Subsections

• 6.1.1 Multiple-Particle Process
• 6.1.2 Giant Isotope Effect

6.1 Characteristics of Hot-Carrier Degradation

During hot-carrier degradation interface states are created along the channel of MOS transistors. This effect is accelerated with the drain voltage and depends on the highly energetic carriers, which are called ``hot''. The carriers bombarding the interface trigger the dissociation of Si-H bonds followed by a release of hydrogen and resulting in de-passivated dangling bonds. This interface state creation is highly localized, which distinguishes the degradation process from another degradation mechanism, from the negative bias temperature instability. While the latter one is considered as a one-dimensional process, hot-carrier degradation is a two-dimensional phenomenon. Carriers gain the highest energy near the drain end of the channel, where also the highest creation rate of interface states can be observed. The interface states created by this process can trap carriers forming interface charges which change the electrostatics of the device. This influences the threshold voltage of the transistor. Additionally these charges act as scattering centers leading to a reduction of the carrier mobility, the transconductance, and finally the drain current.

Over decades, the most severe degradation of n-MOSFET devices over stress-time, meaning the worst-case condition, was usually found at maximum substrate current [223,214]. This maximum current originates from impact-ionization and therefore is related to the existence of high-energetic carriers. Thus, this worst-case scenario is found when the following interrelation between voltages is satisfied: $\ensuremath{V_{\mathrm{GS}}}\approx \ensuremath{V_{\mathrm{DS}}}/2.$ In p-MOSFET devices, the worst-case condition is typically found at the maximum gate current [214,224].

One of the first modeling approaches proposed was the so-called lucky electron model developed in the 80s by Hu et al. [203]. This model, which is explained in Section 6.2.1, also assumes that electrons reach energies high enough to surmount the potential barrier at the $\mathrm{Si-SiO_2}$ interface. The degradation of $g_{\mathrm{m}}$ and $V_{\mathrm{T}}$ is described using the phenomenological power-law relation $t^n$ and a physics-based reaction-diffusion relation is proposed. The application of the lucky electron model with carefully tuned parameters delivered reasonable results in long channel devices. During this time the devices were aggressively down-scaled without a proper reduction in the supply voltages. As a result, the electric field in transistors was substantially increased. This tendency led among other things to the reinforcement of hot-carrier degradation as well as related reliability issues. To avoid that, a special strategy was based on a careful field shaping design, especially regarding LDD structures [225,226,227].

Starting from the sub micrometer nodes the problems seemed to be overcome by the reduction of the drain voltages of scaled transistors. It was assumed that due to the low voltages the carriers cannot overcome the energy barriers required to trigger bond dissociation processes [223]. However, hot-carrier degradation was also observed at lower voltages [222,228] and is still relevant even in highly down-scaled devices. However, the worst-case condition of hot-carrier degradation has shifted to higher gate voltages ( $\ensuremath{V_{\mathrm{GS}}}\approx \ensuremath{V_{\mathrm{DS}}}$ ). This suggests that the worst-case condition changed from the maximum carrier energy to the maximum number of carriers, i.e. the highest current [229,213].

6.1.1 Multiple-Particle Process

The shift of the worst-case condition and the existence of HCD at low voltages suggested that there is not a single mechanism responsible for the interface state generation. Another argument supporting this idea was that the carrier flux rather than energy becomes important in scaled devices. All these considerations were explained in a series of papers published by the group of Hess [230,231]. In long-channel devices carriers can become rather hot and can thereby activate a bond breakage process in a single collision. In contrast, in scaled devices the multiple-particle process plays the dominant role. Si-H bonds are broken by multiple excitations of phonon modes (due to bombardment by several colder particles) which eventually lead to bond breaking [230,231]. This also agrees with the shift of the worst-case condition to maximum currents, i.e. the conditions with the highest number of carriers impinging on the interface, resulting in a high number of collisions.

In the simulation of hot-carrier degradation the single- (SP) and multiple-particle (MP) process, have to be considered. In larger devices where carriers can gain high energies the SP process will dominate. Therefore the worst-case condition will be found in the mid gate-voltage range in conjunction with the highest bulk-current. In highly down-scaled devices the MP process will prevail and the worst-case condition corresponds to the maximum drain-voltage. The highest currents give the maximum number of carriers, thereby enabling the multiple vibrational excitation of the bonds. Depending on geometry and operating conditions one of the two processes can be dominant. However, under real stress/operating conditions commonly both processes are active simultaneously.

6.1.2 Giant Isotope Effect

An experiment supporting the MP theory was performed on hydrogen and deuterium passivated surfaces using a tip of an STM (scanning tunneling microscopy) as a source of carriers tunneling through the vacuum [232]. The surfaces were bombarded by carriers below the threshold energy and the experiment showed that the deuterium passivated surface was much more robust against the electron bombardment than the hydrogen passivated one. In the former case, as shown in Fig. 6.1(a), a much higher current is required to gain the same desorption yield [233]. Two mechanisms have been identified to cause this behavior which were summarized by Hess et al. [230]: The first effect is the higher bonding energy between deuterium and silicon, also known as the large isotope effect. But the differences found in the desorption rate are much higher than the difference of the bonding energy would suggest. That's why this effect is also called the giant isotope effect of hydrogen. The reason for this huge impact was found to be the multiple vibrational excitation of the Si-H and Si-D. Bonds are excited by collisions with many carriers and lifted to higher energy levels until the bonds eventually dissociate. This is true for both, hydrogen and deuterium passivated surfaces. However, since the localized deuterium vibration is more closely matched to the silicon bulk, a more efficient cooling of excited bonds takes place. This leads to reduced bond heating and in consequence to a lower probability of deuterium desorption via the multiple collision mechanism. The behavior of hydrogen bonds at surfaces is comparable to the behavior of them at interfaces. Therefore, one may use the same conclusion to explain why MOS devices passivated with deuterium instead of hydrogen appear to have a higher resistivity against HCD [234]. The difference in the degradation process can be observed in Fig. 6.1(b). As a side effect, this experiment also confirms that interface bond breaking plays an crucial role in device degradation [235].

Figure 6.1: STM measurements from [233] showing the giant isotope effect of deuterium (a) and the threshold voltage degradation of a 0.36 µm n-MOS transistor taken from [235] (b).

(a) Desorption Yield

(b) Threshold Voltage Shift