2.3 Mixed NBTI/HC Conditions

Typically BTI and HCD are discussed and characterized independently from each other with regard to defect creation and annealing, the permanent and recoverable component, and their impact on parameter shifts. Although MOSFETs are not only subjected to either BTI or HCD conditions but also to stress conditions where both mechanisms contribute to degradation, only a limited number of studies is available on their simultaneous contribution or their interplay [21, 25–27, 103]. In this context, the term of mixed BTI/HC stress is used in order to express conditions linked to   0 V and   0 V.

2.3.1 Mixed NBTI/HC stress

So far, oxide defects in the context of BTI where is zero during stress have been discussed. In such a case, could be approximated as laterally homogenous, which means that it has the same value for each lateral defect position (). The behavior of oxide traps depend on the defect properties, which are reflected in the NMP rates. Their contribution to degradation and recovery is given typically by characteristic times, which fulfill the following requirements: and ,. In this subsection the impact of   0 V on the contribution of oxide defects to degradation and recovery is discussed.

In the case of a pMOSFET, as soon as both, and , are less than zero, the lateral dependence of the channel potential () has to be considered. In the simplest case, can be approximated linearly [27]

for those positions where the condition of inversion is fulfilled. At the pinch-off point it can be written as

with

	channel potential
	drain voltage
	gate voltage
	absolute lateral position (0 at source and at drain
	channel length
	threshold voltage.

Since the applied is constant over all lateral positions, but the channel potential increases from source to drain, , which is proportional to the difference of both, will decrease from source to drain. As remains unaffected at the source-side compared to homogeneous NBTI conditions, but is reduced at the drain end of the channel, different lateral positions will contribute differently to degradation and recovery. In a very simplified model based on an exponential dependence of the degradation on the applied gate to channel voltage, a lateral position dependent can be expressed as

with

	position dependent threshold voltage shift
	stress time and temperature dependent constant
	absolute lateral position (0 at source and at drain)
	stress time
	technology dependent constant
	channel potential.

Equation 2.56 shows that while each lateral position contributes equally to for homogeneous NBTI, at inhomogenous NBTI conditions with   0 V and   0 V each position contributes differently. This means that positions within the region near the source, where is very low, contribute more to than positions within the region near the drain, where might even reduce to zero. From the perspective of degradation being the result of capture events of oxide defects, Figure 2.32 shows schematically what would happen from an electrostatic point of view. It is assumed that the shown eight defects, uniformly distributed over all lateral positions, contribute to degradation and recovery at NBTI conditions by capturing a hole during stress and emitting it during recovery. This means that the energy levels of the defects are below the Fermi level at recovery conditions, and at each position is sufficient to shift the energy levels above the Fermi level during stress. In other words all shown defects are within the active energy region and as well as ,. By contrast, in the case of inhomogenous NBTI conditions, remains quite unaffected in the region near the source but is seriously reduced in the region near the drain. As a result, the energy level of source-side defects can be shifted above the Fermi level during stress, thus such defects can capture a hole during stress and emit it during recovery. Quite to the contrary, the energy level of some drain-side defects can no longer be shifted above the Fermi level during stress, thus, the drain-side defects do not capture a hole. Defects in the central region most probably will show a reduced occupancy.

In Figure 2.32 it it can be seen that not only the contribution of oxide defects to the total degradation changes at inhomogneous NBTI conditions compared to homogenous NBTI conditions but also their contribution to recovery. In this context, after homogeneous NBTI stress all eight defects emit a hole during recovery but only three to five defects emit one after inhomogenous NBTI stress. Thus, recovery will be reduced with increasing .

In such a simplified electrostatic picture, the significant change of the behavior of drain-side defects is attributed to the dependence of the characteristic capture and emission times (Equation 2.25 and Equation 2.26) and of the occupancy (Equation 2.17 and Equation 2.18). At the defect level a reduction of typically leads to an increase of , a decrease of and a decrease of the occupancy. Therefore, at inhomogeneous NBTI stress conditions, the transition constants of source-side defects remain nearly unmodified while those of drain-side defects are significantly modified. In other words, the active energy region narrows from source to drain as shown in Figure 2.33. As a consequence, independently of the total number of defects, those at the drain-side will contribute less to degradation and recovery than those in the central region or at the source-side.

As will be discussed in Chapter 5, the whole picture is more complicated since effects like II have to be taken into account as well. As a main result of this thesis, it will be shown that taking only the modified electrostatics during mixed NBTI/HC stress into accound does not reflect the defect behavior in experiments fully.

2.3.2 Step Height Dependence on the Drain Voltage

The drain voltage has not only a considerable impact on the defect behavior during stress as shown in the previous section but also on the behavior during recovery. It has been shown that the exponential step height distribution introduced in Equation 2.2 depends on the readout conditions [17]. A typical drain voltage at recovery conditions () is −0.1 V (for pMOSFETs) and the gate voltage   . Similar to what has been discussed in the previous subsection, the lateral local electrostatic conditions change when   −0.1 V. As a consequence, defects near the drain contribute differently to the recovery trace or an RTN signal than defects near the source and the exponential tail shown in Figure 2.8 decreases.

In the case of an RTN signal, the change of due to an increased readout drain voltage shifts of defects in the vicinity of the drain outside the measurement window. Therefore, such defects can no longer capture and emit charge carriers. Consequently, the number of active RTN defects changes, which affects the exponential step height distribution. In the case of defects which capture a charge carrier under stress conditions and emit it under recovery conditions, only can be affected by a changed readout drain voltage. In particular, of drain-side defects and defects located in the center of the channel is shifted towards smaller emission times if   −0.1 V. Thus, such defects still contribute to the recovery of the device.

However, for defects which capture a charge carrier during stress and emit it during recovery another consequence of an increased has to be considered. According to simulations considering different random dopant configurations it has been shown that the step heights of the active defects change with [104]. This effect is shown in Figure 2.34 for different random dopant configurations and four different lateral defect coordinates using 2.2 nm thick oxide film pMOSFETs with   150 nm and   100 nm. The average behavior of the step height with respect to the drain voltage at a constant gate voltage clearly shows that the shape of the curves is affected by the lateral defect position. For example, while of defects in the vicinity of the source at    (0 is at source and 1 is at drain) increases for increasing , of defects in the vicinity of the drain at    decreases for increasing . Therefore, the characteristic can be used as a defect fingerprint and its lateral position can be extracted.

For the position extraction a simplified technique can be applied [104]. The step heights with respect to the readout drain bias can be fitted linearly using such a simplified technique. The relative lateral position can be extracted using

with

	lateral position in the channel
	channel length
	slope of the linear fit
	constant, found to be approximately [104]
	largest step height observed in the measurements, corresponds
	to
	intercept of the linear fit

This technique is based on the realization that the main information regarding the lateral trap coordinate is given by the slope () and the intercept () of the linear fit. The sign of determines whether the trap is at the source- or at the drain-side. is responsible for the proximity of the defect to one of the electrodes. The shape of with respect to the lateral defect position is symmetric (also shown in [17]) and can be approximated by a Gaussian function

with and .

The standard deviation has been found to be proportional to the channel length. In other words, in experimental data defects which cause small steps in the traces compared to the steps caused by other defects in the same device, are located in the vicinity of the source or the drain. Defects which cause comparably large steps are located near the center of the channel. Depending on the behavior of (increasing or decreasing with increasing ) the defect’s position can be assigned to either the source-side or the drain-side. This technique has been applied successfully to measurement data presented in Chapter 5 in order to extract the lateral defect position [104, 105].