Is the calculated results right?

[yangzw1985]

Hi,everyone! I have performed a calculation of a two probe system,but I am not sure the results is right or not.It is a nanowire, the electrodes is Li.
If it is right, why the transmission spcetra is zero from -12 to 0.3? what is the reason for dos is neraly zero from -12 to -6.33.
In my opinion, the transmission coefficients should in [0,1],why the calculated results is large than 1 .
If it is not right, what is the reason?
Thanks in advance!


Two Probe Method
# -----------------------------------------------------------------------------

# -----------------------------------------------------------------------------
# Basis Set Parameters
# -----------------------------------------------------------------------------
Type               = SZP
Radial Sampling dr = 0.001 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 = GGA.PBE

# -----------------------------------------------------------------------------
# ElectronDensityParameters
# -----------------------------------------------------------------------------
Mesh Cutoff         = 100.00 Rydberg

# -----------------------------------------------------------------------------
# Two Center Integral Parameters
# -----------------------------------------------------------------------------
Cutoff           = 2500.0 Rydberg
Number Of Points = 1024

# -----------------------------------------------------------------------------
# Iteration Mixing Parameters
# -----------------------------------------------------------------------------
Algorithm                 = Pulay
Diagonal Mixing Parameter = 0.05
Quantity                  = Hamiltonian
History Steps             = 6

# -----------------------------------------------------------------------------
# Iteration Control Parameters
# -----------------------------------------------------------------------------
Tolerance  = 0.0001
Criterion  = TotalEnergy
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 = 6.00 V
Voltage at Electrode 1 = 0.00 V

# -----------------------------------------------------------------------------
# TwoProbe Algorithm Parameters
# -----------------------------------------------------------------------------
Electrode Constraint = ElectrodeConstraints.Off
Initial Density Type = InitialDensityType.EquivalentBulk


TwoProbe Calculation
# ----------------------------------------------------------------
# sc  0 : q =  892.92732 e         
sc  1 : q =  684.90167 e  dRho =  1.9157E+01         
sc  2 : q = 2473.95837 e  dRho =  4.1810E+01 
sc  3 : q = 1201.71699 e  dRho =  4.1987E+01
sc  4 : q =  982.03343 e  dRho =  7.6023E+00
sc  5 : q =  962.84064 e  dRho =  1.6014E+00
sc  6 : q =  973.07716 e  dRho =  9.7965E+00
……
……
……
sc 53 : q =  915.01560 e  Etot = -2102.55328 Ry  dRho =  9.4124E-03  dEtot =  4.6753E-03 Ry
sc 54 : q =  915.00734 e  Etot = -2102.53793 Ry  dRho =  4.2077E-03  dEtot =  1.5345E-02 Ry
sc 55 : q =  914.97941 e  Etot = -2102.52283 Ry  dRho =  1.7209E-02  dEtot =  1.5104E-02 Ry
sc 56 : q =  915.01204 e  Etot = -2102.53744 Ry  dRho =  5.2314E-03  dEtot = -1.4610E-02 Ry
……
……
……
sc 72 : q =  915.00480 e  Etot = -2102.49113 Ry  dRho =  1.7967E-03  dEtot =  8.9046E-03 Ry
sc 73 : q =  914.99490 e  Etot = -2102.48034 Ry  dRho =  6.9943E-04  dEtot =  1.0794E-02 Ry
sc 74 : q =  914.99182 e  Etot = -2102.47582 Ry  dRho =  8.5722E-04  dEtot =  4.5136E-03 Ry
sc 75 : q =  914.98750 e  Etot = -2102.47300 Ry  dRho =  2.9140E-04  dEtot =  2.8174E-03 Ry
sc 76 : q =  914.98888 e  Etot = -2102.47257 Ry  dRho =  1.7389E-04  dEtot =  4.3147E-04 Ry
sc 77 : q =  914.99123 e  Etot = -2102.47258 Ry  dRho =  4.5677E-04  dEtot = -7.4374E-06 Ry
# Total Charge =  914.99123
#-------------------------------------------------------------------------------
1.83148628065e-06 A
# -----------------------------------------------------------------------------
# Density Of States
# -----------------------------------------------------------------------------
# Energy (eV)   DOS (1/eV)
       -12.00      -0.0000
       -11.88      -0.0000
       -11.76      -0.0000
       -11.64      -0.0000
       -11.52      -0.0000
       -11.40      -0.0000
       -11.28      -0.0000
       -11.16       0.0000
       -11.04      -0.0000
       -10.91      -0.0000
       -10.79      -0.0000
       -10.67      -0.0000
       -10.55      -0.0000
       -10.43      -0.0000
       -10.31      -0.0000
       -10.19      -0.0000
       -10.07      -0.0000
        -9.95      -0.0000
        -9.83      -0.0000
        -9.71      -0.0000
        -9.59      -0.0000
        -9.47      -0.0000
        -9.35      -0.0000
        -9.23      -0.0000
        -9.11      -0.0000
        -8.98      -0.0000
        -8.86      -0.0000
        -8.74      -0.0000
        -8.62      -0.0000
        -8.50      -0.0000
        -8.38      -0.0000
        -8.26       0.0001
        -8.14      -0.0000
        -8.02       0.0000
        -7.90      -0.0000
        -7.78      -0.0000
        -7.66       0.0000
        -7.54      -0.0000
        -7.42      -0.0000
        -7.30       0.0000
        -7.18       0.0000
        -7.06       0.0000
        -6.93       0.0000
        -6.81       0.0001
        -6.69       0.0002
        -6.57      -0.0001
        -6.45       0.0003
        -6.33       0.0014
        -6.21      43.6697
        -6.09     313.5610
        -5.97    1835.8133
        -5.85     255.5916
        -5.73     301.6276
        -5.61     919.8484
        -5.49   10396.2582
        -5.37    1681.8338
        -5.25    1169.0587
        -5.13     863.9933
        -5.01    1047.4582
        -4.88     859.1584
        -4.76   30709.6591
        -4.64    5664.9851
        -4.52    2392.9317
        -4.40   21963.6432
        -4.28     802.9118
        -4.16    1198.5536
        -4.04    5658.8690
        -3.92    6763.4496
        -3.80    1563.0010
        -3.68    2528.8234
        -3.56    6605.8470
        -3.44     880.7241
        -3.32    2592.4730
        -3.20    3018.0474
        -3.08    1029.6402
        -2.95    1087.2841
        -2.83    4406.8567
        -2.71    1174.6480
        -2.59    1254.3067
        -2.47    1214.6492
        -2.35    1158.5924
        -2.23    1012.5150
        -2.11    1205.0405
        -1.99     986.0920
        -1.87    1040.9024
        -1.75   10139.1649
        -1.63    1125.2415
        -1.51     839.9252
        -1.39     809.8384
        -1.27     767.5566
        -1.15     672.9533
        -1.03     673.2879
        -0.90     782.3003
        -0.78     988.4642
        -0.66     517.9028
        -0.54     776.2505
        -0.42     875.2454
        -0.30    1372.0944
        -0.18    1996.6875
        -0.06     851.8255
         0.06     989.1520
         0.18    1245.0061
         0.30    7386.8019
         0.42    3011.5284
         0.54    1561.7771
         0.66    2055.8332
         0.78    1220.8574
         0.90    1441.7689
         1.03    1321.8829
         1.15    2049.4341
         1.27    7509.2569
         1.39    2491.7969
         1.51    3891.0574
         1.63    2379.6813
         1.75    3529.2401
         1.87    3215.0595
         1.99    3487.7868
         2.11    2874.1205
         2.23    2429.7738
         2.35    3546.4351
         2.47    3115.6033
         2.59    2466.5710
         2.71    2481.1522
         2.83    2520.9049
         2.95    2266.8188
         3.08    2508.2448
         3.20    2171.6688
         3.32    2034.7275
         3.44    2134.7249
         3.56    2461.5119
         3.68    2387.1125
         3.80    2895.1471
         3.92    3534.2278
         4.04    3434.2460
         4.16    3441.7928
         4.28    3085.1989
         4.40    3406.6753
         4.52    5402.4508
         4.64    4311.7731
         4.76    4813.4809
         4.88    3798.2215
         5.01    4479.4174
         5.13    5688.4953
         5.25    4558.5429
         5.37    4933.2018
         5.49    5426.5888
         5.61    5341.6663
         5.73    4602.4075
         5.85    5430.9537
         5.97    5463.8306
         6.09    5126.3264
         6.21    6425.4075
         6.33    6908.0224
         6.45    6358.2039
         6.57    7249.3772
         6.69    6843.0017
         6.81    6274.3779
         6.93    6322.3590
         7.06    7042.4897
         7.18    6621.9105
         7.30    7408.8516
         7.42    7296.5607
         7.54   10569.9742
         7.66    7324.4792
         7.78    7388.6124
         7.90    6651.3762
         8.02    5812.7157
         8.14    6803.5109
         8.26    6981.0642
         8.38    6886.4184
         8.50    6683.9743
         8.62    6821.9234
         8.74    7319.1565
         8.86    7546.8588
         8.98    6542.0635
         9.11    5746.7884
         9.23    5994.8222
         9.35    5763.6548
         9.47    6260.3027
         9.59    5308.0919
         9.71    5691.4112
         9.83    5678.4900
         9.95    6810.3661
        10.07    6255.6074
        10.19    5308.6848
        10.31    5608.0271
        10.43    5386.0939
        10.55    5591.7551
        10.67    4981.8139
        10.79    4924.1806
        10.91    6149.1197
        11.04    5294.6332
        11.16    5115.9215
        11.28    5464.7032
        11.40    4811.5058
        11.52    6131.4459
        11.64    4951.3313
        11.76    4796.5299
        11.88    5917.2959
        12.00    5619.3613
# -----------------------------------------------------------------------------
# Transmission Spectrum
# -----------------------------------------------------------------------------
# Energy (eV)   Coefficient
       -12.00        0.0000
       -11.88        0.0000
       -11.76        0.0000
       -11.64        0.0000
       -11.52        0.0000
       -11.40        0.0000
       -11.28        0.0000
       -11.16        0.0000
       -11.04        0.0000
       -10.91        0.0000
       -10.79        0.0000
       -10.67        0.0000
       -10.55        0.0000
       -10.43        0.0000
       -10.31        0.0000
       -10.19        0.0000
       -10.07        0.0000
        -9.95        0.0000
        -9.83        0.0000
        -9.71        0.0000
        -9.59        0.0000
        -9.47        0.0000
        -9.35        0.0000
        -9.23        0.0000
        -9.11        0.0000
        -8.98        0.0000
        -8.86        0.0000
        -8.74        0.0000
        -8.62        0.0000
        -8.50        0.0000
        -8.38        0.0000
        -8.26        0.0000
        -8.14        0.0000
        -8.02        0.0000
        -7.90        0.0000
        -7.78        0.0000
        -7.66        0.0000
        -7.54        0.0000
        -7.42        0.0000
        -7.30        0.0000
        -7.18        0.0000
        -7.06        0.0000
        -6.93        0.0000
        -6.81       -0.0000
        -6.69        0.0000
        -6.57       -0.0000
        -6.45        0.0000
        -6.33        0.0000
        -6.21        0.0000
        -6.09        0.0000
        -5.97        0.0000
        -5.85        0.0000
        -5.73        0.0000
        -5.61        0.0000
        -5.49        0.0000
        -5.37        0.0000
        -5.25        0.0000
        -5.13        0.0000
        -5.01        0.0000
        -4.88        0.0000
        -4.76        0.0000
        -4.64        0.0000
        -4.52        0.0000
        -4.40        0.0000
        -4.28        0.0000
        -4.16       -0.0000
        -4.04        0.0000
        -3.92        0.0000
        -3.80        0.0000
        -3.68        0.0000
        -3.56        0.0000
        -3.44        0.0000
        -3.32        0.0000
        -3.20        0.0000
        -3.08        0.0000
        -2.95       -0.0000
        -2.83        0.0000
        -2.71       -0.0000
        -2.59       -0.0000
        -2.47        0.0000
        -2.35        0.0000
        -2.23       -0.0000
        -2.11       -0.0000
        -1.99       -0.0000
        -1.87       -0.0000
        -1.75       -0.0000
        -1.63        0.0000
        -1.51        0.0000
        -1.39        0.0000
        -1.27        0.0000
        -1.15        0.0000
        -1.03        0.0000
        -0.90        0.0000
        -0.78        0.0000
        -0.66        0.0000
        -0.54        0.0000
        -0.42       -0.0000
        -0.30        0.0000
        -0.18        0.0000
        -0.06        0.0000
         0.06        0.0000
         0.18        0.0000
         0.30        0.0032
         0.42        0.0002
         0.54        0.0002
         0.66        0.0044
         0.78        0.0004
         0.90        0.0023
         1.03        0.0060
         1.15        0.0279
         1.27        0.0746
         1.39        0.0004
         1.51        0.0354
         1.63        0.0004
         1.75        0.0007
         1.87        0.0007
         1.99        0.0035
         2.11        0.0010
         2.23        0.0006
         2.35        0.0069
         2.47        0.0004
         2.59        0.0001
         2.71        0.0001
         2.83        0.0001
         2.95        0.0001
         3.08        0.0001
         3.20        0.0001
         3.32        0.0002
         3.44        0.0005
         3.56        0.0016
         3.68        0.0040
         3.80        0.0216
         3.92        0.1426
         4.04        0.0972
         4.16        0.0714
         4.28        0.1498
         4.40        0.4083
         4.52        0.9319
         4.64        0.7909
         4.76        0.9820
         4.88        0.6279
         5.01        1.0294
         5.13        1.0912
         5.25        0.8982
         5.37        0.8063
         5.49        1.1106
         5.61        1.0480
         5.73        0.9569
         5.85        1.1946
         5.97        1.3377
         6.09        1.3426
         6.21        1.6044
         6.33        2.2201
         6.45        2.2500
         6.57        2.5156
         6.69        2.5487
         6.81        2.5352
         6.93        2.4782
         7.06        2.5418
         7.18        2.6438
         7.30        2.6943
         7.42        2.5936
         7.54        3.3853
         7.66        2.7909
         7.78        2.7258
         7.90        2.6987
         8.02        2.3512
         8.14        2.4571
         8.26        2.4113
         8.38        2.3143
         8.50        2.2432
         8.62        2.0538
         8.74        2.1957
         8.86        2.3490
         8.98        2.2073
         9.11        2.1481
         9.23        2.4399
         9.35        2.0562
         9.47        2.4358
         9.59        2.3756
         9.71        2.4512
         9.83        2.4723
         9.95        2.4341
        10.07        2.2331
        10.19        1.9886
        10.31        1.9892
        10.43        1.8754
        10.55        2.1120
        10.67        1.5793
        10.79        1.9093
        10.91        1.9426
        11.04        1.8732
        11.16        1.7369
        11.28        1.2620
        11.40        1.5390
        11.52        1.8239
        11.64        1.3091
        11.76        1.1551
        11.88        1.3383
        12.00        1.4121
Terminated Normally
Run finished at  Thu Mar 12 11:45:02 2009!

[Nordland]

Well there are something to considers, and I think your results are correct in these the ATK gives your the correct results for this system.

If it is pure metallic 1d-system, the screening is pretty bad, and therfore applying 6.0V is very strong impact on the symmetry of the system, and therefore the selfconsistent response of the system will try to counter-act the applied bias. If the nanowire is non metallic, then I would try to use the new constraint in ATK 2008.10 called DensityMatrix or increase the length of the electrodes.

Regarding the transmission being in the range from 0 to 1 is only correct for a single band contribution,
and if you have multipel bands in action they will each have a transmission coefficent between 0 and 1,
however the transmission calculated is the sum of these. The reason for this, is that then the total current is the integral between the chemical potentials.

However, how does the DOS and transmission spectrum look like at 0.0 V bias - if we compare we might be able to establish if this is problem or the physical nature of the system....

[yangzw1985]

It is a C nanowire!

My ATK version is 2008.10,but there is no the new constraint called DensityMatrix, it is off or the real space density!I don't the reason why the DensityMatrix is disappear.
Do I have to change off to DensityMatrix in the script menu?

I also want to know the biggest voltage can be used to obtain the accuracy results in ATK calculations,can you give me the answer and the reason?

Thanks!

[Nordland]

To the best of my knowlegde, you can not set the density matrix constraint from the scripter, since it is an new experimental feature, but I think it works really great!
So you have edit it manually in the script - either by using the script editor or an external editor.

In principal there is no limit on how high you can set voltage, however it depends on your machine, as
the voltage goes up, the electric field becomes stronger, and the SCF might become unstable if the the electric field becomes to strong, however this can be compensated by increasing the length of the system in the Z-axises. Therefore the highest voltage you can apply, becomes an issue of the computer size rather than the algorithm ( higher voltages will also increase time of the contour integral, but it scales perfect with the number of CPU).

The largeste voltage I have ever succeded to converge, is a 20 V bias calculation across an MTJ junction, but the system was quite long along the z-axis, and it required some work in order to determine the sufficient size in order to make the system work.

[yangzw1985]

Hi,Nordland! From the calculated transmission spectra and DOS, can you tell me where is the left electrode and the right electrode ? And where is the C nanowires? please tell me the reasons for your decisions or methods to distinguish the electrode and nanawires.
Thanks!

[Nordland]

The transmission specutrm and dos does not contain information about the electrodes.

Is the system a C-wire between Li-surfaces or C-wire insert into a Li-wire?

[yangzw1985]

It is a C-wire between two Li (100)-surfaces.

[yangzw1985]

Hi,everyone! Now,I have some questions.

(1) As we can see clearly from the calculated results, with the applied voltage of 6V, the current value is 1.83148e-06A. The current is very larger as far as I know in the two probe calculation.

We can see from the transmission spectra, the coefficient is zero around the fermi level. From the DOS, there is electrons at the fermi level, but the electrons can not be transmitted through the central scattering region.

As far as I know, the current has been calculated by the Landauer formula in ATK. In Landauer formula, T(E,V_b) is the transmission coefficients in bais window.

Now that the transmission is 0 in the bais window, I don't understand how the current be got in the calculation. In other words, how to explain the larger current value ? Can anyone give me the explaination?

(2) In order to calculated the properties of two probe system, I want to know if the Li electrodes is appropriate for a C wire? Do I have to choose Au or other metals as the electrodes?

Thanks in advance!!

[Nordland]

Have you calculated the transmission spectrum at 6 volt bias as well?

Can you post the transmission spectrum?

[yangzw1985]

Hi,Nordland! At the begin of this subject is the calculated results, it includes current, transmission spectra and DOS!

Here I have also post a calculation with 0.4V of the two probe model. This question is still. Hope you have a look at it, and give your opinion here!

Thank you.

[Nordland]

Okay, forgive me my blindness

Okay. I think I have an idea on what the problem is, as I agree that the current is a bit high for being a result of transmission spectrum.
The function calculateCurrent has a parameter called, number_of_points, which has a default for 100 points. When it calculates the current, it is integrates the transmission spectrum (in your case) from -3 eV to 3 eV. It performs a simple riemann sum with number of points given specified to the calculateCurrent. The default is, as I remember it, 100. And 100 points is enough for a bias of 0.5 - 1 V, but in your case it is way too small.

What value is it set to? Try perform the calculate of the current using 1000 or 5000 points to calculateCurrent

[yangzw1985]

Ok, Nordland! Thank you! Did you have a look at my post file c(0.4V).txt. The current is 10-7A. I think the question is still with low applied voltages. Please have a look at it, and give me more explaintion. I really appreciate your views!

[Nordland]

First we need to get a slightly better transmission spectrum. When calculating the transmission spectrum you should use more energy points. In VNL where you enter the two bounds the lower and upper for the transmission spectrum, you should increase the number of points alot - perhaps by a factor 10 at least. Then we will get good nice transmission spectrum.

I will try to write a more detailed explaination about the current and calculation, but shortly I think that your results are correct, IF you correct the number of points used in calculateCurrent.

[yangzw1985]

Thank you very much! I will try with your suggestion.

And I also want to know the reasons of my second question. (2) In order to calculated the properties of two probe system, I want to know if the Li electrodes is appropriate for a C wire? Do I have to choose Au or other metals as the electrodes?

When we choose the electrodes, do we need pay attention to the atomic weight. In order to clearly distinguish the physical meaning of the two model, we should choose the eletrodes compared with the nanostructures. In other words, if the atom weight of the nanostructures is M, and atom weight of the electrodes is N. Do we need pay attention to keep the value of N-M OR M-N is very larger.

Thanks!

[Anders Blom]

I'm jumping in here with a few comments, if you don't mind

1) Applying a 6 V bias is not really realistic. You'd have a hard time doing it in an experiment, and ATK rarely converges at such high bias. Even if it does, the bias is so large compared to typical band width of the valence band that you are outside the range where the calculations make sense anyway. The valence band of Li is only 4 eV deep!

2) The choice of electrodes is a subtle question, but wouldn't have anything to do with mass. Rather, what matters primarily is what experiments you may be comparing (or which experiment one could do to compare to the calculation), what is physically feasible and realistic, and what effect you are looking for. Li is certainly not a feasible or realistic material to use in any experiment, but it has a simple band structure and works a bit like a "simple transparent metal". So, if the details in the transmission are primarily due to the molecule etc in the central region, and not the electrode material (this is certainly not always the case!), Li can be used as a testing material since it is also fast to compute. But one should be very careful to draw any serious conclusions from such calculations!