Understanding Dielectric Constant and Material Properties

The question asks us to arrange four different materials based on their dielectric constant in ascending order. The dielectric constant, also known as relative permittivity ($\varepsilon_r$), is a measure of how an electric field affects, and is affected by, a dielectric medium. A higher dielectric constant means the material is better at storing electrical energy in an electric field.

Dielectric Constants of Given Materials

Let's look at the approximate typical values for the dielectric constants of the materials provided:

Arranging in Ascending Order

Ascending order means arranging from the smallest value to the largest value. Based on the approximate dielectric constant values:

1. Silicon Dioxide (D) has the smallest dielectric constant (around 4).
2. Silicon Nitride (A) has the next smallest dielectric constant (around 7).
3. Gallium Arsenide (C) has a larger dielectric constant (around 13).
4. Germanium (B) has the largest dielectric constant (around 16).

Therefore, the ascending order of the materials based on their dielectric constants is:

SiO\(_2\) < Si\(_3\)N\(_4\) < GaAs < Ge

Which corresponds to the order of symbols:

(D), (A), (C), (B)

Analyzing the Options

We compare our derived ascending order (D), (A), (C), (B) with the given options:

• Option 1: (A), (B), (D), (C) - Incorrect
• Option 2: (B), (C), (A), (D) - Incorrect
• Option 3: (C), (D), (B), (A) - Incorrect
• Option 4: (D), (A), (C), (B) - Correct

The arrangement (D), (A), (C), (B) correctly orders the materials from the lowest to the highest dielectric constant.

Revision Table: Dielectric Constants

Additional Information on Dielectric Materials

Dielectric materials are essential in electronics, especially in capacitors and as insulators in semiconductor devices. Their dielectric constant determines how effectively they can store charge and reduce the electric field strength within them.

• Materials with lower dielectric constants (like SiO\(_2\)) are often used as gate dielectrics in transistors, although high-k dielectrics are now common for scaling.
• Materials with higher dielectric constants can store more charge in a smaller area, which is useful for reducing the size of components like capacitors.
• The dielectric constant is a dimensionless quantity, defined as the ratio of the permittivity of the substance ($\varepsilon$) to the permittivity of free space ($\varepsilon_0$). $\varepsilon_r = \varepsilon / \varepsilon_0$.
• The dielectric constant can vary slightly depending on factors like frequency, temperature, and the specific process used to manufacture the material. The values used above are common approximations.