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# 1.3 The capacity of an MOS structure to store charge

Figure 1 shows a schematic section through an MOS structure and sets up a colour scheme that distinguishes the different layers. In this case the M-layer is provided by heavily doped polysilicon and the semiconductor base material is p-type silicon.

Figure 1 A schematic of an MOS structure (the p-type silicon is shown in pink)

In Figure 2 the schematic is modified to show what happens in response to positive bias between the M-layer and the S-layer. Initially, the holes in the p-type silicon are repelled by the arrival of positive charge on the M-layer. This is similar to the depletion region that exists at a p-n junction. The repulsion of charge from the depletion region is accomplished by an electric field that is caused to build up under the biased M-layer. Further bias extends the zone from which holes are pushed out.

Figure 2 An MOS structure with bias of (a) 1 V; (b) 2 V; (c) 3 V

To appreciate what happens when yet more bias is applied, it is important to remember that charge carriers in semiconductor material are continually being generated by thermal energy. That is, there is a continual background fizzing of activity as pairs of electrons and holes are generated throughout the silicon. In regions where there are lots of holes, electrons don't survive for long. However, in the region under the positively biased M-layer holes have been pushed out by an electric field, so here electrons live much longer. Not only that but the field sweeps electrons in the opposite direction to the holes, and so they accumulate up against the insulating oxide layer.

The creation and annihilation of electrons and holes goes on all the time in semiconductors. In uniformly doped material, and in the absence of external bias, the local rate of generation equals the rate of loss. It is important to see how these microscopic life cycles of electrons and holes are affected near a biased MOS structure, where an electric field disturbs the local equilibrium. Given time, some kind of steady state is always achieved, with generation and loss in balance overall, but the question is, how long does it take?

Because MOS structures, like p–n junctions, involve depletion regions, they are sometimes said to constitute MOS diodes.

The quantity of the electrons that accumulate at the interface between oxide and semiconductor will establish a steady level as follows. There is a constant trickle of electrons drifting in from the sites across the depletion region where electron-hole pairs are thermally generated. This builds up negative charge that tends to offset the effect of positive charge on the M-layer; that is, it weakens the electric field that maintains the depletion region. In effect, there is a thermally generated current that charges the capacitor formed by the MOS structure. (Because the MOS structure accumulates charge it can also be described as an MOS capacitor.) The more the electrons accumulate, the less effective the field is at keeping back holes. Thus, a few more holes are able to diffuse back in, recombining with, and therefore removing, some of the accumulating electrons. Here, therefore, is a structure that can store charge, much like a capacitor. In fact it is reasonably described as an MOS capacitor, but the MOS structure is effectively a leaky capacitor; see Box 2: Filling a leaking bucket.

## Box 2: Filling a leaking bucket

Imagine a bucket that has a hole in the bottom collecting water from a steadily dripping tap (Figure 3). Let's suppose that the leak rate through the hole depends on the depth of water in the bucket. What happens is that the depth of water in the bucket will increase until the level causes the leak rate to equal the filling rate from the dripping tap.

The MOS capacitor behaves in a similar fashion. The bucket is the equivalent of the capacitance. The dripping tap represents the thermally generated electrons. The quantity of water in the bucket then mirrors the stored charge.

Figure 3 Filling a leaking bucket: (a) leak rate less than supply rate; (b) leak rate equal to supply rate

A balance is struck when holes diffuse back from the p-type silicon outside the depletion region at the same rate that electrons drift in from the depletion region. The time to fill the capacitor can be several seconds, depending on the rate of thermal generation. Figure 4 illustrates the steady-state distribution of charges in the biased MOS structure.

Figure 4 Steady-state distribution of charges in a biased MOS structure (note that details of the thermal generation and back diffusion of holes are not shown)

While charge is building up at the oxide–silicon interface, electrons are displaced from the metal into the external circuit; that is, current flows in the external circuit. Extra positive charge is thereby left behind on the M-layer. This charging of the M-layer is driven by thermal generation of electron–hole pairs, swept in opposite directions by the field. However, once a steady state is reached the thermal current is shorted internally by the back diffusion of holes, so there is no longer any current in the external circuit. The charge added to the M-layer cannot pass through the insulating O-layer. So, when the M-layer is disconnected from the bias supply, positive charge remains there, locked in place by the combined effects of the depletion region and the accumulation of electrons at the oxide interface.