Overview and theory of the physical basis of MOS transistors

The physical basis of MOS transistors

The physical structure, type and working principle of MOS transistors are briefly introduced above. In order to deeply understand the characteristics of MOS transistors, it is necessary to further analyze and discuss the physical properties of MOS systems that make up MOS transistors. For example, how does the Si surface at the junction of semiconductor Si and oxide change with the applied electric field, and what factors are related to the threshold voltage VT of the MOS transistor, etc. These are the main topics discussed in this section.

1. The silicon surface of an ideal MOS system under the action of an external field

As you all know, the actual MOS system is very complicated. For example, there is a work function difference between metal and semiconductor, which will cause electron exchange; at the Si-SiO2 interface, there is a surface state; in the oxide layer, due to ion contamination (mainly sodium ions), there are movable positive Charge; at the Si-SiOn2 interface due to SiO2, a fixed positive charge caused by lack of oxygen, or there are ionization traps in SiO2, etc. These complex factors all affect the surface properties, thereby affecting the performance of the device.

For the convenience of discussion, we first remove the above-mentioned complex factors and assume that there is an ideal system. It is believed that there is no positive charge on the surface in the personalization layer, and there is no work function difference between the semiconductor and the metal. There is no factor that exchanges electrons between metals and semiconductors.

The following is an example of a MOS system with P-type Si as the base to illustrate the effect of an ideal MOS electric field. The direction of the electric field is defined as the positive direction from the outside of the surface to the intermediary. Since it is more convenient to use an energy band diagram to illustrate the current state of the Si surface, we use the change of the surface energy band under the action of an external field to clarify the change of the surface space charge region with the electric field.

1、Е=0（Flat belt）

When the external electric field is zero, there is no electric field on the surface of Si, and the surface of Si is the same as the carrier concentration in the body. Si itself is electrically neutral, and the electron energy is the same from the body to the surface, so the energy band is flat and there is no surface. Space charge zone. As shown in Figure 1-9(a).

2、E<0（accumulation）

If a negative voltage VG is applied to the metal shed relative to the silicon bottom, the electric field ends at the ohmic junction at the beginning. Then, the movable holes inside Si will be subjected to the action of the electric field force to gather on the Si surface to form an accumulation layer, thereby decoagulating the external field into the body. When the thermal equilibrium is reached, a voltage V is applied. Part of it falls in the SiO2 layer (indicated by VG), and the other part falls in the space accumulation layer outside the surface (indicated by VDG), namely:

(1-1)

Since the cavities accumulated on the silicon surface are many seeds, the surface concentration of cavities is very high, but this accumulation layer is very thin. In the surface accumulation layer, because of φ, the energy of electrons at the Si exiting the surface has to increase [-qφs(χ)], so the energy band bends upward. As shown in Figure 1-9(b). Here φs (φ) is the variable of the empty six accumulation zone. At the Si-SiO2 interface χ-0, the value of φs (χ) is the largest, and its value is called the surface potential.

Holes are accumulated on the surface. In order to maintain the neutral condition of the MOS system, a negative charge Qmo equal to the amount of charge in the accumulation layer must be induced on the metal gate. Obviously, when the surface space charge region is accumulating, the MOS transistor It cannot be turned on.

3、E>0（Run out）

If VG is slightly greater than zero, the direction of the electric field is now directed from the Si surface to the body. The holes in Si move against the direction of the electric field under the action of the electric field force, and finally leave a layer of ionized acceptor ions on the surface of Si. Since this layer is composed of a higher level of acceptors, its charge density is basically equal to the acceptor concentration N of bulk doping. We need this situation as depletion, and its space charge region is called the depletion layer, which is similar to the depletion layer in the PN junction. Since the surface potential φs>0 here, the energy at the Si surface should be reduced [-qφs(χ)]. As shown in Figure 1-9(c). The surface energy band bends downward, indicating that the |Er-Ei| at the surface decreases and the hole concentration decreases.

4、E>0（Inversion）

If the VG is further increased, that is, the electric field is further strengthened, the holes on the Si surface are further reduced, and the range of the depletion layer is expanded. At the same time, the minority electron in the P-type Si is subjected to the electric field force and moves to the Si surface and on the surface build up. The surface energy band bends more downwards. The Fermi level EF intersects with the intrinsic Fermi level product E4. At the surface, EF-E4 changes from negative to positive, that is, the surface appears opposite to the conductivity type in the body. The surface is said to be inverted. However, the carriers in the inversion layer are still too few at this time, the space charge region is almost composed of immovable acceptor ions with a concentration of NA, and the drain and source are still in a high resistance state, so the MOS transistor still cannot be turned on.

5、E 》0（Strong inversion）

If the electric field is further enhanced on the above basis, the energy band will bend downward to a greater degree, and even EF-E4 at the surface χ=0 will not only turn to a positive value, but also be equal in value to the body. As shown in Figure 1-9(d). At this time the surface potential:

Where φF is the Fermi potential, which is defined as:

（1-3）

The formula (1-2) shows that when the surface potential reaches twice the Fermi potential, the electron concentration in the P-type silicon surface layer is equal to the hole concentration in the body, that is, the surface has a strong inversion. This is the strong inversion condition. At this time, there are enough electrons in the inversion layer to satisfy the source-drain conduction condition.

The value of φF can be from the formula:

_{It can also be calculated by looking up the chart.}

It can be seen that if the physics of the MOS transistor is to be turned on, it must meet the strong inversion condition. Taking a substrate with a doping concentration of NA=1013/cm as an example, it can be found that φF=0.29V, that is, when φs=0.58V, the surface starts to be strongly inverted.

If N-type silicon is used in the semiconductor material, then the same as the method discussed above, it can be concluded that electron accumulation occurs when E>0, and when E<0, an ionized donor depletion layer may appear, or further reactions may occur. Type and strong inversion type hole layer.

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