Mechanism of etching and surface relief development of PMMA under ...

Mechanism of etching and surface relief development of PMMA under low-energy ion bombardment Y. Kovala) Physicalisches Institut III der Universita¨t Erlangen-Nu¨rnberg, Erwin-Rommel Str. 1, 91058 Erlangen, Germany

共Received 3 September 2003; accepted 2 February 2004; published 22 March 2004兲 The structure of the subsurface layer of polymethylmethacrylate 共PMMA兲 formed by bombardment with low-energy ions of Ar is reported. It was found that the subsurface region contains a graphitized, cross-linked, and low-molecular weight layers. We argue that ion etching of PMMA is mostly determined by the properties of the top graphitized layer and the processes leading to the formation of this layer. Also, it was found that ion etching causes various defects and typical features to appear on the surface of PMMA: bubbles, waves, and a net with a cell of nanometer size. The stratification of PMMA was demonstrated to play an important role for the development of the surface topology. © 2004 American Vacuum Society. 关DOI: 10.1116/1.1689306兴

I. INTRODUCTION Treatment with energetic ions is a powerful method for modification of surface properties of polymers. It was shown that wetting1,2 and adhesion,3 mechanical properties,4,5 interaction with biological environment,6,7 and electrical8 –11 and optical12,13 properties are drastically changed. A popular method of ion treatment of polymers is ion implantation. The energy of ions usually used for implantation is in the range between 100 keV and 1 MeV. Ion implantation causes radiation-induced chemical reactions, which occur also for different types of high-energy radiation, e.g., x-ray, or electron. However, there are several factors which make ion bombardment a unique method. These are 共1兲 high effectiveness of the energy losses in inelastic collisions and 共2兲 direct displacement of the atoms in a cascade region due to elastic interactions. The latter process breaks chemical bonds and so initiates reactions, which are not possible if any other type of radiation is used. Ion bombardment of polymers causes many gaseous products to form. Low molecular fragments appearing as a result of radiation transformations diffuse in the material, reach the surface, and desorb. Thus the polymers after ion bombardment are significantly enriched with carbon. The composition, chemical structure, and other properties of the carbonized material were investigated in details by different methods.14 –22 It was found that a high density of the absorbed energy transforms the polymer into material which possesses properties of ␣-C–H 共characterized by s p 3 hybridization兲 or ␣-C (sp 2 hybridization兲. The presence of the ␣-C phase allows us to discuss graphitization of polymers. The two phases coexist in the modified polymers but the dominant energy losses 共e.g., nuclear or electron兲 and the effectiveness of the energy losses determine the ratio of the phases and their distribution in the material.23–25 Another method using ion treatment of a surface is ion etching. The main difference of this method from ion implantation is low energy of ions, e.g., around 1 keV or less. a兲

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J. Vac. Sci. Technol. B 22„2…, MarÕApr 2004

The decrease of the energy of ions results in the modification of only a thin subsurface layer of a polymer. In this method, the energy losses are mostly due to the nuclear collisions. Moreover, the effectiveness of the energy losses of ions significantly decreases compared to high-energy ions. This leads to a decrease of the ␣-C phase and we can expect suppression of the graphitization process 共see Refs. 8, 23, and 26兲 for low-energy ions. In addition, the process of the energy losses by ions in the subsurface layer occurs simultaneously with etching of the surface. This permanent etching limits the density of the absorbed energy in the subsurface layer.27 The properties of the polymer films modified by lowenergy ion bombardment are the main subject of the present work. The experiments were carried out with polymethylmethacrylate 共PMMA兲. PMMA has been studied extensively including ion bombardment modification. This is partly a consequence of the long term use of this material as a resist in microelectronics technology, including submicron and nanometer-size lithography. PMMA attracts additional attention because, depending on the dose of ion implantation, the behavior of PMMA changes from chain scission to crosslinking. It is well known that low-dose ion implantation causes mostly scissions28 –30 共which leads to low molecular weight PMMA兲 and that an increase of the implantation dose activates cross-linking processes.31 Similar processes occur also in the presence of electron irradiation,32–34 but with a different yield for the reactions. The processes unique to ion bombardment are realized in PMMA at high doses of radiation, because in this case PMMA converts into a graphitized material.17,35–38 As the penetration depth of ions is less than the thickness of the whole sample, the modification becomes nonhomogeneous. The density of the absorbed energy is maximal in the upper layer of PMMA and if the dose of ion bombardment is high enough, this layer converts into graphitized material. The material, which is not reachable by the ions, does not change. There is a region where the density of the absorbed energy changes with depth from its maximum to zero. This

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Y. Koval: Mechanism of etching and surface relief development

means that the PMMA is divided in several layers, namely, graphitized, cross-linked, low molecular weight, and initial unmodified PMMA. As the energy of ions decreases even further, their penetration depth becomes comparable to the size of a molecule of PMMA. In this case, the subsurface layer has an extremely small thickness 共approximately several nanometers兲. A stratification of the subsurface region under these conditions is the subject of our experimental study. Notice that ion bombardment of PMMA occurs in the presence of permanent physical sputtering. The depth of etching can exceed the penetration depth of ions by orders of magnitude. In this case, the subsurface layer is continuously sputtered and renewed. This simple fact significantly changes the process of the polymer etching. We argue that physical sputtering of the top graphitized layer is the limiting process for the etching rate. The simplified model of PMMA etching based on this fact was proposed in earlier works.39,40 In this study, we extend this model and use it for analysis of PMMA etching. Our model can be used not only for PMMA, but for other polymers as well. It is well known that ion etching can generate defects of micrometer and nanometer size on the surface of PMMA.35,40– 42 Few works are devoted to this question. In the present study, we investigate the relief of the PMMA surface after ion etching and reasons for formation and development of defects. Moreover, the relation between the PMMA topology and peculiarities of its ion etching are analyzed using the proposed etching model. II. EXPERIMENTAL DETAILS PMMA was spin coated on thermally oxidized silicon wafers. The 4 and 9% solutions of 950 K PMMA in chlorbenzene were used. After coating, the samples were baked on a hot plate at 170 °C for 10 min. Ion bombardment of PMMA films was fulfilled in a setup for ion-beam etching 共IBE兲 equipped with a Kaufman-type ion gun. Argon ions with energy of 250 eV were used in the most of our experiments. After bombardment by ions with energies 500 and 1000 eV conductance of PMMA was also measured. The topology of PMMA surface was studied with a scanning electron microscope 共SEM兲 LEO 1530. To minimize radiation effects that could change the surface topology, lowenergy electrons 共⬍2 keV兲 and low currents 共less than 50 pA兲 were used for the investigation of polymer surface. Some experiments were carried out with electron-beam lithography. In this case, the same scanning electron microscope with a connected pattern generator was used. With the help of electron-beam lithography two kinds of work were fulfilled: 共1兲 preparation of structures for visualization of the graphitized and low-molecular weight layers and 共2兲 electron irradiation of some areas of PMMA for modification of its properties. The energy of electrons used for electron-beam lithography was 15 keV. Dissolution 共development兲 of PMMA after electron-beam exposure was done in solutions of methyl isobutyl ketone:isopropyl alcohol 共MIBK:IPA兲 in the ratio 1:5 J. Vac. Sci. Technol. B, Vol. 22, No. 2, MarÕApr 2004

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FIG. 1. Preparation of structures for visualization of cross-linked 共I,II兲 and destructed 共III兲 layers. In process 共I兲: 共a兲 making of structures 5⫻15 ␮m2 in PMMA; 共b兲 electron exposure of a line in the center of the structures; 共c兲 ion bombardment; and 共d兲 development. In process 共II兲: 共a兲 making of structures 5⫻15 ␮m2 in PMMA; 共b兲 electron exposure of the two edges of the structures for their cross-linking; 共c兲 ion bombardment; and 共d兲 development in acetone. In process 共III兲: 共a兲 making of structures 5⫻15 ␮m2 in PMMA; 共b兲 ion bombardment; 共c兲 deposition of a Cr film; and 共d兲 development.

共‘‘weak’’ developer兲 and 1:3 共‘‘strong’’ developer兲. In comparison to the weak developer, the strong developer was able to dissolve larger molecular fragments of PMMA. However, developers are poor solvents of PMMA and can only dissolve low-molecular resists. Dissolution of high-molecular or slightly cross-linked PMMA was carried out in acetone, which is a good dissolvent of PMMA. It is well known that only highly cross-linked and graphitized PMMA cannot be dissolved by acetone. For conductivity measurements allowing characterization of the graphitized layer of PMMA, the PMMA film was first bombarded by ions. Second, electrodes were prepared by thermal evaporation of chromium film through a shadow mask. With a Keithley 6517A electrometer, measurements were fulfilled by a two-point technique. III. EXPERIMENTAL RESULTS AND DISCUSSION A. Structure of the top layer of PMMA

We offer two different processes for visualization of the top graphitized and cross-linked layers of PMMA. They are presented in Figs. 1 共I兲 and 共II兲. According to the first process 共I兲, rectangular structures 5⫻15 ␮m2 were produced by electron-beam lithography. After development, the second electron lithography step was carried out. In this step the lines of 1 ␮m width were exposed with the dose of 200 ␮C/cm2 across the rectangular structures 关see Fig. 1 共I兲共b兲兴. After the exposure, the sample was bombarded by ions with the dose 1017 ion/cm2 , and then developed. The structure obtained after the described procedure is shown in Fig. 2共a兲. Being a poor dissolvent, the developer can dissolve only

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FIG. 2. Hanging bridges of graphitized/cross-linked PMMA 共a兲 and 共b兲, obtained by processes 共I兲 and 共II兲, correspondingly. The structures 共c兲 obtained according to scheme 共III兲 with the Cr film, which have elevated edges 共c兲 because of the loss of cohesion to the PMMA surface.

low-molecular weight PMMA. Unexposed PMMA 共initial兲 or strongly modified PMMA 共cross-linked and graphitized兲 does not dissolve in the process of development. The presence of a thin, hanging film above the area of removed PMMA 关see Fig. 2共a兲兴 indicates that IBE leads to the formation of the modified layer of PMMA. This process takes place in the thin 共less than 10 nm兲 subsurface layer. The second process 共II兲 uses a good dissolvent, which removes PMMA only if it is not highly cross-linked or graphitized. The same type of rectangular structures in PMMA as for the first process 共I兲 are produced by electronbeam lithography 关see Fig. 1 共II兲共a兲兴. In the second step, electron exposure was used to cross-link the edges of the structures in the PMMA making them insoluble in acetone. The rectangular areas of 5⫻5 ␮m2 were exposed, as shown in Fig. 1 共II兲共b兲. In this case, the exposure dose was 20 mC/cm2. In the next step, the sample was bombarded by ions with the dose 1017 ion/cm2 and dipped into acetone for 2 min. Finally, the thin film of insoluble in acetone PMMA was hung between the cross-linked supports 关see Fig. 2共b兲兴. The cross-linked PMMA swells in acetone, deforming the supports 关see Fig. 2共b兲兴. The hanging film consists of highly JVST B - Microelectronics and Nanometer Structures

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cross-linked and graphitized PMMA. The thickness of the film is less than in the previous case shown in Fig. 2共a兲, because acetone dissolved not only low-molecular PMMA, but even slightly cross-linked PMMA. Nevertheless, in all cases the hanging film contains both graphitized and crosslinked PMMA. The processes used do not allow us to distinguish between these layers. However, the graphitized material shows a noticeable conductance at variance with the cross-linked PMMA. The conductivity 10⫺4 S/cm was reported for high-doseimplanted PMMA.17 Both the initial and cross-linked PMMA are good insulators at room temperature. First, because the charge effect is absent, the formation of the graphitized layer can be recognized in the process of scanning electron microscopy of the PMMA surface. The direct measurements of the sheet conductance after 250 eV ions bombardment with the dose 1017 ion/cm2 give the value of 10⫺12 S at room temperature. The thickness of the graphitized layer can be estimated as 10 Å. In this case, the conductivity is similar to the value reported in Ref. 17. Apparently, the coincidence is occasional because the conductance of the graphitized PMMA after bombardment by 250 eV ions degrades over time. Moreover, the conductivity of PMMA increases for the higher energy of Ar ions. Bombardment with 500 and 1000 eV Ar ions showed surprisingly substantial growth of the conductivity: roughly two orders of magnitude for every doubling of the ions’ energy. The conductivity increases with temperature. A finite conductivity confirms the formation of the thin, graphitized layer at the surface of PMMA. The existence of the low-molecular weight layer between the graphitized/cross-linked layer and the bulk PMMA is difficult to reveal directly due to the negligible thickness of this layer. However, indirect methods can be applied. The structures in PMMA were prepared by the same procedure as in the experiments for visualization of the graphitized layer 关see Fig. 1共III兲共a兲兴. The strong developer was used in this step. Then the structures were bombarded by ions with the dose of 1017 ion/cm2 . The next step was a thermal evaporation of the 500 Å of chromium. Then the sample was dipped into the weak developer for 2 min. The weak developer allowed us to remove the low-molecular weight layer appearing in the IBE process and to leave the rest of the structure unchanged. The chromium film was mechanically stressed and its bending indicated the presence of the low-molecular weight 共dissolved兲 layer 关see Fig. 2共c兲兴. Thereby we have shown experimentally that bombardment by low-energy ions of Ar results in the formation of the stratified subsurface layer containing graphitized, crosslinked, and low-molecular weight material. B. Model of PMMA ion beam etching

Energetic ions, coming into collision with a target, penetrate into the material and lose their energy in elastic and inelastic collisions. The efficiency of the energy loss is described by (dE/dx) n and (dE/dx) e , which are the energy losses in nuclear and electron interactions per unit length, respectively. The nuclear interactions have dominating sig-

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nificance for low-energy ions. For the PMMA target, the values of (dE/dx) n and (dE/dx) e for Ar ions with the energy of 250 eV are equal to 16 and 1.5 eV/Å, respectively. The distribution of the absorbed energy and ions were calculated with the help of the SRIM2003 program. This is a well-known program used for Monte Carlo simulations of interaction between ions and matter.43 The calculation of parameters of the ions’ distribution gives the mean projected range R p equal to 31 Å and the standard deviation ⌬R p of 9 Å. These data roughly show the depth of the PMMA subsurface layer where modifications by the ions can be expected. The simulations also demonstrated that the recoil atoms are able to penetrate as far as 60 Å. The most important parameters in our case are the distribution of energy loss by an ion in the process of braking and the energy spread in the collisional cascade initiated by the ion. For inelastic interactions, the calculation gives the distribution, which can be described by the Gauss function with the mean of 14 Å and the deviation of 9 Å. The distribution of the energy loss on the phonons excitation can also be approached by the Gauss function. The mean and standard deviation are 16 and 9 Å, respectively. Thus, one can see that the energy losses in inelastic interactions and to phonons have similar distributions. The ratio of the energy of ions, which is spent finally for the inelastic and elastic interactions, is approximately 1:4. The elastic interactions of ions with a target can also lead to the displacement of atoms. However, an uncertainty in the displacement energy of atoms in PMMA and, moreover, change in this parameter due to PMMA modification, makes the calculations of this part of the absorbed energy not very valuable. We notice here that the displaced atoms distribute closer to the surface with respect to the phonons. This shift to the surface is more pronounced for higher values of the energy of the displacement. The speculations described above allows us to take a summary distribution of the energy E(x) lost by ions as a sum of energy losses for inelastic interactions and phonons. E(x) can be described by normal distribution with the mean x 0 of 15 Å and the standard deviation ␴ of 9 Å. Using the obtained distribution of the energy in the subsurface layer E(x), and taking into account moving of the surface of PMMA due to physical sputtering, we write the energy distribution in the process of IBE: ␧ 共 x,t 兲 ⫽ j⫻

冕

t

0

E 共 x⫹ ␯ ⫻ ␶ 兲 d ␶ ,

共1兲

where j is the ion flux, t is the etching time, and v is the etch rate of PMMA. The etch rate is 250 Å/min for the current density of ions 1 mA/cm2. The distribution of the absorbed energy depends on the depth of etching. In particular, the maximum of the distribution shifts to the surface with etching time. When the etching depth reaches the value around 3⫻x 0 , the distribution becomes stationary and does not change with the etching time. The specific value of the maximum of the distribution does not depend on the concrete values of x 0 and ␴. For the Gauss distribution, the maximum is expressed by ␧(0,⬁)⫽E ion J. Vac. Sci. Technol. B, Vol. 22, No. 2, MarÕApr 2004

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FIG. 3. Distribution of the absorbed energy density and the structure of the subsurface layer of PMMA after IBE. Ar ions with energy 250 eV and etching depth more than ⬃x 0 were used for the calculations.

⫻ j/ v . In our case, ␧共0,⬁兲 is equal to 38 eV/Å3. On the contrary, the shape of the distribution depends on the concrete values of x 0 and ␴. According to the data for ion implantation of PMMA,17 the density of the absorbed energy of 38 eV/Å3 is high enough for converting the polymer into the state called graphitized material. The density of the absorbed energy reduces with the distance from the surface and reaches the value of 0.2 eV/Å3 at the depth of ⬃40 Å. This value is a threshold for cross-linking the PMMA under the bombardment with Ar ions having the energy of 400 keV.31 If the etching is deep enough in comparison to x 0 , the energy distribution becomes a steady state and the structure of the subsurface layer can be presented as in Fig. 3. This structure, according to our model, does not change during subsequent etching. The ions bombard the surface of PMMA and physically sputter the graphitized layer. The graphitized layer becomes thinner and the ions have the possibility of penetrating deeper into the PMMA film. The energy lost by these ions causes radiation-chemical reactions in the deeper layers. By doing so, the layers move into the PMMA film and the stratification of the subsurface layer does not change. Because of several factors the thicknesses of the layers obtained from Eq. 共1兲共see Fig. 3兲 should be considered as the assessment. First, we do not take into account that the layers in the subsurface region have different composition and density. Second, ion etching of polymers is determined not only by the sputtering process but also by the gases emitted from the subsurface layer of material. The etch rate of PMMA should be substituted for the sputtering rate of the graphitized material. The sputtering rate can be estimated, as shown below. During formation of the graphitized PMMA, this material loses a considerable quantity of gaseous products of destruction. According to Refs. 34 and 44 electron irradiation 共in some sense similar to ion bombardment兲 of PMMA results in

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the loss of almost 50% of the film thickness during transformation into a cross-linked network. The volume of PMMA decreases as the low-molecular fragments generated in radiation-chemical processes diffuse to the surface of PMMA and desorb. Ion implantation makes changes more significant, i.e., the film thickness decreases by a factor of more than 3 with respect to the original material.35,37 Two processes are responsible for the further decrease of the volume: additional gas formation and increase of the density of the material. Due to the destruction of the PMMA under the graphitized layer, a great quantity of gaseous products forms in the process of etching. The presence of the gases changes the etch rate. So the etching rate is determined by the following: the physical sputtering rate of the graphitized material and the change of the polymer volume because of the gaseous products emission. For polymers consisting of carbon, oxygen, and hydrogen, the etch rate can be expressed in the form v ⫽K 1 ⫻

V0 , V graph

共2兲

where V 0 , V graph are the volumes of the initial and the graphitized polymer. The coefficient K 1 determines the sputtering rate of the graphitized polymer. The ratio of volumes can be expressed as

␳ graph A C⫻N C⫹A O⫻N O⫹A H⫻N H V0 ⫽ ⫻ , graph V graph ␳0 A C⫻N Cgraph⫹A H⫻N H

共3兲

where A C , A O , and A H are atomic masses of carbon, oxygen, and hydrogen, respectively, and ␳ 0 and ␳ graph are the densities of the initial and graphitized polymer. N C , N O , and N H are the quantities of atoms of carbon, oxygen, and hydrogen, respectively, in a monomer unit of the polymer, while graph are the quantity of carbon and hydrogen, reN Cgraph , N H spectively, left in the graphitized material 共or in other words, how many atoms of the monomer unit remains in the material after the graphitization兲. Here we take into account that the graphitized material consists mostly of carbon and hydrogen. The concentration of oxygen left in the graphitized material is negligibly small. For radiation-chemical reactions, the main gaseous product, which contains oxygen, is CO.36,45 Molecules CO2 , HO, and H2 O are also present in the etching products, but their fraction is relatively small. The main part of hydrogen is emitted in the form of H2 . However, some quantity of hydrogen comes out in a composition with carCH bon. We set the quantity of this carbon as N C X . Introducing CH graph /N Cgraph and ␣ ⫽N C X /(N H the coefficients ␤ ⫽N H graph ⫺N H ), expression 共4兲 can be obtained: v ⫽K 1 ⫻

⫻

␳ graph 1⫺ ␣ ⫻ ␤ ⫻ ␳0 N C⫺N O⫺ ␣ ⫻N H

A C⫻N C⫹A O⫻N O⫹A H⫻N H . A C⫹A H⫻ ␤

共4兲

We assume that the graphitized layer has a similar composition and structure for all polymers. Then, polymers with JVST B - Microelectronics and Nanometer Structures

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higher amount of oxygen and hydrogen in respect to carbon have a higher etching rate under the ion bombardment. The coefficient ␣ in Eq. 共4兲 is substantially less than one. The value of ␣ can reach several percent, and ␣ decreases with the higher concentration of hydrogen. Thus the term ␣ ⫻N H has a small influence. The value of ␤ is always less than one and can depend only slightly on the type of polymer. This is due to the substantial decrease of hydrogen concentration because the density of the absorbed energy in the graphitized layer is high. It was reported15–17,25 that the content of hydrogen for the case of ion implantation depends on the polymer, radiation conditions, and depth. However, we expect that IBE produces a ␤ substantially smaller than one. Indeed, the modified layer is very thin and the rebinding of hydrogen atoms is much less probable. Gokan et al.46 presented the data for etching for various polymers. It was found experimentally that etching rates obey the phenomenological law v ⫽K 2 ⫻

N C⫹N O⫹N H . N C⫺N O

共5兲

Here we notice that relations 共4兲 and 共5兲 reveal similar behavior. The proposed model of IBE for polymers can explain the results observed earlier for PMMA resistance to IBE under the influence of preliminary modification.37,39 It was found that the total resistance of the PMMA to IBE was independent of the preliminary implantation with high-energy Ar ions or electrons in a wide range of doses. The total resistance is defined as the time used to etch off the resist completely. Indeed, ion implantation or electron irradiation produces radiation-chemical reactions leading to gas emissions and decreasing thickness of the PMMA film. We argue that IBE produces the same reactions as ion implantation, but in the thin subsurface layer. This means that the preliminary treatment makes transformations which, in any case, will take place during IBE. 共Note that radiation-induced transformations depend on the energy being absorbed nonlinearly, with saturation at high level of the density of the absorbed energy.兲 For example, ion implantation with a dose high enough to graphitize PMMA produces a material that has lost all gaseous products due to destruction. The thickness of the graphitized material is reduced by the factor expressed in formula 共3兲. Further ion implantation cannot produce a morenoticeable quantity of gases. Therefore, no more etching due to radiation-induced formation of gases can take place. For this case, IBE is a result of physical sputtering of the graphitized layer, which is smaller than the etching rate of the initial polymer by exactly the factor of the volumes ratio 共3兲. One can easily find similar result for intermediate doses of ion implantation. Such behavior allows us to determine the etch rate of the graphitized PMMA. The thickness of the PMMA reduces by a factor of ⬃3.8 due to ion implantation with a dose high

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enough for graphitization.35 According to our considerations, the rate of IBE of the graphitized PMMA is ⬃3.8 times less than the rate of IBE of the initial PMMA. One can use the data of Gokan, Esho, and Ohnishi46 and find the coefficient K 1 in formula 共4兲, which is the etch rate of the graphitized material. Comparison of this K 1 with the etch rate of the PMMA in Ref. 46 shows that these etch rates relate as ⬃1:3.5– 4.5, depending on the chosen parameters ␣, ␤, and ␳ graph . Thus the data for the etch rate of the graphitized PMMA was obtained by two different ways and the obtained values are quite close. The model presented here for ion etching of polymers can be considered as an idealized variant that is valid for relatively shallow etching. This limitation results from the fact that the topology of the PMMA changes radically for deep IBE. Many defects appear, the surface is distorted, and the description of the IBE with the use of the model of subsurface layer stratification becomes problematic. However, the proposed model is also important for the understanding of the effects described in the next section. C. Topology of the PMMA surface

Before ion etching, PMMA has a smooth surface. Using the SEM we did not observe any substantial features on the surface of PMMA. The data of atomic-force microscopic investigation of PMMA also does not show any significant defects.42,47 Ion bombardment causes the development of a specific relief with the features of different size. All features can be divided into three types: 共1兲 fine net structure, 共2兲 waved structure, and 共3兲 bubbles 共see Figs. 5– 8兲. The last two types were briefly described in the previous work.40 We expect that all features appear as a result of the radiation-induced processes in the subsurface layer described above, e.g., destruction, cross-linking, and gas formation. To investigate the influence of the radiation processes on the relief formation, we used the method of a preliminary modification of the PMMA properties. The modification was established by electron irradiation 共see details in Sec. II兲 of initial PMMA. The different doses of electron irradiation allowed us to prepare PMMA with a different degree of chain scissions or cross-linking. Moreover, the electron irradiation of PMMA leads to the removal of gaseous products of destruction. The amount of the gases is also determined by the dose of electron exposure. Notice here that IBE of PMMA is, in many respects, determined by the same radiation processes, e.g., gases emitted. The loss of gasses results in the reduction of the PMMA film thickness. The dependence of the PMMA thickness on the dose of electron irradiation is presented in Fig. 4. On the same plot, we show two specific doses of electron irradiation of PMMA. These doses can be used as a threshold dose for cross-linking D g 共where cross-linking starts to prevail over scissions兲 and the dose for the transformation of the PMMA into a highly cross-linked three-dimensional network D 3D . The dose D g was determined as a threshold dose for the PMMA dissolution in the weak developer. D 3D was determined as a dose converting the PMMA into material undisJ. Vac. Sci. Technol. B, Vol. 22, No. 2, MarÕApr 2004

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FIG. 4. PMMA film thickness vs dose of electron exposure. The energy of the electrons was 15 keV. Initial thickness of the PMMA film was 1.4 ␮m. Approximate doses of PMMA gel formation D g and highly cross-linked net formation D 3D are also shown. D g and D 3D are determined as threshold doses of dissolution in the weak developer and in acetone, respectively.

solvable in the PMMA’s good dissolver 共acetone兲. According to the presented data, PMMA started to cross-link when the dose of electron exposure D g was 1.5 mC/cm2 and transformed into the highly cross-linked net at D 3D ⬇10 mC/cm2 . Figure 5 presents a series of pictures of the PMMA surface obtained after IBE with the dose of ions 5 ⫻1018 ion/cm2 . Different doses of the preliminary electron irradiation were used. The characteristic net structure was found in a wide range of doses of electron irradiation. That structure becomes more pronounced as the dose of electron exposure is higher than D g 关see Fig. 5共c兲兴. A further increase of the dose leads to fining of the net structure, and at the doses around D 3D it becomes hardly distinguishable 关see Fig. 5共f兲兴. Thus, IBE of a slightly cross-linked PMMA results in a very clear net structure. The experiments with the hanging bridges of the graphitized and cross-linked PMMA 共see Sec. III A兲 provide an additional argument that the presence of slightly cross-linked PMMA is the most important factor for the formation of the net structure. Indeed, dissolution of the PMMA after IBE in the weak developer does not change the net structure in the hanging film. However, dissolution in the good dissolver 共acetone兲 makes the net structure hard to see. We conclude that the net structure localized mostly in deeper, less-modified layers. That conclusion is also confirmed by the fact that the electron irradiation with doses high enough for strong crosslinking 共larger than D 3D) lead to the disappearance of the net. An important property of the slightly cross-linked PMMA is a reduced mobility of the chains due to the crossings. Simultaneously, the amount of the gaseous products of destruction, which decreases as the radiation-induced modification occurs further, is still significant 共see Fig. 4兲. The net structure, in our opinion, can be the result of the stress release, which takes place during radiation-induced chemical processes and degassing in the IBE process. As well as the fine features, we observed the relatively

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FIG. 6. 共a兲 Waved structure and 共b兲 single bubbles and the bubbles conglomerate on the PMMA surface after IBE by Ar ions with energy of 250 eV and dose 1018 ion/cm2 .

FIG. 5. Net structure on PMMA surface after IBE by Ar ions with energy 250 eV and dose 5⫻1018 ion/cm2 . The dose of preliminary exposure with 15 keV electrons was 共a兲 0; 共b兲 400 ␮C/cm2; 共c兲 1.5 mC/cm2; 共d兲 3 mC/cm2; 共e兲 6.2 mC/cm2; 共f兲 9 mC/cm2; 共h兲 13 mC/cm2; and 共g兲 27 mC/cm2.

large structures that can be called ‘‘waved structure’’ 共see Fig. 6兲. After ion etching, the waved relief was observed and studied also in works.35,40 It was found that the waved topology depends on the preliminary electron irradiation40 or ion implantation.35 For instance, high-dose electron irradiation prevents waved structures from appearing. A crucial condition to the appearance of the waved structure is the presence of the low-molecular weight layer 共see Fig. 3兲. Indeed, between the graphitized/cross-linked and the bulk PMMA, the low-molecular weight layer of PMMA with molecular weight as low as 3 K is located. The mechanical properties of such material are significantly differ from both JVST B - Microelectronics and Nanometer Structures

the initial PMMA and the top, strongly modified layer. It is well known that the decrease of PMMA molecular weight leads to the loss of its mechanical strength, so the deformations take place easily. Therefore, the top graphitized/crosslinked layer lies on the ‘‘weak’’ support, the cohesion of the top layer with the bulk is lost, and this layer can be easily shifted, deformed, lifted, and so on. It is worth while to mention that the waved structure is very sensitive to external factors and can easily change during SEM investigations. The top layer has a worse gas permeability than the rest of the PMMA. For high electron current in SEM, even some kind of blistering can be observed. For small currents, the gases created during SEM investigation in the bulk of PMMA can only lift the top surface film. After the gases leave the film, additional details, including waved structure, can remain because of the permanent plastic deformations. The increase of the temperature during etching enhances the waved structure. SEM images in Fig. 6 also show the third type of the defects, which we call bubbles. The density of the bubbles and their structure also depends on the dose of the preliminary electron irradiation. In the absence of electron radiation, PMMA reveals a high density of bubbles and the bubbles can form complexes, as shown in Fig. 6共b兲. As the dose of the preliminary electron irradiation was increased, the complexes of bubbles disappear and a number of single bubbles decrease. With even higher doses of electron exposure, the formation of the bubbles is strongly suppressed. We argue that gas formation in the subsurface layer of PMMA determines formation of bubble-type defects during IBE. Indeed, as was described in our model of ion etching, radiation-induced chemical reactions result in the appearance of gaseous products. Gases can diffuse to the surface and

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FIG. 7. Cross section of bubbles in PMMA film developed as a result of IBE by Ar ions with energy 250 eV and dose 5⫻1018 ion/cm2 . 共a兲 Normal etching of initial PMMA, 共b兲 normal etching of the PMMA preliminary irradiated with electrons of dose 400 ␮C/cm2, and 共c兲 etching of initial PMMA with 30° between the direction of the surface and ions.

desorb. If the rate of formation of gases is higher than the rate of their emission from the PMMA film, macroscopic defects such as the bubbles can be expected. Notice here that the amount of gases inside PMMA, and correspondingly the formation of the bubbles can be stimulated by the reduced gas permeability of the top graphitized layer. Electron irradiation partially degasses PMMA. The degassing takes place very actively for low doses of electron irradiation. For higher doses, the degassing slows down. For even higher doses of irradiation, the gases created in the process of PMMA destruction are exhausted. High-dose electron irradiation substantially degasses the polymer and formation of the bubbles becomes unlikely. We studied the internal structure of the bubbles by SEM. For that purpose, after IBE the cross sections of the PMMA films were prepared by cleaving the substrate. The micrographs of the cross section are presented in Figs. 7共a兲–7共c兲. The direction of incidence of the ions was 90 共a兲, 共b兲 or 30° 共c兲 from the film surface. It is clearly seen that the bubbles take the shape of channels elongated in the direction of the ion incidence. However, as is shown in Figs. 7共a兲 and 7共c兲, because the PMMA was not treated with electrons, the channels can have a narrowing neck. More or less parallel walls were observed for the preliminary irradiated PMMA 共b兲. Finally, notice that the seriously destroyed area with channel conglomerates can be observed. A top view and crosssection of these defects are shown in Figs. 8共a兲 and 8共b兲, respectively. The density of the bubbles depends on the etching depth. The deeper the IBE of PMMA, the higher the density of the defects. Deep etching of PMMA causes surface roughness J. Vac. Sci. Technol. B, Vol. 22, No. 2, MarÕApr 2004

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FIG. 8. 共a兲 Top view and 共b兲 cross section of a conglomerate of bubbles in the PMMA film after IBE by Ar ions with energy of 250 eV and dose 1019 ion/cm2 .

and many defects. Etching of PMMA with such a rough surface cannot be described within the framework of the proposed in Sec. III B etching model.

IV. CONCLUSIONS In conclusion, we observed that the IBE of PMMA by Ar ions having the energy of 250 eV causes a stratification of the subsurface layer of the polymer. The top layer is transformed into a graphitized material. This layer displays a substantial conductance. Under the graphitized PMMA, a crosslinked stratum can be observed. A low molecular weight layer lies in between the cross-linked layer and bulk PMMA. We calculated the distribution of the density of the energy deposited by ions during IBE and estimated the thickness of the layers to be around 20 to 40 Å. A model of IBE of PMMA was proposed. It was shown that the IBE of PMMA is limited by the rate of the physical sputtering of the graphitized layer. Moreover, according to the proposed model, the etch rate depends on radiationinduced transformations in PMMA and the amount of the gaseous products of destruction that form during IBE. The developed model can be applied not only for PMMA, but also for various carbon-based polymers. The processes leading to the stratification of the subsurface layer significantly influence the PMMA topology. A fine net structure with a lateral dimension on the order of 20 nm appears in the presence of the cross-linked layer in the PMMA. The larger-scale waved structure develops in the presence of the low-molecular stratum, decreasing the cohesion between the top graphitized layer and the bulk of the PMMA. Ion etching also results in the appearance of

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bubbles. The bubbles take a shape of channels elongated into the direction of the ion incidence. The density of the bubbles/ channels grows with the etching time. ACKNOWLEDGMENT The author thanks M. V. Fistul for fruitful discussions and critical reading of the manuscript. 1

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