Dear,
In various research papers related to this topic (for example: Article Analytical Surface Potential and Drain Current Models of Dua...
it can be seen that the gate potential is shown with ΨG that is given by:
ΨG=VG - Φ +X+Eg /2q
my first question is about the unit of components in above equation,
VG (in volt) , workfunction Φ (in Volt) , electron affinity X (in volt) and Eg (in eV) ,
1-Is these true?
2-In this way since the unit of workfunction is eV, Is it true to say Φ is negligible in above formula?
The second question:
In short, we can say that the analytical model for surface potential in a DM-DG-TFET can be obtained based on the solution of Poisson equation (the potential at channel-oxide interface), after using parabolic (young) approximation and with the use of boundary conditions, transforms the 2D poissons equation to a 1D where the particular solution of this 1D equation can be expressed as:
Qi=ΨGi +(qNitsi)/(2Cox) i=1,2,3,4
i=1 is related to the depletion region in source and i=4 is related to the depletion region in drain.
3-What is ΨG1 and ΨG4 equation?
4-In Qi is (qNitsi)/(2Cox) negligible against ΨGi ?
Best Regards
How you write your first equation for the potential depends on where you set your reference potential: the only measurable parameters in experiments are voltages, which are potential differences. Hence, the notation V_G with index G as subscript is insufficient - it should always by V_GX where X is your reference. What do you choose for X? Units are OK in your equation, as energy in eV divided by the elementary charge gives V.
Dear Dr. Walther,
Thanks for your reply, yes its true, X is source and it is better to type V_GS but the source potential is zero.
for the following sample values, what is the value of ΨG ?
V_GS=1 volt , Eg=1.1eV , Φ =4.2eV and X=4eV
I looked up the paper you cite, and you omitted a fifth term from their eqn (4), namely
kT/q ln(N_ch/n_i) which describes approximatetively the decrease of the Fermi level from the mid-gap position for the heavily p-doped source. The equation they give is actually correctly describing the difference in the distances of the Fermi-levels in source and gate from the vacuum level in equilibrium after band alignment. None of the terms is negligible, certainly not the work function, phi. Sketch it for a biased pn-junction and you will see!
Yes, its correct, in this way with the below sample values which calculation is true?
V_GS=1 volt , Eg=1.1eV , Φ =4.2eV , X=4eV , KT/q=0.025 , N_ch=1e16 , n_i=1e10
ΨG=VGS - Φ +X+Eg /2q +KT/q ln(N_ch/n_i)=
1-4.2+4+0.55+0.025ln(1e16/1e10)
or
ΨG=VGS - Φ +X+Eg /2q +KT/q ln(N_ch/n_i)=
1-4.2*1.6e-19+4*1.6e-19+0.55+0.025ln(1e16/1e10)
?
Look at the units and you will see that you either have to add all values in V to a voltage or values in eV to get an energy. The energy 1eV you get by multiplying 1V with the electron charge of e=1.6*10^-19C. So your last summation is INCORRECT as you mix values in eV and V.
I want to add all values in V to get voltage.
then
ΨG=VGS - Φ +X+Eg /2q +KT/q ln(N_ch/n_i)=
1 - 4.2 + 4 + 0.55 + 0.025ln(1e16/1e10)= 1.695 V is correct?
In principle yes, but the signs seem wrong: if the source is X+Eg/2q+kT*ln(1e6) below the vacuum level, and the gate is at Φ below vacuum level and has an additional bias of V_GS,
then I would calculate (in volts)
1+4.2 - [4+0.55+0.025ln(1e6)]=0.305 as the new Fermi level of the gate.
Thank you very much, but why the signs in eqn(4) in cited paper are different?
ΨG is the gate potential that is different for the two gates, and is given by
ΨG=VG - Φ +X+Eg /(2q) +Φt ln(Nch/ni) (4)
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