Calculating Electric Field from Electron Drift and Diffusion in Si Sample"

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SUMMARY

The discussion focuses on calculating the electric field in a silicon (Si) sample based on electron drift and diffusion. The electron concentration is defined as n(x) = 5 * 10^16 cm^-3 * exp(-x^3/2 * 10^-8), with a temperature of 300K and electron mobility of 1300 cm^2/V*s. The total electron current density, Jn, is expressed through the equation Jn = e * n(x) * un * Ex + e * Dn * du/dx. Evaluations of the electric field at x = 10 * 10^-4 for current densities of 15 A/cm^2 and 0 A/cm^2 are also discussed.

PREREQUISITES
  • Understanding of semiconductor physics, particularly silicon behavior.
  • Familiarity with electron mobility and its impact on current density.
  • Knowledge of the drift and diffusion components of current density.
  • Proficiency in using exponential functions in physical equations.
NEXT STEPS
  • Study the derivation of the electron current density equation Jn = e * n(x) * un * Ex + e * Dn * du/dx.
  • Learn about the impact of temperature on electron mobility in semiconductors.
  • Explore methods for calculating electric fields in semiconductor materials.
  • Investigate the effects of varying electron concentrations on current density in silicon.
USEFUL FOR

This discussion is beneficial for students and professionals in electrical engineering, particularly those focusing on semiconductor physics and device design. It is also useful for researchers analyzing electron transport phenomena in silicon materials.

orangeincup
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Homework Statement


A sample of Si, in which 0<=x<=(25*10^-4), electron concentration is n(x)=5*10^16 cm^-3) * exp(-x^3/2*10^-8), temperature is 300k and electron mobility is 1300 cm^2/V*s. The electron current through the Si has both drift and diffusion components and total electron current density through the sample is independent of x.

Find an expression for the electric field as a function of electron current density.
Evaluate the electric field at 10*10^-4 if the electron current density is 15 A/cm^2.
Evaluate the electric field at 10*10^-4 if the electron current density is 0 A/cm^2.

Homework Equations


Jn=e*n(x)*un*Ex+e*Dn*du/dx
Jn=pvd
Jn=(ep)vdp

The Attempt at a Solution


For the first part, I think I know how to solve if I can calculate Jn, since I have all the other values except Jn and Ex(which I need to solve for). Is there an equation which let's me solve for Jn with the values I have? Is there a constant I'm missing?
 
Yeah I solved it, thanks
 

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