Light and matter co-confined multi-photon lithography

Mask-free multi-photon lithography enables the fabrication of arbitrary nanostructures low cost and more accessible than conventional lithography. A major challenge for multi-photon lithography is to achieve ultra-high precision and desirable lateral resolution due to the inevitable optical diffraction barrier and proximity effect. Here, we show a strategy, light and matter co-confined multi-photon lithography, to overcome the issues via combining photo-inhibition and chemical quenchers. We deeply explore the quenching mechanism and photoinhibition mechanism for light and matter co-confined multiphoton lithography. Besides, mathematical modeling helps us better understand that the synergy of quencher and photo-inhibition can gain a narrowest distribution of free radicals. By using light and matter co-confined multiphoton lithography, we gain a 30 nm critical dimension and 100 nm lateral resolution, which further decrease the gap with conventional lithography.

For quenching path 2, 1 ' , the number of quenched free radicals in S1 state, can be calculated from the change of fluorescence intensity of DETC: Where 0 and is the fluorescence intensity in the absence and presence of the quencher.Besides, the number of quenched free radicals for quenching path 3 is: The is the kinetic constant of termination by the quencher at the third quenching process and is the concentration of the quencher.When the photoresist contains the quencher, becomes because the S1-state DETC will be quenched before it transitions to MPL.Therefore, the total amount of radicals quenched by the quencher is Thus, Owing to ∝ and =3, The total change of radical concentration can be reflected by the threshold value of photoresist.So, ∆ can be calculated by in which ℎ0 and ℎ is threshold of photoresist without and with the quencher.0 represents the concentrations of free radical without the quencher.
As shown in Supplementary Table 2, the fluorescence intensity (Fig. 2d) and threshold power values (Supplementary Fig. 17) of photoresists with 0, 5, 10, 15, and 20 mM TEMPO concentration, were given.Substituting the corresponding parameters into Equation (6), it can be calculated that 1 and account for 62% and 38% respectively.
2. Mathematical simulation of MC-MPL. 1 Before discussion, it is worth noting that our model is only valid if the following assumptions are met.Firstly, the distribution of the radicals and the quenchers keeps a non-equilibrium, quasistationary state around the writing spot.Secondly, it is considered the termination of the radical is controlled only by the quencher molecules for simplify the calculation.
The evolution of the concentration of radicals, (, ) , and the concentration of quencher, (, ), is described as the following equations: Here, (, ) stands for the generation rate of radicals induced by excitation laser.kQ is the kinetic constant of termination by the quencher, is the diffusion coefficient of the quencher, ∆ is the Laplace operator.
For simplicity, we consider the generation rate of the radical as a sphericallysymmetric Gaussian photointiation rate profile based on a Gaussian excitation beam: Where, 0 is the generation rate of radicals at the central spot position, r = 0 = 0 .
Besides, As mentioned before, the quasi-equilibrium state of the radicals illustrates that the concentration distribution of the quenchers and radicals remains unchanged during the irradiation process, that means / = 0 and / = 0. Substituting the above equation into Equation (8) and Equation (9), we can get: For the initial conditions for Equation (8) and Equation (9) satisfy: , 0 = 0 and , 0 = 0 .
and with the boundary condition the exact solution of Equation (11) and Equation (12) for Gaussian are Where = 0 2 0 .Since it is the shape of the distribution of radicals that determines the accuracy and resolution of lithography, dimensionless variables / 0 , 0 / 0 and = / are adopted to describe the Equation (13) and Equation ( 14).
Thus, becomes the only factor that determines the stationary solution of Equation ( 12).It can be seen from Equation (12) that = ( = 0), so The dimensionless distributions of the quenchers and radicals with different values of , are given in the Supplementary Fig. 18a and Supplementary Fig. 18b.
As the models show, there are two cases taking = 1 as the critical point.When < 1, the scarcity rate of the quencher in the center is slower than its diffusion rate, leading the quencher concentration at the center of the spot reaches the minimum but is not equal to 0. And the shape of the distribution of radicals become narrower with the increasing of .While at the situation of > 1 , the scarcity rate of the quencher in the center is less than its diffusion rate is faster than its diffusion rate.So, a zero quenchers domains forms in the center.At the range of > 1 , the shape of the distribution of radicals will widen again with the value of increasing.Therefore, it is easy to see that there exists an optimal value of , = 1 , that makes the distribution of the radicals the narrowest.Because = 0 2 0 , the concentration and the diffusion coefficient of the quencher will affect the distribution of free radicals.
For the condition of MPL (without the quenchers), the concentration of radicals, Considering the assumption that the radicals keep non-equilibrium, quasi-stationary, the distribution of radicals is regard as unchanged over time.Therefore, satisfy the following equations for MPL and MC-MPL, respectively.
can set as a correct factor for LMC-MPL to calculate the distribution of radicals.Section B. Supplementary Figures Supplementary Fig.1 Performance of different quenchers.a The threshold power (Pth) curves of Pr1, Pr2, Pr2, Pr4, Pr5 and Pr6 at different writing speed.Pth is defined as the minimum laser power that will allow the photoresist to be retained after development.b SEM images of the linewidth for Pr3, Pr4, Pr5, and Pr6 ().Scale bar: 1 μm.