Книги2 / 1993 Dutton , Yu -Technology CAD_Computer Simulation

Figure 2.10: (a) Linear and (b) parabolic rate constants used in SUPREM for oxide growth in pyrogenic steam. Curves shown as a function of partial pressure in atmospheres (units are different from what in text) [2.22].

and

The physical process represented by B is the oxidant transport through the Si0 2 and the 1.23 eV activation energy corresponds to O2 diffusion in Si02 • For B/A, the 2.0 eV activation energy has historically been connected with Si-Si bond breaking at the Si-Si02 interface, although as Figure 2.9 suggests considerably more physics may be involved.

For H2 0 oxidation, Bi and (B /A)i have the same form as in Eqs. (2.9- 2.10), but the activation energy of each changes at 900 - 950°C. This is shown in Figure 2.10 [2.22]. Based on this data, SUPREM III models Bi and (B / A)i with parameter values as follows:

The change in activation energy (EA) in both Bi and (B/A)i at about 900 - 950°C may be due to viscous flow of the Si02 above this temperature which relaxes some of the stress in the Si02. This makes diffusion of the oxidant easier (due to the lower EA) at higher temperatures. Apparently, the stress in the Si02 at lower temperatures aids the interface bond-breaking process and hence reduces the activation energy of B / A.

B has been found to have no significant substrate orientation dependence. However, B / A is observed to be greater for < 111 > than for < 100 > silicon in both H20 and dry O2 oxidations [2.21], presumably due to higher silicon atom density on the < 111 > plane. Thus,

in Eqs. (2.7-2.8). Dependencies for other orientations have not been determined, although they are expected to lie between the < 111 > and < 100 > rates.

2.3.3Pressure Dependence

The effect of the oxidant partial pressure on the kinetics of silicon oxidation in both dry O2 and pyrogenic steam have been characterized. Work with "pyrogenic steam" has demonstrated oxidation kinetics closely approximating that of the bubbler using H2 and O2 flows of 2 and 1.175 l/min, respectively, which corresponds to an effective PH20= 0.92 atm.

DRY 02

(111). (100) Si

800D -1000D C

o_B..;..(P..:....T~)

B(1.T)

68/A(P,T)

B/A(i.T)

PRESSURE. P (atm)

Figure 2.12: Pressure dependence of Band B/A for conditions of dry oxidation: while B shows a linear dependence, B/A shows a sublinear dependence on pressure.

pendence is unknown at this time, although it may reflect the relative contributions of atomic and molecular O2 reactions at the interface as suggested by Van der Meulen and Ghez [2.24]

2.3.4Substrate Doping Dependence

Under conditions of high substrate doping levels, oxidation rates can be increased substantially [2.25]. Recent work has suggested that the major enhancement is seen in B / A or the interface reaction rate [2.14] [2.15]. These effects are modeled in SUPREM via the reaction in the middle block in Figure 2.9. Increasing substrate doping increases the total silicon substrate vacancy concentrations [2.26]. Those vacancies at the Si/Si02 interface are assumed to act as sites for the oxidation reaction, and hence

where I is a measure of the intrinsic vacancy role in the interface oxidation reaction and is experimentally found to be

and Cv is the normalized total vacancy concentration in the substrate at the interface, given by

where all the energy levels are measured from the valence band edge. The above three expressions are the normalized intrinsic concentrations of vacancies with respective charge states which are determined by their energies in the bandgap [2.27]. Finally, the silicon energy bandgap Eg , intrinsic Fermi level Ei, and intrinsic carrier concentration ni are

It has also been found that the oxidation rate constant B changes at high doping levels. This apparently occurs because dopant atoms segregate into the Si02 during oxidation and make it easier for O2 or H2 0 to diffuse through the Si02 • We would expect this effect to be even more pronounced for boron-doped substrates because of the preferential segregation of boron into growing Si02 layers. However, quantitative data exists only for phosphorus-doped substrates, and SUPREM models this effect of B based on the empirical data, as follows:

(2.18)

and CT is the total chemical concentration of dopants on the substrate side of the Si - Si0 2 interface. The n-type dopants show substantial interface pile-up during oxidation, but there is still some question as to what degree these pile-up peaks are either mobile or electrically active. In any event, the parameter values for Eqs. (2.11) and (2.18) were derived without considering the pile-up and peak levels but rather the doping levels just beyond the very narrow pile-up peaks (~ 100A into the silicon).

2.3.5Chlorine Ambient

The addition of a chlorine species to the oxidizing ambient has become common industrial practice for the passivation of thermally grown silicon dioxide films. Improved threshold stability and more uniform dielectric strength of such films have been well documented [2.28] [2.30]. Significant increases of oxidation rate by such chlorine additions have also been observed in dry 02 ambients [2.28] [2.31] [2.32].

The rate enhancements due to the chlorine affect both Band B / A in a complicated fashion. Both rate constants increase with Hel concentration, although B/A tends to saturate after the Hel concentration reaches 1-2 percent [2.20]. B increases monotonically with Hel concentration [2.20].

These results are apparently a consequence of multiple effects, including H20 generation via Hel + O2 reaction, chlorine effects on the interface where it tends to segregate, and possible effects on the oxidant diffusion through Si02. A quantitative physical model for these effects does not exist at present; so, the enhancements in Band B / A due to Hel have been implemented in SUPREM by adding multiplicative factors in the calculation of both B / A and B,

Figure 2.13: Oxidation rate dX/dt vs. oxide thickness for < 111 >

Many explanations have been proposed, including coupled diffusion of ionized oxygen (02) and holes (2.33), enhanced solubility of O2 in thin Si02 layers, and atomic rather than molecular oxygen oxidation (2.24].

While the mechanism remains unclear, recent experimental data (of which Figure 2.13 [2.34) is an example) has shown that an adequate empirical fit to the data can be obtained if the oxidation rate is enhanced during the initial stages as follows:

Since B / A dominates during the initial growth phase, this is equivalent to increasing B/A as described in Eq. (2.7). The decay length L is

Table 2.1: Thin oxide growth rate parameters used in SUPREM III [2.35]

approximately independent of temperature, and is equal to about 70A. ]( is an activated function of temperature as ](0 exp( -EA/kT). The physical origin of these parameters is not known at present. Values as implemented in SUPREM III are given in Figure 2.1 [2.34].

2.4Impurity Diffusion

Impurity diffusion is an essential part of all semiconductor device fabrication. This subsection concentrates on the many diffusion-related effects modeled in SUPREMo Impurity diffusion may be intrinsic or extrinsic, depending on the concentration of the diffusing and other existing impurities relative to the intrinsic carrier concentration ni at the process temperature (see Eq. (2.17)). Modeling impurity diffusion is relatively straightforward when the impurity concentration (NA or ND) is less than ni, however this is not the case in many situations of practical importance. When N A or N D is greater than ni, diffusion coefficients are concentration dependent. Diffusivity increases markedly as the electron concentration, n, becomes larger than ni (for n-type dopant). There is a limit to the electrical activation possible for each dopant at a given process temperature, as is discussed in detail later in this section. Changes in diffusivity caused by non-equilibrium effects are also presented. An example of one such effect is the base push or emitter dip effect shown in Figure 2.3. Finally, oxidation-enhanced diffusion is introduced as an important process consideration. Oxidation is known to significantly change diffusion coefficients for large distances (tens of micrometers) away from the Si/Si02 interface.

2.4.1Point Defect Kinetics

Simulation of diffusion processes involves the one-dimensional continuity equation

where n is the diffusivity, C and (; are the total and electrically active (charged) impurity concentrations, respectively, and "+" sign for the positively-charged impurities and "-" for the negatively-charged impurities. The potential ¢> based on an assumed equilibrium distribution is given by

where nand ni are the electron and intrinsic carrier concentrations, respectively, at the diffusion temperature, and ni is given by Eq. (2.17).

Specification and interpretation of the diffusivity constant, n, is not a simple task. In general, impurities may diffuse in a semiconductor via vacancyor interstitial-assisted mechanisms as illustrated in Figure 2.14. Figure 2.14 (a) shows the vacancy mechanism whereby the dopant pairs with a vacant silicon lattice site in order to move. Figure 2.14 (b) shows the interstitialcy mechanism where the dopant moves by means of coupling its motion with that of an extra silicon atom in the lattice. In silicon, there is still a good deal of discussion in the literature about the relative importance of the two mechanisms [2.35]. At the present time, it seems clear that both mechanisms playa role in impurity diffusion and that both types of point defects (interstitials and vacancies) are present in silicon at processing temperatures. Yet, depending on the type of impurity, a different fraction of each mechanism is responsible for the diffusion. For example, antimony (Sb) apparently moves only by a vacancy-assisted mechanism whereas phosphorus and boron show much larger, in fact dominant, components of interstitial-assisted diffusion.

When we say that diffusion takes place by means of various pointdefect mechanisms, we mean that in order for an impurity atom to diffuse through the silicon lattice, it must be paired either with a vacancy or with a silicon interstitial. Consider the total active population of a dopant species CTA and its various constituent components given by

(2.28)