NBTI Experiments

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1.3 NBTI Experiments

In the past, a series of distinct measurement techniques has been established, which includes direct-current current-voltage measurements, measure-stress-measure (MSM) technique, on-the-fly (OTF) measurements, capacitance-voltage measurements, charge-pumping, and electron-spin-resonance (ESR). Each of them is suited and thus employed for the analysis of NBTI. part from equipment issues, these measurement techniques strongly differ in the information they provide. In the following, their basic experimental setup and principle functioning are outlined and their specific shortcomings are discussed.

1.3.1 Measure-Stress-Measure Technique

The measure-stress-measure (MSM) technique has traditionally been employed to probe NBTI experimentally [25, 26]. Before the real measurement of NBTI degradation starts, an $ID(VG)$ curve is taken by scanning the device in a range around the initial threshold voltage $Vth0$ . Then the device is subjected to stress bias and only interrupted by short intervals with the gate bias brought back to $Vth0$ . During these short measurement intervals, the drain current $ID$ is monitored and converted to a threshold voltage shift $ΔVth$ based on the initially scanned $ID(VG)$ curve [25]. Alternatively, $Vth$ can be directly obtained by enforcing the initial threshold current $ID0$ [27] or by the shift of complete $ID (VG )$ curves recorded using ultra-short pulses [28, 29].

However, the MSM method suffers from an unavoidable measurement delay [30], which is defined as the time interval between the removal of stress and the first measurement of the drain current. The degradation within this time is not covered by the measurements and so usually leads to an underestimation of the threshold voltage shift. As pointed out in [31], the different delay times seriously affect the interpretation of the degradation data, for instance, the exponent of a time power-law as discussed in Section 1.4. Thus minimizing the measurement delay has long been the subject of numerous studies [27].

1.3.2 On-The-Fly Measurements

On-the-fly (OTF) measurements try to circumvent the unintentional measurement delay and are therefore often regarded as the method of choice for experimentally investigating NBTI. In this method, the gate bias is maintained in the linear regime during the entire measurement run while the drain bias is held at a small but constant level. Alternatively, short voltage pulses can be applied to the drain during measurements only. In both cases, the device degradation is monitored based on the drain current $IDlin$ . Since the threshold voltage is of central interest for NBTI, the drain current has to be converted to $Vth$ using extrapolation schemes [32, 33]. The simplest is based on the SPICE level 1 compact model

ΔVtOhTF = ID-IDI0D0(VG - VtOhT0F) , (1.1)

where $ID0$ and $V OTF th0$ denote $ID$ of the first measurement point [34, 35] and $Vth$ of the undegraded device, respectively. This compact model neglects mobility variations [35, 36, 37] ascribed to the scattering of charge carriers at the trapped charges close at the interface. However, this model benefits from the fact that, in contrast to other extrapolation schemes, only $ID0$ has to be recorded. More complex extrapolations schemes accounting for mobility variations have been proposed but require the determination of the full $IDVG$ curve. Note that these $IDVG$ curves must be measured before stress, thereby already causing a non-negligible amount of degradation, which is not accounted for in the extrapolation scheme.

1.3.3 Electron Spin Resonance

Electron spin resonance (ESR) is a powerful tool to identify paramagnetic defects, which are characterized by an unpaired electron in their orbitals. This electron is associated with a spin whose response to an external magnetic field is measured in ESR experiments. For instance, such paramagnetic defects can be $Si$ -dangling bonds at the $Si∕SiO2$ interface (the so-called $Pb$ centers) [10, 11, 38, 8] or in the dielectric (the numerous variants of $′ E$ centers) [39, 40, 41, 42, 43, 44]. It thereby gives chemical and structural information about the defect under investigation and provides insight into the chemical processes occurring in the dielectrics. In this measurement technique, the defects in the sample are subjected to a large but slowly varying magnetic field $H$ , which splits their energy levels according to the Zeeman effect. An unpaired electron residing in one defect orbital has two possible orientations - namely either parallel or anti-parallel to the magnetic field. The energetical separation of these two orientations equals

ΔE = g0μBH, (1.2)

where $μB$ denotes the Bohr magneton and $g0$ the gyromagnetic factor. Due to energetical considerations, the defect electron preferably aligns parallel to the magnetic field. Furthermore, the sample is additionally exposed to a microwave radiation $ν ~ 9- 10GHz$ , thereby delivering an energy of $hν$ to the electron. In the case of resonance, the condition $hν = g0μBH$ is satisfied and the electron change the orientation of its spin, which causes as a peak in the ESR absorption spectrum. The most frequently employed measurement technique records the ESR signal with respect of the slowly varying magnetic field $H$ . Note that this measurement technique is limited to defects that have only one electron in their orbitals. Therefore, changing the charge state via electron or hole capture will render these defects “ESR-inactive”. Conversely, defects with either no or two electrons in the corresponding orbital can be made “ESR-active” by a charge capture event.

Additional structural information of the investigated defect is available via second-order effects: In solids, the spin-orbit interactions vanish for the ground state in solids but affect the excited states. They alter the gyromagnetic factor to an angle-dependent $g$ -tensor, which reflects the symmetry of the paramagnetic center. Hence, angle-dependent measurements allow the identification of defects on the basis of this symmetry [8, 45]. In this way, it has been revealed that the central $Si$ atoms of $Pb$ and $Pb0$ centers are tetrahedrally back-bonded to three other $Si$ atoms. In contrast, $Pb1$ centers exhibit a lower symmetry, which is traced back to a surface dimer bond. Another second order effect arises from electron-nuclear hyperfine interactions. Due to different orientations of the nuclei magnetic moments, additional characteristic peaks emerge in the ESR spectrum. For instance, the relative heights of these features — more precisely, a ratio of $1∕20$ — is a special signature for the element $Si$ . Therefore all variants of $Pb$ centers could be identified as $Si$ dangling bonds. In the context of NBTI, a series of investigations address hydrogen reactions with $Pb$ centers as well as hydrogenated variants of $E′γ$ centers, namely $10.4G$ doublet and the $74G$ doublet [40, 46, 41]. Another variant of ESR is spin dependent recombination (SDR) [47, 18], in which the recombination via deep traps in the substrate bandgap is hampered due to a magnetic alignment of electrons in the conduction band and in the trap. With this method, it has been suggested that $KN$ centers play an important role in the NBTI degradation of silicon oxynitrides.

1.3.4 Time Dependent Defect Spectroscopy

With the technical advances in the MOSFET technology during the last several years, the device geometries of MOSFETs have been continuously shrunken and reached a point where the device degradation is dominated by the occurrence of single charging or discharging events [48, 49, 50]. As shown in Fig. 1.1, each of these events appears as a step in the recovery traces. Interestingly, one can clearly recognize that those steps differ significantly in their heights. This can be ascribed to the fact that the random distribution of dopants produces a spatially varying electrical potential inside the channel. The resulting inhomogeneous current density from source to drain is frequently referred to as the percolation current path, which is unique for each device. The lateral position of a charged trap within the gate area determines the step height in the drain current and the threshold voltage shift. This height is the signature of each defect and can thus be used for the identification of a single trap. This fact has motivated the use of the so-called spectral maps [51, 52, 53], in which the frequency of emission events is plotted vs. $d$ and $τem$ (see the lower panel of Fig. 1.1). These maps reveal the characteristic emission times for certain stress conditions, which can be varied for the investigation of field and temperature dependence of $τcap$ and $τem$ (Fig. 1.2).

Figure 1.1: The time evolution of the threshold voltage shift for a small-area pMOSFET during recovery. The recorded recovery traces (black lines) in the top panel have several steps marked by the red or blue lines, respectively. The corresponding spectral map shows the emission times vs. the step height. Note that there are regions (ellipses) with an accumulation of points. Each of them can be assigned to one individual defect within the device.

Figure 1.2: Left: The capture time constants $τcap$ as a function of $VG$ for a number of defects at different temperatures extracted from a single device. Open and closed symbols mark measurements carried out at $125∘C$ and $175∘C$ , respectively. The $τcap$ curves show a strong field acceleration and temperature activation. However, the observed field acceleration does not follow the $1∕ID ≈ 1∕p$ dependence (dot-dashed line) as predicted by the conventional SRH model. Right: The same as in the left figure but for the emission time constants $τem$ . The two distinct field dependences (upper and lower panel) suggest the existence of two types of defects present in the oxide. However, the defect $#1$ shows different field behaviors depending on whether the device is operated in the linear or the saturation regime during the measurement. This suggests that the electrostatics within the device are responsible for the two distinct field dependences. It is noteworthy that the drop in $τem$ goes hand in hand with the decrease of the interfacial hole concentration $p$ (dot-dashed line).

TDDS has lead to several essential findings [51, 52, 53, 54] outlined in the following:

The plot in Fig. 1.2 reveals that the defects exhibit a strong, nearly exponential voltage dependence of $τcap$ . Empirically, this dependence can be described by $exp(- c1Fox + c2F 2ox)$ . However, it differs from defect to defect, implying that it is related to certain defect properties.
The time constant plots show a marked temperature dependence, which becomes obvious by the downward shift of the $τcap$ curves for higher temperatures. The activation energies $Eact$ extracted from Arrhenius plots are about $0.6eV$ .
$τem$ of most defects is unaffected by changes in $VG$ (“normal” behavior).
A few defects show a drop in $τem$ towards lower $VG$ (“anomalous” behavior).
The $τem$ of both types shows a temperature activation with a large spread ( $Eact = 0.6 - 1.4eV$ ).

One should keep in mind that some defects exhibit an exponential oxide field dependence of $τem$ in normal random telegraph noise (RTN) measurements [55]. This difference to TDDS findings may arise from the fact that these defects are not assessable by the TDDS measurements.

Astonishingly, several TDDS recovery traces display RTN only after stressing [51]. The noise at one recovery trace is physically linked to defects — in this case hole traps — which continuously exchange charge carriers with the substrate. After a while, the RTN signal vanishes and does not reoccur during the remaining measurement time. The termination of the noise signal is ascribed to hole traps which change to their neutral charge state and remain therein. In [51], this kind of noise has been termed temporary RTN (tRTN) since it occurs only for a limited amount of time.

A similar phenomenon called anomalous RTN (aRTN) has been discovered in the early studies of Kirton and Uren [56]. Therein, electron traps have been observed, which repeatedly produce noise for random time intervals. During the interruptions of the signal, the defects dwell in their negative charge state so that no noise signal is generated. The behavior of these traps has been interpreted by the existence of a metastable defect state.

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