6.5 Tsetseris' Model

There is still no comprehensive atomic-scale scenario describing the effect of BTI including the exact mechanism of degradation, the role of different species, or the origin of low activation energies. By means of first-principles calculations it is possible to investigate the atomic configuration of the semiconductor's structure, including dopants, unwanted defects, and the binding and dissociation energies of atomic bonds.

Tsetseris and co-workers investigated the subject of BTI at atomic level using the ab-initio simulation code VASP [116]. They propose a proton based dissociation model [102] to describe the BTI induced breaking of Si-H bonds at the silicon-dielectric interface, which is described in the following.

The breaking of passivated bonds at the interface and the generation of dangling silicon bonds, , has been suggested as direct mechanism in the reaction-diffusion model

$$\ensuremath{\ensuremath{\textrm{Si}}\text{-}\textrm{H}}\rig... ...ensuremath{\textrm{Si$^\bullet$}}+ \ensuremath{\textrm{H}} .$$ (6.29)

Ab-initio calculations have shown [102] that the removal of hydrogen from the bond and its transport to a remote Si-Si bond raises the energy of the system by 1.9eV. Adding the migration barrier leads to a necessary dissociation activation energy of 2.4eV which is in good agreement with the experimentally obtained value of 2.6eV [117]. When holes are present in the channel the activation energy upon H removal decreases to 2.1eV. These values show, however, that only hot carriers in the channel, which are not available in typical BTI stress conditions (Section 6.3.8), can obtain enough energy to break bonds . Rashkeev et al. [118] propose an alternative depassivation reaction which adds a proton,

$$\ensuremath{\ensuremath{\textrm{Si}}\text{-}\textrm{H}}+ \e... ...remath{\textrm{Si$^\bullet$}}+ \ensuremath{\textrm{H$_2$}} .$$ (6.30)

The proton weakens the bond and after dissociation creates molecular hydrogen, , which diffuses into the dielectric.

Through ab-initio calculations [119] a dissociation energy barrier of 0.95eV is obtained, when the Fermi-level is at the valence band edge, which is the situation of an n-type substrate in inversion. Due to the lower energy barrier, this process can be activated by BTI temperatures.

As source for the required protons the authors suggested hydrogen bound to substrate dopants. The activation energy to dissociate a P-H complex has calculated to be 1.3eV, which is in good agreement with an experimental value of 1.18eV [120]. These energy values are valid in n-type silicon at flat band conditions where hydrogen exists as .

In the depletion region the stability of the P-H complex changes dramatically. In this region the preferred charge state of hydrogen changes from negative to neutral, , resulting in a much lower dissociation activation energy for a P-H complex of only $0.3$-$0.4$eV. For a certain period of time the hydrogen atom located in the inversion layer stays neutral and then transfers into a positively charged proton, , by picking up a hole.

Figure 6.15: Schematic of the NBTI model proposed by Tsetseris et al. [102]. P-H bonds in the depletion region of an n-type substrate are drastically weakened at NBTI stress conditions. After dissociation the hydrogen diffuses to the interface and can de-passivate Si-H bonds generating silicon dangling bonds.

At negative bias stress conditions the free protons drift to the interface. As the energy barrier to cross the interface is very high (1eV) the protons migrate rapidly along the interface. As both, dangling bonds and the protons are positively charged it is very unlikely that a proton passivates an interface trap. They will preferably be located close to Si-H bonds which they can break by forming (6.30). Figure 6.15 gives a schematic overview of the processes involved.

An additional mechanism can be the injection of protons into the dielectric leading to positive oxide charges . These positive charges prevent further protons to be injected. Only when the oxide charges diffuse away from the interface new protons can be injected leading to further degradation [102].

This model is capable of explaining the different susceptibility of n- and p-channel MOSFETs to positive and negative bias stress (Section 6.3.7)

• pMOS, negative bias: The P-H dissociation energy is drastically reduced in the depletion region and the positively charged protons are accelerated towards the interface.
• pMOS, positive bias: As no depletion layer is formed the dissociation energy of P-H is very high. Therefore the degradation is drastically suppressed.
• nMOS: In the p-type substrate B-H bonds exist instead of P-H bonds. However, the dissociation activation energy of these complexes is much larger than for P-H complexes, even in a depletion layer, leading to less hydrogen available to degrade the interface.

When assuming that the atomic hydrogen in the bulk diffuses faster than the molecular hydrogen in the dielectric, Tsetseris' model results in a time exponent of $n=0.25$ [121]. This is not in agreement with recent measurement data (Section 6.3.6) and therefore the model in the present form might be incomplete.