Maeral Scence Smulaons usng PWma Ln-Wang Wang Chef Techncal Advsor, LongXu
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
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.
The accuracy for he small S quanum do 8 22
Folded Specrum Mehod H ref ref H 2 2 N } 2 1 { 2 r E r r V
CdSe quanum do resuls
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
Effec of surface dpole and CdS core n a CdSe rod Cd ermnaed surface Cd and Se ermnaed surface
2 1 2 r r r V r P r V c c c v C LDA 2 1 2 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
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 45 68 71 153 246 Ths s ofen arbued o he onse poenal, besdes 1/ε r I s embarrassng ha we sll canno calculae he smple bndng energy
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
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
Fnal resuls based on he Schrodnger s equaon elemen B Al Ga In Tl ε_b exp mev 45 68 71 153 246 ε_b calc mev 43 57 59 92 112 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 45 68 71 153 246 ε_b calc mev 44 62 71 139 246
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
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
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
The formalsm Freed and Jorner, J. Chem. Phys. 50, 2916 1969. 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 2 2 2 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
Zn-V N cener n GaN n-ype for hole rappng CBM mpury 0.9 ev VBM 299 aom supercell
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
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
The roles of dfferen phonon modes Passvaon modes mulple phonon emsson o sasfy energy conservaon Smulaon modes large elecron-phonon couplng consans
The resuls Exp Sac Adabac Marcus heory Quanum CT rae 1D quanum formula GaP:Zn 3.32 10-10 Ga-O P GaN:Z n Ga -V N 1.46 x 10-7
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
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
Drec wave funcon me evoluon Tme dependen Schrodnger s Eq. for elecron wave funcon Newon s law for nuclear movemen
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!
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
A smplfed formalsm 1 1 2 1 1 j j 2 1 1 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
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
Comparson: new mehod and convenonal mehod CdSe bulk wh random movemen 1 2 = 1 +1fs
Opcal absorpon calculaon New mehod: r-ddf PWscf: perurbav TDDFT a.u 50 aom Au nanocluser
Exced sae coolng n a 100 Al aom cluser Toal energy conservaon
A Cl- on colldng on MoSe2
TD: r-tddft: BO: Born-Oppenhemer Knec and poenal energes
Plasmon excaon for a Ag55 nanocluser
Sngle parcle and plasmon excaon n Ag55
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
Elecron quanum ranspor problem r exp k E r r exp k E r { 1 2 2 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
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
The resuls The scaerng sae wave funcons The ransmsson coeff. of a benzene molecule under dfferen volage bases.
Use ranspor calculaon o sudy 2D TFET
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
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
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, 144110, 2014.
Acceleraon wh he fed Hessan
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
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
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].
Resuls for curved mnmzaon scheme Ieraon seps
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
Perdew e al., PRL 49, 1691 1982 The DFT band gap error
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
Solved hs problem by usng Wanner funcons for W l Usng Wanner90 o generae he Wanner funcons
Calculaons ev Band gap correcon for bulk semconducors 9 8 7 lda cor 6 5 4 3 2 1 0-1 -1 0 1 2 3 4 5 6 7 8 9
Benzene Wanner funcon s no egen fucnon Correc rends Exend o bulk
The energy levels nsde he bands
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!