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7.1.1 Prebake

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 70oC the PAC concentration M0 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,

$\displaystyle M_0 @>{\;{\Delta T}\;}>> X,$ (7.1)

Simple kinetic theory yieldsa

$\displaystyle \frac{d M_0(t)}{d t} = -k_{\mathrm{pre}}(T) M_0(t)\qquad\Longrigh...
...qquad M_0(t_{\mathrm{pre}}) = M_0(0) e^{-k_{\mathrm{pre}}(T) t_{\mathrm{pre}}},$ (7.2)

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

$\displaystyle k_{\mathrm{pre}}(T) = K_{\mathrm{pre}} e^{-E_{\mathrm{pre}}/R T}.$ (7.3)

Here Kpre is the constant Arrhenius coefficient, Epre 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

$\displaystyle m_0(t_{\mathrm{pre}}) = \frac{M_0(t_{\mathrm{pre}})}{M_0(0)}=e^{-k_{\mathrm{pre}}(T)t_{\mathrm{pre}}}.$ (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 post-exposure 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  Kpre and the activation energy  Epre.

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 non-bleachable absorption coefficient B of the resist given in (5.10) has to be modified to include the absorption by the bake products X like

$\displaystyle B = \alpha_PM_0(t_{\mathrm{pre}}) + \alpha_RR + \alpha_XX(t_{\mathrm{pre}}).$ (7.5)

Here $ \alpha_{X}^{}$ is the molar absorption coefficient of the decomposition product X. The stoichiometry of (7.1) gives X(tpre) = M0(tpre) - M0(0) so that

$\displaystyle B = \alpha_PM_0(t_{\mathrm{pre}}) + \alpha_RR + \alpha_X(M_0(t_{\mathrm{pre}})-M_0(0)).$ (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))

$\displaystyle \begin{alignedat}{2}{\text{no bake:}} \qquad& A_{\mathrm{NB}}=(\a...
...rm{FB}}=0, &\qquad B_{\mathrm{FB}} &= -\alpha_XM_0(0)+\alpha_RR.\end{alignedat}$    

These two special cases show how the Dill A and B parameters vary with the normalized PAC decomposition  m0(tpre) of (7.4):

$\displaystyle A=A_{\mathrm{NB}}m_0(t_{\mathrm{pre}}) {}\qquad{\text{and}}\qquad{}B=B_{\mathrm{FB}}+(B_{\mathrm{NB}}-B_{\mathrm{FB}}) m_0(t_{\mathrm{pre}}).$ (7.7)

The bleachable absorption coefficient A decreases proportional to the PAC concentration m0(tpre) after the prebake, whereas the non-bleachable coefficient B only slightly depends on m0(tpre). It decreases if $ \alpha_{P}^{}$ > $ \alpha_{X}^{}$ and decreases otherwise (cf. (7.7) and (7.8)). In Figure 7.1 the dependence of the resist absorption parameter A on prebake time tpre for a specific resist is shown. The plots exhibits a time lag before the decomposition occurs. The reason is a warm-up 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  Kpre $ \cong$ 1.65 1020 1/minutes and the activation energy  Epre $ \cong$ 163.59 kJ/mol can be extracted.

Figure 7.1: Dependence of the Dill absorption parameter A on prebake time tpre for the KODAK 820 resist at a wavelength of 365 nm (after [205]).
\psfrag{bakeTime}{\huge\sf\hspace*{-15mm} bake time [minutes...
...$^\circ$ }
\psfrag{125C}{\huge\sf 125$^\circ$ }
\includegraphics{DEbakeLin.eps}} \resizebox{5cm}{!}{
\psfrag{bakeTime}{\huge\sf\hspace*{-15mm} bake time [minutes...
...$^\circ$ }
\psfrag{125C}{\huge\sf 125$^\circ$ }


... yieldsa
Here we assume that the PAC concentration M0 is homogeneous.
... constant.b
The universal gas constant equals R = kNA with the Boltzmann constant k $ \cong$ 1.38 10-23 J/K and the Avogadro number NA $ \cong$ 6.02 1023 1/mol. R has a value of R $ \cong$ 8.31 J/K mol.

next up previous contents
Next: 7.1.2 Post-Exposure Bake Up: 7.1 Bake Steps Previous: 7.1 Bake Steps
Heinrich Kirchauer, Institute for Microelectronics, TU Vienna