Nonlinear behavior in the hopping transport of interacting charges enables reconfigurable logic in disordered dopant network devices, where voltages applied at control electrodes tune the relation between voltages applied at input electrodes and the current measured at an output electrode. From kinetic Monte Carlo simulations we analyze the critical nonlinear aspects of variable-range hopping transport for realizing Boolean logic gates in these devices on three levels. First, we quantify the occurrence of individual gates for random choices of control voltages. We find that linearly inseparable gates such as the XOR gate are less likely to occur than linearly separable gates such as the AND gate, despite the fact that the number of different regions in the multidimensional control voltage space for which AND or XOR gates occur is comparable. Second, we use principal component analysis to characterize the distribution of the output current vectors for the (00,10,01,11) logic input combinations in terms of eigenvectors and eigenvalues of the output covariance matrix. This allows a simple and direct comparison of the behavior of different simulated devices and a comparison to experimental devices. Third, we quantify the nonlinearity in the distribution of the output current vectors necessary for realizing Boolean functionality by introducing three nonlinearity indicators. The analysis provides a physical interpretation of the effects of changing the hopping distance and temperature and is used in a comparison with data generated by a deep neural network trained on a physical device.

翻译：相互作用电荷在跳跃输运中的非线性行为使得无序掺杂剂网络器件能够实现可重构逻辑，其中控制电极施加的电压调节输入电极电压与输出电极测量电流之间的关系。通过动力学蒙特卡洛模拟，我们从三个层面分析了实现布尔逻辑门所需的关键非线性方面。首先，我们量化了随机选择控制电压时单个逻辑门出现的概率。研究发现，尽管XOR等线性不可分门与AND等线性可分门在控制电压多维空间中出现的区域数量相当，但前者出现的概率显著低于后者。其次，我们采用主成分分析，通过输出电流协方差矩阵的本征向量和本征值，刻画了(00,10,01,11)四种逻辑输入组合对应的输出电流向量分布特征。该方法能够简单直接地比较不同模拟器件的行为，并与实验器件进行对比。最后，我们引入三个非线性指标，量化了实现布尔逻辑功能所需的输出电流向量非线性分布程度。该分析为跳跃距离和温度变化的影响提供了物理解释，并用于与基于物理器件训练的深度神经网络生成数据进行对比。