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"-"D use visual .net code 128 barcode generator toreceive code 128 with .net QR (6"40). where the Debye length is dependent on doping as described in Eq. (6-25). The overall MOS flat band capacitance, CFB, is the series combination of Cdebye and C(.

We can thus determine VFB corresponding to the CFB. Once Cj,VFB, and substrate doping are obtained, all terms in the VT expression (Eq. 6-38) are known.

Interestingly, the threshold voltage VT does not correspond to exactly the minimum of the C-V characteristics, Cmjn, but a slightly higher capacitance marked as point 4 in Fig. 6-16. In fact, it corresponds to the series combination of Q and 2Cdmin, rather than the series combination of Q and Cdmin.

The reason for this is that when we change the gate bias around strong inversion, the change of charge in the semiconductor is the sum of the change in depletion charge and the mobile inversion charge, where the two are equal in magnitude at the onset of strong inversion. We can also determine MOS parameters such as the fast interface state density, D, and mobile ion charges, Qm, from C-V measurements (Figs. 6-21 and 6-22).

The term fast interface state refers to the fact that these defects can change their charge state relatively fast in response to changes of the gate bias. As the surface potential in a MOS device is varied, the fast interface. Field-Effect Transistors states or traps in the band gap can move above or below the Fermi level in response to the bias, because their positions relative to the band edges are fixed (Fig. 6~21b). Keeping in mind the property of the Fermi-Dirac distribution that energy levels below the Fermi level have a high probability of occupancy by electrons, while levels above the Fermi level tend to be empty, we see that a fast interface state moving above the Fermi level would tend to give up its trapped electron to the semiconductor (or equivalently capture a hole).

Conversely, the same fast interface state below the Fermi level captures an electron (or gives up a hole). It obviously makes sense to talk in terms of electrons or holes, depending on which is the majority carrier in the semiconductor. Since charge storage results in capacitance, the fast interface states give rise to a capacitance which is in parallel with the depletion capacitance in the channel (and hence is additive), and this combination is in series with the insulator capacitance C,.

The fast interface states can keep pace with low frequency variations of the gate bias (-1-1000 Hz), but not at extremely high frequencies (~1 MHz). So the fast interface states contribute to the low frequency capacitance CLF, but not the high frequency capacitance CHF. Clearly, from the difference between the two, we ought to be able to compute the fast interface state density.

Although we will not do the detailed derivation here, it can be shown that. C,C F C; ~ CHf q \ C ; - CLF Jcm^eV-1. (6-41). While the fast interfa ce states can respond quickly to voltage changes, the fixed oxide charges Q^, as the name implies, do not change their charge state regardless of the gate bias or surface potential. As mentioned above, the effect of these charges on the flat band and threshold voltage depends not only on the number of charges but also their location relative to the oxide-silicon interface (Fig. 6-22).

Hence, we must take a weighted sum of these charges, counting charges closer to the oxide-silicon interface more heavily than those that are farther away. This position dependence is the basis of what is called the bias-temperature stress test for measuring the mobile ion content, Q m . We heat up the MOS device to ~200-300 C (to make the ions more mobile) and apply a positive gate bias to generate a field of ~1 MV/cm within the oxide.

After cooling the capacitor to room temperature, the C- V characteristics are measured. We have seen how VFB c a n be determined from the C-V curve, using Eq. (6-40) and Ct.

VFB is also given by Eq. (6-37). The positive bias repels positive mobile ions such as Na+ to the oxide-silicon interface so that they contribute fully to a flat band voltage we can call VFB.

Next, the capacitor is heated up again, a negative bias is applied so that the ions drift to the gate electrode, and another C-V measurement is made. Now, the mobile ions are too far away to affect the semiconductor band-bending, but induce an equal and opposite charge on the gate electrode. From the resulting C-V, the new flat band, VFB, is determined.

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