Comparative study of the sidewall shape and proximity effect in bilayer electron beam resist systems

The experimental investigation and simulation of electron beam lithography (EBL) for bilayer and trilayer resist systems have been carried out. Important parameters of the EBL process, such as dissolution rate, resolution, absorbed energy, and resist profile in the investigated bilayer resist systems, have been studied and discussed. Various combinations of resist layers with positive electron resist have been proposed to examine the effects of lithographic process parameters on the resist profile. The results of this work are intended for use in multilayer resist systems to produce high-frequency electronics, where the fabrication of a T-shaped gate is one of the most crucial processes.


Introduction
Fabrication of a T-shaped narrow gate is one of the important key processes for ultra-high-frequency high-electron mobility transistors (HEMTs) [1].Currently, the most widely used method for fabricating T-shaped gates in HEMTs is electron beam lithography (EBL).This method offers directwrite exposure with high resolution, flexibility, stability, and registration accuracy.However, its high operating cost and limited yield remain significant challenges [2].Considering this, the utilization of highly productive EBL devices, such as variable-shape EBL systems, becomes essential.The basic principle of fabricating T-shaped profiles in a bilayer of resists using EBL relies on differences in sensitivity to e-beam irradiation between the two resist layers [3,2].In this process, the resist sensitivity on the top layer should always be higher than that on the bottom layer.The upper layer (resist 1, figure 1 (a)), with relatively higher sensitivity, forms a wider T-shaped gate head when developed, while the lower layer (resist 2, figure 1 (a)), with lower sensitivity, creates a narrower foot of the gate.Typically, the resist chosen for the bottom layer should possess high-resolution capabilities for ultra-short T-shaped gates.A schematic representation of T-shaped gate production is shown in figure 1.
In this work, a comparative study concerning essential EBL parameters in multilayer positive resist systems is presented and discussed in terms of their impact on development of multilayer resist systems for high-frequency electronics production, where the fabrication of a T-shaped gate is one of the most critical processes.
Thin films of all the investigated positive resists on silicon substrates were deposited using spin coating.Resist thickness measurements were performed using a standard Alphastep stylus profiler (KLA).A high-resolution scanning electron microscope, Quanta FEG 250 (FEI), was used for dimensional measurements of the resist profiles at magnifications of 100,000× and 200,000×.The images of the resist profiles were taken under an accelerating voltage of 3 keV without any anti-charge layer on the resist.
Our proposed bilayer and trilayer resist systems on a silicon substrate are summarized in table 1.The upper layer is marked as 1, the intermediate layer as 2, and the lower layer as 3.The electron energy was 40 keV, the beam current was 1.6 A/cm², and the shot size was 3x3 µm².The developer used for resists 950 PMMA A2 and 495 PMMA A6, MMA (8.5) MAA EL11, and SML 300 was MIBK:IPA (1:3), AR-P 6200 (CSAR 62) resist -AR 600-548, with a development time of 60 seconds for all the studied resists.Systems A, C, D, and E were developed in one step, and system B was developed in two steps.The tests for resist profile measurements consisted of a set of long single lines of linewidth 100 nm and 200 nm.Linewidths (L) were measured at four levels of the resist thickness as illustrated in figure 2: L1 -100 nm below the resist thickness, L2at the resist thickness of the bottom layer, L3 -100 nm below L2, L4at the substrate surface (figure 2).Measurements were performed for different exposure dose values (Q) (ranging from a minimal value to significantly higher values).

Sensitivity and dissolution rates of selected bilayer and trilayer resist systems
To identify resists with suitable sensitivity for T-shaped gate fabrication, the sensitivity of the selected bilayer and trilayer resist systems, as summarized in table 1, was measured, and the corresponding dissolution rates were evaluated.The results obtained for these dependencies on exposure dose, considering various bilayer and trilayer resist systems including PMMA, MMA (8.5) MAA, SML 300, and CSAR 62 positive resists on a silicon substrate, are shown and compared in figure 3.In our experiments, we employed a single exposure for both resists, as opposed to two separate exposures in the upper and lower resists [6].Resist systems A, C, D, and E, which use the PMMA and copolymer MMA (8.5) MAA, were developed in a single step due to the compatibility of developers.A two-step development process was necessary for system B.
For profile measurements in a bilayer resist system, copolymer MMA (8.5) MAA was chosen as the top layer due to its lower sensitivity when compared to PMMA.Resists 950 PMMA A2 and 495 PMMA A6 were chosen as the bottom layer.The resist 950 PMMA A2 is a solution of a highresolution PMMA resist with a molecular weight of 950,000 for thicknesses ranging from 50 to 100 nm.The resist 495 PMMA A6 is a solution of PMMA with a molecular weight of 495,000.It is specifically designed for use in thicknesses ranging from 300 to 600 nanometers.
The analysis of the results reveals that the trilayer resist system with the highest measured sensitivity (approximately 70 μm/cm²) is resist system B, composed of 125 nm 950 PMMA A2, 470 nm MMA/MAA EL11, and 365 nm CSAR62.The dissolution rate for this system is exceptionally slow when compared to the other investigated resist systems, ranging from 0.05 nm/sec to 8 nm/sec in AR 600-548 developer.
The system consisting of a 125 nm thin 950 PMMA A2 resist and a 495 nm thin copolymer MMA/MAA EL11 exhibits the highest sensitivity (approximately 220 μm/cm²) among the studied bilayer systems (see figure 3 (a)).Dissolution rates vary within the range of 0.083 nm/sec to 9.92 nm/sec in MIBK:IPA (1:3) developer (see figure 3 (b)).Dissolution rates increase with an increase in the exposure dose, with the highest dissolution rates (approximately 16 nm/sec) observed for other low-sensitivity bilayer and trilayer resist systems studied.

Radial distributions of the absorbed energy in a bilayer resist system
For the selected bilayer resist system, energy deposition function EDF(r) was calculated at different system depths -near the system top, at the interface between both resists, and on the top of the silicon substrate.For this purpose, our Monte Carlo simulation tool was applied and then an analytical approximation of the obtained discrete absorbed energy distributions was performed using a sum of two Gaussians [7].In figure 4 is shown the approximated dependences EDF(r) for bilayer resists system 470 nm MMA (8.5) MAA/125 nm 950 PMMA A2 on silicon substrate at 40 keV at the three characteristic depths.The obtained radial distributions at the three system depths are close and indicate the presence of a proximity effect.green line: at 470 nm in the system depth (interface between MMA (8.5) MAA and 950 PMMA A2); red line: at 650 nm in the depth (interface between 950 PMMA A2 and substrate).

Bilayer positive resists profiles
The bilayer resist system, consisting of 470 nm thin layer of MMA (8.5) MAA on top of 950 PMMA A2 with a thickness of 125 nm, was proposed as case 1.Both resists were developed in a single step using the MIBK:IPA (1:3) developer for 60 seconds.The exposure test consists of single lines with a designed linewidth of 100 nm.The sample was subsequently broken after development to obtain cross-sections of the resists for profile measurements.The bilayer resist system, consisting of a 500 nm thin layer of MMA (8.5) MAA on top of 495 PMMA A6 with a thickness of 500 nm, was proposed as case 2. Both resists were developed in a single step using the MIBK:IPA (1:3) developer for 60 seconds.The exposure test consisted of single lines with a designed linewidth of 200 nm.In case 1, the thickness of the bottom layer is too small, resulting in an oblique rather than vertical resist profile.This is explained as a consequence of a long-term electron scattering from the substrate.Nearly vertical sidewalls were achieved in case 2 by using the thicker bottom layer of a 500 nm of 495 PMMA A6.

Conclusions
An experimental investigation and simulation of electron beam lithography were carried out for multilayer resist systems.The study focused on essential parameters of the EBL process, including sensitivity, contrast, dissolution rate, and resist profile in bilayer and trilayer resist systems.Various combinations of positive electron beam resist layers were designed to examine the impact of lithographic process parameters on the resist profile.A single-step exposure process was applied to all resist systems.Nearly vertical sidewalls were achieved with the two-layer resist system comprising a 500 nm thin layer of MMA/MAA and a 500 nm layer of PMMA.The results of this work are intended for use in the development of multilayer resist systems for high-frequency electronics production.

Figure 1 .
Figure 1.Schematic representation of T-shaped gate fabrication: (a) Bilayer resist system cross-section for T-shaped gate fabrication.(b) T-shaped gate cross-section after lift-off.

Figure 2 .
Figure 2. Illustration of four levels of the resist thickness where linewidths (L) were measured.L1 -100 nm below the resist thickness, L2resist thickness of the bottom layer, L3 -100 nm below L2, L4at the substrate surface.

Figure 3 .
Figure 3. Characteristic curves for the case of various bilayer and trilayer resist systems consist of 950 PMMA A2, 495 PMA A6, MMA (8.5) MAA, SML 300, and CSAR62 positive resists on Si substrate: (a) remaining resist thickness vs. the electron exposure dose and (b) dissolution rates vs. the exposure dose.

Table 1 .
Proposed bilayer and trilayer resist systems of selected positive electron beam resists on silicon substrate.