Markus Bina

The relevance of deeply-scaled FET threshold voltage shifts for operation lifetimes

In nm-sized FET devices with just a few gate oxide defects, the typically measured threshold voltage shifts are not obviously correlated with the device behavior at high gate bias. The largest shifts observed at the threshold voltage after the capture of a single carrier are reduced at higher gate biases. This degradation-mitigating effect is further shown to be amplified at lower channel doping. The understanding gained from 3D numerical simulations is captured in a simple analytic description of a single trapped-charge impact on the FET characteristics in the entire gate bias range. Potential use is illustrated in an improved lifetime projection and in circuit simulations of time-dependent variability.

Predictive Hot-Carrier Modeling of n-Channel MOSFETs

We present a physics-based hot-carrier degradation (HCD) model and validate it against measurement data on SiON n-channel MOSFETs of various channel lengths, from ultrascaled to long-channel transistors. The HCD model is capable of representing HCD in all these transistors stressed under different conditions using a unique set of model parameters. The degradation is modeled as a dissociation of Si-H bonds induced by two competing processes. It can be triggered by solitary highly energetical charge carriers or by excitation of multiple vibrational modes of the bond. In addition, we show that the influence of electron-electron scattering (EES), the dipole-field interaction, and the dispersion of the Si-H bond energy are crucial for understanding and modeling HCD. All model ingredients are considered on the basis of a deterministic Boltzmann transport equation solver, which serves as the transport kernel of a physics-based HCD model. Using this model, we analyze the role of each ingredient and show that EES may only be neglected in long-channel transistors, but is essential in ultrascaled devices.

Reduction of the BTI time-dependent variability in nanoscaled MOSFETs by body bias

We study the impact of individual charged gate oxide defects on the characteristics of nanoscaled pMOSFETs for varying body biases. Both a reduced time-zero variability and a reduced time-dependent variability are observed when a forward body bias is applied. In order to explain these observations, a model based on the modulation of the number of unscreened dopant atoms within the channel depletion region is proposed.

Physical modeling of hot-carrier degradation for short- and long-channel MOSFETs

We present the first physics-based model for hot-carrier degradation which is able to capture degradation in both short- and long-channel SiON nMOSFETs. Degradation is considered to be due to the breaking of Si-H bonds at the SiON/Si interface. Contrary to previous modeling attempts, our approach now correctly considers the intricate superposition of multivibrational bond excitation and bond rupture induced by a solitary hot carrier based on experimentally confirmed distributed activation energies. All processes are treated as competing pathways, leading to bond dissociation from all vibrational levels. These rates are determined by the carrier acceleration integral and by the bond energetics. The acceleration integral is calculated using the carrier energy distribution. Corresponding distribution functions are found by a thorough solution of the Boltzmann transport equation. We demonstrate that electron-electron scattering plays the dominant role. As for the bond energetics, we consider the dispersion of the activation energy as well as its reduction induced by the interaction of the bond dipole moment with the electric field. All the model ingredients are incorporated into the same simulation framework based on the deterministic solver of the Boltzmann transport equation, ViennaSHE.

Modeling of hot carrier degradation using a spherical harmonics expansion of the bipolar Boltzmann transport equation

Recent studies have clearly demonstrated that the degradation of MOS transistors due to hot carriers is highly sensitive to the energy distribution of the carriers. These distributions can only be obtained in sufficient detail by the simultaneous solution of the Boltzmann transport equation (BTE) for both carrier types. For predictive simulations, the energy distributions have to be thoroughly resolved by including the fullband structure, impact ionization (II), electron electron scattering (EE), as well as the interaction of minority carriers with the majority carriers. We demonstrate that this challenging problem can be efficiently tackled using a deterministic approach based on the spherical harmonics expansion (SHE) of the BTE.

A predictive physical model for hot-carrier degradation in ultra-scaled MOSFETs

We present and validate a novel physics-based model for hot-carrier degradation. The model incorporates such essential ingredients as a superposition of the multivibrational bond dissociation process and single-carrier mechanism, dispersion of the bond-breakage energy, interaction of the electric field and the dipole moment of the bond, and electron-electron scattering. The main requirement is that the model has to be able to cover HCD observed in a family of MOSFETs of identical architecture but with different gate lengths under diverse stress conditions using a unique set of parameters.

Origins and implications of increased channel hot carrier variability in nFinFETs

Channel hot carrier (CHC) stress is observed to result in higher variability of degradation in deeply-scaled nFinFETs than bias temperature instability (BTI) stress. Potential sources of this increased variation are discussed and the intrinsic time-dependent variability component is extracted using a novel methodology based on matched pairs. It is concluded that in deeply-scaled devices, CHC-induced time-dependent distributions will be bimodal, pertaining to bulk charging and to interface defect generation, respectively. The latter, high-impact mode will control circuit failure fractions at high percentiles.

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.

Understanding correlated drain and gate current fluctuations

Recently, some experimental groups have observed the occurrence of correlated drain and gate current fluctuations, which indicate that both currents are influenced by the charge state of the same defect. Since the physical reason behind this phenomenon is unclear at the moment, we evaluated two different explanations: The first model assumes that direct tunneling of carriers is affected by the electrostatic field of the charged defect. Interestingly, this model inherently predicts the gate bias and temperature dependences observed in the experiments and is therefore quite promising at a first glance. In the second model, our multi-state defect model is employed to describe trap-assisted tunneling as a combination of two consecutive nonradiative multi-phonon transitions - namely hole capture from the substrate followed by hole emission into the poly-gate. The latter transition is found to be in the weak electron-phonon coupling regime, which requires the consideration of all band states instead of only the band edges. Our investigation shows that the electrostatic model must be discarded since it predicts only small changes in the gate current while the extended variant of the multi-state defect model delivers quite promising results.

On the importance of electron–electron scattering for hot-carrier degradation

Using our physics based model for hot-carrier degradation (HCD) we analyze the importance of the effect of electron–electron scattering (EES) on HCD in transistors with different channel lengths. The model is based on a thorough treatment of carrier transport and is implemented into the deterministic Boltzmann transport equation solver ViennaSHE. Two competing mechanism of Si–H bond-breakage are captured by the model: the one triggered by the multiple vibrational excitation of the bond and another which is due to excitation of one of the bonding electrons to an antibonding state by a solitary hot carrier. These processes are considered self-consistently as competing pathways of the same dissociation reaction. To analyze the importance of the EES process we use a series of nMOSFETs with identical architecture but different gate lengths. The gate length varies in the wide range of 44–300 nm to cover short-channel MOSFETs as well as their longer counterparts. According to previous findings, EES starts to become important at a channel length of 180 nm. This situation is captured in the targeted gate length interval. Our results show that the channel length alone is not a sufficient criterion on the importance of EES and that the applied bias conditions have to be taken into account as well.