1、计算凝聚态物理研究HPCfirst principles calculationsmy work in computational physics1946年年2月月15日，第一台电子数字日，第一台电子数字计算机计算机ENIAC问世，这标志着计算问世，这标志着计算机时代的到来。机时代的到来。时钟频率时钟频率100 KHz，能在，能在1秒钟的时秒钟的时间内完成间内完成5000次加法运算。次加法运算。Jaguar,which is located at the Department of Energys Oak Ridge Leadership Computing Facility and was
2、upgraded earlier this year,posted a 1.75 petaflop/s performance speed running the Linpack benchmark.Jaguar roared ahead with new processors bringing the theoretical peak capability to 2.3 petaflop/s and nearly a quarter of a million cores.One petaflop/s refers to one quadrillion calculations per sec
3、ond.(Year 2009,being No.1 till now)US DOE ASCI systems are claiming the first four positions of the TOP500.The new IBM ASCI White system at Lawrence Livermore National Laboratory is the new number one with 4.9 TFlop/s Linpack performance.This system is built with 512 nodes,each of which contains 16
4、IBM Power3 processors using a shared memory.This type of hierarchical architecture is more and more common for systems used in HPC.(Year 2000)*11月15日21日在美国菲尼克斯举行的SC2003超级计算机会议上，第22届国际高性能计算机性能TOP500排行榜如期揭晓。从榜单上看，虽然第一名仍被基于矢量技术的日本地球模拟器以35.86Tflop/s的Linpack性能值稳占，第二名也依然是Linpack值为13.88Tflop/s、安装于美国能源部洛斯阿拉
5、莫斯国家实验室的ASCI Q，但是从第三名开始便引出了本届排行榜的第一个亮点机群（Cluster）系统的提升，包括最高名次的提升和总数量的提升。A Chinese system called Nebulae,build from a Dawning TC3600 Blade system with Intel X5650 processors and NVidia Tesla C2050 GPUs is now the fastest in theoretical peak performance at 2.98 PFlop/s and No.2 with a Linpack performa
6、nce of 1.271 PFlop/s.This is the highest rank a Chinese system ever achieved.There are now 2 Chinese systems in the TOP10 and 24 in the TOP500 overall.Top 10 in 2010应用是最欠缺的意味机会也最多My cluster at School of Physics系统总的双精度浮点峰值理论性能达24万亿次每秒（2.4T）(峰值计算能力公式=主频*每个时钟周期执行指令数*CPU核数*系统CPU总数;即,2.66*4*4*56=2384Gflo
7、p)One of the applications in scientific research-ab initio calculations of condensed matter*simulations in other scales:molecular dynamicsfinite element methodFirst Principles Calculations Based on Density Functional Theory(DFT)What does“first principles”mean?-Also called ab initio calculations-Mean
8、s from the beginning-No parameters from experiments usedWhat can we calculate?-Electronic structure of condensed matter-magnetic properties-optical properties-structural optimization of defects-molecular dynamics simulationsHistory of Density Functional TheoryWALTER KOHN JOHN A.POPLE 1998 Nobel Laur
9、eate in Chemistry for his development of computational methods in quantum chemistry 1998 Nobel Laureate in Chemistry for his development of the density-functional theory History of Density Functional TheoryBust of Schrdinger,in the courtyard arcade of the main building,University of Vienna,Austria.T
10、he Schrodinger Equation(in 1926):Hti/EHOr the static one:For hydrogen atom:remH2222)(/6.132eVnEn),()(lmnnlmYrRHistory of Density Functional TheoryH2(or He)with two electronsearly approachesHeitler and London(1927)Mullikan(1928)James and Coolidge(1933,the most successful)depends on M parameters M33N,
11、N is the number of electrons M can be significantly reducedSystem with more electrons(e.g.N=100)M3300 10150-Density functional theory provides just a solution to such large systemsHistory of Density Functional TheoryThe basic lemma of Hohenberg-KohnThe ground state density n(r)of a bound system of i
12、nteracting electrons in some external potential v(r)determines this potential uniquely.or v(r)=Fn(r)or to say:n(r)completely characterizes the systemthe system is completely specified by n(r)The Hohenberg-Kohn Variational Principle rdrnrVrnUrnTrnE3)()()()()(rdrnrVrnErnVrnTrnExcH30)()()()()()(or wher
13、e|)()()(33rrddrrrnrnrnVHHistory of Density Functional TheoryVariational principle:E=min En(r)We have single electron equation(Kohn-Sham):0)()(21(2rrvjjeff)(|)()()(rvdrrrrnrvrvxceff|)()(21)()()(drdrrrrnrndrrnrvrnEExcxcjj)()()(rnrnErvxcxcandWhereThe total energy of the system:Approximation for Excn(r)
14、The local density approximation(LDA)Beyond the local density approximationdrrnrnernExcLDAxc)()()(GGA(generalized gradient approximation)meta-GGAHybrid functionals that includes the HF exact exchangeFor a uniform electron gas:78.044.0458.0)(ssxcrrneSimple but the results are surprisingly usefulAbout
15、the VASP code1.Written by Georg Kresse,Martijn Marsman,and Jurgen FurthmullerComputational Physics,Faculty of PhysicsUniversitat WienSensengasse 8,A-1130 Wien,Austria2.http:/cms.mpi.univie.ac.at/VASP/3.CharacteristicsThe code is easy to use:just prepare four files for each calculationThe system that
16、 modeled can be as large as having several hundred atomsThe results are reliableIt is ever developing to include more functionsThe code is well parallel programmed so it runs fast enoughIt is used worldwideProjects in my groupDoping of graphenehydrogen fuel cellPt catalystcarbon alloy to replace Ptw
17、hich kind of structure is the keyhow to realize itGrowth mechanism of semiconductorshow to dope themhow to reduce the effect of extended defectsConductivity at complex oxide interfacesurface effectsdoping effectsMy recent works in the material research1.Passivation of the grain boundaries(dislocatio
18、ns)in semiconductors2.Enhancing dopant solubility via epitaxial surfactant growth3.Extra large hydrogen bonding at the solid-solution interfacePassivation of the grain boundaries(dislocations)in semiconductors Why the passivation is important?The band gap of CdTe is 1.45 eV,ideal for solar energy.Co
19、nversion efficiency record:16.5%.Back contactLarge density ofgrain boundariesDetrimental effect of grain boundaries-recombination center Valence BandConduction BandEgValence BandConduction BandPassivation of the grain boundaries(dislocations)in semiconductors Why passivation is important?The band ga
20、p of CdTe is 1.45 eV,ideal for solar energy.Conversion efficiency record:16.5%.Back contactLarge density ofgrain boundariesCdCl2 heat treatmentCu from the back contact Atomic model of the grain boundariesCdTeCd-core112111S2I2S7S1I1S4S6S3S5each core is mirror symmetricThe cores are periodic along 111
21、In Te-core,the Te atms at S1 and Cd at S2 both form dimersIn Cd-core the Cd at S4 and Te at S5 do not form dimersFormed by incorporating two(111)surfacesTe at S3(Cd at S6)is 5-coordinatedTe at S1(Cd at S4)is 4(3)-coordinatedCd at S2(Te at S5)is 4(3)-coordinated39Te-coreDOS of the grain boundaries I
22、IIITe-coreCd-core II112111States below CBMStates above VBMDeep statesIIIIIICBMVBMDOSS2I2S7S1I1S4S6S3S5Both Cl and Cu prefer the GBs than bulkCl and Cu both favor in the Te-coreCl favors substitutional(S1)other than interstitialCu favors substitutional(S2)other than interstitialWhere do the impuritie
23、s locate?Te-coreCd-corePassivation effect of ClIII IIICBMVBMTe-coreClCd-coreS2S7S1Only half of the Te atoms at S1 are needed to be substitutedThe deep states at S2 and S7 are not affected.The passivation is localized.Passivation effect of ClII IIICBMVBMIClCd-coreIIIIIICBMVBMClCd-coreI2S7Cl cant pass
24、ivate Cd-core.Partial charge density of the deep states in region IIPassivation effect of CuIICBMVBMTe-coreClCuCd-coreCd-coreTe-coreClCuIThe passivation of the deep levels in Te-core is complete.Passivation effect of CuIIIIICBMVBMICuCd-coreCu cant passivate Cd-core.Results The passivations of Cl and
25、 Cu are successful in Te-core but not in Cd-core For high efficiency solar cells,Te-core may dominate To completely passivate the Te-core,Cl and Cu are both needed Co-passivation might be applied to other materials like pc-Si and pc-GaAs For detail,please refer to Phys.Rev.Lett.101,155501(2008).Enha
26、ncing dopant solubility via epitaxial surfactant growthWith Sb or Bi at the surface,the density of Zn dopant can increase by an order of magnitude.GaP:Zn (100)Sb(Bi)Howard,Chapman,and Stringfellow,J.Appl.Phys.100,044904(2006).Zhu,Liu,and Stringfellow,Phys.Rev.Lett.101,196103(2008)H(a)-P(b)-P,H(d)-Sb
27、,HGaPZnGaHSbSbZnGaHAtomic models of the dual-surfactant effectSb(c)-SbFormation energies of the substitutional Zn in sublayerSurfacesFormation energy(Ef)in eVP-terminated(-P)=2.24+mGa-mZnSb-terminated(-Sb)=2.59+mGa-mZnP-terminated with H(-P,H)=2.63+mGa-mZnSb-terminated with H(-Sb,H)=1.78+mGa-mZnBulk
28、=2.80+mGa-mZn Band structures of the surfaces Dashed lines are Fermi levels Energy zero is the VBM of GaP Bands A and B are localized surface states In P-,they are shallow states and locate around VBM In Sb-,these states are much higher but empty In Sb,H-,they are totally filled The electronic origi
29、n of the dual-surfactant effect The surfactant Sb provides the deep levels H will pin the Fermi level as high as possible(close to CBM)The level of the Zn substitutional is always around VBM The higher the Fermi level locates,the more energy the charge transfer gains.This makes the Zn incorporation
30、more favorable.VBCBZnGaSb A general rule?The key of this concept is to find the appropriate surfactants that generate high(low)levels that can transfer electrons(holes)to dopant acceptor(donor)levels in p-type(n-type)doping,thus significantly lowering the formation energy of dopant defects.Sole surf
31、actant Te induced enhancement of N solubility in ZnSe lThe Te induced states are filledlNo H is neededlConsistent with the experiments,see e.g.,Gu et al,J.Electron.Mater.31,799(2002)Lin et al,Appl.Phys.Lett.76,2205(2000).Surfactants for enhancing p-type doing of ZnO with epitaxial growth lp-type ZnO
32、 can be realized if the solubility of Ag or Cu can be significantly increasedlS,Se,or Te may act as surfactantslH helpsDetail:Phys.Rev.B 80,073305(2009)Extra large hydrogen bonding at the solid-solution interfaceq Multiple Exciton Generation(MEG)effect for nano crystalsq Shape control is an importan
33、t issue in nano crystals growth.q Facts of PbS:qEg 0.4 eV with Rocksalt structure(NaCl)q(100)is the natural cleavage surface Lee et al,JACS,2002(100)(111)Energies of PbS surfaces in vacuum(100)(110)(111)*SPb0.058(100)(111)(110)(eV/2)*For(111)data,it is for a pair of Pb-and S-terminated surfacesDepen
34、dence of surface energy on the growth conditionmS=0,S in bulk elemental phasemS=-1.13,Pb in bulk elemental phaseS-2S-1Pb(100)(111)1.85NCHsurfaceCoverageAdsorption energy(eV/molecule)(111)ML0.80 ML0.55(100)ML0.45 ML0.34Adsorption of methylamine is not enough to convert the energy order of PbS surface
35、sDependence of surface energy on the growth conditionmS=0,S in bulk elemental phasemS=-1.13,Pb in bulk elemental phaseAdsorption of CH3NH2 in water solutionPb1.81(1.85)1.07(1.02)1.78(2.32)SThis increase originates from two factors:-increase of the H-bonding strength-the increase of N-S interactionNu
36、mber of H-bonds ML ML00.80 0.5511.20 1.0121.93 1.50Adsorption Enegies(eV/molecule)(111)(100)Dependence of surface energy on the growth conditionmS=0,S in bulk elemental phasemS=-1.13,Pb in bulk elemental phaseConclusionIn vacuum,the energy of PbS(111)surface is much higher than that of(100)surfaceAd
37、sorbing methylamine(CH3NH2)does not change much of the above factWater can form hydrogen bond with methylamineWith water and hydrogen bonds,the adsorption of methylamine on(111)-S surface can be greatly enhanced,making the(111)surface is energetically favored over the(100)surfaceThis study provides a possible mechanism on how to tune the surface energy by selecting specific solutionRefer to Phys.Rev.Lett.104,116101(2010)for detail Home workFind one application of supercomputer in physics related field that you think is interesting*Discussions of next class will base on your findings
