Chapter 8 – Etch Sidewall Profile Simulations

Chapter 8 – Etch Sidewall Profile Simulations

Chapter 8 – Etch Sidewall Profile Simulations 8.1 Introduction

In the preceding Chapters we have shown that the energies and angles at which ions strike the substrate in an RF reactor can be accurately modelled. From the point of view of etching mechanisms, these data are extremely valuable, since it is the inherent directionality of these ions that is believed to underlie the mechanisms of anisotropic etching. Having obtained accurate IEDs and IADs for a variety of etch process conditions, it would be very useful if the resulting etch profile could be calculated. It could be envisaged that in the future, a process engineer might use a computer to calculate the sidewall profiles that would be obtained for a particular reactor and set of process conditions. This would indicate where the engineer should start when attempting to develop a new etch process, and may also reduce the time and cost of some of the lengthy trial-and-error experiments that are usually required in order to obtain the process window.

The work in the following sections is a preliminary attempt to obtain sidewall profiles in this manner. The model requires a detailed description of the main ion-surface interactions that are important to etching processes. There are many ways that high energy ions can interact with a surface (see section 1.5.10), only some of which lead to removal of surface atoms and hence etching [27]. Almost all of these interactions depend critically upon the incident ion mass, energy and impact angle [206]. Consequently, if we wish to model an etch process, we need to know the dependences of the significant interactions with all the relevant ion parameters. Unfortunately, only some of these data are known. Experimental studies of sputtering metal and semiconductor substrates with ions yield useful information [27], but these experiments are usually only performed for a limited set of process conditions, for example ion beams of one energy at normal incidence. We require a more general approach.

A comprehensive and detailed theory of sputtering has been formulated by Sigmund [244]

who derived the expression for the sputtering yield S for ions of up to 1 keV energies:

S(E) = 3E α { 4m1m2 / (m1 + m2)2 } / (4π2 U0) (8.1) where α is a parameter dependent upon m2/m1 and U0 is the surface binding energy. An alternative statistical model of sputtering [245] predicts yield as a function of ion energy, mass and incident angle. This theory assumes that the probability of displacing an atom in the target depends only upon the distance of that atom from the point of ion impact. For ion impact angles of θ, this model predicts that the yield is given by S(E,θ) ~ E2/3 / cos θ (8.2)

Since the sputtering process continually removes the top layer of atoms from the surface, the surface layer of the target undergoes constant change during ion bombardment. For relatively heavy ions and doses, the surface topology that develops is dominated by the erosion process. In


other cases, such as He+ ion sputtering, the He gas becomes implanted into the target and builds up below the surface in pockets and eventually produces blistering of the surface [261].

There have been a number of recent investigations (outlined in ref.[261]) which have studied both experimentally and theoretically the type of topology generated by ion bombardment. For crystals, the features produced on the surface due to ion bombardment exhibit characteristics related to the basic crystallography of the material. Hence, pyramids and etch pits are observed having distinct facets in certain crystallographic planes. For compound semiconductor materials, such as InP, the surface can become enriched with one atomic component and cone formation can occur. For pure Si, a facetted surface can develop under both inert and reactive gas ion bombardment. Many of these features are still not fully explained.

In order to understand some of these effects more fully, erosion theory has been used to model the development of topology [246,247]. The basis of this theory is the dependence of sputtering yield upon the ionic angle of incidence. Computations have been carried out (both in 2 and 3 dimensions) to show how ridges and facets can develop from initially smooth surfaces [246]; however, these models are far too complex to incorporate into a large scale etch profile simulation such as we are proposing.

There have been few attempts to model etch profiles [254,279,281-287] in RF processes. This is mainly due to the lack of detailed knowledge about the energies and angles at which ions strike the electrodes in typical RF reactors. Before we proceed, however, we shall first give a brief résumé of the approaches to the problem that have been adopted by other workers.

Some of the first attempts to model an evolving etch profile were performed by Oldham [281] and Pack and Thurgate [282]. The computer programs employed by these workers (SAMPLE and DEPICT-2, respectively) calculate the time evolution of a profile using two adjustable parameters, the isotropic and anisotropic etch rates. The isotropic component erodes the substrate equally in all directions perpendicular to the surface, while the anisotropic component erodes proportionately to the cosine of the angle formed by the incident ion flux and the surface normal. The values used for these two parameters were determined by comparison with experimental profiles, which limits the applicability of their simulation to previously-defined structures, or to an interpolation between other experiments. The etch rate is determined from a multi-variable polynomial requiring information such as the pressure, power, gas flow rate etc. of the plasma system.

Another program named COMPOSITE [285] considers empirical formulae that describe the etch rates with other etching parameters (such as sputtering and chemical etching rates), but uses only approximate calculations for the incident ion energy and angular distributions. Recently, Ulacia et al [286] developed a model for profile simulation that combines both an acceptable description of the ion flux to the surface with a good description of the surface. IEDs and IADs are calculated from a Monte Carlo simulation program similar to that used by Kushner [138] (see Chapter 5), although only approximate descriptions of the potentials within the sheath are used. The surface is modelled by a series of nodes with known x,y coordinates, joined together by a ‘string’. The incident ion flux to each of these nodes is calculated based on the known IED/IADs and the shadowing effects of resist structures. The time-evolution of this surface string is followed as the etch profile develops. This model has also been extended to include simultaneous etching and deposition [254].

Hope et al [287] have used a similar approach to model etch profiles for O2 etching of organic polymers. They used measured values for the flux of O, O2 and O2

+ arriving at the electrode of


an experimental O2 plasma to calibrate an IED/IAD simulation program. They used a model for the substrate surface based upon hard cubes, each of which is assigned a weighting value of 10 ‘hit-points’. The number of these hit-points in each cube is reduced by the action of incident particles until it reaches zero, at which point the cube is considered to have been etched away. Only non-erodible resists are considered. A more detailed description of a ‘hit-point model’ is given in section 8.3.5.

In most of the above approaches, although profiles have been demonstrated that look very similar to experimental profiles, this is primarily due to the use of previously-etched wafers to accurately calibrate the required fitting parameters. All of the above models use IED/IAD data that were calculated using unrealistic models for ion trajectories through the sheath, and none include a detailed description of the etch rate dependence with ion impact energy and angle. We are now in a position to attempt a more accurate model of surface profiles, since the IED and IAD simulations obtained in the previous sections of this thesis provide a valuable database of all the necessary information.

In order to simplify matters, we shall limit ourselves to Ar plasmas, since we have already demonstrated that we can accurately reproduce both high and low pressure IEDs for these systems. In later sections, however (e.g. section 8.12), we present etch profiles simulated for real RIE processes (e.g. SF6, CCl4, etc.) which we compare to profiles that were obtained experimentally.

Since the sputter yield depends upon the target composition, the composition shall be kept constant. We shall use the most common semiconductor material, Si, and we will require the detailed form of the sputter yield dependence of this substrate as a function of both Ar+ ion impact energy and angle. We shall also need to consider other interaction processes, such as backscattering, since it is possible that ions can reflect off an evolving sidewall to preferentially sputter a trench at the bottom of the feature [47]. Therefore, we shall not only need the backscatter yield as a function of ion energy and angle, but also the energy and angular distributions with which any ion backscatters.

Various models were considered for these purposes, including the sputtering model of Sigmund [244] but were found to be inadequate for the simulation of detailed etch profiles. Logan and Stickney [248,249,251] have developed a hard cube model of the target, whereby surface atoms can only move in one dimension perpendicular to the plane of the surface. They derive expressions [252] for the probability distributions for ions striking this idealised surface being backscattered with certain energies and angles. However, the theory assumes that the ions have a very low energy and so do not significantly damage or sputter the surface. Furthermore, their theory is valid only for light ions striking heavy target atoms in order that the interaction can be modelled as a single collision process. But we require the dynamics of an Ar+ ion striking a relatively light Si atom, where knock-on effects might be important. We therefore require a more sophisticated approach.

There are two well-known computer programs that deal with these problems. These are called TRIM [202] and MARLOWE [253]. They both function in approximately the same way. A Monte Carlo approach is adopted, whereby ions impinge upon a surface and the resulting atom cascades are followed. These programs were originally developed to study ion-induced damage, but by following the trajectories of atoms as they leave the surface, sputtering can also be modelled. No differentiation is made between ionic and neutral incident particles, so bombardment by high energy atoms (as was demonstrated in Chapter 6) can also be simulated.


Backscattered particles such as ions or neutrals (formed from Auger Neutralisation processes, see section 7.3.1.1) can also be followed as they leave the surface. The first program that was obtained by our group was TRIM, so all subsequent modelling has been based upon data calculated using this program. The major difference between TRIM and MARLOWE is that the latter incorporates models for structured surfaces, whereas TRIM only caters for amorphous targets.

8.2 The TRIM Program

TRIM (TRansport of Ions in Matter) is a Monte Carlo simulation program that was originally written in the early l980s by Ziegler and Biersack [202]. The program has been extensively upgraded since then, and the version obtained for use in the present work was TRIM89. The program is public-domain software, which means that it is freely available to anyone who wishes to use it, so long as no commercial profits are made from its use.

A detailed discussion of the theories of ion-surface interactions and the models used to create TRIM are given in ref.[202], so only a brief account of the important features of the model will be summarised here. The program has been extensively modified by the author of this thesis to include details of sputtered atom trajectories and energies. Similar computer models of sputtering have been recently developed by Perez-Martin et al [255]. Furthermore, the version of TRIM used here has been greatly simplified and speeded up by removal of the facility for multi-layered substrates, along with damage and transmitted ion (from thin film targets) calculations. The resulting modified program, which has been used for all the calculations in this thesis is listed in full in Appendix IX. 8.2.1 Main Features of TRIM

The main approach adopted in TRIM for ion-surface interactions is a Monte Carlo simulation, whereby ions impinge upon a surface with a known energy and angle of incidence. It should be noted that TRIM uses the convention that angles are measured from the surface normal, so that 0° is perpendicular to the surface and 90° is parallel to it. This is different to the convention used in the preceding Chapters.

The trajectories of the individual ions are followed as they enter the surface and undergo a series of binary collisions with the target atoms, losing energy in each successive collision. The ion is followed until it either exits the surface (and is counted as a backscattered ion) or runs out of energy and becomes implanted. Backscattered ions are still termed ‘ions’ even though in reality most would have been neutralised by interaction with electrons in the target. This terminology allows the program user to differentiate between the incident ion and target atoms, both of which can be ejected from the surface. If the ions is backscattered, its energy and angle of ejection are stored in data files. Any target atoms struck by the ion will gain energy from the collision. Their trajectories, too, are followed through subsequent collisions until they either lose so much energy that they can no longer do any damage in further collisions, or they pass through the surface layer to leave the target as sputtered atoms. The energy and angle of ejection of any sputtered atoms are also stored in data files. Typically, several thousand ion trajectories are used


to build up distributions with a good signal:noise ratio. The sputter yield and backscatter yield can be calculated directly from the number of sputtered atoms and backscattered ions divided by the total number of ions used. The important features of the model are: (a) The Target Structure: The target is considered to be an amorphous solid with no structure.

Therefore, crystalline or granular structures cannot be modelled using TRIM. The surface is modelled in a way resembling a gas, in that all target atoms are randomly distributed throughout the solid, which has a defined density. Ion trajectories are calculated as straight lines until they undergo collisions with target atoms. These collisions occur at random locations based upon an ionic mean free path that is dependent upon the stopping powers (see b below) of the ion-atom collision partners. Atoms are bound to sites within the target and require a collision of greater than a certain energy to displace them from a site. If an atom is displaced, it leaves behind a vacancy in the amorphous lattice, which constitutes one aspect of damage (see d below). The target remains unchanged throughout the calculation, despite sputtering, implantation and damage effects that occur during the ion bombardment.

(b) Stopping: This is a term that refers to the energy loss experienced by an ion when it collides

with a target atom [202,239]. The total energy loss as a function of distance, z, (–dE/dz), can be regarded as a sum of three components, nuclear, electronic and charge exchange losses. Nuclear stopping results from collisions between the effective unscreened nuclear charges of the ion and target atoms. TRIM uses the so-called Universal stopping formulae to calculate the stopping values for each ion-atom pair. A subroutine calculates all these values prior to entering the main Monte Carlo loop. A separate subroutine is used to calculate the nuclear stopping for H+, He+ and heavier ions, since different formulae are employed in each case (see SUBROUTINE RSTOP in Appendix IX). Electronic stopping occurs continuously as the ion travels through the dense ‘sea of electrons’ within the target. TRIM calculates this energy loss as the ion travels a distance z between collisions and subtracts this from the collision energy. Electronic stopping is only really significant at ion energies greater than A keV, where A turns out to be the atomic weight of the incident ion. For Ar, therefore, this form of energy loss will only be important above about 40 keV, so it will not affect our calculations for impact energies of E ≤ 500 eV. Charge Exchange (or Bohr Straggling) results from electrons transferring from a target atom to the moving ion. This loss process is only really significant when the relative velocity is comparable to the Bohr electronic velocity (about 2×106 m s-1), so for our low energy ions (E < 500 eV which is equivalent to 5×104 m s-1) this is unimportant.

(c) Ion-atom Interaction Potential: The form of the potential used to describe the ion-atom

collisions controls the values of the nuclear stopping parameters, the distance of closest approach and the scattering angles of the post-collision products. TRIM uses the so-called Universal screening function, which is basically an empirically modified version of the inverse square Coulomb potential. The Biersack-Haggmark ‘Magic Formula’ [202] is used to calculate the scattering angles based upon this potential. An example of its use it seen in lines 4420-4860 of TRIM in Appendix IX.


(d) Damage: This is a term that incorporates many phenomena. These include vacancy

production, dislocations, interstitials and collisional mixing, whereby an atom (possibly of a different type) fills a previously-created vacancy site. Since, in this thesis, we are not concerned with damage within the target, all calculations to this end have been ‘commented-out’ within the program. However the relevant code still remains should da mage calculations be required in the future.

(e) The Surface Layer: This is considered to be perfectly flat and infinite in extent. At the

surface there is a plane potential barrier which atoms must overcome in order to leave the target and become sputtered [255]. The magnitude of this barrier is a few eV and can be specified by the user as an input variable. If no value is specified an estimate based upon the energy of sublimation of the target is used as a default value. Atoms of energy E will be sputtered if the component of kinetic energy normal to the surface is greater than that of the potential barrier, Esurf, otherwise they will be reflected back into the bulk. Sputtered atoms leave the surface with energies E – Esurf.

More details about the operation and modelling involved in TRIM can be found in Appendix

IX and ref.[180 and 202]. 8.2.2 Results from TRIM

Only a few of the basic results from TRIM will be discussed here since a detailed study of the program capabilities can be found in ref.[180 and 202]. Examples of some of the data calculated using TRIM are given in fig.8.1-8.8. Only those data directly relevant to this thesis have been included.

(a) Implantation Depth: Fig.8.1 shows a cross-section through an amorphous Si surface illustrating the positions in the target where 400 eV Ar+ ions became implanted. The distribution is tear-shaped, being symmetrical about the initial normal ion direction. This plot shows that ions with energies typical of that found in RIE reactors can penetrate quite deeply (50 Å) into semiconductor surfaces. They can also spread out laterally to distances of 30-40 Å. This point will not be discussed further, but fig.8.1 shows that ions from the plasma process will penetrate considerable distances under any masked feature on the substrate surface.


Fig.8.1. Depth profile of implanted 400 eV Ar+ ions into Si. The ions struck the surface at

normal incidence (parallel to the horizontal axis) at (0,0). (b) Sputtered Atom Energies and Angles: An example of a distribution of sputtered Si atom energies is shown in fig.8.2. Typically, sputtered atoms leave the surface with a Maxwellian-like distribution of mean 0-20 eV depending upon the initial ion energy. The angular distribution (not shown) resembles a cosine distribution (see Appendix III). Atoms can leave the surface at points some distance away from the original impact site. These distances can be up to 20 Å.

Fig.8.2. Energy of sputtered Si atoms when a Si target is bombarded with 400 eV Ar+ ions at

normal incidence.

(c) Backscattered Ion Energies and Angles: The energy at which ions are backscattered from the surface is a complex function of the incident energy and angle. Fig.8.3 shows two distributions for 500 eV Ar+ ions striking Si at angles of (a) 45° and (b) 80°, where normal incidence is 0°. For angles near normal incidence, ions penetrate deeply into the target and


cause multiple cascades. These ions can only escape after having had many collisions, consequently, their energy distribution resembles an exponential-type decay curve. For more glancing impact angles, ions stay close to the surface. We still see an exponential-like decay curve due to those ions that did penetrate deep into the target, but a higher energy feature also appears. This feature is due to those ions that only experienced a small number of collisions in the top few layers of the target before being backscattered.

Fig.8.3. Energy of backscattered Ar+ ions from a Si surface. Initial ion energy was 500 eV at

impact angles of (a) 45° and 9b) 80°.

Fig.8.4 shows the angles at which ions are backscattered from the surface. This angular distribution is a smooth curve extending over the whole range of angles 0-90° (where 0° is normal incidence and 90° is parallel to the surface), with a peak corresponding in general to a value similar to the original impact angle. In other words, we see a broad distribution with the most likely angle of reflection being the same as the angle of impact.

Since some ions undergo many collisions within the solid before being backscattered, they do not exit the surface at the same position at which they entered. Lateral straggling can be of the order of tens of Å (as for sputtered atoms).


Fig.8.4. Angle at which 500 eV Ar+ ions are backscattered from a Si surface. Initial ion

impact angles were (a) 45° and (b) 80°. The number of ions at each angle have been normalised to equal solid angle in the same way as before (see fig.5.4).

(d) Sputter Yield and Backscatter Yield: The probability of sputtering and of backscattering are also both functions of ion impact energy and angle. Fig.8.5 shows the sputter yield for Ar+ ions striking Si as a function of energy. It can be seen that the yield increases approximately linearly for energies up to 500 eV. For ions that strike at normal incidence (i.e. 0°), there is an energy threshold of about 70 eV below which sputtering is not seen. Also, the sputter yield is very small since ions release most of their kinetic energy deep inside the lattice from where atoms cannot escape. For ions having more glancing angles, the threshold energy is reduced, until for angles of > 50° the threshold becomes very small, with a minimum value approximately equal to the energy of sublimation of the solid (typically < 5 eV). The sputter yield increases as the impact angle becomes more glancing, since ions now expend their energy close to the target surface.


Fig.8.5. Sputter yield for Ar+ ions on Si calculated using TRIM.

Initial ion impact angle was (a) 0° and (b) 80°.

Fig.8.6 illustrates the dependence of sputter yield upon ion impact angle for two different ion energies of 100 and 500 eV. The curves show a rapid increase in yield as the angle increases away from the normal, reaching a maximum value at about 80°. At angles greater than this, the ions tend to be predominantly backscattered from the top few surface layers before they are able to give much of their energy to target atoms. For lower ion energies, the form of this curve is reproduced, but at lower yield values.

Fig.8.6. Sputter yield for Ar+ ions on Si calculated using TRIM as a function of ion impact angle.

Ion energies were (a) 500 eV and (b) 100 eV. Angles are measured so that 0° is normal to the surface.


The probability of backscattering (reflection yield) is shown as a function of ion impact

energy in fig.8.7. For a constant impact angle, the curve rises steeply with increasing energy until a plateau is reached. At this point, the curve flattens out and the yield becomes independent of further increases in ion energy. This is a result of the fact that as the ion energy increases, its depth of penetration into the target also increases. For very small energies, the ion is confined to the uppermost few atomic layers and so can easily escape from the surface. With increasing energy, there are two competing processes. Higher energies mean the ions penetrate more deeply, which will reduce the yield. But high energy ions also have a larger mean free path which will allow them to travel further before undergoing a collision and offset the effects of the increased penetration depth. The overall effect of these two processes is to keep the yield roughly constant at higher energies. For ions with angles far from normal incidence (fig.8.7a), the plateau energy is quickly reached, but as the angle moves towards normal incidence (fig.8.7b) so the energy at which the plateau begins moves to several hundred eV due to the increased penetration depth of the ions.

Fig.8.7. Probability of ion reflection (backscatter yield) for Ar+ ions on Si as a function of ion

energy. Initial ion impact angles were (a) 85° and (b) 50°.

Fig. 8.8 shows the probability of reflection for Ar+ ions striking Si as a function of ion impact angle. The curves for energies of 100 and 500 eV are very similar. As expected, with increasing ion impact angle the probability of backscattering increases. Normal or near normal incidence ions are all implanted, while for glancing angles the probability of reflection approaches unity.


Fig.8.8. Probability of ion reflection (backscatter yield) for Ar+ ions as a function of Ar+

impact angle upon Si. Initial ion impact energies were (a) 100 eV and (b) 500 eV. (e) Handling of Data from TRIM: It is clear from the preceding paragraphs that sputter and backscatter yields are both complicated functions of ion impact energy and angle. For the purposes of modelling sidewall profiles TRIM was used to calculate the required data for Ar+ ions of energies 0-500 eV and impact angles 0-89° striking a Si target. The probabilities of sputtering atoms and of backscattering ions for different energies and angles were assembled into two look-up tables (see Appendix IX). A grid of 10 eV and 10° was used to build up the tables, so that for an ion striking the surface with any incident angle and energy the appropriate yields could be obtained by simply retrieving the data from the tables. For angles or energies not in the tables, the yields were calculated by interpolation between the two nearest values.

Since we wished to include ion reflections in the model, it was necessary to know both the energy and angular distributions at which ions are reflected from the surface, for any given incident energy and angle. An example of one such energy distribution was given previously in fig.8.2. TRIM was used to calculate similar distributions for every energy-angle pair. For angles near normal (< 40°) no or very few ions were backscattered (i.e. the reflection yield was effectively zero), therefore, these distributions were not pursued. A maximum of 1000 backscattered ions for both angle and energy was included in each of these distributions. These distributions were then assembled into another data array look-up table. For any given incident ion energy and angle pair, it was then possible to obtain the required backscattered ion energy and angular distributions from the table. One of the energy-angle pairs was selected by choice of a random number between 1 and 1000 allowing the reflected ion trajectory to be calculated. For more information on this, see the notes in Appendix IX.


8.3 The Model Used for Sidewall Profile Simulations

In order to simulate sidewall profiles that result from ion bombardment of a Si substrate, we need a method to model the relevant ion-surface interactions as the profile evolves during the etch process. The model that was devised is a very simplistic description of these interactions and is still in a state of development. The primary aim of the initial work outlined in these simulations is to see if such a basic model of the surface is sufficient to reproduce experimentally observed etch profiles. Only a general qualitative resemblance between real and simulated profiles was sought, in the hope that future models may be able to improve upon these beginnings. The model adopted is a phenomenological approach, whereby previously-obtained data (from IEDs and TRIM) are used to ensure the model has a foundation of known facts. This has advantages in that the model uses known data (sputter rates, ion backscatter yields, etc.) as a basis from which to make predictions rather than ab initio hypotheses. This approach runs into difficulties however, when the detailed form of the ion-surface interactions are considered. This will be discussed in more detail later. The program used to calculate these etch profiles is called SPT FORTRAN and is listed in full in Appendix IX.

The cross-section through an amorphous-Si surface is represented in the model by an integer array in the computer memory. Each element of the array contains a value which describes the portion of the target it represents. There are 5 types of element which contain the numbers ‘0’ to ‘4’. These are ‘0’ Empty element containing no Si atoms ‘1’ Si target ‘2’ Photoresist mask ‘3’ Bottom layer of target ‘4’ Corner of resist (erodible resists only)

A detailed explanation of this notation will be given later. The array models a cross-section through a Si surface, where half of the area we are modelling is masked by a photoresist layer. Thus, we are modelling the effects of etching upon one isolated sidewall feature and no shadowing effects by nearby structures is included in the model so far. The array is composed of several thousands of these elements, with a typical array size being 400×400.

Fig.8.9 illustrates the contents of the array before and after an etch simulation. Initially, the array is almost totally filled with ‘l’s since the target is unetched, with the top row being filled with ‘0’s to represe nt the surface layer. The resist is considered to be non-erodible (but see later) and only one row thick. Thus we are not considering the height of the resist as affecting the etch characteristics. We fill half of the top row of the array with ‘2’s to r epresent the resist mask. The plasma-target interface is therefore wherever two adjacent elements contain ‘0’ and ‘1’, respectively. Hence, the part of the top row of the array that is not covered with resist is the initial interface or surface layer. The bottom row of the array is filled with ‘3’s which act as markers to tell the program when etching should stop. Thus the initial configuration for the array is illustrated in fig.8.9a, along with a diagram of the cross-section through the Si target which it represents.


Fig.8.9. (a) Initial array configuration before etching commences. Only a 10×10 array is

shown for illustrative purposes. The real array is 400×400. The right-hand diagram shows how the array represents the etched Si structure.

(b) Final array after etching to completion. As etching commences ‘1’s are replaced by ‘0’s.

Ions are chosen at random from a previously-calculated IED/IAD pair that was loaded into the program memory prior to calculation. The IEDs and IADs were calculated for specific plasma conditions, e.g. frequency, power, pressure, etc. The choice of the IED/IAD pair determines the ‘etch conditions’ that the target will be subjected to. Thus, if a low pressure IED/IAD pair is used, the surface will experience high energy, directional ion bombardment. For higher pressure IED/IAD pairs, the surface will experience lower energy ions at more glancing angles. The full 10000 (or more) data values for the IED and IAD are loaded into the program. This is so that ions can be chosen from these distributions directly, without having to use approximate fitting procedures which may become prohibitively complicated for IEDs with complex structures. All the data values for energy and angle in the distributions are used in turn. When the final ion data


pair has been used, the program loops back to use the first data pair again. This is a continual process and each energy/angle data pair in the two distributions may be used several thousand times in the calculation of an etch profile.

We now calculate the trajectory of the ion through the array. To do this, we first choose a random azimuthal angle between 0 and 2π. The trajectory of the ion in 3 dimensions is then calculated using this azimuthal angle along with the angle of incidence retrieved from the IAD. The direction of this trajectory is then projected onto the plane of the array, allowing the velocity components of the ion in the horizontal and vertical directions of the array to be calculated.

The initial starting position for the ion is now chosen for the ion. Since the photoresist masks the first half of the top row of the array, the ion cannot strike the Si surface there. Thus, we must choose the initial starting position along the exposed (unmasked) surface layer of the array. Two points along the top row are defined, between which the initial ion position is randomly chosen. Point A is the element at the corner of the resist (given a value of ‘4’, see above and later), and point B is calculated to be a large distance from A measured along the top row of the array. This distance is typically four times the maximum array width to allow for ions with very glancing impact angles. Such ions may start from distances some way from the array and still strike the surface. Too large a distance from A to B, however, slows program execution time unnecessarily, since near normal incidence ions chosen with a starting position close to point B will never enter the ‘area of interest’ defined by the array.

Having obtained the initial starting point along the top row of the array for the ion, along with its direction of travel, its trajectory is followed as it travels through the array from element to element. The ion trajectory is considered to follow a straight line until it strikes a non-zero element. The fate of the ion depends upon which type of array element it encounters.

If the ion encounters an element of value ‘0’, nothing happens since this element represents the gaseous plasma-sheath region. The ion therefore continues onwards unaffected.

If the ion trajectory causes it to encounter an element containing the value ‘1’, the ion is considered to have struck the surface of the Si target. The ion will either be backscattered, implanted or cause sputtering. If sputtering occurs the element of value ‘1’ is changed to a ‘0’ representing a section of the surface that has been removed. The details of this will be explained in section 8.3.1.

If the ion encounters an element of value ‘2’, this represents an ion striking the bulk of the photoresist. Since we are using a non-erodible resist at present, the ion is considered to be absorbed by the resist. A new ion is chosen from the initial starting conditions.

When an ion eventually meets an element of value ‘3’ this means that etching has proceeded to a sufficient extent. All data arrays are saved and the program is halted.

The element of value ‘4’ is us ed for erodible resists and will be explained in section 8.9. If an ion trajectory takes it outside the bounds of the 400×400 array, this ion is considered lost

to the program and a new ion is chosen from the initial starting conditions. A flow diagram of the basic program is shown in fig.8.10.


Fig.8.10. Flow chart for the basic profile simulation program.

After completion of the simulation, the array might typically look like the example shown in

fig. 8.9b. The scale of the diagram is not defined in the program. The only important point is that the horizontal and vertical dimensions are identical, i.e. the elements are square (or in 3 dimensions, cubic). Thus, if we define the width of the array to be 1 µm (and consequently the height as 1 µm also), then each of the 400 elements represents a cube of volume (25 Å)3. However, there are limits to which we can define the dimensions of the array if we wish to maintain a physically realistic model. Too large a value and it becomes unrealistic to imagine


cubic units of say, several mm3 being removed as blocks. Conversely, if the scale is such that each element represents a single Si atom, we have the situation of modelling individual atoms as cubes. It is for this reason that an intermediate array is needed to average out such ambiguities (see section 8.3.4).

There are a few processes which the simple model of etching described so far does not yet include:

(a) Chemistry: No chemical effects are included (but see section 8.10). Thus, features such as

sidewall passivation or spontaneous etching are not modelled. Therefore, the program at present only represents physical sputtering.

(b) Resist Erosion: The resist is non-erodible. Erodible resists are added to the program in section 8.9.

(c) Resist Thickness: The height of the resist is not considered. Shadowing effects due to the resist preventing certain ion trajectories from striking the surface have therefore not been included. Also, ion reflections off the resist sidewall are not included.

(d) Sheath Collisions: The height of etch structures (~ 1 µm), and hence, the height of the array, is considered to be much less than the mean free path of ions in the sheath, even at higher pressures. The mean free path for Ar+ ions in a 10 mTorr plasma and a 100 mTorr plasma is 2.5 mm and 250 µm, respectively. From Equation (6.25), we can calculate that for these two pressures we would expect only 0.04% and 0.4% of ions, respectively, to undergo collisions in a distance of 1 µm. Therefore, we can ignore collisions between ions and neutral gas atoms between the time they enter the main array and the time they strike the Si surface. In other words, all trajectories are effectively ballistic and ions move in straight lines.

(e) Redeposition: Sputtered atom trajectories are not followed. In principle, these atoms could strike and stick to the sidewall of nearby structures. This could be a possible mechanism for sidewall passivation and trenching (see section 8.8).

(f) Ion acceleration: We are also neglecting the effect of the sheath potential upon ion trajectories within the region of interest defined by the array. The array typically represents a region of size about 1 µm square, i.e. a height of about one thousandth of a typical sheath thickness (usually a few mm). If the maximum sheath potential is say, 400 V, over a thickness, lmax, of 4 mm, then the potential dropped across the last 1 µm would be roughly 0.1 V. Ions striking the substrate surface typically have energies of tens or hundreds of eV, therefore, we can safely ignore the small deviations to their trajectories within the ‘area of interest’ caused by an energy increase of 0.1 eV.

(g) Wafer Potential: All IEDs and IADs are calculated for ions striking the electrodes of RIE systems. Placing a semiconducting substrate onto the electrode might affect the electrical characteristics of the discharge and hence IEDs and IADs. The magnitude of the perturbation to the sheath potential and hence to ion trajectories is unknown. Measurements of reactor I-V characteristics (performed on the Minstrel etcher described in Chapter 2) with and without a wafer in the chamber show differences in the RF waveform do occur, but are usually only of the order of a few V. Therefore, we shall assume that the presence of a wafer on the electrode does not affect ion trajectories significantly.


8.3.1 Details of the Ion-Surface Interaction

The model described so far represents the target as being composed of sections (or elements) which are cubic in form. When an ion trajectory causes the ion to encounter an element that contains a value of ‘1’, three processes may occur. Each of these processes is considered to be mutually exclusive, with each having an independent probability for occurring. We shall consider each in turn:

(i) Backscattering: The ion may simply reflect off the surface. The probability of reflection

is known from the previously-calculated yield data stored in the look-up table. The appropriate yield, YB for the ion impact energy and angle are retrieved from the table. A random number R is then chosen between 0 and 1. If R ≤ YB then reflection is deemed to have occurred. The energy and angle at which the ion backscatters is then calculated. This is done by examining the values for the reflected energy and angular distributions stored in another look-up table (calculated by TRIM) for the particular ion impact conditions. Values for the reflected energy and angle are chosen at random from these distributions. The ion is then followed along its new reflected trajectory until it either leaves the main array area of interest or strikes another surface atom, whereupon the test for backscattering is performed again.

(ii) Sputtering: If the ion does not backscatter, there is a chance it may cause sputtering of the target. The probability for this to occur is known from the previously-calculated sputter yields YS. Another random number R is chosen between 0 and 1. If R ≤ YS then sputtering occurs. The value of the array element is then converted to a ‘0’ indicating that the surface element has been removed. We then assume that the ion energy has been expended and its trajectory finishes at this position. A new ion is then chosen from the initial starting conditions. This model for sputtering is the basic one used in the program, but it was later modified to include sputter yields of YS > 1 (see section 8.3.5).

(iii) Implantation: If neither backscattering nor sputtering occurs, the ion is considered to have been implanted into or adsorbed onto the surface, and all its energy expended in processes such as damage effects or heating of the target. A new ion is therefore chosen from the initial starting conditions.

8.3.2 Ion Impact Angle

In any model of this type, whereby experimental macroscopic data are used as a basis to describe microscopic processes, there comes a point where the assumptions present in the model become inadequate. For the purposes of modelling etch profiles we are using data for sputtering and backscattering yields based upon ions striking infinite, flat surfaces. However, as a surface etches, the surface develops etch pits and features which mean that the local surface is no longer flat. We are left with the problem of how to define an ionic impact angle for a surface exhibiting considerable variation in topology. The extreme case is depicted in fig.8.11, where for an ion striking a horizontal surface the impact angle measured from the surface normal is θ, but for the same ion striking a vertical sidewall the required angle is 90°– θ. Since, in the present model, we are removing the surface as blocks of cubic elements, a typical etched surface may resemble


fig.8.12. We need a method to choose the impact angle for a surface such as this.

Fig.8.11. (a) Ions striking a horizontal surface with impact angle θ.

(b) The same ion striking a vertical surface. The impact angle is now 90°–θ.

Fig.8.12. Ions striking an evolving surface created by removing cubic elements.

Several approaches were considered (see sections 8.11 and 9.2), but the initial solution

adopted was to define the impact angle relative to each surface element. The advantage of this method is that it is very simple and extremely fast to calculate. If the ion strikes a horizontal face of an element, then the impact angle φ is the same as before, i.e. φ = θ (see fig.8.13). If a vertical face of the cubic element is struck by the ion, then φ = 90°– θ. The sputter and reflection yields are then obtained from the appropriate look-up tables on the basis of the impact angle, φ. This model is somewhat unrealistic, since it imposes square-cornered morphologies upon the surface which artificially restrict ion impact angles to two orthogonal values, leading to ambiguities in the values of some impact angles. However, since at present we are only trying to obtain a general qualitative resemblance between simulated etch profiles and experimental profiles, this model will be adequate.


Fig.8.13. definition of the ion impact angle, φ.

If small array sizes are used this approximation is less valid, since the ambiguities due to

corner effects become important. However, for large array sizes (> 300×300), such effects are averaged-out and realistic profiles can be produced. This description of the ion-surface interaction is still one of the major problems with the model. A number of suggestions are made in section 9.2 as to how to make the model more physically realistic. 8.3.3 A Typical Etch Profile

In order to demonstrate the way in which simulated profiles are presented by the computer output, fig.8.14a shows a typical etch profile obtained with the model described in the previous sections. Only the interface points are plotted to save time and computer memory. The photoresist is positioned along the top surface of the profile and is indicated by shading. A typical size for an etched feature in the modern semiconductor industry is about 1 µm and that for resist thickness about 2 µm. The roughness of the surface is dependent upon the particular IED and IAD data used for the simulation and the resolution of the array (see section 8.3.4). The scale along the horizontal and vertical axes are number of array elements, in this case 400×400. All profiles will be presented in a similar way to fig.8.14a. Fig.8.14b shows more clearly how the profile plotted in fig.8.14a reflects a cross-section through an etched Si structure on the surface of a wafer.


Fig.8.14. (a) Simulated etch profile. Only the interface between the Si surface and the plasma

are shown. The resist is situated along the top row and is shown as a shaded boundary. (b) A schematic diagram of a cross-section through an etched feature corresponding to (a).

8.3.4 Effect of Array Size

The array size determines the resolution of the final profile. Since we are modelling the microscopic ion-surface collision as an interaction between cubic array elements, any ambiguities in impact angle due to the approximate nature of this model become important at low array resolutions, i.e. for large element dimensions. This can be seen in fig.8.15a and b for array sizes of 50×50 and 200×200, respectively. In the low resolution profile, the rough surface shows random variations in height of about ±8 elements, or 16% of the etch height. The origin of this roughness will be explained in section 8.4. Using the same conditions, but increasing the array resolution to 200×200 reduces the apparent surface roughness to ±15 elements, or 7½% of the total height etched. The degree of roughness changes little for resolutions above 300×300, being about 5% of the total etch height. Therefore, it seems that a resolution of 300×300 is the minimum necessary in order to effectively average-out the corner effects inherent in the model. Typically, resolutions of 400×400 or larger were used, therefore, any roughness that is calculated may be considered to be a genuine prediction of the model. This becomes important when considering the variation of etch profiles with plasma pressure in section 8.4.


Fig.8.15. (a) A simulated etch profile using a 50×50 array.

(b) An etch profile calculated using the same conditions as (a) but using a 200×200 array. 8.3.5 Sputter Yields > 1

In cases where the ion impact energy is large and angle of incidence φ is glancing, sputter yields calculated using TRIM can exceed 1. In other words, more than one atom per ion is removed on average from the surface. This poses a problem for the sputtering model described so far, since we need a method to remove more than 1 array element from a site that contains only 1 element. Three models were investigated to overcome this problem. Model 1: If the sputter yield for a particular ion trajectory was found to be greater than 1, then the array element would be removed (i.e. a ‘0’ placed into it), but the ion would continue onwards along its previous trajectory as if no collision with the surface had occurred. The program would set a flag to indicate that this ion had already caused sputtering. The sputter yield would also be reduced by 1. When the ion encountered the next surface element, the probability of sputtering would be decided based upon this reduced sputter yield. This is a reasonably realistic model, since the second sputtered element should arise from a location adjacent to where the ion originally struck the surface. As long as sputter yields were no greater than 3 this model worked successfully and did not significantly slow down program execution. However, if sputter yields became too large (> 3) a tendency developed for ions to ‘burrow’ into the surface creating pits or channels. Since for Ar+ ions of E ≤ 500 eV striking Si, the maximum sputtering yield is about 2.5, these channelling effects did not occur to any great extent. Model 2: Instead of using an array consisting of integer numbers, a real number (i.e. floating point) array was used. Each array element was given a weighting (called the number of hit-points) which determined the amount of damage that array site could sustain before being removed or sputtered. The number of hit-points was usually 5.0. Every time that an array element was struck by an ion with a sputter yield YS, this yield value would be subtracted from the hit-point value currently stored there. When the number of hit-points in an array element fell below zero, the array site was considered to have been sputtered.

This model has several disadvantages. Firstly, it slowed down computation time by a factor


of about 3. Secondly, since a real number array was used, rather than an integer array, the amount of computer memory required was doubled. Therefore, this model was rejected. Model 3: To overcome some of the problems associated with Model 2, the idea of an integer array was reintroduced. Each array element was given a hit-point value from 0 to 1000, and the sputter yield was multiplied by 100 and converted into an integer variable. Thus, the same procedure could be adopted as in Model 2, but using faster integer arithmetic.

Unfortunately, this model has a few drawbacks, since it underestimates the sputtering capability of some high energy ions. For example if an ion of yield say, 210, stuck an array element that had only 1 hit-point remaining, 209 points-worth of the ion yield was wasted. This is because once an array element was sputtered, the ion energy was expended. For this reason Model 3 was also discarded.

All three models, in fact, gave very similar profiles, showing that multiple sputtering effects are not very important to the overall sputtering model. Therefore, for the purposes of simplicity, computing speed and better correspondence to physical reality, Model 1 was adopted as an adequate description for the multiple-atom sputtering process.

The basic model for surface profile simulations has now been described. The next few sections will contain results obtained from this model while varying some of the plasma conditions used to create the IEDs and IADs employed by the program. 8.4 Variation of Simulated Etch Profiles with Pressure

The simulation program was used to calculate the profiles expected when sputtering Si at a variety of different process pressures. The IED/IAD pairs used for this purpose were calculated using the standard high pressure plasma conditions given previously in table 6.1. As mentioned in section 6.5, as the pressure increases, ions strike the substrate surface with less energy and at more glancing angles. Fig.8.l6(a-g) show profiles calculated for pressures of 1 mTorr to 100 mTorr (i.e. the IEDs and IADs presented in fig.6.11 and 6.12). For very low pressures (e.g. fig.8.16a) the profile shows a vertical sidewall, indicative of anisotropic etching. This directly reflects the predominantly normal incidence ion trajectories obtained at this pressure. The surface also appears very rough and spiky. This rough surface is reminiscent of the black silicon effects described in section 1.3.4.1. The spikes arise as a direct result of normal incidence ions sputtering vertical channels into the surface. Once a cone-shaped spike begins to form, the sidewalls of the spike will have a larger sputter yield, since ions having vertical trajectories will strike these sidewalls at glancing angles. Hence, spikes grow sharper until they reach a limit when the probability of an ion sputtering an element from a spike sidewall is the same as it sputtering the element at the top of the spike. At this point, the surface will recede at a uniform rate, with the degree of roughness remaining constant. This effect limits the size and sharpness of the spikes and hence directly affects surface roughness.


Fig.8.16. Sidewall profiles calculated using IEDs and IADs obtained with the standard high

pressure plasma conditions given in table 6.1, at pressures of (a) 1, (b) 5, (c) 10, (d) 20, (e) 30, (f) 50 and (g) 100 mTorr.

As the pressure is increased, sheath collisions cause ion trajectories to be deflected away from

the vertical. Hence, the sidewall beneath the resist mask can now experience ion bombardment; thus, it etches back to form an undercut or re-entrant structure. The degree of undercut increases with pressure, until by 100 mTorr (fig.8.16g) the lateral erosion is about 20% of the etch depth. This undercutting of the mask at high process pressures is a well known effect and it is for this


reason that RIE processes that require high anisotropy generally operate at low pressures. Another feature evident from fig.8.16(a-g) is that the surface roughness decreases markedly as the pressure increases. By 100 mTorr the surface is very smooth and no signs of the spikes seen at lower pressures are observed. This is because many ions now strike the surface at glancing angles and can undercut spikes as they begin to form. Smoother surfaces with increasing process pressures have been frequently observed for real etch processes [47]. A process engineer therefore often has to choose a pressure regime where he can achieve both a reasonably anisotropic etch profile and a smooth surface. Hence, RIE processes typically operate at around 20-50 mTorr.

To obtain a profile similar to those seen in fig.8.16(a-g) typically, 107 ion trajectories need to be calculated. The exact number of ion trajectories required will be proportional to the ion flux striking the wafer surface. Since this ion flux is considered to be constant with time, the number of ions, n, used by the program to sputter a depth of 400 elements will be directly proportional to the sputter time. Therefore, the reciprocal of the number of ions will be proportional to the sputter rate, all other plasma conditions remaining constant. This allows us to examine the way sputter rate varies with the process parameters.

Fig.8.17 shows a plot of sputter rate (1/n) versus pressure. At low pressures the rate is independent of pressure since there are few sheath collisions to cause ionic energy loss. Above about 10 mTorr, collisions begin to become important, and these cause ions to strike the surface at much reduced energies. Thus, the sputter rate drops approximately linearly with pressure. This shows that the energy dependence of the sputtering yield is the most critical factor in determining sputter rate, rather than the angular dependence. Although the ions strike the surface at more glancing angles which increases their sputtering yield, the fact that they have much less energy is the dominating factor and this causes the overall yield to decrease.

Fig.8.17. Calculated sputter rate (1/number of ions used)

versus pressure for Ar plasmas. a.u. = arbitrary units.


8.5 Variation of Simulated Etch Profiles with RF Voltage

The variation of IEDs and IADs with RF voltage, V0, was detailed in section 5.3.1 for low pressure plasmas. Sputter profiles were calculated using these IED/IAD pairs for V0 varying from 100-500 V along with the standard low pressure plasma conditions given in table 5.5. Since no collisions are included in these calculations, the resulting profiles were all identical and resembled that shown in fig.8.16a with vertical sidewalls and rough, spiky surfaces. The only major observed change in the profile was that the surface became rougher with increasing V0

which is consistent with experimental findings [47]. The sputter rate (1/n) is plotted as a function of V0 in fig.8.18. The trend is a straight line

with a threshold voltage for sputtering of about 100 V. This, again, agrees very well with experimental observations, where etch rate is generally observed to be proportional to RF power (or V0, see section 1.3.4.3.1). The threshold directly reflects the threshold value observed in fig.8.5 for sputtering Si with normal incidence ions.

Fig.8.18. Calculated sputter rate (1/n) as a function of

applied RF voltage, V0, for the standard low pressure plasma conditions. 8.6 Variation of Simulated Etch Profile with Frequency

The IEDs shown in fig.5.28(a-m), along with their corresponding IADs were used to calculate the profiles expected when sputtering at frequencies from 10 kHz to 1 GHz. Again, since only low pressure conditions were used, all the profiles exhibited the vertical sidewall and rough surfaces seen in fig.8.l6a. The sputter rate (1/n) as a function of frequency is shown in fig.8.19. At very low frequencies (i.e. the very low frequency regime) ion energies reflect the time variation of the sheath potential and hence low energy ions dominate the IEDs (see fig.5.28a).


At frequencies of 0.1 to 2 MHz (the low frequency regime, see section 5.2.5) IEDs are dominated by a large peak at high energy. Thus, the average energy of ion bombardment increases with frequency up to about 1 MHz, and hence sputter rates also follow this trend. For frequencies greater than 3 MHz (the high frequency regime, see section 5.2.6), IEDs become roughly symmetrical double-peaked distributions about a constant mean value <E>. Hence, the average energy of ion bombardment falls to <E> as the frequency is increased into the high frequency regime, and then remains constant with further frequency increases. The sputter rate also illustrates this process, showing a sharp drop between 1 and 5 MHz, and thereafter remaining constant as the frequency is increased by up to a factor of 200. This figure makes it clear why low frequency reactors are being used more often nowadays in etch processes. Frequencies of 100-500 kHz are starting to be used in order to exploit the increased ion energies and hence obtain faster etch rates.

Fig.8.19. Calculated sputter rate (1/n) as a function of

frequency for the standard low pressure Ar plasma conditions. 8.7 Etch Profiles Calculated Including High Energy Neutral Particle Bombardment

It was shown in section 6.12 that ions are only a small contribution to the total distribution of energetic particles striking the wafer surface. Fast neutrals (in this case Ar atoms) caused by scattering and charge exchange processes strike the surface in large numbers. Most of these atoms have energies < 50 eV but a significant proportion can have energies up to the maximum ion energies of 400-500 eV. Indeed, most ions are neutralised by an Auger Neutralisation process as they approach a surface (see section 7.3.1.1). The term ‘ion bombardment’ is therefore a misnomer; it should really be ‘fast neutral particle bombardment’. Since TRIM does not distinguish between ions and atoms striking the surface, the INED and INAD distributions described in section 6.12 can be used as inputs from which to calculate an etch profile. This was done for a pressure of 20 mTorr (i.e. using the INED of fig.6.23 and its corresponding INAD).


The resulting etch sidewall profile was very similar to the one shown in fig.8.16d calculated for ion bombardment alone. The only difference was that the profile calculated using the INED/INAD pair exhibited about 5% more mask undercut, which is not very significant considering three times as many trajectories were required to calculate the profile. This is because in order for an atom to initiate sputtering it must have an energy greater than the threshold energy for its particular impact angle (see fig.8.5 in section 8.2.2).

High energy atoms generally strike the substrate at near normal impact angles (see Chapter 6). Consequently, their sputtering threshold energy is about 70 eV. Very few neutrals have energies > 70 eV and so they cannot contribute significantly to the evolution of the sidewall profile. The majority of lower energy neutrals strike the surface with glancing angles and hence have a much smaller sputtering threshold energy. But most of these atoms still possess energies less than the required threshold. The result is that in general fast atoms do not affect the etch profile significantly. These atoms either backscatter, implant harmlessly into the surface, or cause heating or damage effects in the substrate lattice. If, as in the case where chemically reactive species are adsorbed on the Si surface, this sputtering threshold energy is reduced considerably, then energetic atoms might play a far more important role in etching than seen at present. For pure sputtering however, only very high energy ions and atoms are important contributors to the etch profile. 8.8 The Effect of Artificially Increasing Sputter and Backscatter Yields

Ion-induced chemical etching occurs when reactive species that are adsorbed onto the Si surface are struck by energetic ions. The energy released in the collision is enough to initiate chemical reactions on the surface and/or desorb etch products, so enhancing the chemical etch rate. With the present model for sidewall evolution, we are limited to non-chemical sputtering mechanisms.

In order to investigate whether ion-induced chemical effects could be included in the present model the following approach was adopted. By a simple modification to the basic program it was possible to artificially increase the yield values calculated by TRIM for sputtering or backscattering. This was achieved by simply multiplying the yield obtained from the look-up table by a given factor. This factor was specified by the user and could be varied to determine its effects upon calculated profiles. This was attempted first for the sputter yield, which was multiplied by factors of 1.5, 3.0, 5.0, 10.0, 50.0 and 100.0 in turn. The various profiles for each of these increased yields were calculated. The results showed that as the yields were increased the calculation time decreased rapidly, as expected. However, for yields that were increased by a factor of 10 or more, surface roughness became extreme as ion channelling effects became significant (see section 8.3.5). In order to overcome this problem, a larger array would be required to maintain the same resolution. Therefore, modelling chemically-enhanced etching by this method is not practical and an alternative method must be employed (see section 8.10).

The same procedure was used to study the effect of multiplying the reflection yield by factors of 3, 10 and 50 for both the standard low and high pressure plasma conditions. For the low pressure plasmas, increasing the backscatter yield did not change the etch profile greatly, even when using a factor of 50. This showed that sputtering in the low pressure regime is primarily caused by high energy ions which have very small reflection yields. In contrast, for 20 mTorr


plasma conditions, the profiles changed shape from a concave, re-entrant sidewall to a more vertical, anisotropic profile as the factor increased from 3 to 50. The number of ion trajectories used also increased rapidly, showing that most of the ions were being wasted in reflections and no longer contributed to sputtering. The main conclusion is that for higher pressure plasmas, lower energy ions also contribute to the etching since their shallower impact angles increase their sputter yield.

In order to investigate the contribution that ions reflected from the surface make to the evolving profile, modifications were made to the program enabling the removal of the calculation of reflections from the model altogether. For a typical low pressure etch simulation, about 6½ million ion trajectories are used, of which about 10000 (or 0.15%) backscatter from the surface. For a 20 mTorr plasma this becomes 5.1 million ions with 8000 (0.16%) backscattered. From this, it seems that backscattered ions play an insignificant role in evolution of the surface profile. ‘Turning reflections off’ resulted, therefore, in profiles that were indistin guishable from the full calculated profiles for both low and high pressure plasma conditions.

Trenching has been observed experimentally for many processes [47], especially those using high powers and low pressures. One of the mechanisms suggested to account for the trenching phenomenon is that of ions reflecting off the resist or Si sidewall to cause preferential sputtering near the base of the feature [47] (see fig.8.20a). The profile simulations presented using the present model do not show any evidence of trenching, and in fact seem to suggest that backscattered ions are insignificant compared to the majority of other high energy ions striking the surface uniformly. Therefore, this apparently rules out the ion reflection mechanism as a cause of trenching and we must examine alternative explanations for these effects. Two possible mechanisms are depicted in fig.8.20a and b. Local charging of the resist or Si surface may deflect ion trajectories close to the sidewall, hence increasing the number of ions striking the surface near the corner of the feature [256]. In the other mechanism, material sputtered from the sidewall or resist may become redeposited on the wafer surface [47,258]. Since the present model of sputtering does not include a description of either local surface charging or redeposition of sputtered material, it is not surprising, if either of these mechanisms is correct, that trenching effects have not yet been simulated.

Fig.8.20. (a) Trenching caused by local charging of the resist. Positive ions are deflected

away from the resist to strike the Si surface near to the sidewall base. (b) Trenching caused by redeposition of material sputtered from the sidewall onto the Si

surface.


8.9 Erodible Resists

The photoresist mask is never completely impervious to ion bombardment and will gradually etch away as plasma processing progresses. Resist sidewalls are never completely vertical, being typically 10° off vertical. Consequently, ion bombardment will occur both on the top surface of the resist, thinning it, and also on the resist sidewalls causing lateral erosion or etchback. Since our sputtering model does not consider the height of the resist, only the rate of lateral erosion will be important to the simulation of sidewall profiles. If we wish to include the effects of resist erosion in the model, we need a method that is consistent with the rest of the model and allows the masked area to recede gradually as the simulation progresses. To this end, we have defined the corner of the resist as a crucial element in the array, since this element defines the lateral extent of the resist and hence the masked area. This element is given the unique value of ‘4’ to distinguish it from the other resist elements which have the value ‘2’. When an ion encounters the element containing the value ‘4’, there now exists the possibility that resist erosion could occur. The sputter and backscatter yields based upon the ion impact energy and angle are calculated as for Si (elements with value ‘1’), but these yields are then multiplied by a previously-defined factor. This resist erosion factor, RF, determines the rate of resist etchback. If RF > 1 then the resist erodes faster than Si, whereas if RF < 1 then it erodes more slowly. It should be emphasised that RF is not the absolute resist sputter rate, but the lateral etchback rate.

Unfortunately RF cannot be obtained ab initio. It can only be determined by calibration with actual measured resist etchback values observed in an experimental etch process. It should therefore be treated as a fitting parameter. The yields calculated in this way allow the program to determine whether reflection, implantation or sputtering occurs for each ion impact upon the resist corner element. If sputtering occurs then the value ‘4’ is replaced by a ‘0’ to indicate that the resist has receded by one element. The resist element immediately adjacent to this will now be the new resist corner, and so the value it contains is changed from ‘2’ to ‘4’. Finally, the lower limit A (see section 8.3) of the position along the top row of the array from which ion trajectories are started is moved back by one array element consistent with the reduced mask area.


Fig.8.21. Sidewall profiles calculated for the standard low pressure plasma conditions, with

resist etch factor RF of (a) 0, (b) 0.1, (c) 0.2 and (d) 0.3.

The sputtering simulation program was executed a number of times using different values for RF from 0 to 0.3 for both low and high pressure plasma conditions. The profiles obtained for low pressure plasmas are shown in fig.8.21(a-d). As expected, with increasing resist erosion the profile becomes more slanted, but remains straight, i.e. we do not see the development of any curved surfaces or re-entrant profiles. The results are summarised in table 8.1. Processes are often required that produce sloped sidewalls on etched features, e.g. contact hole or via etching processes. These simulations show a possible method to produce these sloped sidewalls. Controlled resist erosion in a low pressure plasma will lead directly to the required sloped sidewalls. In principle, this mechanism could be used for just such processes, however, the resist


hardness, thickness and wall-angle would all have to be controlled very accurately if such processes were to be reproducible.

RF θθ / °° % Etchback 0.0 90 0 0.05 88 2 0.10 86 7 0.15 82 12 0.20 80 16 0.25 78 21 0.30 74 29 Table 8.1. Sidewall angle θ and etchback versus RF. Percentage etchback is defined as: 100x/y.

Resist erosion has an important influence upon the linewidth loss of an etched feature. For an

etch process removing say, 1 µm of Si having a resist mask such that RF = 0.15, the linewidth loss at the top of the feature is calculated to be 0.125 µm at each line edge. For a feature of width 1 µm at the base, therefore, we would lose 0.25 µm at the top of the feature (see fig.8.22), and the feature with a supposedly square cross-section would begin to appear decidedly trapezoidal. For greater values of RF these linewidth losses can rapidly become prohibitively large, hence the requirement for resist hardening techniques such as hard bakes or DUV hardening (see section 1.2.3.3).

Fig.8.22. Linewidth loss expected for a 1 µm-wide feature etched using the standard low

pressure Ar plasma conditions, with RF = 0.15. Each line edge loses 1/8 µm during the etch, consequently the feature exhibits a sloped profile with a 1 µm-wide base tapering to a ¾ µm-

wide top surface.


The profiles obtained for high pressure (20 mTorr) sputtering including resist erosion are shown in fig.8.23(a-f). For very little resist erosion (RF < 0.1), the profiles exhibit the familiar re-entrant profile seen previously. As RF increases, the degree of undercut gradually decreases, until by RF = 0.15, the rate of lateral Si etching balances the rate of lateral resist loss. Hence, we obtain a vertical sidewall (fig.8.23d). This illustrates that it is possible to produce apparently anisotropic etching in a high pressure process. This phenomenon is observed and is occasionally used by process engineers who require vertical sidewalls in a system where only high pressure processes can be obtained. It is often possible to demonstrate seemingly perfect anisotropic etching in these processes, and the reality of the situation will only become apparent when the linewidth loss is measured and found to be excessive. Fig.8.24 shows the effect of this type of process upon etching a 1 µm-wide structure. For values of RF greater than 0.15, the profile remains straight but becomes more sloped (see fig.8.23e and f), showing that if extreme resist loss is permitted, even a high pressure RIE process can produce a sloped profile. These results for high pressure processes are summarised in table 8.2.


Fig.8.23. Calculated profiles using the standard high pressure plasma conditions with resist

etch factors of RF = (a) 0, (b) 0.05, (c) 0.1, (d) 0.15, (e) 0.25 and (f) 0.3. Note that for RF = 0.15 a vertical sidewall is produced reminiscent of anisotropic etching.

RF θθ / °° % Etchback 0.0 117 0 0.05 111 2 0.1 94 9 0.15 90 16 0.20 88 19 0.25 84 25 0.30 81 30 Table 8.2. Sidewall angle, θ, and etchback versus RF. Percentage etchback is defined in table 8.1.


Fig.8.24. A 1 µm feature etched using the standard high pressure (20 mTorr) plasma conditions, with RF = 0.15. The original position of the resist is drawn with dashed lines. The etched feature

exhibits vertical sidewalls but has a 30% linewidth loss.

8.10 Isotropic Chemical Etching

Since most RIE processes use chemically reactive gases to etch the substrate material, there will always be some degree of isotropic chemical etching present in any etch process. For some processes (e.g. Cl2 etching Si), ion-enhanced etching dominates [9,10], and so vertical sidewall profiles are generally formed. For other processes, however, (e.g. Cl2 etching Al), reactive species such as free radicals can etch laterally with a rate that is comparable to the ion-enhanced vertical etch rate [9,10]. These processes lead to isotropic etch profiles similar to those seen for wet etching (see section 1.2.3.4.1).

It would be useful if etching due to these sorts of chemical processes could be included in our sputtering model, albeit in a very primitive fashion. This has been done by the addition of another parameter, CF in to the program. This parameter controls the ratio of the number of surface elements removed by ion bombardment to the number removed by pure chemical action, In other words CF is the effective chemical etch factor. The model separates physical sputtering and chemical etching into two distinct, independent processes. Ion sputtering is allowed to continue in isolation for a certain number of ion trajectories. CF is defined to be this number and is chosen by the program user as an input variable. When the number of ion trajectories equals the value of CF, the program then performs a chemical etch upon the surface elements (see later). After this chemical etch, ion bombardment begins again and continues until another CF trajectories have been computed, whereupon the chemical etch routine is employed again. If CF = 0, then no ion bombardment is calculated and the surface etches by a purely isotropic process, akin to wet etching. If CF is large (i.e. several million), then the surface will only etch by ion sputtering and will have etched to completion before the chemical etch routine is entered for the first time. Thus, CF can be used to control the degree of chemical etching included in the simulation.

The chemical etch routine is fairly simple and consists of only a few steps. Only those array


elements which are at the surface can be chemically etched, therefore these surface elements must first be identified. A surface element is defined as an element containing a value ‘1’ ( i.e. Si) that has another element of value ‘0’ ( i.e. gas) as one of its 8 nearest neighbours in the array. The entire array is searched for elements that fulfill these two criteria, and the coordinates of these surface elements are then stored in memory. Since these elements are considered to be in contact with reactive free radicals in the plasma, each of them will have a certain probability of being chemically removed. This probability will approximately depend upon how strongly bonded the element is to the surface. This in turn will be related to the number of nearest neighbours, N, which the element in question has. We require a model that will calculate the probability of removing each individual surface element based upon the value of N. This probability has been normalised, so that if an element has only 1 nearest neighbour (e.g. it is the top element of a pyramid or spike), its probability of removal is 1, whilst for a surface element that has the maximum number of N = 7 (e.g. an element at the bottom of a trench) then the probability will be 1/7.

Although this model is very primitive, it is extremely fast to calculate and is sufficient for our requirements of simulating the basic trends seen in RIE processes. A probability check is made against a random number, R, chosen between 0 and 1. If R > 1/N then the element is not etched and remains in place in the array. If R ≤ 1/N then the element is considered to be chemically etched. This element cannot be removed from the array immediately since it would affect the calculation of N for neighbouring elements. Instead, its coordinates are stored in the computer memory for later processing. All the previously-identified surface elements are treated in this way, with some remaining unaltered and some being deemed to have been etched. When all the surface elements have been examined, the coordinates of the etched elements are retrieved from memory and the values of these elements changed to ‘0’, indicating their removal from the surface. The program then jumps back to the main routine to continue the ion bombardment loop.

The aspect ratio of the array had to modified in order to accommodate the large undercuts encountered in isotropic etching. The array is now 400×650 elements, with the resist extending along the top row as far as the 450th element.


Fig.8.25. Sidewall profiles calculated for the standard low pressure plasma conditions, with

chemical etch factor CF of (a) 0, (b) 104, (c) 105, and (d) 107.

The simulation program was used to calculate sidewall profiles for varying values of CF for both the standard low and high pressure plasma conditions. A non-erodible resist mask (RF = 0) was used for these calculations. Fig.8.25(a-d) show these profiles for low pressure plasmas with CF varying from 0 to 107 Fig.8.25a illustrates the profile obtained for chemical etching alone (CF = 0), showing the familiar profile seen for isotropic wet etching processes. The surface is very smooth and the degree of lateral etching (undercut) equals that of vertical etching, proving that the simulation models isotropic processes very well. For increasing values of CF the contribution of chemical etching becomes less important, until for CF = 107 the profile is effectively purely anisotropic. It should be possible for a process engineer to use SEM photographs of an experimental sidewall profile to calibrate his etch process and obtain a value for CF. This will be explained further in section 8.12.

Fig.8.26(a-d) show the profiles for varying CF values for high pressure (20 mTorr) plasmas. For low values of CF the profiles resemble those seen for low pressure chemical etching (fig.8.25a); however, as ion bombardment becomes dominant, the surfaces revert to the slightly re-entrant profiles seen previously in fig.8.16.


Fig.8.26. Sidewall profiles calculated for the standard high pressure plasma conditions, with

chemical etch factor CF of (a) 0, (b) 104, (c) 105, and (d) 107. 8.11 Average Surface Model

A major concern with the sputtering model described in previous sections is the necessity to use cubic blocks to describe the surface. These produce corner effects which lead directly to ambiguities in determining the angle of ion impact (see section 8.3.2). An alternative method of deciding this impact angle is to define an average local surface in the region near where the ion strikes. This average surface might better reflect the formulation of the description of ion-surface interactions calculated from TRIM, since this assumes an infinite flat surface. In principle, the cubic model defines such a local average surface, but only for each individual element. A better approximation to the local surface might be obtained from averaging the surfaces of several elements. The best way to attempt this would be to perform a least squares-type fit through the nearest n surface elements, where n was a number defined by the user. This fitting procedure would be very complicated requiring extensive development work. Moreover, it would be very slow to compute. Therefore, it has not been pursued further and is suggested as a possible project for future study.

However, an approximation to this method has been briefly attempted. This approximation uses a series of straight lines joining surface elements a set distance apart. Trial-and-error showed that about 10 equal-length, adjacent lines were needed to obtain an acceptable fit to the whole profile. Ion impact angles were then calculated relative to the gradient of the line nearest to where the ions struck the surface.

Some of the previously-calculated profiles were recalculated using this model for the surface. In almost all cases, the resulting profiles were very similar, or essentially identical, to those seen


with the cubic-element model. The major differences were that at higher pressures the curved, re-entrant profiles tended now to become wrongly flattened. Also trenching at the corner of the feature sidewall was observed in low pressure simulations. This trenching effect was an artifact of this new model, since at the corner of the feature the average surface would be a sloped straight line cutting the corner. This sloped line would ensure that ions with a vertical trajectory would strike this surface at glancing angles rather than at normal incidence. Hence, the surface would etch faster at the corner than elsewhere in the array (see fig.8.6), to produce a small trench. Both of these two effects (flattening of re-entrant profiles and trenching) were eliminated when more than 50 lines were used to fit the surface, at the expense of greatly increasing the computation time. In the extreme case, of course, when several hundred lines are used to fit the surface we are back to the cubic model with all of its intrinsic problems.

The main point is that for two extreme models of the surface, (a) small cubes with a well-defined cubic structure, and (b) a local surface averaged over many surface cubes, the basic profiles obtained were very similar. In reality, a better model might be somewhere between these two extremes, but this study shows that either (a) or (b) can be used as a reasonable first approximation to obtain the profile. Model (a) is preferred over (b) for two reasons. Firstly, it is much faster to compute, and secondly, it does not produce gross artifacts such as trenching or flattening of the profile. Many other models suitable for describing ion-surface interactions are possible. Some of these have been suggested for future investigation in section 9.2.

8.12 Comparison of Sidewall Profiles with Experimental Observations

Although the model described in the previous sections accurately predicts the general trends that have been observed in RIE processes, it would be very useful to be able to compare predictions directly with experimental sidewall profiles observed when sputtering Si in a real fully-characterised process. We have been simulating only Ar+ ion sputtering of amorphous Si, therefore an attempt was made to sputter Si in an Ar plasma using the Minstrel RIE reactor (see sections 2.4-2.7) to perform a direct comparison. Unfortunately, the sputter rate of the single-crystal Si wafer in a pure Ar plasma turned out to be so low that no discernible mass loss could be detected, even when the 3”-diameter wafer was exposed to the plasma for over one hour.

There are a number of reasons for this lack of observed sputtering. Calculations of the expected weight loss for this process were performed, based upon average sputter yields and estimated ion energies at the Minstrel cathode. These calculations showed that the weight loss expected under these plasma conditions, even for a 1-hour sputter process, would be only just detectable (0.1 mg) by an accurate balance. Also, we are assuming that single-crystal Si wafers behave similarly to amorphous Si under Ar+ ion bombardment, which might not be true. Furthermore, we have not considered any native oxide layer which would have been present on the Si wafer. Oxide layers often have very low sputter yields, so the presence of even a small layer on the surface of the wafer might inhibit sputtering considerably. Moreover, the geometry of the Minstrel etcher is designed for RIE processes, whereby products are removed from the wafer surface as volatile gaseous species. For Ar+ sputtering however, Si is ejected from the surface as involatile atoms. It is possible that these atoms just redeposit back onto the Si surface, so reducing the efficiency of sputtering considerably. With all these effects working contrary to an effective sputtering process, it is not surprising that sputtering of Si in the Minstrel reactor


proved elusive. There are two options available to attempt to rectify this situation. The first option is to

increase the process time sufficiently to obtain an adequate etch depth (and hence weight loss). This time would be of the order of 10 hours, which is impracticable. The plasma chamber would become extremely hot in such a long process and deposition of Al sputtered from the chamber walls might also become important. Also, any photoresist exposed to an aggressive sputtering plasma for such a period of time would be severely degraded, if not totally etched away. This option was therefore discarded.

Another option is to change the process in such a way as to increase the etch rate. Increasing the power or decreasing the pressure were attempted, but this also resulted in excessive resist degradation with no real increase in sputter rate.

The only viable alternative is to introduce a chemically reactive species into the plasma. This would mean that the process would be an RIE process and no longer pure sputtering. With this in mind, it was decided to investigate the degree of undercut observed when using process gas mixtures of different composition. However, there is the immediate problem that our IED and IAD simulations at higher pressures are only valid for Ar plasmas, since only the cross-sections relevant to Ar+/Ar collisions have so far been included in the program. Therefore, it was decided that the process gases should be a mixture of Ar and X, where X was the reactive gas (e.g. CF4) and Ar was in large excess. We are assuming that since the Ar is in a large excess, the IED/IAD pair for the plasma conditions could be represented by one calculated for a pure Ar plasma at these conditions, in other words X+ ions (or fragments) do not contribute significantly to the IEDs and IADs. The ratio of the gases was chosen so that the mass flow controllers on the reactor could operate within their calibrated range. This ratio was 85% Ar : 15% X.

The pressure was set at 200 mTorr, which was the minimum obtainable once the required gas flow rates had been set. Patterned Si wafers (see section 2.5) were etched in different processes, the details of which are given in table 8.3 along with the measured plasma conditions. From the values of V0 and Vdc for each process, the effective area ratio, Ae was calculated (noting that the approximate geometrical value is about 0.44). The gases were chosen so that a trend from pure fluorine-based to pure chlorine-based chemistry could be studied, and the results are detailed in table 8.3.

X d / mm lmax / mm V0 / Volts Vdc / Volts Ae kTe / eV Etch Time SF6 3 2.3 220 170 0.29 3 1 mins 28 s CF4 5 3.7 480 380 0.27 2 7 mins CF2Cl2 3 2.3 225 150 0.40 3 11 mins 45s CCl4 2 1.5 130 70 0.47 4 9 mins

Table 8.3. Plasma conditions using in the experimental Si etch processes. The RF voltage, V0, and DC bias, Vdc, were obtained from the DC bias probe attached to the matching network. Ae

was calculated from Equation (1.5.4) using the measured values of V0 and Vdc. The value of kTe is estimated based upon the electronegativity of the gases. Etch time was the time to etch

5000 Å of polysilicon, determined by visual observation of the end-point on reaching underlying oxide. The extent of the dark space, d, was estimated by visual observation. The electrical sheath thickness, lmax, was calculated from Equation (6.39). Other plasma conditions were constant for all processes. These included RF power = 100 W, frequency = 13.56 MHz,

pressure = 200 mTorr, flows: Ar:X = 40:7 sccm.


Various important facts can be discerned from the information given in table 8.3. If the gases are arranged in approximate order of increasing electronegativity (see table 1.1), we obtain CF4 < CF2Cl2 ~ SF6 < CCl4. For this sequence of gases, it can be seen that the RF voltage, V0, decreases and hence lmax decreases as we go from the least electronegative (EN) to the most EN gas. Since we are applying the same RF power in all cases, the ion current must be increasing as we go from CF4 to CCl4. In other words, as well as more negative ions being formed in the plasma region due to electron capture reactions, a correspondingly higher number of positive ions must also be formed in these plasmas. This suggests that a dominant mechanism for negative ion formation might be ion-pair production caused by very high energy electron impact (see section 4.7.7).

Another interesting observation is that the effective electrode area ratio Ae increases as we go from CF4 to CCl4, i.e. from less EN to more EN gases. For very EN gases Ae is almost equal to the geometrical area ratio. This suggests that for less EN gases, where there is an abundance of free electrons, the plasma glow region can ‘leak out’ from the region between the electrodes. Hence, the effective ‘size’ of the plasma region is larger and it is in contact with more of the anode. When there are less free electrons in the plasma, the glow is confined only to the region directly between the electrodes.

The etch rates of the four processes generally increased with fluorine content of the gas mixture, with the Ar/SF6 process etching about 6 times faster than the Ar/CCl4 process.

SEM photographs of the pre-etch resist profile and the post-etch profiles for the Ar/CCl4 and Ar/SF6 processes are given in plates 8.1(a-c). Before etching, the resist shows an 80° profile with a flat top. After etching, however, the resist can be seen to be very damaged, with a large section from the centre being badly eroded. This was because the wafers only had a pre-etch soft-bake at about 100°C and so the resist only obtained a hard outer coating with a soft centre. When this outer coating was etched away (as it did rapidly at the exposed top surface), the softer centre was then exposed to the plasma and proceeded to erode at a much faster rate. Resist erosion also occurred laterally, reducing the linewidth at the bottom of the mask by up to 0.22 µm per line edge for some processes.


Plate 8.1a. SEM photograph of the resist profile prior to etching.

The top surface of the resist is smooth and flat.

Plate 8.1b. SEM photograph of a similar polySi feature after etching in an ar/CCl4 plasma.

Note the anisotropic etch, smooth surface and lack of resist degradation.


Plate 8.1c. SEM photograph of a similar polySi feature after etching in an Ar/SF6 plasma.

The profile now shows significant undercut, with possible redeposition of material on the upper part of the polySi sidewall forming a passivation layer. The resist is badly degraded, especially

in the centre.

It had been hoped that the degree of undercut exhibited by the features etched in the various gas mixtures could be measured. These could then be simulated using the computer program and from the input parameters (RF and CF) required to obtain a good fit to the experimental profile, we could directly obtain a measure for the ratio of chemical physical etching occurring in each process. Unfortunately, in practice, the excessive resist erosion complicated the procedure, since not only did the resist etch, but it probably added a large number of carbonaceous species to the plasma which redeposited onto the evolving Si sidewall protecting it from lateral etching. This sidewall passivation did not appear in the Ar/CCl4 process, but became increasingly prevalent, creeping further down the sidewall as the fluorine content of the plasma increased. The length of the sidewall protected by this passivation layer for the CCl4, CF2Cl2, CF4 and SF6 processes were 0, 0.25, 0.35 and 0.4 µm, respectively. Consequently, the only undercut that could be observed was in the sidewall immediately beneath the passivated surface. Plate 8.lc shows this for the Ar/SF6 process, where undercutting of the lower 0.1 µm of the polysilicon is evident, whilst the top 0.4 µm has been protected by the passivation. Plate 8.lb shows a similar SEM for the Ar/CCl4 process showing no undercut at all. SEM studies of Ar/CF4 and Ar/CF2Cl2 etched features show intermediate degrees of undercut. Fig.8.27 shows schematic diagrams of the observed profiles for each process gas mixture.


Fig.8.27. Schematic diagrams of the observed etch profiles in 1 µm features.

Using the values for the plasma conditions given in table 8.3, Ar IED/IAD pairs for each of

the four processes were calculated. These distributions were then used to simulate the sidewall profile expected for these plasma conditions. We assumed that the polycrystalline structure of polySi was sufficiently like that of amorphous Si to make this procedure valid. Values of the factor CF were adjusted until the simulated profile gave values of the ratio of the lateral undercut to etch depth equivalent to those observed experimentally. The etch depth used was the thickness of polysilicon beneath the passivation layer, e.g. for the CF4 process this was 0.15 µm with an observed undercut of 0.09 µm. The results of these calculations give the approximate ratio of chemical to physical etching occurring in each system, i.e. the ratio of the number of array elements removed by pure chemical means to those removed by ion bombardment alone. The values for the percentage chemical etching and resist erosion factor for each of the processes


is given in table 8.4. Due to uncertainties in the SEM measurements, combined with the inherent errors associated with the assumptions used in these calculations, these results should be taken as only an approximate guide to the general trends involved.

The trend in the data in table 8.4 is that the degree of undercut increases with the fluorine content of the plasma. For Cl-based chemistries no undercut is observed. This suggests that F atoms are able to etch Si spontaneously, whereas Cl atoms require a certain degree of ion bombardment for etching to occur. This ion bombardment is needed to overcome the activation energy for Si-Cl bond formation, or to help desorb product species from the Si surface.

For the Ar/CCl4 process, no sidewall passivation was observed. In fact, the resist etched back slightly producing an 80° slope to the polysilicon sidewall. This suggests that for these plasma conditions the passivating layer is a polymeric fluorocarbon species (possibly containing Si) bonded to the surface of the sidewall. A chlorocarbon polymer either forms less readily in the plasma, or is less effective as a passivant.

It is hoped in the future to be able to repeat these experiments with wafers that have DUV hardened resist features. This should enable more accurate comparisons to be performed between simulated re-entrant profiles and experimental observations, without the complications of severe resist erosion and the related sidewall passivation.

Process gas % Chemical Etch RF

Ar/CCl4 0 0.3 Ar/CF2Cl2 27 0 Ar/CF4 80 0 Ar/SF6 96 0

Table 8.4. The percentage chemical etching estimated by comparison of the simulated etch profiles to observed profiles for each of the four process gases. RF is the resist erosion factor

(see section 8.9) which is 0 in cases where the resist and Si sidewalls did not recede. This was due to formation of a protective passivation layer.

8.13 Conclusions

Although the model used for the sputtering of Si with energetic ions is still very primitive, it nevertheless manages to predict accurately the form of profiles seen in both low and high pressure RIE processes. Modelling also accurately predicts known trends such as etch rate increasing linearly with RF power (or V0). Furthermore, it gives realistic-looking results when resist erosion and isotropic chemical etching are included. These last two effects require empirical fitting parameters whose values have to be determined by a calibration experiment upon a real etch process. The value of these fitting parameters can yield useful information about the mechanisms occurring at the surface of the Si, in particular the rate of pure chemical to pure physical etching that is taking place.

The main conclusions from this preliminary attempt to combine the IED/IAD simulations with a basic model for the Si surface, is that although the model is still very simple and has vast scope for future improvements, it can still be used to obtain useful information about the fundamental mechanisms of dry etching.

Chapter 8 – Etch Sidewall Profile Simulations

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