Chapter 29, Problem 38GP

To determine

The shortest wavelength of light that can strike silicon.

Answer to Problem 38GP

The shortest wavelength is $\text{1}\text{.09}\text{μm}$ and also, it could be used as a window.

Explanation of Solution

Given info:

The energy gap, ${\text{E}}_g\text{=1}\text{.14 eV}$

Formula used:

It is known that ${\text{E}}_{\text{g}}\text{=}\frac{\text{hc}}{\text{λ}}$

Where,

  ${\text{E}}_{\text{g}}$ is the energy gap.

  $\lambda$ is wavelength.

  $h$ is Planck’s constant, $6.63\times {10}^{-34}J\cdot s$

  $c$ is speed of light, ${\text{3×10}}^{\text{8}}\text{ m/s }$

Calculation:

To use silicon to filter the wavelengths, wavelengths should be below the IR. Because it causes the electron to be raised to the conduction band.

So, photon is absorbed in silicon.

Now, calculate shortest wavelength from the expression,

  $\text{λ=}\frac{\text{c}}{\text{f}}\text{=}\frac{\text{hc}}{\text{hf}}\text{>}\frac{\text{hc}}{{\text{E}}_{\text{g}}}$

  $\text{=}\frac{\left(\text{1}{\text{.24×10}}^{\text{3}}\text{eV}\cdot \text{nm}\right)}{\left(\text{1}\text{.14}\text{eV}\right)}\text{=1}\text{.09}{\text{Ä10}}^{\text{3}}\text{nm}\text{=}\text{1}\text{.09}\text{μm}$

Therefore, this is in the IR, shorter wavelengths of visible light will excite electron.

So, silicon could be used as a window.

Conclusion:

The required value is $\text{1}\text{.09}\text{μm}$ .