Basic Quantum Transport Question

In summary, the conversation discusses confusion over the use of units in the book "Quantum Transport: Atom to Transistor" by Datta. The author provides MATLAB files for calculating current in nanotransistors, but there is discrepancy between the units used in the book and in the code. The author uses energy in units of electron volts, while everything else is in SI units. This is resolved by multiplying an extra factor of q when converting back to Joules.
  • #1
carbon9
46
0
Hi dears,

I'm following the book of Datta named "Quantum Transport: Atom to Transistor". But just at the beginning, I'm confused a bit;)

In the book, at chapter 1, there are some equations given for the current in nanotransistors, for example, an equation for a system with density of states D(E) sandwiched between contacts having Fermi functions f1(E) and f2(E) is given by shown in the attachement.

In order to make some calculations, author have given MATLAB files to calculate these formulas. In all of the formulas, current is calculated as:

for iV=1:IV
mu1=ep+VV(iV);
mu2=mu1;
f1=1./(1+exp((E-mu1)/kT1));
f2=1./(1+exp((E-mu2)/kT2));
D=(g./(2*pi))./(((E-ep).^2)+((g./2).^2));
D=D./(dE*sum(D));
I(iV)=dE*2*I0*(sum(D.*(f1-f2).*g1.*g2./g));
end

where

hbar=1.055e-34;
q=1.602e-19;
I0=q*q/hbar;

So, as I understand, he calculates the formula in MATLAB as if the multiply factor of the formula is q^2/hbar not q/hbar. But in the book, all current formulas have q/hbar in front of them.

Could you please give any idea on this?

With regards,
 

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  • #2
In his MATLAB codes he likes to use energy in units of electron volts [ eV ]

And he sweeps the energy values while calculating current, but since everything else is in SI units, he needs to convert back to Joules which is simply done by multiplying by an extra factor of q.
 
  • #3


Hi [Name], thank you for your question. It is common for scientists and researchers to use different units or constants in their calculations, which can lead to confusion when comparing results. In this case, it appears that the author of the book has used a different definition for the current formula, which includes an extra factor of q/hbar compared to the standard definition. This may be due to a convention in the field or a specific choice made by the author for their calculations. It is important to carefully check the units and constants used in any formula to ensure accurate results. If you are still unsure, I would suggest reaching out to the author or consulting with other experts in the field for clarification. Best of luck with your studies. Regards,
 

1. What is quantum transport?

Quantum transport is the study of how particles, such as electrons, move through materials at the quantum level. It involves understanding the behavior of these particles and how they interact with each other and their environment.

2. How is quantum transport different from classical transport?

Quantum transport differs from classical transport in that it takes into account the principles of quantum mechanics, which govern the behavior of particles at the atomic and subatomic level. This leads to different behaviors and properties than those observed in classical systems.

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

Quantum transport has many real-world applications, including in the development of advanced electronics and computing technologies, such as quantum computers. It is also important in understanding the behavior of materials used in renewable energy technologies, such as solar cells and batteries.

4. How is quantum transport studied?

Quantum transport is studied through a combination of theoretical models and experimental techniques. Theoretical models use equations and simulations to predict the behavior of particles, while experiments involve directly observing and measuring the behavior of particles in different materials and environments.

5. What are some challenges in studying quantum transport?

One of the main challenges in studying quantum transport is the complexity of the systems involved. Understanding the behavior of particles at the quantum level requires advanced mathematical and computational techniques. Additionally, the delicate nature of quantum systems makes them difficult to observe and measure accurately.

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