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The purpose of a positive resist prebake is to dry the resist after spin coating
by removing solvent from the film. However, when heated to temperatures
above 70^{o}C the PAC concentration M_{0} before
exposure begins to decompose to a light insensitive product X.
The initial reaction mechanism is thereby identical to
that of the PAC reaction during UV exposure [78,204]
but the dissolution (5.11) is now thermally driven,

(7.1) 
Simple kinetic theory yields^{a}

(7.2) 
whereby
t_{pre} denotes the bake time and
k_{pre}(T) is the dissolution rate constant.
The dependence of the prebake reaction on the temperature T is modeled by the
rate constant
k_{pre}(T).
For typical prebake conditions an Arrhenius law can be prescribed, i.e.,

(7.3) 
Here
K_{pre} is the constant Arrhenius coefficient,
E_{pre} the activation energy,
and R the universal gas constant.^{b} From (7.2) follows that the
normalized PAC concentration after the bake takes the form

(7.4) 
The effect of the decomposition (7.2) is a change in the
chemical makeup of the resist. Consequently, any parameter depending
upon the quantitative composition of the resist also depends upon prebake.
The most important ones fall into three categories: (i) optical exposure
parameters such as the resist absorption coefficient; (ii) diffusion parameters
during postexposure bake; and (iii) development parameters such as the
development rates of unexposed and completely exposed resist.
Following [108] we will now briefly describe a measurement technique
for the Arrhenius coefficient
K_{pre} and the activation
energy
E_{pre}.
Dill's classical `ABC'exposure model does not explicitly take into account
the effects of prebake on the resist composition
(cf. Section 5.1.2). For that the nonbleachable absorption
coefficient B of the resist given in (5.10) has to be
modified to include the absorption by the bake products X like

(7.5) 
Here is the molar absorption coefficient of the decomposition
product X. The stoichiometry of (7.1) gives
X(t_{pre}) = M_{0}(t_{pre})  M_{0}(0) so that

(7.6) 
Considering now the two extreme cases of no bake (NB) at all and
full bake (FB) corresponding to the situation when all PAC is decomposed,
we get (cf. (5.10) and (7.5))
These two special cases show how the Dill A and B parameters vary with the
normalized PAC decomposition
m_{0}(t_{pre})
of (7.4):

(7.7) 
The bleachable absorption coefficient A decreases proportional to
the PAC concentration
m_{0}(t_{pre}) after the prebake,
whereas the nonbleachable coefficient B only slightly depends on
m_{0}(t_{pre}). It decreases if
> and decreases otherwise (cf. (7.7)
and (7.8)).
In Figure 7.1 the dependence of the resist absorption parameter
A on prebake time
t_{pre} for a specific resist is shown.
The plots exhibits a time lag before the decomposition occurs. The reason
is a warmup time of the wafer. In the given example approximately 12 minutes
are required to bring the wafer on the elevated temperature. From these
data the Arrhenius coefficient
K_{pre}
1.65 10^{20} 1/minutes
and the activation energy
E_{pre}
163.59 kJ/mol can be extracted.
Figure 7.1:
Dependence of the Dill absorption parameter A on
prebake time
t_{pre} for the
KODAK 820 resist at a wavelength of 365 nm (after [205]).

Footnotes
 ... yields^{a}
 Here we assume that the PAC concentration
M_{0} is homogeneous.
 ... constant.^{b}
 The universal gas constant
equals R = kN_{A} with the Boltzmann constant
k
1.38 10^{23} J/K and
the Avogadro number
N_{A}
6.02 10^{23} 1/mol. R has a value of
R
8.31 J/K mol.
Next: 7.1.2 PostExposure Bake
Up: 7.1 Bake Steps
Previous: 7.1 Bake Steps
Heinrich Kirchauer, Institute for Microelectronics, TU Vienna
19980417