Table 2-5 Positional difference in coverage expressions.
forward reverse
AOI = (aA + af aaA) AOri = A(l-a,)AO,
A0,2 =2 = (l-a)(l-a,)AO, AOr2 =3 (l-a )(l-a,,)2 Af
AO,) = 4 ( a2 Af r3 Al-a )2(-a
AO4 = A6(-a) (-a)AO,= A ,r4 Ao,
AO, = A(2N-2) (-a )(N-1) (1 -ar)(N-1) Af, A = (N-') (1- a )(N-') (1 -a, )N Af
The patterns for the differences in entering fractional coverage for forward and
reverse passes in terms of cycle number, removal ratio A and the forward and reverse
adsorption fractions a, and a, are given in eqns 2.13 and 2.14 respectively:
AOG = A(2N-2) (I-af )(N-) (1-a)(N-1) (ar + a. af a,) eqn 2.13
AO_ = A(2N-') (1- )(N-1) (1- a,)N (ar + f -a ,A) eqn 2.14
The fractional coverage entering the pin contact for forward or reverse travel for
any cycle (n) is the coverage entering the first cycle in that direction plus the sum of the
differences in fractional coverage up to that cycle (n), as given by eqn 2.15.
n
(f,r)n = O(/,r)l + AO(f,r) eqn 2.15
N=1
Fortunately, there are closed-form solutions to the summations in eqn. 2.15, and the
entering coverage for any cycle with the pin moving either forward or reverse is given in
eqns 2.16 and 2.17, respectively.
c(1- = g- )) eqn 2.16
1 -g