What is the value of N in the CBH model for electrical conductivity?

[r.sahebi]

what is the value of "N" ?

Hi to everyone
in the following equation (electrical conductivity in correlated barrier hopping (CBH) model), N is the density of localized states..
I read these matter in some papers but anyone has reported a value for it.
how i must determine this value?

σ_ac=((π^2 N^2 ε^*)/24) [(8e^2)/(ε^* W_M )]^6 (ω^s/τ^β )

ε^*=ε_1+iε_2
ε^* is complex dielectric constant
ε_1 and ε_2 are the real and imaginary parts of the complex dielectric constant, respectively.
W_M is the maximum barrier height of the material under investigation
τ is the effective relaxation time and the exponent s is related to W_M at low temperature by the relation:

s=1-β=1-(6k_BT/W_M)

k_B is is Boltzmann's constant.

 

[Simon Bridge]

Density of states is either measured or determined theoretically from the (usually approximate) geometry of the system.

i.e. if dN is the number of states between energies E and E+dE, then the density of states is n(E)=dN/dE

 

[r.sahebi]

Hi Mr Simon Bridge
this is an experimental work
we use a LCR meter to find the conductivity that may be obey from the CBH equation

the values of ε and ω are clear but we don't know anything about the value of N

How can i use your suggested relation?

Thanks

 

[Simon Bridge]

What is the aim of the experiment?

Just checking:

σ_ac=((π^2 N^2 ε^*)/24) [(8e^2)/(ε^* W_M )]^6 (ω^s/τ^β )

... would be: $$\sigma_{ac}=\frac{\pi^2N^2\varepsilon^\star}{24}\left( \varepsilon^\star W_{\! M} \right)^6\frac{\omega^s}{\tau^\beta}$$

The density of states would normally be determined by the model you are using - which is normally based on some assumed geometry for the particular whatsit you are testing. The details should be in your notes.

 

[r.sahebi]

AC electrical characterization

what did you type (Math Processing Error) ?

 

[Simon Bridge]

"AC electrical characterization "?
Seriously - that is what you've got under "Aim:"??
That's not an aim. When you have finished the experiment and the calculations, you should know something specific about the thing you did the experiment on. It is something the experiment is designed to help you find out. That's the aim. You should be able to write it out in 1-2 sentences.

If you don't know the aim of the experiment, then you cannot hope to complete it well.

note: I'm not getting any errors - hit the "quote" button under a post to see the raw text.

 

[r.sahebi]

we want to characterize an organic semiconductor material (synthesized in our laboratory for first time). we study DC and AC electrical and optical properties of this material...

one of my friends referred me to an article of Dr Saleh from Al-Quds University.
now i can complete my calculation

Only with respect to conductivity and "s" equations, in the calculations, we have two unknown parameters: N and Ï„.

an equation for calculating the amount of Ï„ is mentioned in the paper of Dr Saleh.

Dear Mr Simon Bridge,
I thank you sincerely foryour guidance

 

[Simon Bridge]

You still sound like you don't know what the aim of the experiment is.
Now I'm having a bit of trouble about the level this experiment is being conducted at - characterizing a new material would normally by post-grad or at least honors level undergrad in NZ, but you are writing (excuse me) as if you are an undergrad new to the whole "how to write experiments" stuff.

When you design an experiment, or a series of them as you have, you should be able to write down a short statement of the aim(s) of the experiment. "Measure AC properties" is not specific enough. In a paper abstract, you can get away with saying "we characterized the organic semiconductor..." but you to be able to say what you used for the characterization.

But I'll give you an example - I once had to model a semiconductor (then new InAs/GaSb heterojunction fyi). This involved working out the density of states. (The actual experiment involved obtaining a V-I curve for the semiconductor at very low temperatures - the analysis compared with the model.)

The material sample was a flat square ... it's sides very much bigger than it's thickness, putting thickness in z, I used a self-consistent calculation to figure out the energy levels in the z-direction while modelling the x-y direction states as an infinite square well.

This is what I mean about using the geometry to model the density of states.
The exact approach will be different for different materials so I cannot just give you an equation.

Aside: if you want to reference a paper here, you need to cite it or it's useless.
i.e. do you mean Prof. Abdelkarim Saleh?
He's done a lot of work with ZnPc films.

Which paper by Dr Saleh?
He's written lots.

 

[r.sahebi]

i just say thank you Mr Bridge
I've found the answer to my question

 

[Simon Bridge]

Well done - perhaps you can post the answer and so help someopne else who is stuck in the same place.
Cheers, and Merry Xmas.

 

[r.sahebi]

σ_ac=σ_tot-σ_dc
-------------------
in CBH model
σ_ac=((π^2 N^2 ε^*)/24) [(8e^2)/(ε^* W_M )]^6 (ω^s/τ^β )
s=1-β=1-(6k_BT/W_M)
------------------------------------------------------------------
slope of Ln(σ) vs. ω plot give us the value of "s"
slope of s vs. T plot give us the value of W_M

we must calculate the value of "Ï„"( using an equation that mentioned in the following paper:
Saleh, A. M., et al. "Dielectric response and electric properties of organic semiconducting phthalocyanine thin films." Journal of Semiconductors 33.8 (2012): 082002.
you can download this paper (it is free))

intercept of Ln(σ) vs. ω plot give us the value of "N"
------------------------------------------------------------------------------------------
Merry Xmas

 

[Simon Bridge]

Cool - well done.
[note: post #2 sentence 1 option 1 ;) ]