. 52 964 Google Scholar
[2]	Zeng M, He Y, Zhang C, Wan Q 2021 Front. Neurosci. 15 690950 Google Scholar
[3]	Wan C, Cai P, Wang M, Qian Y, Huang W, Chen X 2020 Adv. Mater. 32 1902434 Google Scholar
[4]	Zhou F, Chai Y 2020 Nat. Electron. 3 664 Google Scholar
[5]	Wan T, Ma S, Liao F, Fan L, Chai Y 2022 Sci. China Inf. Sci. 65 141401 Google Scholar
[6]	廖付友, 柴扬 2021 物理 50 378 Google Scholar Liao F Y, Chai Y 2021 Physics 50 378 Google Scholar
[7]	Kim Y, Chortos A, Xu W, Liu Y, Oh J Y, Son D, Kang J, Foudeh A M, Zhu C, Lee Y, Niu S, Liu J, Pfattner R, Bao Z, Lee T W 2018 Science 360 998 Google Scholar
[8]	Shi W, Cao J, Zhang Q, Li Y, Xu L 2016 IEEE Internet Things 3 637 Google Scholar
[9]	El-Atab N 2021 Phys. Status Solidi A 219 2100528
[10]	Phong Truong T, Toan Le H, Thi Nguyen T 2020 J. Phys. : Conf. Ser. 1432 012068 Google Scholar
[11]	Li Y, Wang Z, Midya R, Xia Q, Yang J J 2018 J. Phys. D:Appl. Phys. 51 503002 Google Scholar
[12]	Wang Z, Wu H, Burr G W, Hwang C S, Wang K L, Xia Q, Yang J J 2020 Nat. Rev. Mater. 5 173 Google Scholar
[13]	Sebastian A, Le Gallo M, Khaddam-Aljameh R, Eleftheriou E 2020 Nat. Nanotechnol. 15 529 Google Scholar
[14]	Ielmini D, Wong H S P 2018 Nat. Electron. 1 333 Google Scholar
[15]	Wang J, Lv Z, Xing X, Li X, Wang Y, Chen M, Pang G, Qian F, Zhou Y, Han S T 2020 Adv. Funct. Mater. 30 1909114 Google Scholar
[16]	Zidan M A, Strachan J P, Lu W D 2018 Nat. Electron. 1 22 Google Scholar
[17]	Zhang Y, Wang Z, Zhu J, Yang Y, Rao M, Song W, Zhuo Y, Zhang X, Cui M, Shen L, Huang R, Yang J J 2020 Appl. Phys. Rev. 7 011308 Google Scholar
[18]	Sun K, Chen J, Yan X 2020 Adv. Funct. Mater. 31 2006773
[19]	Lv Z, Wang Y, Chen J, Wang J, Zhou Y, Han S T 2020 Chem. Rev. 120 3941 Google Scholar
[20]	李锟, 曹荣荣, 孙毅, 刘森, 李清江, 徐晖 2019 微纳电子与智能制造 1 87 Li K, Cao R, Sun Y, Liu S, Li Q, Xu H 2019 Micro/nano Electronics and Intelligent Manufacturing 1 87
[21]	Ji X, Zhao X, Tan M C, Zhao R 2020 Adv. Intell. Syst. 2 1900118 Google Scholar
[22]	Sun F, Lu Q, Feng S, Zhang T 2021 ACS Nano 15 3875 Google Scholar
[23]	Carrara S 2021 IEEE Sens. J. 21 12370 Google Scholar
[24]	张章, 李超, 韩婷婷, 许傲, 程心, 刘钢, 解光军 2021 电子与信息学报 43 1498 Google Scholar Zhang Z, Li C, Han T T, Xu A, Cheng X, Liu G, Xie G J 2021 Journal of Electronics and Information Technology 43 1498 Google Scholar
[25]	Zhu Y, Zhu Y, Mao H, He Y, Jiang S, Zhu L, Chen C, Wan C, Wan Q 2021 J. Phys. D:Appl. Phys. 55 053002
[26]	Tripathy A, Nine M J, Losic D, Silva F S 2021 Mater. Sci. Eng. R. Rep. 146 100647 Google Scholar
[27]	Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80 Google Scholar
[28]	Zhao M, Gao B, Tang J, Qian H, Wu H 2020 Appl. Phys. Rev. 7 011301 Google Scholar
[29]	Zhang Y, Mao G Q, Zhao X, Li Y, Zhang M, Wu Z, Wu W, Sun H, Guo Y, Wang L, Zhang X, Liu Q, Lv H, Xue K H, Xu G, Miao X, Long S, Liu M 2021 Nat. Commun. 12 7232 Google Scholar
[30]	Kim S J, Kim S B, Jang H W 2021 Science 24 101889
[31]	Tsai S C, Lo H Y, Huang C Y, Wu M C, Tseng Y T, Shen F C, Ho A Y, Chen J Y, Wu W W 2021 Adv. Electron. Mater. 7 2100605 Google Scholar
[32]	Arndt B, Borgatti F, Offi F, Phillips M, Parreira P, Meiners T, Menzel S, Skaja K, Panaccione G, MacLaren D A, Waser R, Dittmann R 2017 Adv. Funct. Mater. 27 1702282 Google Scholar
[33]	Herpers A, Lenser C, Park C, Offi F, Borgatti F, Panaccione G, Menzel S, Waser R, Dittmann R 2014 Adv. Mater. 26 2730 Google Scholar
[34]	Le Gallo M, Sebastian A 2020 J. Phys. D: Appl. Phys. 53 213002 Google Scholar
[35]	Sebastian A, Le Gallo M, Eleftheriou E 2019 J. Phys. D:Appl. Phys. 52 443002 Google Scholar
[36]	Zhang C, Chen Y, Yi M, Zhu Y, Li T, Liu L, Wang L, Xie L, Huang W 2018 Sci. Sin. Inf. 48 115 Google Scholar
[37]	Ho V M, Lee J A, Martin K C 2011 Science 334 623 Google Scholar
[38]	Chen S, Lou Z, Chen D, Shen G 2018 Adv. Mater. 30 1705400 Google Scholar
[39]	Zhou F, Zhou Z, Chen J, Choy T H, Wang J, Zhang N, Lin Z, Yu S, Kang J, Wong H S P, Chai Y 2019 Nat. Nanotechnol. 14 776 Google Scholar
[40]	Zhang L, Yu H, Xiao C, Si J, Xu H, Zhu W, Wang L 2020 Adv. Electron. Mater. 7 2000945
[41]	Wang Y, Gong Y, Yang L, Xiong Z, Lv Z, Xing X, Zhou Y, Zhang B, Su C, Liao Q, Han S T 2021 Adv. Funct. Mater. 31 2100144 Google Scholar
[42]	Yang L, Singh M, Shen S W, Chih K Y, Liu S W, Wu C I, Chu C W, Lin H W 2020 Adv. Funct. Mater. 31 2008259
[43]	Vasileiadis N, Ntinas V, Sirakoulis G C, Dimitrakis P 2021 Materials 14 5223 Google Scholar
[44]	Wang T Y, Meng J L, Li Q X, He Z Y, Zhu H, Ji L, Sun Q Q, Chen L, Zhang D W 2021 Nano Energy 89 106291 Google Scholar
[45]	Li H, Jiang X, Ye W, Zhang H, Zhou L, Zhang F, She D, Zhou Y, Han S T 2019 Nano Energy 65 104000 Google Scholar
[46]	Yang X, Xiong Z, Chen Y, Ren Y, Zhou L, Li H, Zhou Y, Pan F, Han S T 2020 Nano Energy 78 105246 Google Scholar
[47]	Ham S, Choi S, Cho H, Na S I, Wang G 2019 Adv. Funct. Mater. 29 1806646 Google Scholar
[48]	Gao S, Liu G, Yang H, Hu C, Chen Q, Gong G, Xue W, Yi X, Shang J, Li R W 2019 ACS Nano 13 2634 Google Scholar
[49]	Zhao L, Fan Z, Cheng S, Hong L, Li Y, Tian G, Chen D, Hou Z, Qin M, Zeng M, Lu X, Zhou G, Gao X, Liu J M 2019 Adv. Electron. Mater. 6 1900858
[50]	Kumar M, Lim J, Kim S, Seo H 2020 ACS Nano 14 14108 Google Scholar
[51]	Ma F, Zhu Y, Xu Z, Liu Y, Zheng X, Ju S, Li Q, Ni Z, Hu H, Chai Y, Wu C, Kim T W, Li F 2020 Adv. Funct. Mater. 30 1908901 Google Scholar
[52]	Wu Z, Lu J, Shi T, Zhao X, Zhang X, Yang Y, Wu F, Li Y, Liu Q, Liu M 2020 Adv. Mater. 32 2004398 Google Scholar
[53]	Lin Y, Wang Z, Zhang X, Zeng T, Bai L, Kang Z, Wang C, Zhao X, Xu H, Liu Y 2020 NPG Asia Mater. 12 64 Google Scholar
[54]	Huang W, Hang P, Wang Y, Wang K, Han S, Chen Z, Peng W, Zhu Y, Xu M, Zhang Y, Fang Y, Yu X, Yang D, Pi X 2020 Nano Energy 73 104790 Google Scholar
[55]	John R A, Acharya J, Zhu C, Surendran A, Bose S K, Chaturvedi A, Tiwari N, Gao Y, He Y, Zhang K K, Xu M, Leong W L, Liu Z, Basu A, Mathews N 2020 Nat. Commun. 11 3211 Google Scholar
[56]	Shan X, Zhao C, Wang X, Wang Z, Fu S, Lin Y, Zeng T, Zhao X, Xu H, Zhang X, Liu Y 2021 Adv. Sci. 9 2104632
[57]	Liu Y, Wu L, Liu Q, Liu L, Ke S, Peng Z, Shi T, Yuan X, Huang H, Li J, Ye C, Chu P K, Wang J, Yu X F 2021 Adv. Funct. Mater. 32 2110900
[58]	Hu G, An H, Xi J, Lu J, Hua Q, Peng Z 2021 Nano Energy 89 106282 Google Scholar
[59]	Kumar M, Lim J, Seo H 2021 Nano Energy 89 106471 Google Scholar
[60]	Wang S, Wang C Y, Wang P, Wang C, Li Z A, Pan C, Dai Y, Gao A, Liu C, Liu J, Yang H, Liu X, Cheng B, Chen K, Wang Z, Watanabe K, Taniguchi T, Liang S J, Miao F 2021 Natl. Sci. Rev. 8 nwaa172 Google Scholar
[61]	Zhang C, Ye W B, Zhou K, Chen H Y, Yang J Q, Ding G, Chen X, Zhou Y, Zhou L, Li F, Han S T 2019 Adv. Funct. Mater. 29 1808783 Google Scholar
[62]	Kumar M, Singh R, Kang H, Kim S, Seo H 2020 Nano Energy 73 104756 Google Scholar
[63]	Zhang X, Zhuo Y, Luo Q, Wu Z, Midya R, Wang Z, Song W, Wang R, Upadhyay N K, Fang Y, Kiani F, Rao M, Yang Y, Xia Q, Liu Q, Liu M, Yang J J 2020 Nat. Commun. 11 51 Google Scholar
[64]	Tan H, Tao Q, Pande I, Majumdar S, Liu F, Zhou Y, Persson P O A, Rosen J, van Dijken S 2020 Nat. Commun. 11 1369 Google Scholar
[65]	Kim S H, Baek G W, Yoon J, Seo S, Park J, Hahm D, Chang J H, Seong D, Seo H, Oh S, Kim K, Jung H, Oh Y, Baac H W, Alimkhanuly B, Bae W K, Lee S, Lee M, Kwak J, Park J H, Son D 2021 Adv. Mater. 33 2104690 Google Scholar
[66]	Xia Q, Qin Y, Zheng A, Qiu P, Zhang X 2021 Adv. Mater. Interfaces 8 2101068 Google Scholar
[67]	Kumar M, Park J Y, Seo H 2021 Small Methods 5 2100566 Google Scholar
[68]	Wang D, Wang L, Ran W, Zhao S, Yin R, Yan Y, Jiang K, Lou Z, Shen G 2020 Nano Energy 76 105109 Google Scholar
[69]	Shulaker M M, Hills G, Park R S, Howe R T, Saraswat K, Wong H S P, Mitra S 2017 Nature 547 74 Google Scholar
[70]	Vidiš M, Plecenik T, Moško M, Tomašec S, Roch T, Satrapinskyy L, Grančič B, Plecenik A 2019 Appl. Phys. Lett. 115 093504 Google Scholar
[71]	Lee D, Yun M J, Kim K H, Kim S, Kim H D 2021 ACS Sens. 6 4217 Google Scholar
[72]	Ban C, Min X, Xu J, Xiu F, Nie Y, Hu Y, Zhang H, Eginligil M, Liu J, Zhang W, Huang W 2021 Adv. Mater. Technol. 6 2100366 Google Scholar
[73]	Wang T, Huang H M, Wang X X, Guo X 2021 InfoMat. 3 804 Google Scholar
[74]	Gao Z, Chen S, Li R, Lou Z, Han W, Jiang K, Qu F, Shen G 2021 Nano Energy 86 106078 Google Scholar
[75]	Lu Q, Sun F, Dai Y, Wang Y, Liu L, Wang Z, Wang S, Zhang T 2021 Nano Res. 15 423
[76]	Vanarse A, Osseiran A, Rassau A 2016 Front. Neurosci. 10 115
[77]	Wang L, Wang Z, Lin J, Yang J, Xie L, Yi M, Li W, Ling H, Ou C, Huang W 2016 Sci. Rep. 6 35273 Google Scholar
[78]	Sun L, Zhang Y, Hwang G, Jiang J, Kim D, Eshete Y A, Zhao R, Yang H 2018 Nano Lett. 18 3229 Google Scholar
[79]	Wang W, Pedretti G, Milo V, Carboni R, Calderoni A, Ramaswamy N, Spinelli A S, Ielmini D 2018 Sci. Adv. 4 eaat4752 Google Scholar
[80]	Rahman M A, Walia S, Naznee S, Taha M, Nirantar S, Rahman F, Bhaskaran M, Sriram S 2020 Adv. Intell. Syst. 2 2000094 Google Scholar
[81]	Tan H, Zhou Y, Tao Q, Rosen J, van Dijken S 2021 Nat. Commun. 12 1120 Google Scholar
[82]	Mennel L, Symonowicz J, Wachter S, Polyushkin D K, Molina-Mendoza A J, Mueller T 2020 Nature 579 62 Google Scholar
[83]	Mohamad Hadis N S, Abd Manaf A, Ngalim S H, Herman S H 2017 Sens. Bio-Sens. Res. 14 21 Google Scholar
[84]	Pawar A V, Kanapally S S, Kadam K D, Patil S L, Dongle V S, Jadhav S A, Kim S, Dongale T D 2019 J. Mater. Sci. : Mater. Electron. 30 11383 Google Scholar
[85]	Abdul Hadi S, Humood K M, Abi Jaoude M, Abunahla H, Shehhi H F A, Mohammad B 2019 Sci. Rep. 9 9983 Google Scholar
[86]	Song Y G, Suh J M, Park J Y, Kim J E, Chun S Y, Kwon J U, Lee H, Jang H W, Kim S, Kang C Y, Yoon J H 2021 Adv. Sci. 9 2103484

[1]	GAO Yukun, ZHAO Jie, ZHOU Jingjing, ZHOU Jing. Finite element prediction and device performance of piezoelectric fiber composite based smart sensor. Acta Physica Sinica, 2025, 74(5): 057701. doi: 10.7498/aps.74.20241379
[2]	Chen Kai-Hui, Fan Zhen, Dong Shuai, Li Wen-Jie, Chen Yi-Hong, Tian Guo, Chen De-Yang, Qin Ming-Hui, Zeng Min, Lu Xu-Bing, Zhou Guo-Fu, Gao Xing-Sen, Liu Jun-Ming. Perovskite-phase interfacial intercalated layer-induced performance enhancement in SrFeO_x-based memristors. Acta Physica Sinica, 2023, 72(9): 097301. doi: 10.7498/aps.72.20221934
[3]	Ren Kuan, Zhang Wo-Yu, Wang Fei, Guo Ze-Yu, Shang Da-Shan. Next-generation reservoir computing based on memristor array. Acta Physica Sinica, 2022, 71(14): 140701. doi: 10.7498/aps.71.20220082
[4]	Wen Xin-Yu, Wang Ya-Sai, He Yu-Hui, Miao Xiang-Shui. Memristive brain-like computing. Acta Physica Sinica, 2022, 71(14): 140501. doi: 10.7498/aps.71.20220666
[5]	Shan Xuan-Yu, Wang Zhong-Qiang, Xie Jun, Zheng Jia-Hui, Xu Hai-Yang, Liu Yi-Chun. Recent progress in optoelectronic memristive devices for in-sensor computing. Acta Physica Sinica, 2022, 71(14): 148701. doi: 10.7498/aps.71.20220350
[6]	Hu Wei, Liao Jian-Bin, Du Yong-Qian. An analytic modeling strategy for memristor cell applicable to large-scale memristive networks. Acta Physica Sinica, 2021, 70(17): 178505. doi: 10.7498/aps.70.20210116
[7]	Ding Zi-Ping, Liao Jian-Fei, Zeng Ze-Kai. A new type of ultra-broadband microstructured fiber sensor based on surface plasmon resonance. Acta Physica Sinica, 2021, 70(7): 074207. doi: 10.7498/aps.70.20201477
[8]	Pang Hui-Zhong, Wang Xin, Wang Jun-Lin, Wang Zong-Li, Liu Su-Yalatu, Tian Hu-Qiang. Sensing characteristics of dual band terahertz metamaterial absorber sensor. Acta Physica Sinica, 2021, 70(16): 168101. doi: 10.7498/aps.70.20210062
[9]	Shi Chen-Yang, Min Guang-Zong, Liu Xiang-Yang. Research progress of protein-based memristor. Acta Physica Sinica, 2020, 69(17): 178702. doi: 10.7498/aps.69.20200617
[10]	Shao Nan, Zhang Sheng-Bing, Shao Shu-Yuan. Mathematical model of memristor with sensory memory. Acta Physica Sinica, 2019, 68(1): 018501. doi: 10.7498/aps.68.20181577
[11]	Shao Nan, Zhang Sheng-Bing, Shao Shu-Yuan. Analysis of memristor model with learning-experience behavior. Acta Physica Sinica, 2019, 68(19): 198502. doi: 10.7498/aps.68.20190808
[12]	Chen Yi-Hao, Xu Wei, Wang Yu-Qi, Wan Xiang, Li Yue-Feng, Liang Ding-Kang, Lu Li-Qun, Liu Xin-Wei, Lian Xiao-Juan, Hu Er-Tao, Guo Yu-Feng, Xu Jian-Guang, Tong Yi, Xiao Jian. Fabrication of synaptic memristor based on two-dimensional material MXene and realization of both long-term and short-term plasticity. Acta Physica Sinica, 2019, 68(9): 098501. doi: 10.7498/aps.68.20182306
[13]	Xu Wei, Wang Yu-Qi, Li Yue-Feng, Gao Fei, Zhang Miao-Cheng, Lian Xiao-Juan, Wan Xiang, Xiao Jian, Tong Yi. Design of novel memristor-based neuromorphic circuit and its application in classical conditioning. Acta Physica Sinica, 2019, 68(23): 238501. doi: 10.7498/aps.68.20191023
[14]	Yu Ya-Juan, Wang Zai-Hua. A fractional-order memristor model and the fingerprint of the simple series circuits including a fractional-order memristor. Acta Physica Sinica, 2015, 64(23): 238401. doi: 10.7498/aps.64.238401
[15]	Liao Wen-Ying, Fan Wan-De, Li Hai-Peng, Sui Jia-Nan, Cao Xue-Wei. Quasi-crystal photonic fiber surface plasmon resonance sensor. Acta Physica Sinica, 2015, 64(6): 064213. doi: 10.7498/aps.64.064213
[16]	Meng Fan-Yi, Duan Shu-Kai, Wang Li-Dan, Hu Xiao-Fang, Dong Zhe-Kang. An improved WOx memristor model with synapse characteristic analysis. Acta Physica Sinica, 2015, 64(14): 148501. doi: 10.7498/aps.64.148501
[17]	Liu Dong-Qing, Cheng Hai-Feng, Zhu Xuan, Wang Nan-Nan, Zhang Chao-Yang. Research progress of memristors and memristive mechanism. Acta Physica Sinica, 2014, 63(18): 187301. doi: 10.7498/aps.63.187301
[18]	Liang Yan, Yu Dong-Sheng, Chen Hao. A novel meminductor emulator based on analog circuits. Acta Physica Sinica, 2013, 62(15): 158501. doi: 10.7498/aps.62.158501
[19]	Xu Bi-Rong. A simplest parallel chaotic system of memristor. Acta Physica Sinica, 2013, 62(19): 190506. doi: 10.7498/aps.62.190506
[20]	Jia Lin-Nan, Huang An-Ping, Zheng Xiao-Hu, Xiao Zhi-Song, Wang Mei. Progress of memristor modulated by interfacial effect. Acta Physica Sinica, 2012, 61(21): 217306. doi: 10.7498/aps.61.217306

期刊类型引用(2)

1.	赵宁，江英华，周贤韬. 基于单光子的高效量子安全直接通信方案. 物理学报. 2022(15): 36-41 . 百度学术
2.	张晨涛，石小涛，朱文新，朱金龙，郝向英，金锐博. 利用域排列算法设计铌酸锂晶体实现3μm中红外波段频域纯态单光子源. 物理学报. 2022(20): 81-87 . 百度学术

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板