School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian , China

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1 Plasma Science and Technology, Vol.14, No.1, Jan Feature Profile Evolution During Etching of SiO 2 in Radio-Frequency or Direct-Current Plasmas ZHAO Zhanqiang ( ), DAI Zhongling ( ), WANG Younian ( ) School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian , China Abstract We have developed a plasma etching simulator to investigate the evolution of pattern profiles in SiO 2 material under different plasma conditions. This model focuses on energy and angular dependent etching yield (physical sputtering in this paper), neutral and ion angular distributions, and reflection of ions or neutrals on the surface of a photoresist or SiO 2. The effect of positive charge accumulation on the surface of insulated mask or SiO 2 is studied and the charge accumulation contributes to a deflection of ion trajectory. The wafer profile evolution has been simulated using a cellular-automata-like method under radio-frequency (RF) bias and direct-current (DC) bias, respectively. On the basis of the critical role of angular distribution of ions or neutrals, the wafer profile evolution has been simulated for different variances of angles. Observed microtrenching has been well reproduced in the simulator. The ratio of neutrals to ions has been considered and the result shows that because the neutrals are not accelerated by an electric field, their energy is much lower compared with ions, so they are easily reflected on the surface of SiO 2, which makes the trench shallower. Keywords: profile evolution, RF bias, reflection, etching yield PACS: Kh, Kj doi: / /14/1/14 1 Introduction Topography evolution during etching of semiconductor devices is extremely important in the manufacture of large scale integrated circuits, the successful application of plasma etching technologies has induced a drastic change in the manufacturing process of large scale integrations (LSIs) from the conventional liquid-based wet process within a fairly short period. These changes reduce the number of steps in the manufacturing process, and thus reduce the manufacturing cost of the devices [1]. One of the most basic steps in integrated circuit (IC) manufacturing is the deposition of silicon dioxide (SiO 2 ) on a wafer. Subsequent removal of all or part of this oxide layer is critical to device fabrication. But understanding of the origin of profile characteristics has fell behind for ultralarge-scale integration (ULSI) [2]. Therefore, a fundamental understanding of mechanisms that affect profile evolution is necessary [3 7]. The bias voltage of the etchable substrate surface is an extremely important factor during the evolution of feature profile, which allows the determination of etching behavior at different ion bombardment energies. In the etching of a nanometer-scale trench, local charge accumulation is one of the origins of anomalous process. The influence of a local charging on the etching rate of SiO 2 is very important in an arranged trench pattern, and the angular distribution of ions or neutrals must be discussed from the viewpoint of the local charging [8,9]. Experimental evidence of bottom charging in arranged holes during etching is demonstrated in Ar and CF4 plasma [10,11]. Self-consistent modeling of a feature profile evolution which results from a topographical charging on the SiO 2 insulator wall has been proposed in a simple surface process with fluorocarbon radical accumulation in a 2f- CCP etcher in previous works [12 14]. The notching phenomenon describes the opening of a notch in a conductive material at the interface with an underlying insulator. ARNOLD and SAWIN [15] gave an explanation that the electric fields induced distortion of ion trajectories and the local electric fields were formed as a result of microstructure charging brought about by the directionality difference between ions and electrons at the wafer surface. OOTERA [16] considered the energy distribution of electrons arriving at the microstructure but neglected the ion energy distribution and the effect of an oscillating sheath. Thus, because of the importance of the sheath in the etching processes, it is necessary to study feature profile evolution by considering not only ratio of neutrals to ions, and incident angles of ions, but also the characteristics of the sheath. In this paper, we investigate the evolution of pattern profiles by combining a sheath model with a trench model. We will present the profile evolution with the ratio of neutrals to ions, variance of angle, and the energy of ions or neutrals taken into consideration. The supported by National Natural Science Foundation of China (Nos and ), and the Important National Science and Technology Specific Project of China (No. 2011ZX )

2 ZHAO Zhanqiang et al.: etching of SiO 2 is based on the etching yield model previously described for the Cl etching of polysilicon, which is an empirical method. The paper is outlined as follows: Section 2 describes a self-consistent sheath model and etching profile evolution simulation model. Section 3 presents some results and relevant discussions, including the characteristics of incident angle, the ratio of neutrals to ions, and the bias amplitude. Finally, the conclusion is given in section 4. 2 Model The sequence of microscopic reaction steps is very important in plasma etching. Electrons can be accelerated by electric fields (E-field) such as DC, RF, or microwave E-fields and collide with suitable precursor molecules to make them ionize to produce ions and radicals [17 19]. Consequently, an electron-free spacecharge region forms between a plasma and a contacting solid surface, which is designated as a sheath. Sheaths [4,15] are critically important for plasma etching. The reason is that positive ions are accelerated toward the surface when entering a sheath. Most of the ion energy is obtained due to the acceleration in the sheath E-fields established by the self-biasing wafer chuck. The accelerated ions bombard the surface with bombardment energy much greater than the thermal energy. The fabrications of high-speed semiconductor circuits are dependent on etching submicrometer trenches and holes with straight walls, which are determined by sheath-accelerated ions that strike the collector at a normal angle. Electrons enter the sheath with an isotropic angular distribution. In addition, the ions are accelerated in the presheath to the Bohm velocity and the potential at this position is considered to be equal to 0. The velocities of ions in the direction perpendicular to the wafer grow larger than the thermal velocities of ions in the parallel direction. This initial directional difference grows greater as the particles traverse across the sheath. Finally, ions with energy of tens of volts or more through the acceleration of E- fields bombard the trench bottom. At the same time, the electrons, which are still in an isotropic Maxwellian distribution, are decelerated in the sheath, and eventually most of them are returned to the plasma. Only a few electrons through the sheath edge arrive at the wafer surface where they charge the nonconductive photoresist to the floating potential. The electrons entering the trench are few, whereas the ions deposit positive charges onto the trench bottom and make the etching happen. In this paper, we use a self-consistent sheath model [20] which includes the time-dependent terms in ion fluid equations and an equivalent voltage equation. We think, in a low pressure plasma, it is reasonable to neglect the collision effects in the sheath [21,22]. Also, we can neglect the ion thermal motion effects since the ion temperature is much smaller than the directional Feature Profile Evolution During Etching of SiO 2 in RF or DC Plasmas kinetic energy in the sheath region. Thus, the onedimensional spatiotemporal variation of the ion density n i (x, t), the ion drift velocity u i (x, t), and the electric potential inside the sheath, V (x, t), are described by the cold ion fluid equations, n i t + (n iu i ) = 0, (1) x u i t + u u i i x = e V m i x, (2) where m i is the ion mass, e is the electronic charge, and the Poisson equation, 2 V x 2 = e ε 0 (n i n e ), (3) where ε 0 is the permittivity of free space, n e (x, t) is the electron density, and V (x, t) is the electric potential [25]. We can consider that the electrons are inertialess and the electron density in the sheath is given by a Boltzmann distribution ( ) ev (x, t) n e (x, t) = n 0 exp, (4) k B T e where n 0 is the plasma density, T e is the electron temperature, and k B is the Boltzmann constant. In the model, a RF source is applied to the electrode and the voltage on the electrode can be expressed as V e (t) = V dc + V L sin(ωt), (5) where V e (t) is instantaneous voltage on the electrode, V dc is the self-bias voltage, and V L is the voltage amplitude of the source. For insulating substrates, the charges accumulated on the substrate surface should involve both the ion current and the electron current Q(t) = t 0 [I i (τ) I e (τ)]dτ, (6) where I i (τ) and I e (τ) are the ion and electron currents, respectively [22], and Q(t) is the charge. The sum of the voltage induced by the accumulated charges on the surface of the insulator is given by V s (t) = V e (t) + Q(t) C f, (7) where V s (t) is the voltage on the surface of the insulator, C f = κε 0 A/d f is the effective capacitance of the insulating substrate, and d f is the thickness of the insulating substrate. To solve Eqs. (1) (7), we need to choose appropriate boundary conditions and assume that the plasma-sheath boundary is at the location x = d s (t) (in Fig. 1). The ion density should be equal to the electron density: i.e, the quasi-neutral condition n i (d s, t) = n e (d s, t). In addition, we also assume that ions enter the sheath with a velocity equal to the Bohm velocity u B = k B T e /m i, u i (d s, t) = u B. (8) 65

3 Plasma Science and Technology, Vol.14, No.1, Jan Fig.1 Schematic diagram of the sheath model Finally, we assume that the potential at the sheath edge is approximately zero, i.e. V (d s, t) = 0, (9) and take the value of the potential at the insulating substrate (x = 0) to be V (0, t) = V s (t). (10) The closed set of nonlinear Eqs. (1) (7) which determine the spatiotemporal dependence of the radio-frequency sheath with the boundary conditions (8) (10) will be solved numerically by using a finite difference scheme with an iterative process [23 25]. The iteration is repeated until the solutions converge to a self-consistent periodic steady state. Through above calculations, we can get the energy of ions on the insulator and assume the angles of ions have a Gaussian distribution. The particles incident angles are determined by randomly sampling from their respective distribution functions: Gaussian angular distributions for ions and neutrals. Consequently, we can simulate the evolution of etching feature using the ions which arrive at the insulator. In our simulation of etching feature evolution, the two-dimensional region used for computations is shown in Fig. 2. A conducting collector of SiO 2, which represents the substrate being etched, is at Fig.2 The schematic diagram of computation region. The wafer is SiO 2. Ions and electrons are emitted from the sheath at the top the bottom of the trench. Ions are accelerated by the sheath electric field (E-field) toward the dielectric block, and the surface they strike first is often photoresist. The photoresist surface and the trench walls are divided into small cells. The dielectric has width 2L=200 and the height is H = 900, while the depth of photoresist is D = 280, and the aspect ratio is AR = D/2W. Because the trenches are much smaller than both the Debye lengths and sheath, scale invariance justifies the use of the simpler Laplace equation rather than the Possion equation, to describe particle trajectories in the model. The dimensionless Laplace equation is 2 V = 0, (11) so we can get the potential in the trench using an iteration u (k+1) i,j = 1 ( ) u (k) i+1,j 4 + u(k+1) i 1,j + u(k) i,j+1 + u(k+1) i,j 1, (12) where u i,j is the potential of a point of the grid, k is a point of time, and i and j is a point of the grid. For insulating substrates, we can use Eq. (3) to get the potential of the substrate. Using the Boltzmann relation of electrons and equating the ion and electron fluxes n i v i = n e v e, (13) where n s = n i = n e at the sheath edge by definition. When ions strike the surface of a photoresist cell or SiO 2, we can get their potential [12] V i,j = T ev [ln(f i,j 2L/ s) 4.68], (14) where 2L is the width of the dielectric, s is the scale of one cell, and F i,j = N i,j /N is the fraction of all ions that end up in one cell. The Laplace solver is used to calculate the 2D electric fields. Motions of ions and electrons in the simulation domain will be influenced by local electric fields. The time-independent trajectory of each ion emitted from the sheath is then computed in this electric field. The simulation of ion transport through the sheath depends on a stochastic generation of ions at the ion sheath-plasma boundary (sheath edge), so the trajectory of the particle is computed using only the x and y components and is followed by the Newton equations of motion in the 2D plane: M dv x dt = qe x(t), M dv y dt = qe y(t) (15) where M and q are the mass and charges of particle, and E x (t) and E y (t) are the transverse and parallel components of the electric field, defined with respect to the wafer surface normal. For ions the q is 1. When an ion impacts a target cell (a plasma-material in-interface cell, for example), the cell neighborhood is examined. Within a circle of radius R = 3 2 centered on the target cell (in Fig. 3), we consider the four cells adjacent to the target, i.e. down, up, right, and left cells, and using the method of least square, we can fit a straight line with the direction of l = (l 1, l 2 ). Among such cells, all these that are plasma-material interface and their 66

4 ZHAO Zhanqiang et al.: Feature Profile Evolution During Etching of SiO2 in RF or DC Plasmas Using the above group of equations, we can get b ± b2 4ac j2 =, (21) j = t t j2a j2. We can see j1 that there are two values from the group of equations, but one of them is in accordance with the incident direction, which we will omit, the other one is what we need. When l1 = 0, the reflected direction is reverse to the incident direction. When the trajectory intersects a surface of one cell, its contribution to Ni,j is counted. We can use the potential of each cell and use it in the first iteration. The trajectories of ions can be recalculated until Vi,j converges to steady value. In this model, all collisions, secondary emission, and surface currents are neglected, and we assume that the ions only bombard the surface. Then, the etching yield can be estimated. Under these assumptions, we have used a surface kinetic model involving two simulation parameters: the direct inelastic scattering (DIS) probability (Pd ) and the relative etching yield (Y ) on the surface. These probabilities can be expressed in terms of the incident energy (Ei ) and angle (θi ) as follows [26] : p π (22) Pd = 1 C1 Ei cos( θi ), 2 p p Y = C2 ( Ei Eth )(1 Pd ), (23) So the angle of reflection is θr = arctan Fig.3 The schematic diagram of reflections of ions or neutrals on the surface of photoresist or SiO2 centers coordinates are stored. A linear fit of these data points provides the local slope. When ions interact with the surface of SiO2, there are two possibilities. They either are reflected from the surface or interact with the materials according to the etching yield (largely physical sputtering in this article). To decide which process is concerned in a specific case, the incident angle is compared to the local slope at the target cell position. When the ions are reflected by the surface there are no energy losses. In the simulation, we consider that the ions with incident angles above 80o from normal are reflected without etching. Following above concerns, we can determine the direction of incident particle ~i = (i1, i2 ) = (vx, xy ), where ii and i2 are the direction vector of incident direction. So the incident vy angle is θi = arctan, using horizontal and vertical vx velocity vx and xy respectively. During the process of reflection, we assume the direction of reflected ion to be ~j = (j1, j2 ), where j1 and j2 are the direction vector of reflection direction. Incident ions comply with specular law of reflection, and the inner product between incident and plane direction vector is equal to the one between reflected and plane direction vector. i1 l1 + i2 l2 = j1 l1 + j2 l2, (17) where C1 and C2 are adjustable parameters and Ei (ev) is an energy threshold, which is 10 ev in this article. Pd should be between 0 and 1, if the value at the right hand side of Eq. (3) is beyond this range, Pd is set to be 0. C1 = 0.25, C2 = 0.13, and θi is the incident angle of an ion. In the simulation, we only consider reflections of ions from the photoresist and wafer. With the evolution of etching topography, we use a cellular automata like method to simulate the profile evolution: we consider that every cell has 150 atoms, which could be lost when particles come into and go out; when the number of atoms of a cell becomes zero, a boundary cell becomes a vacuum region cell. When a cell doesn t lose all the atoms, we assume that the ions will accumulate on the surface of SiO2 and the fields which are affected by the accumulation of ions can be calculated, and when a cell loses all atoms, the charges are neglected. ~ ~ i = j. (18) 3 ~i ~l = ~j ~l, (16) using this equation, we can get and we know Using Eqs. (17) and (18), we can get a group of equations i1 l1 + i2 l2 = j1 l1 + j2 l2, (19) i21 + i22 = j12 + j22, (20) when l1 6= 0, we can let t1 = i1 + i2 1 + t22, b = 2t1 t2, c = t21 i21 i22. l2 l2 t2 =, a = l1 l1 Results and discussion In this paper, we numerically investigate the influence of reflections of ions, RF bias, DC bias, aspect ratio, the ratio of neutrals to ions, and the variance of incident angle on the evolution of the etching profile. Reflection of particles from surfaces of photoresists and SiO2 plays a critical role in the evolution of etching topography. Besides, as the etching evolves, more SiO2 surfaces are exposed to be bombarded by ions, which results in charge accumulation there. The charging will 67

5 Plasma Science and Technology, Vol.14, No.1, Jan change the local electric field in the etched area and affect ion motion in the vicinity of the area. It is shown that this local electric field perturbation has a profound effect on the notch shape and depth. In order to simplify the calculation, we assume this transient charging of the SiO2 surface is local and will not affect significantly the steady-state electric field in the trench area or the equipotential of SiO2. Since the notch is small and shadowed from the plasma, the number of electrons which arrive at the SiO2 surface must be small and will be neglected in our calculation. Now we discuss the situation where a SiO2 wafer is under DC bias, as shown in Fig. 4, and the reflection is not considered. The amplitude of voltage is Ve = 200 V, 400 V, 600 V respectively. It can be noticed that with an increase involtage amplitude, the depth of trench becomes deeper correspondingly, and because the reflection is not considered on the surface of SiO2, the angle distribution of ion plays a dominating role at this moment. So with increasing voltage, the transverse direction of trench becomes wider and wider. sequently, we can see from the figure that the profile under the RF bias is smoother. Fig.5 The evolution of feature profile with consideration of the reflection at different amplitudes of voltage (a) 50 V, (b) 80 V, (c) 200 V under direct-current (DC) bias Fig.6 The evolution of feature profile with consideration of the reflection at different amplitudes of voltage (a) 50 V, (b) 80 V, (c) 200 V under radio-frequency (RF) bias Fig.4 The evolution of feature profile without consideration of the reflection at different amplitudes of voltage (a) 200 V, (b) 400 V, (c) 600 V under direct-current (DC) bias On the basis of Fig. 4, we take into consideration the reflection of ions on the surface of SiO2 in Fig. 5. To some extent, the reflection balances the angle distribution of ions, and the width of the trench is not as wide as that shown in Fig. 4. Because photoresist charging is considered, the electric field near the entrance is strong enough and causes a large deflection of ions. Consequently, the etching rate is higher in the middle of the trench, with the increase of amplitude of bias, the depth of trench becomes deeper, and during this process, the charges of surface of SiO2 play a role in altering the trajectories of ions. So when the etching continues, the trench becomes slightly wider. But the amplitude of bias plays the primary role. In order to describe the difference in etching between RF bias and DC bias, we simulate the evolution of feature profile under RF bias in Fig. 6. Because under the RF bias, there will be a few low-energy ions, whose velocities along vertical direction are smaller, and these ions can easily be reflected on the surface of SiO2. Con68 The feature profile evolution with different ratio of neutrals to ions is shown in Fig. 7, where neutrals are introduced at a source plane above the top of feature, and the ratio of neutrals to ions is σ = 0, 0.5, 0.7 respectively. It can be noticed that with the increase of ratio of neutrals to ions, the depth of trench becomes much shallower and the profiles are much smoother. The reason is that the neutral particles are not accelerated by electric field, whose energy is smaller than that of ions, thus etching yields are smaller. Fig.7 The evolution of feature profile with consideration of the reflection at different ratio of neutrals to ions (a) 0 (b) 0.5 (c) 0.7 at the amplitude of voltage 80 V under direct-current (DC) bias

6 ZHAO Zhanqiang et al.: We make a comparison between DC bias and RF bias under the same conditions about ratio of neutrals to ions in Fig. 8. Feature Profile Evolution During Etching of SiO 2 in RF or DC Plasmas Fig.8 The evolution of feature profile with consideration of the reflection at different ratio of neutrals to ions (a) 0, (b) 0.5, (c) 0.7 at the amplitude of voltage 80 V under radio-frequency (RF) bias In order to perfectly consider the influence of the angle distribution of ions on the profile evolution under DC and RF bias, we conduct specific simulations for different incident angles, α=5, 10, 15 respectively, as shown in Figs. 9 and 10. When α increases, the reflections become more frequent and the notches becomes more evident. By comparing respectively Fig. 7 with Fig. 8 and Fig. 9 with Fig. 10, it can be seen that the bottom of the trench is smoother and has better uniformity under RF bias, which is due to the difference in the charging effect and the ion energy between DC bias and RF bias. Fig.10 The evolution of feature profile with consideration of the reflection for different incident angles (a) 5 (b) 10 (c) 15 at the amplitude of voltage 80 V under radio-frequency (RF) bias of ions or neutrals plays a dominant role in the evolution of feature profile. Different ion energy will result in a different etching rate. The angle distribution of ions or neutrals also plays a critical role in the evolution of feature profile, and for various incident angles, we can know that as the angle becomes slightly bigger, it will easily lead to a microtrench. Under RF bias, there will be some low-energy ions, which will result in smoother trench. However, the effect of specific plasma chemistry is not taken into consideration in this paper, which is of a rather general character with regard to any ions present in the plasma. In further study, we will focus on ion-assisted chemical etching, taking into account chemical reactions, different driven source-wave forms and reactor scales. In addition, the aspect ratio (depth/width) and the collisions between ions and neutrals in the sheath are very important parameters during wafer profile evolution, which will be considered in the future. References Fig.9 The evolution of feature profile with consideration of the reflection for different incident angles (a) 5, (b) 10, (c) 15 at the amplitude of voltage 80 V under direct-current (DC) bias 4 Conclusion We have present a self-consistent sheath model and a 2D numerical simulation of etching profile evolution of SiO 2, and feature profile evolution under different conditions is obtained by this simulation. The etching artifacts under RF bias are characterized and discussed. If the reflection is not considered, the angle distribution 1 Abe H, Yoneda M, Fujiwara N. 2008, Jpn. J. Appl. Phys., 47: 1435S 2 Hwang G S, Giapis K P. 1997, J. Vac. Sci. Technol. B, 15: 70 3 Lieberman M A, Lichtenberg A J. 2005, Principles of Plasma Discharges, Materials Processing. 2nd edition, Wiley, New York 4 Oehrlein G S, Doemling M F, Kastenmeier B E E, et al. 1999, IBM J. Res. Develop., 43: Robiche J, Boyle P C, Turner M M, et al. 2003, J. Phys. D: Appl. Phys., 36: Armacost M, Hoh P D, Wise R, et al. 1999, IBM J. Res. Develop., 43: 39 7 Arikado T, Horioka K, Sekine M, et al. 1988, Jpn. J. Appl. Phys., 27: 95 8 Matsui J, Nakano N, Petrovic Z L, et al. 2001, Appl. Phys. Lett., 78: Ohmori T, Makabe T. 2008, Applied Surface Science, 254: Ohmori T, Goto T K, Kitajima T, et al. 2003, Appl. Phys. Lett., 83:

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