Lecture 12 (CHE 323) Thermal Oxidation, part 3

Name: Lecture 12 (CHE 323) Thermal Oxidation, part 3
Uploaded: 2013-09-11T18:29:32.000Z
Duration: 1 h 10 min 14 s
Description: Thermal Oxidation, part 3 Using the Deal-Grove Model

Chemical Processes for Micro and Nanofabrication: Thermal Oxidation - Lecture 12 Part 3

Overview of the Deal-Grove Model

Chris Mack introduces the lecture on thermal oxidation, referencing Chapter 4 of the Campbell textbook.

The Deal-Grove model outlines three sequential steps in the oxidation process:

Diffusion of reactants from bulk gas to silicon dioxide surface.

Absorption of oxidant (oxygen or water) onto the surface according to Henry's law.

Diffusion through oxide film followed by reaction at the silicon interface.

Rate Equation Derivation

A simplified rate equation is derived, showing that oxide growth rate depends on both oxide thickness and constants A and B.

The standard form includes a second-order term, first-order term, and an initial oxide thickness constant t_0 , which affects growth rates based on existing oxide layers.

Oxidation Characteristics

The constants A and B relate to fundamental parameters like diffusivities, partial pressures, and mass transfer coefficients.

Experimental data illustrates wet versus dry oxidation at 1000°C; wet oxidation occurs significantly faster than dry oxidation.

Initial linear growth transitions to parabolic behavior as oxide thickness increases over time.

Understanding Initial Thickness Impact

Initial thickness t_0 complicates predictions; it does not simply add linearly to new growth but slows down the overall rate due to diffusion requirements.

This nonlinear aspect means that oxidation effectively starts at a negative time offset relative to when actual measurements begin.

Properties of Oxide Growth Models

Two regimes are identified based on oxide thickness relative to parameter a/2 :

For thin oxides ( T_Ox << a/2 ), growth is linear with a constant rate defined by B/a .

For thick oxides ( T_Ox >> a/2 ), growth becomes parabolic where thickness relates quadratically with time.

Modeling Oxide Growth: The Deal-Grove Model

Overview of the Deal-Grove Model

The parabolic rate constant B is often emphasized in discussions about oxide growth, despite the presence of two parameters A and B . It's crucial to compare models against experimental data to validate their effectiveness.

Validating the Model Against Data

All models operate under certain assumptions, which may not hold true in all scenarios. Identifying these limitations is essential for accurate application.

The Deal-Grove model shows excellent agreement with data during wet oxidation across various oxide thicknesses, indicating its reliability in this context.

Limitations of the Model

For dry oxidation, particularly with thin oxides (less than 30 nm), the model fails to predict growth rates accurately due to incorrect assumptions regarding initial conditions.

Historically, thicker oxide films were common in semiconductor manufacturing; however, modern practices often involve thinner films where the Deal-Grove model's predictions are inadequate.

Adjustments to Improve Accuracy

Alternative models have been developed that extend the Deal-Grove framework by incorporating additional terms to account for faster growth rates observed at thinner oxide levels.

To reconcile discrepancies between predicted and actual growth rates, an empirical adjustment factor ( t_0 ) is introduced into the model based on experimental observations.

Fitting Experimental Data

Initial growth rates are significantly higher than those predicted by the Deal-Grove model. After approximately 30 nm thickness, predictions align well with observed data.

An assumption of a fictitious initial thickness (23 nm), necessary for fitting purposes, highlights a limitation in using this model for very thin oxides.

Parameterization and Temperature Dependence

The introduction of an empirical fudge factor allows better alignment with experimental results while maintaining reliance on established parameters from previous studies.

The parameter t_0 , found consistent across various temperatures for dry oxidation but not wet oxidation, emphasizes differences in modeling approaches based on environmental conditions.

Summary of Constants and Their Implications

A three-parameter model including A , B , and t_0 —with temperature-dependent values—provides a more comprehensive understanding of oxidation processes.

Table 4.1 from Campbell's textbook illustrates how constants vary with temperature while maintaining a fixed value for t_0 = 23textnm .

Precision and Variability in Measurements

Constants derived from experiments show reasonable accuracy within ±2%, although some values exhibit greater variability due to their small magnitude impacting overall growth rate predictions.

Crystallographic Orientation Effects

Understanding Oxidation Parameters in Silicon Dioxide

Predicting Thickness and Interpolation

The use of non-111 wafers requires adjustments to oxidation parameters, allowing predictions of thickness based on oxidation time using the Deal-Grove model.

Data is plotted on an Arrhenius plot, showing a linear relationship between the logarithm of rate constants and the inverse of absolute temperature.

Rate Constants and Activation Energy

A straight line indicates effective interpolation for different temperatures; however, activation energies differ significantly between parabolic (B) and linear (B/a) rate constants.

The activation energy for B/a is similar for both wet and dry conditions but varies greatly for B, indicating distinct behaviors under different oxidation environments.

Fundamental Parameters Influencing Rates

The parameter 'a' relates to oxygen diffusivity through silicon dioxide and includes factors like mass transport coefficients.

The linear rate constant B/a depends on Henry's law constant (H), partial pressure of oxidants, and density variations between H2O and O2.

Temperature Dependence Analysis

Diffusivity (D) shows exponential temperature dependence while H has a lesser effect; thus, D primarily influences the temperature behavior of B.

Activation energy for KS aligns closely with silicon-silicon bond energy (~2 eV), confirming that breaking this bond is critical for subsequent reactions with oxygen.

Differences Between Wet and Dry Oxidation

Wet oxidation occurs faster than dry due to higher values of both B and B/a; this is attributed mainly to differences in solubility represented by Henry's law constant (H).

Dry vs. Wet Oxidation: Key Differences

Understanding the Proportionality in Oxidation Rates

In wet oxidation, the reaction rates are proportional to the partial pressure of the oxidant, aligning with expected behavior. However, dry oxidation presents a different scenario where b/a is proportional to the partial pressure of O2 raised to a power between 0.5 and 1, typically around 7 or 8.

The observed difference in dry oxidation suggests that both atomic and molecular oxygen may be involved in the reaction process, leading to confusion regarding their roles.

Crystal Orientation Impact on Reaction Rates

Different crystal orientations (100, 110, and 111 wafers) affect the density of silicon-silicon bonds available for reactions at the silicon dioxide interface. The 111 orientation has approximately 74% more bonds per unit area than the 100 orientation.

The effective value of K_s , which incorporates bond concentration, varies with crystal orientation; thus affecting b/a . For instance, b/a is found to be about 1.68 times smaller for 100 wafers compared to 111 wafers.

Effects of Substrate Doping on Oxidation Rates

Higher substrate doping levels increase b/a , but not b . This indicates that changes in surface reaction rate constants ( K_s ) are responsible for this discrepancy due to increased crystal defects from higher doping levels.

Crystal defects provide favorable sites for breaking bonds during oxidation processes, enhancing overall reaction rates.

Role of HCl in Dry Oxidation Processes

Adding HCl (1-5%) during dry oxidation helps remove metal ion contaminants like sodium and potassium from both gas and film. Interestingly, this addition also increases oxidation rates by facilitating water formation through reactions with O2.

Geometry of Oxide Growth During Reactions

When growing an oxide film, expansion occurs both upwards and downwards from the original silicon surface due to differences in densities between silicon and silicon dioxide.

Silicon Dioxide Growth and Its Implications

Understanding Silicon Dioxide Thickness Ratios

The ratio of the thickness of silicon consumed to the thickness of silicon dioxide grown is 0.455, indicating a significant relationship between these two measurements during oxide film growth.

As silicon dioxide grows, it expands both upwards and downwards, consuming 0.455 of its thickness downward compared to 0.545 upward from the original surface, which affects three-dimensional structures beyond flat wafers.

Impact on Oxide Film Growth

The volume expansion resulting from this growth will have significant implications for processes like LOCOS isolation, which will be discussed in detail later in the lecture.

Key Learning Outcomes

Students should be able to apply the Deal-Grove model for calculations related to oxidation time and thickness based on given parameters such as linear and parabolic rate constants.