The Relationship between Carrier Mobility and Drain Voltage at the Interface of MOS Field Effect Transistor

In a low electric field, the drift speed υd of electrons is proportional to the applied electric field Ez, which can be expressed by υd=μEх. Therefore, the drift mobility of electrons μ is constant, but as the electric field strength increases, electrons and acoustic phonons collide inelastically. As a result, the proportion of energy given to acoustic phonons by electrons increases. Therefore, although the drift speed of electrons increases, But it does not increase in proportion to the electric field. If the electric field is further increased, the kinetic energy of the electrons becomes very large, and optical phonons are released, and the drift speed of the electrons no longer increases. The relationship between carrier mobility and drain voltage. This phenomenon can occur inside the crystal or on the surface. Figure 1.14 is the measured curve of the relationship between the drift velocity of electrons in the inversion layer of the silicon N-type surface and the electric field 8).

Especially for MOS field-effect transistors for high-frequency or high-speed switching with a short channel length, even if the drain-source voltage is not too large, the electric field strength in the channel tends to increase, and the drift speed of carriers is not high. The area proportional to the electric field. Considering this effect, the relationship between the drift speed and electric field shown in Figure 1.14 can be written as

Where μo is the low electric field download current mobility

υs is the saturation value of the carrier drift velocity when the electric field is extremely strong.

Let's study how the static characteristics of MOS field effect transistors change.

To make the discussion uncomplicated, formula (1.11) can be rewritten as

Substitute the formula (1.77) into the υd in this formula, and use the relational formula, Get

Hence

It can be seen from the above formula that after the drain voltage increases, the carrier velocity is saturated, so the transconductance will be reduced to the relationship between the carrier mobility and the drain voltage.

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