Книги2 / 1993 Dutton , Yu -Technology CAD_Computer Simulation

shown in the figure consists of layers of oxide and nitride to mask a later oxidation step - then the majority of the dose will be deposited at some projected range determined by the composite stopping power of the multiple layers. Figure 2.4 (b) shows the resulting depth profile, including the portions of the dose now left in the surface masking layers. Subsequent discussion will explain the discontinuities across the nitride, oxide, and silicon interfaces.

Although many fabrication sequences contain sufficient thermal cycling to overcome and mask the initial implanted profile shape, current trends toward reduced thermal cycles after ion implantation require more accurate models for the profile shape immediately after implant. The effect of multiple layers is also an important issue. It is not the intent of this book to discuss all options for modeling ion implanted profiles. Other review material is available on the subject [2.1]' [2.2]. The emphasis here will be to explain the options available in SUPREMo

We begin by discussing the standard Gaussian and two-sided Gaussian distribution models. Next, we present the default model in SUPREM III, the Pearson IV (PIV) distribution model. Section 2.2.2 discusses the application of the PIV model to implants through multi-layer structures. Finally, a costly but accurate numerical technique, Boltzmann Transport Analysis (BTA), is introduced in Section 2.2.4.

2.2.1Gaussian Profiles

The simple Gaussian profile is easily understood and written as follows:

(2.1 )

Unfortunately, except for the most rudimentary profile calculations followed by substantial thermal cycles, this approach is inadequate. By contrast, the two-sided Gaussian profile given by

is adequate for a broader range of applications. In fact, given an arbitrary empirical profile, the two-sided Gaussian is an excellent first-order approximation to use in determining the effects of subsequent thermal cycles. Figure 2.5 shows a schematic representation of the two-sided Gaussian profile. SUPREM contains an internal table of coefficients to

Figure 2.5: Schematic representation of a two-sided Gaussian profile indicating the meaning of 0'1, 0'2.

fit a two-sided Gaussian, based on the results of Gibbons and Mylroie

[2.3].

The two-sided Gaussian model has several limitations. Although it works well for a first-order approximation of profiles, the actual distributions can be substantially different. For example, both phosphorus and boron can penetrate deep into the substrate if channeling is not minimized.

2.2.2Pearson IV Profiles

To model deviations from the ideal or two-sided Gaussian shapes, SUPREM III adjusts profiles with the coefficients for a Pearson IV type distribution. Figure 2.6 shows a comparison of the Gaussian, two-sided Gaussian, and Pearson IV distributions for implanted boron. The Pearson IV and two-sided Gaussian profiles are comparable, while the simple Gaussian result matches the other two only in the peak region. The Pearson IV distributions are the default option in SUPREM for boron; that is, without any other specification the program automatically uses this form of a distribution function. Figure 2.7 shows how the PIV profile varies with the increased ion energy for boron. Details concerning the features of PIV distributions and the coefficients used to calculate

Distance from surface (microns)

Figure 2.6: Semi-logarithmic plot of boron concentration versus depth for implantation profiles computed using Gaussian, two-sided Gaussian, and Pearson IV distribution functions.

them are not included here, but can be found elsewhere [2.2] [2.4] [2.5]. The coefficients used in the PIV distribution functions in SUPREM are extracted from the work of Christel et al. [2.6] and are built into the SUPREM data files.

2.2.3Multi-layer Implantation

The approach used in SUPREM for multi-layer implants is as follows. Starting from the surface, the first layer encountered is considered to be semi-infinite. Using the PIV distribution model, the profile through the end of that layer is computed, as shown in Figure 2.8 (b), for layer I with a thickness of ~1. The shaded area represents the total charge in layer I and the solid line is the required profile.

Next the second layer is considered. Once again, the PIV distribution model is computed. This time, layer 2 is considered to be semiinfinite and to start at the surface, as shown in Figure 2.8 (c). The position xl for starting the second layer profile is adjusted so that the

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(e)

FINAL PROFILE

Figure 2.8: Schematic representation of how ion implantation is modeled for multilayer targets, (a) shows the three-layer system, the ensuing figures show the computation in: (b) layer 1, (c) layer 2, (d) layer 3, and (e) the composite profile.

it is advantageous to use numerical solutions such as BTA to directly simulate the resulting distributions [2.6]. Although BTA is an order of magnitude slower and more costly than modified analytic approaches such as PIV, it can model complex kinetic effects quite accurately.

The BTA option in SUPREM III can be enabled by specifying keyword "Boltzmann" at the implant step. In this case, SUPREM III proceeds to compute the actual profile using a refined grid structure as specified by the user. The details of this simulation technique are not presented here but can be found in [2.6]. In general, BTA can be thought of as a summation of ions stopped at each grid due to scattering events computed based on energetics and scattering cross-sections. Hence, one might visualize the process as resembling Figure 2.8 with the grid spacings being many "~'s" specified to more accurately model the detailed kinetics of ion stopping and scattering. The computation proceeds by following the energy of individual ions until that energy falls below some critical value, at which point the ion is considered stopped. A distribution function accounting for the total dose of implanted ions is generated, and hence the actual profile for a given dose can be generated.

There are several advantages to the BTA approach. First, the basic computational technique does not vary with material. As the material changes, only the physical parameters need to be changed, so multilayer targets pose no problem. Second, it is possible to account for multiple events such as damage layers created due to the "knocking-on" of atoms in the silicon lattice. Here the random particle events are followed over time and summed to generate the profiles. A number of process simulators based on the Monte Carlo (MC) approach have been developed [2.7] [2.8]. However, as with the BTA, they are costly in terms of computational effort.

Although MC simulation is also a promising approach, the practical solution is likely to be the use of such simulation techniques as MC or BTA to fit coefficients either for a PIV distribution alone or for a combined PIV/channeling tail model (such as the exponential function used in SUPREM II).

2.3Oxidation

The ability to form Si02, which is stable and has excellent mechanical and electrical properties, has been a crucial factor in the development and maturing of silicon IC technology. The rate of Si0 2 growth on silicon surfaces has historically been described by the well-known linearparabolic growth law [2.9]

where Xo is the oxide thickness at time t, Xi is the thickness of any oxide present at t = 0, and Band B / A are the parabolic and linear rate constants, respectively. Constant B is proportional to the oxidant solubility (and hence to oxidant partial pressure) and to the oxidant diffusion coefficient in the Si0 2. Constant B / A is also, to the first order, proportional to oxidant solubility (and hence to the partial pressure) and to k s , the Si-Si02 interface reaction rate constant. The two rate constants Band B / A separate the overall oxidation process into diffusion of the oxidant species through any existing Si0 2 layer and reaction at the Si-Si0 2 interface, either one of which may become rate-limiting depending on temperature and Si02 thickness. Anything which affects the rate of diffusion of O2 or H20 through the Si02 layer (such as high dopant concentrations in the Si02) should affect B. Alternatively, anything which affects the Si-Si0 2 interface chemical reaction rate (such as substrate crystal orientation) should affect B / A. However, the detailed mechanisms which may be responsible for these changes in Band B / A are not apparent from Eq. (2.4).

2.3.1Physical Mechanisms

In modern structures which emphasize lower process temperatures and thinner Si02 layers, the interface reaction rate constant B / A is increasingly becoming the dominant, rate-limiting parameter. It has become clear in recent years that the detailed mechanisms involved in B / A are responsible for many important process phenomena. A substantial amount of work in thermal oxidation over the past several years has greatly clarified the detailed reactions occurring at the Si-Si0 2 inter-

face during oxidation. Much of this work can be summarized as shown in Figure 2.9 [2.10] [2.11]. This figure contains the physical origin of

Figure 2.9: Schematic view of the silicon oxidation process. The role of vacancy and interstitial effects are indicated.

several of the new process models in SUP REM III.

As the oxidizing interface moves into the silicon substrate, a small excess of silicon atoms are believed to be present in each lattice plane [2.12] [2.13]. Substantial mismatch should thus occur at the interface, resulting in significant strain (top block in Figure 2.9). Thus, alternative mechanisms which ease the interface mismatch are expected to playa role in the oxidation process.

The middle and bottom reactions postulate the roles of substrate point defects in such reactions. A site is provided for oxygen bonding to lattice silicon atoms either through the presence of a silicon vacancy (Siv) or by the creation of a silicon interstitial (Sir) . The Siv reaction has been used to explain quantitatively the enhanced oxidation rates observed in heavily doped substrates [2.14] [2.15]. In this case, the substrate is extrinsic at the oxidation temperature with the result that the Fermi level is not at the mid-gap position. Because Siv can exist in a number of charge states, (Y+, Y-, y=), the concentrations of the charged vacancies depend on the Fermi level position. In n+ and p+