A toppled structure with sliding in the Siwalik Hills

a rX iv:c ond-ma t/1183v2[c ond-m at.m trl-sci ]9J a n201Optical properties of self-assembled quantum wires for application in infra-red detection Liang-Xin Li,Sophia Sun,and Yia-Chung Chang Department of Physics and Materials Research Laboratory University of Illinois at Urbana-Champaign,Urbana,Illinois 61801(February 1,2008)Abstract We present theoretical studies of optical properties of Ga 1−x In x As self-assembled quantum-wires (QWR’s)made of short-period superlattices with strain-induced lat-eral ordering.Valence-band anisotropy,band mixing,and effects due to local strain distribution at the atomistic level are all taken into ing realistic ma-terial parameters which are experimentally feasible,we perform simulations of the absorption spectra for both inter-subband and inter-band transitions (including the excitonic effect)of this material.It is shown that the self-assembled QWR’s have favorable optical properties for application in infra-red detection with normal inci-dence.The wavelength of detection ranges from 10µm to 20µm with the length of QWR period varying from 150˚A to 300˚A .I.INTRODUCTIONQuantum-well infra-red photodetectors(QWIP’s)have been extensively studied in recent years. The main mechamism used in QWIPs is the inter-subband optical transition,because the wavelengths for these transitions in typical III-V quantum wells can be tailored to match the desired operating wavelength(1-20µm)for infra-red(IR)detection.Due to its narrow band absorption,QWIP’s are complementary to the traditional HgCdTe detectors,which utilize the inter-band absorption, and therfeore are applicable only for broad-band absorption.The main drawback of QWIP’s is the lack of normal-incidence capability,unless some processing is made to create diffraction gartings on the surface,which tends to reduce the responsivity of the material to the incident radiation. Because electrons in quantum wells have translational invariance(within the effective-mass model) in the plane normal to the growth axis,the electron inter-subband transitions for normal-incident radiation is zero(or very small even if the coupling with other bands is considered).One way to break the translational invariance is to introduce the surface diffraction grating as commonly adopted in many QWIP’s fabricated today.A better(and less expensive)way to break the in-plane translational invariance is to utilize the strain-induced lateral modulation provided in self-assembled nano-structure materials.These nano-structures inculde quantum dots and quantum wires.Because the lateral modelation is formed via self-assembly,the fabrication of this type of materials will be much more efficient once the optimized growth parameters are known.Hence,it will be cost effective to use them for device fabrications.Self-assembled III-V QWR’s via the strain-induced lateral-layer ordering(SILO)process have attracted a great deal of attention recently.[21−23]The self-assembly process occurs during the growth of short-period superlattices(SPS)[e.g.(GaAs)2/(InAs)2.25]along the[001]direction on InP substrate.The excess fractional InAs layer leads to stripe-like islands during the initial MBE growth.[4]The presence of stripes combined with strain leads to natural phase separation as additional layers of GaAs or InAs are deposited and the structure becomes laterally modulated in terms of In/Ga composition.A self-assembled QWR heterostructure can then be created by sandwiching the laterally modulated layer between barrier materials such as Al0.24Ga0.24In0.52As(quarternary),Al0.48In0.52As (ternary),or InP(binary).[4-6]It was found that different barrier materials can lead to different degree of lateral composition modulation,and the period of lateral modulation ranges from100˚A to 300˚A depending on the growth time and temperature.In this paper,we explore the usefulness of InGaAs quantum wires(QWR’s)grown by the strain-induced lateral ordering(SILO)process for IR detection.Our theoretical modeling inculdes the effects of realistic band structures and microscopic strain distributions by combining the effective bond-orbital model(EBOM)with the valence-force-field(VFF)model.One of the major parameters for the IR detectors is the absorption quantum efficiency which is directly related to the absorption coefficient byη=1−e−αl whereαis the absorption coefficient and l is the sample length.Thus,to have a realistic accessment of the materials for device application,we need to perform detailed calculations of the absorption coefficient,taking into account the excitonic and band structure effects.Both inter-subband and inter-band transitions are examined systematically for a number of structure parameters (within the experimentally feasible range)chosen to give the desired effect for IR detection.It is found that the wavelengths for the inter-subband transitions of InGaAs self-assembled QWR’s range from10to20µm,while the inter-band transitions are around1.5µm.Thus,the material provides simultaneneous IR detection at two contrasting wavelengths,something desirable for appli-cation in multi-colored IR vedio camera.Several structure models with varying degrees of alloy mixing for lateral modulation are con-sidered.For the inter-band absorption,the excitonic effect is important,since it gives rise a large shift in transition energy and substantial enhancement of the absorption spectrum.To study the excitonic effect on the absorption spectrum for both discrete and contunuum states,we use a large set of basis functions with afinite-mesh sampling in the k-space and diaginalize the exciton Hamilto-nian directly.Emphasis is put on the analysis of line shapes of various peak structures arising from discrete excitonic states of one pair of subbands coupled with the excitonic(discrete and continuum) states associated with other pairs of subbands.Wefind that the excitonic effect enhances thefirst absorption peak around1.5times and shifts the peak position by20-30meV.II.THEORETICAL MODELThe QWR structures considered here consist of8pairs of(GaAs)2(InAs)2.25short-period super-lattices(SPS)sandwiched between Al0.24Ga0.24In0.52As barriers.The SPS structure prior to strain induced lateral ordering(SILO)is depicted in Fig.1.With lateral ordering,the structure is modeled by a periodic modulation of alloy composition in layers with fractional monolayer of(In or Ga)in the SPS structure.In layers7and9(starting from the bottom as layer1),we havex In=x m[1−sin(πy′/2b)]/2for y′<b0for b<y′<L/2−bx m{1+sin[π(y′−L/2)/2b]}/2for L/2−b<y′<L/2+bx m for L/2+b<y′<L−bx m{1−sin[π(y′−L)/2b]}/2for y′>L−b,(1)where x m is the maximum In composition in the layer,2b denotes the width of lateral composition grading,and L is the period of the lateral modulation in the[110]direction.The experimental feasible range of L is between100˚A and300˚A.The length of L is controled by the growth time and temperature.In layers3and13,we havex In=0for0<y′<5L/8−bx m{1+sin[π(y′−5L/8)/2b]}/2for5L/8−b<y′<5L/8+b,x m for5L/8+b<y′<7L/8−bx m{1−sin[π(y′−7L/8)/2b]}/2for7L/8−b<y′<7L/8+b0for7L/8+b<y′<L.(2)Similar equation for x Ga in layers5and11can be deduced from the above.By varying the parameters x m and b,we can get different degrees of lateral alloy mixing.Typically x m is between0.6and1, and b is between zero and15a[110]≈62˚A.A VFF model[13-15]is used tofind the equilibrium atomic positions in the self-assembled QWR structure by minimizing the lattice energy.The strain tensor at each atomic(In or Ga)site is then obtained by calculating the local distortion of chemical bonds.Once the microscopic strain distribution in the model structure is determined,the energy levels and wave-functions of self-assembled quantum wires are then calculated within the effective bond-orbital model(EBOM).Detailed description of this method can be found in Refs.24,25−26.EBOM used here is a tight-binding-like model in which two s-like conduction bands(including spin)and four valence bands with total angular momentum J=3/2(due to spin-orbit coupling of p-like orbitals with the spinor).Thus,the present model is comparable to the six-band k·p model as adpoted in Ref.?To minimize the computing effort,we express the electron and hole states for the quantum wire structures in terms of eigen-states of a quantum well structure with different in-plane wave vectors.The quantum well consists of8pairs of(GaAs)2(InAs)2short-period superlattice(SPS)plus two InAs monolayers(one inserted after the second pair of SPS and the other after the sixth pair of SPS),so the the total In/Ga composition ratio is consistent with the(GaAs)2(InAs)2.25SPS.The whole stack of SPS’s is then sandwiched between two slabs of Al0.24Ga0.24In0.52barriers.Let us denote the quantum well eigen-states as|n,k1,k2 QW where n labels the subband,k1denotes the wave vector along thewire([1¯10])direction and k2labels the wave vector in the[110]direction,which is perpendicular to the wire and the growth axis.Expanding the quantum well states in terms of bond-orbitals,we have |n,k1,k2 QW=1L α,R f n,k1,k2(α,R z)exp(ik2R2)exp(ik1R1)|uα(R) ,where L is the sample length along the wire axis,f n,k1,k2(α,R z)is the eigen-vector for the quantum well Hamiltonian and uα(R)denotes anα-like bond orbital state at site R(α=1,···,6for two s-like conduction-band and four J=3/2valence-band orbitals).Here R runs over all lattice sites within the SPS layer(well region)and AlGaInAs layer(barrier region).We then diagonalize the hamiltonian for the quantum wire(QWR)within a basis which consists of the quantum well states with k2’s separated by reciprocal lattice vectors g m=m(2π/a[110]);m= ly,|i,k1,k2 = n,m C i,k1(n,k2+g m)|n,k1,k2+g m QWwhere C i,k1(n,k2+g m)is the eigen-vector for the quantum-wire hamiltonian matrix for the i−th QWR subband at wave vector(k1,k2).In terms of the bond orbitals,we can rewrite the QWR states as|i,k1,k2 = α,R F i,k1,k2(α,R)|uα(R)whereF i,k1,k2(α,R)=1Ln,mC i,k1(n,k2+g m)f n,k1,k2+g m(α,R z)exp[i(k2+g m)R2]exp(ik1R1)is the QWR envelope function.For the laterally confined states,the dispersion of bands versus k2is negligible;thus,the k2dependence can be ignored.The absorption coefficeient for inter-subband transitions between subbands i and j is given by αij(¯hω)=4π2e2¯hwhere n r is the refractive index of the QWR,V is the volume of the QWR sample restricted within the SPS region,f i(f j)is the Fermi-Dirac distribution function for subbnad i(j).The optical matrix elements between QWR subband states are related to those between bond orbitals byi,k1,k2|ˆǫ·p|j,k1,k2 = α,α′,τF∗i,k1,k2(α,R)F j,k1,k2(α′,R) uα(R)|ˆǫ·p|uα′(R+ τ) ,where τruns over on-site or the12nearest-neighbor sites in the fcc lattice.The optical matrix elements between bond orbitals are related to the band parameters by requiring the optical matrix elements between bulk states near the zone ceneter to be identical to those obtained in the k·p theory28.We obtain27langleu s(R)|pαuα′(R) =2a)(E p/Eg−m0/m∗e)τα;α=x,y,z,whereταis theα-th of the lattice vectorτin units of a/2,E p is the inter-band optical matrix element as defined in Ref.28,and m∗e is the electron effective mass.Next,we study the inter-band transitions.For this case,the excitonic effect is important.Here we are only interested in the absorption spectrum near the band edge due to laterally confined states.Thus,the dispersion in the k2direction can be ignored.The exciton states with zero center-of-mass momentum can then be written as linear combinations of products of electron and holes states associated with the same k1(wave vector along the wire direction).We write the electron-hole product state for the i-th conduction subband and j-th valence subband as|i,j;k1 ex=|i,k1 |j,k1≡α,β,R e,R h F i,k1(α,R e)G j,k1(β,R h)|u(α,R e)>|u(β,R h)>.The matrix elements of the exciton Hamiltonian within this basis is given byi,j,k1|H ex|i′,j′,k′1 =[E i(k1)δi,i′−E j(k1)δj,j′]− R e,R h F∗ii′(R e)v(R e−R h)G jj′(R2),(4) where v(R e,R h)=4πe2F ii′(R e)= αF∗i,k1(α,R e)F i′,k1(α,R e)describes the charge density matrix for the electrons.Similarly,G jj′(R h)= βG∗j,k1(β,R h)G j′,k1(β,R h)describes the charge density matrix for the holes.In Eq.(x),we have adopted the approximation u(α,R e)| u(β,R h)|v|u(α′,R′e) |u(β′,R′h) ≈v(R e−R h)δα,α′δβ,β′δR e,R′eδR h,R′h,since the Coulomb potential is a smooth function over the distance of a lattice copnstant,except at the origin,and the bond orbitals are orthonormal to each other.At the origin(R e=R h),the potential is singular,and we replace it by an empirical constant which is adjusted so as to give the same exciton binding energy as obtained in the effective-mass theory for a bulk system.The results are actually insensitive to the on-site Coulomb potential parameter,since the Bohr radius of the exciton is much larger than the lattice constant.After the diagonalization,we obtain the excitonic states as linear combinations of the electron-hole product states,and the inter-band absorption coefficient is computed according to4π2e2¯hαex(¯hω)=m0E p/2is needed,In order to obtain a smooth absorption spectrum,we replace theδfunction in Eq.(1)by a Lorentzian function with a half-widthΓ,δ(E i−E)≈Γ/{π[(E i−E)2+Γ2]}(7)Γis energy width due to imhomogeneous broadening,which is taken to be0.01eV(??).III.RESULTS AND DISCUSSIONSWe have performed calculations of inter-subband and inter-band absorption spectra for the QWR structure depicted in Fig.1with varaying degree of alloy mixing and different lengths of period (L)in lateral modulation.Wefind that the inter-subband absorption spectra are sensitive to the length of period(L),but rather insensitive to the degree of of alloying mixing.Thus,we only present results for the case with moderate alloy mixing,which are characterized by parameters b=33˚A and x m=1.0.In all the calculations,the bottom layer atoms of QWR’s are bounded by the InP substrate,while the upper layer atoms and GaAS capping layer atoms are allowed to move freely. This strucure is corresponding to the unclamped struture as indicated in reference10.For different period length L of QWR’s,the strain distribtion profiles are qualitatively similar as shown in reference10.As L decreases,the hydrostatic strain in rich In region(i.e.right half zone of QWR’s unit)increase,while it decreases in rich Ga region.The bi-axial strain has the opposite change with L.The variation of hydrostatic and bi-axial strains with deducing QWR’s period reflects in the potential profiles as the difference of CB and VB band eage increases,which can be seen in Figure2.It can be easily understood that the shear strains increase when L is decuded.The potential profiles due to strain-induced lateral ordering seen by an electron in two QWR structures considered here(L=50a[110]and L=40a[110])are shown in Fig.2.more discussions...The conduction subband structures for the self-assembled QWRs with alloying mixing(x m=1.0 and b=8a[110])for(L=50a[110]and L=40a[110])are shown in Fig.3.All subband are grouped in pairs with a weak spin splitting(not resolved on the scale shown).For L=50a[110],the lowest three pairs of subbands are nearly dispersionless along the k2direction,indicating the effect of strong lateral confinement.The inter-subband transition between thefirst two pairs give rise to the dominant IR response at photon energy around60meV.For L=40a[110],only the lowest pair of subbands(CB1) is laterally confined(with a weak k2dispersion).The higher subbands corresponding to laterally unconfined states(but remain confined along the growth axis)and they have large dispersion versus k2.Wefind three pairs of subbands(CB2-CB4)are closely spaced in energy(within5meV?).State orgion of degeneracry??The valence subband structures for the self-assembled QWRs with alloying mixing(x m=1.0and b=8a[110])for(L=50a[110]and L=40a[110])are shown in Fig.4.more discussions??A.Inter-subband absorptionInter-subband absorption spectrum is the most relavent quantity in determining the usefulness of self-assembled QWR’s for application in IR detection.Fig.5shows the calculated inter-subband absorption spectra of the self-assembled QWR structure(as depicted in Fig.1)for three different lengths of period:L=72,50,and40a[110](approximatley300˚A,200˚A,and160˚A,respectively).In the cacluation,we assume that these QWR structures are n-type doped with linear carrier density around1.65×106cm−1(which corresponds to a Fermi level around25meV above the condunction band minimum).For comparison purposes,we show results for polarization vector along both the[110](solid curves)and[001]directions(dashed curves).The results for[1¯10]polarization are zero due to the strict translational invariance imposed in our model calculation.The peak positions for the inter-subband transition with normal incidence(with[110]polarization) are around65meV,75meV,and110meV for the three cases considered here.All these are within the desirable range of IR detection.As expected,the transition energy increases as the length of period decreases due to the increased degree of lateral confinement.However,the transition energy will saturate at around110meV as we further reduce the length of period,since the bound-to-continuum transition is already reached at L=40a[110].The absorption strengths for thefirst two cases(L=72a[110]and L=50a[110])are reasonably strong(around400cm−1and200cm−1,respectively).They both correspond to the bound-to-bound transitions.In contrast,the absorption strength for the third case is somewhat weaker(around50 cm−1),since it corresponds to the bound-to-continuum transition.For comparison,the absorption strength for typical III-V QWIPs is around??The inter-subband absorption for the[001]polarization is peaked around??meV.The excited state involved in this transition is a quantum confined state due to the Al0.24Ga0.24In0.52barriers. Thus,it has the same physical origin as the inter-subband transition used in typical QWIP structure. Although this peak is not useful for IR detection with normal incidence,it can be used as the second-color detection if one puts a diffraction grating on the surface as typically done in the fabrication of QWIPs.B.Inter-band absorptionThe inter-band optical transitions are important for the characterization of self-assembled QWR’s, since they are readily observable via the Photoluminescence(PL)or optical transimission experiment. For IR-detector application,they offer another absorption peak at mid IR wavelengths,which can be used together with the inter-subband transitions occured at far IR wavelengths for multi-colored detection.Thus,to understand the full capability of the self-assembled QWR material,we also need to analyze the inter-band absorption.Fig.6shows the squared optical matrix elements versus k2for two self-assembled QWR’s con-sidered in the previous section(with L=50and40a[110]).For the case with L=50a[110],the optical matrix elements for both[110]and[1¯10]polarizations are strong with a polarization ratio P[1¯10]/P[110] around2.This is similar to the case with L=72a[110]as reported in Ref.xx.For the case with L=40a[110],the optical matrix elements for both[110]and[1¯10]polarizations are weak.This is due to the fact that the electrons and hole are laterally confined in different regions in the QWR,as already indicated in the potential profile as shown in Fig.2(b).Thus,the inter-band absorption for this case will be uninteresting.Fig.7shows the inter-band absorption spectra for SILO QWR’s with L=72and50a[110], including the excitonic effects.The PL properties of the L=72a[110]structure with alloying mixing characterized by x m=0.1and b=8a[110]has been studied in our previous paper.The QWR structure has a gap around0.74eV with a PL polarization ratio(P[1¯10]/P[110])around3.1.The absorption coefficient for this structure has a peak strength around250cm−1.The binding energy for the ground state exciton labeled1-1(derived primarily from the top valence subband and the lowest conduction subband)is around20meV.Thus,the peak position in the absorption spectrum shifts from0.76meV(without the excitonic effect)to0.74meV(with the excitonic effect).The exctionic effect also enhances the peak strength from200cm−1to250cm−1.The other peak structures(labeled 2-2,2-3,...etc.)are derived primarily from the transitions between the lower valence subbands to the higher conduction subbands).For the QWR structure with L=50a[110],we obtain similar absorption spectrum with a peak strength around400cm−1(??).The exciton binding is around40??meV,and the excitonic en-hancement factor of thefirst peak is around1.15(??),higer than the case with L=72a[110].This indicates that the case with L=50a[110]has stronger lateral confinement for electrons and holes, which leads larger exciton binding energy and stronger excition oscillator strength(due to the largerprobability that the electron and hole appear at the same position).The secondary peaks due to excitonic states derived from higher subbands are also subtantially stronger than their counterparts in the L=72a[110]case.IV.SUMMARY AND DISCUSSIONSWe have studied the inter-subband and inter-band absorption spectra for self-assembled InGaAs quantum wires for consideration in IR-detector application.Detailed band structures,microscopic strain distributions,and excitonic effects all have been taken into account.A number of realistic structures grown via strain-induced lateral ordering process are examined.Wefind that the self-assembled InGaAs quantum wires are good candidate for multi-colored IR detector materials.They offer two groups of strong IR absorption peaks:one in the far-IR range with wavelengths covering10 -20µm(via the inter-subband transition),the other in the mid-IR range with wavelengths centered around1.5µm(via the inter-band transition).Due the strain induced lateral modulation,the inter-subband transition is strong for normal incident light with polarization along the direction of lateral modulation([110]).This gives the self-assembled InGaAs quantum wires a distinct advantage over the quantum well systems for application in IR detection.The inter-subband absorption is found to be sensitive to the length of period(L)of laterial modulation with the aborption peak position varying from60meV to110meV as the length of period is reduced from300˚A to160˚A.However,further reduction in the length of period does not shift the absorption peak very much,as the excited states become laterally unconfined.For the inter-band transition,wefind that the excitonsic effect enhances the absorption peak strength by about10-20%,and shift the peak position by about20-40meV for the structures considered.The reduction in the period length(L)leads to stronger lateral confinement,hence larger exciton binding and stronger absorprtion strength.As conclusion,this paper should give the experiment the realistic guidance in the growth of the IR detector and present the interesting physical thoughts for the theoretists and experimentists.In conclusion,we successfully demonstrated that self-assembled quantum wires are promising IR-detector materials and we provided theoretical modeling for the optical characteristics for realistic QWR structures,which can be used to guide future fabrication of quantum wire infrared detectors.REFERENCES1A.R.Adams,Electron.Lett.22,249(1986).2A.C.Gossard,P.M.Petroff,W.Weigman,R.Dingle,and A.Savage,Appl.Phys.Lett.29,323 (1976);E.E.Mendez,L.L.Chang,C.A.Chang,L.F.Alexander,and L.Esaki,Surf.Sci.142, 215(1984).3Y.C.Chang and J.N.Schulmann,Appl.Phys.Lett.43,536(1983);Phys.Rev.B31,2069(1985).4G.D.Sanders,Y.C.Chang,Phys.Rev.B31,6892(1985);32,4282(1985);35,1300(1987).5R.B.Zhu and K.Huang,Phys.Rev.B36,8102(1987).6R.B.Zhu,Phys.Rev.B37,4689(1988).7Hanyou Chu and Y.C.Chang,Phys.Rev.B39(1989)108618S.T.Chou,K.Y.Cheng,L.J.Chou,and K.C.Hsieh,Appl.Phys.Lett.17,2220(1995);J.Appl. Phys.786270,(1995);J.Vac.Sci.Tech.B13,650(1995);K.Y.Cheng,K.C.Hsien,and J.N. Baillargeon,Appl.Phys.Lett.60,2892(1992).9L.X.Li and Y.C.Chang,J.Appl.Phys.846162,2000.10L.X.Li,S.Sun,and Y.C.Chang,J.Appl.Phys.,2001(in print).11Y.Miyake,H.Hirayama,K.Kudo,S.Tamura,s.Arai,M.Asada,Y.Miyamoto,and Y.Suematsu, J.Quantum electron.QE-29,2123-2131(1993).12E.Kapon,S.Simhony,J.P.Harbison,L.T.Florez,and P.Worland,Appl.Phys.Lett.56,1825-1827(1990)13K.Uomi,M.Mishima and N.Chinone,Appl.Phys.Lett.51,78-80(1987)14Y.Arakawa and A.Yariv,J.Quantum.Electron.QE-22,1887-1899(1986).15D.E.Wohlert,S.T.Chou,A.C Chen,K.Y.Cheng,and K.C.Hsieh,Appl.Phys.Lett.17,2386 (1996).16D.E.Wohlert,and K.Y.Cheng,Appl.Phys.Lett.76,2249(2000).17D.E.Wohlert,and K.Y.Cheng,private communications.18Y.Tang,H.T.Lin,D.H.Rich,P.Colter,and S.M.Vernon,Phys.Rev.B53,R10501(1996). 19Y.Zhang and A.Mascarenhas,Phys.Rev.B57,12245(1998).20L.X.Li and Y.C.Chang,J.Appl.Phys.846162,1998.21S.T.Chou,K.Y.Cheng,L.J.Chou,and K.C.Hsieh,Appl.Phys.Lett.17,2220(1995);J.Appl. Phys.786270,(1995);J.Vac.Sci.Tech.B13,650(1995);K.Y.Cheng,K.C.Hsien,and J.N. Baillargeon,Appl.Phys.Lett.60,2892(1992).22D.E.Wohlert,S.T.Chou,A.C Chen,K.Y.Cheng,and K.C.Hsieh,Appl.Phys.Lett.17,2386 (1996).23D.E.Wohlert,and K.Y.Cheng,Appl.Phys.Lett.76,2247(2000).24Y.C.Chang,Phys.Rev.B37,8215(1988).25J.W.Matthews and A.E.Blakeslee,J.Cryst.Growth27,18(1974).26G.C.Osbourn,Phys.Rev.B27,5126(1983).27D.S.Citrin and Y.C.Chang,Phys.Rev.B43,11703(1991).28E.O.Kane,J.Phys.Chem.Solids1,82(1956).Figure CaptionsFig.1.Schematic sketch of the unit cell of the self-assembled quantum wire for the model structure considered.Each unit cell consists of8pairs of(2/2.25)GaAs/InAs short-period superlattices(SPS). In this structure,four pairs of(2/2.25)SPS(or17diatomic layers)form a period,and the period is repeated twice in the unit cell.Filled and open circles indicate Ga and In rows(each row extends infinitely along the[1¯10]direction).Fig.2.Conduction band and valence band edges for self-assembled QWR structure depicted in Fig. 1for(a)L=50a[110]and(b)L=40a[110].Dashed:without alloy mixing.Solid:with alloy mixing described by x m=1.0and b=8a[110].Fig.3.Conduction subband structure of self-assembled QWR for(a)L=50a[110]and(b)L=40a[110] with x m=1.0and b=8a[110].Fig.4.Valence subband structure of self-assembled QWR for(a)L=50a[110]and(b)L=40a[110] with x m=1.0and b=8a[110].Fig.5.Inter-subband absorption spectra of self-assembled QWR for(a)L=72a[110],(b)L=50a[110], and(c)L=40a[110]with x m=1.0and b=8a[110].Solid:[110]polarization,dashed:[001] polarization.Fig. 6.Inter-band optical matrix elements squared versus k1of self-assembled QWR’s for(a) L=50a[110]and(b)L=40a[110]with x m=1.0and b=8a[110].Fig.7.Inter-band absorption spectra of self-assembled QWR’s for(a)L=72a[110]and(b)L= 50a[110]with x m=1.0and b=8a[110].Solid:[110]polarization with excitonic effect.Dotted:[1¯10] polarization with excitonic effect.Dashed:[110]polarization without excitonic effect.。

The Structure of Solids and TheirPropertiesIntroduction:Solids are one of the three basic states of matter, along with liquids and gases. In a solid, the particles are closely packed together and held in place by strong, attractive forces. This results in a rigid and definite shape, which is one of the fundamental properties of solids. However, the structure of solids and their properties go much deeper than just their shape. In this article, we will explore the various aspects of solids, from their crystal structures to their unique mechanical, electrical, and thermal properties.Crystalline Structure:Most solids are crystalline, meaning that their atoms are arranged in a highly ordered and repeating pattern. This arrangement gives rise to a characteristic crystal structure, which can be determined by X-ray diffraction or other methods. There are many different types of crystal structures, each with its own set of properties and behaviors.One of the most common types of crystal structures is the cubic structure, in which the atoms are arranged in a simple repeating cube. This structure is seen in metals like copper and aluminum, as well as in ionic compounds like sodium chloride. Other common crystal structures include the tetragonal, orthorhombic, and hexagonal structures, which have varying degrees of symmetry.The crystal structure of a solid plays a significant role in determining its mechanical and physical properties. For example, metals with a cubic crystal structure tend to be ductile and malleable, while those with a hexagonal or tetragonal structure are often harder and more brittle. The crystal structure can also affect the electrical conductivity and thermal conductivity of a solid.Mechanical Properties:The mechanical properties of solids refer to how they respond to external stresses and strains. These properties can be described by various measures, such as elasticity, plasticity, hardness, and toughness. Elasticity refers to a material's ability to deform and return to its original shape when the stress is removed. Plasticity refers to a material's ability to be permanently deformed without breaking. Hardness refers to a material's resistance to indentation or scratching, while toughness refers to its ability to absorb energy and resist fracture.The mechanical properties of a solid depend on several factors, including the crystal structure, composition, and processing. For example, metals with a high degree of crystalline order tend to be more ductile and less prone to fracture than those with a more random structure. Similarly, alloys that contain elements with similar atomic radii tend to have higher strength and hardness than those with large mismatches.Electrical Properties:The electrical properties of solids play a crucial role in various technological applications, from electronics to energy generation and storage. Conductors are materials that allow electric charges to flow freely through them, while insulators are materials that resist the flow of charges. Semiconductors are materials that have intermediate conductivity, allowing them to be used in electronic devices like transistors and diodes.The electrical conductivity of a solid depends on several factors, including the crystal structure, composition, and defects. For example, metals with a high degree of crystalline order tend to be good conductors, while insulators often have a highly ordered structure with few defects. Semiconductors have a specific band structure that allows them to be easily manipulated for use in electronic devices.Thermal Properties:The thermal properties of solids refer to how they respond to changes in temperature, including their ability to conduct, store, and transfer heat. Heat capacity is a measure of how much heat a material can absorb or release without undergoing a change intemperature, while thermal conductivity is a measure of how rapidly heat can be conducted through a material.The thermal properties of a solid depend on several factors, including the crystal structure, composition, and defects. For example, metals with a high degree of disorder tend to have lower heat capacity than those with a more ordered structure. Similarly, materials with high thermal conductivity often have a highly ordered structure with few defects, while those with low thermal conductivity often have a more random structure.Conclusion:Solids are a fundamental part of our daily lives, from the metals in our cars to the silicon chips in our electronics. Understanding the structure of solids and their properties is essential for designing and improving the materials we use. From the mechanical properties that determine a material's strength and toughness to the electrical and thermal properties that govern its behavior under different conditions, the intricate nature of solids continues to fascinate and inspire scientists and engineers around the world.。

The effect of front ZnO:Al surface texture and optical transparency on efficient light trapping in silicon thin-film solar cellsMichael Berginski,a͒Jürgen Hüpkes,Melanie Schulte,Gunnar Schöpe,Helmut Stiebig,and Bernd Rech b͒Institute of Photovoltaics(IPV),Forschungszentrum Jülich GmbH,D-52425Jülich,GermanyMatthias WuttigInstitute of Physics(IA),RWTH Aachen University,D-52056Aachen,Germany͑Received18June2006;accepted27January2007;published online9April2007͒This study addresses the material properties of magnetron-sputtered aluminum-doped zinc oxide͑ZnO:Al͒films and their application as front contacts in silicon thin-film solar cells.Optimizedfilmsexhibit high conductivity and transparency,as well as a surface topography with adaptedlight-scattering properties to induce efficient light trapping in silicon thin-film solar cells.Weinvestigated the influence on the ZnO:Al properties of the amount of alumina in the target as wellas the substrate temperature during sputter deposition.The alumina content in the target influencesthe carrier concentration leading to different conductivity and free carrier absorption in the nearinfrared.Additionally,a distinct influence on thefilm growth of the ZnO:Al layer was found.Thelatter affects the surface topography which develops during wet-chemical etching in dilutedhydrochloric acid.Depending on alumina content in the target and heater temperature,threedifferent regimes of etching behavior have been identified.Low amounts of target doping and lowheater temperatures result in small and irregular features in the postetching surface topography,which does not scatter the light efficiently.At higher substrate temperatures and target doping levels,more regularly distributed craters evolve with mean opening angles between120°and135°andlateral sizes of1–3␮m.These layers are very effective in light scattering.In the third regime—atvery high substrate temperatures and high doping levels—the postetching surface is ratherflat andalmost no light scattering is observed.We applied the ZnO:Alfilms as front contacts in thin-filmsilicon solar cells to study their light-trapping ability.While high transparency is a prerequisite,lighttrapping was improved by using front contacts with a surface topography consisting of relativelyuniformly dispersed craters.We have identified a low amount of target doping͑0.5–1wt%͒andrelatively high substrate temperatures͑about350–450°C as sputter parameters enablingshort-circuit current densities as high as26.8mA/cm2in␮c-Si:H pin cells with an i-layer thicknessof 1.9␮m.Limitations on further improvements of light-trapping ability are discussed incomparison with the theoretical limitations and Monte Carlo simulations presented in the literature.©2007American Institute of Physics.͓DOI:10.1063/1.2715554͔I.INTRODUCTIONVarious solar cell concepts can be used to utilize the photovoltaic effect for energy production.1–3At present,the photovoltaic world market is dominated by crystalline silicon cells which accounted for nearly95%of world photovoltaic cell and module production in2004.4The remaining share of the world photovoltaic market mainly relies on thin-film so-lar cell concepts.It can be assumed that several thin-film module companies already operate profitably.5Even though thin-film solar cell production based on copper-indium dis-elenide͑CIS͒,cadmium telluride͑CdTe͒,and amorphous silicon had comparably small market shares in2004of about 0.25%,1.1%,and3.9%,respectively,these concepts are be-lieved to be candidates for a significant production volume in the future.5–7Thin-film solar cells might be among the very few photovoltaic techniques to reach the very low cost target ofϽUS$1/watt.Such low costs are required for photovol-taics to compete with retail electricity prices but,in the in-termediate term,this can only be achieved by increasing the production capacity significantly.5,6,8However,in the case of CIS and CdTe thin-film technologies,the use of nonabundant materials like In,Se,and Te may mean that these materials will become a dominant price factor in mass production.6 Silicon is an abundant material.Thus,silicon thin-film solar cells,due to their low costs,have a good chance of gaining a significant market share once mass production has started.There are a variety of different technical realizations for silicon thin-film solar cells.For example,silicon thin-film solar cells can be made by using one single amorphous sili-con͑a-Si:H͒junction.However,these cells are degraded to some extent upon light soaking due to the light-induced cre-ation of metastable defects,known as the Staebler-Wronski effect.9,10This problem can be reduced by using a very thin a-Si:H layer or a stack of thin layers,because in this latter case the photogenerated carriers need to move only a short distance before reaching the electrodes.11,12A significant in-a͒FAX:ϩ492461613735;electronic mail:m.berginski@fz-juelich.deb͒Current address:Department of Silicon Photovoltaics͑SE1͒,Hahn-Meitner-Institut Berlin GmbH,D-12489Berlin,Germany.JOURNAL OF APPLIED PHYSICS101,074903͑2007͒0021-8979/2007/101͑7͒/074903/11/$23.00©2007American Institute of Physics101,074903-1crease in efficiency is possible if the long wavelength re-sponse is also enhanced.Thus,another approach is to use astack of amorphous silicon and amorphous silicon germa-nium͑a-SiGe:H͒.13A further approach is to employ micro-crystalline silicon␮c-Si:H.14,15Microcrystalline silicon so-lar cells are stable against light soaking or show only a verylittle degradation as compared to amorphous silicon solarcells.16,17Thus,a stack consisting of a thin amorphous sili-con top cell and a microcrystalline bottom cell in a so-calledmicromorph tandem structure offers the potential for fairlyhigh efficiency at low cost in mass production.18–21A stabi-lized efficiency of12.0%has recently been published for atandem structure module22͑for comparison,solar modules with sliced single crystalline and polycrystalline silicon havebeen reported to show efficiencies of up to22.7%and15.3%,respectively23͒.Even though silicon thin-film mod-ules still show rather low efficiencies compared to the other approaches,from the application point of view the annual energy production and especially the cost per unit of annual energy production is much more relevant.Focusing on these figures,thin-film amorphous silicon performs better than crystalline silicon due to a lower temperature coefficient for power loss.5Thus,the aim of future research and develop-ment in the area of thin-film silicon solar cells is low cost annual energy production rather than merely high nominal efficiency.Even though microcrystalline silicon solar cells or mi-cromorph tandem cells can utilize a broader spectral rangethan amorphous silicon solar cells,an efficient light-trappingscheme is still essential to enhance the intrinsically low ab-sorbance of microcrystalline silicon in the long wavelengthrange͑wavelength␭of aboveϷ850nm͒.24,25Light trappingis achieved by combining textured transparent conductiveoxide͑TCO͒films as front contacts and highly reflectiveback contacts.However,due to the multiple passage of scat-tered light within the solar cell device,parasitic light absorp-tion in the photovoltaic nonactive layers͑highly doped n-and p-type silicon layers,front TCO,and back reflector͒isincreased as well.In the p-i-n configuration the cell is illuminated throughTCO coated glass.The TCO has to have counteracting prop-erties:high conductivity to obtain low series resistance andlow carrier concentration to avoid absorption losses in thered and near-infrared͑NIR͒wavelength range.It should benoted that in the NIR the absorbance of a single passagethrough a1␮m thick layer of␮c-Si:H is lower than that of typical TCOs.In earlier work,Agashe et al.studied the in-fluence of the target doping concentration on the electrical, structural,and optical properties of sputter-deposited and as-deposited smooth ZnO:Alfilms.26They found much lower parasitic absorptions with similar conductivity values using sputter targets with a low amount of alumina.Besides the transparency,it is crucial to develop a TCO with a suitable surface texture which scatters the light very efficiently in order to extend the effective path length within the active silicon layers.27,28Thus,a special design of the TCO is nec-essary to fulfill all these requirements.For initially smooth sputter-deposited ZnO:Alfilms a surface texture is realized by postdeposition wet-chemical etching.29,30Kluth et al.re-lated the influence of pressure and substrate temperature dur-ing radio frequency͑rf͒sputter deposition of ZnO:Al at a fixed alumina content of2wt%in the sputter target to struc-tural properties and postetching surface topography in a modified Thornton model.30They showed that,depending on sputter parameters,craterlike surface topography with typical lateral length scales of1–2␮m and depths of about 200–400nm develops in a self-organized fashion.This etch-ing behavior is affected very sensitively by structural ZnO:Al properties.Thefilm structure can be controlled by the depo-sition parameters,but there are a number of hidden param-eters that are not yet fully understood.31For example,Hüp-kes et al.and Kluth et al.showed that the amount of oxygen added to the process gas strongly influencesfilm properties.32,33Another of these unknown influence factors might be the target alumina concentration͑TAC͒.In the present study,we extend the modified Thornton model by introducing the alumina content in the target as an influential parameter for varying the etching behavior and thus surface topography for light scattering.This knowledge is essential for developing surface-textured ZnO:Alfilms for efficient light trapping based on the improved optical and electrical properties of as-deposited smooth thinfilms found by Agashe et al.We briefly show structural,optical,and electrical properties supporting the results of Agashe et al. with additional data.Aiming to design an optimized front TCO for thin-film solar cells,we study the growth of the ZnO:Alfilms and characterize the surface texture of thefilms after etching in HCl.Finally,optimizedfilms are applied in solar cells and calculations of an effective light pass en-hancement factor are presented.We focus on single junction microcrystalline silicon thin-film solar cells in order to study the light-trapping ability of the front contacts,particularly in the long wavelength range.Optimized ZnO:Alfilms can later be applied in stacked multijunction cells with amorphous and microcrystalline silicon absorber layers.Finally,in order to quantify the success of the experimental achievements,we compare the light-trapping ability in our cells with simula-tions of nearly idealized conditions and statistical mechani-cally derived general limitations.II.EXPERIMENTAL DETAILSZnO:Alfilms were prepared on Corning1737glass by rf magnetron sputtering from ceramic targets in static or dy-namic modes.The amount of doping was varied by using ZnO:Al2O3targets with0.2,0.5,1,or2wt%of Al2O3.The concentration of Al2O3in the target is henceforth referred to as TAC.At constant deposition pressure of0.3Pa͑in the case of0.2,0.5,and2wt%TAC͒and0.1Pa͑in the case of 1wt%TAC͒the substrate temperature was varied in a range of60–490°C.Substrate temperature was calibrated by a thermal sensor and was controlled by the heater temperature. Film characterization was done by a four-point probe,room temperature Hall effect measurements at room temperature and by x-ray diffraction analysis.Optical transmittance and reflectance of smoothfilms,as well as the total and diffuse transmission on texture-etchedfilms͑in order to calculate the haze͒,were measured in air with a dual beam spectrometer.For textured ZnO:Alfilms,CH2I2was applied in transmit-tance and reflectance measurements as an index-matching fluid to avoid systematic measurement errors due to light scattering of the roughfilms.34By wet-chemical etching in diluted hydrochloric acid͑0.5%HCl͒,the approximately 800nm thick initially smoothfilms͑rms roughness of about 15nm͒were transformed into surface-texturedfilms with a typical rms roughness of more than100nm.The surface topography and characteristic feature sizes were studied by scanning electron microscopy͑SEM͒and atomic force mi-croscopy͑AFM͒.The surface topographies determined by atomic force microscopy were statistically analyzed.How-ever,the most effective way to characterize the light-trapping ability of a specific TCOfilm is by applying it in solar cells. For this purpose,we deposited␮c-Si:H single junction solar cells by plasma-enhanced chemical vapor deposition ͑PECVD͒at13.56MHz excitation frequency in a30ϫ30cm2reactor.35Double layers of sputter-deposited ZnO:Al͑80nm͒and thermally evaporated silver͑700nm͒served as the back reflector and rear side contact.Details ofcell preparation are given elsewhere.28Solar cell character-istics were measured using a sun simulator͑Wacom-WXS-140S-Super͒under standard test conditions͑AM 1.5,100mW/cm2at25°C͒.The external quantum efficiency ͑QE͒of some solar cells was measured by differential spec-tral response at zero bias.From the QE the short-circuit cur-rent density,which corresponds to the maximum current den-sity generated by the solar cell,was calculated employing theAM 1.5solar spectrum with an illumination density of100mW/cm2with the corresponding photonflux.In the fol-lowing,the short-circuit current density calculated in thisway is referred to as the cell current density.III.RESULTSA.Structural,electrical,and optical ZnO:Alfilm propertiesAs is typical of magnetron-sputtered ZnO:Alfilms,36allthefilms in this study exhibit a strong texture with the c axispredominantly orientated parallel to the substrate normal.Therefore,the x-ray diffraction spectra in Bragg-Brentanogeometry exhibit strong peaks corresponding to the͓001͔direction.All other peak intensities are at least a factor of onehundred lower than that of the͑002͒peak.Figure1showsthe peak position and full width at half maximum͑FWHM͒of the͑002͒peak as function of substrate temperature T.While the peak position shifts towards higher angles withincreasing substrate temperature in the case of low TAC,thetrend is opposite for the target with2wt%TAC.A shift ofpeak position towards lower angles usually indicates com-pressive stress,which is attributed to high-energy ion bom-bardment during growth by sputter deposition.The FWHMof the͑002͒peak decreases with substrate temperature forlow doping concentration and,once again,only in case of2wt%TAC does the FWHM strongly increase at high sub-strate temperatures.This means that the number of coher-ently scattering crystal planes decreases.This either corre-sponds to crystallite size or is limited by microstress within asingle crystallite.The TAC influences the amount of Al doping and in this way determines the number of free carriers in the ZnO:Al films.37Figure2shows the carrier concentration N and mo-bility␮as a function of substrate temperature T.While in the case of0.5and1wt%TAC,the carrier concentration tends to be maximal at substrate temperatures of300–350°C;films sputtered with a TAC of0.2and2wt%gradually change their carrier concentration.Increasing the substrate temperature during sputtering leads to a higher N in case of 0.2wt%TAC and to a lower N in case of2wt%TAC.The carrier mobility seems to be maximal at a certain substrate temperature which increases when TAC is reduced.Carrier mobility was further improved by optimized deposition con-ditions compared to the data of Agashe et al.26Figure3shows transmission and absorption spectra of ZnO:Alfilms sputtered at afixed substrate temperature of 375°C using0.2,0.5,and2wt%TAC.The absorption was calculated using transmission and reflection spectra.Increas-ing the TAC mainly increases the absorption of NIR light and the carrier concentration N͑see inset,values are given in 1020cm−3͒in thefilms.Simultaneously,the resistivity␳͑see FIG.1.X-ray diffraction spectra in Bragg-Brentano geometry were evalu-ated with respect to the position͑upper graph͒and the full width at half maximum͑lower graph͒of the dominant͑002͒peak.The data points at,e.g., 300°C and1wt%TAC were measured for nominally identical ZnO:Al films.Scattering of data points is caused by statistical experimentalerrors.FIG.2.Carrier concentration N͑top graph͒and carrier mobility␮͑bottom graph͒measured using Hall measurements in van der Pauw geometry.inset,values are given in 10−3⍀cm ͒decreases.In addition,the fundamental absorption band edge is shifted to smaller wavelengths ͑Burstein-Moss shift 38,39͒.Note that this effect is partially masked by the index-matching fluid applied dur-ing measurements.For high doping levels,the parasitic free carrier absorption mechanism significantly reduces the trans-mission in the active range of the solar cells ͑up to about 1100nm ͒.A compromise has to be found between transmis-sion and conductivity in order to prepare optimized ZnO:Al front contacts for solar cells.However,even though high transmission and low resistance are prerequisites,earlier work has shown that surface roughness,feature size,and shape are key parameters for highly efficient light trapping.27,40Thus,we concentrate in the following section on ZnO:Al surface structure observed after etching.B.Postetching surface topographyAfter deposition the initially smooth films were surface textured by wet-chemical etching in diluted hydrochloric acid.The etching time was adapted in such a way that ap-proximately 150nm of the film thickness was removed,leading to a final thickness of about 650nm.Depending on the TAC and substrate temperature,three clearly different postetching surface structures appear.One specimen of each type is shown in Fig.4͑a ͒.The first type ͑denoted by I in Fig.4͒typically comprises a very rough surface with lateral fea-ture sizes of about 300nm and with rather steep edges.For the second type ͑II ͒,the surface is almost uniformly covered by large craters with diameters ranging from 1to 3␮m and depths of about 150–400nm.The third type ͑III ͒develops a comparatively flat surface with plenty of shallow craters with depths of up to about 100nm and a few large craters with lateral diameters of up to 3␮m and depths of up to 700nm ͑limited by film thickness ͒in the case of the large craters.The postetching topography types I,II,and III are found in different growth regimes,as illustrated in Fig.4͑b ͒.With increasing T the growth changes from types I and II to III.The transition temperature for changing the regimes shifts to higher values if TAC is reduced.At the same time the Trange for type II films becomes narrow.The transition be-tween the regimes is not sharp.In order to incorporate these findings into the modified Thornton model introduced by Kluth et al.,30the substrate temperature axis has to be res-caled taking TAC into account since increasing substrate temperature and increasing TAC both have similar effects on changing growth conditions.Four examples of type II topographies are illustrated by SEM micrographs in Fig.5.Over a broad range of TAC and substrate temperature a postetching surface topographycanFIG. 3.Transmission ͑left axis ͒and absorption ͑right axis ͒spectra of surface-textured front contacts sputtered at substrate temperature of 375°C using ZnO:Al 2O 3targets with 0.2,0.5,and 2wt %TAC,respectively.The optical data can only be considered for ␭Ͼ400nm,as CH 2I 2is strongly absorbing for smaller wavelengths.The discontinuity in the data around ␭=900nm is due to an artifact of the measurementsystem.FIG.4.͑a ͒AFM 10ϫ10␮m 2measurements ͑top ͒and ͑b ͒schematic distri-bution of etching behavior types in a matrix of parameter substrate tempera-tures and TAC ͑crosses:type I,squares:type II,and circles:type III ͒.The parameter space where we expect to find type II films ishatched.FIG.5.SEM micrographs of texture-etched ZnO:Al films of surface topog-raphy type II.be achieved that is uniformly covered by similarly sized cra-ters.Changing the TAC has only a minor influence on the crater size distribution if the substrate temperature is ad-justed.AFM measurements were used to determine the rms roughness values that are given as a function of substrate temperature in Fig.6.In the case of 0.2,0.5,and 1wt %TAC,the rms roughness increases steeply beyond a certain substrate temperature.This transition temperature increases with decreasing TAC.Films sputtered from 2wt %TAC show decreasing rms roughness with increasing T .Correlat-ing this behavior to the postetching surface topography types indicates that surface topographies of regime II typically have the highest rms roughness of up to 160nm.In general,with surface topography changing from type I or III to type II the rms values increase significantly.Besides calculating rms roughness,we analyzed the AFM data with a computer program developed by Stiebig and Schulte ͑for details,see Ref.41͒.The computer program defines—by means of each set of three neighboring AFM data points—a corresponding plane.The inclination of these planes was calculated with respect to the film normal.The angles can be expressed in terms of crater opening angles ␥,which correspond to twice the inclination angle to the sub-strate normal.Figure 7shows a histogram of opening angles for two examples of types I and II surface topography.Bymeans of a Gaussian fit,the mean crater opening angles and corresponding FWHM values were obtained ͑see Fig.8͒.While the histogram of the film with surface topography type I ͑sputtered at heater temperature of 65°C ͒is centered around angles of approximately 90°with a broad variation,the frequency distribution of the film of type II ͑sputtered at 460°C ͒is centered around significantly higher angles and is comparatively paring all the data ͑see Figs.4and 8͒,we find a mean ␥in the range of 120°–135°for type II topographies.The FWHM of the crater opening angle distri-butions is between 20°and 45°.Type I topographies ͑TAC of 0.2and 1wt %͒show a considerably larger FWHM,indicat-ing that in this case there is much more deviation in surface topography feature dimensions.C.Light scattering and solar cell applicationIn order to further study the light scattering of the texture-etched films,the haze of these layers was determined ͑Fig.9shows haze values at a fixed wavelength of ␭=1␮m ͒.While the analysis of the AFM topography has shown a continuous shift in crater opening angle,the haze value increases perceptibly when substrate temperature ex-ceeds a critical value.This temperature coincides with the change in topography type from I to II.Again,thelayersFIG.6.Calculated rms roughness data points using AFM measurements of texture-etched ZnO:Al films with different TACs.Guide-to-the-eye lines are additionallydrawn.FIG.7.Relative frequency distribution of crater opening angles ͑data points ͒and Gaussian fit ͑lines ͒of two films sputtered using a TAC of 0.2wt %and different substrate temperatures.The center of the Gaussian fit and its FWHM areindicated.FIG.8.Mean values ͑top ͒and FWHM ͑bottom ͒of the crater opening angle ␥distributions determined by Gaussian fit of the frequency distribution functions of the AFM data ͑compare Fig.7͒.FIG.9.Haze values at wavelength ␭=1␮m.Type II topographies tend to have the highest haze values.Films sputtered using 2wt %TAC in general have lower haze values.sputtered using a TAC of 2wt %deviate in their behavior:the haze decreased significantly for high substrate tempera-tures.In the investigated temperature range,we cover a to-pography type change from II to III for TAC of 2wt %cor-responding to a decrease in haze values.In order to study the light-trapping ability in thin-film solar cells,we applied the ZnO:Al films in ␮c -Si:H single junction cells with intrinsic ␮c -Si:H layer absorber thick-ness of about 1␮m.Figure 10shows the QE data and cell reflections of solar cells prepared on ZnO:Al films with dif-ferent surface topography types.In the case of type I topog-raphy ͑TAC of 0.2wt %,T =290°C ͒,a certain degree of light trapping is already apparent because of the roughness of these layers.Due to the poor electrical quality of the ZnO:Al film,the quantum efficiency of the corresponding cell had to be measured with applied negative bias in order to collect all the carriers generated.The cell current density of this cell was 22.1mA/cm 2.The electrical performance and light-trapping ability was improved by using type II front contacts ͑TAC of 0.2wt %,T =460°C ͒,consisting of relatively uni-formly dispersed craters.In this case,the cell current density reached 22.9mA/cm 2due to an improved QE in the red and NIR wavelength ranges.The gain in efficiency is consider-able due to the much better electrical properties of the ZnO:Al leading to a high fill factor and open circuit voltage.A front TCO with type III topography ͑TAC of 2wt %,T =375°C ͒is noticeably less successful in trapping the light within the cell.It mainly consists of flat regions without significant light scattering,leading to a low QE with a cell current density of only 17.2mA/cm 2and interference fringes similar to cells prepared on smooth front contacts.28Figure 11shows a summary of cell current densities as a function of TAC and substrate temperature during sputtering.These results can be partly explained by employing the rms roughness and haze data ͑see Fig.6͒and the assumption that higher roughness implies better light trapping.It should benoted that this model is too simple to explain the light-trapping ability in all details.A detailed discussion of the relation of surface topography and light trapping can be found in the literature.40,41In the case of 2wt %TAC,the topography type changes from regime II to regime III by increasing the substrate temperature from 300to 400°C.Due to the poor light-trapping ability of type III films,the cell current density drops steeply towards the level of cells fabricated on nontextured front contacts ͑cf.data of Rech et al.:15.6mA/cm 2͒.28In the case of 0.2,0.5,and 1wt %TAC,we mainly studied topography types I and II.There is a rather steep increase in roughness changing the surface topography re-gime.The cell current densities observed for type II front contacts are significantly higher than 21mA/cm 2.Neverthe-less,the highest currents are found for type II films and are found at high substrate temperatures with a rather low TAC.To further study the necessity of TCO transparency for optical cell efficiency we deposited a series of ␮c -Si:H solar cells with varying silicon thicknesses of 0.5,1,and 1.9␮m on type II front contacts with TAC of 0.5wt %͑T =375°C ͒and TAC of 1wt %͑T =300°C ͒.Figure 12shows the quantum efficiencies of these cells as well as the cell reflections of the two cells with a 1.9␮m ␮c -Si:H layer.Reducing the parasitic absorption in the front TCO increases the quantum efficiency and the cell reflection and thus short-ens the gap between quantum efficiency and 1−R .With in-creasing thickness of the intrinsic silicon layer the influence of parasitic losses in the front TCO,in the doped silicon layers,and at the back reflector is reduced since the absor-bance of the intrinsic silicon layer increases relative to the parasitic absorption.A cell current density of up to 26.8mA/cm 2has been achieved experimentally in the case of an intrinsic silicon layer thickness of 1.9␮m ͑see quan-tum efficiency in Fig.12͒.The QE data shown in Fig.12were used to estimate an effective light pass enhancement factor f .In order to con-sider the different TCO absorptions A TCO during the first pass before entering he ␮c -Si:H,QE is normalized to:QE rescaled =QE/͑1−A TCO ͒.The absorption A TCO was calculated from the transmission and reflection ͑see Fig.3͒.Using an ab-sorber layer thickness d and absorption coefficient ␣ofFIG.10.Quantum efficiency ͑left axis ͒and cell reflection ͑right axis ͒of a series of ␮c -Si:H solar cells with intrinsic silicon layer thickness of about 1␮m.Front TCOs of surface topography types I,II ͑both with 0.2wt %TAC ͒,and III ͑2wt %TAC ͒are compared.Cell current densities were cal-culated using the solar AM 1.5spectrum ͑see inset,values are given in mA/cm 2͒.The cell with front contact of type I was measured with an ap-plied bias of −0.5V due to poor electrical properties of the corresponding front TCO.The discontinuity in the data of the cell reflection around ␭=900nm is due to an artifact of the measurement system.Note the different direction of the right axis.In this case,the reflection curves can be inter-preted as total cellabsorption.FIG.11.Current densities calculated using measured quantum efficiencies of ␮c -Si:H pin cells ͑i -layer thickness of 1␮m ͒.In the case of very high-Ohmic front contacts the cells were measured with a negative bias of up to −0.5V in order to be able to collect all the carriers generated.。

钙钛矿配体连接方式英文回答：The ligand connectivity in perovskite structures can vary depending on the specific compound and its composition. Perovskite materials are typically composed of a metal cation, such as calcium (Ca), and a ligand, such astitanium (Ti), which forms a coordination complex with the metal cation. The ligands can be connected to the metal cation in different ways, resulting in various coordination geometries.One common ligand connectivity in perovskite structures is the octahedral coordination, where the ligands surround the metal cation in a symmetrical manner. In this arrangement, six ligands are connected to the metal cation, forming an octahedron. Each ligand is connected to themetal cation through a single bond. This octahedral coordination geometry is often observed in perovskite compounds with a general formula of ABX3, where A is themetal cation, B is another metal cation, and X is the ligand.Another ligand connectivity in perovskite structures is the tetrahedral coordination, where the ligands are connected to the metal cation in a tetrahedral arrangement. In this case, four ligands are connected to the metal cation, forming a tetrahedron. Each ligand is connected to the metal cation through a single bond. This tetrahedral coordination geometry is less common in perovskite compounds, but can still be found in certain materials.In addition to these two common coordination geometries, there can be variations and combinations of ligand connectivity in perovskite structures. For example, some perovskite compounds may exhibit a combination ofoctahedral and tetrahedral coordination, where both typesof ligand connectivity are present in the structure. This can result in a more complex arrangement of ligands around the metal cation.It is important to note that the specific ligandconnectivity in perovskite structures can greatly influence the properties and behavior of the material. The arrangement of ligands can affect factors such as the stability, electronic structure, and optical properties of the perovskite compound. Therefore, understanding theligand connectivity is crucial for designing andengineering perovskite materials with desired properties.中文回答：钙钛矿结构中的配体连接方式可以根据具体的化合物和其组成而有所不同。

拓扑物态总理报告英语## Topological Quantum Matter: A Prime Ministerial Report.Topological quantum matter is a new state of matterthat has emerged as a major focus of research in condensed matter physics. These materials have unusual electronic properties that are protected by topology, a branch of mathematics that deals with the properties of shapes and spaces.One of the most striking features of topological quantum matter is its ability to conduct electricity without any loss of energy. This is in contrast to ordinary metals, which lose energy due to the scattering of electrons by impurities and other defects. The ability of topological materials to conduct electricity without loss of energy is due to the topological protection of their electronic states.Topological quantum matter has been found to occur in a variety of materials, including semiconductors, insulators, and superconductors. Some of the most well-known examples of topological materials include topological insulators, topological superconductors, and Weyl semimetals.Topological insulators are materials that areinsulating in the bulk but conducting on the surface. This is due to the fact that the surface of a topological insulator has a different topology than the bulk. The surface of a topological insulator is home to a type of electron called a Dirac fermion, which is a massless particle that behaves like a relativistic electron.Topological superconductors are materials that are superconducting in the bulk but insulating on the surface. This is due to the fact that the surface of a topological superconductor has a different topology than the bulk. The surface of a topological superconductor is home to a type of electron called a Majorana fermion, which is a particle that is its own antiparticle.Weyl semimetals are materials that are semimetals, meaning that they have a non-zero density of electrons and holes. Weyl semimetals are characterized by the presence of Weyl fermions, which are massless particles that behavelike relativistic electrons.Topological quantum matter has a wide range ofpotential applications, including in the development of new electronic devices, such as topological insulators for spintronics and topological superconductors for quantum computing. Topological quantum matter also has thepotential to lead to new discoveries in physics, such as the discovery of new particles and the development of new theories of quantum matter.Recommendations.In light of the great potential of topological quantum matter, I recommend that the government take the following steps to support research in this area:Increase funding for research in topological quantummatter.Establish a national center for topological quantum matter research.Create a fellowship program to support graduate students and postdoctoral researchers working intopological quantum matter.Develop educational programs to train the next generation of scientists in topological quantum matter.By taking these steps, the government can help to ensure that the United States remains a leader in the field of topological quantum matter and that this exciting new area of research continues to yield new discoveries and applications.Conclusion.Topological quantum matter is a new and exciting state of matter with the potential to revolutionize ourunderstanding of physics and lead to the development of new technologies. The government should take steps to support research in this area in order to ensure that the United States remains a leader in this field.。

Fig.1.Schematic drawing of the various slag layers formed in the mould.©2003ISIJof the fluxes have property values which are consistent with those derived from empirical rules. Thus there is simplicity in the way that mould fluxes perform the required func-The complexity arises from the huge range of “in mould conditions” that the flux has to deal with. The large number of variables in the continuous casting process and their ef-fect on both the surface quality of the product and on process control are shown in Fig. 2. The mould flux is ex-pected to compensate for many of the variations in casting conditions by being “flexible” and “forgiving”. Given the large differences in the casting conditions at different plants, it is not surprising that fluxes known to work suc-cessfully on one plant, frequently do not perform so well on another plant.The principal factors affecting flux performance are:Casting conditions (casting speed, V c , oscillation charac-teristics).Steel grade and mould dimensions.Mould level control (which can lead to depressions etc .).Metal flow since turbulent flow can lead to several prob-lems eg gas and slag entrapment.In this study we will examine the effects of mould flux on lubrication and heat transfer and how flux performance is affected by both casting conditions and steel grade being cast. Then we will look at how the mould flux is expected to deal with problems caused by turbulent metal flow in the mould and how recent developments affecting metal flow control may help to simplify the tasks carried out by mould Mould Flux LubricationThe liquid mould flux lubricates the steel strand. It is im-portant that there is liquid lubrication throughout the strand since problems (such as star cracking) can occur if the flux crystallises completely in the lower half of the mould and liquid lubrication is lost.4)The liquid friction (F l ) is given by Eq. (1) where V m is the velocity of the mould. It can be seen that the friction decreases as the viscosity (h ) decreas-es and the liquid flux film thickness (d l ) increases.F l ϭh (V m ϪV m )/d l (1)Powder consumption provides a measure of the lubrication supplied and it is very dependent upon mould size since the friction increases as the distance from the corner increases.Thus frictional forces are much larger in slabs Ͼblooms billets. Powder consumption (Q t ) is usually measured as kg flux (tonne steel)Ϫ1. However, Q t can be converted to with units of kg flux m Ϫ2(of mould) using Eq. (2),Q s ϭf *.Q t .7.6/R ϭd l r (2)where f * is the fraction of powder producing slag, density of the liquid slag and R is the surface area to vol-ume of the mould and is given by 2(w ϩt )/wt where are the thickness of the mould. The effect of mould dimen-sions on powder consumption, Q s , can be clearly seen in Fi g. 3since R has values of Ͻ10 for slabs, 10–15 for blooms, Ͼ20 for billets and Ͼ30 for thin slabs.2003ISIJ1480Fig.2.Schematic diagram showing the cause of various defects and operational problems.Fig.3.Powder consumption, Q s as a function of the parameter,R ϭ(surface area/volume).ϭ2/(RϪ5) (3)Empirical rules for the selection of fluxes for “optimum casting” in terms of casting speed and flux viscosity haveWolf subsequently converted these into empirical rules to derive the required powder consump-However, powder consumption is also dependent upon other casting parameters such as the oscillation char-acteristics, solidification or break temperature etc. The vari-reported for powder consumptionTable 1. Itoyama17)reported a model contained contributions from (i) flow emanating from the molten pool, (ii) flow between parallel plates (mould and strand), (iii) the oscillation of the mould and(iv) slag trapped in oscillation marks (Qom ).In order to test the validity of these various relationships we have collected plant data from steel-plants all round the world when casting slabs, blooms, billets and thin slabs. Database 1 was collected from plant data from single tri-als for billet-bloom-slab and thin slab-casting in Ͼ30 steel-works. The following data were included: powder con-, mould dimensions, casting speed, steel composition and flux chemical composition, viscosity and. The variation in powder consump-tion values for runs carried out under similar casting condi-%.19)Database 2 contained all the information listed for Database 1 plus the oscillation characteristics, frequency). Mean powder consumption values were derived in trials with identical casting conditions but% variation in the casting speed. The varia-tion of averaged powder consumption values is less than The performances of the various relationships werechecked by comparing the calculated Qs against the mea-; the results are given in Fig. 4.It can be seen from Fig. 4 and Table 1 thatthe Tsutsumi, Maeda and Kwon relations provide thesfollowed by modified Wolf andthe required viscosity (at 1573K) of the flux can now be calculated for the specific casting conditions and mould dimensions. (The Tsutsumi relation16)has been adopted when the oscillation characteristics areavailable and the modified Wolf relationthese data are not available.)(iii)there are deviations from these relations for billet-casting where frequently high-viscosity fluxes areused to minimise problems related to turbulent metalflow (e.g.slag entrapment) because the lubrication re-quirements for billets are low.It should also be noted that low powder consumption can occur when casting steels containing Ti, due to the copious formation of TiN which prevents the infiltration of liquid slag into the mould/strand gap.It is our belief that these high viscosity fluxes operate ona different principal to conventional fluxes. Most conven-tional fluxes show a marked increase in viscosity when crystalline solids are formed at the break temperature (on cooling (Fig. 5(a)). However, high-viscosity slags form super-cooled liquids on cooling (Fig. 5(b)) which persist down to their glass transition temperatures,(dPa s)ϭ1013.4). No break temperature would be recorded with this type of slag. Furthermore, a super-cooled liquid will move with the strand despite having a high viscosity value.There are also a small number of fluxes (about 10which work well enough in practice but do not fit the re-quirements derived from the empirical rules.Thus, in summary, the only flux properties which are im-portant for lubrication are the viscosity and the break tem-perature.3.Mould Flux and Heat TransferHeat transfer in the mould can be conveniently classified into vertical and horizontal heat transfer. Decreased vertical heat transfer has been reported20)of pinholes and (ii) the depth of oscillation marks by reduc-ing the length of steel meniscus. However, it is the horizon-tal heat transfer between steel shell and mould which is the more important since it has such a significant effect on the surface quality of the steel.Horizontal heat transfer is complex involving two mech-anisms, namely, lattice or phonon conductivity (diation conductivity (kR). Radiation conductivity involves absorption and re-emission of radiated energy and can be the dominant mechanism in glassy materials at high tem-1481peratures.21–23)However, k R can be significantly decreased by the presence in the slag film of (i) crystallites which scatter the radiation and (ii) transition metal oxides (e.g.FeO) which absorb the radiation. It has been estimated that ϭ10–30% k c 21–23)for heat transfer across slag films formed during slab casting. However, it may be much more significant in glassy slag films formed using high-viscosity fluxes for billet casting. The overall resistance to thermal transfer (R *total ) between shell and mould can be regarded as a series of resistances as shown in Fig. 6and Eq. (4).R *total ϭR *Cu/sl ϩ(d /k )l ϩ(d /k )gl ϩ(d /k )cry (4)where R *Cu/sl is the interfacial resistance and d and k are thethickness and thermal conductivity of the layers in the slag film and subscripts l , gl and cry denote the liquid, glass and crystalline layers, respectively.Y amauchi 23)introduced the contribution from radiation conduction as a parallel resistance. The most significant terms affecting (R total ) are (i) R Cu/sl and (ii) the thickness of the solid slag film i.e.d solid ϭd gl ϩd cry . The interfacial resis-tance R Cu/sl was found to increase with (i) increasing solid slag thickness, d solid and (ii) increasing crystallinity. This is best understood as an increase in R Cu/sl results from an in-crease in the thickness of an air gap, formed as glass trans-forms into the more-dense, crystalline phase (r cry Ͼr gl Thus the two key parameters are (i) the thickness of the solid slag film (d solid ) and (ii) the % crystalline phase devel-oped in the slag film.Longitudinal cracking in medium carbon (MC) steels re-sults from the 4% mismatch in the thermal shrinkage coef-2003ISIJ1482Fig.5.Arrhenius plots showing log 10viscosity (dPa s) versus reciprocal temperature (K Ϫ1) for (a) conventional flux and (b) high-viscosity flux for billet-casting.Fig.6.Schematic diagram showing the thermal resistances be-tween shell and mould.Fig.4.Measured versus calculated powder consumption values using (a) Wolf equation, (b) modified Wolf equation, (c)Ogibayashi equation, (d) Jenkins equation, (e) Modified Jenkins equation, (f) Tsutsumi equation, (g) Maeda equa-tion and (h) Kwon equation.Fig.7.Heat flux as function of liquidus and solidus temperatures of flux.23)Fig.8.Break temperature as a function of flux viscosity.Fig.9.Flow diagram for model to calculate required powder consumption, viscosity and break temperature.19) Problems and Defects4.1.Control of Metal FlowThe complexity in mould flux performance arises when we try to use the flux to combat problems other than those related to lubrication and heat transfer. One example is using the mould flux to deal with problems arising from turbulent metal flow (e.g.slag and gas entrapment and SEN erosion). One way of reducing these problems is to use a high-viscosity flux but this has the disadvantage that it re-duces powder consumption.©2003ISIJ10.Schematic drawing showing double roll flow.ϭ1393K–%MO: b T solϭ1515K–x(MO) where xϭmole3.The effect of different flux components on relevant properties. (a Tbrfraction and MOϭoxide and c refers to %F:)ISIJ1484There is a basic simplicity in the way fluxes work since there are only three properties determining the opti-mum lubrication and heat transfer for the given casting con-ditions, mould dimensions and steel grade, namely, the vis-cosity, break temperature and % crystallinity in the slag When the mould flux is used to combat other prob-slag entrapment due to turbulent metal flow) this frequently leads to the use of fluxes which do not provide optimal lubrication and heat transfer.Several new devices could help to reduce turbu-lence in the metal flow and if these were successfully im-plemented they would allow the mould flux to concentrate on providing optimum lubrication and horizontal heat trans-fer.AcknowledegementsThe authors would like to thank Dr. Adrian Normanton (Corus Teesside Technology Centre), Mr. Tim Mallaband (Metallurgica UK), Ms. Carolina Bezerra (Carboox, Brazil) and Dr. Shuji Takeuchi (Kawasaki Steel) for valuable dis-cussions and the provision of information.Nomenclaturedl:Thickness (m)f:Frequency of oscillation (Hz)f*:Fraction of powder containing slagQs:Powder consumption (kg1485。

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**A Steelpan Band Gig**In the vibrant realm of musical performances, a steelpan band gig emerges as a soul-stirring and electrifying experience that leaves an indelible mark on both the heart and the senses.The prelude to a steelpan band gig is an atmosphere crackling with energy and anticipation. The venue, alive with the buzz of eager conversations and the hum of excitement, awaits the moment when the first beats of the steelpan will resound. As the stage lights up and the musicians take their positions, a palpable sense of expectancy fills the air.The opening notes of the steelpan band explode like a burst of fireworks, igniting the atmosphere with a contagious rhythm. The initial moments are a visceral invitation to surrender to the pulsating beats and let the music carry you away.The middle of the gig is a symphony of syncopation and melody. The steelpans, each with its distinct tone and pitch, come together in a harmonious blend that is both intoxicating and mesmerizing. I recall a particular performance where the band played a medley of Caribbean classics. The way the pans interwove, creating a rich tapestry of sound that evoked images of sandy beaches and tropical breezes, was truly magical.One of the most captivating aspects of a steelpan band gig is the sheer exuberance and joy that emanates from the musicians and permeates the audience. The infectious energy is contagious, making it impossible to resist moving to the rhythm.Steelpan music has deep roots in Caribbean culture, carrying with it the spirit of celebration, community, and resilience.As Duke Ellington said, "Music is a powerful force. It can make you laugh, it can make you cry, it can make you dance, it can make you think." A steelpan band gig embodies this sentiment, as it has the power to evoke a wide range of emotions and unite people in a shared experience.In conclusion, a steelpan band gig is not just a musical event; it is a celebration of life, a testament to the power of rhythm, and a bridge that connects people from different walks of life through the universal language of music.It is a moment where time stands still, and the boundaries of worry and stress dissolve in the face of the infectious beats. The magic of a steelpan band gig lies in its ability to create memories that will be cherished for a lifetime.。

Mid-Infrared Fiber LasersMarkus Pollnau1and Stuart D.Jackson21Advanced Photonics Laboratory,Institute for Biomedical Imaging,Optics and Engineering,Swiss Federal Institute of Technology1015Lausanne,Switzerlandmarkus.pollnau@epfl.ch2Optical Fibre Technology Centre,Australian Photonics CRC.The University of Sydney206National Innovation Centre,Australian Technology ParkEveleigh NSW1430,Australias.jackson@.auAbstract.The current state of the art in mid-infraredfiber lasers is reviewed in this chapter.The relevantfiber-host materials such as silicates,fluorides,chalco-genides,and ceramics,thefiber,pump,and resonator geometries,and the spectro-scopic properties of rare-earth ions are sers at transitions ranging from1.9to4µm occurring in the rare-earth ions Tm3+,Ho3+,and Er3+and their population mechanisms are discussed on the basis of the fundamental spectroscopic properties of these ions.Continuous-wave,fundamental-mode power levels ranging from a few mW near4µm up to≈10W near2µm have been demonstrated in recent years.Power-scaling methods and their limitations,the possibilities to op-timize the population mechanisms and increase the efficiencies of these lasers,as well as the prospects of future mid-infraredfiber lasers in a number of rare-earth ions at transitions in the wavelength range beyond3µm and extending to5µm are described.1IntroductionSince the introduction of the double-cladfiber more than a decade ago and with the recent technological advances in thefields offiber fabrication and beam-shaped high-power diode lasers,the performance of diode-pumpedfiber lasers has steadily improved.Today,fiber lasers can compete with their cor-responding bulk crystalline systems in certain applications,especially when transverse-fundamental-mode,continuous-wave(CW)laser operation at out-put powers in the milliwatt to multiwatt range is required.The increased recent interest infiber lasers emitting at mid-infrared wavelengths between 2and3µm primarily relates to the high potential of these wavelengths for applications in laser microsurgery.Due to the high absorption of water in the spectral region at2.7–3.0µm,high-quality laser cutting or ablation has been demonstrated in biological tissues.In addition,laser wavelengths near 2µm could be suitable for tissue welding.A number of other potential laser applications in the mid-infrared spectral region,e.g.environmental trace-gas I.T.Sorokina,K.L.Vodopyanov(Eds.):Solid-State Mid-Infrared Laser Sources,Topics Appl.Phys.89,219–255(2003)c Springer-Verlag Berlin Heidelberg2003220Markus Pollnau and Stuart D.Jacksondetection,are currently becoming increasingly important.In all these appli-cations fiber lasers may find their niches.The high development costs of fabricating fibers with sufficiently low losses in the mid-infrared spectral region has impeded the necessary research efforts in the field of mid-infrared fiber lasers.The currently available fiber materials that are suitable as host materials for specific rare-earth-doped fiber lasers in the spectral region 2–5µm will be introduced in Sect.2.More than any other idea,the invention of the double-clad fiber geometry has accelerated the output-power scaling and hence the success of fiber lasers.The various aspects of the fiber,pump,and resonator geometries will be de-scribed in Sect.3.A significant number of spectroscopic investigations has led to a better understanding of the population mechanisms of rare-earth-doped laser systems.The fundamental spectroscopic properties of rare-earth ions in solid-state host materials will be reviewed in Sect.4.Equipped with this general information,the performance of the most important mid-infrared fiber laser transitions in the wavelength range 2–3µm can be understood in detail.Sect.5will be devoted to the Tm 3+fiber lasers at 1.9and 2.3µm,whereas the Ho 3+fiber lasers at 2.1and 2.9µm will be discussed in Sect.6.An impressive example of the variety of population mechanisms and operational regimes in a single system is the Er 3+2.7µm fiber laser transition that will be investigated in Sect.7.At wavelengths beyond 3µm,it becomes increasingly difficult to find suitable host materials for actively doped laser systems.This statement holds true for glass fibers in the same way as for crystalline materials.The prospects of future mid-infrared fiber lasers in this wavelength range will be discussed in Sect.8.Besides general introductions to the different topics of lasers [1,2]that include many aspects relevant also to mid-infrared fiber lasers,a comprehen-sive introduction to the field of rare-earth-doped fiber lasers can be found in [3].2Fiber MaterialsThe choice of the fiber material involves a number of considerations:the maximum phonon energy,the environmental durability,the draw ability,the rare-earth solubility,and the purity of the starting materials.The maximum phonon energy of the glass sets the overall infrared transparency range of the fiber and the multiphonon relaxation rates which influence the quantum efficiency.The multiphonon relaxation rates for the common fiber glasses as a function of the energy gap between energy levels are shown in Fig.1.The optical transparency range relates to both the size of the band gap and also the infrared absorption cut-off,hence to the vibrational frequency νof the anion–cation bonds of the glass.For an ordered structure,ν=(1/2π) k/M ,(1)Mid-Infrared Fiber Lasers221101010M u l t i p h o n o n R e l a x a t i o n R a t e (s -1)Energy Gap (cm )Fig.1.Calculated and measured multiphonon relaxation rates as a function of the energy gap between energy levels for glasses with different maximum phonon energies.(Data taken from [4,5])where M =m 1m 2/(m 1+m 2)is the reduced mass for two bodies m 1,m 2vibrating with an elastic restoring force k .While for disordered structures like glass,this is not an accurate expression,nevertheless,it does highlight the important contributions to the glass transparency.The relative cation–anion bond strength is intimated by the field strength Z /r 2,where Z is the valence state of the cation or anion and r is the ionic radius.Generally,glasses composed of large anions and cations with low field strengths display high transparency in the mid-infrared spectral region.The important physical properties of the popular glasses used for optical fibers are shown in Table 1.Table 1.Properties of popular fiber materialsFibermaterialMax.phonon energy (cm −1)Infrared transparency (µm)Propagation losses (λat minimum)(dB/km)Thermal conductivity (W/K m)Silica1100[4]<2.50.2(1.55µm) 1.38[6]ZBLAN550[7]<6.00.05(2.55µm)0.7–0.8[8]GLS 425[5]<8.00.5(3.50µm)0.43–0.5[9]2.1SilicatesThis glass is perhaps the most important material used for optical fiber pro-duction [3,10],however,the maximum phonon energy is high (≈1100cm −1)and has so far limited the emission wavelength of mid-infrared fiber lasers us-ing this material to ≈2.2µm [11].Silica is robust and involves the very effec-222Markus Pollnau and Stuart D.Jacksontive modified chemical vapor deposition(MCVD)technique forfiber fabrica-tion.Reducing the OH−content in the glass,which has two main absorption peaks in the range1.3–2.0µm[12],improves the near-to-mid-infrared utility. Rare-earth ions such as Nd3+and Er3+which have highfield strengths have low solubility in silicate glass which can lead to clustering and micro-scale phase separation.2.2FluoridesThe use offluoride glasses,especially the heavy-metalfluorides[13,14],as host materials for mid-infraredfiber lasers has found wide acceptance.The most common form of heavy-metalfluoride glass is thefluorozirconate(ZrF4) composition and the most widespreadfluoridefiber material is ZBLAN[15], a mixture of53mol.%ZrF4,20mol.%BaF2,4mol.%LaF3,3mol.%AlF3, and20mol.%NaF.Since it can be readily drawn into single-mode optical fiber[16]it is particularly important to mid-infraredfiber lasers[17].The large atomic weight of the zirconium atom combined with relatively weak bonding provides a maximum phonon energy for ZBLAN of≈550cm−1and allows for high infrared transparency up to≈6µm.Multiphonon relaxation, however,becomes significant for transitions at wavelengths longer than≈3µpared to silica,ZBLAN has a lower damage threshold and a lower level of inhomogeneous spectral-line broadening(Sect.4.1)because the rare-earth ion is placed in sites of a less perturbed network.The crystal-field strength is also comparatively weaker[18].An overview of the spectroscopic properties of rare-earth ions doped into ZBLAN has been given in[7].2.3ChalcogenidesChalcogenides are composed of the chalcogen elements S,Se and Te[19,20,21]. They are environmentally durable,have a low toxicity and have reasonably large glass forming regions.When the rare-earth ions are doped into these glasses[22],the radiative transition probabilities and,therefore,the absorp-tion and emission cross-sections are high as a result of the high refractive in-dex(≈2.6)of the glass and the high degree of covalency of the rare-earth ion with the surrounding medium.Maximum phonon energies of300–450cm−1 produce low rates of multiphonon relaxation,see Fig.1,and therefore high quantum efficiencies.The low thermal conductivity,see Table1,is however an important factor to be considered in the design of chalcogenide-based lasers. Of the large number of rare-earth chalcogenides studied for luminescent emis-sion,the most important glasses are the sulfide glasses GaLaS(GLS)[23]and GeGaS[24]because of the reasonably high rare-earth solubility.2.4CeramicsStudies into the use of ceramics as host materials for the rare earths have recently made a lot of progress[25].These ceramics are composed of nano-Mid-Infrared Fiber Lasers223 crystallites of materials such as Y3Al5O12(YAG)and can be produced ina simple and cost-efficient process at relatively low temperatures.This allows the fabrication of materials with very high melting points[26]that are difficultto grow by other techniques such as the Czochralski method[27].This class ofmaterials is also available infiber geometry[28].Ceramicfibers combine the characteristics of crystalline materials such as high absorption and emissioncross-sections,large thermal conductivity,and even the possibility of doping with transition-metal ions[28]with the convenience of guiding the pump andsignal light in afiber.Currently,the losses of thesefibers are comparativelyhigh,but further improvement can be expected.3Fiber,Pump,and Resonator GeometriesThe light oscillating in afiber-laser resonator can be either free running or deliberately modulated depending on whether CW or pulsed output,re-spectively,is desired.Consequently,a large number of techniques for pulsedoperation including Q-switching and mode locking offiber lasers have been explored.These techniques have been investigated intensively for the commonlaser transitions at1µm in Nd3+and Yb3+and at1.5µm in Er3+,and are usually described in combination with these lasers.The smallfiber size limitsthe peak power through the damage-threshold intensity(propagating powerper core area)and,hence,crystalline lasers in bulk geometries or optical parametric processes are often preferred when high-energy short pulses areneeded.This argument accounts especially for mid-infrared ZBLAN-basedfiber lasers,because thesefibers possess a lower damage threshold compared to silicafibers.The description of mid-infraredfiber lasers is,therefore,con-fined to CW operation and specific techniques for pulsed operation offiber lasers are not discussed in this chapter.In an analogous way to the optical excitation of bulk gain media,dopedopticalfibers can be either end pumped(core pumped)or side pumped (cladding pumped).The former method is less scalable since it relies onthe use of expensive high-beam-quality pump sources because core areas areusually<100µm2.On the other hand,the larger cladding area(>104µm2) allows for high-power diode-array pumping[29,30,31,32,33].The obvious sim-plicity of the core-pumping method negates further explanation and we will concentrate on the cladding-pumping technique:one of the most important developments infiber-laser technology.3.1Fiber Designs for Cladding PumpingIn the design offibers for cladding pumping,the core of thefiber is gener-ally made to guide a single-transverse LP01mode.The shape of the mul-timode pump cladding,see Fig.2,however,remains somewhatflexible and can be shaped with a number of considerations in mind.The pump cladding,224Markus Pollnau and Stuart D.Jackson (a)(b)(d)CorePump cladding Outer cladding Jacket Fig.2.Principal double-clad fiber geometries which include (a )circular shaped pump cladding with axially positioned core,(b )circular shaped pump cladding with off-axially positioned core,(c )rectangular shaped pump cladding and (d )D-shaped pump claddingwhich in turn is surrounded by a low-refractive-index transparent polymer or glass,provides a high numerical aperture (NA)of 0.3–0.55for the pump cladding.There are three main double-clad-fiber layouts:circular,circular with offset core,and rectangular as shown schematically in Fig.2.Maxi-mum pump-light absorption sees the core near the outer edge of the circular pump cladding [34]because a portion of the launched light is skew to the fiber axis and produces an inner caustic and never crosses the central re-gion of the pump cladding.Scrambling these skew rays by bending [35]or by using a graded and slightly elliptical pump cladding [36]increases the pump-absorption efficiency as does spatially varying refractive-index fluctuations in inhomogeneous pump claddings [37].Inner caustics can be avoided by rectilinearly shaping the pump cladding [38]which has the ancillary advantage of matching the shape of diode-array output.The overall absorption coefficient of the fiber is reduced by the ratio of the core area to the area of the pump cladding [34].The propagation losses for the rectangular-shaped pump cladding are higher and the effective numerical aperture lower as compared to the circular shape [39];however,in certain cases higher dopant concentrations can provide shorter fiber lengths that also lead to reduced nonlinear effects.A D-shaped or trun-cated circular pump cladding [40],see Fig.2d,is also effective while be-ing easier to make than rectangular preforms.The circular-multimode pump cladding may also have the gain medium distributed in a ring around the edge of the pump cladding either discretely or continuously in multi-core [41]and M-profile [42]arrangements,respectively.The effective absorption coef-ficient is now further increased while maintaining high-beam-quality output.A large-mode-area core [43]can also increase the effective absorption coeffi-cient of the fiber.Recently,double-clad pump schemes have been demonstrated also with holey fibers [44].These structures offer the additional advantage of single-mode guiding over a broad spectral range [45].Mid-Infrared Fiber Lasers 2253.2Fiber-Laser ResonatorsTypical free-running fiber-laser resonators are shown schematically in Fig.3.In the simplest resonator,see Fig.3a,the pump light passes through a dichroic mirror that is highly reflective for the oscillating laser light.Fresnel reflection at the cleaved output end facet of the fiber can provide sufficient feedback for laser oscillation;however,with an output-coupler mirror –and pump retro-reflector –placed at the output end of the fiber the optical efficiency can be maximized.In an alternative arrangement,the pump light can be launched into the output end of the fiber,see Fig.3b.A dichroic mirror oriented at 45◦to the fiber axis extracts the laser output and a broadband highly reflecting mirror is placed at the rear fiber end.To scale the output power,each end of the fiber can be pumped,see Fig.3c.Periodic V-grooves [46]or prism coupling [47]along the fiber to distribute the pump access allow one to further scale the output power and are useful for pumping fiber ring resonators.Spectrally combining the output from a number of separate fiber lasers is also a promising power-scaling technique [48,49,50].The highest reported fiber-laser output powers of 110W in a singly Yb 3+-doped fiber [51]and 150W in a Nd 3+,Yb 3+-codoped fiber [52]have been obtained using arrangements as shown schematically in Fig.3c.Bragg gratings can substitute the fiber-butted mirror if spectrally well-defined output is required.PumpPump Pump Pump Output Output OutputMM M MMFiberFiberFiber(a)(b)(c)Fig.3.Schematic diagram of resonators used for free-running fiber lasers with (a )a single-end co-propagating pump,(b )a single-end counter-propagating pump and (c )dual end pumps.M represents the mirror226Markus Pollnau and Stuart D.Jackson3.3Thermal IssuesAs higher pump powers become available from laser-diode systems,it is gen-erally recognized that thermal and thermo-optical issues set limitations to the power scalability of end-pumped bulk-laser systems.Owing to the unfavor-able temperature dependence of thermal and thermo-optical parameters[53], the large heat load in the crystal leads,firstly,to a significant temperature increase in the rod,secondly,to strong thermal lensing with pronounced spherical aberrations,and ultimately,to rod fracture in a high-average-power end-pumped system.Due to its geometry,thefiber provides potentially high pump-and signal-beam intensities without the drawbacks of significant thermal and thermo-optical effects.Its large surface-area-to-volume ratio means that the heat generated from multiphonon relaxation in the core is dissipated effectively by radiation and convection from the outer surface of thefiber.This is es-pecially true for single-clad,core-pumped single-modefibers where this ratio is highest[54].Double-cladfibers have a relatively smaller surface-area-to-volume ratio and thermal issues need to be taken into account[6,55,56]. Thermal management will be required when very high output powers are desired.In particular,for high-power mid-infrared operation,thermal man-agement may be very important because of the decreased quantum efficiency and the consequently higher amount of heat dissipation.4Spectroscopic and Laser Propertiesof Rare-Earth IonsThe structure of a glass is less well defined as compared to a crystalline mate-rial.The local variation of the chemical environment of active ions in a glass has a number of consequences.Most important,the active ions may undergo chemical reactions during the fabrication process and be incorporated in the host in several oxidation states with different spectroscopic properties.Oxi-dation states other than the desired one may act as impurities that introduce undesired optical effects such as parasitic pump absorption,the reabsorption of oscillating laser light,the lifetime quenching of the laser ion,and the trap-ping of the excitation energy.A stable oxidation state of the optically active ion is thus highly desirable.The necessity of a stable oxidation state excludes a number of transition-metal ions from the list of suitable dopants in glass environments.This is one of the possible reasons why examples of transition-metal-ion-doped lasers in glass hosts are rare.On the other hand,most of the rare-earth ions prefer to stabilize in the trivalent oxidation state and are, therefore,suitable candidates as glass andfiber dopants.This chapter will, therefore,concentrate on the rare-earth ions as active dopants offiber lasers.Mid-Infrared Fiber Lasers227 4.1Spectra of Rare-Earth Ions in GlassesThe optical transitions of lanthanide(rare-earth)ions in the visible and in-frared spectral region occur within the4f subshell.This subshell is shielded by the outer5s and5p subshells and the influence of the host material isrelatively small compared to,e.g.,the3d transitions in transition-metal ions.The electronic structure of trivalent rare-earth ions derives from the perturba-tion of the4f energy level in the central-field approximation by the noncen-trosymmetric electron–electron interaction,the spin–orbit interaction,andthe crystal-field splitting(Stark effect);see the example of the energy-level scheme of Er3+in Fig.4.The spin–orbit multiplets are commonly denotedby their2S+1L J terms in Russell–Saunders coupling,although the4f elec-trons of lanthanide ions exhibit intermediate coupling and the total angularmomenta J of the spin–orbit multiplets are linear combinations of the totalorbital angular momenta L and total spins S.Single crystal-field(Stark)tran-sitions between two spin–orbit multiplets cannot be distinguished in glasses at ambient temperature,because inhomogeneous spectral-line broadening oc-curs due to the local variation of the ligand electricfield.Also homogeneous (lifetime)broadening mechanisms are relevant in a number of glasses.This spectral-line broadening makes glasses the preferred hosts when broadband,Fig.4.Energy-level scheme of triva-lent erbium indicating the splitting ofthe4f11configuration in the central-field approximation by the noncen-trosymmetric electron–electron inter-action,the spin–orbit interaction,andthe Stark splitting by the local elec-tricfield of the host material(indi-cated only for selected spin–orbit mul-tiplets)228Markus Pollnau and Stuart D.Jacksoncontinuous tunability of lasers is desired.On the other hand,the spectral-line broadening leads to lower absorption and emission cross-sections for the same transition in glasses compared to single-crystalline hosts.The reducedcross-sections lead to generally higher pump threshold of laser transitions inglasses,a fact that is compensated infiber geometry because a high pump confinement is achieved over the wholefiber length.4.2Intraionic ProcessesGenerally,the probability of an allowed electric-dipole transition is seven or-ders of magnitude larger than that of an allowed magnetic-dipole transition.Since electric-dipole transitions within the4f subshell are parity forbidden,the intensities of radiative transitions in rare-earth ions are weak and the radiative lifetimes of the emitting states are long,typically in the ms range.Mixing of the4f states with higher-lying(typically5d)electronic states of opposite parity at ion sites without inversion symmetry,however,means thatelectric-dipole transitions become partially allowed and are usually the dom-inant transitions between4f electronic states.The oscillator strengths f and integrated absorption and emission cross-sectionsσof these spin–orbit mul-tiplet-to-multiplet transitions can be calculated with the help of the semi-empirical Judd–Ofelt theory[57,58].If the degree of inhomogeneous spectral-line broadening is relatively small and the absorption and emission spectraremain structured,as is the case for ZBLAN,the cross-sectionsσ(λ)at in-dividual wavelengths that are relevant to pump absorption and stimulatedemission of narrow laser lines must be determined experimentally.Besides ground-state absorption(GSA),excited-state absorption(ESA) of pump photons,see Fig.5a,can play a significant role infiber lasers,specif-ically in the case of high-intensity core pumping.An experimental examplewill be given later in Sect.7.1.Since the absorption increases exponentially with the absorption coefficientα(λP)=Nσ(λP),ESA becomes relevant forthe population dynamics of a laser when(a)the ESA and GSA cross-sectionsσ(λP)are comparable at the pump wavelengthλP and(b)the population density N of the excited state in which the second pump-absorption steporiginates becomes a significant fraction of the density of ions in the ground state,i.e.,a large degree of ground-state bleaching must be present for ESA to play a significant role.A radiative transition from an excited state i to a lower-lying state j is characterized by the radiative rate constant A ij.If the decay occurs to sev-eral lower-lying states,the overall radiative rate constant A i is the sum of all individual rate constants.The branching ratio of each radiative transition is defined asβij=A ij/A i.Radiative decay of excited states is in competition with nonradiative decay by interaction with vibrations of the host material, called multiphonon relaxation.The rate constant of a multiphonon relaxation process decreases exponentially with the energy gap to the next lower-lying state and with the order of the process,i.e.,the number of phonons required(a)Ion (b)12Donor Ion Acceptor IonAcceptor Ion (c)Sensitizing Ion ALaser Ion B(d)1Laser Ion AQuenching Ion B (e)Donor Ion Acceptor Ion(f)1Donor Ion Acceptor Ion Fig.5.Intra-and interionic processes infiber lasers:(a)excited-state absorption (ESA);(b)energy migration;(c)sensitization and(d)quenching of a laser ion by an ion of a different type;(e)cross-relaxation and(f)energy-transfer upconversionto bridge the energy gap[59,60].This fact is illustrated in Fig.1for differ-ent glasses.The rate constant of multiphonon relaxation increases with host temperature.The measurable luminescence lifetimeτi of an excited state i is the inverse of the sum of the overall radiative rate constant A i and the rate constant of multiphonon relaxation,W i.The radiative quantum efficiency is defined asη=A i/(A i+W i).The influence of multiphonon relaxations is stronger in oxides as com-pared tofluorides because of the smaller atomic mass m2of the anion and the larger elastic restoring force k,see(1),due to stronger covalent bonds in oxides[3],both resulting in larger maximum phonon energies in oxides.A brief example:The luminescence lifetime of the4I11/2upper laser level of the erbium3µm laser(Sect.7)is partly quenched by multiphonon relaxation. Typically,nonradiative decay becomes dominant iffive or less phonons are required to bridge the energy gap.With an energy gap between the4I11/2and the next lower lying4I13/2levels of≈3400–3500cm−1,radiative decay pre-vails for phonon energies below≈600cm−1,roughly the maximum phonon energy of ZBLAN,see Table1.Fluorides are,therefore,preferred over oxides as host materials for most of the mid-infrared laser transitions.Like absorption,the strength of a stimulated-emission process is char-acterized by the emission cross-sectionσ(λL)of the laser transition.From a simple analysis,for one resonator round-trip of oscillating laser photons, the productτσ(λL)withτthe luminescence lifetime of the upper laser level, is identified as a“figure of merit”for a possible laser transition.The larger this product,the lower is the expected pump threshold of the laser transition. This“figure of merit”,however,does not take into account the numerous par-asitic effects that can occur in the population dynamics of a laser system,such as pump ESA,reabsorption of laser photons,and energy-transfer processes. It is often these parasitic processes that lead to surprising performance char-acteristics–as likely in the negative as in the positive sense–and make the interpretation of rare-earth-doped solid-state lasers challenging.Examples will be discussed in Sects.5–7.4.3Interionic ProcessesIn addition to intraionic excitation and decay mechanisms,radiative en-ergy transfer due to reabsorption of emitted photons by other active ions in the sample and nonradiative energy-transfer processes due to multipole–multipole or exchange interactions between neighboring active ions can occur. Radiative energy transfer leads to an increase in the luminescence lifetime. Among the nonradiative energy-transfer processes,most common is the elec-tric dipole–dipole interaction,which can occur as a direct[61]or phonon-assisted[62]energy transfer.A direct energy transfer requires spectral reso-nance between the involved emission and absorption transitions whereas an indirect transfer can also be nonresonant,i.e.,an existing energy gap between the emission and absorption transitions involved in the transfer is bridged by。