The Stochastic Origin of Random Telegraph Noise

In this paper, random telegraph noise (RTN) in advanced multi-Fin bulk FinFETs are comprehensively studied for the first time. Based on the statistical experiments, the complete categories of simple and complex RTNs are identified and analyzed in details. Especially, the anomalous “reversal RTN” induced by 2 metastable states in single oxide trap, are found not rare, but appears at a certain percentage, which provides a unique opportunity for statistically studying the metastable states directly from RTN measurements. In addition, anomalous layout dependence of RTN amplitudes are observed, with respects to Fin number. The results are helpful for deep understanding of reliability physics and robust circuit design against RTN.

As the generally-accepted simple understanding, the random telegraph noise (RTN) induced by a single trap is explained by the “normal” two-state trap model, and the RTNs caused by two or more traps in one device are regarded as the independent superposition effect of these traps. While in real cases, both the above points cannot illustrate many complex RTN (cRTN) results in practice. In this paper, two categories of complex RTNs, which are induced by the metastable trap-states and the trap coupling effect, respectively, are investigated based on experimental results in detail. The RTN with metastable states are explained based on the observed “anomalous” RTN data. The physical mechanisms of the trap coupling effect on RTN amplitudes and time constants are studied based on experiments. The results are helpful for comprehensive understanding and modeling of RTN and switching traps, thus is useful for the accurate evaluation on the impacts of RTN on nanoscale CMOS devices and circuits.

As well known, the implementation of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{high}-\kappa$</tex> dielectrics (e.g., <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{HfO}_{2})$</tex> in nanoscale devices is unavoidable to cope with the device scaling required by the market. Nevertheless, due to the higher defect density compared to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{SiO}_{2}$</tex> , hafnium oxide exhibits stronger and more complex Random Telegraph Noise (RTN), namely one of the most relevant defect-related reliability issues in ultra-thin oxides. However, depending on the device type, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{HfO}_{2}$</tex> can be characterized by different defect density and therefore leading to a different RTN signals. In particular, in Resistive Random Access Memory (RRAM) devices RTN arises very often but shows a high degree of complexity (e.g., multilevel, anomalous, temporary RTN) and instabilities [3], [4] which hinders its characterization. Conversely, in MOSFETs RTN has a small occurrence and it typically exhibits a simple behavior (i.e., 2-level signal) if detected. In this work, we fully analyze such phenomena in different devices providing a unified and physics-based framework which is also confirmed by experiments. The results of this study will be crucial for the design of new devices and circuits for emerging RTN-based applications, such as True Random Number Generators (TRNGs).

In this paper, based on the complex random telegraph noise (RTN) data in FinFETs, the impacts of the trap coupling effect on RTN amplitude are studied statistically. The coupling effect is found to be enhanced by the double-side coupling mechanism in FinFETs. The non-monotonic V g dependence of amplitude coupling strength is observed for the first time, which is contributed by the evolution of channel percolation paths. In addition, the impacts of HCI and NBTI stresses on the coupling strength are studied. Based on the new understandings on coupling effect in FinFETs, the impacts of amplitude coupling on typical digital circuits are also investigated. The results are helpful for comprehensive understanding of the RTN coupling mechanism in nanoscale FinFET technology and RTN-aware circuit design.

Some memristors with metal/insulator/metal (MIM) structure have exhibited random telegraph noise (RTN) current signals, which makes them ideal to build true random number generators (TRNG) for advanced data encryption. However, there is still no clear guide on how essential manufacturing parameters like materials selection, thicknesses, deposition methods, and device lateral size can influence the quality of the RTN signal. In this paper, an exhaustive statistical analysis on the quality of the RTN signals produced by different MIM‐like memristors is reported, and straightforward guidelines for the fabrication of memristors with enhanced RTN performance are presented, which are: i) Ni and Ti electrodes show better RTN than Au electrodes, ii) the 50 μm × 50 μm devices show better RTN than the 5 μm × 5 μm ones, iii) TiO2 shows better RTN than HfO2 and Al2O3, iv) sputtered‐oxides show better RTN than ALD‐oxides, and v) 10 nm thick oxides show better RTN than 5 nm thick oxides. The RTN signals recorded have been used as entropy sources in high‐throughput TRNG circuits, which have passed the randomness tests of the National Institute of Standards and Technology. The work can serve as a useful guide for materials scientists and electronic engineers when fabricating MIM‐like memristors for RTN applications.

One of the emerging challenges in the scaling of MOSFETs is the reliability of ultra-thin gate dielectrics. Various sources can cause device aging, such as hot carrier aging (HCA), negative bias temperature instability (NBTI), positive bias temperature instability (PBTI), and time dependent device breakdown (TDDB). Among them, hot carrier aging (HCA) has attracted much attention recently, because it is limiting the device lifetime. As the channel length of MOSFETs becomes smaller, the lateral electrical field increases and charge carriers become sufficiently energetic (“hot”) to cause damage to the device when they travel through the space charge region near the drain. Unlike aging that causes device parameters, such as threshold voltage, to drift in one direction, nano-scale devices also suffer from Random Telegraph Noise (RTN), where the current can fluctuate under fixed biases. RTN is caused by capturing/emitting charge carriers from/to the conduction channel. As the device sizes are reduced to the nano-meters, a single trap can cause substantial fluctuation in the current and threshold voltage. Although early works on HCA and RTN have improved the understanding, many issues remain unresolved and the aim of this project is to address these issues. The project is broadly divided into three parts: (i) an investigation on the HCA kinetics and how to predict HCA-induced device lifetime, (ii) a study of the interaction between HCA and RTN, and (iii) developing a new technique for directly measuring the RTN-induced jitter in the threshold voltage. To predict the device lifetime, a reliable aging kinetics is indispensable. Although early works show that HCA follows a power law, there are uncertainties in the extraction of the time exponent, making the prediction doubtful. A systematic experimental investigation was carried out in Chapter 4 and both the stress conditions and measurement parameters were carefully selected. It was found that the forward saturation current, commonly used in early work for monitoring HCA, leads to an overestimation of time exponents, because part of the damaged region is screened off by the space charges near the drain. Another source of errors comes from the inclusion of as-grown defects in the aging kinetics, which is not caused by aging. This leads to an underestimation of the time exponent. After correcting these errors, a reliable HCA kinetics is established and its predictive capability is demonstrated. There is confusion on how HCA and RTN interact and this is researched into in Chapter 5. The results show that for a device of average RTN, HCA only has a modest impact on RTN. RTN can either increase or decrease after HCA, depending on whether the local current under the RTN traps is rising or reducing. For a device of abnormally high RTN, RTN reduces substantially after HCA and the mechanism for this reduction is explored. The RTN-induced threshold voltage jitter, ∆Vth, is difficult to measure, as it is typically small and highly dynamic. Early works estimate this ∆Vth from the change in drain current and the accuracy of this estimation is not known. Chapter 6 focuses on developing a new ‘Trigger-When-Charged’ technique for directly measuring the RTN-induced ∆Vth. It will be shown that early works overestimate ∆Vth by a factor of two and the origin of this overestimation is investigated. This thesis consists of seven chapters. Chapter 1 introduces the project and its objectives. A literature review is given in Chapter 2. Chapter 3 covers the test facilities, measurement techniques, and devices used in this project. The main experimental results and analysis are given in Chapters 4-6, as described above. Finally, Chapter 7 concludes the project and discusses future works.

Effect of threading dislocations contributing to the increased 1/f noise in strained-Si MOSFETs is studied. Results of low-frequency noise study of strain-engineered MOSFETs are presented including 1/f and random telegraph noise (RTN). From the bias dependency of 1/f noise the correlated mobility fluctuation model (in NMOSFETs) is identified as the dominant noise mechanism. The low-frequency noise study reveals electrical stress-induced device degradation shown by the increased 1/f noise and complex RTN indicating reliability issues. A detailed low-frequency noise study in highly-scaled, strained MOS devices is presented indicating the capabilities of LF noise study for assessing device quality and lifetime essential in reliability analysis.

Random telegraph noise (RTN) is often considered a nuisance or, more critically, a key reliability challenge for miniaturized semiconductor devices. However, this picture is gradually changing as recent works have shown emerging applications based on the inherent randomness of the RTN signals in state-of-the-art technologies, including true random number generator and IoT hardware security. Suitable material platforms and device architectures are now actively explored to bring these technologies from an embryonic stage to practical application. A key challenge is to devise material systems, which can be reliably used for the deterministic creation of localized defects to be used for RTN generation. Toward this goal, we have investigated RTN in Au nanocrystal (Au-NC) embedded HfO2 stacks at the nanoscale by combining conduction atomic force microscopy defect spectroscopy and a statistical factorial hidden Markov model analysis. With a voltage applied across the stack, there is an enhanced asymmetric electric field surrounding the Au-NC. This in turn leads to the preferential generation of atomic defects in the HfO2 near the Au-NC when voltage is applied to the stack to induce dielectric breakdown. Since RTN arises from various electrostatic interactions between closely spaced atomic defects, the Au-NC HfO2 material system exhibits an intrinsic ability to generate RTN signals. Our results also highlight that the spatial confinement of multiple defects and the resulting electrostatic interactions between the defects provides a dynamic environment leading to many complex RTN patterns in addition to the presence of the standard two-level RTN signals. The insights obtained at the nanoscale are useful to optimize metal nanocrystal embedded high-κ stacks and circuits for on-demand generation of RTN for emerging random number applications.

Tunneling magnetoresistive (TMR) heads have been observed to exhibit relatively large low-frequency noise. Observation in a saturating field reveals that a substantial part of this noise is of electrical origin. Two distinctly different electrical noise phenomena are observed: 1/f noise and random telegraph (RT) noise. 1/f noise appears in all heads, RT noise only in some. The magnitude of the noise tracks the device resistance and the electrical bias. Therefore, the question arises if it is caused by resistance fluctuations or by the electrical bias. To answer this question, the paper describes a measurement setup to determine the TMR device noise in thermodynamic equilibrium (no bias). It is concluded that at zero bias there is no electrical low-frequency noise; neither 1/f noise nor RT noise was detected. Further, the paper proposes an electroacoustic model for the origin of the 1/f noise and estimates the expected magnitude. For the RT noise, in addition to the well-known trapped charge blocking model, an electromigratory model is proposed to better cover all observed RT noise features

The reduction of random telegraph noise (RTN) at the circuit level using common noise canceling methods, such as correlated double sampling (CDS), has proven difficult. Therefore, reduction of RTN at the device level is increasingly being investigated. In this paper, RTN characteristics are analyzed source follower transistor. Impacts of RTN levels are investigated before and after intentional hot carrier agings (HCA). Unlike channel hot carrier (CHC) stress, which showed small changes in RTN characteristics or decreased RTN levels, drain avalanche hot carrier (DAHC) stress resulted in increasing power spectral density levels below 10 Hz. This implies low-frequency RTN is closely related to interface charge density (Nit). The Nit generated by DAHC would results in the increase of influence of RTN on active traps in channel near drain junction. On the other hands, in case of CHC, it seems that the RTN characteristic is weakened by changing the dominant current path distributed around the active trap by charged trap.

Statistical characterization of two-level random telegraph noise (RTN) amplitude distribution in a hafnium oxide resistive memory has been performed. We find that two-level RTN in HRS exhibits a large amplitude distribution tail, as compared to LRS. To investigate an RTN trap position in a hafnium oxide film, we measure the dependence of electron capture and emission times of RTN on applied read voltage. A correlation between an RTN trap position and RTN amplitude is found. A quasi-two-dimensional RTN amplitude simulation based on trap-assisted electron sequential tunneling is developed. Our study shows that RTN traps in a rupture region of a hafnium oxide film are responsible for an RTN large-amplitude tail in HRS mostly.

Since devices actually operate under AC signals in digital circuits, it is more informative to study random telegraph noise (RTN) at dynamic AC biases than at constant DC voltages. We found that the AC RTN statistics largely deviates from traditional DC RTN, in terms of different distribution functions and the strong dependence on AC signal frequency, which directly impacts on the accurate prediction of circuit stability and variability. The AC RTN characteristics in high-к/metal-gate FETs are different from that in SiON FETs, and both of which cannot be described by classical RTN theory. A physical model based on quantum mechanics is proposed, which successfully explains the new observations of AC RTN. It is also demonstrated that, if using DC RTN statistics instead of AC RTN, a large error of 30% overestimation on the read failure probability in ultra-scaled SRAM cells will occur. These new understandings are critical for the robust circuit design against RTN in practical digital circuits.

In this paper, we investigate the impacts of single trap induced Random Telegraph Noise (RTN) on Ferroelectric FinFET (FE-FinFET) with P-type and N-type substrates respectively, compared to FinFET. The trap position dependent RTN amplitude (AI <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ds</sub> /I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ds</sub> ) along the channel length and fin height directions are examined. For FE-FinFET and FinFET at V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">gs</sub> - 0V, N-type substrate with smaller work function lowers the channel conduction band energy near the bottom of fin along the fin height direction. Therefore, the maximum electron current density occurs at the bottom of fin which becomes the most critical position introducing worst RTN amplitude for N-type substrate. However, for FE-FinFET and FinFET with P-type substrate, the worst RTN amplitude occurs at 0.5 fin height position. Therefore, along the fin height direction, the worst RTN amplitude occurs at different position for FE-FinFET/FinFET with N-type and Ptype substrates respectively. Our results show that FE-FinFET exhibits smaller RTN amplitude than FinFET due to its smaller trap induced threshold voltage shift (ΔV <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> ). Besides, for both FEFinFET and FinFET, N-type substrate shows smaller RTN amplitude and RTN induced ΔV <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> variations than P-type substrate. In other words, RTN induced variations can be suppressed by substrate doping optimization for FE-FinFET and FinFET.

It is difficult to measure the random telegraph noises (RTN) of MOSFET subthreshold currents at the sub-pA level directly and accurately. In this work, we used a charge integration method similar to the operation of the CMOS image sensors (CIS) to characterize the RTN of subthreshold currents approximately from 1 fA to 1 nA, using a test chip of 1M cell array in a 40 nm process. We found that each RTN trap was active only within a specific window of gate voltages. The trap became less active or inactive outside the corresponding window of operations. We showed that the sets of RTN-active devices under different gate voltages were different. Furthermore, the choice of sampling frequency in measuring RTN and the number of sampled data points determined the observable range of RTN emission and capture time constants. For the data measured by sampling periods of 3.82 s, 299 ms, and 372 $\mu {\mathrm{ s}}$ , different sets of RTN traps were observed with different spans of time constants. The combined time constants range was about 7 orders of magnitude. For single-trap RTN, we found and verified a relation between the probability of trap occupancy (PTO) and the ratio of root-mean-square random noise (RN) versus the RTN amplitude.

Gate current random telegraph noise and single defect conduction