Probability of quantum tunneling?

In summary, the conversation discusses the calculation of probability for electron quantum tunneling through an insulator, the practicality of observing this phenomenon, and the size and electricity flow of MIM and MIIM diodes. It also touches on the role of oxidation in electron flow and the possibility of non-oxidized atoms allowing for current flow without quantum tunneling.
  • #1
Dembara
24
1
As simply as possible, could someone try to explain how one would go about calculating the probability of a electron/(electric voltage) quantum tunneling through an insulator (preferably using an example please)?
And how small would the insulator, and how large would the current/voltage have to be for it to be a practical to observe that tunneling took place, and how much would you expect to observe?

Also, as a bit of a side not, how small is the insulator generally in a MIM diode? and what about in a MIIM diode? and how much electricity goes through each of them, and how quickly?
 
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  • #2
Anyone know?
 
  • #3
Dembara said:
Anyone know?
Please be patient. You can't expect a reply 25 mins after posting.
 
  • #4
StevieTNZ said:
Please be patient. You can't expect a reply 25 mins after posting.
I meant it as is it common knowledge, estimates, incredibly variant or something else? (also I wanted to get my post to the top of the forum :P, which I now realize is not allowed, sorry for that)
Though I think (after looking through some other stuff) you can calculate the probability with the Schrodinger equation, it would still be nice if someone could present a brief example please.
 
  • #5
Not sure exactly what you want to know, but for a free electron of energy E, hitting a rectangular potential barrier ## V_0 ## of width a, the tunneling amplitude is,
## \frac{1}{T} = 1+\frac{k^2+q^2}{2kq} \sinh^2(qa)##
where ## q=\sqrt{\frac{2m}{\hbar^2} (E-V_0)} ##
and ## k =\sqrt{\frac{2m}{\hbar^2} \ E} ##

You can just plug in numbers yourself to see various situations if you want.
As an side note: I was told by a professor that since all exposed wires quickly have an insulating oxide layer forming around them, that the only way electrons go between touching wires is via tunneling.
 
  • #6
DelcrossA said:
Not sure exactly what you want to know, but for a free electron of energy E, hitting a rectangular potential barrier ## V_0 ## of width a, the tunneling amplitude is,
## \frac{1}{T} = 1+\frac{k^2+q^2}{2kq} \sinh^2(qa)##
where ## q=\sqrt{\frac{2m}{\hbar^2} (E-V_0)} ##
and ## k =\sqrt{\frac{2m}{\hbar^2} \ E} ##

You can just plug in numbers yourself to see various situations if you want.
As an side note: I was told by a professor that since all exposed wires quickly have an insulating oxide layer forming around them, that the only way electrons go between touching wires is via tunneling.

Okay, thank you, I'll try it out.
Also, I may be completely wrong here but anyway, doesn't oxidation require rogue oxidizer molecule/atom, so wouldn't it be highly improbably every atom/molecule of the conductor immediately oxidized (though it would attract any rouge oxidizers)? And couldn't the oxidized state still be (at least somewhat) conductive (though obviously not as conductive, not necessarily an insulator right)?
Though due to the way things interact in general, referring to how things don't touch due to virtual photons, could you consider that to always cause things to need to quantum tunnel?And do you have any idea about MIM (metal-insulator-metal) diodes?
 
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  • #7
Dembara said:
Okay, thank you, I'll try it out.
Also, I may be completely wrong here but anyway, doesn't oxidation require rogue oxidizer molecule/atom, so wouldn't it be highly improbably ever atom/molecule of the conductor immediately oxidized? And couldn't the oxidized state still be (at least somewhat) conductive?

Not every copper atom, just those exposed on the surface to oxygen ("the only way" is really just figurative if your being technical). And, most oxides are pretty poor conductors at normal temperatures. Though I do know that some oxides are being incorporated into alloys to make superconductors - but that's only for temperatures around the boiling point of liquid nitrogen.
 
  • #8
DelcrossA said:
Not every copper atom, just those exposed on the surface to oxygen ("the only way" is really just figurative if your being technical). And, most oxides are pretty poor conductors at normal temperatures. Though I do know that some oxides are being incorporated into alloys to make superconductors - but that's only for temperatures around the boiling point of liquid nitrogen.
By every atom, I was referring to every atom at the surface, I just worded it poorly. but don't you still need the rouge oxidizers? Oxygen won't always oxidize a substance, isn't it like 1/1000 or something like that?
 
  • #9
Dembara said:
By every atom, I was referring to every atom at the surface, I just worded it poorly. but don't you still need the rouge oxidizers? Oxygen won't always oxidize a substance, isn't it like 1/1000 or something like that?

I really don't know. But, I wouldn't think 1/1000 is really that improbable considering how many atoms were talking about. Moreover, only the point of contact needs to have a small layer of oxide for what we're discussing.
 
  • #10
DelcrossA said:
I really don't know. But, I wouldn't think 1/1000 is really that improbable considering how many atoms were talking about. Moreover, only the point of contact needs to have a small layer of oxide for what we're discussing.
That is completely correct, as the source that told my that number (I can't remember were it was, but it gave a number that was in the 1/1000 range) but I would still think that some of the atoms wouldn't immediately oxidize (its not as though they are touching 5000 more times more atoms, since oxygen makes up approximately 1/5 of the troposphere), and all you would need it one atom not to be oxidized (that touches another none oxidized atom) to get a current able to pass through without quantum tunneling.

Also, I would like to point out this is getting a weee bit off topic, and is starting to be more relevant to chemistry.
 

FAQ: Probability of quantum tunneling?

1. What is the concept of probability of quantum tunneling?

The probability of quantum tunneling refers to the likelihood of a quantum particle passing through a potential energy barrier that it does not have enough energy to surmount. This phenomenon is possible due to the probabilistic nature of quantum mechanics, where particles can exist in multiple states simultaneously and have a non-zero chance of "tunneling" through a barrier.

2. How is the probability of quantum tunneling calculated?

The calculation of the probability of quantum tunneling depends on the specific system and potential energy barrier involved. In general, it involves solving the Schrödinger equation and analyzing the wave functions of the particle on either side of the barrier. The resulting probability is typically very small, but can be increased by decreasing the width or height of the barrier or increasing the energy of the particle.

3. What are some real-world applications of quantum tunneling?

Quantum tunneling has several practical applications, including in electronic devices like transistors and flash memory. It is also crucial in understanding nuclear reactions, such as radioactive decay, and plays a role in chemical reactions and the functioning of enzymes in biological systems.

4. Can the probability of quantum tunneling be controlled or manipulated?

In most cases, the probability of quantum tunneling is a natural phenomenon that cannot be directly controlled or manipulated. However, scientists have been able to engineer materials and structures to alter the potential energy barriers and thus increase or decrease the probability of quantum tunneling in certain scenarios.

5. Are there any limitations to the concept of probability of quantum tunneling?

While the probability of quantum tunneling has been observed and studied extensively, it is still a topic of ongoing research and there are limitations to our understanding of it. For example, the exact mechanisms behind why certain particles are able to tunnel through barriers while others cannot are still not fully understood. Additionally, the concept of quantum tunneling is only applicable at the quantum level and does not hold true in classical physics.

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