An \(n\) -type semiconductor is known to have an electron concentration of \(5 \times 10^{17} \mathrm{m}^{-3}\). If the electron drift velocity is \(350 \mathrm{m} / \mathrm{s}\) in an electric field of \(1000 \mathrm{V} / \mathrm{m}\), calculate the conductivity of this material

Understanding n-type semiconductors is crucial for grasping how many electronic devices function. These semiconductors are formed when a pure semiconductor, usually silicon, is doped with a certain type of atoms called donor atoms. These atoms have more valence electrons than the silicon, typically five instead of four.

When these donor atoms substitute some silicon atoms in the crystal lattice, they introduce extra electrons into the system. These extra electrons are relatively free to move and contribute to the electrical conductivity. The term 'n-type' comes from the fact that the charge carriers are negatively charged electrons ('n' stands for negative). In the context of our textbook exercise, the concentration of these charge carriers, the electron concentration, is an essential parameter for determining the semiconductor's overall conductivity.

The concept of electron drift velocity might sound complex, but it's an important factor in understanding electric current at the microscopic level. It's defined as the average velocity that a free electron attains due to an electric field applied across a conductor or semiconductor. It's not a speed in the traditional sense—instead, think of it as the average, sluggish saunter resulting from the frequent collisions with the lattice atoms that cause resistance.

In our exercise, the drift velocity is the speed at which electrons are 'drifting' due to the electric field. It's a crucial component of current density, and thereby, conductivity. When we talk about the drift velocity of electrons in n-type semiconductors, it directly affects how efficiently an electric charge can move through the material.

Current density is a concept that might seem abstract but is actually straightforward—it represents the electric current per unit area of cross-section in an electrical conductor. Measured in amperes per square meter, it's a vector quantity, meaning it has both a magnitude and a direction. The current density tells us how densely packed the current is, flowing through a conductor.

Why is this important? Because high current density in a small area can cause heating and, in extreme cases, damage to the material. It's an essential consideration in electrical engineering when designing circuits and devices. Referring to our n-type semiconductor example, the calculation of current density from the given electron drift velocity and concentration is a step towards finding the material's conductivity.

Perhaps one of the most fundamental principles in electrical engineering and physics is Ohm's Law. Simply put, Ohm's Law states that the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to the resistance of the conductor. The formula is typically written as V = IR, where V is the voltage, I is the current, and R is the resistance.

In the context of a semiconductor, we often discuss conductivity rather than resistance, which is the inverse of resistance—think of it as the ease with which electrons can flow through a material. Our exercise utilizes a rearranged form of Ohm's Law to solve for conductivity, \( \sigma \), using the current density and the electric field. This allows us to quantify the semiconductor's ability to conduct electric current.