PhysRevLett.104.040502 [topological quantum computation using semiconductor heterostructures

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Generic New Platform for Topological Quantum ComputationUsing Semiconductor HeterostructuresJay D.Sau,1Roman M.Lutchyn,1Sumanta Tewari,1,2and S.Das Sarma11Condensed Matter Theory Center and Joint Quantum Institute,Department of Physics,University of Maryland,College Park,Maryland20742-4111,USA2Department of Physics and Astronomy,Clemson University,Clemson,South Carolina29634,USA(Received17July2009;published27January2010)We show that aﬁlm of a semiconductor in which s-wave superconductivity and Zeeman splitting are induced by the proximity effect,supports zero-energy Majorana fermion modes in the ordinary vortex excitations.Since time-reversal symmetry is explicitly broken,the edge of theﬁlm constitutes a chiral Majorana wire.The heterostructure we propose—a semiconducting thinﬁlm sandwiched between an s-wave superconductor and a magnetic insulator—is a generic system which can be used as the platform for topological quantum computation by virtue of the existence of non-Abelian Majorana fermions.DOI:10.1103/PhysRevLett.104.040502PACS numbers:03.67.Lx,71.10.Pm,74.45.+cIntroduction.—In two spatial dimensions,where permu-tation and exchange are not necessarily equivalent,par-ticles can have quantum statistics which are strikingly different from the familiar statistics of bosons and fermi-ons.In situations where the many body ground state wave function is a linear combination of states from a degenerate subspace,a pairwise exchange of the particle coordinates can unitarily rotate the ground state wave function in the degenerate subspace.In this case,the exchange statistics is given by a multidimensional unitary matrix representation (as opposed to just a phase factor)of the2D braid group, and the statistics is non-Abelian[1].It has been proposed that such a system,where the ground state degeneracy is protected by a gap from local perturbations,can be used as a fault-tolerant platform for topological quantum compu-tation(TQC)[2].Recently,the ¼5=2fractional quantum hall(FQH) state at high magneticﬁelds and at low temperature has been proposed as a topological qubit[2].This theoretical conjecture,however,awaits experimental veriﬁcation [3,4].An equivalent system,in which the ordered state is in the same universality class as the5=2FQH state,is the spinless(spin-polarized)p xþip y superconductor or su-perﬂuid[5].In aﬁnite magneticﬁeld,a vortex excitation in such a superconductor traps a single,nondegenerate,zero-energy bound state.The key to non-Abelian statistics is that the second-quantized operator for this zero-energy state is self-Hermitian, y¼ ,rendering a Majorana fermion operator.If the constituent fermions have spin,the spin-degeneracy of the zero-energy excitation spoils the non-Abelian statistics.To circumvent this problem in a realistic superconductor such as strontium ruthenate,it has been proposed that the requisite excitations are the exotic half-quantum vortices[6].Even though quenching the spin degeneracy by either the application of a magneticﬁeld[7]or by using spinless atomic systems[8]is possible in principle,it is practically very difﬁcult.Therefore,it is desirable to have systems whose most natural excitations themselves follow non-Abelian statistics in spite of the electrons carrying a spin quantum number.The recent proposal by Fu and Kane[9] points out one such system—the surface of a strong TI in proximity to an s-wave superconductor—which supports a nondegenerate Majorana fermion excitation in the core of an ordinary vortex.In this Letter,we propose a simple generic TQC platform by showing that it is possible to replace the TI with a regular semiconductorﬁlm with spin-orbit coupling,provided the time-reversal symmetry is broken by proximity of theﬁlm to a magnetic insulator. It is encouraging that the s-wave proximity effect has already been demonstrated in2D InAs heterostructures which additionally also have a substantial spin-orbit cou-pling[10].Thus,the structure we propose is one of the simplest to realize non-Abelian Majorana fermions in the solid-state context.Theoretical model.—The single-particle effective Hamiltonian H0for the conduction band of a spin-orbit coupled semiconductor in contact with a magnetic insula-tor is given by(we set@¼1henceforth)H0¼p22mÃÀ þV z zþ ð~ Â~pÞÁ^z:(1) Here,mÃ,V z,and are the conduction-band effective mass of an electron,effective Zeeman coupling induced by proximity to a magnetic insulator(we neglect the direct coupling of the electrons with the magneticﬁeld from the magnetic insulator),and chemical potential,respectively. The coefﬁcient describes the strength of the Rashba spin-orbit coupling,and are the Pauli matrices.Despite the similarity in the spin-orbit-coupling terms,H0and the Hamiltonian for the TI surface in Ref.[9]differ by the existence of a spin-diagonal kinetic energy term in Eq.(1). Because of the spin-diagonal kinetic energy,there are,in general,two spin-orbit-split Fermi surfaces in the presentsystem,in contrast to the surface of a TI in which an odd number of bands cross the Fermi level [9].In Eq.(1),for out-of-plane Zeeman coupling such that j V z j >j j ,a single band crosses the Fermi level.Thus,analogous to a strong TI surface (but arising from qualitatively different physics),the system has a single Fermi surface,which is suggestive of non-Abelian topological order if s -wave superconductivity is induced in the ﬁlm.The proximity-induced superconductivity in the semi-conductor can be described by the Hamiltonian,^H p ¼Zd r f Á0ðr Þ^c y "ðr Þ^c y #ðr ÞþH :c :g ;(2)where ^c y ðr Þare the creation operators for electrons withspin and Á0ðr Þis the proximity-induced gap.The corre-sponding BdG equations written in Nambu space become,H 0Á0ðr ÞÁÃ0ðr ÞÀ y H Ã0 y Éðr Þ¼E Éðr Þ;(3)where Éðr Þis the wave function in the Nambu spinorbasis,Éðr Þ¼½u "ðr Þ;u #ðr Þ;v #ðr Þ;Àv "ðr Þ T .Using the solu-tions of the BdG equations,one can deﬁne Bogoliubov quasiparticle operators as ^ y ¼R d r Pu ðr Þ^c y ðr Þþv ðr Þ^cðr Þ.The bulk excitation spectrum of the BdG equations with Áðr Þ¼Á0has a gap for nonvanishing spin-orbit coupling.BdG equations for a vortex.—We now consider thethe vortex-like conﬁguration of the order parameter:Á0ðr; Þ¼Á0ðr Þe { .Because of the rotational symmetry,the BdG equations can be decoupled into angular momen-tum channels indexed by m with the corresponding spinor wave function,Ém ðr; Þ¼e {m ½u "ðr Þ;u #ðr Þe i ;v #ðr Þe Ài ;Àv "ðr Þ T :(4)Since the BdG equations are particle-hole symmetric,if Ém ðr Þis a solution with energy E ,then { y y ÉÃm ðr Þis also a solution at energy ÀE in the angular momentum channel Àm .Here, y is deﬁned to be the Pauli matrix in Nambu spinor space.Thus,a zero-energy solution can be non-degenerate only if it exists in the m ¼0angular momen-tum channel.The radial BdG equations describing the zero-energy state Éðr Þin the m ¼0channel can be written asH 0Á0ðr ÞÁ0ðr ÞÀ y H Ã0 yÉðr Þ¼0;H 0¼À ð@2r þ1r @r ÞþV z À ð@r þ1r ÞÀ @rðÀ@2r À1@r þ12ÞÀV z À !(5)with ¼12m Ã.Additionally,since the BdG matrix is real,both ÉÃðr Þand { y y Éðr Þare also E ¼0solutions.Thus,Éðr Þcan be nondegenerate only if { y y Éðr Þ¼{ Éðr Þ,where the ð{ y y Þ2¼À1imposes the constraint ¼Æ1.Fixing a value of allows one to deﬁne Éðr Þin terms of the reduced spinor É0ðr Þ¼½u "ðr Þ;u #ðr Þ T using the relations v "ðr Þ¼ u "ðr Þand v #ðr Þ¼ u #ðr Þ.The corresponding reduced BdG equations take the form of a 2Â2matrix differential equation:À ð@2r þ1r @r ÞþV z À Áðr Þþ ð@r þ1r ÞÀ Áðr ÞÀ @r À ð@2r þ1r @r À1r 2ÞÀV z À!É0ðr Þ¼0:(6)We now approximate the radial dependence of Á0ðr ÞbyÁ0ðr Þ¼0for r <R and Á0ðr Þ¼Á0for r !R .In view of the stability of the putative Majorana zero-energy solution to local changes in the Hamiltonian [5],such an approxi-mation can be made without loss of generality.For r <R ,the analytical solution of Eq.(6)is given by É0ðr Þ¼½u "J 0ðzr Þ;u #J 1ðzr Þ T with the constraintz 2þV z À zz z 2ÀV z À u "u #¼0:(7)Here,J n ðr Þare the Bessel functions of the ﬁrst kind.Thecharacteristic equation for z isð z 2À Þ2ÀV 2zÀ 2z 2¼0:(8)Since the Bessel functions are symmetric,we use the roots13behaved at the origin:É1ðr Þ¼½u "J 0ðz 1r Þ;u #J 1ðz 1r Þ T and É2ðr Þ¼½u "J 0ðz 3r Þ;u #J 1ðz 3r Þ T .Therefore,the full solu-tion at r <R is É<0ðr Þ¼c 1É1ðr Þþc 2É2ðr Þ.At large distances r >R ,where Á0ðr Þ¼Á0,the solu-tion to Eq.(6)is complicated.Nevertheless,one can write the solution as a series expansion in 1=r :É0ðr Þ¼e {zr ﬃﬃﬃr p X n ¼0;1;2...a nr n (9)where a n are the corresponding spinors.The zeroth order coefﬁcient a 0satisﬁes the following equation:z 2þV z ÀÁ0þ{z À Á0À{z z 2ÀV z Àa 0¼0:(10)FIG.1(color online).Schematic picture of the proposed het-erostructure exhibiting Majorana zero-energy bound state insidean ordinary vortex.The higher order coefﬁcients a n can be calculated from a 0using a set of recursion relations [11].The characteristic equation for Eq.(10)has 4complex roots for z ,which are shown in Fig.2.Physical solutions of Eq.(6)at r >R ,É>0ðr Þ¼P n>2c n Én ðr Þ,require that Im ½z n >0.[Here Én ðr Þis the solution corresponding to the eigenvalue z n ].Thus,for ð 2þÁ20Þ>V 2z ,there are two solutions for ¼Æ1.On the other hand,for ð 2þÁ20Þ<V 2z ,there are threesolutions for ¼À1and only one for ¼1.To obtain a unique solution for the zero-energy state,the2-component wave functions É>0ðr Þand É<0ðr Þshould satisfy four boundary conditions at r ¼R ,namely,the continuity of É0ðR Þand É00ðR Þ.One additional constraint comes from the normalization of the wave function in all space.Thus,there are ﬁve independent constraints for the coefﬁcients c n .A unique zero-energy solution exists if the number of unknown coefﬁcients c n is ﬁve,which is thecase for ð 2þÁ20Þ<V 2z and ¼À1.In this case,the wave functions É<0ðr Þ¼P n ¼1;2c n Én ðr Þand É>0ðr Þ¼Pn ¼3;4;5c n Én ðr Þhave 2and 3unknown coefﬁcients,re-spectively.In all other cases the number of unknowns c n is smaller than 5,and thus,as we have checked explicitly,solutions for the zero-energy eigenfunction do not exist.From these arguments,one can conclude that,for ð 2þÁ20Þ<V 2z ,an ordinary vortex in the superconducting con-densate contains a unique nondegenerate E ¼0solution inthe m ¼0angular momentum channel.The numerical solution for the zero-energy state is shown in Fig.2(e).It is straightforward to check that the zero-energy solution corresponds to a self-Hermitian second-quantized operator ¼ y :it is a Majorana fermion excitation.We can also consider the special case with ¼0,V z ¼0in the above equations,which describes the recent pro-posal for TQC [9]using zero-energy Majorana boundstates at vortices on the interface of a TI and an s -wave superconductor.In this case,we ﬁnd a single solution for r <R and a pair of independent solutions for r >R .Since the BdG differential equation is now only ﬁrst order,we need only match the 2-component spinors themselves (de-rivatives need not match)which yields 3equations for the 3coefﬁcients.This leads to a unique Majarana fermion solution at the vortex,which is consistent with Ref.[9].Interestingly,in contrast to our Hamiltonian for >0,the condition for the existence of a Majorana fermion for ¼0is given by V 2z <ðÁ20þ 2Þ.The model considered in Ref.[9]and our present system have a similar order parameter structure.In both cases,the order parameter component h c "ðr Þc #ðr 0Þi has an s -wave orbital symmetry while the order parameter components h c "ðr Þc "ðr 0Þi and h c #ðr Þc #ðr 0Þi have p x þ{p y and p x À{p y orbital symme-tries,respectively.On the surface of a TI,because of time-reversal invariance,jh c "ðr Þc "ðr 0Þij ¼jh c #ðr Þc #ðr 0Þij .In our system,the ratio of the order parameter components in the two spin sectors is different from 1,and approaches 1in the limit 2= )V z .In both cases,however,the supercon-ducting pairing potential is s -wave,and is induced by proximity effect.Therefore,the superconducting state and the associated non-Abelian topological character are expected to be robust in the presence of ﬁnite disorder.Topological phase transition.—We have shown above that a nondegenerate Majorana state exists in a vortex in the superconductor only in the parameter regime ð 2þÁ20Þ<V 2z .This suggests that there must be a quantum phase transition (QPT)separating the parameter regimesð 2þÁ20Þ<V 2z and ð 2þÁ20Þ>V 2z ,even though the system in both regimes is an s -wave superconductor.A nondegenerate zero-energy solution cannot disappear un-less a continuum of energy levels appears around E ¼0.Such a continuum of states at E ¼0can only appear if the bulk gap closes,which can be used to deﬁne a topological quantum phase transition.In the present system,such a phase transition can be accessed by varying either the Zeeman splitting or the chemical potential.A similar to-pological quantum phase transition has already been pre-dicted for ultracold atoms with vortices in the spin-orbit coupling [12].The bulk gap of the present system can be calculated from the bulk excitation spectrum,E 2¼V 2z þÁ20þ~ 2þ 2k 2Æ2ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃV 2z Á20þ~ 2ðV 2z þ 2k 2Þq ;(11)where ~¼ k 2À .As seen in Fig.3,the excitation gap ﬁrst increases as a function of Á0(proximity-induced pair potential)and then decreases and vanishes at a criticalpoint,Á0c ¼ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃV 2zÀ 2q ,before reopening and increasing with Á0.The critical point marks the phase transition between a topologically nontrivial (left)and a topologi-cally trivial (right)s -wave superconducting phases.The scale of the gap in the topologically nontrivial phase issetFIG.2(color online).Upper panel:complex roots of the Eq.(10)for different values of and with Á0Þ0.Lower panel:Numerical solution for the Majorana zero-energy state É0ðr Þ¼½u ðr Þ;v ðr Þ T for ¼À1and <V z .The dashed (red)and solid (blue)lines correspond to u ðr Þand v ðr Þ,respectively.Here we used the following parameters: ¼ ¼V z ¼1, ¼0,Á0¼0:1and R ¼1.The boundary conditions used are É0ð0Þ¼ð1;0ÞT and É0ðr ¼40Þ¼ð0;0ÞT .by the strength of the spin-orbit coupling and the posi-tion of the critical point.The fact that the phase on the right-side of the critical point does not support a nonde-generate Majorana mode can be veriﬁed by observing that,for these values of Á0,it is possible to reduce V z such that j V z j <j j without the gap vanishing at any point.This is the phase without Majorana Fermion excitations.In fact,this phase can be reached from the conventional s -wave superconductor with V z ¼0and ¼0without crossing a phase transition.Majorana edge modes and TQC.—In analogy with Ref.[9],we ﬁnd that an interface between two supercon-ductor layers,which can be deposited on the semiconduc-tor thin ﬁlm,supports a pair of zero-energy excitations when the phase difference between the superconductors is .This geometry can be analyzed in a way that closely follows our derivation of the localized state in a vortex in the m ¼0channel,since the BdG Hamiltonian can again be reduced to a real matrix.In this case,we ﬁnd that,in theparameter regime ð 2þÁ20Þ<V 2z ,there are 3linearly independent solutions on each side of the interface.Since the number of constraints to be satisﬁed at the interface (we assume the interface to be of negligible width)remains 5as before,one expects a pair of independent zero-energy solutions.The interface,therefore,constitutes a nonchiral Majorana wire,which can be exploited for braiding in a way completely analogous to Ref.[9]to perform TQC.Majorana bound states as well as Majorana edge modes in our system can be studied experimentally using nonlocal Andreev reﬂection [13]and electrically detected interfer-ometry [14,15]experiments.The experimental implementation of this proposal in-volves a heterostructure of a magnetic insulator (e.g.,EuO),a strong spin-orbit coupled semiconductor (e.g.,InAs),and an s -wave superconductor with a large T c (e.g.,Nb).Using these materials,it is possible [11]to induce an effective superconducting pairing potential Á0$0:5meV and a tunneling-induced effective Zeeman split-ting V z $1meV .Additionally,the strength of spin-orbit interaction in InAs heterostructures is electric-ﬁeld tun-able and can be made as large as %50meV #A[16].With these estimates,the quasiparticle gap E g is of the order of 1K.Given that the chemical potential is gate-tunable and can be of the of the order of Á0,we numerically estimate the magnitude of the excitation energy for the bound states in a vortex core of size $20nm to be of the order of 0.1K [11],which sets the temperature scale for TQC in this system.Conclusion.—Our proposed TQC platform should be simpler to implement experimentally than any of the TQC candidates proposed in the literature so far,since it involves a standard heterostructure with a magnetic insu-lator,a semiconductor ﬁlm,and an ordinary s -wave super-conductor.We believe that the proposed scheme provides the most straightforward method for the solid-state real-ization of non-Abelian Majorana fermions.A signiﬁcant practical advantage of the proposed TQC scheme is its ge-neric simplicity:it requires neither special samples or ma-terials nor ultralow temperatures or high magnetic ﬁelds.This work is supported by DARPA-QuEST,JQI-NSF-PFC,and LPS-NSA.We thank M.Sato and S.Fujimoto for discussion.S.T.acknowledges DOE/EPSCoR Grant DE-FG02-04ER-46139and Clemson University start up funds forsupport.[1] C.Nayak et al.,Rev.Mod.Phys.80,1083(2008).[2]S.Das Sarma,M.Freedman,and C.Nayak,Phys.Rev.Lett.94,166802(2005).[3] A.Stern and B.I.Halperin,Phys.Rev.Lett.96,016802(2006).[4]P.Bonderson,A.Kitaev,and K.Shtengel,Phys.Rev.Lett.96,016803(2006).[5]N.Read and D.Green,Phys.Rev.B 61,10267(2000).[6] D.A.Ivanov,Phys.Rev.Lett.86,268(2001).[7]S.Das Sarma,C.Nayak,and S.Tewari,Phys.Rev.B 73,220502(R)(2006).[8]S.Tewari et al.,Phys.Rev.Lett.98,010506(2007).[9]L.Fu and C.L.Kane,Phys.Rev.Lett.100,096407(2008).[10] A.Chrestin,T.Matsuyama,and U.Merkt,Phys.Rev.B55,8457(1997).[11]J.D.Sau,R.Lutchyn,S.Tewari,and S.Das Sarma (to bepublished).[12]M.Sato,Y .Takahashi,and S.Fujimoto,Phys.Rev.Lett.103,020401(2009).[13]J.Nilsson,A.R.Akhmerov,and C.W.J.Beenakker,Phys.Rev.Lett.101,120403(2008).[14]L.Fu and C.L.Kane,Phys.Rev.Lett.102,216403(2009).[15] A.R.Akhmerov,J.Nilsson,and C.W.J.Beenakker,Phys.Rev.Lett.102,216404(2009).[16] C.Yang et al.,Phys.Rev.Lett.96,186605(2006).∆0,red0.511.52E g ,r e dFIG.3(color online).Quasiparticle gap versus pairing poten-tial for various values of the chemical potential .Here,E g;red ¼E g =V z ,Á0;red ¼Á0=V z , red ¼ =V z ,and red ¼ =ﬃﬃﬃﬃﬃﬃﬃﬃﬃV z p .The maximum value of the gap in the topologically nontrivial super-conductor,and the corresponding area in the phase diagram,decreases with increasing values of .For large negative ,the system makes a transition to a semiconductor.The phase to the right of the critical point is the topologically trivial s -wave superconductor.。

Topological Insulator

按照电子态结构的不同，传统意义上的材料被分为“金属”和“绝缘体”两大类。

而拓扑绝缘体是一种新的量子物质态，完成不同于传统意义上的“金属”和“绝缘体”。

这种物质态的体电子态是有能隙的绝缘体，而其表面则是无能隙的金属态。

这种无能隙的表面金属态也完全不同于一般意义上的由于表面未饱和键或者是表面重构导致的表面态，【拓扑绝缘体的表面金属态完全是由材料的体电子态的拓扑结构所决定，是由对称性所决定的，与表面的具体结构无关】。

也正是因为该表面金属态的出现是有对称性所决定的，他的存在非常稳定，基本不受到杂质与无序的影响。

除此之外，【拓扑绝缘体的基本性质是由“量子力学”和“相对论”共同作用的结果，由于自旋轨道耦合耦合作用，在表面上会产生由时间反演对称性保护的无能隙的自旋分辨的表面电子态】。

这种表面态形成一种无有效质量的二维电子气（与有效质量近似下的二维电子气完全不同：例如广泛使用的场效应晶体管中的二维电子气），它需要用狄拉克方程描述，而不能用薛定谔方程。

正是由于这些迷人的重要特征保证了拓扑绝缘体将有可能在未来的电子技术发展中获得重要的应用，有着巨大的应用潜在。

寻找具有足够大的体能隙并且具有化学稳定性的强拓扑绝缘体材料成为了人们目前关注的重要焦点和难点。

【拓扑绝缘体的表面金属态完全是由材料的体电子态的拓扑结构所决定，是由对称性所决定的，与表面的具体结构无关】这句话的意思是拓扑绝缘体的“拓扑”，不是实空间的拓扑结构，而是动量空间的拓扑结构。

说起拓扑，大家也许会联想到Möbius带，或者Klein瓶的东西，但实际上拓扑绝缘体与实空间的这些几何结构都没有关系，它的表面形貌和其它材料没有什么差别。

但是表面的电子态却按照不同自旋而具有不同的chirality，这是普通材料所没有的。

而且这种表面态是一定会存在的，不管你的表面多么不平整或者有多少杂质，只要两个相对的表面不要靠得太近，那么chiral 的表面态一定会茁壮地存在。

【昆虫系统基因组学】Phylogenomics resolves the timing and pattern of insect evolution

DOI: 10.1126/science.1257570, 763 (2014);346 Science et al.Bernhard Misof Phylogenomics resolves the timing and pattern of insect evolutionThis copy is for your personal, non-commercial use only.clicking here.colleagues, clients, or customers by , you can order high-quality copies for your If you wish to distribute this article to othershere.following the guidelines can be obtained by Permission to republish or repurpose articles or portions of articles): November 6, 2014 (this information is current as of The following resources related to this article are available online at/content/346/6210/763.full.html version of this article at:including high-resolution figures, can be found in the online Updated information and services, /content/suppl/2014/11/05/346.6210.763.DC1.html can be found at:Supporting Online Material /content/346/6210/763.full.html#ref-list-1, 58 of which can be accessed free:cites 161 articles This article/cgi/collection/evolution Evolutionsubject collections:This article appears in the following registered trademark of AAAS.is a Science 2014 by the American Association for the Advancement of Science; all rights reserved. The title Copyright American Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005. 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J.Jin,L.Agosto,T.Wang,R.B.Altman,and M.R.Wasserman for assistance;C.Walsh,J.Binely,A.Trkola,and M.Krystal for reagents;and members of the Structural Biology Section,Vaccine Research Center,for critically reading the manuscript.We thank I.Wilson and J.Sodroski for encouraging us to extend our approach to a R5-tropic Env.The data presented in this paper are tabulated in the main paper and in the supplementary materials.This work wassupported by NIH grants R21AI100696to W.M.and S.C.B;P0156550to W.M.,S.C.B.,and A.B.S.;and R01GM098859to S.C.B.;by the Irvington Fellows Program of the Cancer Research Institute to J.B.M;by a fellowship from the China Scholarship Council-Yale World Scholars to X.M.;by grants from the International AIDS Vaccine Initiative ’s (IAVI)Neutralizing Antibody Consortium to D.R.B.,W.C.K.,and P.D.K.;and by funding from the NIH Intramural Research Program (Vaccine Research Center)to P.D.K.IAVI's work is made possible by generous support from many donors including:the Bill &Melinda Gates Foundation and the U.S.Agency for International Development (USAID).This study is made possible by the generous support of the American people through USAID.The contents are the responsibility of the authors and do not necessarily reflect the views of USAID or the ernment.Reagents from the NIH are subject to nonrestrictive material transferagreements.Patent applications pertaining to this work are the U.S.and World Application US2009/006049and WO/2010/053583,Synthesis of JRC-II-191(A.B.S.,J.R.C.),U.S.Patent Application 13/202,351,Methods and Compositions for Altering Photopysical Properties of Fluorophores via Proximal Quenching (S.C.B.,Z.Z.);U.S.Patent Application 14/373,402Dye Compositions,Methods of Preparation,Conjugates Thereof,and Methods of Use (S.C.B.,Z.Z.);and International and US Patent Application PCT/US13/42249Reagents and Methods for Identifying Anti-HIV CompoundsSUPPLEMENTARY MATERIALS/content/346/6210/759/suppl/DC1Materials and Methods Figs.S1to S15Tables S1to S3References (46–56)4April 2014;accepted 15September 2014Published online 8October 2014;colonize and exploit terrestrial and freshwa-ter ecosystems.They have shaped Earth ’s biota,exhibiting coevolved relationships with many groups,from flowering plants to hu-mans.They were the first to master flight and establish social societies.However,many as-pects of insect evolution are still poorly under-stood (2).The oldest known fossil insects are from the Early Devonian [~412million years ago (Ma)],which has led to the hypothesis that in-sects originated in the Late Silurian with the earliest terrestrial ecosystems (3).MolecularEarly Ordovician origin (4),which implies that early diversification of insects occurred in marine or coastal environments.Because of the absence of insect fossils from the Cambrian to the Silurian,these conclusions remain highly controversial.Fur-thermore,the phylogenetic relationships among major clades of polyneopteran insect orders —including grasshoppers and crickets (Orthoptera),cockroaches (Blattodea),and termites (Isoptera)—have remained elusive,as has the phylogenetic position of the enigmatic Zoraptera.Even the closest extant relatives of Holometabola (e.g.,SCIENCE 7NOVEMBER 2014•VOL 346ISSUE 6210763RESEARCH |REPORTSbeetles,moths and butterflies,flies,sawflies,wasps,ants,and bees)are unknown.Thus,in order to understand the origins of physiological and mor-phological innovations in insects (e.g.,wings andmetamorphosis),it is important to reliably re-construct the tempo and mode of insect diversifi-cation.We therefore conducted a phylogenomic study on 1478single-copy nuclear genes obtained from genomes and transcriptomes representing key taxa from all extant insect orders and other arthropods (144taxa)and estimated divergence dates with a validated set of 37fossils (5).Phylogenomic analyses of transcriptome and genome sequence data (6)can be compromised by sparsely populated data matrices,gene paral-ogy,sequence misalignment,and deviations from the underlying assumptions of applied evolution-ary models,which may result in biased statistical confidence in phylogenetic relationships and tem-poral inferences.We addressed these obstacles by removing confounding factors in our analysis (5)(fig.S2).We sequenced more than 2.5gigabases (Gb)of cDNA from each of 103insect species,which represented all extant insect orders (5).Addition-ally,we included published transcript sequence data that met our standards (table S2)and offi-cial gene sets of 14arthropods with sequenced draft genomes (5),of which 12served as refer-ences during orthology prediction of transcripts (tables S2and S4).Comparative analysis of the reference species'official gene sets identified 1478single-copy nuclear genes present in all these species (tables S3and S4).Functional annotation of these genes revealed that many serve basic cellular functions (tables S14and S15and figs.S4to S6).A graph-based approach using the best reciprocal genome-and transcriptome-wide hit criterion identified,on average,98%of these genes in the 103de novo sequenced transcriptomes,but only 79%and 62%in the previously published transcriptomes of in-and out-group taxa,respec-tively (tables S12and S13).After transcripts had been assigned and aligned to the 1478single-copy nuclear-encoded genes,we checked for highly divergent,putatively misaligned transcripts.Of the 196,027aligned transcripts,2033(1%)were classified as highly divergent.Of these,716were satisfactorily re-aligned with an automated refinement.How-ever,alignments of 1317transcripts could not be improved,and these transcripts were excluded from our analyses (supplementary data file S5,/10.5061/dryad.3c0f1).Nonrandom distribution of missing data among taxa can inflate statistical support for incorrect tree topologies (7).Because we detected a non-random distribution of missing data,we only considered data blocks if they contained infor-mation from at least one representative of each of the 39predefined taxonomic groups of un-disputed monophyly (table S6).In this represent-ative data set,the extent of missing data was still between 5and 97.7%in pairwise sequence com-parisons,with high percentages primarily because of the data scarcity in some previously published out-group taxa (table S19and figs.S7to S10).We inferred maximum-likelihood phylogenetic trees (Fig.1)with both nucleotide (second-codon positions only and applying a site-specific rate model)and amino acid –sequence data (applying a protein domain –based partitioning scheme to improve the biological realism of the applied evolutionary models)from the representative data set (5)(figs.S21,S22,and S23,A and D).Trees from both data sets were fully congruent.The absence of taxa that cannot be robustly placed on the tree (rogue taxa)in the amino acid –sequence data set and the presence of a few rogue taxa that did not bias tree inference in the nucleotide sequence data set (5)indicated a suf-ficiently representative taxonomic sampling.To detect confounding signal derived from nonrandom data coverage,we randomized ami-no acids within taxa,while preserving the dis-tribution of data coverage in the representative data set (5).This approach revealed no evidence of biased node support that could be attributed to nonrandom data coverage (5)(figs.S11and S12and table S20).Phylogenomic data may violate the assumption of time-reversible evolu-tionary processes,irrespective of what partition scheme one applies,which could lead to in-correct tree estimates and biased node support.Because sections in the amino acid –sequence alignments of the representative data set violat-ing these assumptions were present,we tested whether the observed compositional heteroge-neity across taxa biased node support but found no evidence for this (5)(fig.S20).We next dis-carded data strongly violating the assumption of time-reversible evolutionary processes (tables S21and S22,data files S6to S8,and figs.S13to S19).Results from phylogenetic analysis of this filtered data set (5)were fully congruent with those obtained from analyzing the unfiltered representative data set.The nucleotide sequence data of the representative data set containing also first and third codon positions strongly violated the assumption of time-reversible evolutionary processes,but still supported largely congruent topologies (fig.S23,B to D).In summary,our phylogenetic inferences are unlikely to be biased by any of the above-mentioned confounding factors.Our phylogenomic study suggests an Early Ordovician origin of insects (Hexapoda)at ~479Ma [confidence interval (CI),509to 452Ma]and a radiation of ectognathous insects in the Early Silurian ~441Ma (CI 465to 421Ma)(Figs.1and 2).These estimates imply that insects colonized land at roughly the same time as plants (8),in agreement with divergence date estimates on the basis of other molecular data (4).The early diversification pattern of insects has remained unclear (2,7,9).We received support for a monophyly of insects,including Collembola and Protura as closest relatives (10),and Diplura as closest extant relatives of bristletails (Archae-ognatha),silverfish (Zygentoma),and winged in-sects (Pterygota)(Fig.1).Furthermore,our analyses corroborate Remipedia,cave-dwelling crustaceans,as the closest extant relatives of insects (11,12).A close phylogenetic relationship of bristletails to a clade uniting silverfish and winged insects (Dicondylia)is generally accepted.However,the monophyly of silverfish has been questioned,with the relict Tricholepidion gertschi considered more distantly related to winged insects than7647NOVEMBER 2014•VOL 346ISSUE 6210 SCIENCE1Zoologisches Forschungsmuseum Alexander Koenig (ZFMK)/Zentrum für Molekulare Biodiversitätsforschung (ZMB),Bonn,Germany.2China National GeneBank,BGI-Shenzhen,China.3BGI-Shenzhen,China.4Australian National Insect Collection,Commonwealth Scientific and Industrial Research Organization (Australia)(CSIRO),National Research Collections Australia,Canberra,ACT,Australia.5Abteilung Arthropoda,Zoologisches Forschungsmuseum Alexander Koenig (ZFMK),Bonn,Germany.6Department of Entomology,Rutgers University,New Brunswick,NJ 08854,USA.7Department of Biological Sciences,Rutgers University,Newark,NJ 08854,USA.8Scientific Computing,Heidelberg Institute for Theoretical Studies (HITS),Heidelberg,Germany.9Institut für Spezielle Zoologie undEvolutionsbiologie mit Phyletischem Museum Jena,FSU Jena,Germany.10Steinmann-Institut,Bereich Paläontologie,Universität Bonn,Germany.112.Zoologische Abteilung(Insekten),Naturhistorisches Museum Wien,Vienna,Austria.12Department of Integrative Zoology,Universität Wien,Vienna,Austria.13Institut für Spezifische Prophylaxe und Tropenmedizin,Medizinische Parasitologie,Medizinische Universität Wien (MUW),Vienna,Austria.14Manaaki Whenua Landcare Research,Auckland,New Zealand.15Center for Advanced Modeling,Emergency Medicine Department,Johns Hopkins University,Baltimore,MD 21209,USA.16Biozentrum Grindel und Zoologisches Museum,Universität Hamburg,Hamburg,Germany.17Evolutionary Morphology Laboratory,Graduate School of Science and Engineering,EhimeUniversity,Japan.18Sugadaira Montane Research Center/Hexapod Comparative Embryology Laboratory,University of Tsukuba,Japan.19Land and Water Flagship,CSIRO,Canberra,ACT,Australia.20Florida Museum of Natural History,University of Florida,Gainesville,FL 32611,USA.21Entomology,Staatliches Museum für Naturkunde Stuttgart (SMNS),Germany.22Ecology Evolution and Genetics,Research School of Biology,Australian National University,Canberra,ACT,Australia.23National Evolutionary Synthesis Center,Durham,NC 27705,USA.24Department of Biological Sciences,Macquarie University,Sydney,Australia.25Department für Botanik und Biodiversitätsforschung,Universität Wien,Vienna,Austria.26Natural History Museum of Crete,University of Crete,Post Office Box 2208,Gr-71409,Iraklio,and Biology Department,University of Crete,Iraklio,Crete,Greece.27Department of Biological Sciences and Feinstone Center for Genomic Research,University of Memphis,Memphis,TN 38152,USA.28Centro Universitario de Ciencias Biólogicas y Agropecuarias,Centro de Estudios en Zoología,Universidad de Guadalajara,Zapopan,Jalisco,México.29Leibniz Supercomputing Centre of the Bavarian Academy of Sciences and Humanities,Garching,Germany.30Institute of Evolutionary Biology and Ecology,Zoology and Evolutionary Biology,University of Bonn,Bonn,Germany.31Department of Life Sciences,The Natural History Museum London,London,UK.32Abteilung Entomologie,Biozentrum Grindel und Zoologisches Museum,Universität Hamburg,Hamburg,Germany.33Fakultät für Informatik,Karlsruher Institut für Technologie,Karlsruhe,Germany.34California Academy of Sciences,San Francisco,CA 94118,USA.35Department of Entomology,College of Natural Resources and Environment,South ChinaAgricultural University,China.36Yokosuka City Museum,Yokosuka,Kanagawa,Japan.37Department of Entomology,North Carolina State University,Raleigh,NC 27695,USA.38Systematic Entomology,Hokkaido University,Sapporo,Japan.39Department of Biology,University of Copenhagen,Copenhagen,Denmark.40Princess Al Jawhara Center of Excellence in the Research of Hereditary Disorders,King Abdulaziz University,Jeddah,Saudi Arabia.41MacauUniversity of Science and Technology,Avenida Wai Long,Taipa,Macau,China.42Department of Medicine,University of Hong Kong,Hong Kong.43Department of Ecology,Evolution,and Natural Resources,Rutgers University,New Brunswick,NJ 08854,USA.*Major contributors.†Corresponding author.E-mail:xinzhou@ (X.Z.),b.misof.zfmk@uni-bonn.de (B.M.),kjer@ (K.M.K),wangj@ (J.W.)RESEARCH |REPORTSRESEARCH|REPORTSrelationships.maximum-likelihoodoptimized and sampledare labeled indicateorigin of events.SCIENCE 7NOVEMBER2014•VOL346ISSUE6210765estimates.correspondrange estimatesare Additionally,separatelybarsthe inferredcommon course,bewithRESEARCH|REPORTSother silverfish (13).We find that silverfish are monophyletic,consistent with recently published morphological studies (14),and estimate that Tricholepidion diverged from other silverfish in the Late Triassic (~214Ma)(Figs.1and 2).This result implies parallel and independent loss of the ligamentous head endoskeleton,abdominal styli,and coxal vesicles in winged insects and silverfish (5).The diversification of insects is undoubtedly related to the evolution of flight.Fossil winged insects exist from the Late Mississippian (~324Ma)(15),which implies a pre-Carboniferous origin of insect flight.The description of †Rhyniognatha (~412Ma)from a mandible,potentially indicative of a winged insect,suggested an Early Devonian to Late Silurian origin of winged insects (3).Our results corroborate an origin of winged insect lineages during this time period (16)(Figs.1and 2),which implies that the ability to fly emerged after the establishment of complex terrestrial ecosystems.Ephemeroptera and Odonata are,according to our analyses,derived from a common ancestor.However,node support is low for Palaeoptera (Ephemeroptera +Odonata)and for a sister group relationship of Palaeoptera to modern winged in-sects (Neoptera),which indicates that additional evidence,including extensive taxon sampling and the analysis of genomic meta-characters (17),will be necessary to corroborate these relationships.We find strong support for the monophyly of Polyneoptera,a group that comprises earwigs,stone-flies,grasshoppers,crickets,katydids (Orthoptera),Embioptera,Phasmatodea,Mantophasmatodea,Grylloblattodea,cockroaches,mantids,termites,and Zoraptera (18–20).We estimated the origin of the polyneopteran lineages at ~302Ma (CI 377to 231Ma)in the Pennsylvanian (Figs.1and 2),con-sistent with the idea that at least part of the rich Carboniferous neopteran insect fauna was of poly-neopteran origin.Finally,our analyses suggest that the major diversity within living cockroaches,man-tids,termites,and stick insects evolved after the Permian mass extinction.Given that the oldest known fossil hemipterans date to the Middle Pennsylvanian (~310Ma)(21),it had been thought that the stylet marks on liv-erworts from the Late Devonian (~380Ma)(22)could not have been of hemipteran origin.Our study indicates that true bugs (Hemiptera)and their sister lineage,thrips (Thysanoptera),all of which possess piercing-sucking mouthparts,orig-inated ~373Ma (CI 401to 346Ma),which gives support to the possibility of a hemipteroid origin of Early Paleozoic stylet marks.True bugs,thrips,bark lice (Psocoptera),and true lice (Phthiraptera)(together called Acercaria)were thought to be the closest extant relatives of Holometabola (Acercaria +Holometabola =Eumetabola)(10).However,convincing morpho-logical features and fossil intermediates support-ing a monophyly of Acercaria are lacking (13).We recovered bark and true lice (Psocodea)as likely closest extant relatives of Holometabola (5),which suggests that both groups started to diverge in the Devonian-Mississippian ~362Ma (CI 390to 334Ma)(Figs.1and 2).However,this result did not receive support in all statistical tests and,therefore,should be further investigated in future studies that embrace additional types of characters (17).We estimated that the radiation of parasitic lice occurred ~53Ma (CI 67to 46Ma),which implies that they diversified well after the emer-gence of their avian and mammalian hosts in the Late Cretaceous –Early Eocene and contradicts the hypothesis that parasitic lice originated on fea-thered theropod dinosaurs ~130Ma (23).Within Holometabola,our study recovered phylogenetic relationships fully congruent with those suggested in recent studies (2,24,25).Although we estimated the origin of stem lineages of many holometabolous insect orders in the Late Carboniferous,we dated the spectacular diver-sifications within Hymenoptera,Diptera,and Lepidoptera to the Early Cretaceous,contem-porary with the radiation of flowering plants (21,26).The almost linear increase in interordinal insect diversity suggests that the process of di-versification of extant insects may not have been severely affected by the Permian and Cretaceous biodiversity crises (Fig.2).With this study,we have provided a robust phylogenetic backbone tree and reliable time estimates of insect evolution.These data and analyses establish a framework for future com-parative analyses on insects,their genomes,and their morphology.REFERENCES AND NOTES1.The term “insects ”is used here in a broad sense andsynonymous to Hexapoda (including the ancestrally wingless Protura,Collembola,and Diplura).2.M.D.Trautwein,B.M.Wiegmann,R.Beutel,K.M.Kjer,D.K.Yeates,Annu.Rev.Entomol.57,449–468(2012).3.M.S.Engel,D.A.Grimaldi,Nature 427,627–630(2004).4.O.Rota-Stabelli et al.,Curr.Biol.23,392–398(2013).5.Materials and methods are available as supplementarymaterial on Science Online.6.Transcriptome refers to the sequencing of all of the mRNAs ofan individual or many individuals present at the time of preservation.7. E.Dell ’Ampio et al .,Mol.Biol.Evol.31,239–249(2014).8. bandeira,Arthro Syst.Phylo.64,53–94(2006).9.K.Meusemann et al .,Mol.Biol.Evol.27,2451–2464(2010).10.W.Hennig,Die Stammesgeschichte der Insekten(Kramer,Frankfurt am Main,1969).11.With the notable exception of Cephalocarida,for which RNA-sequencing data were unavailable to us.12.B.M.von Reumont et al .,Mol.Biol.Evol.29,1031–1045(2012).13.N.P.Kristensen,Annu.Rev.Entomol.26,135–157(1981).14.A.Blanke,M.Koch,B.Wipfler,F.Wilde,B.Misof,Front.Zool.11,16(2014).15.J.Prokop,A.Nel,I.Hoch,Geobios 38,383–387(2005).16.These estimates are robust whether or not †Rhyniognatha(Pragian stage,~412Ma)is used as a calibration point.17.O.Niehuis et al .,Curr.Biol.22,1309–1313(2012).18.H.Letsch,S.Simon,Syst.Entomol.38,783–793(2013).19.K.Ishiwata,G.Sasaki,J.Ogawa,T.Miyata,Z.-H.Su,Mol.Phylogenet.Evol.58,169–180(2011).20.K.Yoshizawa,Syst.Entomol.36,377–394(2011).21.A.Nel et al .,Nature 503,257–261(2013).bandeira,S.L.Tremblay,K.E.Bartowski,L.VanAllerHernick,New Phytol.202,247–258(2014).23.V.S.Smith et al .,Biol.Lett.7,782–785(2011).24.R.G.Beutel et al .,Cladistics 27,341–355(2011).25.B.M.Wiegmann et al .,BMC Biol.7,34(2009).26.J.A.Doyle,Annu.Rev.Earth Planet.Sci.40,301–326(2012).ACKNOWLEDGMENTSThe data reported in this paper are tabulated in the supplementary materials and archived at National Center for BiotechnologyInformation,NIH,under the Umbrella BioProject ID PRJNA183205(“The 1KITE project:evolution of insects ”).Supplementary files are archived at the Dryad Digital Repository /10.5061/dryad.3c0f1.Funding support:China National GeneBank and BGI-Shenzhen,China;German Research Foundation (NI 1387/1-1;MI 649/6,MI 649/10,RE 345/1-2,BE1789/8-1,BE 1789/10-1,STA 860/4,Heisenberg grant WA 1496/8-1);Austria Science Fund FWF;NSF (DEB 0816865);Ministry of Education,Culture,Sports,Science and Technology of Japan Grant-in-Aid forYoung Scientists (B 22770090);Japan Society for the Promotion of Science (P14071);Deutsches Elektronen-Synchrotron (I-20120065);Paul Scherrer Institute (20110069);SchlingerEndowment to CSIRO Ecosystem Sciences;Heidelberg Institute for Theoretical Studies;University of Memphis-FedEx Institute ofTechnology;and Rutgers University.The authors declare no conflicts of interest.SUPPLEMENTARY MATERIALS/content/346/6210/763/suppl/DC1Materials and Methods Supplementary Text Figs.S1to S27Tables S1to S26Data File Captions S1to S14References (27–187)17June 2014;accepted 23September 201410.1126/science.1257570SCIENCE 7NOVEMBER 2014•VOL 346ISSUE 6210767RESEARCH |REPORTS。

Enhancement of Laser-Induced Fluorescence

Enhancement of Laser-Induced Fluorescence by Intense Terahertz Pulses in GasesJingle Liu and Xi-Cheng Zhang,Fellow,IEEEAbstract—The enhancement of laser-inducedﬂuorescence by in-tense terahertz pulses was studied both theoretically and experi-mentally using selected gases.Semiclassical physical picture incor-porating photoionization,electron heating,impact excitation,and dissociative recombination was used to explain the plasma dynam-ics under terahertz radiation in picosecond scale.The dependences of enhancedﬂuorescence on the terahertzﬁeld,laser intensity, and atomic properties were systematically investigated with neon, argon,krypton,xenon,methane(CH4),ethane(C2H6),propane (C3H8),and n-butane(C4H10)gases.In noble gas plasma,both narrow line emission and broad continuum emission were found to be enhanced by the terahertzﬁeld.Their enhancement ratios and time-dependent enhancedﬂuorescence are greatly inﬂuenced by the scattering cross section and ionization potential of atoms.In alkane gas plasma,the enhancement of theﬂuorescence emission from various molecular fragments was also observed.Index Terms—Alkane gas,ﬂuorescence,impact ionization,laser-induced plasma,noble gas,terahertz(THz)wave.I.I NTRODUCTIONT HE INTERACTION of the intense laser pulse and gases has been heavily studied in the areas of multiphoton ion-ization[1],[2],laserﬁlamentation[3],supercontinuum[4], high harmonic generation[5],[6],and terahertz(THz)wave generation[7],[8].Laser-inducedﬂuorescence in gases has also been employed in optical diagnostics of plasma[9].The laser-induced nitrogen plasma in the presence of a THz pulse has recently been studied by measuring the THz-radiation-enhanced-emission-of-ﬂuorescence(THz-REEF)[10].The electron acceleration in the THzﬁeld increases the electron im-pact ionization rate of high-lying states of nitrogen molecules, and thus,enhances theﬂuorescence emission.The discovery of the THz-REEF provides a method to study the light–plasma interaction in the long-wavelength limit as well as a promising technique of broadband THz wave remote sensing.However, the inﬂuence of electricﬁeld oscillating at THz frequency on aManuscript received January22,2010;revised March12,2010;accepted March12,2010.This work was supported in part by the Ofﬁce of Naval Re-search,by the National Science Foundation,by the Defense Threat Reduction Agency,and by the Department of Homeland Security through the DHS-ALERT Center under Grant2008-ST-061-ED0001.The views and conclusions contained in this document are those of the authors and should not be interpreted as neces-sarily representing the ofﬁcial policies,either expressed or implied,of the U.S. Department of Homeland Security.The authors are with the Center for Terahertz Research,Rensselaer Polytech-nic Institute,Troy,NY12180USA(e-mail:liuj3@;zhangxc@). Color versions of one or more of theﬁgures in this paper are available online at .Digital Object Identiﬁer10.1109/JSTQE.2010.2046142laser-induced plasma in different gases has not been systemat-ically investigated yet.The roles of atomic/molecular structure and laser intensity in THz-wave-enhancedﬂuorescence from monoatomic gas or polyatomic gas are not fully understood. The comprehensive study of interaction between THz pulse and gas plasma offers a physical insight into the complex interplay between ultrashort laser pulse ionization,THz-wave-induced electron heating,electron impact ionization,and dissociative re-combination.This systematic study is also of great importance for characterizing the population trapping behavior in noble and alkane gases[11],[12],plasma characterization[13],and THz wave generation/detection in gaseous media[7],[14]–[19].In this paper,we report that the laser-inducedﬂuorescence in noble gases(neon,argon,krypton,and xenon)and in alkane gases(methane,ethane,propane,and n-butane)can be enhanced by intense THz pulses.Since the noble gases are chemically in-ert and structurally simpler compared to the complex molecules, no vibrational structures and photoinduced fragmentation occur. Their simple and well-understoodﬂuorescence spectra are ideal for the systematic studies.The enhancement of both narrow spectral line emission and broad continuum emission of noble gas atoms is experimentally observed.Dynamics of THz-REEF are mainly controlled by the atomic properties,laser pulse en-ergy,and THzﬁeld.We also investigated the THz-REEF with alkane gas molecules since their saturated hydrocarbon struc-tures are major constituents of larger organic molecules,includ-ing those of biochemical and radiological signiﬁcance.Pho-todissociation of these molecules occurs in the intense laser ﬁeld.Theﬂuorescence from molecular fragments such as C2 and CH in the THzﬁeld is studied.II.T HEORETICAL B ACKGROUNDAs the gas is irradiated by the intense laser pulse,photoioniza-tion releases free electrons from atoms/molecules while many high-lying states in atoms/molecules are produced by the ab-sorption of multiple laser photons.These high-lying states have large principal numbers.Their energy levels are very close to the ionic continuum.Therefore,they are very“fragile”and can be easily ionized via collision with the neighboring energetic electrons.When an external THzﬁeld is applied on the laser-induced plasma,free electrons are accelerated and collide with other atoms/molecules at larger velocity than that without the THzﬁeld.As a result,more high-lying states are ionized via col-lision and moreﬂuorescing upper states are formed[10].As one of the most important aspects in THz-REEF,theﬂuorescence enhancement ratio represents the magnitude of the overall inﬂu-ence of the THz pulse on the plasma.The characterization and explicit description of theﬂuorescence enhancement ratio are1077-260X/$26.00©2010IEEEessential for the understanding of the interaction between the THz pulse and plasma.In order to explicitly describe ﬂuores-cence enhancement ratio,two most major physical processes,i.e.,electron acceleration and energy transfer via electron–atom collision,are mathematically elaborated in detail.The average energy transferred from one electron to atoms during the i th collision at time t i is∆E i = +∞−∞(m v 2(0)/2+m v (0)∆ v 1)k (1−k )i −1×ρ( v (0))d v (0)+kmi j =1∆ v 2j (1−k )i −j(1)where m and M are electron and atom masses,k =2mM/(m +M )2 1,and ρ( v (0))is the initial electron veloc-ity distribution after photoionization and satisﬁes the condition +∞−∞ρ(v (0))d v (0)=1.Here,∆ v i =− t i t i −τe E THz (t )dt/m is the electron velocity change by the THz ﬁeld during the time period between two neighboring collisions.In the excitation of the multiple cycle laser pulse,the electron velocity distribution is symmetric,i.e.,ρ( v (0))=ρ(− v (0)).Therefore,the ∆E i can be simpliﬁed to∆E i =m v 2(0) k (1−k )i −1/2+km i j =1∆ v 2j (1−k )i −j(2)where v 2(0) is the average of thev 2(0).The amount of to-tal energy transfer in all the collisions (at t 1,t 2,t 3...)can be obtained by summing up ∆E i∆E total =∞ i =1 ∆E i =m v 2(0) /2+m ∞ l =1∆ v 2l (3)where the ﬁrst term is the initial kinetic energy of electron and is determined by the laser pulse energy and ionization potential of atoms.The second term is the energy gained from the THz ﬁeld and is dependent on the THz time-domain waveform and elec-tron relaxation time or scattering frequency.From (3),we can de-scribe the ﬂuorescence enhancement ratio,I FL ( E THz )/I FL (0),as I FL ( E THz )/I FL (0)= I MP +Cm v 2(0) /2+Cm ∞ l =1∆ v 2l/(I MP +Cm v 2(0) /2)(4)where I FL (0)is the ﬂuorescence emission when the THz ﬁeldis zero.Here,I FL (0)includes the collision-induced ﬂuores-cence emission (∝m v 2(0) /2)and transition from upperstates which are directly excited by absorbing multiple photonsI MP ,and C is a constant that represents the impact excitationefﬁciency.It can be seen that the enhancement ratio largely depends on ∞l =1∆ v 2l / v 2(0) .III.E XPERIMENTAL S ETUPIn the experiment of the THz-REEF in gases,as shown in Fig.1,a desktop Ti:sapphire regenerative ampliﬁer provides laser pulses with 80fs pulse duration,600µJ pulse energy,1kHz Fig.1.Experimental setup of THz-REEF in gases.BS,beam splitter.PM,parabolic mirror.PMT,photomultiplier tube.repetition rate,and 800nm central wavelength,respectively.Thelaser pulse is split into two by a 70/30beam splitter.Here,70%of the pulse energy is used to generate THz pulses via tiltedpulse front excitation in LiNbO 3crystal [20].In this THz pulsegeneration scheme,the phase front of laser pulse is spatiallytilted by an optical grating.This tilted pulse front allows thematch between the phase velocity of the THz wave and group velocity of the laser pulse inside the LiNbO 3crystal.The overallefﬁciency of the THz generation through the optical rectiﬁcation can be as high as 0.1%(output THz pulse energy/laser pulseenergy)because of the good phase match and large nonlinearoptical coefﬁcients of LiNbO 3.The emitted intense single-cycleTHz pulse has 100±2kV/cm peak ﬁeld and 1–2ps pulseduration.The laser pulse with other 30%of total energy is focused by a convex lens with 100mm effective focal length to form laser plasma in a gas cell.The gas cell windows are 1-mm-thick quartz plates,which are transparent in both the THz and the vis-ible range.The energy of the plasma-exciting laser pulse can becontinuously changed by a neutral attenuator.Accordingly,theoptical intensity at the focus is in the range of 1013–1014W/cm 2.The THz pulse is collinearly focused into the plasma region.Thetime delay between the THz pulse and laser pulse is tuned by atranslation stage and is deﬁned as positive when the peak of THzpulse is ahead of the laser pulse.The gas pressure and speciesin the cell are controlled by a gas inlet and a vacuum pump.The ﬂuorescence emissions from gas plasma are collected by abroadband convex focusing lens,and spectrally resolved by amonochromator and photomultiplier tube (PMT).The spectralsensitivity of the detection system peaks at 400nm and mono-tonically drops to less than 1%at 900nm.In the spectral regionof interest,i.e.,400–900nm here,the measured ﬂuorescenceemission at longer wavelength would “appear”weaker than thatof the same intensity at shorter wavelength.The amplitude ofthe THz ﬁeld,E THz ,is controlled by rotating two metal wire THz polarizers (not shown)located in between THz emitter and plasma.LIU AND ZHANG:ENHANCEMENT OF LASER-INDUCED FLUORESCENCE3IV.F LUORESCENCE E NHANCEMENT IN N OBLE G ASES Noble gas atoms have simple and well-studied atomic proper-ties such as atomic spectra,ionization potential,and scattering cross section.These characteristics make them ideal testbeds for systematic investigation of the THz-REEF,which involves pho-toionization,electron heating,impact ionization,and electronic transition.Neon(Ne),argon(Ar),krypton(Kr),and xenon(Xe) were speciﬁcally selected as gas media.Helium(He)was not studied because the ionization potential of He atom(24.6eV) is too high for ionization to be appreciable at the laser intensity involved here.The ionization potentials of Ne,Ar,Kr,and Xe are21.6,15.8,14,and12.1eV,respectively.When maximal laser energy140µJ was used to ionize Ne,Ar,Kr,and Xe gases at atmospheric pressure,signiﬁcant ionization occurred and was accompanied by the appearance of the visible plasma.Here,we aim to study the dependence ofﬂuorescence emission on pulse energy,THzﬁeld strength,and gas species in detail.In the mea-surements in Section IV-A–IV-D,the THz pulse is temporally delayed behind the laser pulse so that the plasma is inﬂuenced by the entire THz pulse.In the measurement in Section IV-E, the time delay between the THz pulse and laser pulse is varied while theﬂuorescence signal is being recorded.A.NeonThe laser pulse energy dependence of the Neﬂuorescence spectra between580and760nm was measured at the pressure of 760torr when the THz beam was blocked.The results are shown in Fig.2(a).The broadening of theﬂuorescence lines here is mainly due to the current instrumental resolution of1–2nm rather than stark or pressure broadening.The Neﬂuorescence starts becoming signiﬁcant as the pulse energy is larger than 60µJ.All the line emissions are increased with laser pulse energy.The spectral positions of the measured emission lines agree well with those found in[21].All the observed lines are Ne I lines(neutral Ne atom).No obvious Ne II or Ne III line was observed because the photoemission from excited Ne atoms is much stronger than that from Ne ions at current excitation pulse energy.Fig.2(b)and(c)plots Ne spectra in the presence of the THzﬁeld with pulse energies of100and120µJ,respectively. As the THzﬁeld is increased from0to100kV/cm,the emission of all the lines is increased homogeneously by more than a factor of2.As discussed in previous work on nitrogen gas[10],the ﬂuorescence enhancement in gas plasma can be explained by the THz-wave-assisted electron heating and subsequent electron impact ionization of the high-lying states.The measuredﬂuorescence enhancement results from the in-creased population of upper states(3p states here)since most of the observed lines in this spectral region are from3p→3s transitions of Ne atom.One possible explanation for this3p population increase is that after more high-lying states are ion-ized,more excited states A∗are populated through ion conver-sion A+A++A→A+2+A and dissociative recombination A+2+e→A+A∗[22],[23].Considering the analogy between kinetics of various atoms of noble gases,A={Ne,Ar,Kr,Xe} is used as a symbol of one of these atoms for convenience.Here,Fig.2.(a)Neﬂuorescence spectra between580and760nm at different laser pulse energies(without THzﬁeld).Neﬂuorescence spectra at the laser pulse energies of(b)100µJ and(c)120µJ in the THzﬁeld.ser pulse energy dependence of(a)ﬂuorescence and(b)enhance-ment ratio of Ne702nm line in the THzﬁeld.A+2is a molecular ion.Populated excited states A∗is2p state for Ne.Fig.3(a)shows the laser pulse energy dependence of the Neﬂuorescence line at702nm in the THzﬁeld.This line is assigned to2s22p5(2P◦3/2)3p→2s22p5(2P◦1/2)3s transition. As the pulse energy increases,the backgroundﬂuorescence I FL(0kV/cm)increases and so does the enhancedﬂuorescence,4IEEE JOURNAL OF SELECTED TOPICS IN QUANTUMELECTRONICSFig.4.(a)Arﬂuorescence spectra between680and780nm at different laser pulse energies(without THzﬁeld).Arﬂuorescence spectra at laser pulse energies of(b)80µJ,(c)100µJ,and(d)140µJ in the THzﬁeld.i.e.,I FL(100kV/cm)−I FL(0kV/cm).The relative enhance-ment ratio versus pulse energy is plotted in Fig.3(b).The en-hancement ratio is nearly constant from60to120µJ.B.ArgonSimilar to the measurement in Ne,the pulse energy depen-dence of Arﬂuorescence spectra between680and780nm was measured at760torr,as shown in Fig.4(a).All the lines ob-served in this region are from4p→4s transition of Ar atom. Fig.4(b)–(d)shows the Ar spectra in the THzﬁeld with pulse energies of80,100,and140µJ,respectively.At each pulse energy,all the line emissions are increased homogeneously by the THzﬁeld.The strongest line in this region is Ar I line at 763nm.The pulse energy dependence of763nm line emis-sion and its relative enhancement ratio are plotted in Fig.5(a)Fig.5.Pulse energy dependence of(a)absolute and(b)relative enhancement of Ar763nm line in the THzﬁeld.and(b).The enhancement ratios vary with pulse energy and are 124%,123%,and110%,respectively,at aforestated energies. The smaller enhancement ratio at140µJ is due to the larger initial electron velocity and larger electronic screening of the THzﬁeld in denser plasma.By comparing Fig.5with Fig.3,we noticed that the en-hancement ratio I FL( E THz)/I FL(0)of Arﬂuorescence is much smaller than that of Ne for the same pulse energy,THzﬁeld,and gas pressure.From(4),it can be seen that larger enhancement ratio in Ne can be mainly attributed to the smaller v(0)in Ne whose ionization potential is higher.C.KryptonAs shown in Fig.6(a),theﬂuorescence spectra of Kr in the wavelength region from820to900nm was measured at dif-ferent excitation pulse energies at760torr when the THz beam was blocked.The observed larger line emission and contin-uum emission of Kr than those of Ne and Ar were due to the lower ionization potential.The line emission is from bound–bound transition and continuum emission is from free–bound and free–free transition.The THzﬁeld dependence of the emis-sion spectra between750and890nm at pulse energies of60, 70,and90µJ,respectively,is shown in Fig.6(b)–(d).The large signal in the shadow area is from the scattering of the laser beam.All the emission lines in this region are from the5p→5s transition of Kr atom and are enhanced by the same factor. Fig.7(a)and(b)shows the pulse energy and THzﬁeld depen-dence of the line emission at759nm and continuum emission. The enhancement ratios for the line emission and continuum emission are plotted in Fig.7(c).The line emission enhance-ment can be attributed to the same reason as discussed earlier for Ne.The continuum emission enhancement could be sim-ply explained by the increased electron–ion radiative recom-bination resulting from the THz-wave-assisted electron impact ionization,and thus,larger free electron density.Both enhance-ment ratios decrease with the pulse energy and get close to 1at120µJ.This means theﬂuorescence enhancement is sat-urated at the high pulse energy and the THz-wave-enhanced ﬂuorescence is negligible compared to the backgroundﬂuores-cence,i.e.,∞l=1∆ v2l/ v2(0) 1.LIU AND ZHANG:ENHANCEMENT OF LASER-INDUCED FLUORESCENCE5Fig.6.(a)Krﬂuorescence spectra between820and900nm at different laser pulse energies(without THzﬁeld).Krﬂuorescence spectra at laser pulse energies of(b)60µJ,(c)70µJ,and(d)90µJ in the THzﬁeld.The difference between the line enhancement ratio and the continuum enhancement ratio is possibly due to the different transition channels and/or differentﬂuorescence life times of line emission and continuum emission.D.XenonFig.8(a)shows the Xeﬂuorescence spectra at different laser pulse energies without a THzﬁeld present,while Fig.8(b)–(d) showsﬂuorescence spectra in the THzﬁeld at laser pulse en-ergies of40,75,and80µJ.As shown in Fig.9(a)and(b), the intensity of Xe I823nm line emission resulting from5s25p5(2P◦3/2)6p→5s25p5(2P◦3/2)6s transition[24]and con-tinuum emission was measured at the pulse energy from30to 130µJ.The enhancement ratios of both are plotted in Fig.9(c).Fig.7.Pulse energy dependence of(a)759nm line and(b)continuum emis-sion in Kr plasma in the THzﬁeld.(c)Pulse energy dependence of the en-hancement ratio in the THzﬁeld.Shadow area is the enhancement saturationregion.Fig.8.(a)Xeﬂuorescence spectra between810and850nm at different laser pulse energies(without THzﬁeld).Fluorescence spectra at laser pulse energies of(b)40µJ,(c)75µJ,and(d)80µJ in the THzﬁeld.6IEEE JOURNAL OF SELECTED TOPICS IN QUANTUMELECTRONICSFig.9.Pulse energy dependence of (a)823nm line and (b)continuum emis-sion in Xe plasma in the THz ﬁeld.(c)Laser pulse energy dependence of the enhancement ratio in the THz ﬁeld.Shadow area is the enhancement saturationregion.Fig.10.Time-dependent enhancement of the ﬂuorescence emission in Ar,Kr,and Xe gases when the excitation pulse energy is 70uJ and pressure is 30torr.Compared to that of Kr,the enhancement saturates at lower pulse energies.Above 80µJ,the Xe ﬂuorescence enhancement becomes much less signiﬁcant and very close to 1.The smaller threshold of saturation region in Xe (80µJ),than that in Kr (120µJ),is mainly because of the larger screening effect and higher electron temperature of Xe plasma.E.Time-Dependent Fluorescence EnhancementTo further study the relationship between the time-dependent THz-REEF and atomic properties (ionization potential and scat-tering cross section),the enhanced ﬂuorescence in Ar,Kr,and Xe was measured at the same excitation power and same pres-sure as the time delay between the THz pulse and laser pulse is continuously tuned.As shown in Fig.10,the shape of the time-dependent THz-REEF varies signiﬁcantly from Ar to Xe at 30torr.The “spike shape”as observed in Ar occurs when the re-laxation time is much larger than the THz pulse duration.In contrast,the “two-step stairs”shape,as observed in Xe plasma,occurs when the relaxation time is much shorter than the THz pulse duration.The relaxation time can be obtainedthroughFig.11.Fluorescence spectra of alkane gases in the THz ﬁeld.ﬁtting the measured time-dependent THz-REEF with (3).The ﬁtted relaxation times for Ar,Kr,and Xe are 4±0.3,1.3±0.14,and 0.4±0.04ps,respectively.This difference of the electron relaxation time in three gases is attributed to different ionization potentials and scattering cross sections of Ar,Kr,and Xe atoms.In tunneling ionization,the lower the ionization potential,the higher the electron velocity v (0).At the same time,the scat-tering cross section increases from Ar to Xe due to the larger size of the atom.The electron relaxation time is τ=1/(σv e N s )where v e is the average electron velocity and N s is the scatter density,which is proportional to gas pressure [13].Therefore,the larger electron velocity and bigger scattering cross section result in the shortest electron relaxation time in Xe plasma.V .F LUORESCENCE E NHANCEMENT IN A LKANE G ASES The THz-REEF experiment was performed in several linear alkane gases including methane (CH 4),ethane (C 2H 6),propane (C 3H 8),and n -butane (C 4H 10)whose ionization potentials are very low (12.6,11.5,10.95,and 10.55eV ,respectively)[25],[26].In order to reduce the electronic screening effect at highLIU AND ZHANG:ENHANCEMENT OF LASER-INDUCED FLUORESCENCE7plasma density(>1016cm−3),relatively low laser pulse energyand low gas density(pressure)were used.An intense laserﬁeldcan break alkane gas molecules into small fragments such as CHand C2via photodissociation.The THz pulse,coming after thelaser pulse,would affect the dynamics of the plasma contain-ing these molecular fragments.Fig.11shows theﬂuorescencespectra of methane,ethane,propane,and n-butane measured inthe THzﬁeld.Both the CH radical and C2Swan bandﬂuo-rescences were observed in all alkane gases,except only CHradicalﬂuorescence was observed in methane.The emissionline at431nm is assigned to A2∆→X2Πtransition of CHradical and labeled in red.The emission lines at437,473,516,and563nm are assigned to theν=−2,1,0,−1progressionsof the C2Swan bands(d3Πg→a3Πu),respectively,and la-beled in blue in Fig.11[27].Both the CH and C2ﬂuorescenceswere enhanced by the THzﬁeld but by different factors.Forexample,under irradiation of the THz pulse with100kV/cmpeakﬁeld,the enhancement ratio of C2ﬂuorescence is around20%while enhancement ratio of CHﬂuorescence is11%inC3H8at5torr.The mechanism for this different enhancementratio is not very clear currently.One possible explanation is thatTHz-wave-assisted electron impact affects the formation andexcitation processes of CH and C2differently.VI.C ONCLUSIONThe systematic study of the enhancement of laser-inducedﬂuorescence by intense THz pulses has been performed in no-ble gases and alkane gases.Besides the previous exploration innitrogen gas,the phenomena of THz-REEF were also observedin the experiments with all the gases tested here.Both nar-row line emission from atom or molecular fragments and broadplasma continuum emission can be enhanced by the THzﬁeld.The ion conversion A+A++A→A+2+A and dissociativerecombination A+2+e→A+A∗are proposed to explain theenhanced line emission from noble gases.The dependences ofﬂuorescence enhancement on laser pulse energy,THzﬁeld,andgas species were experimentally investigated in detail.As istheoretically predicted,the enhancement ratio is measured to behighly dependent on the initial electron velocity and electronacceleration in the 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High_PSR_Low_Drop-Out_Regulator_With_Feed-Forward_Ripple_Cancellation_Technique

IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 45, NO. 3, MARCH 2010565High PSR Low Drop-Out Regulator With Feed-Forward Ripple Cancellation TechniqueMohamed El-Nozahi, Student Member, IEEE, Ahmed Amer, Student Member, IEEE, Joselyn Torres, Student Member, IEEE, Kamran Entesari, Member, IEEE, and Edgar Sánchez-Sinencio, Fellow, IEEEAbstract—A low drop-out (LDO) regulator with a feed-forward ripple cancellation (FFRC) technique is proposed in this paper. The FFRC-LDO achieves a high power-supply rejection (PSR) over a wide frequency range. Complete analysis and design steps of the FFRC-LDO are presented in this paper. Kelvin connection is also used to increase the gain–bandwidth of the LDO allowing for faster transient performance. The LDO is implemented in 0.13 m CMOS technology and achieves a PSR better than 56 dB up to 10 MHz for load currents up to 25 mA. Load regulation of 1.2 mV for a 25 mA step is measured, and the whole LDO consumes a quiescent current of 50 A with a bandgap reference circuit included. To our knowledge, this is the ﬁrst LDO that achieves such a high PSR up to 10 MHz. Index Terms—CMOS, DC-DC converters, feed-forward ripple cancellation, low drop-out regulator, power-supply rejection.Fig. 1. Block diagram of typical power management system.I. INTRODUCTION HERE is a great interest in efﬁcient power management ICs. An important building block in power management is the low drop-out (LDO) linear regulator which often follows a DC-DC switching converter, as shown in Fig. 1. It is used to regulate the supplies ripples to provide a clean voltage source for the noise-sensitive analog/RF blocks. Designing a stable LDO for a wide range of load conditions, while achieving high power-supply rejection (PSR), low drop-out voltage, and low quiescent current, is the main target using state-of-the-art CMOS technologies [1]–[4]. Recently, there has been an increasing demand to integrate the whole power management system into a single system-on-chip (SoC) solution. Hence, operating frequencies of switching converters are increasing to allow higher level of integration [5]. This trend increases the frequency of output ripples and therefore the subsequent LDO regulator should provide high PSR up to switching frequencies. Conventional LDOs have poor PSR at high frequencies (above 300 kHz) especially the ones implemented using sub-250 nm technologies. The main reasons for poor PSR are summarized as follows: 1) Finite output conductance of the pass transistor, 2) low DC gain of sub-250 nm tech-TManuscript received June 03, 2009; revised December 09, 2009. Current version published February 24, 2010. This paper was approved by Associate Editor Philip Mok. This work was supported in part by Texas Instruments Inc. The authors are with the Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX 77843 USA (e-mail: melnozahi@; ahmed.amer@; jotorres@; kentesar@; e.sanchez@; sanchez@). Color versions of one or more of the ﬁgures in this paper are available online at . Digital Object Identiﬁer 10.1109/JSSC.2009.2039685nologies which requires complex gain stages to achieve better regulation, and 3) ﬁnite bandwidth of the feedback path. Researchers have contributed to improve power-supply rejection techniques. Some of those techniques are: i) Using simple RC ﬁltering at the output of the LDO [6]; ii) Cascading two regulators [6]; iii) Cascading another transistor with the pMOS pass transistor along with RC ﬁltering, using special technologies such as drain-extended FET devices, and/or charge-pump techniques to bias the gate of one of the transistors [7]–[9]. Simple RC ﬁltering reduces the voltage ripple at the input of the LDO. However, this technique increases the drop-out voltage in LDO regulators that supply high current due to the high voltage drop across the resistance. Using an nMOS or pMOS transistor to cascade with the pMOS pass transistor can achieve high powersupply rejection over a wide frequency range. This technique increases the area and leads to a high drop-out voltage [7]. Charge pump techniques increase complexity and lead to higher power consumption because a clock is necessary along with RC ﬁltering to remove clock ripples [9]. In summary, the main idea behind all previously proposed techniques is to provide more isolation between the input and output along the high-current signal path. Hence, the area consumption and drop-out voltage are large, which is not suitable for low-voltage technologies. In addition, these techniques provide high PSR at low frequencies, but are unable to provide sufﬁcient PSR (better than 50 dB) at frequencies up to several MHz. To overcome the drawbacks of previously reported PSR LDO regulators, we introduce a high PSR low voltage LDO regulator based on a feed-forward ripple cancellation (FFRC) approach [10]. The proposed LDO topology preserves traditional loop dynamics structure, while providing high PSR over a wide frequency range. In addition, it enables the design for high supply currents and low quiescent current consumption. The paper is organized as follows: Section II discusses main PSR limitation sources in conventional LDOs. Section III presents the proposed FFRC-LDO. The stability analysis using a single bond-wire and a Kelvin connection are presented in Section IV (To our knowledge, this analysis is not presented before for LDO regulators).0018-9200/$26.00 © 2010 IEEEAuthorized licensed use limited to: Central South University. Downloaded on March 01,2010 at 02:46:07 EST from IEEE Xplore. Restrictions apply.566IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 45, NO. 3, MARCH 2010Fig. 3. Total PSR of LDO and PSR due to each path in Fig. 2. Fig. 2. Input to output ripple paths in conventional LDOs.Section V demonstrates the circuit implementation. Measurement results are shown in Section VI, and conclusions are provided in Section VII. II. PSR OF CONVENTIONAL LDOS In this section, fundamental limitations for PSR improvement of conventional LDOs at high frequencies are investigated. It is shown that PSR at high frequencies is mainly limited by the dominant pole of the error ampliﬁer and equivalent self inductance (ESL) and resistance (ESR) of the off-chip capacitor. The ﬁnite PSR of the conventional LDO is due to several paths between the input and output of the LDO. Fig. 2 shows various paths that could couple input ripples to the output of the LDO. Path 1 is the main path regulated by the LDO loop. Path 2 is caused by the ﬁnite conductance of the MOS pass transistor, , and it is more signiﬁcant for technologies with lower feature sizes. Path 3 is as a result of the ﬁnite power-supply rejection ratio (PSRR) of the error ampliﬁer, and ﬁnally path 4 is due to the ﬁnite PSR of the bandgap circuit. The LDO transfer function due to paths 1 and 2 is given byget ampliﬁed at high frequencies. The upper and lower limits of PSR across the entire frequency spectrum due to paths 1 and 2 are given by(2) For paths 3 and 4, the transfer function is given by(3) is the power-supply rejection ratio of the error where is the power-supply rejection of the ampliﬁer, and bandgap circuit. Equation (3) shows that the ﬁnite PSR due to and . paths 3 and 4 is an ampliﬁed quantity of The ampliﬁcation is given by the ratio of feedback resistances . At higher frequencies due to the dominant as goes to zero, and hence, pole of error ampliﬁer, ripples leaking through the error ampliﬁer and bandgap do not appear at the output. In summary, all four paths affect the PSR at low frequencies and only paths 1 and 2 affect the PSR at high frequencies. Fig. 3 demonstrates the effect of each path on the overall PSR of the conventional LDO. Several techniques could be applied , to reduce the PSR at lower frequencies by decreasing and increasing gain of error ampliﬁer. However at higher frequencies, the dominant pole of the error ampliﬁer degrades the PSR of the LDO, and the off-chip capacitor is considered as an open circuit because of its ESL. None of the previously presented techniques have solved this problem satisfactorily. Usually, the PSR of LDO starts to degrade around 10–100 kHz [9]. A proposed solution for achieving high PSR at higher frequencies is demonstrated in the next section. III. PROPOSED FEED-FORWARD RIPPLE CANCELLATION LDO The PSR at low frequencies can be enhanced by increasing the feedback gain of the LDO. However at high frequencies, the PSR is mainly due to paths 1 and 2 in Fig. 2, and is limited by the dominant pole of the feedback loop. To achieve higher PSR(1) where and are the transconductance and channel resistance of the pass transistor, . is the total load and ) that apimpedance (without feedback resistances , and and are the DC gain and dominant pear at node pole of the error ampliﬁer, respectively. Equation (1) shows that PSR depends on the feedback gain at lower frequencies. For sub-250 nm technologies, increasing is challenging for conventional LDO designs. As the frequency increases, the dominant pole of the error ampliﬁer reduces the feedback gain; therefore, the PSR due to paths 1 and 2 starts to degrade. Without considering ESL and ESR of the off-chip capacitor, starts to decrease at higher frequencies because the off-chip capacitor shorts ripples to ground. However, due to ESL and ESR this effect does not happen at high frequencies, and the off-chip capacitor represents an open circuit. In this case, ripples at the output mayAuthorized licensed use limited to: Central South University. Downloaded on March 01,2010 at 02:46:07 EST from IEEE Xplore. Restrictions apply.EL-NOZAHI et al.: HIGH PSR LOW DROP-OUT REGULATOR WITH FEED-FORWARD RIPPLE CANCELLATION TECHNIQUE567Fig. 4. Block-level representation of the feed-forward ripple cancellation LDO.at both DC and high frequencies, ripples generated in paths 1 and 2 should be removed. The basic idea of the proposed LDO is demonstrated below. Its sensitivity to process–temperature (PT) variations is also discussed. A. Basic Idea To eliminate input ripples from appearing at the output, a zero transfer gain is necessary from the input to the output in Fig. 2. In the ideal case (without considering ), this is achieved by implementing a feed-forward path that replicates same input ripples at the gate of the pass transistor. Hence, the gate-overdrive voltage is independent of input ripples, and as a result no ripple appears across the load. In the actual case ), part of the ripples leak through the ﬁnite output (with , and should be removed. This is done by resistance of increasing the ripple amplitude appearing at the gate of to cancel ripples that leak through by an amount of . Fig. 4 presents a simpliﬁed block-level description of the proposed FFRC-LDO. Supply ripples, appearing at the source of , are reproduced at the gate of using the pass transistor feed-forward path. The generated ripples at the gate are higher in magnitude than input ripples to cancel additional ripples ap(path 2 in Fig. 2). The pearing at the output due to feed-forward path is implemented using a feed-forward ampliﬁer and a summing ampliﬁer. The summing ampliﬁer is used to merge the feedback regulating loop with feed-forward path at . the gate of the transistor Optimum value of the feed-forward gain is obtained with the help of a mathematical model of the FFRC-LDO, as shown in , the mathematical Fig. 5. Without the feed-forward path, model is similar to a conventional LDO. The transfer gain of the yields systemFig. 5. Mathematical model of the FFRC-LDO.where and are the DC gain and dominant pole of the summing ampliﬁer, respectively. To remove the ripples at the output, (4) is set to be zero. The optimum value for the feedforward ampliﬁer is then given by(5) Equation (5) demonstrates that the optimum feed-forward gain has to contain a zero in its transfer function. The zero cancels the effect of the pole existing at the gate of the pass transistor to extend the frequency range of the ripple rejection. Hence, this cancellation technique is limited by internal poles of the summing and feed-forward ampliﬁers. The zero is imin Fig. 4. plemented using the capacitor The simulated PSR of the LDO with and without FFRC technique is demonstrated in Fig. 6. Using the conventional architecture, the achieved PSR is less than 60 dB and it starts to degrade around 330 kHz. This frequency is located at the dominant pole of the error ampliﬁer. Using the FFRC-LDO the PSR at DC is enhanced by 20 dB. Besides, the additional zero increases the frequency at which the PSR starts to increase to 9 MHz. This simulation shows the effectiveness of the FFRC-LDO to enhance the PSR at both DC and high frequencies. The PSR(4)Authorized licensed use limited to: Central South University. Downloaded on March 01,2010 at 02:46:07 EST from IEEE Xplore. Restrictions apply.568IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 45, NO. 3, MARCH 2010Fig. 7. PSR schematic simulations of FFRC-LDO for various load conditions (R = 40; 100; 200; 10 000 ). Fig. 6. PSR schematic simulations of conventional and FFRC-LDO (R 40 ). The effect of PT variations are also demonstrated.=starts initially to increase around 330 kHz, which is the bandwidth of the error ampliﬁer. Then around 1 MHz, the introduced zero stops the increase in the PSR. Due to the self-resonance frequency of the off-chip capacitor and ﬁnite non-dominate poles of the feed-forward and summing ampliﬁers, the PSR starts to degrade again at high frequencies. The main advantage of this FFRC approach is achieving a high PSR for a wide frequency range, without the need to increase the loop bandwidth and hence the quiescent power consumption. Moreover, this approach preserves the same low drop-out voltage of a conventional regulator, since supply rejection does not occur on the high-current signal path. The gain of the feed-forward and summing ampliﬁers is based on the ratio of resistors to reduce its dependency to process-temperature (PT) variations. Fig. 6 shows the simulated variations of PSR of the FFRC-LDO for a temperature ranging from 40 to 125 C, and across process corners. Simulations over PT variations indicate that the LDO achieves comparable performance to that measured in the lab, making the LDO robust for high-performance power management ICs. The variation of the PSR versus the load current is shown in Fig. 7. As depicted, the PSR has its best value for a current of 5 mA at low frequencies. As the current increases, PSR is degraded due to the dependency of the DC gain of on the output current. For small currents, the transistor is biased in deep saturation with a DC gain of 20 dB. As the current increases, the transistor operating point moves near the linear region, and therefore, the DC gain is reduced to 14 dB at has to a load current of 25 mA. This example shows that be conﬁgurable if the LDO is designed to cover a wide range of currents. in Fig. 4 The biasing voltage of the summing ampliﬁer, has to be adjusted such that the output DC voltage of the summing ampliﬁer is higher than zero. There is a minimum value for proper operation of the FFRC-LDO. is for given byFig. 8. Modeling of ﬁnite PSR of feed-forward ampliﬁer (a) without feedback connection, and (b) with feedback connection.As high PSR is only required when the output is stabilized, this system biases the positive terminal of the feed-forward am. The maxpliﬁer directly from the output, i.e., imum input voltage that can be applied in this case is 2 V for an . Connecting the output output voltage of 1 V and requires no additional voltage reference circuit. directly to However, in a different design, another reference voltage can be added if the output voltage of the LDO is not high enough to satisfy the condition in (6). B. Effect of Finite PSRR of Summing and Feed-Forward Ampliﬁers The effect of ﬁnite PSRR of summing and feed-forward ampliﬁers is studied in this section. It will be demonstrated that the PSR performance of these two ampliﬁers do not affect the PSR of the LDO signiﬁcantly. 1) Feed-Forward Ampliﬁer: The ﬁnite PSR of an ampliﬁer can be modeled as an additive voltage at its output as shown in the equivalent model in Fig. 8(a). With the help of the equivalent , that appears due model in Fig. 8(b), the output voltage, to the ﬁnite PSR of the ampliﬁer is given by (7) where is the power-supply rejection of the feed-forward is the openampliﬁer without the feedback connection, and loop gain of the feed-forward ampliﬁer. In our design, dB and loop gain is 38 dB. Hence, dB. The voltage can be modeled as an additive at the output of the ampliﬁer in Fig. 5.(6)Authorized licensed use limited to: Central South University. Downloaded on March 01,2010 at 02:46:07 EST from IEEE Xplore. Restrictions apply.EL-NOZAHI et al.: HIGH PSR LOW DROP-OUT REGULATOR WITH FEED-FORWARD RIPPLE CANCELLATION TECHNIQUE569Considering only the effect of , on the supply rejection , due of the LDO, the output PSR of the whole LDO, to the feed-forward ampliﬁer is given by(8)Equation (8) shows that the poor PSR of the feed-forward ampliﬁer is attenuated by feedback resistances and the gain of is about error ampliﬁer. Combining all these effects, 93 dB in the designed FFRC LDO. Equation (8) also demonstarts to degrade beyond the bandwidth strates that of the error ampliﬁer, and hence it is important to maximize the bandwidth. In this design, a small capacitive load (summing ampliﬁer) exists at the output of the error ampliﬁer, leading to a bandwidth of 330 kHz. Beyond this value, the contribution of to the total PSR is higher, but its value is still not signiﬁcant. 2) Summing Ampliﬁer: Similar to the feed-forward ampliﬁer, the PSR of the summing ampliﬁer is reduced through its loop , gain. This effect is also modeled as an additive voltage, at the output of the ampliﬁer that is given by (9) where is the power supply rejection of the summing amis the gain of pliﬁer without the feedback connection, and the summing ampliﬁer without the feedback connection. The , due to the ﬁnite PSR output PSR of the whole LDO, of the summing ampliﬁer is given byFig. 9. Open-loop equivalent circuit with single bond wire connection.A. Single Bond-Wire Fig. 9 shows the open-loop circuit diagram of the proposed LDO when a single bond wire is used to interface with the external components. The equivalent series inductance (ESL) and resistance (ESR) of the off-chip capacitor is also considered in the analysis. The open-loop gain of the LDO is given by(10)Equation (10) shows that the ﬁnite PSR of the summing ampliﬁer is attenuated by its loop gain, error ampliﬁer gain, and the summing ampliﬁer gain. Simulations show a higher than 95 dB is achievable. In summary, the above analysis showed that the ﬁnite PSR of the feed-forward and summing ampliﬁer can be neglected in the analysis as stated earlier in this section. IV. STABILITY ANALYSIS In this section, the design of a stable LDO is demonstrated. Ideally, the feed-forward path does not affect the stability of the LDO because it does not exist in the feedback loop. However in of feed-forward ampliﬁer this implementation, the node to remove the need for another reference is connected to voltage. Hence, the feed-forward path appears in the feedback, but still it does not affect the stability as demonstrated in this section. The effect of packaging is considered to highlight the importance of considering the inductance of the bond wire. Two cases are considered: 1) a single bond-wire and 2) a Kelvin connection (two bond-wires).(11) , , , and are as shown in Fig. 9, , , where are the effective transconductance of error ampliﬁer, and summing ampliﬁer, and pass transistor, respectively, and and are the total resistance and capacitance at the output of and are the total resistance and error ampliﬁer. Also, is the gain capacitance at the output of summing ampliﬁer. is the additional term due to conof the error ampliﬁer, and necting of the feed-forward ampliﬁer to . does not affect the stability of the LDO because it is much smaller than , and the loop bandwidth is determined by the output pole. In this analysis the output impedance of the feed-forward ampliﬁer . Fig. 10 shows is neglected because it is much smaller than is connected stability simulation results of the LDO when and when it is connected to a constant reference voltage. to As depicted, the feed-forward path does not affect the stability of LDO even if is connected to .Authorized licensed use limited to: Central South University. Downloaded on March 01,2010 at 02:46:07 EST from IEEE Xplore. Restrictions apply.570IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 45, NO. 3, MARCH 2010Fig. 10. Schematic simulations of the open-loop gain and phase frequency reis connected to V or to a constant reference voltage. sponses when V F, L : nH, R nH, C m ,R , (L R ).=0 = 14 =4= 04= 30 = 40 Fig. 11. Schematic simulations of the open-loop gain and phase frequency F, responses for different values of L using single bond-wire. (C : nH, R L m per 1 nH, R m ,R , R ).= 04 = 14 = 40 = 30 =4 = 40 The term in (11) is the one that is different in single bond wire case and Kelvin connection case. For the single bond is given by wire case,(12) is the series resistance of the bond-wire. Equations where (11) and (12) show that the open-loop transfer function consists is the dominant pole of the of four poles and two zeros. can be neglected because it appears at very high freloop. quency (GHz range). The other two poles in (11) are the ﬁrst two non-dominant poles. If and are neglected, only onereal zero appears and it is used to cancel the ﬁrst in this case). However in the non-dominant pole ( practical case, and have values of at least 2 and 0.4 nH, respectively. These ﬁnite values produce two zeros. Increasing reduces the value at which these two zeros apthe value of pear. The simulated frequency response for different values of , while nH, is shown in Fig. 11. In this simulation, it is assumed that the series resistance of the bonding wire is 40 beyond a m for each 1 nH. Fig. 11 shows that increasing speciﬁc value may lead to an instability of the LDO. The main reason for the instability is that higher values of reduce the value of , and hence, the two zeros move towards the DC frequency. Fig. 12 shows zero locations of (12) , the ﬁrst zero cancels for different values of . For the ﬁrst non-dominant pole by adjusting the value of , and the second zero appears above the gain-crossover frequency. increases, two zeros start to move towards DC, and as As a result, the gain-crossover frequency is located at higher frequencies. This situation lead to instability of the LDO because the higher non-dominant poles change the phase abruptly at higher frequencies (Fig. 11). To solve this problem, the dominant pole should be decreased to a lower frequency to guarantee the second zero is located after the gain-crossover frequency. requires reducing the gain-bandwidth As a result, increasing product (GBW), and hence the speed of the LDO, when the zero (due to ESR) is used to compensate any non-dominate pole. This example shows the location of zeros is very sensitive to , and it may affect the functionality of LDO. In summary, the disadvantage of using a single bond-wire can be summarized as follows: 1) zeros are sensitive to the value of , 2) the loop bandwidth has to be decreased, hence lowering the speed, and 3) there is a voltage drop across the bond-wire due to its series resistance which affects the load regulation. Kelvin connection solves these issues.Authorized licensed use limited to: Central South University. Downloaded on March 01,2010 at 02:46:07 EST from IEEE Xplore. Restrictions apply.EL-NOZAHI et al.: HIGH PSR LOW DROP-OUT REGULATOR WITH FEED-FORWARD RIPPLE CANCELLATION TECHNIQUE571Fig. 12. Zero locations of (v =i )j for different values of L . (C = = 40 m per 1 nH, R = 30 m, R = 40 , 4 F, L = 0:4 nH, R R = 14 ).Fig. 14. Schematic simulations of the open-loop gain and phase frequency responses for different values of L using Kelvin connection. (C = 4 F, = 40 m per 1 nH, R = 30 m, R = 40 , L = 0:4 nH, R = 14 ). RFig. 13. Open-loop equivalent circuit with a Kelvin connection.B. Kelvin Connection To remove the dependency of the two zeros in (12) to , a Kelvin connection is used as an interface with the external load (Fig. 13). The Kelvin connection relies on closing the loop using two bond wires that are connected to the same pin of the is given by package. In this case,Fig. 15. Simulation of the open-loop gain and phase responses versus frequency of the LDO schematic using Kelvin connection for (R = 40 and 10 K). (L = 2 nH C = 4 F, L = 0:4 nH, R = 40 m per 1 nH, R = 30 m, R = 14 ).(13)do not Equation (13) shows that the zeros in depend on , and hence a more robust design can be implemented. The zero produced using the ESR of off-chip capacitor, , can be used to compensate the ﬁrst non-dominant pole, as a result allowing for a larger GBW product. Fig. 14 shows the simulated open-loop gain of the proposed LDO using a Kelvinconnection for different values of . As depicted, the magniwhen comtude response does not change signiﬁcantly with pared to a single bond-wire case. Hence, the design of a more stable LDO system is feasible using the Kelvin connection. The simulated open-loop transfer function of the LDO schematic using a Kelvin connection is shown in Fig. 15. For , the LDO achieves a phase heavy load condition margin of 53 with a GBW of 1.65 MHz. The ﬁrst non-domiand nant pole is due to the error ampliﬁer appears at 330 kHz. This pole is compensated using the real zero produced by ESR of the capacitor. The pole at the gate of the pass transistor appears at a much higher frequency because of the small output resistance of summing ampliﬁer and the useAuthorized licensed use limited to: Central South University. Downloaded on March 01,2010 at 02:46:07 EST from IEEE Xplore. Restrictions apply.572IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 45, NO. 3, MARCH 2010Fig. 16. Transistor-level implementation of the FFRC-LDO.of smaller technology that reduces the node capacitance. For k a GBW of 90 kHz with the light load condition a phase margin of 74 is obtained (Fig. 15). An important observation in Fig. 15 is the complex poles that result in peaking after the unity gain frequency. In case of a single wire, this peaking crosses 0 dB leading to instability. However using the Kelvin connection, the peaking amplitude has been reduced. The peaking beyond the unity gain frequency increases with because of the substrate coupling through the n-well enclosing the high resistivity poly resistors. The n-well is connected to the output voltage at the drain of the pass transistor. Increasing increases the amount of substrate coupling, and therefore the peaking increases. Similar situation happens for the single bond-wire case. The transient performance in this case is better than the single bond-wire case because one can design for a stable LDO with higher loop bandwidth. In addition, the extra inductor does not affect the transient load/line regulation because it does not appear along the high current variation path. Finally, an additional advantage of the Kelvin connection is better load regulation compared to the single bond-wire case because the output voltage is sensed after the voltage drop across the bond-wire resistance. V. CIRCUIT IMPLEMENTATION The complete transistor-level implementation of the FFRC-LDO is shown in Fig. 16. The error ampliﬁer utilizes current sources with improved output impedance as active loads [12]. This implementation boosts the output impedance of the ampliﬁer through the feedback loop formed by transistors and . The resultant gain is higher than 55 dB. In addition, exceeds 90 dB at DC to guarantee that the output PSRFig. 17. Schematic level simulations of the gain and PSRR of the error ampliﬁer.of the LDO is not limited by error ampliﬁer as deﬁned in (3). , is added to stabilize the internal feedback The capacitor, schematic loop of the error ampliﬁer. The gain and level simulations of the stand-alone error ampliﬁer are shown in Fig. 17. The error ampliﬁer achieves a 3 dB bandwidth of 180 kHz, and consumes a current of 12 A. This simulation shows that the PSR of the LDO does not depend on the bandwidth of the error ampliﬁer when the FFRC technique is used. Process, voltage and temperature (PVT) variations showed a variation less than 5 dB. in the gain and The error ampliﬁer has a limited output swing. This limited swing could be problematic for conventional LDOs when the error ampliﬁer drives the pass transistor to accommodate a wide range of load currents. However in the presented LDO, the summing ampliﬁer drives the gate of the pass transistor. The summing ampliﬁer is implemented using a two stage ampliﬁer conﬁguration with resistive feedback, as shown in Fig. 16. A wide output swing is achieved from the second stage of this ampliﬁer. The pass transistor gate capacitance is used to create the dominant pole of the ampliﬁer, and hence, no additional capacitor isAuthorized licensed use limited to: Central South University. Downloaded on March 01,2010 at 02:46:07 EST from IEEE Xplore. Restrictions apply.。

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