A pure silicon crystal of length l(0.1 m) and area A(10^-4 m^2) has the mobility of electron (

step 1 Hello students. In this question we have a pure silicon crystal having length L equals to 0 .1 m

A pure silicon crystal of length l(0.1 m) and area A(10^-4...

A pure silicon crystal of length $l(0.1 \mathrm{~m})$ and area $A\left(10^{-4} \mathrm{~m}^{2}\right)$ has the mobility of electron $\left(\mu_{e}\right)$ and holes $\left(\mu_{h}\right)$ as $0.135 \mathrm{~m}^{2} / \mathrm{Vs}$ and $0.048 \mathrm{~m}^{2} / \mathrm{Vs}$, respectively. If the voltage applied across it is $2 \mathrm{~V}$ and the intrinsic charge concentration is $n_{l}=1.5 \times 10^{6} \mathrm{~m}^{-2}$, then the total current flowing through the crystal is : (a) $8.78 \times 10^{-17} \mathrm{~A}$ (b) $6.25 \times 10^{-17} \mathrm{~A}$ (c) $7.98 \times 10^{-17} \mathrm{~A}$ (d) $2.456 \times 10^{-17} \mathrm{~A}$

A pure silicon crystal of length $l(0.1 \mathrm{~m})$ and area $A\left(10^{-4} \mathrm{~m}^{2}\right)$ has the mobility of electron $\left(\mu_{e}\right)$ and holes
$\left(\mu_{h}\right)$ as $0.135 \mathrm{~m}^{2} / \mathrm{Vs}$ and $0.048 \mathrm{~m}^{2} / \mathrm{Vs}$, respectively. If the
voltage applied across it is $2 \mathrm{~V}$ and the intrinsic charge concentration is $n_{l}=1.5 \times 10^{6} \mathrm{~m}^{-2}$, then the total current flowing through the crystal is :
(a) $8.78 \times 10^{-17} \mathrm{~A}$
(b) $6.25 \times 10^{-17} \mathrm{~A}$
(c) $7.98 \times 10^{-17} \mathrm{~A}$
(d) $2.456 \times 10^{-17} \mathrm{~A}$

Key Concepts

Charge Carriers

In semiconductors, electrical conduction is achieved through the movement of electrons and holes. Electrons are negatively charged particles, while holes represent the absence of an electron and behave like positive charge carriers. Their concentrations and contributions play a critical role in determining the current flow within the material.

Mobility

Mobility is a measure of how quickly charge carriers can move through a semiconductor when an electric field is applied. It quantifies the ease with which electrons and holes traverse the material, impacting the overall conductivity. Higher mobility means that carriers can accelerate more readily, leading to increased current under a given electric field.

Drift Current

Drift current arises when charge carriers move under the influence of an electric field. In an intrinsic semiconductor, both electrons and holes drift in opposite directions relative to the field, and the total current is the sum of the contributions from both types of carriers. This current is directly related to the carrier concentration, their mobility, and the strength of the electric field.

Electric Field

The electric field in a material is defined as the voltage applied across the material divided by the distance between the ends. It serves as the driving force that accelerates charge carriers, resulting in a drift current. Understanding the electric field is essential for analyzing how applied voltage translates to carrier movement and conduction.

Conductivity

Conductivity is a measure of a material's ability to conduct electric charge. In semiconductors, it depends on the concentration of charge carriers and their mobilities, as well as the elementary charge. For intrinsic semiconductors, conductivity can be expressed as the product of the charge, the intrinsic carrier concentration, and the sum of the mobilities of electrons and holes.

Transcript

Please give Ace some feedback