Specific Process Knowledge/Lithography/Coaters: Difference between revisions

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 ===Spin-off===
-The spin-off cycle determines the thickness of the resist coating. For a given resist, the thickness is primarily a function of the spin-off speed and the spin-off time, both following an inverse power-law (y=k*x^-a). The acceleration to the spin-off speed also influences the thickness, but the effect is dependent on previous steps. The spin-off is usually a simple spin at one speed, but it may be comprised of several steps at different spin speeds. After spin-off, the wafer is decelerated.
+The spin-off cycle determines the thickness of the resist coating. For a given resist, the thickness is primarily a function of the spin-off speed and the spin-off time, both following an inverse power-law:
-The coated thickness, t, as a function of the spin-off speed, w, follows an inverse power-law, t = k * w<sup>-a</sup>. The constant, k, is a function of the resist viscosity and solid content, and the spin-off time. The exponent, a, is dependent on solvent evaporation, and is typically ~½ for UV resists. This means that from the thickness t<sub>1</sub> achieved at spin speed w<sub>1</sub>, one can estimate the spin speed w<sub>2</sub> needed to achieve thickness t<sub>2</sub> using the relation: <br> t<sub>1</sub>*w<sub>1</sub><sup>½</sup> = t<sub>2</sub>*w<sub>2</sub><sup>½</sup> => w<sub>2</sub> = w<sub>1</sub> * t<sub>1</sub><sup>2</sup>/t<sub>2</sub><sup>2</sup>. <br> For thick SU-8, however, a is observed to be ~1 (probably due to the low solvent content and/or the formation of skin). In this case, the relation simply becomes: <br> t<sub>1</sub>*w<sub>1</sub> = t<sub>2</sub>*w<sub>2</sub> => w<sub>2</sub> = w<sub>1</sub> * t<sub>1</sub>/t<sub>2</sub>. <br>
+<math>y = k \sdot x^{-a}</math>
+The acceleration to the spin-off speed also influences the thickness, but the effect is dependent on previous steps. The spin-off is usually a simple spin at one speed, but it may be comprised of several steps at different spin speeds. After spin-off, the wafer is decelerated.
+The coated thickness, <math>t</math>, as a function of the spin-off speed, <math>w</math>, follows an inverse power-law:
+<math>t=k \sdot w^{-a}</math>
+The constant, <math>k</math>, is a function of the resist viscosity and solid content, as well as the spin-off time. The exponent, <math>a</math>, is dependent on solvent evaporation, and is typically ~½ for UV resists. This means that from the thickness <math>t_1</math> achieved at spin speed <math>w_1</math>, one can estimate the spin speed <math>w_2</math> needed to achieve thickness <math>t_2</math> using the relation:
+<math>t_1 \sdot w_1^{1/2} = t_2 \sdot w_2^{1/2} \rArr w_2 = w_1 \sdot \frac{t_1^2}{t_2^2}</math>
+For thick SU-8, however, <math>a</math> is observed to be ~1 (probably due to the low solvent content and/or the formation of skin). In this case, the relation simply becomes:
+<math>t_1 \sdot w_1 = t_2 \sdot w_2 \rArr w_2 = w_1 \sdot \frac{t_1}{t_2}</math>
 ===Backside rinse===