Material Science Simulations using PWmat

Transcription

1 Maeral Scence Smulaons usng PWma Ln-Wang Wang Chef Techncal Advsor, LongXu

2 Oulne 1 Charge pachng mehod for nanosrucure calculaons 2 Shockley-Read-Hall nonradave decay calculaons 3 Real-me TDDFT smulaons 4 Quanum ranspor calculaons 5 Acceleraed aomc relaxaon 6 DFT band gap correcon They are examples of our mehodology developmens, and hey wll be able o be calculaed by PWma n he fuure

3 Charge pachng: free sandng quanum dos In 675 P 652 LDA qualy calculaons egen energy error ~ 20 mev 64 processors IBM SP3 for ~ 1 hour Toal charge densy CBM VBM mofs The band edge egensaes are calculaed usng lnear scalng folded specrum mehod FSM, whch allows for 10,000 aom calculaons.

4 The accuracy for he small S quanum do 8 22

5 Folded Specrum Mehod H ref ref H 2 2 N } 2 1 { 2 r E r r V

6 CdSe quanum do resuls

7 Quanum do and wre calculaons for semconducor maerals IV-IV: S III-V: GaAs, InAs, InP, GaN, AlN, InN II-VI: CdSe, CdS, CdTe, ZnSe, ZnS, ZnTe, ZnO

8 Effec of surface dpole and CdS core n a CdSe rod Cd ermnaed surface Cd and Se ermnaed surface

9 2 1 2 r r r V r P r V c c c v C LDA r r r V r P r V v v v c C LDA Naural band algnmen 0.28 ev 0.54 ev A selfconssen calculaon for a bound excon ],, [ 2 1 ' ' ' r r W r r Lm W r P bulk r r 4 ] [ 2 r r V r C V V C

10 The Shallow Level Problem and Challenge S shallow accepors: B, Al, Ga, In, Tl Effecve mass/k.p heory: all her bndng energy = 32 mev The expermenal values mev B Al Ga In Tl Ths s ofen arbued o he onse poenal, besdes 1/ε r I s embarrassng ha we sll canno calculae he smple bndng energy

11 How o ge he poenal Vr? LDA Kohn-Sham equaon of a closed shell sysem as approxmaon for GW Eq.: 1 2 V r r r V V V 2 Use 512 aom perodc supercell, one accepor a he cener, 2048 elecron o ge V 512,N r 64,000 aoms V Coul negh r 1 Rmpury 0 r R 512 aoms r ousde he box r nsde he box Vr=1/εr+V bulk r V, Coul r V512 N r Vnegh r

12 64,000 aom VBM wavefuncons 20a In mpury Only showng he wavefuncon whn he 40968a box n mpury Bu even he 64,000 aom calculaons are no compleely converged, exrapolaon s needed o ge he ε_b

13 Fnal resuls based on he Schrodnger s equaon elemen B Al Ga In Tl ε_b exp mev ε_b calc mev Concluson: he rend s correc, bu quanavely, s no que correc ye. LDA s no good enough! We hen nroduce he correcon from 64 aom GW calculaons elemen B Al Ga In Tl ε_b exp mev ε_b calc mev

14 Calc. Eb mev Accepor level n S and GaAs, GaP Exp Eb mev S:B, S:Al, S:Ga, S:In, S:Tl, GaP:B, GaAs:S, GaAs:Ge, GaAs:Sn,GaAs:Mg

15 Oulne 1 Charge pachng mehod for nanosrucure calculaons 2 Shockley-Read-Hall nonradave decay calculaons 3 Real-me TDDFT smulaons 4 Quanum ranspor calculaons 5 Acceleraed aomc relaxaon 6 DFT band gap correcon They are examples of our mehodology developmens, and hey wll be able o be calculaed by PWma n he fuure

16 Deep sae decay: wha we need o calculae? SRH carrer nonradave recombnaon A long sandng problem haven been solved by ab no mehod mpury 1 Elecronc sae energes: Usng convenonal deep sae calculaon mehods EN+1-EN. 2 Phonon frequences and modes: We wll use an approxmae mehod o calculae he dynamc marx 3 Elecron-phonon couplng consans: We wll nroduce a new varaonal algorhm

17 The formalsm Freed and Jorner, J. Chem. Phys. 50, ω k : phonon frequency for mode k, ΔE sl : dfference beween saes s and l C k sl s H k l Elecron-phonon couplng consan E M : he reorganzaon energy j j s l D j j 1/ 2 j Q j Q j j j n M 1/ 2 D 2 s lke he reorganzaon energy E yk / 2 λ k

18 Zn-V N cener n GaN n-ype for hole rappng CBM mpury 0.9 ev VBM 299 aom supercell

19 Approxmaed Hessan marx for phonon mode ' ', 2 ' R R R R M k k R k ' ' 1 ' 1 ', ' 2 ' R R F M M R R E M M R R M R R R R R

20 Elecron-phonon calculaons C k sl s H k l Ψ s, ψ l are already known, bu need hundreds of SCF calc. o ge δh/δμ k. New algorhm: one SCF calculaon o ge all C k sl: r occ 2 l k fxed Then normal SCF calculaon o ge he KS wave funcons, and Feynman-Hellman mehod o calculae he aomc forces F R Then one can prove usng varaonal prncple: F R l H R k Then, F R, ogeher wh phonon mode μ k R can be used o consruc C k sl. Smlar formalsm also works for hybrd funconal

21 The roles of dfferen phonon modes Passvaon modes mulple phonon emsson o sasfy energy conservaon Smulaon modes large elecron-phonon couplng consans

22 The resuls Exp Sac Adabac Marcus heory Quanum CT rae 1D quanum formula GaP:Zn Ga-O P GaN:Z n Ga -V N 1.46 x 10-7

23 Oulne 1 Charge pachng mehod for nanosrucure calculaons 2 Shockley-Read-Hall nonradave decay calculaons 3 Real-me TDDFT smulaons 4 Quanum ranspor calculaons 5 Acceleraed aomc relaxaon 6 DFT band gap correcon They are examples of our mehodology developmens, and hey wll be able o be calculaed by PWma n he fuure

24 Real-me TDDFT mehod r-tddft R-TDDFT can be used o sudy many phenomena Sysem response o an arbrary Vr, perurbaon Nonlnear response coeffcens Ulra-fas dynamcs carrer coolng and charge njecon Ion-collson Carrer ranspors We wll mplemen r-tddft as Ehrenfes dynamcs me dependen Schrodnger s eq for elecron dynamcs Newon s law for nuclear dynamcs E o 1 R 2 R M 2 R H M R E DFT [, R] 2 KS[ ] R F R F R R E DFT [, R] Hellman-Feyman force

25 Drec wave funcon me evoluon Tme dependen Schrodnger s Eq. for elecron wave funcon Newon s law for nuclear movemen

26 Convenonal real-me TDDFT mehod exp H exp H 1H Need HΔ << 1 For PW, H ~ 200 ev, Δ < 2x10-5 fs!! I could be a housand mes slower han ab no MD!

27 A new algorhm o accelerae he me negraon,,, V j C C C j j ] [ R H I only needs o solve ϕ every Δ~ 0.2 fs. H H H 1 1 Δ Δ Φ 0 Φ Δ Φ 2Δ d = 10-4 fs, C

28 A smplfed formalsm j j j j ', 1 1 ', 1 ' 1 ', H H H H ' ', ',,, C V C C Insead of: ',, ' ', C H C We do: no need o dagonalze H every d V j can have sharp peak wh

29 Inegrae ψ from 1 o 1 +Δ d Δ H, ' 1, ' 1 H, ' C, C ' d e e H, ' C ', H 0.5d d C 0.5 d 0.5d 1 H 0.5 d e e C d 10-3 fs Taylor expanson Due o he runcaon of adabac bass ypcally 10 ev above CBM, he negraon of C does no ake me

30 Comparson: new mehod and convenonal mehod CdSe bulk wh random movemen 1 2 = 1 +1fs

31 Opcal absorpon calculaon New mehod: r-ddf PWscf: perurbav TDDFT a.u 50 aom Au nanocluser

32 Exced sae coolng n a 100 Al aom cluser Toal energy conservaon

33 A Cl- on colldng on MoSe2

34 TD: r-tddft: BO: Born-Oppenhemer Knec and poenal energes

35 Plasmon excaon for a Ag55 nanocluser

36 Sngle parcle and plasmon excaon n Ag55

37 Oulne 1 Charge pachng mehod for nanosrucure calculaons 2 Shockley-Read-Hall nonradave decay calculaons 3 Real-me TDDFT smulaons 4 Quanum ranspor calculaons 5 Acceleraed aomc relaxaon 6 DFT band gap correcon They are examples of our mehodology developmens, and hey wll be able o be calculaed by PWma n he fuure

38 Elecron quanum ranspor problem r exp k E r r exp k E r { V r} r E r exp k E r In comng wave Transmed wave Refleced wave I s a Schrodnger s equaon wh an open boundary condon

39 The dea For a gven E, solve l r from he lnear equaon 1 2 { V r E} l r Wl r 2 for many W l r, hen recombne hese l r o ge he proper open boundary condons a he elecrode. W l r are only nonzero near he boundary of he supercell The above lnear equaon s solved usng he conjugae graden mehod n an lower egen saes deflaed space so he marx s posve defne. Transpor calculaon usng nonlocal pseudopoenal and PW bass

40 The resuls The scaerng sae wave funcons The ransmsson coeff. of a benzene molecule under dfferen volage bases.

41 Use ranspor calculaon o sudy 2D TFET

42 Oulne 1 Charge pachng mehod for nanosrucure calculaons 2 Shockley-Read-Hall nonradave decay calculaons 3 Real-me TDDFT smulaons 4 Quanum ranspor calculaons 5 Acceleraed aomc relaxaon 6 DFT band gap correcon They are examples of our mehodology developmens, and hey wll be able o be calculaed by PWma n he fuure

43 Fng a Lennard-Jones LJ poenal o ge approx. Hessan On he flgh fng o yeld he approxmaed Hessan marx Then use for CG or BFGS aomc relaxaons

44 The fed Hessan marx for Cd4Se4 and S20 DFT LJ Cd4Se4 S 20 Zhanghu Chen, Jngbo L, Shu-Shen L and Lnwang Wang. Phys. Rev. B. 89, , 2014.

45 Acceleraon wh he fed Hessan

46 Use surrogae poenal on-he-flgh fed poenal as our gude. A curved lne mnmzaon algorhm The precondon s only useful close o he mnmum Wha happen f he nal confguraon s far away from he mnmum Improve he lne-mnmzaon sep The bes lne pah mgh no be a sragh lne, perhaps s a curved lne roaon of a molecule or orson angle, ec For some sysems, hs can be addressed by usng he proper nernal coordnaes Bu we need a more general approach

47 The procedure Sep 1: Inalzaon Sep 2: Force fng for he force feld Sep 3: Compue curved pah from force feld Sep 4: Do curve lne mnmzaon usng DFT Sep 5: Back o sep 2 for nex eraon

48 On he flgh fng of he force feld Meal clusers Gupa Force feld for meal clusers Fng objecve for aj, bj, pj, qj, rj0: mn k Gupa DFT 2 k k T F F Resrcon: aj=aj, pj=pj ; cu-off dsance; parameer regon resrcon, e.g. [amn amax].

49 Resuls for curved mnmzaon scheme Ieraon seps

50 Oulne 1 Charge pachng mehod for nanosrucure calculaons 2 Shockley-Read-Hall nonradave decay calculaons 3 Real-me TDDFT smulaons 4 Quanum ranspor calculaons 5 Acceleraed aomc relaxaon 6 DFT band gap correcon They are examples of our mehodology developmens, and hey wll be able o be calculaed by PWma n he fuure

51 Perdew e al., PRL 49, The DFT band gap error

52 Enforce he lnear condon l l l l LDA w w H H l l l l s s E E l ] 1 1 [ 2 N E s N E s w s E s E l l l l LDA l l Bu for bulk sysems, w l s exended, and λ l s zero

53 Solved hs problem by usng Wanner funcons for W l Usng Wanner90 o generae he Wanner funcons

54 Calculaons ev Band gap correcon for bulk semconducors lda cor

55 Benzene Wanner funcon s no egen fucnon Correc rends Exend o bulk

56 The energy levels nsde he bands

57 Conclusons There are much o be done for algorhm developmens We have many new algorhms and mehods All hese algorhms are planned o be mplemened n PWma We can do many problems wh PWma Thank you!