# Basic Quantum Transport Question

1. Nov 29, 2008

### carbon9

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. Apr 1, 2009

### sokrates

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.