Gray-scale photolithography using microfluidic photomasks -- Data Supplement - Supporting Information -- Proceedings of the National Academy of Sciences

Supporting information for Chen et al. (2003) Proc. Natl. Acad. Sci. USA, 10.1073/pnas.0435755100

Supporting Text
Transmittance Measurements
. Beer’s law states that the transmittance T through a thickness H_L of fluid medium containing a dye of absorptivity ε and concentration C_d can be expressed as log T = –εC_dH_L. We used a spectrophotometer (Hewlett Packard 8453) to measure the transmittance of H_L = 1 cm of varying concentrations of dye solutions at the wavelengths corresponding to the emission lines of the mercury lamp (365, 405, and 435 nm) used for exposing photoresist. A plot of –logT vs. C_dH_L (Fig. 5, orange, blue, and green squares) for each wavelength reveals the linearity expected from Beer’s Law. The linear fits (solid lines) had r² values of 0.9994, 0.9985, and 0.9991 for T_365nm, T_405nm, and T_435nm, respectively. Average Transmittance
. The relative intensities of the emission lines (365, 405, and 436 nm) of our lamp were 2, 4, and 3, respectively, as measured by a UV-intensity meter (Vari-Wave, Quintel). Thus we can find an average transmittance T_avg as T
_avg = (2 × T_365nm + 4 × T_405nm + 3 × T_435nm)/9

for each C_dH_L value (Fig. 5, black squares). The log(T_avg) values also follow a clear linear relationship with C_dH_L and can be linear-fitted to –log(T_avg) = ε_avgC_dH_L (Fig. 5, black line, r² = 0.9933) to find ε_avg = 9.19373 liters/g·cm. For simplicity, we use this value to generate the T_avg simulation in Fig. 3. We note that T_avg is an average over wavelength. To consider the effect of a double exposure, one must use an effective transmittance (i.e., averaged over time). Because both exposures lasted the same amount of time, t = 78 s, the effective transmittance, T_eff, is the average of the two transmittances over the total exposure time, 2t. The energy deposited in the photoresist is E = I_o × T × t, where I_o is the intensity of the UV lamp, and t is the exposure time. In two subsequent exposures of same duration t through masks of different T, the total energy is E_T = I_o × (T₁ + T₂) × t. This is equivalent to the energy deposited in a single exposure of duration 2t through a mask of effective transmittance, T_eff = (T₁ + T₂)/2, E_T = I_o × T_eff × 2t.

Transmittance in the Microfluidic Photomasks (µFPMs).
In a typical µFPM with H_L = 50 µm, the light-absorbing path is 200 times shorter than the 1-cm-long path used for Fig. 5, hence we used ˜200 times higher C_d values in the microchannels to study the same range of C_dH_L values. Fig. 6 shows measured photoresist heights after exposure through µFPMs in eight different experiments (five different C_d values per µFPM, with C_dH_L in the range of 0–270 mg·cm/liter); the µFPMs had a channel height H_L = 62.4 µm (circles) or H_L = 38.9 µm (triangles). The lowest T_avg (darkest gray) that can be achieved depends on the solubility of the dye, which is 140 g/liter in 3:5 water/glycerol. For a 50-µm-high µFPM, the maximal C_dH_L value would be 700 mg·cm/liter, yielding T_avg = 4 × 10^–7. From Fig. 6 it is clear that for the exposure and developing times used in this work (156 s and 9 min, respectively), the dynamic range of photoresist falls within C_dH_L = 0–100 mg·cm/liter, i.e., T_avg = 10–100% (see Fig. 6, top axis). In this range, we were able to reliably achieve photoresist heights ranging from 0% to 100% of the original unexposed height, demonstrating that an arbitrarily large number of gray-scale levels can be obtained. Note that the curves would vary with photoresist type and would shift down with longer developing times or higher exposure doses, and therefore the actual dependence of photoresist height on T_avg (as in any gray-scale photolithography approach) needs to be calibrated for different experimental protocols. Phase Effect at the Microchannel Walls
. At every PDMS–liquid–photoresist interface, a phase shift of δ = 2πΔnH_L/λ occurs (1), where Δn is the difference between the refractive index of PDMS and that of the liquid, λ is the wavelength of incident light, and H_L (H_L >> λ) is the height of the microchannel. Thus small variations in H_L result in unpredictable interference conditions ranging from fully constructive to fully destructive. To make the refractive index of the dye solution match that of PDMS (i.e., Δn ˜ 0), we add glycerol (in an amount empirically determined for each dye concentration) to the solution. The rationale for choosing glycerol is that n_PDMS = 1.4, somewhat in between n_water = 1.33 and n_glycerol = 1.47 (20ºC and 589 nm; ref. 2). For the channel in Fig. 2D (67 µm high), a water/glycerol ratio of 3:5 and a dye concentration C_d =39.3 g/liter resulted in no ripples.

1. Rogers, J. A., Paul, K. E., Jackman, R. J. & Whitesides, G. M. (1997) Appl. Phys. Lett. 70, 2658–2660.

2. Lide, D. R. (2002) CRC Handbook of Chemistry and Physics (CRC, Cleveland), 83rd Ed.