6.1  Measurement Techniques

For an explanation of many BTI experiments it is instructive to introduce one often employed basic element of a BTI experiment first. In this work this basic element is termed a single ‘stress-relax’ cycle for BTI (cf. Figure 6.2). Before the experiment starts, the fresh device is characterized by measuring the Id -Vg, Id -Vd or capacitance-voltage curves, while taking great care not to significantly change the device characteristics by prematurely BTI stressing the device. However, stressing the pristine device in this inital characterisation stage is often unavoidable. For the experiment itself the drain voltage Vd is often regulated to be as small as possible to guarantee low field conditions. Nevertheless, constraints imposed by the measurement setup often require a higher Vd, to for example, minimise noise in the measurement data. Whenever one is assesing homogenous BTI and not interested in the Vth shift either during stress or relaxation, then Vd is often chosen to be at zero volts during the respective phase. While the gate voltage Vg is precisely controlled to cycle between stress and relaxation, the drain current can be recorded to measure the threshold voltage deviation ΔVth. If a fast heater, such as a poly-heater device  [121], is available it is also possible to cycle the temperature in the same fashion. In a setup where the temperature can be cycled, the device temperature during stress T_s is usually much lower than the relaxation temperature T_r. The relaxation gate voltage V _r is normally chosen to be equal to the nominal threshold voltage V _th0. Next the gate voltage is set to the stress value, where V _s normally corresponds to strong inversion for a well defined time ts (stress). After bias temperature stress the gate voltage is, ideally instantly, set back to its relaxation value (relax/measurement) and kept there for a given time tr until the experiment ends. During this stress-relax cycle the drain current is recorded and compared to the inital measurement taken before the experiment. Due to the fast transient nature of BTI often a logarithmic time-stepping in the recording of the drain current is chosen to capture the transient behavior of the drain current right after bias or temperature changes. Additionally, most often one is restricted by the measurement range and bandwidth of the equipment and can only measure the drain current over the recovery time (recovery trace). In this work, BTI is defined as the set of gate voltages Vg and device temperatures T, which cause a change in the threshold voltage Vth in a given time. Thus we define bias temperature stress as an increase in threshold voltage |ΔVth| and drain current shift |ΔId| over time. Relaxation is defined as a decreasing threshold voltage |ΔVth| and drain current shift |ΔId| over time bringing the actual threshold voltage Vth closer to its nominal value V _th0.

6.1.1  Measure Stress Measure Technique

The measure stress measure (MSM) technique is a succession of multiple stress and Id -Vgmeasurement cycles  [122]. First an initial Id - Vgcurve is measured on the fresh device. Then the device is subjected to bias temperature stress for ts seconds. Right after stress a final Id - Vgcurve is taken. Note that during the measurement of the final Id -Vgcurve the device unavoidably relaxes. This cycle can be repeated many times in order to measure the degradation over various stress times. In an extended MSM measurement one records several relaxation phases after single exponentially growing stress phases, where the device temperature is kept constant during the whole experiment. The actual extended experiment, for bias stress, is shown in Figure 6.3. In the MSM technique the threshold voltage shift is obtained by comparing the measured drain current at a certain gate voltage against an initially measured Id - Vgcurve. This is possible since the gate voltage for relaxation is chosen to be equal close to the nominal threshold voltage. Additionally, it is also a possibility to record a fast Id - Vgcurve just before or during switching the gate voltage from Vs to Vr. In  [123] it was shown that the MSM technique is quite insensitive to mobility changes induced by stress. Nevertheless, it was also shown that the mobility variations induced are linearly dependent on temperature. This dependence has to be taken into account, when comparing MSM measurements taken at different device temperatures.

6.1.2  On-the-Fly Technique

The on-the-fly (OTF) technique is a method of extracting the threshold voltage shift from the recorded drain current with different levels of accuracy and not a separate measurement setup. In OTF the first recorded drain current under stress conditions at a fixed drain voltage is used as a reference to determine the threshold voltage shift. However, due to an inherently unavoidable delay between the onset of stress and the first recorded drain current there will always be an error in the reference drain voltage. Thus one is obliged to keep this delay in the first measurement point as small as possible in order to minimize this systematic error. This is also the major drawback of any OTF method. To extract the threshold voltage shift induced by operating the device under stress conditions, usually a SPICE Level 1 model is used  [116, 124, 125]. In the simplest method (OTF1), the drain voltage Vd and the SPICE parameter θ are assumed to be small and the effective mobility μ_eff (SPICE parameter) is assumed to be constant throughout the experiment. With these assumptions the threshold voltage shift ΔVth in the OFT1 method can be obtained by

(6.1)

where I_d0 is the reference drain current and Vth0 is the threshold voltage corresponding to I_d0. Since the OTF1 method cannot, due to the assumptions made, predict or at least compensate for mobility changes, other OTF methods  [126] have been developed. Nevertheless, all of them suffer from the unavoidable measurement delay between stress and the first measurement point I_d0. In addition, all OTF methods also feature the inherent modelling error of the employed SPICE models to determine ΔVth. An example of recorded stress and recovery traces using the OTF method is shown in Figure 6.1. However, due to the inherent errors in OTF data the MSM-method and variants thereof are often used, especially when one is only interested in the recovery traces.

6.1.3  Direct Current Current Voltage

First introduced in  [127] and  [128], the direct-current-current-voltage (DCIV) method is used to directly monitor the defect density by measuring the bulk current Ib, which is the result of the carrier recombination in the oxide and at the silicon-oxide interface (cf. Figure 6.4).

In order to monitor the stress induced degradation, DCIV experiments  [127, 128] are performed on fresh devices before and after stress using a drain voltage Vd high enough to forward bias the pn junctions. When assessing bias temperature stress, a DCIV experiment is conducted before and after stress to compare the defect densities before and after stress.

6.1.4  Time Dependent Defect Spectroscopy

Time dependent defect spectroscopy (TDDS) is a data analysis technique to assess border traps in the oxides of MOSFETs, where the devices need to be sufficiently small in order to be able to discriminate different traps  [105]. Figure 6.5 shows the ΔVth recovery traces recorded after bias temperature stress on a small area (L × W = 2μm × 160nm) n-channel MOSFET. The only assumption TDDS does require is that the step-height and emission time of a single defect/charge carrier trap in the oxide (cf. Chapter 4) uniquely characterizes a particular trap. The technique itself works as follows: First a statistical significant number of subsequent ‘stress-relax’ cycles on a single device at a certain but fixed drain voltage are recorded for a certain but fixed stress temperature. The recovery traces can then be compared by accounting for the residual degradation from the previous relax phase. Inspecting ΔVth over recovery time from each relaxation phase and employing the initial assumption that each trap can be uniquely identified by a characteristic step-height one is able to calculate the characteristic time constant, e.g. the emission time τe  [129]. In Figure 6.6 the extraction technique is illustrated. Furthermore, TDDS can be used to produce so called discrete Capture-Emission-Time (CET) maps  [29]. To this end, the TDDS method shown in Figure 6.6 is not only applied to the recovery traces but also to the ΔVth recorded during the stress phase of the stress-relax experiments. Then by identifying the various traps by the individual step heights they cause it is possible to combine these two TDDS maps to a single discrete CET map.

Figure 6.5:

Five recovery traces from a stress-relax experiment. The experiment has been carried out in a temperature controlled environment on a n-channel MOSFET, where the ΔVth has been calculated from ΔId using an initial Id -Vgcurve. Multiple of these traces are used to identify the capture and emission times of single traps. The data has been provided by Michael Waltl.

Figure 6.6:

Assembly of a TDDS map from drain current measurements during device relaxation. All recorded recovery traces are plotted on the same time axis, where 0s corresponds to the onset of relaxation. Then the characteristic step-heights are identified by an algorithm published in  [129]. Each step-height corresponds to a capture/emission event and its time of occurance and step-height are marked (diamonds) in a map (lower figure). Clusters of points in this map most likely correspond to the same trap. This way single traps and their time constants can be identified. Taken from  [129].