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Table of Contents

Table of ContentsOpening a band gap in silicene and bilayer graphene with an electric field

Bilayer grapheneBuilding a bilayer graphene structureCalculation and analysis

SiliceneOptimizing the geometryBand structure

ReferencesMore reading

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Docs » Tutorials » Graphene and other 2D materials »Opening a band gap in silicene and bilayer graphene with an elect ric f ield

Opening a band gap in sil icene and bilayerOpening a band gap in sil icene and bilayergraphene with an electr ic f ieldgraphene with an electr ic f ieldVersion:Version: 2017

In this tutorial you will learn how to insert metallic gate elect rodes in an QuantumATK bulk calculat ion anduse them to apply elect ric f ields. You will use these features to study the opening of a band gap in bilayergraphene and in silicene under the presence of an elect ric f ield. It is assumed that you are familiar with thebasic funct ionalit ies of Quant umAT KQuant umAT K.

Bilayer grapheneBilayer graphene

B ui l di ng a bi l aye r graphe ne st ruc t ureB ui l di ng a bi l aye r graphe ne st ruc t ure

1. Create a new empty project and open BuilderBuilder (icon ).2. Insert graphite (not graphene!) from Dat abaseDat abase .3. Open Bulk Tools ‣ Lat t ice Parameters. Select Cartesian coordinates and set the value of c lat t ice

constant to be 25 Å.

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4. Go to Coordinate Tools ‣ Center and click “Appy” to center the system.

5. To insert the metal elect rodes, open Miscellaneous ‣ Spat ial Regions..., right -click the table (the areaunder the headers Region Type/Value) and click “Insert region” twice.

6. Set the voltage to 0 V for the f irst metallic region, and 10 V for the second. Change their size so thatthey cover the ent ire hexagonal unit cell (see the f igure below). It does not matter if the regions st ickoutside the cell, those parts will be ignored in the calculat ion anyway.

The applied voltage results in 4 V/nm in the z direct ion, just above the f ield that has been found inexperiments to open a band gap.

Cal c ul at i o n and anal ysi sCal c ul at i o n and anal ysi s

We will then analyze the band st ructure of the graphene bilayer under the stat ic elect ric f ield.

1. Send the graphene bilayer st ructure to Script Generat orScript Generat or.2. Insert a New Calculat orNew Calculat or block

3. Open the New Calculat orNew Calculat or block, and choose the “ATK-SE: Extended Hückel” method. For goodaccuracy, set the k-points to be 9x9x1.

4. Under “Huckel basis set ” select the “Cerda. Carbon [graphite]” basis set , which describes the sp2bonding of graphene very well.

5. Unt ick the “No SCF iterat ion” opt ion to carry out the computat ion self-consistent ly.

WarningWarning

It is ext remely important to include self-selconsistency; otherwise the f ield will not have any effectat all!

6. Go to “Poisson solver”, set “Mult i-grid” in SolverSolver, and choose “Dirichlet ” in Boundary Condit ioinsBoundary Condit ioins onboth sides in the C direct ion.

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For this part icular calculat ion, you can choose any boundary condit ion in the C direct ion since themetal gates will f ix the potent ial at the boundaries anyway, but “Dirichlet ” is the physically correctcondit ion when a constant value of the potent ial is desired at the boundary.

7. Add a Bandst ruct ureBandst ruct ure block by clicking Analysis ‣ Bandstructure.

8. Double-click the Bandst ruct ureBandst ruct ure block and change the route to G, M, K, G. Also increase the number ofpoints per segment to 200.

9. Name the output f ile “bilayer_graphene_efield.nc”.

10. Send the calculat ion to Job ManagerJob Manager, save the Python script in the window that appears and run thecalculat ion. It should take no more than 20-30 seconds to run.

After the calculat ion, visualize the band st ructure and zoom in around the K point , where a band gap isopening with increasing the st rength of the elect ric f ield. The following f igures, from top to bot tom,show the band st ructure of the bilayer graphene with an applied elect ric f ield of 0, 10, and 20 Volts,respect ively.

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You can use DFT as well, the results will be similar.No at tent ion was paid to the interlayer distance. You can change it a bit to see how the bandstructure changes. Note, however, that you cannot use DFT/GGA to opt imize this distancebecause no energy minimum will be found, due to the absence of dispersion correct ions (the layersare bound by Van der Waals forces, not captured in standard GGA). LDA works, fortuitously, becauseof a cancellat ion of errors, but the results cannot really be t rusted.

Sil iceneSil icene

To study the effect of elect ric f ields on silicene you f irst need a good model of this material. Theapproach will be to start with graphene and turn it into silicene, opt imize the geometry, and then repeatthe same steps followed to calculate the bilayer graphene under the presence of an elect ric f ield.

Opt i mi z i ng t he ge o me t ryOpt i mi z i ng t he ge o me t ry

1. In BuilderBuilder, add graphene (not graphite this t ime) from Dat abaseDat abase to St ashSt ash following the same stepsexplained above for the bilayer graphene.

2. Change the two C atoms to Si by select ing them (using the left mouse but ton while holding down theCtrl but ton of your keyboard) and using the “Periodic Table” tool .

3. The lat t ice constant of silicene is not the same as for graphene, but rather than guess it , it will simplybe part of the geometry opt imizat ion to determine it . To start from a reasonable guess, click BulkTools ‣ Lat t ice Parameters. Make sure to keep the fract ional coordinates constant , set the lat t iceparameter a to be 3.8 Å and increase the c lat t ice parameter to 20 Å.

4. In BuilderBuilder, go to Coordinate Tools ‣ Center, in order to center the configurat ion.

5. The f lat geometry where both Si atoms are in the same plane is a local minimum in the potent ial energysurface. Therefore, click the “Rat t le” tool a few t imes to add a small perturbat ion to thecoordinates. This ensures that the geometry opt imizat ion will converge to the global minimum.

6. Send the geometry to Script Generat orScript Generat or by using the “Send To” but ton .7. In Script Generat orScript Generat or, insert New Calculat orNew Calculat or and Opt imiz eGeomet ryOpt imiz eGeomet ry blocks by double-clicking the

icons in the Blocks panel:

New Calculator. Opt imizat ion ‣ Opt imizeGeometry.

8. Use 21x21x1 k-points for good accuracy, and choose GGA-PBE for exchange-correlat ion. You can inprinciple use the default DoubleZetaPolarized basis set , but here you will use the “Tight Tier 1” basisset , which provides slight ly bet ter results.

9. In the Opt imiz eGeomet ryOpt imiz eGeomet ry block, set the force tolerance to be small (0.01 eV/Å) and the st resstolerance to be even smaller (0.0005 eV/Å ). Unconstrain the cell in the x and y direct ions.3

10. Name the output f ile “silicene_opt imize.nc” and save the Python script .11. Send the script to Job ManagerJob Manager, save the script and run the job. The calculat ion will take about 10

minutes. When it f inishes, drop the Bulk Configurat ion with ID “gID001” on BuilderBuilder, and inspect thegeometry. You will f ind a nicely opt imized silicene sheet with a buckling of about 0.5 Å and anopt imized lat t ice constant of 3.86 Å. Both values are in good agreement with those reported in theliterature [1-2].

B and st ruc t ureB and st ruc t ure

Using the opt imized st ructure, repeat the steps above for the bilayer graphene to insert metallic gatesand compute the band st ructure with elect ric f ields. Not ice that , in the case of silicene, you need to makethe spat ial region larger in the XY plane, since the cell is also larger. Use 20 V as the voltage on the secondelect rode.

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You should use the same calculator set t ings as for the opt imizat ion. The calculat ion will take less thana minute.

In the plot below you can see the band st ructure at zero f ield (top) and with 20 V applied on the gate(bot tom), which produces a band gap of about 0.1 eV. By t rying different values of the voltage you will f indthat the band gap increases essent ially linearly with the f ield as shown in [3].

Not ice that in this case, if you look closely, the band gap is not exact ly at the K point .

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If you apply a t ransverse f ield to a single graphene layer, no gap opens up. The reason is that thegraphene is completely f lat , and so the f ield just gives a constant shift of the potent ial. In the case ofsilicene the gap appears because the sheet is naturally bukled.

ReferencesReferences

[1] S. Cahangirov, M. Topsakal, E. Akturk, H. Sahin, and S. Ciraci, Two- and One-Dimensional HoneycombStructures of Silicon and Germanium, Physical Review Letters 102, 236804 (2009)

[2] N. D. Drummond, V. Zolyomi, and V. I. Fal’ko, Electrically tunable band gap in silicene, Physical Review B 85,075423 (2012)

[3] R. Zhou, “Structural And Electronic Propert ies of Two-Dimensional Silicene, Graphene, and RelatedStructures”, Master Thesis, Wright State University, Electrical Engineering, Dayton OH, USA (2012)

More readingMore reading

Z. Ni et al., “Tunable Bandgap in Silicene and Germanene”, Nano Let ters 12, 113-118 (2011)

Next

C. Xu et al., “Giant magnetoresistance in silicene nanoribbons”, Nanoscale 4, 3111-3117 (2012)Y. Wang et al., “Half-metallic Silicene And Germanene Nanoribbons. Towards High-performanceSpint ronics Device”, Nano 7, 1250037 (2012)L. Pan et al., “Thermoelect ric propert ies of armchair and zigzag silicene nanoribbons”, Phys. Chem.Chem. Phys. 14, 13588 (2012)H. Li et al., “High performance silicene nanoribbon f ield effect t ransistors with current saturat ion”,European Physical Journal B 85, 1 (2012)R. Quhe et al., “Tunable and sizable band gap in silicene by surface adsorpt ion”, Sci. Rep. 2, 853(2012)

For a similar study on hexagonal boron-nit ride (hBN), see

K. Tang et al., “Elect ronic and t ransport propert ies of a biased mult ilayer hexagonal boron nit ride”,European Physical Journal B 85, 301 (2012)

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