edfas.org 9 ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 27 NO. 1 of 1 Hz, and each GR noise contribution is described by Eq 1, the input-referred power spectral density may be written as:[23] (Eq 2) In order to estimate the noise parameters, it is suggested to use the behavior of the input-referred noise multiplied by the frequency versus the frequency. In this representation, the flicker noise will exhibit a plateau giving the Kf level, and the slope of the linear increase of the Sv(f ) . f with the frequency in the highest frequency range may give the white noise level Wn. If only one GR noise contribution is present, a bump centered at the characteristic frequency will appear. As the “bump” takes place at the characteristic frequency, f0, this allows for an easy determination of f0. The plateau of the Lorentzian S0, if the white noise level may be neglected around f0 is given by:[10,15] (Eq 3) As shown in Fig. 1, the noise spectra may be perfectly represented using the model of Eq 2. A methodology to estimate the noise parameters if more than one Lorentzian contributes to the total noise is given in reference 15, where the first step is estimating the characteristic frequency and the plateau corresponding to the higher level of GR contribution. The traps located in the depleted region of the semiconductor material are characterized by a discrete and unique deep energy level, ET. The GR noise will arise when the Fermi level crosses the trap level in the semiconductor bandgap. If the applied device polarization changes, the Fermi level changes. However, as long as a crossing point exists between the Fermi and the trap level, the same trap will be probed. Considering the Shockley-Read-Hall (SRH) model, the characteristic time constant will be given by the τ0 -1 = c n nt (or cp pt), [10,13] where c n = σnvth and cp = σpvth are the capture rates for electrons and holes, σn and σp are the electron and hole capture cross sections, vth is the thermal velocity; nt and pt being the carrier concentration when the quasiFermi level crosses the trap with energy ET. Consequently, the characteristic time constant, τ0, or the corresponding corner frequency, f0, is independent on the applied device polarisation at a fixed operation temperature.[10-12] In a general way, the evolution of the characteristic relaxation time of GR noise contribution at a fixed temperature as a function of the applied gate bias makes it possible to locate the trap.[10-12] Typical examples are given in Fig. 2. The variation of the characteristic time constant with temperature at fixed polarization may allow for the identification of the energy difference between the appropriate band energy and the trap energy and the capture cross section of the trap through the Arrhenius plot, which may be constructed using:[10-12] (Eq 4) where kB is the Boltzmann constant, T is the temperature, h is the Planck constant, me* and mh * are the effective mass of electrons and holes, respectively, and Mc is the number of conduction band energy minima. Equation 4 is valid for n-channel devices. The physical nature of these traps can be found by comparing the energy and capture cross section of the identified traps with data in the literature. An example of the evolution of the normalized voltage noise spectral density multiplied by frequency at fixed Fig. 1 Typical noise measurement and model using Eq 2: flicker noise, white noise, and 1 GR noise contribution are considered to obtain the best agreement between measurement and model. Device: standard UTBOX, equivalent oxide thickness (EOT) of 2.1 nm, thickness of the buried oxide (TBOX) of 15 nm, thickness of the silicon film (TSi) of 16 nm, ratio between the channel gate length and width (LG / WG) of 1 µm / 1µm, operated at a drain current polarization (ID) of 1 µA (for an applied drain to source voltage (VDS) of 50 mV) and at a temperature of 230 K. [16] Estimated noise parameters: Wn = 3.5∙10-14 V2⁄Hz, Kf = 2.6∙10-10 V2, S 0 = 5∙10-10 V2⁄Hz, f0 = 3Hz.
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