Many different failure mechanisms exist in semiconductor devices. For virtually all of them the root cause can be traced back to a relocation or displacement of material or charge. Atoms, ions, electrons, or holes are shifted from their designated to a harmful position. An isolated single movement usually does not cause a device failure. However, in highly down-scaled semiconductor devices, also single defect can lead to device failure. A major problem is the accumulation or depletion around an initially single defect, which consequently leads to further degradation of the device until parameters shift out of their specification or a severe failure occurs.
A representative failure mechanism based on transport of material is electromigration. In modern microelectronic devices, interconnect wires are required to carry high current densities. The positively charged metal ions in the interconnects are exposed to two counteracting forces. Due to the positive charge, ions experience a force towards the cathode. On the other hand, the mean velocity of the electrons is oriented towards the anode. A part of their moment is transmitted on to the atoms which also causes a force on the ions. This second force dominates at high current flow conditions which results in an effective force on ions oriented in the same direction as the electron flow. This effect is called electron wind . The major part of the mass transport in interconnects follows grain boundaries and interfaces. This transport produces areas that suffer from material depletion and areas that suffer from material accumulation. The former ones are called voids and can grow until the interconnect is cut. Hence, the resistivity suddenly increases leading to a drop of the current. In areas of material accumulation, the additional atoms form hillocks. Most reliability considerations for electromigration have been done statistically. Commonly, the time until a massive resistivity increase appears. A frequently used estimation for the mean time-to-failure is expressed as 
Another example of a reliability issue due to atomistic transport in semiconductor devices is related to hydrogen transport. In device fabrication hydrogen is especially important for the passivation of dangling bonds at silicon/silicon-dioxide (Si/ ) and polysilicon/silicon-dioxide interfaces. Under stress conditions the hydrogen atoms can break free, leaving back traps. This hydrogen release and possibly also the transport, is an important failure mechanism in negative bias temperature instability (NBTI) and hot-carrier degradation. The former will be briefly described in the next section. The hot-carrier degradation and related modeling approaches for hydrogen dissociation are discussed in Chapter 6.
Semiconductor oxides in electronic devices serve as isolation structures, as gate dielectrics, and as protection against environmental harms. Especially the native oxide of silicon, silicon dioxide, forms a stable and reliable interface on top of silicon surfaces. is an insulator with a very high bandgap of about 9eV  and with high resistivity, high breakdown voltage, and an adequate permittivity . It can be grown easily and in a well-controlled manner with a low defect density. Considering this excellent behavior in the fabrication process, the wide usage of silicon and its oxide becomes evident. Green et al.  stated, that is with the exception of its lower dielectric constant an ideal dielectric material.
Due to the importance of and the Si/ interface, it is obvious that its reliability is of crucial significance and a considerable amount of research has been related to that topic. Like all insulators, loses its insulating property at certain electric fields, where a breakdown occurs. The maximum electric field a dielectric material can be used without severe damage is called dielectric strength. The breakdown can occur because of intrinsic or extrinsic phenomena, whereas the first ones are due to weaknesses of the material itself and the latter ones are due to defects at the surface or in the bulk of the oxide. Because of the extremely down-scaled semiconductor devices, oxides have to resist enormous electric fields. The operation conditions get close to the dielectric strength which increases the risk of wearout and its consequences on device behavior.
During operation various mechanisms can lead to the creation and activation of oxide or interface defects acting as traps. As a consequence, the device degrades and parameters can drift out of their specification. Especially MOSFET devices are affected by oxide degradation. This wearout process during device operation can increase the gate leakage current which is called stress-induced leakage current (SILC) . The ongoing degradation can further lead to breakdown, which is believed to be caused by a critical density of defects . This time-dependent dielectric breakdown (TDDB) is a very important reliability issue . It is still under discussion which physical processes are responsible for oxide deterioration, leading to SILC and TDDB, and in a further consequence how the are interrelated. The defects for the two processes are often assumed to be the same , however, there are also opinions against this connection, which claim that different processes and different defects are relevant for the two degradation mechanisms .
The monitoring of oxide degradation is based on measurements of different phenomena. The interface trap creation is commonly assessed using capacity over voltage and charge pumping experiments . Measurement techniques like constant-current stress (CCS) and constant-voltage stress (CVS) are used to analyze the SILC and TDDB degradation. Changes of the voltage during CCS or the current during CVS suggest that charge trapping in the oxide leads to changes in the tunnel current density . Another widely discussed observation is the substrate hole current. It is measured in n-channel MOS devices with source and drain grounded and a positive voltage applied to the gate. The hole current which is some orders of magnitude below the electron current seems to be correlated to the oxide deterioration . Measurements show that breakdown is observed after a certain hole fluence through the oxide is reached. One explanation for this is the Anode Hole Injection (AHI) . Here, electrons tunnel from the cathode into the anode and transfer their excess energy to holes. These holes gain high energy and can be injected back into the oxide. With a given probability they can cause the observed bulk hole current. In this AHI model, these injected holes create the oxide damage. Estimations of the time to breakdown ( ) using the AHI model lead to a relation where the logarithm of depends linearly on the reciprocal oxide field and is therefore called the `1/E'-model . Early empirical models, however, suggested a linear dependence of the logarithm of on the electric field. These models are therefore called the `E'-model. Several physical explanations have been suggested for this phenomenon, however, none of them correlates the degradation with the electron tunnel current . One of the oldest `E'-models, the thermochemical model , for example, gives a physical explanation based on Si-Si bond breaking in . Interestingly, both, the `E'- and the `1/E'-model allow to fit TDDB data rather well over limited field ranges used in acceleration tests . Obviously, the extrapolations to low electric fields give very different lifetime projections. A wide range of measurements and especially long-term measurements close to normal operating fields of approximately 5MV/cm are required to clearly distinguish between the models . However, for low electric fields increases drastically which makes measurements nearly impossible.
Breakdown mechanisms due to the accumulation of oxide defects are often explained using the percolation model . Generated electron traps are believed to form a breakdown path from the anode to the cathode. In this model, the traps are represented using spheres, which are randomly placed in the oxide volume (see Fig. 3.7).
If two spheres overlap, conduction is possible between them. An oxide is broken if a single breakdown path is generated . In oxides thicker than approximately nm the heat generated by the localized current immediately propagates and results in thermal damage. This leads to a highly conductive short across the oxide, which is called hard breakdown . However, in thinner oxides a non-destructive or soft breakdown is observed . Here, a more resistive current path is created. Therefore, no thermally induced lateral extension of the percolation path is triggered . Both, hard and soft breakdown can be described using the percolation model . Good agreement is found by comparing this model with measurements. By partitioning the oxide capacity into a row of small independent capacitances, one can empirically assume that the failure of a single component leads to the failure of the whole oxide. Therefore, the breakdown mechanism can be explained by the weakest-link theory, which can be fit using the Weibull distribution [70,95] (see Fig. 3.5).
A recently and heavily discussed reliability topic is the negative bias temperature instability (NBTI). It can be observed by applying negative voltages to the gate of a MOSFET with all other contacts connected to ground. Since negative gate voltages are more common in p-MOSFETs, p-type transistors are more susceptible than the n-types. The degradation leads to a shift of the threshold voltage, a change in the subthreshold slope, and a reduction of the mobility. Its underlying mechanism becomes stronger at elevated temperatures and high voltages. In contrast to the other degradation mechanisms discussed so far, a relaxation can be observed as soon as NBTI stress ends. However, a part of the damage remains permanent or at least relaxes only very slowly .
NBTI has already been known for forty years and has long been explained and modeled by the reaction-diffusion (RD) theory . In this model, the de-passivation of centers is assumed as the main degradation mechanism NBTI. centers are dangling bonds at the Si/ interface. During the production of the devices, hydrogen is used to passivate these bonds and to make them electrically inactive. During stress, this hydrogen is released causing the device degradation. In the RD model, the de-passivated hydrogen is assumed to diffuse away from the interface through the oxide leaving back dangling bonds at the interface. The degradation is therefore diffusion dominated. In the relaxation phase hydrogen near the interface can passivate the interface again. Hence, the diffusion process of hydrogen plays an important role in the RD model. Various NBTI stress measurements have been fitted successfully with this method. However, modeling of the relaxation phase shows considerable deviations between measurements and simulations. The model predicts a retarded relaxation which is not found in measurement data. Subsequently the tendency changes insofar that the prediction relaxes too fast. During NBTI stress the forward and the backward reactions contribute to the degradation. Considering that the relaxation alone is evidently not described correctly, the correctness of the RD model is questionable. Hence, extensions to the RD approach have been suggested, that assumed a dispersive hydrogen transport in the oxide [98,99]. But this and other variations do not seem to fit satisfyingly. Additionally, many published approaches seem to be based on tainted measurement data and it shows that it is very important to consider the measurement techniques used to quantify the degradation of device parameters . This is caused by the fact that measurements are commonly performed by gate voltage sweeps and subsequent current measurements to estimate the threshold voltage. This requires an interruption of the stress cycle and relaxation immediately takes place. Since the time constants for relaxation are very small, measurement results can change significantly with the measurement delay.
Recently an advanced physically based NBTI modeling approach has been proposed by Grasser et al. . In this work, the degradation is described using two stages. The key ingredient in this model is the near-interfacial oxygen vacancy in the amorphous gate dielectric. Holes from the silicon are captured by this defect, breaking up the Si-Si bond (state 1) which creates a positively charged center (see the transition from state 1 to 2 in Fig. 3.8).
On hole emission, i.e. on electron capture, the defect is neutralized (state 3) but does not relax immediately to its initial configuration. Now, the neutral center can recapture a hole returning to the charged state 2 or the structure relaxes back to its precursor configuration. The hole capture and emission between state 2 and 3 can be very efficient. Therefore, such a kind of defect is called switching trap. The states 1, 2, and 3 represent the first stage in this two-stage model. The second stage of the degradation process is initiated by the dangling bond of the positively charged Si atom of the center. It attracts a hydrogen atom, which comes originally from the passivated interface, where it leaves back a positive interface charge. Repassivation of those dangling bonds requires free hydrogen atoms. For a full recovery, the defect has to pass through state 2 and 3. Hence, the full relaxation is slow, especially from stage 2. At least a part of those traps seems to remain permanent. The possible transitions between the four states of this model are illustrated in Fig. 3.8. The simulation results using this model in comparison with measurement data of devices with different technologies and geometries deliver very promising results [101,102]. Also the fast and the slow/permanent degradation observed in measurements are described very well using this two-stage model [101,102].
Another reliability concern comes from hot-carriers in the channel. Due to the high electric fields along the channel in MOS transistors, carriers gain a considerable amount of energy. This is especially true at the drain end of the channel. These carriers can break silicon-hydrogen bonds at the interface which generates interface traps. Hence, charges can get trapped and consequently change the device parameters. This degradation mechanism is essential for the operation of high-voltage devices and is discussed in detail in Chapter 6.
High energetic carriers are not only responsible for interface reliability. Another hot-carrier process, impact-ionization is also of special interest for reliability engineering. It is especially pronounced at the drain end of the channel region in MOSFET devices. The cascaded impact-ionization carrier generation increases the carrier concentrations, the current densities, and finally leads to avalanche breakdown. Devices have to be designed carefully to avoid breakdown under all operating conditions within the specifications [103,104]. In some applications the breakdown conditions initiated by, for example, electrostatic discharge or power supply peaks, cannot be fully prevented. The breakdown can lead to latch-up, snap-back, or immediate device failure with all consequential reliability issues. The topic of modeling and simulation of impact-ionization is an important part of this thesis, addressed in Chapter 5.
MOSFET transistors and especially CMOS (Complementary MOS) integrated circuits inherently suffer under the high susceptibility of the gate oxides to electrostatic discharge (ESD). In integrated circuits ESD stress leads to gate oxide or thermal junction breakdown [105,106,107]. The risk of ESD shocks is not only present before and during assembly, but also prior to the packaging and bonding of the die. On the semiconductor wafer, for example, etching, testing, and dicing can also introduce ESD [106,108]. The risk of damage obviously increases with the ongoing shrinking of the gate oxide. Since ESD events cannot be fully avoided during the product life-cycle, the most practical approach is the integration of protection circuits against ESD threats directly in the microelectronic structures .
Most work in reliability research concerning ESD is related to the optimization of existing protection structures and to the development of new structures [109,110]. The procedure of transferring ESD protection devices from one technology node to the next one is not straightforward. Thereby changes in the dimensions, the introduction of buried oxides, and different EPI (epitaxy layer) thicknesses introduce new uncertainties. Various structures are used as protection circuits. The first protection structures in the beginning of CMOS technology, required serial resistors. Hence, the overall performance of the integrated circuit was reduced. However, optimal designed ESD devices are electrically invisible during functional operation, but become active quickly, if needed, to keep the voltage low and to dissipate high currents. To accomplish this, new devices were introduced, one of them is the silicon controlled rectifier (SCR) based on -structures . This type of device is hard to calibrate and small process variations can lead to significant changes in the turn-on voltage. Nowadays, a very common structure is the gate-grounded NMOS transistor (ggNMOS), which makes use of the parasitic bipolar transistor . To minimize the fabrication costs, the same technology as for the integrated circuit itself is used. The ggNMOS is actually built like a common MOSFET, only the dimensions have to be adapted (see Fig. 3.9).
Source and gate are grounded and the drain is connected to the external input pin that needs to be clamped down to a low voltage. On ESD events, the rising voltage generates an increased reverse current leading to impact-ionization near the drain region. Eventually, the drain junction breaks down yielding a high carrier generation rate. Electrons are driven towards the drain and holes are driven to the area (actually the bulk contact). This hole current flow under the source area increases the electrostatic potential in the bulk so that the source-bulk junction gets forward biased and electrons are injected into the bulk. The increased electron current leads to a positive feedback and to a further increased impact-ionization generation. Hence, the resistance between source and drain drops. In the I/V characteristics this gives a negative differential resistance (see Fig. 3.10). The lower the voltage drops, the lower is the dissipated heat during ESD.
Structures like the ggNMOS are used to protect integrated circuits efficiently against ESD events. Especially measures to prevent damage due to electrostatic discharge events caused by people touching the device are carefully implemented. This stress event is also well modeled by the human body model (HBM).
One of the most often considered environmental influences is the temperature [112,113,114]. High temperatures in silicon devices lead to changes of the device parameters and to accelerated device degradation [115,116,117]. It has to be ensured that cooling is properly designed for all environmental temperatures that can be expected . Since most degradation mechanisms are thermally activated, elevated temperatures during usage decrease the lifetime of the device. A proper buffer in the design is needed to ensure design goals.
Other environmental impacts include radiation-induced degradation which can lead to displacement or ionization effects . Also mechanical, physical, as well as chemical influences may penetrate the protection layers of integrated circuits and eventually degrade the device or open up paths to the semiconductor surface . By such a path, foreign atoms, or simply moisture, can react with the metalization . Therefore, a proper coating and packaging is very important for protection against environmental impacts .