I-V curve wouldn't converge at larger bias

[perfetti]

Dear all,
       I am trying to calculate the conductance of a two probe device, and I have optimized the distance between the electrode and the central part. Then I throw it to I-V curve calculation. However, The scf loop would only converge for the first two voltage biases as 0V, and 0.5 V, and it wouldn't converge  for the following 1 V and larger bias.
       I am not sure if my setting was wrong, or if there's a possible solution for this? Could I just use the two points of 0V and 0.5V, and get a conductance?
       Any advice would be appreciated.    
       Best regards.

[Anders Blom]

In general it can be expected that convergence is more difficult at higher bias, and the system is more sensitive to proper parameter settings in non-equilibrium. Usually you don't have too worry too much about it until you reach 2-3 V, however. But it's very important to apply the technique of boot-strapping the finite bias calculation from the converged state at lower bias (climb in bias). See http://quantumwise.com/publications/tutorials/mini-tutorials/98. In case you do, perhaps you need climb in smaller step (like 0.1 V).

In principle the zero-bias conductance is defined already by the zero-bias result, but after that the whole point of the exercise is that the conductance is bias-dependent, so you don't have much choice but to converge it. However, points spaced by 0.5 V of course doesn't give a very accurate estimate of the slope of the I-V curve, i.e. the conductance, so you may under any circumstance need to take smaller steps.

[perfetti]

Thanks Dr. Blom.
     I saw in literature they got an I-V curve with the bias voltage range from 0 to 2V, however, they calculate the conductance via averaging the data below 0.1V. seehttp://apl.aip.org/resource/1/applab/v96/i10/p102108_s1?view=fulltext.
     I am not sure what should I do? Should I just use a smaller range, like from 0 to 0.5V, and averaging the data below 0.1 V? Or should I mount the whole voltage range from 0 to 2 V via 0.1V steps? It would seem to be a great amount of work. But on the other hand, I saw in all the literature they plot I-V curve from 0-2V.
     Thanks.
     

In general it can be expected that convergence is more difficult at higher bias, and the system is more sensitive to proper parameter settings in non-equilibrium. Usually you don't have too worry too much about it until you reach 2-3 V, however. But it's very important to apply the technique of boot-strapping the finite bias calculation from the converged state at lower bias (climb in bias). See http://quantumwise.com/publications/tutorials/mini-tutorials/98. In case you do, perhaps you need climb in smaller step (like 0.1 V).

In principle the zero-bias conductance is defined already by the zero-bias result, but after that the whole point of the exercise is that the conductance is bias-dependent, so you don't have much choice but to converge it. However, points spaced by 0.5 V of course doesn't give a very accurate estimate of the slope of the I-V curve, i.e. the conductance, so you may under any circumstance need to take smaller steps.

[Anders Blom]

When it comes to these things one really has to get the basic definitions of what you want right, since that influences how you obtain it. If you are looking for the zero-bias conductance, you really only need the zero-bias calculation. But of course in many situation that value is different from what you get by approximating a numerical derivative by doing a small-bias calculation, simply because the conductance is bias-dependent (and, even at 0.1 V you don't get a very good approximation of the derivative). Also, are you looking for the differential conductance (dI/dV) or the conductance (rarely used, but formally I/V). As mentioned, the concepts and expectations need to be defined.

[perfetti]

Dear Dr. Blom,
        I am looking for the conductance I/V.
        So do I need to calculate the I-V curve from 0 - 2V with a 0.1V step?
 
       

When it comes to these things one really has to get the basic definitions of what you want right, since that influences how you obtain it. If you are looking for the zero-bias conductance, you really only need the zero-bias calculation. But of course in many situation that value is different from what you get by approximating a numerical derivative by doing a small-bias calculation, simply because the conductance is bias-dependent (and, even at 0.1 V you don't get a very good approximation of the derivative). Also, are you looking for the differential conductance (dI/dV) or the conductance (rarely used, but formally I/V). As mentioned, the concepts and expectations need to be defined.

[Anders Blom]

If you want I/V then you need to compute I, for the particular V, pretty simple. But the conductance will depend on V.

[perfetti]

Sorry, Dr. Blom. I didn't make it clear.
If I want to plot the I-V curve in the range 0-2V, what should I do?
Should I use a 0.1V step and climbing up?

If you want I/V then you need to compute I, for the particular V, pretty simple. But the conductance will depend on V.

[Anders Blom]

Basically yes. I can't promise it will converge better, but it increases the probability.