Prateek Sharma

Understanding and Modeling the Temperature Behavior of Hot-Carrier Degradation in SiON nMOSFETs

Using our physics-based model for hot-carrier degradation (HCD), we analyze the temperature behavior of HCD in nMOSFETs with a channel length of 44 nm. It was observed that, contrary to most previous findings, the linear drain current change (AId,lin) measured during hot-carrier stress in these devices appears to be lower at higher temperatures. However, the difference between the AId,lin values obtained at different temperatures decreases as the stress voltage increases. This trend is attributed to the single-carrier process of Si-H bond rupture, which is enhanced by the electron-electron scattering. We also consider another important modeling aspect, namely, the vibrational life-time of the Si-H bond, which also depends on the temperature. We finally show that our HCD model can successfully capture the temperature behavior of HCD with physically reasonable parameters.

Modeling of Hot-Carrier Degradation in nLDMOS Devices: Different Approaches to the Solution of the Boltzmann Transport Equation

We propose two different approaches to describe carrier transport in n-laterally diffused MOS (nLDMOS) transistor and use the calculated carrier energy distribution as an input for our physical hot-carrier degradation (HCD) model. The first version relies on the solution of the Boltzmann transport equation using the spherical harmonics expansion method, while the second uses the simpler drift-diffusion (DD) scheme. We compare these two versions of our model and show that both approaches can capture HCD. We, therefore, conclude that in the case of nLDMOS devices, the DD-based variant of the model provides good accuracy and at the same time is computationally less expensive. This makes the DD-based version attractive for predictive HCD simulations of LDMOS transistors.

A model for hot-carrier degradation in nLDMOS transistors based on the exact solution of the Boltzmann transport equation versus the drift-diffusion scheme

We present two schemes for carrier transport treatment to be used with our hot-carrier degradation (HCD) model. The first version relies on an exact solution of the Boltzmann transport equation (BTE) by means of the spherical harmonics expansion (SHE) method, whereas the second one uses a simplified drift-diffusion (DD) scheme to avoid the computationally expensive SHE approach. We use both versions of the model to simulate the change of the characteristics of an nLDMOS transistor subjected to hot-carrier stress and compare these theoretical degradation traces with the experimental ones. The similarity in the results of the SHE- and DD-based models together with the flexibility of the latter approach makes it attractive for fast and predictive HCD simulations for LDMOS devices.

Predictive and efficient modeling of hot-carrier degradation in nLDMOS devices

We present a physical model for hot-carrier degradation (HCD) which is based on the information provided by the carrier energy distribution function. In the first version of our model the distribution function is obtained as the exact solution of the Boltzmann transport equation, while in the second one we employ the simplified drift-diffusion scheme. Both versions of the model are validated against experimental HCD data in nLDMOS transistors, namely against the change of such device characteristics as the linear and saturation drain currents. We also compare the intermediate results of these two versions, i.e. the distribution function, defect generation rates, and interface state density profiles. Finally, we make a conclusion on the vitality of the drift-diffusion based version of the model.

Hot-Carrier Degradation Modeling of Decananometer nMOSFETs Using the Drift-Diffusion Approach

We extend our previously suggested drift-diffusion (DD)-based hot-carrier degradation model to the case of decananometer transistors. Special attention is paid to the effect of electron–electron scattering, which populates the high energy tail of the carrier distribution function, by using a rate balance equation. We compare the results of the DD-based model with the results obtained from a spherical harmonics expansion of the Boltzmann transport equation as well as experimental data. We also study the accuracy and limits of the applicability of the DD-based model and conclude that this model is able to capture hot-carrier degradation in nMOSFETs over a range of gate lengths from 65 to 300 nm with excellent accuracy.

On the limits of applicability of drift-diffusion based hot carrier degradation modeling

We study the limits of the applicability of a drift-diffusion (DD) based model for hot-carrier degradation (HCD). In this approach the rigorous but computationally expensive solution of the Boltzmann transport equation is replaced by an analytic expression for the carrier energy distribution function. On the one hand, we already showed that the simplified version of our HCD model is quite successful for LDMOS devices. On the other hand, hot carrier degradation models based on the drift-diffusion and energy transport schemes were shown to fail for planar MOSFETs with gate lengths of 0.5–2.0 µm. To investigate the limits of validity of the DD-based HCD model, we use planar nMOSFETs of an identical topology but with different gate lengths of 2.0, 1.5, and 1.0 µm. We show that, although the model is able to adequately represent the linear and saturation drain current changes in the 2.0 µm transistor, it starts to fail for gate lengths shorter than 1.5 µm and becomes completely inadequate for the 1.0 µm device.

On the temperature behavior of hot-carrier degradation

We show that - in contrast to previous findings - hot-carrier degradation (HCD) in scaled nMOSFETs with a channel length of 44 nm appears to be weaker at elevated temperatures. However, the distance between degradation traces obtained at 25 and 75° C reduces as the stress voltages increase and at a certain voltage the changes of the linear drain current measured at 25 and 75° C are almost identical in the entire stress time window. We apply our physics-based model for hot-carrier degradation to analyze the temperature behavior of this detrimental phenomenon. This behavior is interpreted in terms of competing single- and multiple-carrier processes of Si-H bond dissociation with the corresponding rates having the opposite temperature dependencies. One of the most important aspects relevant to the temperature behavior of HCD is the bond vibrational life-time which decreases with the temperature.

Modeling of hot-carrier degradation in LDMOS devices using a drift-diffusion based approach

We model hot-carrier degradation (HCD) in n- and p-channel LDMOS transistors using an analytic approximation of the carrier energy distribution function (DF). Carrier transport, which is an essential ingredient of our HCD model, is described using the drift-diffusion (DD) method. The analytical DF is used to evaluate the bond-breakage rates. As a reference, we also obtain the DF from the solution of the Boltzmann transport equation using the spherical harmonics expansion (SHE) method. The distribution functions and interface state density profiles computed using the SHE and DD-based approaches are compared. The comparison of the device degradation characteristics simulated by these two approaches with the experimental data shows that the DD-based variant, which is considerably less computationally expensive, provides good accuracy. We, therefore, conclude that the DD-based version is efficient for predictive HCD simulations in LDMOS devices.

Comparison of analytic distribution function models for hot-carrier degradation modeling in nLDMOSFETs

Abstract We analyze the applicability of different analytic models for the carrier distribution function (DF), namely the heated Maxwellian, the Cassi model, the Hasnat approach, the Reggiani model, and our own concept, to describe hot-carrier degradation (HCD) in nLDMOS devices. As a reference, we also obtain the carrier distribution function as a direct solution of the Boltzmann transport equation using the spherical harmonics expansion method. The DFs evaluated with these models are used to simulate the interface state generation rates, the interface state density profiles, and changes of the linear and saturation drain currents as well as the threshold voltage shift. We show that the heated Maxwellian approach leads to an underestimated HCD at long stress times. This trend is also typical for the Cassi and Hasnat models but in these models HCD is underestimated in the entire stress time window. While the Reggiani model gives good results in the channel and drift regions, it cannot properly represent the high-energy tails of the DF near the drain, and thus leads to a weaker curvature of the degradation traces. We show finally that our model is capable of capturing DFs with very good accuracy and, as a result, the change of the device characteristics with stress time.

On the effect of interface traps on the carrier distribution function during hot-carrier degradation

We study the effect of interface states, generated during hot-carrier stress, on the carrier energy distribution functions (DFs) and check whether this effect perturbs the results of our hot-carrier degradation model. These studies are performed using SiON nMOSFETs with a gate length of 65 nm as exemplary devices. We carry out simulations with different values of the spatially uniform interface state density (Nit) as well as with a coordinate dependent Nit evaluated for real stress conditions. In both cases, the effect of Nit on carrier distribution functions appears to be strong. As for the degradation characteristics, we show that Nit profiles computed with perturbed distribution functions can be substantially different from those obtained with non-perturbed DFs, especially at long stress times. The same trend is visible also for changes in the linear drain current. Additional simulations performed for operating conditions with and without the effect of Nit show that if this effect is not taken into account, this leads to severe underestimation of the device life-time.