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Cryogenic semiconductor device models are essential in designing control systems for quantum devices and in benchmarking the benefits of cryogenic cooling for high-performance computing. In particular, the saturation of subthreshold swing due to band tails is an important phenomenon to include in low-temperature analytical MOSFET models as it predicts theoretical lower bounds on the leakage power and supply voltage in tailored cryogenic CMOS technologies with tuned threshold voltages. Previous physics-based modeling required to evaluate functions with no closed-form solutions, defeating the purpose of fast and efficient model evaluation. Thus far, only the empirically proposed expressions are in closed form. This article bridges this gap by deriving a physics-based and closed-form model for the full saturating trend of the subthreshold swing from room down to low temperature. The proposed model is compared against experimental data taken on some long and short devices from a commercial 28-nm bulk CMOS technology down to 4.2 K. [ABSTRACT FROM AUTHOR]

Vertical, gigapascal-level mechanical stress (MS) is induced at different locations along the channel of 40-nm effective gate length planar CMOS field-effect transistor (FET) devices and electrical parameter variations are investigated. In both p-and n-channel devices, the threshold voltage, mobility, and ON-current are seen to change proportionally with the additional MS, while gate-induced drain-leakage current increases exponentially. A clear effect of the location of the applied force along the source–drain direction is observed on the transistor parameters. Simulations show that a mechanical load located closer to the FET source induces a stronger asymmetry between the source and drain stresses. This leads to asymmetric subband splitting/warping, which reduces the backscattering rate at the source, in line with theoretical predictions on the importance of the channel barrier near the source for current in quasi-ballistic transistors. [ABSTRACT FROM AUTHOR]

Using the framework developed in the first part of this work, we demonstrate the capabilities of the extended two-state nonradiative multi-phonon (NMP) model by reproducing leakage current characteristics of two selected technologies. First, we identify the temperature-activated leakage mechanism in SiC / SiO2 stacks using a tens of nanometer thick thermally grown oxide as trap-assisted tunneling (TAT) through defects. Interestingly, this effect can be reproduced with the same parameters in a SiC / SiO2 stack with deposited oxide. Our simulations demonstrate that these charge transition centers are distributed within only a few nanometers from the SiC / SiO2 interface. The low thermal activation of the leakage current is linked to the low relaxation energies of the involved traps compared with those typically involved in bias temperature instability (BTI) and Random Telegraph Noise (RTN). Second, a similar mechanism can explain TAT characteristics and transient charge trapping currents in Metal–Insulator–Metal (MIM) capacitors with a ZrO2 insulating layer. By comparison of our model parameters to theoretical density functional theory (DFT) calculations, we identify self-trapped electrons (polarons) as a likely cause for these effects, as they have the required low relaxation energies. [ABSTRACT FROM AUTHOR]

Due to the potential for technological application, there has been an explosion of interest in heavily polycrystalline ferroelectric nanofilms, such as those of doped hafnium oxide. However, the heavily polycrystalline nature of these materials invalidates conventional modeling approaches as the dynamics have been found to be: 1) nucleation-limited; 2) involve grains of ferroelectric material interspersed among grains of alternative, nonferroelectric material; and 3) the direct interaction between these grains is observed to be minimal. In this article, we consider seven separate compact or “0-D” models of such polycrystalline films. Four of these models are based on a Landau paradigm and two are based on a Monte Carlo (MC) paradigm. The seventh is the traditional Preisach model. Although all of these models have been used in the literature to model novel polycrystalline ferroelectric nanofilms, here we compare and contrast the accuracy and physical appropriateness of each model by comparing both their static and dynamic properties against experimental data. We then find that although all models except single-grain models are capable of reproducing the static properties, only the MC models replicate the long-time dynamical properties. Thus, it is demonstrated that not all models are equally valid for the accurate modeling of such films. [ABSTRACT FROM AUTHOR]

Sequential 3-D stacking of multiple CMOS device tiers in a single fabrication flow requires the development of reliable high- ${k}$ /metal gate (HKMG) stacks at a reduced thermal budget (<525 °C). The omission of the customary high-temperature gate-stack annealing results in excessive dielectric defect densities. We have recently demonstrated on MOS capacitors the insertion of “defect decoupling” layers–LaSiOx for nMOS and Al2O3 for pMOS–at the interface between SiO2 and HfO2 as a promising approach to engineer the high- ${k}$ band lineup and minimize charge trapping for improved bias-temperature-instability (BTI) reliability. In this article, we demonstrate this approach in planar transistors, which allows assessing the impact of defect decoupling on carrier mobility. First, a comparative study on the impact of LaSiOx and Al2O3 insertion is performed, highlighting the different strategies for improving positive BTI (PBTI) and negative BTI (NBTI) reliability. Second, a comprehensive investigation on the effects of LaSiOx and Al2O3 insertion is conducted with a focus on BTI reliability and channel carrier mobility: a lack of penalty (Al2O3) or even improved carrier mobility (LaSiOx) is reported for the dipole-inserted gate stacks. Furthermore, we explore the simplified dual gate-stack integration for CMOS flow. A severe PBTI reliability penalty is observed if an Al2O3 layer (for hole trap decoupling) is deposited in the nMOS gate-stack, even if on top of the beneficial LaSiOx (for electron trap decoupling). In contrast, the pMOS gate-stack is found to be more tolerant to the presence of a residual LaSiOx layer on top of the beneficial Al2O3 layer, suggesting a viable strategy for the simplified dual gate-stack integration. Finally, the reliability improvement is validated also on a FinFET test vehicle. [ABSTRACT FROM AUTHOR]

Charge trapping is arguably the most important detrimental mechanism distorting the ideal characteristics of MOS transistors, and nonradiative multiphonon (NMP) models have been demonstrated to provide a very accurate description. For the calculation of the NMP rates at room temperature or above, simple semiclassical approximations have been successfully used to describe this intricate mechanism. However, for the computation of charge transition rates at cryogenic temperatures, it is necessary to use the full quantum mechanical description based on Fermi’s golden rule. Since this is computationally expensive and often not feasible, we discuss an efficient method based on the Wentzel–Kramers–Brillouin (WKB) approximation in combination with the saddle point method and benchmark this approximation against the full model. We show that the approximation delivers excellent results and can, hence, be used to model charge trapping behavior at cryogenic temperatures. [ABSTRACT FROM AUTHOR]

We present time-zero characterization and an investigation on bias temperature instability (BTI) degradation between 4 and 300 K on large area high- ${k}$ CMOS devices. Our measurements show that negative BTI (NBTI) on pMOSFETs freezes out when approaching cryogenic temperatures, whereas there is still significant positive BTI (PBTI) degradation in nMOSFETs even at 4 K. To explain this behavior, we use an efficient implementation of the quantum mechanical nonradiative multiphonon charge trapping model presented in Part I and extract two separate trap bands in the SiO2 and HfO2 layer. We show that NBTI is dominated by defects in the SiO2 layer, whereas PBTI arises mainly from defects in the HfO2 layer, which are weakly recoverable and do not freeze out at low temperatures due to dominant nuclear tunneling at the defect site. [ABSTRACT FROM AUTHOR]

Hot-carrier-induced degradation of short p-channel field-effect transistors in the presence of externally applied vertical mechanical force is investigated. The mechanical stress was induced in the devices by applying a normal load with a nanoindenter. Using finite element modeling, the induced stress to the channel was estimated to reach GPa range. It is shown that compressive mechanical stress considerably enhances the impact ionization rate and the generation of secondary electron-hole pairs. These can be trapped in the gate oxide and cause a hot-electron-induced punch-through effect and effective p-channel length reduction even after both mechanical and electrical stresses are removed. The presented findings indicate the importance of mechanical stress control and engineering for improving the device reliability. [ABSTRACT FROM AUTHOR]

A comprehensive investigation on the hot-carrier-induced interface state generation and its impact on carrier mobility in nMOSFET is performed. I – V compact modeling and charge pumping (CP) characterization are used as independent ways to evaluate the interface state density as a function of hot-carrier-induced aging. From the two techniques, similar power-law time exponents of the interface state density kinetics are obtained. Assisted by the quasi-spectroscopic (temperature-resolved) CP measurement, the extracted interface state density is further correlated with the I – V modeling results: an universal mobility degradation normalization parameter Nit,ref = ~ 4.1 × 1011/cm2 is reported, irrespective of the effective oxide thickness (EOT), stress temperature, or the relative degradation of the device under test (DUT). Supported by the fundamental principles deployed in the derivation and the broad range of experimental conditions considered for its validation, the reported normalization parameter could serve as a modeling constant in the commonly used I – V compact models to correlate the mobility degradation with the interface state density induced by hot carrier stress. [ABSTRACT FROM AUTHOR]

We report measurements of multiple hot-carrier (HC) stress and high-temperature anneal cycles repeated on the same nFETs fabricated in a commercial 40-nm bulk CMOS technology. We model this cycled HC degradation anneal assuming Si–H bond breakage during stress and bond passivation during anneal, with the bond dissociation and passivation energies following a bivariate Gaussian distribution. Our model can describe multiple stress and anneal time scenarios well using a single parameter set and provides insights into the recovery behavior of HC-induced defects. We find no correlation between bond dissociation and passivation energies and observe that the repeated HC stress and anneal cycles suppress the low energies from the distribution of bond passivation energies, changing its shape from the Gaussian to a non-Gaussian form. [ABSTRACT FROM AUTHOR]

Low thermal budget junction-less transistors with back-gate are fabricated as top-tier devices for 3-D sequential integration. The impact of back-gate bias on carrier mobility and bias temperature instability (BTI) reliability is investigated. The back-gate bias is shown to modulate the carrier mobility: specifically, mobility is increased under forward back-gate bias (FBB), which is ascribed to the carrier redistribution from the front-gate interface toward back-gate interface. Regarding BTI reliability, if a back-gate bias (VBG) is applied only during ON-state and a constant front-gate stress VG is used, BTI reliability is not influenced by the applied VBG (due to its negligible impact on the front-gate oxide field, Eox). Therefore, supplying an FBB during ON-state can be used to adjust device performance—as VBG modulates the channel current through Vth and mobility—without reliability penalty. On the other hand, if the back-gate bias is applied during both ON- and OFF-states, while a constant stress Vov is maintained by adjusting the front-gate VG [i.e., VG – Vth (VBG) is kept constant under different VBG’s], the BTI reliability can be improved under FBB (due to a reduced Eox in the front-gate) without performance loss. The latter property can be used to improve the device reliability under circuit operation. [ABSTRACT FROM AUTHOR]

The impact of out-of-plane mechanical stress on a hafnium zirconium oxide (HZO) based ferroelectric field effect transistor (FeFET) is studied using a nanoindenter combined with in-situ probing. It is demonstrated that the hysteresis loop shrinks with increasing compressive stress. The device current shows significant dependence on mechanical stress. By ab initio simulations, the Landau potentials of HZO under stress are calculated. The parameters of the Landau-Khalatnikov (LK) equation are extracted and used as input to a TCAD model. The simulation results match well to the experimental results. [ABSTRACT FROM AUTHOR]

In modern MOS technologies continuous scaling of the geometry of transistors has led to an increase of the variability between nominally identical devices. To study the variability and reliability of such devices, a statistically significant number of samples needs to be tested. In this work we present a characterization study of defects causing BTI and RTN, performed on custom built arrays consisting of thousands of nanoscale devices. In such nanoscale devices, variability and reliability issues are typically analyzed for individual defects. However, the large number of measurements needed to extract statistically meaningful results make this approach infeasible. To analyze the large set of measurement data, we employ statistical distributions of the threshold voltage shifts arising from defects that capture and emit charge. This allows us to extract defect statistics using a defect-centric approach. Defect distributions are characterized for various gate, drain and bulk biases, and for two geometries to verify the methodology and to obtain statistics suitable for TCAD modeling and lifetime estimation. With the TCAD models we extrapolate the observed degradation of the devices. Finally, we investigate the influence of bulk and drain stress biases on the defects and observe that the impact of bulk bias on the device degradation is similar to that of the gate bias. In contrast, drain stress with drain biases up to −0.45V appears to be negligible for the investigated technology. Our measurements also clearly reveal that the overall BTI degradation is heavily dependent on the gate-bulk stress bias, while the extracted number of RTN defects seems to be independent on stress. [ABSTRACT FROM AUTHOR]

Reliability is an important consideration during semiconductor technology development, which ensures that the performances of devices, circuits, and systems are maintained over a specified period of time, leading to successful products. Device reliability is at the core of overall product reliability, which continues to remain an important area of research and has attracted the attention of IEEE Transactions on Electron Devices (T-ED) authors and readers throughout the years. Device reliability can be classified into two broad areas: gradual drift of device performance over time or sudden failure, and both are of importance for logic, memory, RF, and power devices. Different aspects of device reliability are usually reported, such as the development of electrical or physical characterization methods, investigation and modeling of a particular phenomenon, impact of material and processes on reliability, and development of reliability tolerant technologies. [ABSTRACT FROM AUTHOR]

We present a statistical analysis of the cumulative impact of random traps (RTs) and dopants (RDs) on hot-carrier degradation (HCD) in n-channel FinFETs. Calculations are performed at three combinations of high stress voltages and for conditions close to the operating regime. We generate 200 different configurations of devices with RDs and subsequently solve the Boltzmann transport equation to obtain the continuous interface trap concentration ${N} _{\text {it}}$. These deterministic densities ${N} _{\text {it}}$ for each individual configuration are randomized and converted to 200 different configurations of RTs, yielding a total amount of 40,000 samples in our study. The analysis shows that at high stress voltages (with both RTs and RDs taken into account) probability densities of linear drain currents and device lifetimes are close to a bi-modal normal distribution, while in the operating regime such a trend is not visible. [ABSTRACT FROM AUTHOR]

This paper presents a physically unclonable function (PUF) based on the randomness of soft gate oxide breakdown (BD) locations in MOSFETs, namely, soft-BD PUF. The proposed PUF circuit features a self-limiting mechanism that generates exactly one soft-BD spot in a pair of NMOS transistors. Highly stable “0” and “1” bits with an equal probability of 0.5 are extracted based on the locations of the generated BDs. A differential readout scheme is employed based on the proposed reference-free sense amplifier (SA), resulting in good current sensitivity and side-channel attack resilience. The soft-BD PUF, fabricated in a 40-nm CMOS process, comprises all essential periphery circuits. Measurements show that the soft-BD PUF has good data stability in a wide operating range. The native bit error rate is 0% for $V_{\text {DD}}=1\,\,\text {V}$ and above, shown by measuring 10k readout cycles among 10k PUF cells. Data stability degrades at lower supply voltage and higher temperature due to the conductivity of PUF cells and the offset of SAs. Under the nominal $V_{\textrm {DD}}$ of 0.9 V in this technology, the throughput is shown to be at least 40 Mb/s and the PUF readout consumes only 51.8 fJ/bit. The averaged hamming weight and hamming distance are 0.497 and 0.496, respectively, showing a good randomness and uniqueness. The resulting PUF data show good statistical properties by passing all the relevant tests in the NIST 800-22 suite. [ABSTRACT FROM AUTHOR]