Task 6. Flatband voltage (Calculate the flatband voltage）

 

Flatband voltage is defined as the gate voltage when the band of semiconductor is not bent as shown in figure 3.

In ideal case, VG=0  In actual case, VG≠0. There are two reasons. The first one is that there is a work function difference between the metal and the semiconductor.

The second one is that the net charge density in the oxide layer is actually non-zero, such as Fixed charge of oxide.

Figure 3: Band diagram of flat band

As VG is gradually reduced, the accumulation capacitance becomes smaller and has the effect of reducing the measured capacitance. When VG is equal to zero volts. The semiconductor capacitance is now defined by the so-called Debye length:


thus:

Figure 4: The a.c. equivalent circuit at flatband.

thus:

The area:


Then,




The corresponding Flatband voltage VFB is close to 0.93 V.

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Task5. Work Function Difference (Calculate the work function difference assuming a gold (Au) gate.）

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