Validity of the Parabolic Effective Mass Approximation in Silicon and Germanium n-MOSFETs With Different Crystal Orientations

This paper investigates the validity of the parabolic effective mass approximation (EMA), which is almost universally used to describe the size and bias-induced quantization in n-MOSFETs. In particular, we compare the EMA results with a full-band quantization approach based on the linear combination...

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Bibliographic Details
Published in:IEEE transactions on electron devices 2007-08, Vol.54 (8), p.1843-1851
Main Authors: van der Steen, J.-L.P.J., Esseni, D., Palestri, P., Selmi, L., Hueting, R.J.E.
Format: Article
Language:English
Subjects:
Applied sciences
Approximation
Approximation methods
Band structure
Crystal structure
Crystals
Devices
Dispersion
effective mass approximation
Eigenvalues and eigenfunctions
Electron density
Electronics
Exact sciences and technology
full-band
Germanium
Mathematical analysis
Mathematical models
Quantization
quantization models
quantum confinement
Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices
Silicon
Transistors
Validity
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Summary:This paper investigates the validity of the parabolic effective mass approximation (EMA), which is almost universally used to describe the size and bias-induced quantization in n-MOSFETs. In particular, we compare the EMA results with a full-band quantization approach based on the linear combination of bulk bands (LCBB) and study the most relevant quantities for the modeling of the mobility and of the on-current of the devices, namely, the minima of the 2-D subbands, the transport masses, and the electron density of states. Our study deals with both silicon and germanium n-MOSFETs with different crystal orientations and shows that, in most cases, the validity of the EMA is quite satisfactory. The LCBB approach is then used to calculate the values of the effective masses that help improve the EMA accuracy. There are crystal orientations, however, where the 2-D energy dispersion obtained by the LCBB method exhibits features that are difficult to reproduce with the EMA model.
ISSN:0018-9383
1557-9646
DOI:10.1109/TED.2007.900417