Question

Look up the diameter of a silicon atom, in pm. The latest semiconductor chips have fabricated lines as small as \(14 \mathrm{nm}\). How many silicon atoms does this correspond to?

Short answer

The diameter of a silicon atom is approximately 220 pm, which is 0.22 nm. In a 14 nm fabrication line, there are approximately 64 silicon atoms.

Step-by-step solution

Find the diameter of a silicon atom in pm

Look up the diameter of a silicon atom in a reliable source like a textbook, scientific article, or reputable online source. The diameter of a silicon atom is approximately 220 pm.

Convert the diameter of the silicon atom to nanometers

Now, we need to convert the diameter of the silicon atom from picometers to nanometers. There are 1000 pm in 1 nm. To convert the diameter of a silicon atom to nm, divide its diameter (in pm) by 1000. \( Diameter_{nm} = \frac{Diameter_{pm}}{1000} \) \( Diameter_{nm} = \frac{220}{1000} \) \( Diameter_{nm} = 0.22 \, nm \) The diameter of a silicon atom is 0.22 nm.

Calculate the number of silicon atoms in a 14 nm fabrication line

To calculate the number of silicon atoms in a 14 nm fabrication line, divide the diameter of the fabrication line (14 nm) by the diameter of a silicon atom (0.22 nm). \( Number \, of \, atoms = \frac{14 \, nm}{0.22 \, nm} \) \( Number \, of \, atoms \approx 63.64 \) Since we can't have a fraction of an atom, we round to the nearest whole number: 64 atoms.

State the result

In a 14 nm fabrication line, there are approximately 64 silicon atoms.

Key concepts

Nanometers

Nanometers, abbreviated as nm, are a unit of measurement in the metric system. A nanometer is one-billionth of a meter, which is represented as 10^-9 meters. It's incredibly tiny! Nanometers are commonly used in fields like physics and chemistry to measure things that are extremely small, like atoms and molecules.
Nano-scale measurements are especially important in the technology industry, particularly in the fabrication of semiconductor chips. Modern technology has advanced to the point where we can measure and manipulate materials at the nanometer scale. This precision allows for the creation of smaller and more powerful electronic components.
In the context of semiconductor chip fabrication, line sizes of around 14 nm, as mentioned in the exercise, are quite common. This means that the features on these chips, like transistors, are only 14 nm wide. Working at such a small scale allows for more components to be packed onto a single chip, enhancing performance without increasing size.

Picometers

Picometers, denoted as pm, are another unit of measurement in the metric system, even smaller than nanometers. One picometer is one-trillionth of a meter, represented as 10^-12 meters. This unit is typically used to measure atomic and subatomic dimensions.
For instance, in this exercise, we looked at the diameter of a silicon atom, which is about 220 pm. To put this in perspective, while a nanometer is already incredibly tiny, a picometer is 1000 times smaller! Measuring in picometers provides a more precise understanding of atomic structures, which is crucial for applications in nanotechnology and material sciences.
Understanding picometers helps scientists and engineers as they explore ways to manipulate matter on an atomic level. The ability to measure in such fine detail is essential for designing materials with specific properties and for developing new technologies.

Semiconductor Chips

Semiconductor chips are the brains of countless electronic devices. They are responsible for processing information and executing instructions. These chips are made from semiconductor materials, like silicon, that have properties between conductors and insulators. This makes them ideal for controlling electrical signals.
The fabrication of semiconductor chips involves creating extremely tiny structures on the chip's surface. As our exercise indicates, modern chips feature line sizes that can be as small as 14 nm. This ability to work on a nano-scale means more transistors and components can fit onto a single chip, making electronic devices faster and more efficient.
Understanding concepts like nanometers and picometers is essential for grasping how these chips are made and how they function. The decrease in size of chip features over the years, known as Moore's Law, has consistently doubled the performance of chips while reducing costs. This evolution has been critical in the development of our smartphones, computers, and numerous other high-tech devices.