Author Topic: Current calculation comparison with Smeagol  (Read 15061 times)

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Offline carbn9

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Current calculation comparison with Smeagol
« on: December 6, 2008, 18:04 »
Dear ATK users,

First of all, I'm very happy since new versions of ATK will be released by Quantumwise. Thanks.

I addition, I'd like to ask a question that I asked at Smeagol discuss group but could not get a satisfactory answer there:

"
I've just installed Smeagol and tried the Au nanowire example provided by the package. The current calculation is as follows (.CUR file)
 
0.00000000D+00    0.00000000D+00
0.24148777D-01     0.25318921D-04
0.48728283D-01     0.50981350D-04
0.73308789D-01     0.76277083D-04
 
Thus, as I understand, for a bias of 1V, the current is   7.6277083E-05. Is it right?
 
On the other hand, I have made an input file describing the Au nanowire of the example of Smeagol. The input file of ATK for Au nanowire I have created is attached. I have applied a 1V bias to nanowire just as in Smeagol. The output of ATK is also given as attachement. But I get a current value of  3.4018175915e-005 A.  That is lower than the half of the value calculated using Smeagol. Where can this difference come from?
 
Thank you for your interest.
 
Maresh Kubar".

The answer on Smeagol forum was:

"the wire has about 1 quantum of conductance (transmission =1), so that
the current at 1 volt is about

I=1/12900 A = 77 microAmpere

This is approximately what smeagol gives as result. This system is
unphysical anyway, since you can not apply one Volt on such a 1D chain,
it is just an example to test the code. It is therefore probably not the
best system to compare results at finite bias for different codes"


Could you please give an idea on this question?

Regards,
Maresh
« Last Edit: December 7, 2008, 22:24 by admin »

Offline Anders Blom

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Re: Current calculation somparison with Smeagol
« Reply #1 on: December 6, 2008, 20:59 »
Generally speaking, if the system is set up correctly, a perfect 1D system should give integer values of the conductance at each energy, but there are many pitfalls so one needs to check the parameters and geometry carefully.

I could however not find any input file, seems somehow it wasn't attached to the post?
« Last Edit: December 6, 2008, 21:02 by Anders Blom »

Offline carbn9

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Re: Current calculation somparison with Smeagol
« Reply #2 on: December 7, 2008, 09:06 »
Dear Dr. Blom, Thank you for the reply. I'd attached the file after editing the post so I think there occured an error. Here's the code I've used:
Code
from ATK.TwoProbe import *
from ATK.MPI import processIsMaster

# Opening vnlfile
if processIsMaster(): file = VNLFile('D:/Atomistix_works/Au_nanowire/Au_nanowire_c1.vnl')

# Scattering elements and coordinates
scattering_elements = [Gold, Gold, Gold, Gold, 
                       Gold, Gold, Gold, Gold]
scattering_coordinates = [[  6. ,   6. ,   0. ],
                          [  6. ,   6. ,   2.8],
                          [  6. ,   6. ,   5.6],
                          [  6. ,   6. ,   8.4],
                          [  6. ,   6. ,  11.2],
                          [  6. ,   6. ,  14. ],
                          [  6. ,   6. ,  16.8],
                          [  6. ,   6. ,  19.6]]*Angstrom
        

electrode_elements = [Gold, Gold]
electrode_coordinates = [[ 6. ,  6. ,  0. ],
                         [ 6. ,  6. ,  2.8]]*Angstrom

electrode_cell = [[ 12. ,   0. ,   0. ],
                  [  0. ,  12. ,   0. ],
                  [  0. ,   0. ,   5.6]]*Angstrom

# Set up electrodes
electrode_configuration = PeriodicAtomConfiguration(
    electrode_cell,
    electrode_elements,
    electrode_coordinates
    )

# Set up two-probe configuration
twoprobe_configuration = TwoProbeConfiguration(
    (electrode_configuration,electrode_configuration),
    scattering_elements,
    scattering_coordinates,
    electrode_repetitions=[[1,1],[1,1]],
    equivalent_atoms=([0,0],[1,7])
    )
if processIsMaster(): nlPrint(twoprobe_configuration)
if processIsMaster(): file.addToSample(twoprobe_configuration, 'Au_nanowire')

######################################################################
# Central region parameters
######################################################################
exchange_correlation_type = LDA.PZ

iteration_mixing_parameters = iterationMixingParameters(
    algorithm = IterationMixing.Pulay,
    diagonal_mixing_parameter = 0.1,
    quantity = IterationMixing.Hamiltonian,
    history_steps = 6
)

electron_density_parameters = electronDensityParameters(
    mesh_cutoff = 150.0*Rydberg
)

basis_set_parameters = basisSetParameters(
    type = DoubleZetaPolarized,
    radial_sampling_dr = 0.005*Bohr,
    energy_shift = 0.01*Rydberg,
    delta_rinn = 0.8,
    v0 = 40.0*Rydberg,
    charge = 0.0,
    split_norm = 0.15
)

iteration_control_parameters = iterationControlParameters(
    tolerance = 0.0001,
    criterion = IterationControl.Strict,
    max_steps = 1000
)

electrode_voltages = (1.0,0.0)*Volt

two_probe_algorithm_parameters = twoProbeAlgorithmParameters(
    electrode_constraint = ElectrodeConstraints.Off,
    initial_density_type = InitialDensityType.EquivalentBulk
)

energy_contour_integral_parameters = energyContourIntegralParameters(
    circle_points = 30,
    integral_lower_bound = 3*Rydberg,
    fermi_line_points = 10,
    fermi_function_poles = 4,
    real_axis_infinitesimal = 0.01*electronVolt,
    real_axis_point_density = 0.02*electronVolt
)

two_center_integral_parameters = twoCenterIntegralParameters(
    cutoff = 2500.0*Rydberg,
    points = 1024
)

######################################################################
# Homogeneous electrode parameters
######################################################################
homogeneous_electrode_electron_density_parameters = electronDensityParameters(
    mesh_cutoff = 150.0*Rydberg
)

homogeneous_electrode_iteration_control_parameters = iterationControlParameters(
    tolerance = 0.0001,
    criterion = IterationControl.Strict,
    max_steps = 10000
)

homogeneous_electrode_brillouin_zone_integration_parameters = brillouinZoneIntegrationParameters(
    monkhorst_pack_parameters = (1, 1, 100)
)

homogeneous_electrode_iteration_mixing_parameters = iterationMixingParameters(
    algorithm = IterationMixing.Pulay,
    diagonal_mixing_parameter = 0.1,
    quantity = IterationMixing.Hamiltonian,
    history_steps = 6
)

homogeneous_electrode_eigenstate_occupation_parameters = eigenstateOccupationParameters(
    temperature = 300.0*Kelvin
)

######################################################################
# Collect Homogeneous electrode parameters
######################################################################
homogeneous_electrode_parameters = ElectrodeParameters(
    brillouin_zone_integration_parameters = homogeneous_electrode_brillouin_zone_integration_parameters,
    electron_density_parameters = homogeneous_electrode_electron_density_parameters,
    eigenstate_occupation_parameters = homogeneous_electrode_eigenstate_occupation_parameters,
    iteration_mixing_parameters = homogeneous_electrode_iteration_mixing_parameters,
    iteration_control_parameters = homogeneous_electrode_iteration_control_parameters
)



######################################################################
# Initialize self-consistent field calculation
######################################################################
two_probe_method = TwoProbeMethod(
    electrode_parameters = (homogeneous_electrode_parameters,homogeneous_electrode_parameters),
    exchange_correlation_type = exchange_correlation_type,
    iteration_mixing_parameters = iteration_mixing_parameters,
    electron_density_parameters = electron_density_parameters,
    basis_set_parameters = basis_set_parameters,
    iteration_control_parameters = iteration_control_parameters,
    energy_contour_integral_parameters = energy_contour_integral_parameters,
    two_center_integral_parameters = two_center_integral_parameters,
    electrode_voltages = electrode_voltages,
    algorithm_parameters = two_probe_algorithm_parameters
)
if processIsMaster(): nlPrint(two_probe_method)

runtime_parameters = runtimeParameters(
    verbosity_level = 10,
    checkpoint_filename = 'D:/Atomistix_works/Au_nanowire/Au_nanowire.nc'
)

# Perform self-consistent field calculation
scf = executeSelfConsistentCalculation(
    twoprobe_configuration,
    two_probe_method,
    runtime_parameters = runtime_parameters
)

######################################################################
# Calculate physical properties
######################################################################
current = calculateCurrent(
    self_consistent_calculation = scf,
    brillouin_zone_integration_parameters = brillouinZoneIntegrationParameters((1, 1)),
    green_function_infinitesimal = 1.0e-5*electronVolt,
    number_of_points = 100
)
if processIsMaster(): nlPrint(current)

and the output file is
Quote
# ----------------------------------------------------------------------------- # Homogeneous Two Probe Configuration # ----------------------------------------------------------------------------- # Electrode                0      1 Equivalent Atoms      (0, 0) (1, 7) Electrode Repetitions (1, 1) (1, 1) # ----------------------------------------------------------------------------- # Index  Element  x (Ang)  y (Ang)  z (Ang)       0       Au     6.00     6.00     0.00       1       Au     6.00     6.00     2.80       2       Au     6.00     6.00     5.60       3       Au     6.00     6.00     8.40       4       Au     6.00     6.00    11.20       5       Au     6.00     6.00    14.00       6       Au     6.00     6.00    16.80       7       Au     6.00     6.00    19.60 # ----------------------------------------------------------------------------- # Electrodes 0 and 1 # ----------------------------------------------------------------------------- # Index  Element  x (Ang)  y (Ang)  z (Ang)       0       Au     6.00     6.00     0.00       1       Au     6.00     6.00     2.80 # ----------------------------------------------------------------------------- # Supercell Vectors # ----------------------------------------------------------------------------- # Vector number  x (Ang)  y (Ang)  z (Ang)               0    12.00     0.00     0.00               1     0.00    12.00     0.00               2     0.00     0.00     5.60 # ----------------------------------------------------------------------------- # Two Probe Method # ----------------------------------------------------------------------------- # ----------------------------------------------------------------------------- # Basis Set Parameters # ----------------------------------------------------------------------------- Type               = DZP Radial Sampling dr = 0.005 Bohr Energy Shift       = 0.01 Rydberg Delta R(inner)     = 0.8 v0                 = 40 Rydberg Charge             = 0 Split Norm         = 0.15 Element            = All # ----------------------------------------------------------------------------- # Exchange Correlation # ----------------------------------------------------------------------------- Exchange Correlation Type = PZ # ----------------------------------------------------------------------------- # ElectronDensityParameters # ----------------------------------------------------------------------------- Mesh Cutoff         = 150.00 Rydberg # ----------------------------------------------------------------------------- # Two Center Integral Parameters # ----------------------------------------------------------------------------- Cutoff           = 2500.0 Rydberg Number Of Points = 1024 # ----------------------------------------------------------------------------- # Iteration Mixing Parameters # ----------------------------------------------------------------------------- Algorithm                 = Pulay Diagonal Mixing Parameter = 0.1 Quantity                  = Hamiltonian History Steps             = 6 # ----------------------------------------------------------------------------- # Iteration Control Parameters # ----------------------------------------------------------------------------- Tolerance  = 0.0001 Criterion  = Strict Max. Steps = 1000 # ----------------------------------------------------------------------------- # Energy Contour Integral Parameters # ----------------------------------------------------------------------------- Circle Points           = 30 Integral Lower Bound    = 3 Rydberg Fermi Function Poles    = 4 Real Axis Infinitesimal = 0.01 eV Real Axis Point Density = 0.02 eV # ----------------------------------------------------------------------------- # Electrode Voltages # ----------------------------------------------------------------------------- Voltage at Electrode 0 = 1.00 V Voltage at Electrode 1 = 0.00 V # ----------------------------------------------------------------------------- # TwoProbe Algorithm Parameters # ----------------------------------------------------------------------------- Electrode Constraint = ElectrodeConstraints.Off Initial Density Type = ElectrodeConstraints.EquivalentBulk  2.052, d(-2): -0.054, d(-1): -0.076, d(0): -0.039, d(1): -0.076, d(2): -0.054, py:  0.069, pz:  0.387, px:  0.069 ] # ---------------------------------------------------------------- # Total charge = 85.5735 # ---------------------------------------------------------------- %endblock Results::MullikenPopulations # sc 114 : q =   85.57355 e  Ebs =  -12.55344 Ry  dRho = 6.5800E-005  dEbs = 8.4550E-005 Ry  dH = 6.9135E-005 Ry # # SelfConsistent loop : Iteration converged after 114 steps. # 3.4018175915e-005 A Terminated Normally Run finished at  Mon May 17 07:19:20 2008!
Regards, Maresh

Offline Anders Blom

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Re: Current calculation somparison with Smeagol
« Reply #3 on: December 7, 2008, 20:42 »
I can have a closer look at this, but it is immediately obvious from the input that the electrode is much too short. I'll write a bit more later about why, because this is a very important, and perhaps not entirely well document aspect.

But the short story is that you should probably put 4 or 6 gold atoms in the electrode, at minimum, perhaps 8 even. It's quite cheap for such a small system.

I would also increase the central region to 12 or 16 atoms, and again this would not be very expensive. The reason is that 1D chains are especially poor at screening the electrostatic interactions "spilling over" from the repeated copies of the system in the x-y plane. Such interactions, which are not "physical" in this system, even if the system itself is not entirely physical, break degeneracies and thus can disrupt the simple integer transmission plateaus you would expect in a system like this.

While a 1D chain is a nice toy-model, it is really not very physical. So, it might be easy to solve using simplified models, but when you a apply a more general 3D tool like full DFT as in ATK, it's not that simple any more... The system is susceptible to Peierls distortions and as noted above the poor screening often becomes a problem. Thus, while such systems appear like a simple check of a program, they will quickly bring out some quite subtle and complex issues that are not necessarily noticeable for more realistic systems. On the other hand, they are quite useful for debugging and, truth be told, to learn about the aforementioned subtleties :-)

So, perhaps you can rerun with more atoms and noticed, and I think there should be a difference in the results. It is also a good idea to compute and plot the transmission spectrum T(E) at both 0 V and 1 V, to get a more complete picture of where the value of the current comes from.

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Re: Current calculation comparison with Smeagol
« Reply #4 on: December 7, 2008, 22:25 »
Admin mod of the original post was just to correct a spelling mistake in the subject line, to help searches :-)

Offline ipsecog

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Re: Current calculation comparison with Smeagol
« Reply #5 on: December 8, 2008, 01:11 »
I noticed in the script that the calculation was run with the old default value of radial_sampling_dr. You may want to change the value (0.005 Bohr) to the new default (0.001 Bohr), although this would not really account for any weirdness in the transmission spectrum. But it's simply a better value for this parameter in general.

Another point to note is that the calculation takes over 100 steps to converge. In ATK 2008.02 two new convergence criteria were introduced, and by using IterationControl.TotalEnergy (the new default), I've noticed that the calculations often converge twice as fast (in half as many steps, that is)! This is not due to any new approximations; the results are virtually the same as before. Apparently the "Strict" criterion was too strict, and spent a huge amount of iterations converging the very small far off-diagonal corners of the density matrix, which anyway do not contribute noticeably to the physical properties. Anyway, it seems only appropriate that a DFT code should use the total energy as convergence criterion! :-)

Offline carbn9

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Re: Current calculation comparison with Smeagol
« Reply #6 on: December 8, 2008, 19:04 »
Thanks to Dr. Blom and ipsecog firstly.

I'll try to increase the number of atoms in the electrode and adjust the radial sampling parameter. Then, I'll post the results again to post.

Thanks again,

Regards

Offline kstokbro

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Re: Current calculation comparison with Smeagol
« Reply #7 on: December 10, 2008, 22:56 »
Hi,
I had a look at your system.
I is completely valid to calculate the transmission spectrum at zero bias.
However, at finite bias the system violates the underlying framework of the TranSiesta approach.
The problem is that you have a very high current in a one-dimensional system. This means that there is running a current in the electrodes, thus they are out of equilibrium. In the TranSIESTA approach you calculate the properties of the electrodes with an equilibrium algorithm, thus the electrode properties are not correctly described.
Another problem is that in an ideal one-dimensional system,  there is no well defined voltage drop within the system, and the voltage drop will depend on the particular boundary conditions applied.

A way to overcome these problems is to use 3-D electrodes, and I recommend you to do that.
Kurt

Offline Nordland

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Re: Current calculation comparison with Smeagol
« Reply #8 on: December 11, 2008, 12:44 »
When the electrode unitcell is too short, you will always have scattering - even in a perfect system.
The surface green function used for calculating the self-energies is calculated under the assumption (in ATK)
that it should only consider contribution for the the nearest neighbour unitcells. However if the electrode
unitcell is very small, it will interact with more unitcells and hence this assumption gives rises to a small error,
that will lead to scattering for inbound electrons.

I have attached a small script for illustrating this problem and feel free to play around with it.

I have also attached a small graph of some of the results for a specific perfect chain.
In this case it is clear that if you use a 2-layered electrode, you will have scattering in a perfect system,
and if you use 3-layered electrodes you will not.

Offline serhan

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Re: Current calculation comparison with Smeagol
« Reply #9 on: January 1, 2009, 20:06 »
Hello Nordland, I've tried your script for a 1-D chain but by changing the atom type from Lithium to Gold. Then I obtained the following transmission spectrum:
Code
        -2.00        5.9971
        -1.95        5.9970
        -1.90        5.9950
        -1.85        5.9858
        -1.80        5.9384
        -1.75        4.9143
        -1.70        3.9980
        -1.65        3.9982
        -1.60        3.9983
        -1.55        3.9984
        -1.50        3.9985
        -1.45        3.9987
        -1.40        3.9988
        -1.35        3.9988
        -1.30        3.9988
        -1.25        3.9988
        -1.20        3.9987
        -1.15        3.9985
        -1.10        3.9982
        -1.05        3.9978
        -1.00        3.9973
        -0.95        3.9966
        -0.90        3.9956
        -0.85        3.9943
        -0.80        3.9925
        -0.75        3.9900
        -0.70        3.9857
        -0.65        3.9774
        -0.60        3.9506
        -0.55        2.9998
        -0.50        2.9998
        -0.45        2.9998
        -0.40        2.9998
        -0.35        2.9998
        -0.30        2.9998
        -0.25        2.9998
        -0.20        2.9997
        -0.15        2.9997
        -0.10        2.9997
        -0.05        2.9996
         0.00        2.9995
         0.05        2.9993
         0.10        2.9991
         0.15        2.9985
         0.20        2.9964
         0.25        1.0000
         0.30        1.0000
         0.35        1.0000
         0.40        1.0000
         0.45        1.0000
         0.50        1.0000
         0.55        1.0000
         0.60        1.0000
         0.65        1.0000
         0.70        1.0000
         0.75        1.0000
         0.80        1.0000
         0.85        1.0000
         0.90        1.0000
         0.95        1.0000
         1.00        1.0000
         1.05        1.0000
         1.10        1.0000
         1.15        1.0000
         1.20        1.0000
         1.25        1.0000
         1.30        1.0000
         1.35        1.0000
         1.40        1.0000
         1.45        1.0000
         1.50        1.0000
         1.55        1.0000
         1.60        1.0000
         1.65        1.0000
         1.70        1.0000
         1.75        1.0000
         1.80        1.0000
         1.85        1.0000
         1.90        1.0000
         1.95        1.0000
         2.00        1.0000
Terminated Normally
Run finished at  Thu Jan 01 20:05:23 2009!
As it can be seen, there are transmission coefficients like 5.9 or so unlike the case of Lithium that had only some numbers close to unity. Why do I obtain such a difference? Have I to modify the calculation parameters since Gold has more valence electrons compared to Li? Regards Serhan

Offline Anders Blom

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Re: Current calculation comparison with Smeagol
« Reply #10 on: January 1, 2009, 21:44 »
Hi Serhan,

the results are ok in terms of the transmission being different from unity. The transmission coefficients are not restricted to being <=1 since each valence electron provides a possible transmission channel. This is most obvious in 1D systems (like atomic chains as here, but also e.g. carbon nanotubes) where there is no k-point dependence in the XY directions, and you simply get T(E)=number of bands at energy=E, as your results show.

If you plot the band structure of the gold chain (not bulk gold, there is a big difference, of course!), you will see a perfect correspondence between the number of bands at each energy and T(E).
« Last Edit: January 1, 2009, 23:13 by Anders Blom »

Offline Nordland

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Re: Current calculation comparison with Smeagol
« Reply #11 on: January 1, 2009, 23:00 »
Hey Serhan.

The range of gold atoms are much much longer than the range of lithium atoms due to the d-shells in the gold atoms.
If I look at the values you have reported in your results, I can guess that you have modifed my scripts such that you have 3-layered electrodes,
and 4 atom wide central region.
If you look at the transmission at -1.75 eV you get a transmission value of 4.9143. ( I just redo the calculation and got this value for -1.75)

Since it is perfect metallic system, there can be no scattering of any kind, so the value should have been much closer to 5 or 4. If the value had been something like
4.9981 or 3.992 something, it was most likely not a result of scattering and therefore can be improved by lowering the green_function_infinitesimal given to the calculateTransmissionSpectrum. If this value is lowered, then it can be brought even closer to an integer value.

However the point is in this case, it is clearly a result of scattering, and hence since it is 1d metallic system it is due to a too short electrode.
To check this you can redo the calculation with 6 layered electrodes ( and 6 atoms in the central region ) and you will get a value of 3.995!, which proves that this behavior was to due to a unphysical scattering due to too short electrodes.

I have attached a plot where I have calculated the transmission in much finer detail around -1.75 eV ( more clearly at -3.5 eV), so you can see the difference between 3-layered electrodes and 6-layered electrodes.

Happy new year,
   Nordland

Offline serhan

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Re: Current calculation comparison with Smeagol
« Reply #12 on: January 2, 2009, 07:02 »
Dear Anders Blom and Nordland,

Again thanks for your explainatory answers.

After calculating the current in a two-probe system, I tried to logically compare the simulated results with the results of the transmission spectrum equation (S. Datta, "Quantum Transport"):



where D(E-U) is the self consistent density of states in the channel, gamma1 and gamma2 are the coupling coefficients of the channel to electrode1 and electrode2, respectively. (gamma=gamma1+gamma2). So, in the situation of the 1-D chain of Gold atoms, I now understand that, T(E-U)=D(E-U)=5 for example at E-U=-1.75eV. (4.9143 from simulation.) So, if T(E-U)=D(E-U) (I've understood this equality from your and Dr. Blom's explainations), then can I conclude that 2*pi*(gamma1*gamma2)/(gamma1+gamma2)=1 and we can calculate the coupling coefficients as gamma1=gamma2=1/pi for an ideal atomic chain (if of course electrodes are taken long enough :) ). If electrodes are short, then gamma1 and gamma2 decreases and T(E-U) diverges from D(E-U) of the channel.  ???

I wish also happy new year..

Serhan



« Last Edit: January 2, 2009, 07:06 by serhan »

Offline Anders Blom

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Re: Current calculation comparison with Smeagol
« Reply #13 on: January 2, 2009, 07:40 »
Right! The values of gamma1 and gamma2 are of course fixed for a perfect 1d chain (in the way stated in the previous post). What changes if the electrodes are too short is that ATK makes an approximation in calculating these values.

Offline serhan

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Re: Current calculation comparison with Smeagol
« Reply #14 on: January 3, 2009, 18:11 »
Thank you Dr. Blom.  :)

By the way, it would be useful if some documents explaining the general modelling and simulation mechanism of ATK or more generally the analysis of two-probe systems could be uploaded to the scientific publications section of the forum...

Serhan