Real-time optical characterization of GaP heterostructures by p-polarized reflectance

Transcription

1 Thin Soli Films Real-time optical characterization of GaP heterostructures by p-polarize reflectance N. Dietz a,, K. Ito b a Department of Physics, North Carolina State Uniersity, Raleigh, NC 27695, USA b Center for Research in Scientific Computation, North Carolina State Uniersity, Raleigh, NC 27695, USA Abstract The stringent tolerances in the engineering of avance optoelectronic integrate circuits with respect to control thickness an composition of ultra-thin layers require the evelopment of monitoring an control techniques that follow the eposition process with sub-monolayer resolution. These emans le to the evelopment of surface-sensitive real-time optical sensors that are able to move the control point close to the point where the growth occurs, which in a chemical beam epitaxy process is the surface reaction layer, built up of physisorbe an chemisorbe precursor fragments between the ambient an film interface. In this contribution, we explore the application of p-polarize reflectance spectroscopy Ž PRS. in the context of real-time monitoring an control of pulse chemical beam epitaxy Ž PCBE. uring low temperature growth of epitaxial GaP heterostructures on SiŽ 00. substrates by PCBE. The effect of perioic alterations in composition an thickness of a surface reaction layer Ž SRL. is monitore by PRS as a perioic moulate reflectance amplitue, enote as fine structure. Using a reuce orer kinetic moel we emonstrate the linkage of the PRS response towars surface reaction chemistry, film growth rate, an film properties. Mathematical control algorithms are introuce that link the PR signals to the growth process control parameters. 998 Elsevier Science S.A. Keywors: P-polarize reflectance spectroscopy; Pulse chemical beam epitaxy; Reuce orer kinetic moel. Introuction Research concerning the integration of polar compoun semiconuctors on non-polar Si substrates is motivate by several ecaes of technological applications an is becoming even more important with regar to the avance state of silicon technology. However, the progress in unerstaning an controlling thin film growth has been very slow, consiering how little is known about chemical reaction pathways an reaction kinetics parameters uring the ecomposition process of the metal-organic Ž MO. precursors. To gain a better unerstaning of the eposition process an the surface chemistry involve, non- Corresponing author. Tel.: ; fax: ; ietz@mte.nscu.eu intrusive real-time optical process techniques have been evelope uring the last ecae, which focus on the monitoring of either bulk-film properties 4 or surface processes by reflection high energy electron iffraction Ž RHEED. or reflectance ifference spectroscopy Ž RDS. 5. For real-time close-loop eposition control, a prouct-riven virtual substrate approach was recently introuce 6. For monitoring both the bulk an surface, we have recently ae p-polarize reflectance spectroscopy Ž PRS. an emonstrate its capability uring pulse chemical beam epitaxy Ž PCBE. of III-V heteroepitaxial growth. The emonstrate high sensitivity of PRS towars surface reaction processes in the context of real-time monitoring of PCBE has opene new possibilities for characterization an control of thin film eposition processes 73. So far, the PR response uring heteroepitaxial GaPGa In P growth on Si uner x x $ Elsevier Science S.A. All rights reserve PII S Ž

2 ( ) N. Dietz, K. Ito Thin Soli Films PCBE conitions has been moele uner the simplifie assumption of a surface reaction layer Ž SRL. perioically moulate in thickness. The moulation in composition an, with it, the moulation in the ielectric function of the SRL have been neglecte. Control of a growth process using the optical signature from the SRL that fees the unerlying growth requires etaile instantaneous simulation an preiction of the surface chemistry an its link to the optical properties of the outermost layer in a multilayer stack. In this contribution, we introuce a reuce orer kinetic moel to escribe the growth process with a mathematically reuce number of surface reaction equations using heteroepitaxial GaP growth as an example. 2. Surface chemistry In the case of GaP heteroepitaxy on Si employing triethylgallium, GaŽ C H an tertiarybutylphosphine TBP, Ž C H. PH as source vapors, efficient fragmentation an sufficient retention of fragments on the surface occurs within a limite process winow in the temperature range 533 KT 683 K for SiŽ The kinetics of pyrolysis for the growth of GaP on SiŽ 00. utilizing triethylgallium an tertiary-butylphosphine as source vapors has been iscusse in etail elsewhere 3,5. Its progression can be summarize in three consecutive steps: GaŽ C H. GaŽ C H. C H, Ž GaŽ C H. GaC H C H, Ž GaC H Ga C H, where the vertical ashes an superscript ots enote lone electron pairs an single valence electrons, respectively. Also, the thermal ecomposition of TBP has been stuie in etail 6,7 an procees through a series of consecutive reactions, that can be summarize by 3 Ž C H. PH PH C H, Ž C H Ž C H. PH Ž C H. PH C H Ž an C H PH PHC H. Ž The vertical ashes an superscript ots enote lone electron pairs an single valence electrons, respectively. For GaP growth on SiŽ 00., we have shown that the ecomposition of TBP is fast an elimination of ethyl raicals from the fragments represents the rate limiting step 8. Depening on the elay between the an TBP source vapor pulses, carry-over of fragments from one precursor pulse cycle to the next may occur, which establishes in steay-state a surface reaction layer Ž SRL., consisting of a mixture of reactants an proucts of the chemical reactions that rive the epitaxial growth process. In a realistic moel, the SRL represents a multicomponent mixe phase with a variety of raical reactions ae to the above reactions Ž. Ž The thickness an composition of the SRL epens on the relative heights an withs of the employe an TBP source vapor pulses an their repetition rate. We note that some of the intermeiate fragments of the source vapor molecules in the SRL that fee III-V CBE, such as H-V-H, V-H, R-III-R, III-R carry a permanent ipole moment. Thus ipole-ipole interactions are likely to contribute to the stabilization of the SRL. In view of intermolecular interactions, eviations of the SRL from ieal behavior can be expecte. The objective of this paper is to relate the measure PRS signal to the activities of the reactants an proucts in the SRL, an lay the founation for the use of PRS in investigations of the kinetics of epitaxial growth an real-time moeling for close loop process control. Base on the above reaction chemistry, we moel the linkage between the measure PRS signal an the surface kinetics on the basis of a reuce orer kinetic moel an a four-meia stack: ambientsrlepilayersubstrate, which represents the simplest possible escription of the optical response uner the conitions of PCBE processes. 3. Reuce orer kinetic moel For the interpretation of the time-epenence of the four meia stack reflectance, R Ž. 4 t, in terms of the chemical kinetics in the SRL that rives epitaxial growth, the ielectric function of the SRL,, must be linke to its composition. Such a linkage can be establishe via the Sellmeier equation 3 : 2 4 qn f A kj l l 2 2 k j kj Ý c m Ý i 4q 2 N A ÝlxF l l Ž. Ž 7. m that escribes the ielectric function of a pure substance in terms of the electronic transitions from fille states k to empty states j allowe by symmetry for the molecules of this particular meium 9. The ielectric function of the SRL is obtaine by summing over the contributions of all its constituents, ientifie by the label l. In Eq. Ž. 7, enotes the frequency at kj

3 66 ( ) N. Dietz, K. Ito Thin Soli Films Fig.. Schematic representation of a precursor cycle sequence use for the growth of a binary compoun semiconuctor grown via two organo-metallic precursors. For GaP growth, the first precursor is TBP an the secon precursor is. which is evaluate, q an m are the electronic charge an mass. fkj is the oscillator strength of the electronic transition kj expresse in terms of the component of the polarization vector of the exciting electromagnetic wave along the matrix element of the electric ipole operator kj q² r : k j. The reuce orer kinetic moel for the binary compoun semiconuctor GaP, summarizes all reactions Eqs. Ž.Ž. 6 in one ominant bimolecular reaction for the TBP pyrolysis Žfirst precursor, PC. an two ominant bimolecular reactions for the ecomposition Ž secon precursor, PC2.. Both precursors are supplie sequentially separate by pauses as shown schematically in Fig.. The experimental set-up an growth conitions have been escribe in previous publications 7,20. With the above mentione assumptions, the ifferential rate equations for the molar concentrations nl of SRL constituents in the GaP system can be written as n Ž t. n anž t. a n Ž t. n Ž t., t PC 4 3 Ž 8. n Ž t. n a n Ž t., t 2 PC2 2 2 Ž 9. n Ž t. a n Ž t. anž t. a n Ž t. n Ž t. t Ž 0. with a final incorporation reaction n Ž t. a n Ž t. n Ž t.. Ž. t Eq. Ž. 8 escribes the reuce orer TBP pyrolysis, where npc enotes a perioic supply function expresse in terms of the molar concentration of TBP reaching the surface; a is a generalize reaction parameter for the ecomposition of TBP into active surface phosphorous. Eq. Ž. 9 an Eq. Ž 0. escribe the reuce orer ecomposition reaction process of with a perioically supplie molar concentration, n PC2, of an two generalize reaction parameters a 2 an a 3. The formation of GaP an its incorporation in the unerlying film is summarize in the reaction Eq. Ž.. At this point, the SRL is treate as a homogeneous ieal solution an the surface area, A, is assume to be constant for simplicity. Also note that the surface structure, number of reaction sies an inhomogeneous reactions are not explicitly aresse at this point an are integrate into the reaction parameter a 4. From the system Eqs. Ž. 8 Ž. we can extract the film growth rate g as fl g nv. Ž 2. fl A t 4 GaP The temporal thickness evolution of the SRL is given by Ž t. nv nvnv. Ž 3. A where Vl are the molar volumes of the constituents in the SRL. The effective ielectric function of the SRL can be parameterize an expresse as the sum over all molar concentrations nl contributing to the SRL: n Ž t. n Ž t. 2 F F 2 Ý n t Ý n t k k k k n Ž t. 3 F Ž k,2,3. Ž 4. 3 Ý n t k k The link to the PR signal is escribe in the following section. 4. Control metho The reuce orer kinetic moel escribe in Sec. 3 provies a moel for the composition an thickness of the SRL, in terms of the effective ielectric function Ž,t. an Ž t., respectively. It also gives the instantaneous growth rate g Ž. fl t of the GaP film. These are incorporate in Fresnel s equation that etermines the reflectance amplitue, rr, of the p- polarize light as follows. Consier the four-layer meia compose of ambientsrlfilmsubstrate. We moel the reflectionrefraction of the surface reaction layer by an effective meium with the homogeneous ielectric function Ž. t an the thickness Ž. t. Let us enote the four meia by the inices n0,,2,3 labele from the ambient to the substrate. The reflection coefficient r from the Ž n. n,n -st meia to n-th meia is given by

4 r n,n 2 2 n n0sin n n0sin ( ) N. Dietz, K. Ito Thin Soli Films sin sin n n 0 n n 0 5 algorithm 2. Or, the optimal control law can be given in the state feeback as f Ž t. KŽt,nt ˆ. nt. ˆ Ž 2. where n is the complex ielectric function of the n-th meia. The factor n for the n-th meia is given by 2 n 2 n n0sin, Ž 6. where n is the thickness of the n-th meia. The reflectance amplitue rr4 of p-polarize light is then given by rr 4 r r e 2 j r e 2 jž 2. 2 j2 r r r e j 2 jž 2. 2 j r r e r r e r r e or, equivalently by r re 2 i r r e 2i 2 0 ˆ 2 23 rr4 with ˆr 2 i 2 i r ˆre r r e , 7 Here, r, r an are functions in Ž. 0 2 t an Ž. t. Since r is a given constant Ž 23 ielectric functions for film an substrate are assume to be fixe., we Ž. 2i 2 Žt. can efine the function str e as s 4 i 2 sin g sž t.. Ž 8. t 3 0 fl The PR signals at the two ifferent angles of incience i, I,2 are given by the real-time measure- ments 2 Ž. R t rr H t, t,s t. 9 i 4 i Now, for example we can formulate the problem of controlling the growth rate of GaP film as follows. One can etermine T 2 H fl 0 min g Ž t. g Ž t. t Ž 20. over the flow rate f Ž. t that establishes the molar supply concentrations n of in Eq. Ž. PC2 9, subject to the moel ynamics escribe in Eqs. Ž.Ž In Eq. Ž 20., g is the esire growth rate function. Suppose all reaction rate parameters a i an the initial conitions of n Ž. i t, i,2,3 in our moel are known. Then we have the so-calle open loop control problem in Eq. Ž 20., an we can etermine the optimal control function for f Ž. t by the stanar control 23 The state feeback control is more robust than the open-loop control, but in orer to implement the feeback control we nee to observe the full state ˆnt. Ž. In the case of real-time an run-to-run control problems we are not able to etermine all necessary rate constants an the state variables n Ž. i t, I,2,3. Moreover, the reaction rate parameters ai may be time-epenent ue to temperature moulations anor inhomogeneities in compositionthickness of the surface reaction layer. Thus, we employ the control metho base on the active feeback law Ž 2. with real-time state an parameter estimation. Specifically, the control signal f Ž. t is given by f Ž t. KŽt,nt,p ˆ ˆŽ t.. Ž 22. where K is the state feeback law an ˆnt Ž. an ˆpt Ž. are estimates of the state function an the reaction rate parameter base on the PR signals. We can construct the feeback law, for example by the ynamically programming metho 2 anor by the LQR metho applie to the linearization of the moel Eq. Ž 20. at the reference point. The real-time estimate of the state an the rate constants base on the PRS signals can be constructe by applying filtering algorithms base on variants of the Kalman-filter Ž2, Ito, unpublishe results.. This approach provies a real-time control metho that can be robust with respect to the temperature fluctuations an variations in the growth conitions. Also, the monitoring of the growth process can be achieve in terms of on-line estimates of the state variables. 5. Results Fig. 2 shows the evolution of the PR signals uring growth of GaP on SiŽ 00. at 350C, recore for two angles of incience, 680. an 740., at 6905 nm an at nm, respectively. A precursor cycle sequence time of 3 s has been use with a continuous hyrogen flow uring the entire cycle time. The fine structure observe in the PR signal Ž see inset in Fig. 2. is strongly correlate to the time sequence of the supply of precursors employe uring the steay-state growth of GaP. Each peak in the fine structure correspons to a complete precursor cycle with the start of the oscillation always coinciing with the leaing ege of the first TBP pulse of the sequence. As can be seen in Fig. 2, the amplitue in the fine structure unergoes perioic changes ur-

5 68 ( ) N. Dietz, K. Ito Thin Soli Films Fig. 2. Heteroepitaxial GaP growth on Si uner PCBE conitions at 350C monitore at two incience angles, 68 an 74. The inset shows an enlargement of the PR fine structure as a response to the thickness- an composition-moulate SRL. ing the eposition time. This amplitue moulation in the fine structure can be analyze to extract the average complex ielectric function of the SRL as well as its average thickness 2. For GaP growth with a 3-s pulse cycle time, an average ielectric function of Ž 9.5, 2.5. with an average thickness of 5 A for the SRL has been calculate with a growth rate of 0.78 As 2. Using these values, we can generate the initial starting conitions for the unknown generalize reaction rate parameters a i an the initial conitions of n Ž. t, in Eqs. Ž. 8 Ž., which are subject to parameter i estimation. Fig. 3 shows the temporal evolution of n Ž. t, Ž. t, Ž. i t an the four-meia stack reflectance for a pulse cycle sequence of 3 s, where the surface is sequentially expose to a TBP pulse from 0.0 to 0.8 s an a pulse from.5 to.8 s. The molar concen- trations n Ž. i t in Fig. 3b are the solution of the cou- ple ifferential system Eqs. Ž.Ž The thickness of the SRL an its ielectric function are compute using Eq. Ž 3. an Eq. Ž 4.. The reflectance RP in Fig. 3e is given by Eq. Ž 6.. These oscillations in R P are superimpose on interference fringes, resulting from back reflection at the substrate-layer interface as shown in Fig. 4. The temporal evolution of the PR signals in Fig. 4 are simulate for two angles of incience 74., an 68, with wavelengths of Fig. 3. Moeling of PR response uring GaP growth on Si uner PCBE conitions at 350C: Ž. a precursor cycle sequence; Ž. b molar concentrations n Ž. t of constituents in the SRL; Ž c. i thickness Ž. t an ielectric function Ž. t moulation; an Ž. e four meia stack reflectance calculate for 74., nm an a growth rate of 0.78 As nm an 690 nm, respectively. The fine structure shown in Fig. 3 is not resolve in Fig. 4. A comparison with the experimental ata in Fig. 2 shows an excellent agreement of the overall fine structure evolution. Deviations encountere uring the initial growth perio are ue to a change surface chemistry uring the nucleation an overgrowth process, which has not been accounte for in this moel. The number of parameters involve in this simulation totals to, with four unknown reaction kinetics parameters to escribe the ecomposition an loss process, four parameters for the molar volumes an three parameters that escribe the optical oscillator strength for each constituent in the SRL. Even so, some of these parameters, such as the molar volumes an optical oscillator strengths can be estimate from literature ata, a larger set of experimental ata is require in orer to go to the next step from qualitative to quantitative analysis of surface reaction kinetics. 6. Conclusion We introuce a reuce orer kinetic moel using generalize reaction rate parameters to escribe the

6 ( ) N. Dietz, K. Ito Thin Soli Films References Fig. 4. Moeling of PR response at two angles of incience, 74. Ž nm. an 68 Ž 690 nm., simulating GaP growth on Si uner PCBE conitions at 350C. thickness an composition evolution of the SRL. The molar concentrations ni in the SRL are irectly linke to the growth rate of the unerlying film. An on-line parameter estimate of the state functions an the reaction rate parameters a i using the PRS signals can be use to analyze the PRS fine structure an to provie the control signal. The reuce orer kinetic moel provies the link between the flow rate an GaP growth rate as well as the analysis of surface chemistry processes. The successful application of this approach will not only provie the closest possible feeback control-loop, but also will give a more etaile unerstaning of the surface reaction chemistry uner steay-state thin film growth. W.G. Breilan, K.P. Killeen, Proc. Mater. Res. Soc. 406 Ž W.G. Breilan, K.P. Killeen, J. Appl. Phys. 78 Ž K.P. Killeen, W.G. Breilan, J. Electron. Mater. 23 Ž S.D. Murthy, I.B. Bhat, B. Johs, S. Pittal, P. He, J. Electron. Mater. 24 Ž D.E. Aspnes, J.P. Harbison, A.A. Stuna, L.T. Florez, Appl. Phys. Lett. 52 Ž D.E. Aspnes, IEEE J. Select. Top. Quantum Electron. Ž N. Dietz, A. Miller, K.J. Bachmann, JVST A 3 Ž K.J. Bachmann, N. Dietz, A.E. Miller, D. Venables, J.T. Kelliher, JVST A 3 Ž N. Dietz, K.J. Bachmann, Vacuum 47 Ž K.J. Bachmann, U. Rossow, N. Sukii, H. Castleberry, N. Dietz, JVST B 4 Ž N. Dietz, U. Rossow, D.E. Aspnes, K.J. Bachmann, Appl. Surface Sci. 02 Ž N. Dietz, N. Sukii, C. Harris, K.J. Bachmann, JVST A 5 Ž K.J. Bachmann, N. Sukii, N. Dietz, C. Hoepfner, S. LeSure, H.T. Tran, S. Beeler, K. Ito, H.T. Banks, J. Crystal. Growth Ž 997. Ž in press.. 4 J.T. Kelliher, N. Dietz, K.J. Bachmann, Proc. SOTAPOCS 8, Honolulu, Hawaii, The Electrochemical Society, Pennington, NJ, 994, p A.J. Murrell, A.T.S. Wee, D.H. Fairbrother, N.K. Singh, J.S. Foor, G.J. Davies, D.A. Anrews, J. Cryst. Growth 05 Ž S.H. Li, C.A. Larsen, N.I. Buchan, G.B. Stringfellow, W.P. Kosar, D.W. Brown, J. Appl. Phys. 65 Ž G.H. Fan, R.D. Hoare, M.E. Pemble, I.M. Povey, A.G. Taylor, J.O. Williams, J. Cryst. Growth 24 Ž K.J. Bachmann, U. Rossow, N. Dietz, Mater. Sci. Eng. B 37 Ž G. Burns, Soli State Physics, Acaemic Press, Orlano, 985, 46 p. 20 N. Dietz, K.J. Bachmann, MRS Bull. 20 Ž W.H. Fleming, R.W. Rishel, Deterministic an Stochastic Optimal Control, Springer Verlag, New York, 975. Acknowlegements This work has been supporte by the DOD-MURI Grant F