Thermal Oxidation - Page 2 of 2: Oxide Growth Models

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Thermal Oxidation (Page 2 of 2)

During dry oxidation, the silicon wafer reacts with the ambient oxygen, forming a layer of silicon dioxide on its surface. In wet oxidation, hydrogen and oxygen gases are introduced into a torch chamber where they react to form water molecules, which are then made to enter the reactor where they diffuse toward the wafers. The water molecules react with the silicon to produce the oxide and another byproduct, i.e., hydrogen gas.

These oxidation reactions occur at the Si-SiO2 interface, i.e., silicon at the interface is consumed as oxidation takes place. As the oxide grows, the Si-SiO2 interface moves into the silicon substrate. As a result, the Si-SiO2 interface will always be below the original Si wafer surface. The SiO2 surface, on the other hand, is always above the original Si surface. SiO2 formation therefore proceeds in two directions relative to the original wafer surface.

The amount of silicon consumed by the formation of silicon dioxide is also fairly predictable from the relative densities and molecular weights of Si and SiO2, i.e., the thickness of silicon consumed is 44% of the final thickness of the oxide formed. Thus, an oxide that is 1000 angstroms thick will consume about 440 angstroms of silicon from the substrate.

For oxidation processes that have very long durations, the rate of oxide formation may be modeled by a simple equation known as the Parabolic Growth Law : xo² = B t, where xo is the thickness of the growing oxide, B is the parabolic rate constant, and t is the oxidation time. This shows that the oxide thickness grown is proportional to the square root of the oxidizing time, which means that the oxide growth is hampered as the oxide thickness increases. This is because the oxidizing species has to travel a greater distance to the Si-SiO2 interface as the oxide layer thickens.

Oxidation processes that have very short durations, on the other hand, may be modeled by another simple equation known as the Linear Growth Law : xo = C (t + t), where xo is the thickness of the growing oxide, C is the linear rate constant, t is the oxidation time, and t is the initial time displacement to account for the formation of the initial oxide layer at the start of the oxidation process.

The Linear and Parabolic Growth Laws were developed by Deal and Grove, and are collectively known as the Linear Parabolic Model. This oxide growth model has been empirically proven to be accurate over a wide range of temperatures (700-1,300 deg C), oxide thicknesses (300-20,000 angstroms), and oxidant partial pressures (0.2-25 atmospheres).

Oxide growth rate is affected by time, temperature, and pressure. More specifically, oxide growth is accelerated by an increase in oxidation time, oxidation temperature, or oxidation pressure. Other factors that affect thermal oxidation growth rate for SiO2 include: the crystallographic orientation of the wafer; the wafer's doping level; the presence of halogen impurities in the gas phase; the presence of plasma during growth; and the presence of a photon flux during growth.

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