Unit of plank constant in the calculation of tunneling probability

In summary, the conversation discusses the use of the WKB approximation to calculate the band-to-band probability. The formula used takes into account various parameters such as lambda, the Plank constant, and bandgap. The question is raised about which unit of the Plank constant is used - J-s or eV-s. Despite the change in relevant length scale or bandgap, the probability remains almost unchanged.
  • #1
Flyyoung
2
0
I'm calculating the band-to-band probability using the WKB approximation given by T=exp(-4*lamda*sqrt(2*m*Eg^1.5)/(3*q*hbar*(deltaPhi+Eg))). I am wondering which unit of the plank constant is used here? The one in J-s which is 6.62e-34 or in eV-s which is 4.13e-15? However, the former one results in 0 and the latter gives 1, and the change of lamda (the relevant length scale) or deltaPhi or Eg doesn't really make an impact on the probability. Why is this?

Many thanks!
 
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  • #2
Actually (q*hbar) gives 1.05e-34, however, still it doesn't give any clue why the probability is almost insensitive to the change of deltaPhi/relevant length scale/bandgap :( Anyone can help please?
 

Related to Unit of plank constant in the calculation of tunneling probability

1. What is the unit of plank constant in the calculation of tunneling probability?

The unit of plank constant in the calculation of tunneling probability is Joule second (J·s) or electronvolt second (eV·s).

2. How is the plank constant used in the calculation of tunneling probability?

The plank constant is used in the calculation of tunneling probability through the equation P = A e-2G, where P is the tunneling probability, A is a constant, and G is the energy barrier which is affected by the plank constant.

3. Why is the plank constant important in tunneling probability calculations?

The plank constant is important in tunneling probability calculations because it is a fundamental constant in quantum mechanics that relates the energy of a particle to its wavelength. In tunneling, the plank constant is used to determine the probability of a particle tunneling through a potential barrier.

4. How does the value of the plank constant affect the calculation of tunneling probability?

The value of the plank constant directly affects the calculation of tunneling probability as it determines the energy of the particle and the width of the potential barrier. A higher value of the plank constant leads to a higher energy and a thinner potential barrier, resulting in a higher probability of tunneling.

5. Are there any alternative methods for calculating tunneling probability without using the plank constant?

There are alternative methods for calculating tunneling probability, such as the WKB approximation, which does not require the use of the plank constant. However, the plank constant is a fundamental constant in quantum mechanics and is essential in accurately predicting tunneling behavior.

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