Calculate the maximum space charge width for a given semiconductor doping concentration.

Consider silicon at $T=300 \mathrm{~K}$ doped to $N_{a}=10^{16} \mathrm{~cm}^{-3}$ . The intrinsic carrier concentration is $n_{i}=1.5 \times 10^{10} \mathrm{~cm}^{-3}$ .

Question

Calculate the maximum space charge width for a given semiconductor doping concentration.

Consider silicon at [latex]T=300 \mathrm{~K}[/latex] doped to [latex]N_{a}=10^{16} \mathrm{~cm}^{-3}[/latex]. The intrinsic carrier concentration is [latex]n_{i}=1.5 imes 10^{10} \mathrm{~cm}^{-3}[/latex].

Accepted Answer

From Equation (10.4), we have

[latex]\phi_{f p}=V_{t} \ln \left(\frac{N_{a}}{n_{i}} ight)[/latex] (10.4)

[latex]\phi_{f p}=V_{t} \ln \left(\frac{N_{a}}{n_{i}} ight)=(0.0259) \ln \left(\frac{10^{16}}{1.5 imes 10^{10}} ight)=0.3473 \mathrm{~V}[/latex]

Then the maximum space charge width is

[latex]x_{d T}=\left[\frac{4 \epsilon_{s} \phi_{f p}}{e N_{a}} ight]^{1 / 2}=\left[\frac{4(11.7)\left(8.85 imes 10^{-14} ight)(0.3473)}{\left(1.6 imes 10^{-19} ight)\left(10^{16} ight)} ight]^{1 / 2}[/latex]

or

[latex]x_{d T} \cong 0.30 imes 10^{-4} \mathrm{~cm}=0.30 \mu \mathrm{m}[/latex]

Comment

The maximum induced space charge width is on the same order of magnitude as pn junction space charge widths.

Question 10.1: Calculate the maximum space charge width for a given semicon...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions