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Disusun oleh: Agustian Noor
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| bet | 47/57 | | Sana | 09.05.2021 | | Hajmi | 0,62 Mb. | | #14427 |
(mc13)
The capacitance of an MOS capacitor as calculated using the simple model is shown in the figure below. The dotted lines represent the simple model while the solid line corresponds to the low frequency capacitance as obtained from the exact analysis.
mosexact.xls - moslfcap.gif
Fig. 6.6.1 Low frequency capacitance of an MOS capacitor. Shown are the exact solution for the low frequency capacitance (solid line) and the low and high frequency capacitance obtained with the simple model (dotted lines). The red square indicates the flatband voltage and capacitance, while the green square indicates the threshold voltage and capacitance. Na = 1017 cm-3 and tox = 20 nm.
Flat band capacitance
The simple model predicts that the flatband capacitance equals the oxide capacitance. However, the comparison with the exact solution of the low frequency capacitance as shown in the above figure reveals that the error can be substancial. The reason for this is that we have ignored any charge variation in the semiconductor. We will therefore now derive the exact flatband capacitance.
To derive the flatband capacitance including the charge variation in the semiconductor we first linearize Poisson's equation. Since the potential across the semiconductor at flatband is zero, we expect the potential to be small as we vary the gate voltage around the flatband voltage. Poisson's equation can then be simplified to:
The solution to this equation is:
(mc16)
(mc17)
where LD is called the Debye length. The solution of the potential enables the derivation of the capacitance of the semiconductor under flatband conditions, or:
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