Ultra-fast short-time NBTI stress and relaxation measurements from theµs to the seconds regime using different temperatures, stress voltages, and oxide thicknesses have been performed. A large dataset is examined here using well defined extraction parameters (t0,ref, tskip, and ǫ). Amongst them the reference time t0,ref is identified as the most crucial one. It can be seen that depending on the range used for the data extraction (ǫ) the reference time t0,ref is also changed. While a settled gate pulse, i.e. a small ǫ, does not contain the full degradation and relaxation data and may therefore indicate a wrong distribution of time constants, too broad limits ofǫrel may produce spurious relaxation transients due to a limited resolution of smaller than 1µs. Comparing the different gate voltage criteria taken for the OTF routine yields that choosing a rather large ǫrel reflects the completely different fast-VTH measurement method best.
In the initial degradation phase, which is often explained by elastic hole trapping, the data can be well fit by a logarithmic time dependence [12,15,42]. As this log-dependence is considerably distorted during long-term measurements, alternatively a power-law using an exponent considerably smaller (n ≈0.04) than generally observed during long-time stress (n ≈0.12) can be used. However, the main disadvantage of the power-law is that the fit is ill defined for up to medium stress conditions.
Only high temperatures and/or highVG,str show the aforementioned smalln.
Moreover, the extracted activation energy of about 0.1 eV is compatible with the values typically obtained during long-time stress [106]. The temperature and voltage dependencies of stress and relaxation rule out elastic and thus temperature-independent hole tunneling as being responsible for short-time NBTI degradation as proposed by [94, 104]. A possible explanation could involve an inelastic tunneling process [98].
Chapter 7
Relaxation of Negative/Positive BTI
As the time constant distribution of the microscopic defects behind BTI turn out to be a key issue, the apparent differences in relaxation behavior of negative and positive BTI (NBTI and PBTI) on pMOSFETs, as depicted in Fig. 7.1, are now examined under that perspective.
Although PBTI on pMOSFETs is not regarded as technologically important as NBTI, it provides a valuable probe of the underlying physical degradation mechanism. The most intriguing observation is that both negative and positive bias stress create positive charges in the oxide [30], which was already demonstrated in Chapter 4.2. However, so far the NBTI and PBTI stress conditions were only compared in a qualitative way, i.e. strong inversion was usually opposed to strong accumulation with undetermined specifications concerning the exact gate voltages or oxide electric fields applied.
10-6 10-4 10-2 100 102 104 106 Relaxation Time [s]
0 10 20 30 40 50
∆VTH [a.u.]
VG,str = -2.2 V (Device #1)
VG,str = -2.2 V (Device #2 scaled to #1)
t = 1 ms ...100 ksstr
T = 125 °C VD,str = -65 mV
NBTI/pMOS SiON 2.2 nm
10-6 10-4 10-2 100 102 104 106 Relaxation Time [s]
0 2 4 6 8 10 12 14 16
∆VTH [a.u.]
VG,str = 2.1 V (scaled) VG,str = 1.9 V
t = 1 ms ... 100 ksstr
T = 125 °C VD,str = -65 mV
PBTI/pMOS SiON 2.2 nm
Figure 7.1: While after short stress the relaxation does not show significant differences except slightly varying slopes, the distinct relaxation behavior after NBTI and PBTI is obvious when monitoring the long-term relaxa-tion tail after the last stress sequence. The stress time is increased in steps of one decade with the only exception at 50 ks. Note that degradation data obtained with equal absolute values of the oxide electric field are compared here.
63
-2 0 2
Figure 7.2: For comparing NBTI and PBTI one has to apply proper opposite fields.
This is accomplished by measuring the C(V)-characteristics. Larger area de-vices with a W/L = 20µm/20µm have to be used to get satisfactory signal-to-noise ratios. The three ox-ide thicknesses are 1.8 nm (Top Left), 2.2 nm (Top Right), and 5.0 nm (Bottom Left). Though the oxide is slightly nitrided (6%), the ǫr of SiO2
was used to calculate the oxide electric fieldsEox, using a flatband voltage of 0.7 V. The capacitance of the limiting case of an ideal parallel plate capaci-tor of the same thickness is plotted for comparison.
For a quantitative analysis of the recovery following NBTI and PBTI stress, long stress times tstr between 100 s and 100 ks are essential. The same technology (6 %-SiON-pMOSFET) as used in Chapter 6 was compared by the fast-VTH method of [15] using three different oxide thicknesses (tox = 1.8 nm,2.2 nm, and 5.0 nm) and the corresponding geometries of W/L = 20µm/0.12µm, 20µm/0.12µm,and 20µm/0.24µm at a constant temperature of 125◦C. Depending on the oxide thickness the same applied stress voltage causes a totally different oxide electric field. This is due to capacity of the MOSFET with its principle already explained in Chapter 2.6. The resulting electric field at the surface of the semiconductorEs can be experimentally estimated by using the following relation:
where C(V) denotes the capacity of the MOSFET, Vfb the flatband voltage, and W and L the width and length of the device. TheC(V)-characteristics and the corresponding electric field are
Chapter 7. Relaxation of Negative/Positive BTI 65
Figure 7.3: Samples with an oxide thickness of 2.2 nm stressed using various NBTI/PBTI-conditions from 100 s up to 10 ks. Depending on the type of stress, there is either no deviation from a logarithmic recovery behavior, a deviation downwards (PBTI) or upwards (NBTI). While for weak NBTI/PBTI-conditions (Eox =±6 MV/cm andtstr= 100 s) a logarithmic fit of the relaxation is possible, this is not the case for the other heavier stress conditions.
shown in Fig. 7.2 for the different device geometries with a constant flatband voltage of 0.7 V.
From this figure it can further be seen that in addition to the nonzero flatband voltage the electric field during NBTI and PBTI is not symmetric. To create comparable degradation conditions (not comparable degradation shifts) for both NBTI and PBTI, the same effective field is of interest, i.e.
the same magnitude, but opposite sign. Based on the experimental C(V)-characteristics in Fig. 7.2 the required stress voltage VG,str can be obtained for both NBTI and PBTI. As an example, to achieve an Eox =±6 MV/cm fortox = 2.2 nm gate voltages of +2.65 V for PBTI and −2.05 V for NBTI have to be applied.