MIT6_012F09_lec12_sub - MOSFETs in the Sub-threshold Region...

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MOSFETs in the Sub-threshold Region (i.e. a bit below V T ) Clifton Fonstad, 10/28/09 In the depletion approximation for n-channel MOS structures we have neglected the electrons beneath the gate electrode when the gate voltage is less than the threshold voltage, V T . We said that it is only when the gate voltage is above threshold that they are significant, and that they are then the dominant negative charge under the gate. Furthermore, we say that above threshold all of the gate voltage in excess of V T induces electrons in the channel; thus our model is that the sheet charge density under the gate, q N * , is q N " = 0 for v GC # V T $ ox t ox v GC % V T ( ) for V T # v GC ( ) ( (1) As MOS integrated circuit technology has evolved to exploit smaller and smaller device structures, it has become increasingly important in recent years to look more closely at the minority carriers present under the gate when the gate voltage is less than threshold, i.e. in what is called the “sub-threshold” region. These carriers cannot be totally neglected, and play an important role in device and circuit performance. At first they were viewed primarily as a problem, causing undesirable “leakage” currents and limiting circuit performance. Now it is recognized that they also enable a very useful mode of MOSFET operation, and that the sub- threshold region of operation is as important as the traditional cut-off, linear, and saturations regions of operation. To begin our study of the sub-threshold region, we will first quickly review the electrostatics of the MOS capacitor, and the electrostatic potential profile predicted by the depletion approximation model. Then we will use this result to derive a more accurate expression than that in Equation 1 for q N * below threshold, and use the resulting expression to, among other things, assess the assumption that the contribution of the mobile electrons underneath the gate to the net charge density in the depletion region is negligible compared to the contribution from the ionized acceptors. Finally we will look at the current-voltage characteristic of a MOSFET operating in the sub-threshold region, and merge it with our earlier model so that we then have a model in which the mobile electron charge is taken into account and the drain current is no longer identically zero when v GS is less than V T .
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6.012 Supplementary Notes: MOSFETs in the Sub-threshold Region (i.e. a bit below V T ) The Electrostatics of the MOS Capacitor with v BC = 0 Consider the MOS capacitor with v BC = 0 illustrated in Figure 1, the same structure we used when we first looked at the MOS capacitor using the depletion approximation. In the depletion p-Si n+ B C G SiO 2 + v GC (= v GB ) FIGURE 1 A MOS capacitor connected as a two-terminal capacitor with v GC = v GB = 0. approximation, we assume that Equation 1 holds and that the net charge density profile,
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This note was uploaded on 11/07/2011 for the course COMPUTERSC 6.012 taught by Professor Charlesg.sodini during the Fall '09 term at MIT.

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MIT6_012F09_lec12_sub - MOSFETs in the Sub-threshold Region...

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