Modelling of Threshold Voltage with Non-uniform Substrate Doping

K. Y. Lim and X. Zhou

School of Electrical & Electronic Engineering, Nanyang Technological University
Nanyang Avenue, Singapore 639798
(Phone: 65-7991368, Fax: 65-7912687, Email: exzhou@ntu.edu.sg)

Figures

Fig. 1 | Fig. 2 | Fig. 3 | Fig. 4 | Fig. 5 | Fig. 6

Fig-1

Fig. 1 Threshold voltage of long-channel MOSFETs for various uniform substrate doping. (Symbols: extracted from maximum slope linear extrapolation method; Lines: calculated from equation (13) with x as a fitting parameter.)

Fig-2

Fig. 2 Fitting parameter x used in Fig. 1 versus substrate doping.

Fig-3

Fig. 3 Effective doping concentration versus the centroid of channel profile. (Symbols: extracted from simulation data; Lines: calculated from equations (9)-(11).)

Fig-4

Fig. 4 The extracted parameter c2 for different total peak concentration. The nominal value of c2 is 0.038.

Fig-5

Fig. 5 Threshold voltage versus substrate bias for various channel doping profiles. (Symbols: simulation data; Lines: model equation.)

Fig-6

Fig. 6 Directly-fitted h based on equation (9) (symbols) as compared to the calculated h (lines) based on equation (11) with c2 = 0.038.