discussion on the e57355usion el as am sour is shortly given starting fr om ide al ases to al el ls homo geneity pr oblems short eview gar ding the thermo dynamic appr ach to the MBE is ointe out cusing on the ossibility that despite the fact that M ID: 30225 Download Pdf

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discussion on the e57355usion el as am sour is shortly given starting fr om ide al ases to al el ls homo geneity pr oblems short eview gar ding the thermo dynamic appr ach to the MBE is ointe out cusing on the ossibility that despite the fact that M

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Basics of Molecular Beam Epitaxy (MBE) ernando Rinaldi brief intr duction to the MBE te chnique is pr esente with main attention to the el- emental sour MBE. discussion on the eusion el as am sour is shortly given starting fr om ide al ases to al el ls homo geneity pr oblems. short eview gar ding the thermo dynamic appr ach to the MBE is ointe out. cusing on the ossibility that, despite the fact that MBE pr esses cur under str ong none quilibrium onditions, for the III/V elements, thermo dynamic appr ach an use on the asis of quations for mass action in ombination with

the quations describing the onservation of the mass of the inter acting elements. 1. In tro duction Molecular eam epitaxy is tec hnique for epitaxial gro wth via the in teraction of one or sev eral molecular or atomic eams that ccurs on surface of heated crystalline substrate. In Fig. sc heme of ypical MBE system is sho wn. The solid sources materials are placed in ev ap oration cells to pro vide an angular distribution of atoms or molecules in eam. The substrate is heated to the necessary temp erature and, when needed, con tin uously rotated to impro the gro wth homogeneit According to Fig.

2, the molecular eam condition that the mean free path of the particles should larger than the geometrical size of the ham er is easily fullled if the total pressure do es not exceed 10 orr. Also, the condition for gro wing sucien tly clean epila er ust satised, e.g. requiring for the monola er dep osition times of the eams and the bac kground residual ap or res the relation res 10 or ypical gallium ux of 10 19 atoms and for gro wth rate in the order of m/h, the conclusion is that res 10 11 orr. Considering that the stic king co ecien of gallium on GaAs

atoms in normal op erating conditions is appro ximately unit and that the stic king co ecien of most of the ypical residual gas sp ecies is uc less than 1, the condition ab results to not so strict, nev ertheless ultra high acuum (UHV) is required. Th us, UHV is the essen tial en vironmen for MBE. Therefore, the rate of gas ev olution from the materials in the ham er has to as lo as ossible. So yrolytic oron nitride (PBN) is hosen for the crucibles whic giv es lo rate of gas ev olution and hemical stabilit up to 1400 C, molyb den um and tan talum are widely used for the sh utters, the

heaters and other comp onen ts, and only ultrapure materials are used as source. reac UHV, bak eout of the whole ham er at appro ximately 200 for 24 is required an

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Ann ual Rep ort 2002, Opto electronics Departmen t, Univ ersit of Ulm time after ha ving en ted the system for main tenance. cry ogenic screening around the substrate minimizes spurious uxes of atoms and molecules from the alls of the ham er. Despite this big tec hnological problems, MBE systems ermit the con trol of comp osition Fig. 1: ypical MBE system. 10 −10 10 −8 10 −6 10 −4 10

−2 10 Pressure (Torr) 10 −2 10 10 10 10 10 Mean free path (cm) Fig. 2: Mean free path for nitrogen molecules at 300K. and doping of the gro wing structure at monola er lev el hanging the nature of the incoming eam just op ening and closing mec hanical sh utters. The op eration time of sh utter of appro ximately 0.1 is normally uc shorter than the time needed to gro one monola er (t ypically 1{5 s). Careful ariation of the temp eratures of the cells via PID con trollers ermits the con trol of the in tensit of the ux of ev ery comp onen or dopan of etter than %. The UHV en

vironmen of the system is also ideal for man in- situ haracterization to ols, lik the RHEED (reection high energy electron diraction). The oscillation of the RHEED signal exactly corresp onds to the time needed to gro monola er and the diraction pattern on the RHEED windo giv es direct indication er the state of the surface as can seen in Fig. 3. time Fig. 3: RHEED oscillations.

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Basics of MBE 2. Eusion Cells The eusion cells used in MBE systems exploit the ev ap oration pro cess of condensed materials as molecular ux source in

acuum. The understanding of the prop erties of real eusion cells is complicated and not straigh tforw ard, so easier mo dels are needed and just the main complications are subsequen tly added. In closed enclosure, for pure substances, an equilibrium is estabilished et een the gas and the condensed phase. Suc systems ha only one degree of freedom that means that the pressure eq is function of the temp erature and can appro ximately expressed the Clap eyron equation [1 eq exp (1) Where in (1) is the ev ap oration en thalp and the Boltzmann constan t. Under this equilibrium condition,

observ that when the eq is ery lo w, it is ossible to treat the incoming and the outcoming ux indep enden tly close lo ok to the uxes of particles ha ving mass on the condensed phase surface sho ws that the maxim um alue for the ev ap orated ux is eq (2) This assumes that eac molecule from the gas phase is alw ys trapp ed the surface and an equal opp osite ux of material ust lea the condensed phase to main tain the equilibrium pressure. Considering no that the impinging eam is partially reected and only fraction is accommo date on the surface, the

complete expression for the ux lea ving the surface can easily found as (3) The factor is dep enden on the microscopic status of the surface and is strongly un- predictable and ecause of (3) the ux of material. The Kn udsen ev ap orating metho ercome this problem pro viding molecular eam that is indep enden of An ideal Kn udsen cell is comp osed of large enclosure ere the condensed material is in thermo- dynamic equilibrium with the gas phase and of an orice so small that the equilibrium pressure eq is not erturb ed. The orice geometry has to fulll

additional conditions, one for the diameter that fullls at eq and one for its all thic kness assumed to anishingly thin. Under these conditions, the orice is surface with an ev ap oran pressure eq and has not the abilit to reect an of the incoming molecules resulting in and the um er of molecules er time unit of the created eam is where is the orice area. The ideal Kn udsen cell exhibits an angular distribution of the ev ap orated particles that follo ws cosine la w, where the angle is referred to the normal to cos (4)

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Ann ual Rep ort 2002, Opto

electronics Departmen t, Univ ersit of Ulm so that the ux at distances uc bigger than the orice dimensions is prop ortional to cos Using Clausing’s mo del [2 for the conductance of molecular o in cylindrical tub e, Da yton has studied the deviation from idealit giv en when L=d is not longer 0. In this calculations mo del is necessary to describ the in teraction of the molecules with the orice alls. Random reection is the simplest approac h, but also more complicated ones are ossible in olving also temp orary adsorption and surface diusion [3 ].

Ho ev er, an estimation of for the surface of the condensed material is not required. When L=d increases, the eam is more fo cused on the normal direction and for L=d the deviation from the cosine la is relev an t. These mo dels are imp ortan to ols to measure eq and so thermo dynamic quan tities related with (1). When it is not ossible to consider the enclosure as innitely large and when it is therefore imp ortan to consider the inuences of the main dy of the cell, the alue of the co ecien is needed [4]. This is also the case of cylindrical and conical cells, that are

widely used in MBE systems, there is no thermo dynamic equilibrium et een condensed and gas phase and therefore the alue of is necessary to calculate the emerging ux. Nev ertheless, assuming for homogeneous distribution on the condensed phase material surface, it is ossible to estimate the shap of the outcoming ap our eam using all the mo delling discussed efore. Man ariables Fig. 4: Example of the geometrical cong- uration for conical eusion cell. 0.5 GaAs(s) Ga(l) GaAs(s) GaAs(s) As(s) liquid Fig. 5: Simplied phase diagram sec- tion) for GaAs. (s) is the solid

and (l) is liquid phase. gas phase is alw ys presen t. are in olv ed in this problem, lik sho wn in Fig. 4. or example, ery often the source material is in liquid form (Ga, Al, In) and so an additional angle is required to set up the geometry of the system. Some materials et the crucible surface (e.g. alumin um in PBN crucibles), so other ariables are needed to sp ecify the osition of the ev ap orating surface. complex ork of optimization is therefore necessary in relation to the fact that in MBE system man cells ust op erate and for eac one suitable geometrical conguration cell

substrate ust prop erly hosen. Con trol and homogeneit of the cells temp erature are crucial, ecause of the strong dep endence of the ux on temp erature. W-Re thermo couples are used for the hemical stabilit at high temp eratures and for the ery lo outgassing rate. an talum heater elemen ts and radiativ shields are hosen for the excellen refractory prop erties. These elemen ts are often self-supp orting prev en ting the use of material that do es not ha suc lo rate of gas ev olution. Great care is

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Basics of MBE also needed to decrease the temp erature dierence

et een heater and crucible. This is necessary to oid ery high temp erature outgassing from tan talum, and to reduce the dissipated heat whic causes ossible uncon trolled outgassing from other parts of the acuum ham er. 3. Thermo dynamic Approac In the past there as lot of con tro ersy concerning the ossibilit of applying thermo dy- namics to the gro wth pro cesses in MBE. In the 1980s, MBE as dev eloping exp erimen tally ery successfully and most of the problems particularly regarding AlGaAs and InGaAlAs materials ere solv ed empirically In recen ears, the need for MBE gro with new er

materials rev ealed the imp ortance of closer theoretical mo deling of the gro wth pro cesses. In the case of MBE, it seems that the system cannot describ ed thermo dynamic represen tation, ecause the dieren parts lik sources, substrate, and alls are at dier- en temp eratures. Ho ev er, it is ossible to assume that the temp erature of the system is the temp erature of the substrate if the thermalization time is uc shorter than the time required to gro monola er. So consider an equilibrium state in whic the par- tial pressures are the ones relativ to uxes of atoms or

molecules lea ving the substrates surface at its temp erature. The alidit of this assumption is conrmed facts. First that the uxes of atoms or molecules lea ving the substrate ha its temp erature irresp ectiv of the temp erature of uxes arriving at the surface. Second, the nature of the arsenic molecules, e.g. in the GaAs system, lea ving the substrate is indep enden of the nature of the arsenic molecules reac hing the surface. In this case, ha to consider the follo wing reaction with the asso ciated mass action equation [5 2As (g) As (g) and As As 98 10 exp 35 (5)

where the pressures are measured in atmospheres and in eV. The dimeric fraction of arsenic molecules lea ving the substrate exactly follo ws the temp erature eha viour pre- dicted (5) [6 ]. Starting these assumptions it is ossible to mo del the basic eha vior of the I/V binary comp ounds in MBE conditions. or binary comp ound, phase diagram lik the one sk etc hed in Fig. ust considered. In the region lab eled with GaAs(s) is presen in equilibrium with Ga(g) and As (g) and As (g)(with just small deviation, exaggerated in the gure, from the Ga As stoic hiometry ossible via oin defect,

but alw ys uc smaller than 10 ev en at high temp eratures). Using the Gibbs Phase Rule [7] that relates the um er of comp onen ts and the um er of dieren phases to the um er of degrees of freedom it is easy to recognize that in the region of the phase diagram 2. So temp erature and pressure are indep enden t. In the region 2, liquid gallium is presen and therefore as phases are presen t. Hence function exists. In the region 1, the reactions et een the comp onen ts are GaAs(s) Ga(g) As (g) and 2As (g) As (g) (6)

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Ann ual Rep ort 2002, Opto electronics Departmen t, Univ

ersit of Ulm The mass action equation is Ga As GaAs 73 10 11 exp 72 (7) Under normal MBE gro wth conditions, when 450 C, it is ossible to neglect the As con tribution to the total pressure. Therefore the total pressure is giv en Ga As GaAs As As (8) The gallium pressure is maxim um on the left side of the diagram, where it appro ximately corresp onds to the gallium pressure on pure liquid gallium, mo ving to the righ t, ecause of (7), this partial pressure will decrease while the arsenic pressure is increasing. or some range in temp erature, the pressure sho ws minim um for suitable stoic

hiometry of the solid phase. This is the condition that has to applied to nd the ux in free sublimation, i.e. sublimation in acuum. The reason for the minim um condition is ery general [8]. In comp ound the pressure is the sum of the pressures of its comp onen ts. If the partial pressure of the comp onen is bigger than the one of the comp onen A, the comp osition of the condensed phase will enric hed with A, mo ving the system to lo er partial pressure. If minim um for certain exists, this will asymptotically reac hed. In this oin the sublimation is congruen t. In our case the

equation for minim um of the pressure is dp dp As dp dp Ga (9) Solving this with the (8) will bring the result Ga As (2 GaAs (10) This corresp onds to congruen sublimation of GaAs. When the temp erature increases er certain temp erature max the pressure of the more olatile comp onen t, in this case arsenic, increases faster and there will no minim um in the region 1. Under this condition, liquid gallium phase is created. The temp erature max is called \temp erature of maxim um sublimation". max is calculated imp osing Ga from (10) equal to the alue of the gallium pressure er the liquid gallium

Ga 88 10 exp 74 (11) The alue of max is appro ximately 630 C. The free sublimation rate is so giv en Ga Ga (12) where Ga is dened (9) and is the olume ccupied pair of gallium and arsenic atoms in GaAs. When an external As ux is supplied, so that ext As As for the (7) will obtain reduced Ga ev ap orated ux red Ga GaAs ext As (13)

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Basics of MBE Thereb suppression of the sublimation ccurs. The rate of ev ap oration in ersely pro- ortional to the square ro ot of the arsenic ux to the substrate is exp erimen tally observ ed in MBE systems. or an

external As ux in (13), ext As ust exc hanged with ext As It is imp ortan to emphasize that in the previous calculations ha used the fact that the stic king co ecien of gallium on GaAs is 1, ecause the outcoming ux, and so the related pressure, is alw ys giv en (3). When an external gallium ux is added the gro wth rate can expressed Ga ext Ga Ga (14) Just considering that the arsenic ux is alw ys uc bigger than the one of gallium, neglecting the fraction of arsenic that will tak part in the gro wth pro cess, and considering alw ys the condition As As for

the gro wth rate get ext Ga GaAs ext As (15) Also the temp erature dep endence implicit in (15) as exp erimen tally found [9 ]. So for the ypical ext As with alue of 10 10 orr whic is used, the gro wth rate is mainly con trolled the gallium ux. solid arsenic phase is nev er formed in MBE system ecause the ypical arsenic pressure ould for this temp erature, 500 C, in orr range. The excess arsenic ux xes oin in the phase diagram and so determines the yp and concen tration of oin defects. This considerations are alid for man I/V comp ounds [10 ]. Comp ounds max C) AlAs 63

10 10 exp 39 902 GaAs 73 10 11 exp 72 630 GaP 26 10 11 exp 71 571 InAs 76 10 11 exp 34 508 InP 34 10 11 exp 02 268 or eac comp ound equations lik (11) can used to calculate the max Extremely in ter- esting is an erview on the ternary comp ounds. Al Ga As, Ga In As, Al In As ere successfully analyzed. The problem in ternal comp ound is the estimation of the activities co ecien that tak the nonideal nature of the allo in to accoun t. Al Ga As is sp ecial case ha ving GaAs AlAs 1. In other cases, e.g. GaAs can write the follo wing equations Ga As GaAs GaAs and Ga GaP GaP (1 (16)

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Ann ual Rep ort 2002, Opto electronics Departmen t, Univ ersit of Ulm together with the (5) and another mass action equation for the reaction 2P 2(g) 4(g) Considering that again the dimers are the dominating sp ecies, for 500 C, and ne- glecting the amoun of group-V elemen ts that tak part in the gro wth pro cess can nd for the resulting nal comp osition of GaAs GaP GaP GaAs GaAs ext ext As (17) Ev en neglecting the inuence of the activit co ecien ts in (17), go qualitativ agree- men can found with the exp erimen tal data [11 ]. References [1] R.A. Sw

alin, Thermo dynamics of solids New ork: John Wiley Sons, 1972. [2] J.F. O’Hanlon, User’s Guide to acuum chnolo gy New ork: John Wiley Sons, 1989. [3] W.L. Win terb ottom and J.P Hirth, \Diusional con tribution to the total o from Kn udsen cell," J. Chem. Phys. ol. 37, no. 4, pp. 784{793, 1962. [4] K. Motzfeldt, \The thermal decomp osition of so dium carb onate the eusion metho d," J. Phys. Chem. ol. 59, pp. 139{147, 1955. [5] D.T.J. Hurle, \Revised calculation of oin defect equilibria and non-stoic hiometry in gallium arsenide," J. Phys. Chem. Solids ol. 40, pp.

613{626, 1979. [6] C.T. xon, J.A. Harv ey and B.A. Jo yce, \The ev ap oration of GaAs under equilib- rium and non-equilibrium condition using mo dulated eam tec hnique," J. Phys. Chem. Solids ol. 34, no. 10, pp. 1693{1701, 1973. [7] H.A.J. Oonk, Phase The ory ol. 3. Amsterdam, Netherlands: Elsevier Scien tic Publishing Compan 1981. [8] F.A. Kr oger, The Chemistry of Imp erfe ct Crystals ol. 1. Amsterdam, Netherlands: North Holland Publishing Compan 1973. [9] J.M. an Ho and .I. Cohen, \Mass action con trol of AlGaAs and GaAs gro wth in molecular eam epitaxy ," Appl. Phys. ett. ol. 47,

no. 7, pp. 726{728, 1985. [10] .S. Kop’ev and N.N. Leden tso v, \Molecular eam epitaxy of heterostructures made of I/V comp ounds," Sov. Phys. Semic ond. ol. 22, no. 10, pp. 1093{1101, 1988. [11] S. Gonda and Y. Matsushima, \Molecular eam epitaxy of GaP and GaAsP," Jap. J. Appl. Phys. ol. 15, no. 11, pp. 2093{2101, 1976.

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