How Fast Do Electrons Drift in a Silicon Resistor?

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SUMMARY

The discussion centers on calculating the drift velocity of electrons in a silicon resistor at 300 Kelvin, with specific dimensions (100μm long, 1μm thick, 5μm wide) and a conductivity of 7.128 Ωcm. The resistance is noted as 28058Ω with a voltage of 5V applied. The relevant formulas include Jn,drift = qn(μnE) and I = nqvdA, where n is the electron concentration (1.01x103), μn is the electron mobility (1350 cm2/Vsec), and the electric field E must be derived from the voltage and resistor dimensions.

PREREQUISITES
  • Understanding of semiconductor physics, particularly drift and diffusion currents.
  • Familiarity with the concepts of electric field and mobility in semiconductors.
  • Knowledge of basic electrical engineering principles, including Ohm's law.
  • Proficiency in using formulas related to current density and drift velocity.
NEXT STEPS
  • Calculate the electric field (E) in the resistor using E = V/L, where V is the voltage and L is the length of the resistor.
  • Explore the relationship between drift velocity (vd) and current density (Jn) in semiconductors.
  • Investigate the effects of temperature on electron mobility (μn) in silicon.
  • Learn about the role of hole mobility (μp) and its impact on overall conductivity in semiconductors.
USEFUL FOR

This discussion is beneficial for electrical engineers, semiconductor physicists, and students studying electronics who are interested in understanding electron behavior in silicon resistors and related calculations.

de1337ed
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Problem:

An Si resistor is at 300Kelvin, and is 100μm long, 1μm thick, 5μm wide. The conductivity is 7.128 Ωcm. The resistance is 28058Ω. A voltage of 5v is applied. What is the drift velocity of the electrons, given that n = 1.01x103?
Other constants:
μn = 1350 cm2/Vsec
μp = 450 cm2/Vsec
---
My work:
So basically,
I have the formula Jn,drift = qn(μnE).
The question asks for drift velocity, does that mean I'm trying to find Jn,drift or just the mobility factor μnE? What exactly is Jn,drift? In either scenario, how do I find E field if I'm only given a voltage? It's not like I can integrate b/c Voltage is constant through the resistor.
I was also considering using I = nqvdA. But I was getting some outrageous velocity with this.
Ideas?
Thank you.
 
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de1337ed said:
Problem:

An Si resistor is at 300Kelvin, and is 100μm long, 1μm thick, 5μm wide. The conductivity is 7.128 Ωcm. The resistance is 28058Ω. A voltage of 5v is applied. What is the drift velocity of the electrons, given that n = 1.01x103?
Other constants:
μn = 1350 cm2/Vsec
μp = 450 cm2/Vsec
---
My work:
So basically,
I have the formula Jn,drift = qn(μnE).
The question asks for drift velocity, does that mean I'm trying to find Jn,drift or just the mobility factor μnE? What exactly is Jn,drift? In either scenario, how do I find E field if I'm only given a voltage? It's not like I can integrate b/c Voltage is constant through the resistor.
I was also considering using I = nqvdA. But I was getting some outrageous velocity with this.
Ideas?
Thank you.

Jn,drift is probably the drift current of negative carriers (electrons). In a semiconductor you may have also drift current of holes as well as diffusion currents of both types of carriers.
 

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