Sensing of Biomolecules - Bionanoelectronics: Bioinquiring and Bioinspired Devices - page 59

channel. In the channel, the density of electrons overcomes the hole density, and it
reaches its maximum value for

s D 2 F ; (2.2)

where F D˙ .E i E F /=e D .k B T=e/ln.N s =n i / is the Fermi potential. In ( 2.2 ), E i
and n i are, respectively, the intrinsic energy and concentration of charge carriers; E F
denotes the Fermi energy; and the C or sign is associated to the p -type or n -type
substrate, respectively. The maximum width of the depletion layer is then given by

x dep;max D Œ4" s k B T ln.N s =n i /=.e 2 N s / 1=2 ; (2.3)

and the corresponding charge per unit area is

q dep D eN s x dep : (2.4)

The threshold voltage can be determined from the equality

V th D V fb C 2 F q dep =C ox ; (2.5)

where V fb is the flat band voltage, which corresponds to a gate voltage that does not
bend the substrate energy bands, and C ox is the dielectric capacitance per unit area.
Typical values for V th are situated in the 0.2-0.4 V range.
The electric charge in the inversion layer is finally given by the expression

q n D C ox .V G V th /; (2.6)

which shows that it is directly proportional to the gate voltage, as is the current.
The MOSFET, as can be seen from Fig. 2.2 , consists of two diode regions named
source S and drain D, which surround a MOS capacitor. The voltage between source
and drain is denoted by V D , while V G stands for the voltage between gate G and
source. The electrons in the channel are transported toward the drain if the drain
is forward biased with V D , case in which V G >V th , the electron distribution being

V G

V D

SiO 2

G

D

S

p -Si

channel

depletion layer

Fig. 2.2 The MOSFET transistor