Indexing current-voltage characteristics using a hash function

TL;DR

An indexing method for current–voltage characteristics that assigns proximity numbers to similar devices and the application of the locality-sensitive hashing (LSH) algorithm to Coulomb blockade phenomena observed in pMOSFETs and nanowire transistors is demonstrated.

Abstract

Differentiating between devices of the same size is essential for ensuring their reliability. However, identifying subtle differences can be challenging, particularly when the devices share similar characteristics, such as transistors on a wafer. To address this issue, we propose an indexing method for current-voltage characteristics that assigns proximity numbers to similar devices. Specifically, we demonstrate the application of the locality-sensitive hashing (LSH) algorithm to Coulomb blockade phenomena observed in PMOSFETs and nanowire transistors. In this approach, lengthy data on current characteristics are replaced with hashed IDs, facilitating identification of individual devices, and streamlining the management of a large number of devices.

Figures (7)

• Figure 1: (a)(b)(c) Coulomb diamonds were observed in the differential conductance characteristics $(dI_D/dV_S)$ of trap states in a conventional pMOSFET with a channel length $L = 125 \, \text{nm}$ and width $W = 220 \, \text{nm}$ at a temperature of $T = 1.54 \, \text{K}$. A silicon oxynitride layer was used for the gate dielectric. Although these devices share the same layout parameters (length and width), they exhibit different characteristics owing to variations in the distribution of trap sites. Additionally, the hash values for datasets (a), (b), and (c) are provided in section (d). $N_i$ represents the number of data points for each dataset.
• Figure 2: $I_{\rm D}$-$V_{\rm G}$ characteristics of the GAA silicon nanowire transistor at $V_{\rm D}=50$mV. (a)(b) 3 nm width, and (c)(d) 4 nm width. No.141 (marked by a red circle) in both (a)(b) deviate from others. (e) Schematic of GAA silicon nanowire FET, where $L$=100 nm, $H$=3 nm.
• Figure 3: (a) Euclidean distances between the datasets from day 1 and day 2 for 3 and 4 nm nanowire transistors. "3nm & 4nm" represents the Euclidean distance between the datasets of 3 nm-day1 and 4 nm-day1. (b) Differences in the hash values for the same dataset as in (a) for nanowire transistors. The random numbers $\{ {\bf a}, b\}$ are varied, where "[0]" and "[10]" correspond to the results from the first and 11 th sets of random numbers.
• Figure 4: (a) Hash values for the 3 and 4 nm nanowire transistors when the random numbers ${\bf a}$ and $b$ are changed. varied. The dotted circle highlights chip No. 141, corresponding to Fig. \ref{['fignanowire']}.(b)Histogram of hash value distributions. (c)Distance ratio defined Eq.(3) as the function of $w$.
• Figure 5: (a) Distance of hash values of $I_{\rm D}$-$V_{\rm D}$ of the 3 and 4 nm nanowires for different $V_{\rm G}s$. (b) Distance of hash values of $I_{\rm D}$-$V_{\rm D}$ of the 3 and 4 nm nanowires when the data (a) are treated as a vectors.