Oxide Growth Calculator

What is Oxide Growth?

Oxide growth is a process in semiconductor manufacturing where a layer of oxide (typically silicon dioxide) is grown on the surface of a silicon wafer. This process is crucial for creating insulating layers in integrated circuits and other semiconductor devices. The growth of oxide layers is typically achieved through thermal oxidation, where the silicon wafer is exposed to an oxygen-rich environment at high temperatures.

Formula

The oxide growth can be approximated using the Deal-Grove model, which is simplified for this calculator as:

\[ x_f = x_i + \sqrt{t} \cdot e^{-\frac{1}{T}} \]

Where:

• \( x_f \) is the final oxide thickness (nm)
• \( x_i \) is the initial oxide thickness (nm)
• \( t \) is the oxidation time (hours)
• \( T \) is the temperature (K)

Calculation Steps

Let's calculate the final oxide thickness for the following parameters:

• Initial oxide thickness (\( x_i \)): 10 nm
• Oxidation time (\( t \)): 4 hours
• Temperature (\( T \)): 1000°C (1273.15 K)

1. Calculate \( \sqrt{t} \): \[ \sqrt{4} = 2 \]
2. Calculate \( e^{-\frac{1}{T}} \): \[ e^{-\frac{1}{1273.15}} \approx 0.9992 \]
3. Multiply the results from steps 1 and 2: \[ 2 \times 0.9992 \approx 1.9984 \]
4. Add the initial thickness: \[ x_f = 10 + 1.9984 \approx 11.9984 \text{ nm} \]

Example and Visual Representation

Let's visualize the oxide growth process:

This visual representation shows:

• The silicon substrate
• The initial oxide layer (10 nm)
• The grown oxide layer (~2 nm)
• The oxygen-rich environment at high temperature