Answer:
[tex]E=1.44*10^-7-2.6exp(\frac{-x}{18} )v/m[/tex]
Explanation:
From the question we are told that:
Temperature of silicon [tex]T=300k[/tex]
Electron concentration [tex]n(x)=10^{16}\exp (\frac{-x}{18})[/tex]
[tex]\frac{dn}{dx}=(10^{16} *(\frac{-1}{16})\exp\frac{-x}{16})[/tex]
Electron diffusion coefficient is [tex]Dn = 25cm^2/s \approx 2.5*10^{-3}[/tex]
Electron mobility is [tex]\mu n = 960 cm^2/V-s \approx0.096m/V[/tex]
Electron current density [tex]Jn = -40 A/cm^2 \approx -40*10^{4}A/m^2[/tex]
Generally the equation for the semiconductor is mathematically given by
[tex]Jn=qb_n\frac{dn}{dx}+nq \mu E[/tex]
Therefore
[tex]-40*10^{4}=1.6*10^{-19} *(2.5*10^{-3})*(10^{16} *(\frac{-1}{16})\exp\frac{-x}{16})+(10^{16}\exp (\frac{-x}{18}))*1.6*10^{-19}*0.096* E[/tex]
[tex]E=\frac{-2.5*10^-^7 exp(\frac{-x}{18})+40*10^{4}}{1.536*10^-4exp(\frac{-x}{18} )}[/tex]
[tex]E=1.44*10^-7-2.6exp(\frac{-x}{18} )v/m[/tex]
