Class Notes Physics (PHY113)

Unit 5
Solid State Physics

Free Electron Theories of Solids

, Introduction
Sample: (copper, silicon, glass, or such)
If a voltage V is applied across a sample, a current i
proportional to it will flow:
𝑽 = 𝑹𝒊 (𝟏)
Where 𝑹 is a proportionality constant, called
resistance of the sample.
The fact that there is a potential difference V
across the sample means that there is an electric
field 𝑬 in the sample. If the sample is uniform in
geometry and quality, 𝑬 will be constant, and it
follows that 𝒃
𝑽𝒂𝒃 = 𝑽 = 𝑬 𝒅𝒙 = 𝑬𝒅 (𝟐)
𝒂
Where 𝒅 is the length of the sample.
The current density 𝑱, can be defined as the current per unit cross-sectional area
(𝑨), 𝒊
𝑱= (3)
𝑨
𝑨
From (1), (2), and (3), we get: 𝑬𝒅 = 𝑹𝑨𝑱 → 𝑬 = 𝑹 𝒅 𝑱 = 𝝆𝑱 (𝟒)
Where, 𝝆 is called electrical resistivity of the sample 𝑱 = 𝝈𝑬 (𝟓)
Where,𝝈 is called conductivity and 𝝈= 1/ 𝝆 .

, Introduction
Electrical resistivity, 𝝆, and electrical conductivity, 𝝈, are both quantities
characteristic of the material and independent of the geometry of the sample.




One of the reasons that the electrical
properties of solids are so interesting
and have drawn so much attention can
be found by looking at Table 1, which
lists the electrical conductivity of
example materials at room temperature.