Boltzmann transport equation & drift-diffusion equation ~ Please help me

In summary, the Boltzmann transport equation is a mathematical model used to describe the behavior of particles in a medium, taking into account factors like collisions and external fields. It differs from the drift-diffusion equation, which is a simpler model that only considers overall particle movement. Both equations have various applications, particularly in semiconductor physics, but also have limitations and make certain assumptions about particle behavior. Careful consideration of these assumptions and conditions is necessary when applying these equations.
  • #1
minywall1
1
0
Boltzmann transport equation & drift-diffusion equation ~ Plz help me!

1.
From the Boltzmann transport equation,
derive the energy conservation equation for mass conserving particles.
Use the momentum equation to subtract the mechanical energy component,
and then derive the equation for thermal energy conservation.


2.
Assuming the local thermodynamic equilibrium (i.e. df/dx = dfo/dx)
derive the drift-diffusion equation for charge flow.
 
Physics news on Phys.org
  • #2


Derivation is really easy, you only need some vector calculus identities. However, the full thing is
here.
 

1. What is the Boltzmann transport equation?

The Boltzmann transport equation is a mathematical model that describes the behavior of particles in a medium, such as electrons in a semiconductor. It takes into account factors like collisions and external fields to determine the distribution of particles over time and space.

2. How is the Boltzmann transport equation different from the drift-diffusion equation?

The Boltzmann transport equation is a more comprehensive model that considers individual particle behavior, while the drift-diffusion equation is a simpler macroscopic model that describes the overall movement of particles in a medium.

3. What are the main applications of the Boltzmann transport equation and drift-diffusion equation?

These equations are commonly used in the field of semiconductor physics to understand and predict the behavior of electrons and holes in devices such as transistors and solar cells. They are also used in other areas of physics, such as plasma physics and gas dynamics.

4. What are the assumptions made in the Boltzmann transport equation and drift-diffusion equation?

The Boltzmann transport equation assumes that particles move freely between collisions, while the drift-diffusion equation assumes that particles move randomly and are affected by an average electric field. Both equations also assume that the particles are in thermal equilibrium.

5. Are there any limitations of the Boltzmann transport equation and drift-diffusion equation?

Yes, both equations have limitations in certain scenarios. For example, the Boltzmann transport equation may not accurately describe high-energy particles, and the drift-diffusion equation may not be suitable for systems with strong electric fields or non-uniform distributions of particles. It is important to carefully consider the assumptions and conditions before applying these equations.

Similar threads

A Conservation Laws from Continuity Equations in Fluid Flow
    • Classical Physics
Replies
2
Views
789
Trouble with Galilean transform problem heat equation
    • Advanced Physics Homework Help
Replies
8
Views
2K
A Why are the Navier-Stokes equations inconsistent in this case?
    • Classical Physics
Replies
18
Views
996
I A Bold New Take on Quantum Theory
    • Quantum Interpretations and Foundations
Replies
25
Views
1K
I Particle behavior in Penning trap
    • High Energy, Nuclear, Particle Physics
Replies
13
Views
915
I Stress-energy tensor and energy/momentum conservation clarification
    • Special and General Relativity
Replies
21
Views
2K
I Interpretations of diffusion in Quantum Mechanics.
    • Quantum Interpretations and Foundations
Replies
2
Views
2K
Boltzmann Transport Equation : Hall Effect in the Relaxation Time Approximation
    • Advanced Physics Homework Help
Replies
1
Views
5K
Other Nonequilibrium Thermodynamics Request
    • Science and Math Textbooks
Replies
2
Views
1K
  • Poll
Transport Phenomena by Bird, Stewart, Lightfoot
    • Science and Math Textbooks
Replies
3
Views
6K

Hot Threads

Recent Insights

Back
Top