Homework in Solid state material

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SUMMARY

The discussion focuses on calculating the electric field near a depth of 500nm in silicon, where the electron concentration varies linearly from 5x1015 cm-3 at the surface (x=0) to 1015 cm-3 at x=500nm. The vertical electron current density is constant at Jn=100 A/cm2, and the mobility is given as 1250 cm2/Vs. The relevant equation for total electron current density is Jn = q Dn (dn/dx) + q μn E, where q is the charge of an electron (1.6E-19 C) and Dn is approximately 0.026 μn at room temperature.

PREREQUISITES
  • Understanding of semiconductor physics, particularly silicon properties
  • Familiarity with electron mobility and current density concepts
  • Knowledge of the relationship between drift and diffusion currents
  • Basic proficiency in calculus for differentiation (dn/dx)
NEXT STEPS
  • Study the derivation and application of the equation Jn = q Dn (dn/dx) + q μn E
  • Explore the concept of electron mobility in semiconductors and its temperature dependence
  • Learn about the diffusion coefficient Dn and its calculation in semiconductor materials
  • Investigate the effects of electric fields on charge carrier behavior in silicon
USEFUL FOR

This discussion is beneficial for electrical engineers, semiconductor physicists, and students studying solid-state materials, particularly those interested in charge transport phenomena in silicon.

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Here is the problem:

The electron concentration in a region of silicon depends linearly on depth with concentration of 5x10^15 cm^-3 at surface (x=0) and 10^15 cm^-3 at depth of x=500nm. If the vertical electron current density in this region is constant at Jn=100 A/cm^2, calculate the electric field near x=500nm. assume that the mobility is constant at 1250cm^2/Vs.

If anyone can at least explain the meaning of each value written in the problem and the formula that can be used to solve this problem ..

Thank you...
 
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The equation that you need is for the total electron current density (drift plus diffusion).

J_n = q D_n \frac{dn}{dx} + q \mu_n E

q = 1.6E-19

D_n = (kT/q) u_n which is approx 0.026 u_n at room temperature.

Since you know J_n and dn/dx then E is the only unknown.
 

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