VLSI Fabrication Principles_Ghandi (Wiley, 2E)

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458 NATIVE FILMS7.1 THERMAL OXIDATION OF SILICON 59

j = k N 1 (7.10).1.4 Kinetics of Oxide Growth

The kinetics of oxide growth on silicon may be determined [8] with reference

to the model of Fig. 7.3. Assume that a silicon slice is brought in contact with

the oxidant, with concentration N , in the gas phase, resulting in a surface con-

centration of N o molecules cmp3 for this species . In typical oxidation systems,

the mass transfer coefficient is extremely high, so that the magnitude of N o isessentially the solid solubility of the species at the oxidation temperature. At

1000°C the solid solubility of these species is 5.2 x 1016 molecules ~ r n - ~or

dry oxygen and 3x l0l9molecules cmp3 for water vapor at a pressure of 1 atm.

The oxidizing species is assumed to diffuse in molecular form through the

silicon dioxide layer, resulting in a concentration N 1 at the surface of the silicon.

Transport of the species may occur by both drift and diffusion. Writing D as

the diffusivity and ignoring the effects of drift, the flux density of oxidizing

species arriving at the gas-oxide interface is given by j , where

where k is the interfacial reaction rate constant. These fluxes must be equal

under steady-state diffusion conditions. Combining Eqs. (7. 9) and (7. 10)gives

The reaction of the oxidizing species with the silicon results in the formation

of Si02.Writing n as the number of molecules * of the oxidizing impurity that

are incorporated into unit volume of the oxide, the rate of change of the oxidelayer thickness is given by

Solving this equation, subject to the boundary value that x = 0 at t = 0, gives

and x is the thickness of the oxide at a given point in time. This is sometimesreferred to as Henry's law.

On arrival at the silicon surface the species enters into chemical reaction

with it. If it is assumed that this reaction proceeds at a rate proportional to the

concentration of the oxidizing species, thenso that

Equation (7.14) reduces to

for small values of t , and to



for large values. Thus in the initial stages of growth, in which the reaction

*n = 2.2 x ~ r n - ~or dry oxidation, and 4.4 x cmp3 for we t oxidation.Fig. 7.3 Model for oxidation kinetics.

460 NATIVE FILMS 7.1 THERMAL OXIDATION OF SILICON

is kinetically controlled, the oxide thickness varies linearly with time. In later

stages the reaction is diffusion-limited and the oxide thickness is directly pro-

portional to the square root of time.

Equation (7.13) is often written in the more compact form

Using this form, Eqs. (7.15) and (7.16) can be written as

for small values of t , and

for large values. For this reason , the term B/A is referred to as the linear rate

constant whereas the parabolic rate constant is given by B. Measured values

for these rate constants as a function of temperature are given [9] in Figs. 7.4

and 7.5 for both dry and wet oxidation (pHZO 640 torr). The data of Fig.

7.4 are shown for both (111) and (100) silicon. This orientation-dependence

effect will be considered in Section 7.1.4.2. Mathematical relations, describing

the behavior of these rate constants, are given in Table 7. 1 at the end of this

chapter.Insight into the physical processes involved during the thermal oxidation

of silicon can be gleaned by study of these figures. Thus, Fig. 7.4 shows that

the logarithm of the linear rate constant falls inversely with T at a slope of

2 eV/molecule for dry oxygen, and 2.05 eV/molecule for wet oxidation. This

is in close agreement with the energy required to break Si-Si bonds, which is

1.83 eV/molecule. The logarithm of the parabolic rate constant (Fig. 7.5) also

falls inversely with T, but at a slope of 1.23 eV/molecule for dry oxidation.

The comparable activation energy for diffusion of oxygen in fused silica is

about 1.18 eV/molecule, as shown in Fig. 7.1. The corresponding value for wet

oxidation is 0.78 eV/molecule, which compares favorably with the activation

energy of diffusion of H 2 0 n fused silica (0.79 eV/molecule).

To an approximation, the linear rate constant varies directly with the con-

centration of oxidizing species at the surface, and thus with its partial pressure.

This has been experimentally verified for both wet and dry oxidation conditions.

Finally, the parabolic rate constant for wet oxidation is found to be much larger

Temperature 10001T (K- ' )

Fig. 7.4 Linear rate constant versus temperature. From Deal [S]. Reprinted with

mission of the publisher, The Electrochemical Society, Inc.

per-



than that for dry oxidation. This is primarily due to the significantly greater solid

solubility of water over oxygen in silica glass (about 3 decades larger), whichmore than compensates for the slightly lower diffusivity as seen in Fig. 7.1.

Temperature 1000IT (K-' )

Fig. 7.5 Parabolic rate constant versus temperature. From Deal [S]. Reprintedpermission of the publisher, The Electrochemical Society, Inc.

with

! ' 462 NATIVE FILMS,

7.1 THERMAL OXIDATION OF SILICON 463

I 7.1.4.1 Initial Growth Phase

I The theory for the kinetics of oxide formation has been found to apply very well

to growth in wet oxygen and steam. There is consistent evidence, however,

to indicate the presence of an extremely rapid initial growth phase with dry

oxygen, generally existing for the first 250 A of growth. Considerable effort

has been made to explain this rapid growth behavior, since oxides of this typeand thickness are critically important for use as gate insulators in MOS devices.

A number of theories have been proposed and are briefly summarized here.

One set of theories postulates the movement of charge species through the

oxide. For example, it has been proposed [l o] that the molecular oxygen, on

entering the oxide, dissociates to form a negative-charged 0; or 0,"-,and one

o r two holes respectively. The holes have considerably higher mobility than the

oxygen ion, and run ahead of it; the result is the formation of a space-charge.-region. The resulting field enhances the diffusion of th e oxygen in the layer,

by providing an additional drift component. This enhancement occurs until the

oxide thickness exceeds the thickness of the space charge region. This region

of high space-charge density is near the gas-oxide interface, with the rest of

tlie oxide layer being almost space-charge neutral. Its thickness region is thuson the order of the extrinsic Debye length, and is given by

where E is the relative permittivity of the oxide (~ 3. 9 ). his Debye length isabout 150 A in dry oxygen, but only 5 A for water vapor." In practice, an

accelerated oxidation rate is seen for a depth of about 230f 0 A in dry oxygen

processing, but is unnoticed for wet oxygen or steam processing.

Equation (7.17) can be rewritten as

in order to include this rapid oxidation phase. Here, T is a time displacement

which can be used to adjust the initial oxide layer (at t = 0).

A second set of theories, based on the structure of the oxide during the ini-

tial growth phase, have also been proposed [ ll ]. Transmission electron micro-

scope studies of silica structure have shown the presence of pores, about 10

A in diameter, in very thin oxides grown in dry oxygen. These allow the oxi-

dant to remain in direct contact with the silicon in the early phases of growth.

Such pores have not been observed in wet oxides, presumably because their

defect density is some four orders of magnitude larger than that obtained withdry oxygen (lo2' cm-3 as compared to 1016 ~ m - ~ ,espectively). Yet another

argument is that the basic assumption of Henry's law, as given by Eq. (7.9),

only holds for infinitely thick layers, and that the solubility of oxygen in Si02

is greatly increased when the oxide thickness is less than the mean spacing

between solute molecules.A third set of theories postulate a two-stream oxidation process, with

enhanced growth resulting from the presence of a thin region of material in

which excess sites for oxidation are present [12]. Using this model, the exper-

imental data were fitted to the theory by modifying Eq. (7.12) to the form

where L is a characteristic length, of value 70 f 10 A, or growth in the

800-1000°C range. The pre-exponent ial term C has an Arrhenious type of tem-perature dependence, with an activation energy of 2.37 and 2.32 eV/molecule

for growth on lightly doped (100) and (111) silicon respectively.

Dissolved oxygen, due to indiffusion in the very early phase of growth, is

yet another possible candidate for the formation of a thin region of rapid oxidegrowth [13]. The diffusivity of oxygen in silicon is 2 . 8 ~o5A2/s at 1000°C, so

that indiffusion to a 50-A depth can occur within the first 10 ms of exposure of

bare silicon to oxygen. However, its extent falls off with oxide growth because

of a rapid reduction in this surface concentration as oxidation proceeds.

7.1.4.2 Doping Dependence Effects

Heavily doped silicon oxidizes at a faster rate than lightly doped material. How-

ever, detailed studies of boron- and phosphorus-doped material have shown con-

siderable differences in oxide growth behavior. Thus, during oxidation, boronis preferentially incorporated into the silicon dioxide because of its relatively

small segregation coefficient* (= 0.15 to 0.3). This results in a weakening of

the bond structure of the silica film, and an increase in the diffusivity of the

oxidizing species through it. Consequently, there is an increase in the parabolic

rate constant with boron doping concentration, but little change in the linear

rate constant [14].

Phosphorus, on the other hand, has a large segregation coefficient (=lo), is

only slightly incorporated into the growing oxide, and piles up at the Si-Si02

interface. This causes an increase in the reaction rate, with a corresponding

increase in the linear rate constant. On the other hand, the lack of phosphorus



*This is because the solid solubility of water in silica is three orders of magnitude larger than thatof oxygen.

*Defined as the ratio of the equilibrium concentration of the impurity in silicon to its equilibriumconcentration in the oxide. See Section 4.8.1.

VLSI Fabrication Principles_Ghandi (Wiley, 2E)

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