Nanotechnology-Enabled Sensors

6.3 Gas Sensing with Nanostructured Thin Films 315
β gas − −α
O + α.
e + S ↔ O βS
2
2 , (6.34)
where O2 gas is the oxygen molecule in the ambient atmosphere, e - is the
electron that reaches the surface when it has sufficient energy and S is an
unoccupied chemisorption site for oxygen. The number of electrons is de-
noted as nS (nS = [e - ]).
−α
βS
O is a chemisorbed oxygen species with:
α = 1 for singly ionised form
α = 2 for doubly ionised form
β = 1 for atomic form
β = 2 for molecular form
Using mass action law, and defining the activation energies for adsorption
and desorption as the reaction constants kads and kdes, respectively, Eq. (2.1)
can be rewritten as: 32
α β / 2
−α
S O =
2 des βS
k .[ S].
n . p k .[ O ] . (6.35)
ads
If we assume that [St] is the total number of available surface sites, the
surface coverage with chemisorbed oxygen, θ, can be defined as:
and using the conservation of surface sites:
it can be written as:
where
[ O S ]
[ S ]
α −
β
θ = , (6.36)
−α
t
[ S ] + [ Oβ
S ] = [ St
] , (6.37)
β
α
( 1 − θ ). k . n . p 2 = k . θ , (6.38)
ads
S
O2
pO is the concentration of oxygen in the gaseous phase. This equa-
2
tion defines the relationship between the surface coverage of adsorbed
oxygen and the number of electrons with enough energy to reach the surface.
Eq. (6.38) is not sufficient for extracting the relationship between nS and
p O , as the surface coverage, θ, and nS are related. The electroneutrality
2
condition (this condition states that the charge in the depletion layer is
equal to the charge captured at the surface) together with the Poissons
des