Basic knowledge of MOS transistor characteristics, output characteristics, detailed transconductance expressions

Integrated circuits are made up of transistors, so it is desirable for the characteristics of a single transistor to be simple in the design of integrated circuits. For this reason, simple expressions with rough approximations are often used. The main points are as follows.

One of these simple expressions is that the current flowing through the MOS transistor is proportional to the square of the effective gate voltage in the saturation region 1). MOS transistor characteristics. This relationship is based on the fact that when the carrier charge Qs induced in the semiconductor is proportional to the effective gate voltage, and the electric field generated by the drain voltage at the source terminal is also proportional to the effective gate voltage, the characteristic curve tends to be saturated.

Another approximation about the current is when the speed of the drift charge reaches the limit speed (the speed of electrons in silicon is about 8.5×106 cm/sec). This approximation indicates that the source-drain distance is shortened, and the drift speed tends to a certain value when the electric field is increased. One limit. Therefore, this approximation can be used to limit the maximum current. In this approximation, since the current has nothing to do with the electric field, the current is proportional to the first power of the effective voltage.

The effective gate voltage that determines this current can be obtained from the voltage applied between the gate and the source and the following threshold voltage

。

(1) Threshold voltage

As mentioned above, in the area where the leakage current flows, the threshold voltage is to be usedWhen expressing the relationship between the leakage current and the gate voltage, the relationship curve between the leakage current in the current region and the gate voltage can be extrapolated, and the gate voltage at which the leakage current becomes zero is defined as。This is an error-free method that can be used. MOS transistor characteristics. That is, when applied to a region where the gate voltage exhibits a square-law characteristic, the gate voltage at which the leakage current in the square-law region becomes zero is taken as the threshold voltage。

MOS transistors are generally composed of a semiconductor substrate and source and drain regions of opposite conductivity types, and no current flows through the substrate. Since the channel carriers are the same type as the source and drain, the carriers are the same type as the source and drain. It can also be considered that when the semiconductor surface is inverted under the action of an electric field, the transistor starts to flow current, but according to the square When the current flows through the Q characteristics, the surface carrier concentration opposite to the substrate conductivity and the substrate impurity concentration NB become almost the same order, and the increase in the charge of the surface depletion layer can be ignored. At this time, the surface potential фs is twice the Fermi potential фPB in the body, but the direction is opposite to the direction of фPB, as shown in Figure 3.13. In other words, inThe change in the nearby gate voltage not only generates movable charges in the channel, but also charges and discharges impurity charges in the depletion layer, which deviates from the square-law characteristics. However, in the vicinity of the square-law characteristics well, it can be Extrapolate the square law characteristics to obtain the gate voltage when the leakage current is zero.

Threshold voltageAvailable surface potential-2фPB, the voltage induced by the surface depletion layer charge QB at this time through the gate capacitance (capacitance per unit area Co)，It is expressed by the voltage -Qo/Co of the effective charge Qo in the compensation oxide film and the work function difference фMS between the gate metal and the semiconductor. that is

In the formula, the positive sign indicates the N channel, and the negative sign indicates the P channel.

(2) Output characteristics

The current IDS between the drain and the source is continuous in the channel. If the channel length is L and the width is W, then there is

Integrate both sides of the equation from x=0 to L. After finishing, we get

This formula is established when the highest voltage in the channel-the drain voltage VDS is lower than ；If VDS is higher than，The depletion layer between the drain and the channel widens, and a voltage drop occurs in the widened part. In the channel where carriers are intentionally present, the highest voltage is always。Therefore, the current tends to be saturated, and its value is approximately constant, expressed by the following formula

But the drain voltage VDS is higher than，Assuming that the width of the depletion layer extending between the drain and the channel is ΔL, because there is

The current is not fully saturated, and the effective channel length is modulated by the drain voltage, so the output conductance shown in Figure 3.14 4) appears, which is very similar to the base region modulation effect in a bipolar transistor. MOS transistor characteristics. If the substrate impurity concentration is high, the ΔL will be small, and the output conductance will decrease accordingly, and the gm (to be discussed below) will also decrease3), so choose the most appropriate concentration according to the application.

(3) Transconductance gm

Transconductance is defined as the variation of the leakage current IDS with the input voltage, that is, the gate voltage VGS, and it is one of the important parameters representing the performance of the device. After the equations (3.3) and (3.4) are differentiated, the following equations are obtained

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