Investigation of Low Frequency Noise in CryoCMOS devices through Statistical Single Defect Spectroscopy

TL;DR

This work tackles the nontrivial origin of low-frequency and 1/f noise in CryoCMOS by statistically interrogating single defects across a large nMOS ensemble. Using ML-assisted RTN extraction and time-domain noise reconstruction, the authors reveal a trimodal distribution of threshold shifts at cryogenic temperatures, interpret the modes via percolation theory, and quantify defect localization to oxide layers, with bulk HfO2 defects driving most RTN activity at 5 K while interface defects dominate LFN. Crucially, there is no observed correlation between defect time constants and step heights, undermining elastic tunnelling as the governing mechanism. The findings enhance understanding of defect dynamics in multi-layer oxides at cryogenic temperatures and have implications for modeling and reliability of CryoCMOS systems in quantum-classical integration.

Abstract

High 1/f noise in CryoCMOS devices is a critical parameter to keep under control in the design of complex circuits for low temperatures applications. Current models predict the 1/f noise to scale linearly with temperature, and gate oxide defects are expected to freeze out at cryogenic temperatures. Nevertheless, it has been repeatedly observed that 1/f noise deviates from the predicted behaviour and that gate oxide defects are still active around 4.2 K, producing random telegraph noise. In this paper, we probe single gate oxide defects in 2500 nMOS devices down to 5 K in order to investigate the origin of 1/f noise in CryoCMOS devices. From our results, it is clear that the number of defects active at cryogenic temperatures resulting in random telegraph noise is larger than at 300 K. Threshold voltage shifts due to charged defects are shown to be exponentially distributed, with different modalities across temperatures and biases: from monomodal at 300 K to trimodal below 100 K. The third mode is interpreted in the framework of percolation theory. By fitting these distributions, it is shown that more than 80% of the detected defects belongs to the oxide bulk. Afterwards, starting from the raw data in time domain, we reconstruct the low frequency noise spectra, highlighting the contributions of defects belonging to different branches and, therefore, to different oxide layers. This analysis shows that, although interface traps and large defects associated with the third mode are the main sources of 1/f noise at 5 K, bulk oxide defects still contribute significantly to low-frequency noise at cryogenic temperatures. Finally, we show that defect time constants and step heights are uncorrelated, proving that elastic tunnelling model for charge trapping is not accurate.

Figures (6)

• Figure 1: Fig.1 (a) The measured chip consists of 2500 individually addressable HKMG nMOS devices (WxL=90 nm x 28 nm). (b) Transfer characteristics $I_\mathrm{d}(V_\mathrm{gs})$ of all the devices from 300 K down to 5 K. (c) Drain current at stationary overdrive voltage showing a single defect, two levels RTN. (d) A similar measurement but showing two defects RTN.
• Figure 2: Fig.2 (a) At T=300 K, the $\Delta V_\mathrm{th}$ CCDF follows a monomodal exponential distribution, even though the oxide gate stack consists of $\mathrm{HfO_2/SiO_2}$. Small $\mathrm{HfO_2}$ defects are probably hidden in the background noise. At T=5 K, two additional modes appear. The smallest mode is now visible because of the smaller background noise and the higher measurement sensitivity due to the larger $g_m$. The large defects belonging to the third mode are likely caused by the higher sensitivity to disorder at cryogenic temperatures. (b) PDF of the components of the trimodal exponential $\Delta V_\mathrm{th}$ distribution at 5K a $V_\mathrm{ov}=0$ V. Each mode consists of an exponential distribution with given $\eta$ and $n$. The first mode is attributed to defects belonging to $\mathrm{HfO_2}$; the second mode is attributed to defects belonging to $\mathrm{SiO_2}$; the third mode is attributed to defects abnormally large. (c) Probability of a defect falling within particular range of values, defined by the calculated crossing points $x_\mathrm{CP1}$, $x_\mathrm{CP2}$. More than 80% of detected defects have $\Delta V_\mathrm{th} \leqslant 2.8$ mV, and more than 60% of defects within this interval belongs to $\mathrm{HfO_2}$, showing that bulk defects activity is still predominant at T=5 K. (d) $\eta (T)$ extracted from fitting the CCDF at different T. Its increase at low temperatures and at $V_\mathrm{ov}=0$ V is attributed to a larger sensitivity to disorder at cryogenic temperatures.
• Figure 3: Fig.3 (a) Drain current density simulated with a commercial TCAD tool at $\mathrm{T=4.2}$ K. At $V_\mathrm{gs}<V_\mathrm{th}$, the drain current is not homogeneous due to the presence of both random dopants and oxide defects. This non homogeneity translates in the formation of conductive paths, where carriers can flow through, and insulating regions, where carriers are forbidden to flow. Percolation generally increases at cryogenic temperatures, since particles' kinetic energy decreases and surface potential fluctuations can provoke the formation of localized states which, in turns, are responsible for the anomalously large $\Delta V_\mathrm{th}$ observed. (b) By increasing $V_\mathrm{ov}$, the channel gets stronger and, therefore, more homogeneous, and percolation is reduced. (c) At higher $V_\mathrm{ov}$, the third mode disappears from the CCDF, since the electrostatic impact of defects is reduced by the stronger channel. (d) $\eta_\mathrm{SiO_2}$ is rather constant as function of $V_\mathrm{ov}$, independently on the temperature.
• Figure 4: Fig.4 (a) Comparison between the noise power $N_\mathrm{P}$ calculated by considering all the measured traces and by considering just the traces with detectable RTN. $N_\mathrm{P}$ values are comparable, meaning that the background noise of the smart array is negligible, and most of the noise comes from the detected RTN traces. (b) $S_\mathrm{Vg}$ of the entire array across temperature. The spectra are the linear mean of all the power spectral densities of individual RTN traces. The resulting spectra are 1/f, even at T=5 K. The noise increase as the temperature is lowered, consistently with what has been measured on large area devices. (c) $S_\mathrm{Vg}(V_\mathrm{ov})$ for different temperatures. The temperature trend at $V_\mathrm{ov}=0 V$ is due to a larger percolation in this bias regime, since the channel is not full formed. With increasing $V_\mathrm{ov}$, percolation effects are mitigated, and $S_\mathrm{Vg}$ decreases. (d) Contribution of different defects branches to $S_\mathrm{Vg}$ at T=5 K. As $V_\mathrm{ov}$ increases, $\mathrm{SiO_2}$ defects become the main source of noise. Indeed, on one hand, higher overdrives reduce percolation effect, and on the other hand the defects bands probed change with $V_\mathrm{ov}$.
• Figure 5: Fig.5 (a) Plot of $f_\mathrm{T}(1-f_\mathrm{T})$ versus $E_\mathrm{T}-E_\mathrm{F}$ for different temperatures. The coloured area under the curves represents the integral and it is equal to $k_B\mathrm{T}$. The figure is taken from asanovski_understanding_2023. (b) The total number of detected defects $n$ increases rapidly at $\mathrm{T} < 300$ K.