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Reactions of the (100) face of gallium arsenide with atomic and molecular chlorine Ha, Jae Hee 1989

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REACTIONS OF THE (100) FACE OF GALLIUM ARSENIDE WITH ATOMIC AND MOLECULAR CHLORINE by JAE HEE HA B.Sc, Korea University, 1982 M.Sc, University of California, Los Angeles, 1985 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY THE FACULTY OF Department in GRADUATE STUDIES of Chemistry we accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 1989 •jae Hee Ha, 1989 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia Vancouver, Canada DE-6 (2/88) ii ABSTRACT Reactions of the (100) face of a gallium arsenide single crystal with atomic and molecular chlorine were studied in the temperature range from 25 to 160°C. Small chips cut from 3 inch undoped gallium arsenide wafers were mounted on a silicon heat sink and etched in a Pyrex reaction tube. The etch rate was monitored by laser interferometry, surface profilometry, and mass spectrometry which was also used to detect the etch product. For atom etching, chlorine atoms were produced by a 2450 MHz microwave discharge in CI2. The chlorine atom pressure was measured by titration with nitrosyl chloride. The etching by molecular chlorine was found to be first order in CI2 at low pressures. An activation enthalpy of 24.0( ± 2.8) kcal and a pre-exponential factor of 5.8xl0 ( 1 3 * ^ |um min"1 Torr"1, were measured for this low pressure reaction. At pressures above 15.0 Torr the reaction was found to reach a limiting rate with an activation enthalpy of 13.7 ( ± 1.6) kcal and a pre-exponential factor of 7.9x10(7 ± °- 5 ) (am min"1. A mechanism is proposed in which the first step is dissociative adsorption of CI2 on the GaAs surface and this is followed by a reaction of the adsorbed atoms to form volatile products. The reaction with chlorine atoms showed a first order dependence on the partial pressure of Cl atoms and an activation enthalpy and pre-exponential factor of 9.0 ( ± 1.2) kcal and 8. 7x10(6 ± ° ' 7 0 ) |um min"1 Torr"1, respectively. The etching of GaAs(100) both in atomic and molecular chlorine displayed crystallographic effects under the experimental conditions studied. A mesa with inward sloping planes and a mesa with outward sloping planes were obtained for both the atomic and molecular processes. iii Table of Contents ABSTRACT ii List of Figures vi List of Tables ix List of Appendices x Acknowledgements xi Chapter 1 Introduction 2.1 Semiconductor Materials 1 1.2 The Chemistry of Semiconductor Etching 3 1.3 Wet and Dry Etching 8 1.4 Surface Structure of GaAs {100}, {110}, and {111} Faces 15 1.5 Previous Studies of the Kinetics of GaAs Etching with Cl Atom 18 1.6 Previous Studies of the Kinetics of GaAs etching with C l 2 22 1.7 Purpose of This Study 25 Chapter 2 Apparatus and Procedure 2.1 Introduction 27 2.2 General Review of Apparatus and Procedure 27 2.3 Reaction Tube and Preparation 32 2.3.1 Reaction Tube and Preparation for the CI2 Etching Experiment 32 2.3.2 Reaction Tube for Cl Atom Etching Experiment 35 2.4 Gas Handling System 35 2.4.1 Gas Handling System in CI2 Etching Experiment 35 2.4.2 Gas Handling System in Cl Atom Etching Experiment 36 2.5 Pressure Measurement and Flow Calibration 36 2.6 Preparation and Purification of Gases 37 2.7 Production of Cl Atoms and Measurement of Their Partial Pressures 40 2.8 Sample Preparation and Sample Holders 44 2.9 Measurement of Etch Rates and Detection of Etch Products 47 2.9.1 Mass Spectrometry 47 2.9.2 Mass Spectrometer Signal Calibration 50 2.9.3 HeNe Laser Interferometry 50 2.9.4 Surface Profilometry 51 Chapter 3 Result and Kinetic Analysis 3.1 Etching Inhibition by Oxide Layer 52 3.2 Formation of a Liquid Layer 52 3.3 Etch Product Analysis 53 3.4 Results of the CI2 Etching Experiments 60 3.5 Results of the Cl Atom Etching Experiments 87 3.6 Crystallographic Etching and Surface Morphology 107 3.7 On the Significance of Dislocations.. 108 Chapter 4 Discussion and Error Analysis 4.1 The C l 2 Reaction 113 4.1.1 The "Low Pressure Rate Constant" ki 113 4.1.2 The "High Pressure Limiting Rate Constant" k 2 114 4.2 The Cl Atom Reaction 116 4.3 The Complete Mechanism 119 4.4 Conclusion 121 4.5 Error Analysis 122 Appendices 126 References 140 vi List of Figures Figure 1.1 A typical isotropic etch profile 5 Figure 1.2 A typical anisotropic etch profile 7 Figure 1.3 A parallel plate plasms/sputtering reactor 10 Figure 1.4 Redeposition and Trenching caused by sputtering 13 Figure 1.5 The zincblende lattice observed at right angles to a [111] axis 17 Figure 1.6 Surface structure of the {111}, {110}, and {100} faces of GaAs 20 Figure 2.1 Schematic diagram of experimental apparatus used in C l 2 etching (DES-1) 29 Figure 2.2 Schematic diagram of experimental apparatus used in Cl etching (DES-2) 31 Figure 2.3 Reaction tube for C l 2 etching experiment 34 Figure 2.4 Chlorine pressure versus flow(dP/dt) 39 Figure 2.5 Square root of glow intensity versus pressure of NOC1 added 46 Figure 2.6 An exploded view of Si sample holder 49 Figure 3.1 Profile of etched GaAs(100) surface between two silicon nitride masked areas. T = 66°C and Pci2 = 15.5 Torr 55 vii Figure 3.2 Profile of etched GaAs(lOO) surface between two S13N4 masked areas. T = 76°C and P C i 2 = 0.09 Torr 57 Figure 3.3 Arsenic chloride ions detected by mass spectrometer 59 Figure 3.4 The etch rate of GaAs(lOO) by CI2 as a function of the pressure of C l 2 (below 16.0 Torr) at 91°C 62 Figure 3.5 The etch rate of GaAs(lOO) by CI2 as a function of the pressure of C l 2 (above 15.0 Torr) at 91°C 64 Figure 3.6 A typical interferogram observed in CI2 etching 66 Figure 3.7 A plot of ln (etch rate) versus ln (Pci2) at several temperatures 72 Figure 3.8 A plot of the reciprocal GaAs etch rate versus the reciprocal pressure of CI2 at 76, 91, and 100°C 80 Figure 3.9 A plot of the reciprocal GaAs etch rate versus the reciprocal pressure of CI2 at 126 and 142°C 82 Figure 3.10 An Arrhenius plot of k2 and K s s k2 86 Figure 3.11 A typical interferogram observed in CI atom etching 90 Figure 3.12 The total etch rate of GaAs(100) by C l 2 and CI as a function of the pressure of CI at temperatures 91, 100, 110, 132, and 156°C 94 Figure 3.13 The corrected etch rate of GaAs(100) by CI as a function of the pressure of CI at temperatures 91, 100, 110, 132, and 156°C 98 Figure 3.14 The corrected etch rate of GaAs(100) by CI as a function of the pressure of CI for three different total pressures at 91 and 132°C 102 viii Figure 3.15 An Arrhenius plot of kci 106 Figure 3.16(a) A top view of schematic diagram of Si3N4 mask pattern 109 Figure 3.16(b) and (c) SEM photographs of channels etched in the (100) plane of GaAs by C l 2 110 Figure 3.17(a) A top view of schematic diagram of Si3N4 mask pattern I l l Figure 3.17(b) and (c) SEM photographs of channels etched in the (100) plane of GaAs by Cl and C l 2 112 Figure 4.1 Errors in In kci and 1/T 125 List of Tables ix Table 2.1 Values of corrected CI pressure at different flow tube temperatures 43 Table 3.1 List of etch rates of GaAs(lOO) with C l 2 measured by three different techniques at 91°C 68 Table 3.2 List of etch rates of GaAs(lOO) with C l 2 measured at several temperatures 70 Table 3.3 List of values of the slope at low pressures 74 Table 3.4 Experimental values of k 2 and K s s k 2 obtained at several temperatures 84 Table 3.5 Experimental values of total etch rates in CI etching as a function of the pressure of CI at several temperatures 92 Table 3.6 Values of corrected etch rates in CI etching as a function of the pressure of CI at several temperatures 96 Table 3.7 Values of corrected etch rates in CI etching as a function of the pressure of CI for three different total pressures at 91 and 132°C 100 Table 3.8 The values of kci at different total presssures and several temperatures 104 List of Appendices Appendix 1 Circuit diagram of cadmium sulfide photo-detector 126 Appendix 2 Procedure for silicon nitride mask deposition 127 Appendix 3 Derivation of equation 2.9 128 Appendix 4 Kinetic analysis of experimental data for heterogeneous reactions 129 Appendix 5 Steady state analysis of the C^/GaAs reaction (3.1 and 3.2) mechanism 131 Appendix 6 Steady state analysis of the CVGaAs reaction (3.9 and 3.10) mechanism 133 Appendix 7 Estimating upper lomit of reverse reaction 3.9 135 Appendix 6 Steady state analysis of the combined Cl/CVGaAs reaction mechanism 138 A c k n o w l e d g e m e n t s I would first like to thank my supervisor, Professor E . A . Ogryzlo for his inspiring guidance, interest, and support during the course of this work. I sincerely appreciate his encouragement and patience, as well as his never-ending help and comments on preparing this thesis. T o Professor Ogryzlo, I owe every possible success of this thesis. I am grateful for the efficient services rendered by the Electrical and Mechanical shops. In particular, my sincere thanks are owed to B i l l Handerson, Charlie McCafferty, Ron Marwick, Brin Powell, Brion Snapkauskau, Brian Greene, Rowry Chan, and David Tokin for their efforts. I would like to express my deepest gratitude to Hiroshi Kato in Electrical Engineering for his help in preparing G a A s samples, without which this research could not have proceeded. I am grateful to Proferror N . Basco for his guidance and reading the final version of this thesis under extremely short notice. I also wish to thank Professor A . Storr for his providing GaCl3 sample and Professor M . W . Blades for making the laser available for use in this research. I would like to thank Rita V . Kasza and Oliver Lee for their calculations in preparing this thesis. I am also grateful to Mary Mager for her assistance in operating S E M machine. I would like to extend my sincere appreciation to the staff of the UBC Chemistry Department for their kindness and good will. I owe a special gratitude to my parents for their encouragement and support during my research. Finally, I reserve my deepest gratitude for my husband; for without his understanding and advice, I would not have been able to bring this thesis to completion. Chapter 1 I n t r o d u c t i o n 1.1 Semiconductor Materials The special properties of semiconductor materials have been essential to the development of the microelectronics industry. The world's first important semiconductor device, the transistor, was invented in 1947 by William B. Shockley, John Bardeen and Walter H. Brittain at the Bell Laboratories. Since then, semiconductors have also been used in electronics as amplifiers, on-off switches, resistors, capacitors, emitters, diodes, radiation emitters, and detectors. The demand for miniaturization and the development of microelectronics led in 1959 to the incorporation of the semiconductor in integrated circuits (IC's) which are the basis of today's computer and other microprocessor controlled systems. These IC's consist of combinations of such electronic components on a single semiconductor crystal that have functions like logic, memory and switching. The first transistors were made of germanium. However because of the inferior quality of its oxide and its small band gap which limited its use to temperature below 70°C, the industry quickly turned to silicon. For over 20 years Si was used almost exclusively in the fabrication of semiconductor devices. There are several reasons for this choice. Si is homogeneous and it forms highly ordered crystals. As an elemental semiconductor it is relatively easy to purify and can undergo a variety of processing steps without suffering from problems of decomposition. Si has a relatively wide band gap which makes it possible to operate Si based microcircuits at temperatures as high as 125-175°C 1 . Despite the widespread use of silicon in the semiconductor industry, Si has several disadvantages which severely limit its uses. 2 Si is an indirect gap semiconductor and thus silicon devices and microcircuits can not be employed in many electro-optical applications. Furthermore Si has a relatively low electron mobility which ultimately restricts its use in the computing and communications industries where speed is critical. Therefore there is a growing interest in the development of other elements and compounds which exhibit semiconducting properties superior to Si. Compound semiconductors, particularly 3A-5A compounds such as GaAs have been found to be superior to Si in several respects. The electron mobility of GaAs (8800 cm2/Vs) is about five times higher than that of Si (1900 cm2/Vs), allowing for the development of higher speed circuits which also consume only about 3 one tenth the power. GaAs also has a wider band gap of 1.44 eV, compared to only 1.11 eV for Si, allowing it to function at higher temperatures. Another major advantage of GaAs is that it is a direct gap semiconductor so it can more easily emit and absorb light, making it ideal for optoelectronics. In addition GaAs IC's can withstand a radiation dosage 10,000 times higher than Si IC's can, which is very important for space electronics. Finally GaAs has a high resistance to current flow and is considered a semi-insulating rather than semiconducting material like Si. Dense circuits made with GaAs do not need isolation areas or wells, which require additional 4 fabrication steps and create parasitic capacitance problems. There are, however, some disadvantages in the use of GaAs. It is a synthetic compound of two elements, Ga, which can only be obtained as a by-product of mining operations, and As, which is highly toxic. Both elements contain impurities which are difficult to eliminate and which distort the electronic properties that result when they are 3 combined. Fabrication has been very expensive and it is sensitive to decomposition because it is a compound semiconductor. Although it has the disadvantages stated above and little is known about the chemistry and physics involved, the physical properties of G a A s and its characteristics as a semiconductor have led to the continuing, rapid development of GaAs technology. 1.2 The Chemistry of Semiconductor Etching T h e fabricat ion of microelectronic devices from raw semiconductor materials requires many steps. In view of the subject of this thesis only the step involving the etching of semiconductor wafers will be considered. Etching is a process by which exposed material on a semiconductor surface is removed; the material which is to remain intact is covered by a mask (usually a metal or metal oxide) or resist (usually a photosensitive organic polymer). The mask or resist is later removed to leave behind a pattern on the surface corresponding to structural features with specific electronic functions. Etching may be either anisotropic or isotropic. The profile resulting from isotropic etching is characterized by round walls, a curved bottom, and either mask erosion or undercutting as illustrated in F i g . 1.1. Such etching results in an inaccurate reproduction of the mask pattern onto the wafer surface. Isotropic etching results from the action of an etchant that reacts isotropically i.e. equally fast in all directions in the crystal. A n ideal anisotropic etching profile is characterized by vertical walls, a flat bottom, little or no mask erosion, and an etched area not extending beyond the openings of the mask (Fig. 1.2), resulting in the accurate pattern transfer onto the wafer surface. Even though the mechanism of anisotropic etching is not well understood, it is clear that anisotropic etching results when etching occurs very much faster in the vertical direction than in the lateral . 5 ' 6 Since such profiles are observed when the etching occurs in a plasma where 4 Figure 1.1 A typical isotropic etch profile Regions of undercutting Mask or Resist 6 Figure 1.2 A typical anisotropic etch profile TT77777. Mask or Resist < Vertical walls—> Flat bottom Wafer ions are present, it has been suggested that energetic ion bombardment perpendicular to the surface breaks bonds in the upper layers of the surface, creating a damaged horizontal surface which can react more quickly than the sidewalls. A second possibility is that ion bombardment clears the products on the bottom surface so that the layers of atoms below can react continuously, while the sidewalls are not struck or cleared by the ions.6 Another mechanism suggests that incident ions provide thermal energy to the bottom surface which enables it to react faster 7 8 9 than the sidewalls. 1.3 Wet and Dry Etching Current etching techniques are normally classified as either wet or dry. Wet etching involve the removal of surface material by placing the wafer in a solution containing chemical species which will react with the material to form soluble products that are swept away from the surface. This method usually results in isotropic etching with a degree of undercutting and pattern distortion which produce ill-defined surfaces. As a result it is not possible to obtain submicron resolution by wet etching. Consequently, this method is not useful for producing submicron features except for films that are only a few atomic layers thick. For greater automation, increased processing speed, and smaller features dry etching techniques are found to be superior. Drying etching involves the removal of material from the wafer surface by gaseous etchants (gaseous molecules, atoms, or ions) in a vacuum system. Typically, a wafer is placed between two electrodes across which a radio frequency field is applied (Fig. 1.3). In one variation, gases such as Ar or He flow into the reactor and are ionized by the RF discharge to produce high energy particles which can be made to bombard the wafer surface. This etching technique called sputtering involves the removal of surface material by ion impact on the surface, giving high directionality in the etched features. 9 Figure 1.3 A parallel plate plasms/sputtering reactor E : Electrode RF : Radio frequency generator W : Semiconductor wafer gas 4 o c plasma W W E 1 pump However, the mask or photoresist usually erodes quickly due to the high energy ion-bombardment. This can result in distortion of critical dimensions of features being etched. In addition sputtering causes redeposition and trenching of material which alter the edge profile and the linewidths (Fig. 1.4). Finally it tends to show more etching near the center of the electrodes due to uneven ion distribution over the electrodes. An alternative technique is plasma-assisted etching which involves reactive gases such as halogens in addition to the inert carrier gas. Although some etching occurs due to sputtering, it is known that using this process most of etching occurs by a chemical process. Usually halogen containing gases are discharged to generate chemically reactive species which then react with the substrate surface to form volatile products (with vapor pressures greater than 10"5-10"4 Torr at the surface temperature) which are removed by a vacuum pumping system. A wide variety of materials have been successfully etched in a plasma environment. Although Si and silicon oxide have been the principal application of plasma etching, there has also been work done with other electronically important materials such as 3A-5A compound semiconductors. The most valuable aspect of this technique is the ability to etch in a highly directional manner, with good resolution, allowing for the production of submicron features. Selectivity (the etching of one material relative to another) can also be managed, to a large extent, by altering the etchant gas. Because lower ion energies are used, a gentler chemical reaction occurs in plasma etching than in "sputtering", resulting in better surface morphology with less redeposition, less damage to photoresists, and better surface smoothness. However, plasma etching can have some harmful effects on the semiconductor material being etched, such as the possible deposition of undesirable residues. When etching occurs by discharging halocarbon compounds, polymers can form and build up on the substrate surface, inhibiting the etching reaction. Some workers10'11 1 2 Figure 1.4 Redeposition and Trenching caused by sputtering VZZZZZJ Redeposition Trenching Mask or Resist 777777, Wafer feel that this deposit plays an active role in producing an anisotropic etch by coating the side walls and virtually eliminating a lateral etch. This surface contamination and anisotropy can be affected by adding 12 13 14 gases such as H2 or O2 ' to the etchant gas or by using C l 2 or F2 as the etchant. Despite this contamination problem plasma etching plays an important role in the manufacture of semiconductors and other devices requiring fine-line lithography. Variations of this 15-19 method such as reactive ion etching (RIE) and reactive ion beam 20-25 etching (RIBE) are also used to etch Si and 3A-5A compound semiconductors, yielding fine linewidths, directional etching, and etch selectivity. Nevertheless improvements in selectivity, edge profile control, uniformity, reproducibility, overall process control, and throughput are still needed for these techniques. Some recent work in several laboratories indicates that photon assisted dry etching could provide an attractive alternative process capable of both anisotropy and selectivity comparable to plasma etching but without damage to the quality of the components caused 26-39 by the energetic ion bombardment. Laser radiation can affect gas-solid reactions by interacting 40-with the gas, the solid, the interface or some combination of these. 42 Excitation of a gas-phase species can be electronic or vibrational, and may lead to dissociation or ionization, thus changing the etchant characteristics. Laser light can also excite species adsorbed on a surface. This can, for example, increase the rate of reaction of a molecule with the surface. Finally, light can be used to cause excitation in the solid material. Some observations suggest that either 33 39 43 photogenerated carriers ' ' or heat generated by the 40 42 radiation ' can affect reaction rates at the surface of semiconductors. Excitation of either the adlayer or bulk can cause a change in the desorption rate of molecules on the surface as well. In 39 42-49 various experiments, ' a number of the advantages of laser induced etching process have been shown, including maskless, direct patterning, low-temperature etching, selectivity, and highly anisotropic features. A combination of laser-induced etching with 1 5 plasma processing ' ' has been demonstrated. Such a combination has shown capabilities not attainable using either laser-induced or plasma techniques alone, i.e. highly directional etching with much less damage to the semiconductor surface. 1.4 Surface Structure of GaAs{100}, {110}, and {111} Faces Gallium arsenide crystallizes in a zincblende structure which can be considered to consist of interpenetrating face centred cubic sublattices of gallium and arsenic, with one sublattice displaced one quarter of the way along the main diagonal of the unit cell of the 52 53 other. ' This is illustrated in Fig. 1.5 where the solid lines outline the two f.c.c. unit cells of the constituent atoms. An important consequence of this displacement of the two sublattices is an asymmetry (sometimes called a polarity) along the <111> directions. For the particular arrangement chosen in Fig. 1.5 the top face is called the (111)A face and the bottom face is called the (111)B face, while down is called the [111]A direction and up is called the [111]B direction. When a crystal is cleaved along a (111) plane it is these single bonds that break revealing Ga-atoms on the (111)A face (one is labelled A in Fig. 1.5) or As-atoms on the (111)B face (one is labelled B in Fig. 1.5). On each surface these atoms are bound to the rest of the crystal by three bonds, leaving one dangling bond on each atom (assuming that the surface species are Ga" and As+) or perhaps a vacant sp3 hybrid orbital on Ga and a lone-pair on As (if the atoms are neutral). A consequence of the A and B faces is a difference in 52 the chemical reactivity of these two faces. Its consequences for the current experiments will be discussed later. There are alternate layers of Ga and As in the [100] direction of a GaAs crystal as shown in Figure 1.5. Because the atoms in every (100) layer have identical bonding to the crystal this is not a natural cleavage plane and there is rio difference in chemical reactivity between the [100] and 't'100] directions. Each atom of As or Ga on a surface is bound to the underlying layer by two bonds and it is 1 6 Figure 1.5 The zincblende lattice observed at right angles to a [111] . 52 axis. o Ga As 11111 directions (111) or A-face (HI) or B-face normally considered that there are therefore two (potential) dangling bonds on each surface atom. The (110) face is more difficult to visualize with the limited number of atoms shown in Fig. 1.5. In contrast to the (100) and (111) planes an equal number of Ga and As atoms occur in each (110) plane. Each Ga atom is bound to two As atoms in the plane. A third bond is directed into the interior of the crystal. Consequently there is normally considered to be only one "dangling" bond sticking out of the surface from each atom. The (110) plane is a natural cleavage plane for the crystal. The description of the bonding characteristics of surface atoms on each of the faces discussed above is summarized in Fig. 1.6. 1.5 Previous Studies of the Kinetics of GaAs Etching with Cl Atoms 54 Donnelly et al. investigated the GaAs(100) etching in a chlorine plasma at 0.30 Torr over a substrate temperature range of 100 to 350°C. Etch rates which were determined from optical emission of Ga exhibited an Arrhenius-like dependence on substrate temperature, giving an activation energy of 10.5 kcal. Sputter Auger analysis of the etched GaAs surface showed that it was Ga-rich and there was between one-half and one monolayer of chlorine coverage. They also observed that the etched-surface morphologies of GaAs are strongly dependent on temperature, changing from rough to smooth at about 125°C. Although the 10.5 kcal activation energy is very close to the heat of vaporization of GaCb (11.4 kcal), they rejected the possibility that the desorption of GaCb from the surface is rate determining step. Their conclusion is based on the observation that the rate of evaporation of GaCl3 which they calculated from vapor pressure data exceeded the observed etch rate by several orders of magnitude. They tentatively proposed two possible alternative rate determining steps. O Q £ possibility is the dimerization of strongly adsorbed GaCl3(S) on the surface to form Ga2Cl6(S) where the subscript(s) indicates a surface species. 19 Figure 1.6 Surface structure of the {111}, {110}, and {100} faces of GaAs. Dotted lines indicate dangling bonds, solid lines indicate bonds in the surface plane, and the triangle-shaped bold lines indicate bonds in the crystal, (a) : {111}A (b) : {111}B (c) : {110} (d) : {100} 2GaCl 3 ( s ) • Ga2Cl6(s) (1.1) The other is a relatively slow chemical reaction of an etchant species with the GaAs surface which can be written C1(S) + surface species • gaseous products (1.2) However there is no direct evidence for such rate controlling steps. The GaAs(lOO) etching with low-pressure chlorine atoms produced by electron-cyclotron resonance (ECR) was studied by Sugata and Asakawa. In contrast to the observation by Donnelly et al., they could not observe any etching by Cl atoms at a substrate temperature below 190°C and with only C l 2 molecules, etching occurred only above a substrate temperature of 290°C. The activation energy they obtained for Cl atom etching is 6.0 kcal in the temperature range between 250 and 400°C. d'Agostino et al. also studied the undoped GaAs(lOO) etching process in an Ar-Cl 2 rf discharge at 200 mTorr in the 70 to 300°C substrate temperature range. X-ray photoelectron spectroscopy (XPS) analyses which was performed to probe surface composition after etching indicated that As and Ga oxides inhibit the etching process. However they found that once all the surface oxide has been removed by Cl atoms, the activation energy for the GaAs(100) etching in an Cl 2 -Ar plasma has a value of -11 kcal. 57 Skidmore et al. have studied the etching of GaAs with a novel dry etching technique that combines chlorine atoms generated in a microwave plasma with an argon ion beam. They observed that chlorine atoms spontaneously react with the substrate at room temperature while the C l 2 molecules need some additional thermal activation. The etch rate observed with 0.8 mTorr of C l 2 and at 30°C was significantly higher than for atom etching (1400 A / m i n ) than molecular etching (<10 A / m i n ) . Chlorine-containing compounds such as C C 1 2 F 2 5 8 and SiCU, 5 9 and mixtures such as Cl 2-CCi4 6° and BC^-Ar 1 9 have also been used to generate CI atoms for the etching. of GaAs. However there have been no detailed kinetic studies for these systems. 1.6 Previous Studies of the Kinetics of GaAs etching with C l 2 There have been several studies for the kinetics of the reaction of GaAs with CI2, but there is very little agreement between them. Indeed, the etch products of the reaction remain controversial. A theoretical study of the GaAs/Cl 2 system has been reported by McNevin. 6 1 Her thermodynamic calculation predicted that the etch products should be AsCh and GaCh and the etch rate should be a constant 670 jum/min at 0.3 Torr of CI2 in the temperature range from 50 to 180°C. The calculation was based on an assumed constant CI2 sticking coefficient of 1 in this temperature range. The chemical etching was predicted to increase with increasing CI2 pressure up to the saturation limit. Further increases in CI2 pressure above the saturation limit were predicted not to result in further increases in the etch rate because of the solid GaCb covering the surface. The predicted CI2 saturation limits ranged from 20 Torr at 70°C to 380 Torr at 130°C. 62 McNevin and Becker investigated the kinetic mechanism for ion-assisted etching of GaAs in CI2 using a modulated Ar + ion beam. From a comparison of the mass spectrometric cracking pattern of the etch products with those of GaCh and A S C I 3 , they concluded that A S C I 3 , GaCl2 and GaCl are the major etch products. According to their experimental results, the etch rate increases with increasing CI2 pressure up to a saturation limit which is independent of the flux of CI2 beam incident on the surface within the range studied and the ion-enhanced etching rate decreases with increasing sample temperature over the range 300-500 K. The observation of a ~1 ms delay in the appearence of the AsCb signal caused by the ion bombardment and the results stated above led them to propose the following kinetic mechanism for the thermal etching of GaAs by Cl 2 . In the proposed model, it was assumed that dangling bonds on the surface As atoms are rapidly saturated by the chlorine to produce AsCl(S). The reaction of this surface species with chlorine on the surface is then followed in a Langmuir-Hinshelwood type reaction between two surface species. The proposed steps are C l 2 • C l 2 ( s ) (1.3) AsCl(s ) + C l 2 ( s ) — ^ AsCl 3 (s) (1.4) Ga<8) + Cl 2 (s) GaCl 2 ( s ) (1.5) Finally these surface reactions are followed by the rapid desorption of the products: AsCl 3 ( s ) rapid . AsCl3(g) (1.6) GaCl 2 ( s ) r a p i d • GaCl2(g) (1.7) The rate laws which are derived for this reaction mechanism under the steady state production of AsCl 3 and GaCl 2 are d(AsCl3) _ k A s ( C l 2 ) dt " (Cl 2 ) + (k. a/ka) d(GaCl2) _ k G a (Cl 2 ) dt " (Cl 2 ) + (k. a/k.) These rate laws are consistent with the results they obtained. However, as others have pointed out, the model has the strange property of not requiring the same emission rates of AsCl 3 and GaCl 2 when a steady state is achieved! 63 Balooch et al. proposed a totally different mechanism in their study of the GaAs/Cl 2 reaction with and without simultaneous bombardment by energetic ions. They found that the reaction probability for C l 2 on GaAs rose from 0.002 at 298 K to a maximum 0.5 at 700 K. From the temperature dependencies of the product ions observed in the mass spectrometer, they concluded that AsCl 3 and GaCl3 are the main products at temperatures up to 550 K, but above 550 K monochlorides are the main products. However, for a 300 K surface temperature, no GaCl 2 + signal is observed, with or without ion bombardment. They explained this by proposing slow evaporation of GaCl3 which is unresponsive to the modulated driving force of the incident C l 2 beam. The gallium chloride ions were observed at temperatures above 350 K. Furthermore they observed that the waveform of the G a C l 2 + signal dropped to the apparatus background level when the ion beam was turned off i.e. when only the thermal reaction is occuring. With the above observations, they proposed the following mechanism for the thermal reaction of GaAs with Cl 2 . Cl 2 ; = r C12(S) (1.10) C12(S) + As • AsCl3(S) (1.11) Cl 2 (s) + Ga • GaCl 3 ( s ) (1.12) AsCl 3 ( s ) • AsCl3(g) (1.13) GaCl 3 ( s ) • GaCl3(g) (1.14) The last step is assumed to be very slow forming a GaCl3 "scale" on the surface which is responsible for the lack of reactivity of chlorine towards GaAs at room temperature. They also observed that the AsCl 2 + signal dropped rapidly when ion bombardment is stopped. Although they explained this by surface contamination from impurities in the vacuum system, it still leaves the question of how the surface contamination can cause this rapid signal drop. 64 In contrast Qin et al. concluded from their recent observation of the relative peak heights of GaCl x + ions in time-of-flight spectra that the gallium containing etch products in their laser-assisted reaction of GaAs with CI2 are GaCl and GaCh. Their experimental results also indicated that the reaction is initiated by CI2 dissociative chemisorption on the surface when the normal component of the incident CI2 translational energy is higher than 7 kJ/mol. From these observations, they proposed that the reactions of adsorbed CI with GaCl(S) and GaCl2( S) are the rate determining steps C l ( s ) + GaCl ( s ) • GaCl2(S) (1.15) C l ( s ) + GaCl2(S) • GaCl3(S) (1.16) Very recently a molecular beam study of the CI2 + GaAs reaction has been performed by Hou et al. for surface temperatures in the range 300-500 K . 6 5 Using a rotating mass spectrometer they observed three neutral reaction products GaCb, A S C I 3 , and AS4 at temperatures above 350 K, while they observed only AsCb and GaCb below 350 K. To our knowledge, this is the first time that A S 4 product has been observed in the CI2 + GaAs etching reaction. Based on this interesting observation, they proposed that at temperatures above 350 K, the AsCl x initially formed when CI2 collides with a reactive As site can transfer its CI atoms to Ga. The excess As is removed as A S 4 at these temperatures because it is a thermodynamically favored As species. However the most interesting question is why no one else has reported A S 4 in the products. In view of these divergent results there is a need for a more thorough examination of the CVGaAs reaction as a function of pressure and temperature. 1.7 Purpose of This Study The principal objectives of this study were to investigate the pressure and temperature dependencies of the rate constants for the etching of GaAs by CI2 and CI in the hope that such data shed new light on the mechanism of the reactions. These objectives included the development of an apparatus for the downstream etching of GaAs by CI atoms, capable of monitoring the etch products and etch rates. The (100) face of GaAs was mainly used for this study because this (100) face is the most commonly used slice orientation for GaAs device fabrication. Chapter 2 Apparatus and Procedure 2.1 Introduction Two different flow systems were designed and constructed to study the etching of GaAs samples by gaseous chlorine molecules and atoms. They are referred to as downstream etching systems(DES) because the atoms are created upstream from the point at which the substrates are situated. The details of these two flow systems(DES-l and DES-2) and the differences between them will be described here. 2.2 General Review of Apparatus and Procedure Figs. 2.1 and 2.2 show schematic diagrams of each experimental apparatus used in the study of chlorine molecule and atom etching experiments, respectively. Chlorine atoms can be generated in both systems for reasons which will be discussed later. However, only the second system had the facility to measure the atom concentration in the reaction tube. Sample chips cut from 3 inch undoped GaAs(lOO) wafers were mounted on the Si heat sink and inserted in the reaction tube. The CI2 was pumped over the GaAs sample at a flow rate that exceeded the reaction rate by at least a factor of 50 so that the CI2 was not significantly diluted by the gaseous products. For atom etching, CI atoms were produced by a 2450 MHz microwave discharge in CI2. 28 Figure 2.1 Schematic diagram of experimental apparatus used in C l 2 etching(DES-l) C : chart recorder CEM : channel electron multiplier CTRL : mass spectrometer control unit D : discharge tube DP : diffusion pump GaAs : gallium arsenide sample HL : HeNe laser HV : high voltage power supply I : ionizer assembly MKS : MKS Baratron pressure gauge MWG : microwave generator P : pinhole PT : photomultiplier tube Q : quadrupole mass filter RF/DC: RF/DC generator RP rotary pump RT reaction tube S signal T trap at liquid nitrogen temperature TC Al-Cr thermocouple VG vacuum gauges 2 9 3 0 Figure 2.2 Schematic diagram of experimental apparatus used in Cl etching(DES-2) Al-Cr TC probe : Al-Cr thermocouple probe CS photocell : cadmium sulfide photocell PMT : photomultiplier tube microwave cavity etchant C l 2 -ft utrant (NOCI) I HcNe laser 4 I I I I I photodiode 1 chan recorder 11 i i 11 heating tape ) )4W i P M T 3D Al-Cr T C probe pressure gauge cryostatic pump The CI atom pressure was measured by titration with nitrosyl chloride. The etch rates were determined by HeNe laser interferometry, surface profilometry, and mass spectrometry which was also used for etch product analysis. 2.3 Reaction Tube and Preparation 2.3.1 Reaction Tube and Preparation for the CI2 Etching Experiment The reaction tube shown in Fig. 2.3 was designed to flow a steady stream of etchant gas over the substrate and to leak a small sample of the volatilized products into the quadrupole mass spectrometer for analysis. The pyrex reaction tube with a heating jacket has a central tube with a relatively narrow diameter(18 mm I.D.) which produces a fast flow of gases such that a steady concentration of etchant gas can be drawn out into the tube. The discharge tube which is located at the upstream end of the flow tube is made of quartz to withstand high temperature and ion bombardment from the discharge. A 3.5 inch glass flange which was fitted into the downstream end of the reaction tube connected the reaction tube to the mass spectrometer by means of a rubber O-ring. A stainless steel disc with a 0.003 inch diameter pinhole was inserted between the flow tube and the mass spectrometer ionizer assembly. The reaction tube has several ports for introducing reactant gases, measuring pressure, pumping out exhaust gases, and introducing GaCl3 and A S C I 3 standards for mass spectrometer signal calibration. In order to control the temperature of the substrate, either water heated in a Precision Scientific Co. Model P-3 hot water bath or air heated by a tungsten filament wire was pumped through the heating jacket. However for later experiments, an electrical heating tape, which was wrapped around the reaction tube and connected to a VARIAC, was used for controlling the temperature. The tube was first cleaned with a detergent solution, rinsed thoroughly with deionized water, then washed with hot, concentrated Figure 2.3 Reaction tube for CI2 etching experiment silica discharge to pressure in potassium hydroxide solution, and rinsed well with deionized water again. The reaction tube was then dried thoroughly by a heating gun. The discharge tube was poisoned with phosphoric acid 6 6, heated at around 300°C for a few hours to remove most of the water. Then chlorine gas was discharged for an hour to remove the remaining H2O present in the discharge tube. Halocarbon 25-5s grease was applied to all glass-to-glass joints, O-rings and wherever grease was required. 2.3.2 Reaction Tube for Cl Atom Etching Experiment The reaction tube shown in Fig. 2.2 was 40 cm long and had an internal diameter of 2.5 cm. It consisted almost entirely of pyrex to allow a clean view of the substrate and the chemiluminescence from partially dissociated chlorine. The quartz discharge tube was attached to the upstream region of the reaction tube by B a 14/23 grease-sealed joint so that the discharge tube could be separate from the system for cleaning or poisoning without removing the reaction tube. A 10 cm(8 mm I.D.) long pyrex inlet was located at the end of the reaction tube for the introduction of the NOC1 titrant and was connected to the NOC1 preparation system through an O-ring fitting. Three more ports were included in the design; one was for the measurement of pressure and the other two were for the removal of exhaust gases at controlled flow rates. 2.4 Gas Handling System 2.4.1 Gas Handling System in CI2 Etching Experiment Chlorine and argon gases were directly used from commercial gas cylinders. Monel and stainless steel regulators were used for chlorine and argon gases, respectively, which flowed to the reaction tube through 1/4 inch tubings connected to the discharge tube with a Cajon joint. Steel tubing was used for the CI2 line, while copper tubing was used for the Ar line. Each gas flow was regulated by a Nupro shut off valve plus a Nupro needle valve (monel for the CI2 line, and steel for argon). Swagelok fittings were used for all metal-to-metal tubing connections and all metal-to-glass connections were made with Cajon fittings. A Duo-Seal Mode 1397 rotary pump protected by a liquid nitrogen cooled trap was used to evacuate the vessel before beginning the experiment and then to maintain a steady flow of the 02 /Ar gas mixture. The liquid nitrogen trap removed most of the CI2 from the stream but the pump oil had to be changed frequently because of the CI2 which reached the rotary pump. The trap was connected to the line by an O-ring seal. Two valves on either side of the trap allowed it to be isolated and cleaned or changed during the course of an experiment without breaking the vacuum of the system. 2.4.2 Gas Handling System in CI Atom Etching Experiment There are several significant differences between the gas handling techniques used in DES-1 and DES-2. First of all, in DES-2, both nylon and copper tubings were used for the Ar line and teflon tubing was used for some parts of the CI2 line to provide more flexibility in the lines. Secondly, instead of monel valves, a steel shut off valve and a steel needle valve were included in the CI2 lines to adjust the pressure of CI2 gas. It was found that these valves, which were located at the low pressure side of CI2 flow system were not damaged by CI2 gases. Thirdly, nitrosyl chloride flowing from a NOC1 reservoir was introduced into the reaction tube through a teflon shut off valve and a teflon needle valve which controlled the flow of NOC1. All the NOC1 lines were made of glass tubing. Finally, a teflon shut off valve and a teflon needle valve placed right before a liquid nitrogen trap allowed for more efficient control over the flow rates of exhaust gases. 2.5 Pressure Measurement and Flow Calibration The pressure within the reaction tube was measured with an MKS Baratron absolute pressure gauge (with a pressure range of 0-100 Torr) for C l 2 etching experiments and with an MKS Baratron differential pressure gauge (with a pressure range of 0-10 Torr) for Cl atom etching experiments. The chlorine flow was metered on a conventional ball flow meter(Matheson, tube 604). To calibrate the system volume(Vs), Ar gas at a certain pressure (Pv) which is in a vessel of known volume(5273 ml) was expanded into an evacuated system. V s was calculated by equation 2.1. V s = 5273 ml * ( ? p ? f ) (2.1) r f where Pf is the pressure of the system after Ar gas expansion. Nitrosyl chloride and chlorine flow rates (dP/dt) were measured by recording the rate of pressure rising in the closed system. The values of dP/dt for CI2, which were measured in the system used for CI2 etching, are plotted against the pressure of CI2 in Fig. 2.4. For CI2 etching a typical flow was 31 seem at 1.0 Torr of C l 2 and for Cl atom etching most of the experiments were carried out with Pci2=0.50 Torr and CI2 flow=56 seem. 2.6 Preparation and Purification of Gases Chlorine (99.99% pure, Matheson) and argon (99.99% pure, Linde) were used without further purification. Nitrosyl chloride was prepared in the 12.99 liter reservoir with a cold finger by the '67 reaction of an excess of nitric oxide with molecular chlorine. The 68 NOCl was condensed in an ethyl bromide slurry (-119°C) which trapped the NOCl and from which excess NO could be pumped off. 69 The purity of NOCl was checked by its melting point(-65°C). Nitric oxide supplied by Matheson was used directly from the cylinder. 38 Figure 2.4 Chlorine pressure versus flow(dP/dt) The solid line is the result of fitting the data to the equation dP/dt(Torr/min) = 3 IP 150 Pressure of Chlorine (Torr) 2.7 Production of Cl Atoms and Measurement of Their Partial Pressures A conventional microwave discharge apparatus was used to produce chlorine atoms in the quartz discharge tube connected to the reaction tube. 100 (Raytheon Microtherm) and 200 (Microtron) watt, 2450 MHz generators were used to create the microwaves, which were directed into the discharge tube via a foreshortened 1/4 wave coaxial cavity. The microwave cavity had a teflon-tipped brass slider and a tuning stub for adjusting the coupling. In order to prevent melting of the discharge tube, air was circulating through the discharge cavity for cooling. The discharge is initiated by free electrons generated with a hand-held tesla coil. The intensity of the red glow emitted from partially dissociated 70,71 chlorine ' was monitored by a cadmium sulfide photocell and a photomultiplier tube with red filters which were located before and after the titration point, respectively. The circuit diagram of the cadmium sulfide photodetector is in Appendix 1 The reaction of atomic chlorine with nitrosyl chloride described by equation 2.2 was used to measure absolute Cl atom flow and • , 72-76 hence the partial pressure, Cl + NOCl • NO + Cl 2 (2.2) The end point was determined by titration with nitrosyl chloride to the extinction of the red glow resulting from the Cl atom recombination reaction. This was monitored by a photomultipler tube placed 14 cm downstream from the point of titration, while the stability of the Cl atom concentration was monitored by the photo cell located before the titration point. Within the wavelength range of the red filter (530-650 nm) used to sample the emssion, the observed light intensity was proportional to the atom pressure 75 squared. At the end point, the flow of atomic chlorine (fei), is equal to the flow of nitrosyl chloride (fNoci), and the partial pressure of Cl can be calculated from a knowledge of the total flow (ft) and total pressure (Pt) with the following equation. Pel = ^ - Pt (2.3) Because the sample was placed 15 cm downstream from the titration port, some corrections were made for the loss of atoms between the two points. To determine the actual pressure of CI atoms right over the sample we calculated both the homogeneous and heterogeneous 77 78 recombination of CI atoms ' along the tube described by equations 2.4 and 2.5. C1 + C1+C12 — ^ - CI2 + CI2 (2.4) CI + wall —^s- ^ C l 2 (2.5) The rate law governing these reactions is given by: '-^f1 = 2krPCi2Pci2 + kwPci (2.6) Integrating equation 2.6 with respect to time results in equation 2.7 and CI atom pressure(Pci) over the sample was calculated from this equation. Pel = ^ (2.7) ( 2k rPci 2Pci 0 + k w \ Po. / e t W ' " 2 k ' P c l ' where PciG is the pressure of CI atoms at the titration point. The values of kr and k w were obtained from the reference 71, 77, and 78 79 and the value of k w (0.8 s-1) was corrected for the reaction tube diameter of this system. The corrected CI pressures at the sample, Pci are tabulated in Table 2.1. Table 2.1 Values of corrected C l pressure at different flow tube temperatures Pci^Torr) Pci2f(Torr) Pci0(Torr) T(°Q Pci(Torr) 0.50 0.47 0.061 91 0.056 100 0.056 110 0.056 132 0.057 156 0.057 0.43 0.14 91 0.12 100 0.12 110 0.12 132 0.13 156 0.13 0.39 0.23 91 0.20 100 0.20 110 0.20 132 0.21 0.20 0.16 0.072 91 0.066 132 0.067 2.55 2.48 0.14 91 0.11 132 0.12 2.43 0.25 91 0.19 132 0.21 Pci* : pressure of Q2 before it is discharged Pct2f : pressure of CI2 after it is discharged Prior to the determination of the atom concentration, the pressure, power, and flow rate were optimized to maximize the range of CI atom pressures that could be achieved. At low pressure, the atom concentration increased with increasing power, but as the pressure increased, the effect of a power increase was reduced principally because atom recombination rates increased as the square of the atom concentration. An optimum pressure existed between 0.3 and 0.8 Torr, where the losses from atom recombination were low and atom concentrations were sensitive to microwave power change. At low flow rates, atom recombination processes reduced the atom concentration because of the long residence time in the reaction tube, while at high flow, the CI2 dissociation was reduced because of the short residence time in the discharge. A typical titration plot of the square root of glow intensity versus pressure of NOC1 added is shown in Fig. 2.5. 2.8 Sample Preparation and Sample Holders The GaAs(lOO) wafers which were obtained from Cominco (Johnson and Matthey) in Trail, British Columbia, Canada were grown by the "liquid encapsulation Czochralski" technique and then annealed as a boule at about 900°C. The impurity level is in the range of 1015 cm"3 i.e. about 100 ppb with the most common impurities C, Si, and S. The stoichiometric ratio of As to Ga is reported to lie between 1.000 and 1.002 and the reported dislocation level in these undoped GaAs( 100) wafers is 5 x 104 cm"2. This is an average of a level which varies by a factor of 5 across the wafer, the highest values being at the edges and in the middle of the wafer. Small samples were cut from polished 3 inch undoped GaAs(100) wafers. The GaAs(100) wafers were covered with silicon nitride stripes 10 to 50 |im wide and 10 to 50 |um apart, with the stripes running in both the [Oil] and [Oil] direction. This Si3N4 stripe mask was deposited by Hiroshi Kato in the U. B. C. Center for Advanced Technology in Microelectronics, and the deposition procedure is described in Appendix 2. 45 Figure 2.5 Square root of glow intensity versus pressure of NOCl added pressure of C l 2 discharged : 0.50 Ton-pressure of Cl : 0.23 Torr 46 0.0  0.10 0.20 0.30 Pressure of NOCI Added (Torr) At first a monel boat-shape sample holder on which the GaAs sample was glued with Epoxy was used in the mass spectrometry experiments. However because of surface contamination due to long sample mounting time and poor thermal contact between the sample and the monel heat sink because of an insulating Epoxy layer, the Si sample holder (1.5 cm x 3.0 cm) depicted in Fig. 2.6 was used for most experiments. The small GaAs samples being etched were pressed with glass springs against a polished Si heat sink in which an Al-Cr thermocouple was embedded. Experiments indicated that intimate contact between the sample and a heat sink was very important to keep the sample temperature from rising by heat released from GaAs-Cl/Cl2 reaction and Cl atom recombinations. Prior to insertion in the flow system the sample was washed 80 81 82 with 38% HC1 to remove the native oxide layer. 2.9 Measurement of etch rates and detection of etch products 2.9.1 Mass spectrometry An EAI 1100A quadrupole mass spectrometer (Electronic Associates 83 Incorporated), which had been modified, was used to detect etch product molecules leaked from the reaction tube. The ions produced by a tungsten-filament electron-impact ionization-source were injected into a quadrupole analyzer which was adjusted for mass-to-charge ratio of the ions of interest. Mass selected ions striking the detector, which was a high current channel electron multiplier, causes a cascade of electrons which results in a current that is amplified by an ammeter (Keithley 410 Micro-Microammeter) and recorded. To increase the sensitivity, the ionizer assembly and channel electron multiplier had been raised 4.7 cm from the base to bring the ionizer within 0.5 cm from the pinhole. The vacuum within the mass spectrometer housing was maintained by a 4 inch water cooled diffusion pump (Varian Model VH-4) backed by a Sargent Welch Duo-Seal Model 1405 rotary pump. Typical pressures in the mass spectrometer ranged from lxlO - 6 Torr with no gas flowing in Figure 2.6 An exploded view of Si sample holde GaAs ^ „ G L A S S „ "SPRING" 7 TC PROBE S i0 2 ^ COVERED EPOXY SILICON PLATE SO the reaction tube to 5x10-5 Torr with a pressure of 4 Torr in the reaction tube, which is the maximum pressure at which the mass spectrometer could be properly operated. 2.9.2 Mass Spectrometer Signal Calibration In order to convert the intensities of the mass spectrometer signals to flow rates of the products in moles/min, a calibration curve of AsCb pressure against signal intensity for either AsCl + or AsCb + was first obtained. The A s C l 2 + signal was not used because of high background peaks in that region of the mass spectrum. The calibration curves were linear and passed through the origin. The intensity of an etch-product peak was divided by the slope of the corresponding calibration curve to convert it to pressure. The pressure of the etch-product was then converted to flow rate by multiplying the flow rate at that given pressure by the AsCh partial pressure divided by the total pressure. Finally the flow rate of the product was converted into an etch rate in units of jim/min by the Eq. 2.8 E.R. = fe(moles/min) * N A * | x 5 * 104 (2.8) where N A is Avogadros' number, S is the surface area of the etched sample in cm2- and D is the density of GaAs = 2.2xl0 2 2 GaAs molecules/cm3. 84 85 2.9.3 HeNe Laser Interferometry A 0.5 mW HeNe C.W. laser beam(632.8nm) was reflected off the wafer surface on to either a photomultiplier tube or a photodiode. Interference between the 633 nm radiation reflected from the stationary masked surface and that reflected from the etching surface produced a sinusoidal intensity as a function of time. Peak to peak distance of the sinusoidal intensity(d) corresponds to half of the wavelength of the laser radiation, (derivation of Eq. 2.9 is in Appendix 3) nX = 2d (6 = 0) (2.9) when the angle between incoming beam and reflected beam(6) is zero. 8 was experimentally set at very close to zero. 2.9.4 Surface Profilometry A sample covered with the silicon nitride mask described in section 2.8 was exposed to fixed C l 2 and/or CI pressures for a known length of time and then the etch depth on the wafer chip was measured relative to the mask height with a Tencor stylus profiler which scans over the sample surface. This method provided the most direct measurement of the etch rate. However it was susceptible to error if the etch rate was not constant or if there was a significant induction period before the etching began. A method of continuously monitoring the etch rate was provided by laser interferometry from which the results were compared with those obtained from surface profilometry. Chapter 3 Result and Kinetic Analysis 3.1 Etching Inhibition by Oxide Layer Great care had to be taken to ensure that the native oxide layer was removed from the wafer surface with the HC1 wash, and did not re-form because of exposure to air. Otherwise, the etching reaction did not occur until the layer was penetrated by Cl atoms or by raising the sample temperature very high. The same phenomenon was discussed by d'Agostino et al. and in their paper. The results of X-ray photoelectron spectroscopy (XPS) and scanning electron microscope (SEM) analysis confirmed the presence of this oxide layer which is mostly composed of A S 2 O 5 and Ga20s. It is possible that a similar surface contamination prevented Sugata et 5 5 al. from observing any etching of GaAs by CI2 below 290°C. 3.2 Formation of a Liquid Layer Novel behavior was observed at temperatures below 70°C when the CI2 pressure was greater than 15 Torr, but later it was found that it occurs even at higher temperatures when the pressure of CI2 was much higher than 15 Torr. This new phenomenon is illustrated in Fig. 3.1 where the profile of the etched (100) GaAs surface between two silicon nitride stripes is shown. For comparison, the surface profile of etched GaAs(lOO) with Pci2 = 0.09 Torr and at 76°C is shown in Fig. 3.2. It can be seen that the etch rate near the stripes is very much greater than it is in the middle of the exposed GaAs area. The etch rate in the middle is consistent with the values obtained at slightly higher temperatures. The etch depth near the edge is anomalously large. The explanation of this accelerated rate became obvious when experiments were performed at 25°C and 20 Torr of Ch. Under these conditions the GaAs was quickly covered with a liquid layer which grew in extent with time until it covered the entire sample. When the liquid was washed away with acetone the etched surface was found to be more irregular than it was in the absence of the liquid layer, and to have been etched an order of magnitude faster than would be expected from measurements at temperatures above 70°C. It is obvious from these observations that the profile illustrated in Fig. 3.1 is a result of the accumulation of this "liquid" in the "corners" next to the silicon nitride mask, and the consequent more rapid etch rate under the liquid. The mixture of ASCI3, GaCb and C l 2 has been shown to produce a compound with the 86 87 formula GaAsCls and the structure [AsCl^GaCU -] ' with a melting point of 5°C. It is quite probable that this is the identity of the liquid 88 which gathers on the GaAs surface. Since an AsCl3(i) + Cl2(g) mixture is known to be a very good chlorinating agent, it could account for the acclerated etch rate which occurs under the liquid. 3.3 Etch Product Analysis As shown in Fig. 3.3 the ions AsCl + , A s C l 2 + , and A s C l 3 + (Intensity ratio = 31:100:49) were observed in the mass spectrometer. The fragmentation pattern of the AsCb produced by etching was the same as that of the standard AsCb used for calibration, strongly suggesting that A S C I 3 is the etch product. This 63 observation is consistent with the conclusions of Balooch et al. that the major products of the C^/GaAs thermal reaction are GaCb and A S C I 3 . We had the same difficulty that Balooch et al. did in detecting 54 Figure 3.1 Profile of etched GaAs(lOO) surface between two silicon nitride masked areas : T = 66°C and Pci2= 15.5 Torr 56 Figure 3.2 Profile of etched GaAs(lOO) surface between two silicon nitride masked areas. T = 76°C and P C i 2 = 0.09 Torr 0 7 Cfl c o o 2- 0.8 o 1.2-J -j— 1 r -2 5 5 0 7 5 Position (Microns) 58 Figure 3.3 Arsenic chloride ions detected by mass spectrometer. T = 91°C and PCi 2 = 0.52 Torr M a s s GaCi3. It is possible that the ionization efficiency of this species is very low and beyond the limit of our instruments. Hui et al. 6 5 have successfully detected GaCh and concluded that it is indeed the principal gallium containing product. It is perhaps worth noting that under ion bombardment which occurs 62 in "plasma etching" systems and in the laser-induced etching 64 systems GaCi2 (possibly GaCl) has been identified as the principal product at temperature above 350 K. However GaCl 2 and GaCl have not been observed in thermal reaction. 3.4 Results of the C l 2 Etching Experiments The first series of quantitative experiments were performed at 91°C to determine the order of the reaction with respect to CI2. The results are shown in Fig. 3.4 and 3.5 which give the etch rate as a function of chlorine pressure. A typical interferogram observed in CI2 etching is shown in Fig. 3.6. Etch rate data from three different techniques (mass spectrometry, laser interferometry, and surface profilometry) which are tabulated in Table 3.1 show good agreement. However, laser interferometry and surface profilometry were preferred because the mass spectrometer could not be operated at a system pressure higher than 4 Torr and because of uncertainties in the conversion of mass spectrometer signals into etch rates. As shown in Fig. 3.4 and 3.5, the reaction clearly displays a saturation effect, i.e. the rate increases with increasing CI2 pressure at low pressures, but becomes independent of C l 2 above 15 Torr. The etch rates at other temperatures are tabulated in Table 3.2. To determine the order of the reaction, ln(etch rate) is plotted against ln(Pci2) and the result is presented in Fig. 3.7. At low pressures the slope, i.e. the order appears to be approaching 1. The actual values determined from the lowest few points at each temperature are listed in Table 3.3. To emphasize the fact that the points can not be fitted to 1/2-order a line with a slope of 1/2 is drawn for each temperature. We conclude from these observations that the reaction approaches first Figure 3.4 The etch rate of GaAs(lOO) by CI2 as a function of the pressure of CI2 (below 16.0 Torr) at 91°C. O : etch rate measured from surface profilometry f j : etch rate measured from HeNe laser interferometry X : etch rate measured from mass spectrometry 62 C E E CD "5 cn o U J Pressure of Chlorine (Torr) 63 Figure 3.5 The etch rate of GaAs(lOO) by Ch as a function of the pressure of C l 2 (above 15.0 Torr) at 91°C. 0 : etch rate measured from surface profilometry • : etch rate measured from HeNe laser interferometry 64 0 2 0 4 0 6 0 8 0 1 0 0 Pressure of Chlorine (Torr) 65 Figure 3.6 A typical interferogram observed in Ch etching P C i 2 = 0.50 Torr, T =. 132°C, and etch rate =1.81 jam/min Intensity of HeNe Laser (ARB units) — — r o c n O c n o O O O O 99 6 7 Table 3.1 List of etch rates of GaAs(lOO) with C l 2 measured by three different techniques at 91°C. technique used pressure of ChCTorr) etch rate (uintoin) surface profilometry 0.09 0.0219 0.40 0.0797 0.42 0.0851 0.72 0.113 0.95 0.152 1.23 0.168 1.48 0.197 3.17 0.274 5.28 0.337 15.55 0.379 51.0 0.447 99.0 0.460 HeNe laser inierfcrometry 0.09 0.0224 0.20 0.0428 0.40 0.0873 0.70 0.0974 0.95 0.176 51.0 0.431 98.0 0.427 mass spectrometry 0.52 0.100 0.97 0.149 1.22 0.161 1.74 0.199 2.07 0.231 2.50 0.250 3.14 0.271 3.54 0.274 69 Table 3.2 List of etch rates of GaAs(lOO) with C l 2 measured at several temperatures. 70 T(°C) pressure of Q 2 (Torr) etch rate (^ lnVmin) 76 0.09 0.25 0.50 0.90 1.27 1.62 2.00 2.33 20.8 0.00491 0.0131 0.0237 0.0393 0.0480 0.0604 0.0719 0.0797 0.169 100 0.20 0.20 0.50 0.50 0.70 0.70 1.03 1.19 5.28 7.07 14.14 0.0742 0.0913 0.180 0.202 0.270 0.244 0.295 0.328 0.560 0.601 0.720 110 0.09 0.09 0.50 0.50 3.17 0.128 0.139 0.582 0.542 0.904 126 142 0.09 0.50 0.50 0.70 0.70 2.41 2.53 3.18 3.32 15.55 0.09 0.16 0.19 0.21 0.24 0.53 0.85 0.90 1.30 20.3 0.341 1.06 1.01 1.33 1.40 1.70 1.85 1.97 1.99 2.19 0.897 1.39 1.77 1.90 1.97 2.61 3.34 3.35 3.48 4.89 7 1 Figure 3.7 A plot of In (etch rate) versus In (Pci2) at several temper-atures The dashed lines are drawn with a slope of 1 at each temperature The dotted-dashed lines have a slope of 0.5 72 Table 3.3 List of values of the slope at low pressures T(°C) slope at low pressure limit 76 0.92 91 0.88 100 0.95 110 0.84 126 0.86 142 0.87 75 order at low pressures and zero order at high pressures. The behavior shown in Fig. 3.4, 3.5 and 3.7 is characteristic of a two step reaction in which the first step has a C l 2 dependence and the second does not. The most general formulation of such a two step mechanism is given by Eq. 3.1 and 3.2, Cl 2 + Sf S c (3.1) K - i S c — p r o d u c t + S f (3.2) where ki, k.i, and k 2 are the etch rate constants which are discussed in detail in Appendix 4 and Sf represents a free surface site which can react with C l 2 to produce a surface-bound intermediate Sc. The subscript c is used to indicate that the site is covered and hence can not react with C l 2 until a product molecule is desorbed to re-expose Sf. Under these circumstances S c + Sf = SQ, where SG is the total number of surface sites available for reaction, and the rate law governing the steady state etch rate (E.R.) of such a surface is given by Eq. 3.3 (derivation of Eq. 3.3 is in Appendix 5 ). E.R.= ( ^ ^ ) P ^ k 2 (3.3) V k . i + k 2 / Pel* + 1 To simplify the expression we write the etch rate constant ratio ki/(k_i + k2) = K s s , a constant governing the steady state concentration of the intermediate Sc. Eq. 3.3 becomes: K s s Pci 2 E R = K s s P c l ^ l k 2 <3'4> or in its "straight line" form _ L _ j _ i i _ E R . - k 2 + K s s k 2 P c i 2 ( 3 ' 5 ) which predicts that a plot of 1/E.R. versus 1/Pci2 should be a straight line with slope = 1/K s sk 2 and intercept l/k 2. Such plots are presented in Fig. 3.8 and 3.9 for the data obtained at several temperatures. The values of k 2 and K s s k 2 extracted from the straight lines are listed in Table 3.4. To determine the activation energies for k 2 and K s s k 2 these -H* /RT constants were assumed to fit the Arrhenius equation (Ae ). The Arrhenius plots for these two constants are given in Fig. 3.10. Because all of our experiments were performed at constant pressures the activation "energy" obtained from the slope of the Arrhenius plot (Fig. 3.10) is an enthalpy whose value differs from the value of commonly quoted activation energy by the amount of nRT i.e. E* = H* + nRT (where n is number of gaseous species which combine to form the transition state). Within experimental error the plots are linear and the straight lines yield the following values for k2 and K s s k 2 : k 2 = 7.9xl0<7 ± 0-5)e-(13.7 ± 1.6)xl(rVRT m m i n - i ( 3 6 ) K s s k 2 = 5.8xl0<13 ± %<24-0 ± 2.8)xl03/RT ^m m i n - i T o r r - i ( 3 7 ) where H* is in units of calories. To assess the compatibility of the assumed mechanism with these values for A and H* we should consider two circumstances under which K s s assumes a simpler form. Case 1: k_i>>k2, i.e. the concentration of the intermediate species S c is determined principally by the equilibrium constant K a = ki/k.i. The rate law then becomes reminiscent of the "Langmuir 89 isotherm" and would be expected to prevail when C l 2 is relatively weakly bound to Sf in step 3.1. Such a mechanism has been proposed 90 91 for the etching of silicon and germanium by bromine. The basic requirement of a "preadsorption" mechanism of this form is that the activation enthalpy of K s s k 2 (now K a k 2 ) be lower than that for k2 by an amount equal to the enthalpy of adsorption of C l 2 on the surface as represented by step 3.1 in the mechanism. For the Cl 2/GaAs reaction this mechanism clearly fails the test since K ak2 has an activation enthalpy 10.3 kcal higher than k2. If instead of being a simple adsorption process reaction 3.1 is a "dissociative adsorption" represented by equation 3.8 Cl 2 + S f = ^ = * 2C1 ( S ) (3.8) K - i the activation enthalpy for K a k 2 can exceed k 2 provided reaction 3.8 is endothermic. If, as would be expected, this is followed by a process which is first order in [C1(S)] the overall order of the reaction with respect to C l 2 would become 1/2. Such behavior has, in fact been observed in the reaction of Br 2 with Si. However, since our results reported in Fig. 3.7 indicate that at low pressure the reaction approaches first order in C l 2 and not 1/2 order this limiting mechanism is unsatisfactory. Case 11: k-i<< k 2 i.e. the back reaction in step 3.1 does not occur at a significant rate. The simplified mechanism can be written by Eq. 3.9 and 3.10, Cl 2 + S f k l > 2C1 ( S ) (3.9) k2 C l ( s ) — • product +S f (3.10) and the rate law becomes (see Appendix 6) E . R . = ^ ^ - (3.ID or in its linear form Comparing equation 3.12 with 3.5 we see that K s sk2 is equal to kj and can thus have a value unrelated to k 2. This mechanism is therefore compatible with our data. Eq. 3.9 and 3.10 are the simplest rate controlling steps which are consistent with our data and chemically reasonable. C1(S) represents individually adsorbed CI atoms on the GaAs surface(Sf). Insofar as either or both reactions are reversible, ki and k 2 would represent "net" reaction rates in the forward direction. We noted above that if the reverse of reaction 3.9 occurs at all it could not be very large relative to the rate of reaction 3.10 because the order of the reaction with respect to the pressure of C l 2 would become 1/2 rather than the observed order which appears to be approaching 1 at low pressures, we estimate the maximum contribution from the back reaction of 3.9 (see Appendix 7) is 3%, which is within the quoted experimental error for these rate constants. Our conclusion is that if there is a back reaction we can not detect it, and, in fact, have evidence that suggests it might not be occurring under our conditions. 79 Figure 3.8 A plot of the reciprocal GaAs etch rate versus the reciprocal pressure of C l 2 at 76, 91, and 100°C. 8 0 1/Chlor?ne Pressure (Torr"1) 8 1 Figure 3.9 A plot of the reciprocal GaAs etch rate versus the reciprocal pressure of CI2 at 126 and 142°C. Table 3.4 Experimental values of k 2 and K s sk2 obtained at several temperatures T k 2 K s s k 2 (°Q (|im/min) ((im/min/Torr) 76 0.19( ± 0.01) 0.055( ± 0.005) 91 0.44( ± 0.03) 0.23( ± 0.02) 100 0.79( ± 0.08) 0.48( ± 0.05) 126 2.2( ± 0.2) 4.4( ± 0.5) 142 4.9( ± 0.5) 13( ± 1.3) 85 Figure 3.10 An Arrhenius plot of k2 (open circles) and K s sk2 (closed circles) 3.5 Results of the CI Atom Etching Experiments Some preliminary experiments were performed by discharging 0.50 Torr of CI2. At temperatures under 70°C the liquid layer described in section 3.2 was observed. To avoid any complications resulting from this liquid layer, most CI atom etching experiments were performed above 90°C. A typical interferogram observed in CI etching is shown in Fig. 3.11. The GaAs etch rates were measured as a function of atomic chlorine pressure (Pel) at five different temperatures (91, 100, 110, 132, and 156°C). These results are presented in Fig. 3.12 and Table 3.5, indicating that the etch rates vary linearly to the pressure of CI. Assuming that the atoms and molecules behave as independent etchants, the etch rates for atoms alone were calculated by subtracting the calculated etch rates for molecules in Table 3.5 from the total etch rates. These corrected atom rates are tabulated and plotted in Table 3.6 and Fig. 3.13, respectively. To test the validity of this assumption, some etching experiments were performed at different pressures of CI2 and the results, which are listed in Table 3.7, were plotted in Fig. 3.14 and compared with those shown in Fig. 3.13. All points fall on the same line. We take this to indicate that chlorine atom and chlorine molecule etch rates are additive. Within experimental error the chlorine atom etch rate appears to observe a simple first order rate law in the pressure and temperature range of our experiments i.e. E.R. = kciPci (3.13) where kci is the etch rate constant for the Cl atom etching (refer to Appendix 4). The overall reaction can be written: Cl(g) + GaAs k c i » GaCl3(g) + AsCl3(g) (3.14) Therefore the slope of each line in Fig. 3.13 and 3.14 determines the value of kci at each temperature. The values of kci calculated from these lines are listed in Table 3.8. An Arrhenius plot of these values of kci is presented in Fig. 3.15 and yields the following Arrhenius equation for kci. kci = 8.7xlf# ± ° - 7 )e-( 9 - 0 ± L2)xltf/RT m m i n - i T o r r - i ( 3 1 5 ) The details of the kinetic mechanism for atom etching will be discussed in section 4.2. 89 Figure 3.11 A typical interferogram observed in Cl atom etching experiment when 0.50 Torr of C l 2 discharged. T = 132°C, Pci = 0.057 Torr, and total etch rate by Cl and C l 2 = 7.50 fim/min v© © 9 1 Table 3.5 Experimental values of total etch rates in Cl etching as a function of the pressure of Cl at several temperatures. All etch rates were measured when 0.50 Torr of C l 2 was discharged. E.R. by Ch™: measured etch rates of molecular chlorine at a pressure of 0.50 Torr (when the discharge was turned off) E.R. by C i2 C : calculated etch rates of molecular chlorine at each temperature by the following equations. 1 1 1 1 at 91°C : = ; T ^ T ~ — + ER. 0.23 P C i 2 0.44 at 100°C : ~r = 7T7^^— + 1 EH. "0.48 Pcu 0.79 a t l l 0 ° C : ^ = ^ l 1 at 132°C : E i t . ~ 1 . 2 P C i 2 1.2 J _ _ L _ 1 ER. "6.5 Pci, + 3.2 at 156°C : E.R. - 3 4 p c l 2 + 8 . 3 T Pa total etch rate E.R-by Cl2m E.R.by C12C (°Q (Torr) (Torr) (umfain) (uxnAnin) (um^ nin) 91 0.47 0.056 1.99 0.103 0.0930 0.47 0.056 1.81 0.44 0.12 4.81 0.0885 0.44 0.12 5.06 0.40 0.20 6.75 0.0821 0.40 0.20 7.00 0.40 0.20 7.06 100 0.47 0.056 2.43 0.180 0.181 0.47 0.056 2.23 0.44 0.12 5.42 0.172 0.44 0.12 5.54 0.40 0.20 8.55 0.160 0.40 0.20 8.47 0.40 0.20 8.22 0.40 0.20 8.63 110 0.47 0.056 3.38 0.431 0.378 0.47 0.056 3.36 0.47 0.056 3.45 0.44 0.12 6.33 0.361 0.44 0.12 5.93 0.40 0.20 11.5 0.337 0.40 0.20 12.1 132 0.47 0.057 7.50 1.81 1.56 0.47 0.057 7.83 1.54 0.47 0.057 6.78 0.44 0.13 16.8 1.51 0.44 0.13 16.2 0.44 0.13 17.3 0.44 0.13 16.5 0.44 0.13 17.3 0.40 0.21 26.4 1.43 0.40 0.21 26.6 0.40 0.21 24.8 0.40 0.21 25.5 0.40 0.21 26.7 0.40 0.21 24.9 156 0.47 0.057 19.0 5.65 5.59 0.44 0.13 35.0 5.16 5.45 0.44 0.13 34.5 0.44 0.13 33.2 0.44 0.13 35.3 93 Figure 3.12 The total etch rate of GaAs(lOO) by C l 2 and CI as a function of the pressure of CI at temperatures of 91, 100, 110, 132, and 156°C. All etch rates were measured when 0.50 Torr of C l 2 was discharged. The closed circles represent the averages of several experiments 94 Pressure of CI Atom (Torr) 95 Table 3.6 Values of corrected etch rates in CI etching as a function of the pressure of CI at several temperatures k: obtained from a least squares fit of total etch rates kci: obtained from a least squarea fit of corrected etch rates corrected E.R. for CI = total E.R. - calculated E.R. for C l 2 • to o 3 3 H ooooo • • • • « oooooooooooooo o o o o o o o 4k 4k 4k 4k 4k 4k 4k 0 0 4 k 4 k < J ^ l ^ O O O O O O O O *4k 4k 4k 4k 4k *4> 4k 4k ooooooo *4k 4k 4k *4k *4k 4k 4k O O O 4k 4k «J <vl oooop »-»i-* »-••-* Q oooooooooooooo b t o t o b f c j M U U U U U b b b -vl *>4 O O O O O O O K > i s > L . i - b b b OS ON ON O O O O O O O O . O O O O W M W * 0\ Ch O O O O O O O • • • • • • • K>K>tOi—>—OO ChCh 9 M M M M M M M M M M M « A » U ) • • • • • • • • • • • f^ * i># tAW>»*4fcfc>>OOOOOO^IU>K>«J4k - * - - • • • • • . ru«o<oo ooeooooou«u»K>io • • • • • • • • 4 k O O > O J U > K > O M Ch Ch Ch 4*. 4k «~ OO K> -«J to N> O ^ m I 90 B & 224(123) 116(110) f f 42(14) H-I 224(123) 118(110) •—s H-Ol w 42(14) f f 1 f I 97 Figure 3.13 The corrected etch rate of GaAs(lOO) by Cl as a function of the pressure of Cl at temperatures of 91, 100, 110, 132, and 156°C. All etch rates were obtained when 0.50 Torr of C l 2 was discharged. corrected E.R. for Cl = total E.R. - calculated E.R. for CI2 The closed circles represent the averages of several experiments 98 I56°C Pressure of Cl Atom (Torr) 99 Table 3.7 Values of corrected etch rates in Cl etching as a function the pressure of Cl for three different total pressures (0.20, 0.50, and 2.55 Torr) at 91 andl32°C. k: obtained from a least squares fit of total etch rates kci: obtained from a least squarea fit of corrected etch rates corrected E.R. for Cl= total E.R. - calculated E.R. for C l 2 100 T CQ (Torr) Pel CTonr) E.R.(corr.) (Hmfain) k (umAnhvTorr) (umAnia/ToTT) 91 0.16 0.16 0.072 0.072 2.56 2.33 34(±5) 34(15) 91 0.47 0.47 0.44 0.44 0.40 0.40 0.40 0.056 0.056 0.12 0.12 0.20 0.20 0.20 1.90 1.72 4.72 4.97 6.67 6.92 6.98 34(±3) 34(13) 91 2.50 2.50 2.46 2.46 2.46 0.11 0.11 0.19 0.19 0.19 3.28 3.65 6.21 6.17 6.32 33(±4) 33(14) 132 0.17 0.17 0.064 0.064 7.11 7.45 116(±16) 114(116) 132 0.47 0.47 0.47 0.44 0.44 0.44 0.44 0.44 0.40 0.40 0.40 0.40 0.40 0.40 0.057 0.057 0.057 0.13 0.13 0.13 0.13 0.13 0.21 0.21 0.21 0.21 0.21 0.21 5.94 6.27 5.22 15.3 14.7 15.8 15.0 15.8 25.0 25.2 23.4 24.1 25.3 23.5 116C± 10) 118(110) 132 2.49 2.49 2.45 0.12 0.12 0.21 12.9 13.2 24.3 115(116) 115(116) 101 Figure 3.14 The corrected etch rate of GaAs(lOO) by Cl as a function of the pressure of Cl at temperatures 91 and 132°C. ||:etch rate measured when 0.20 Torr of Ch was discharged O e^tch rate measured when 0.50 Torr of Ch was discharged J^:etch rate measured when 2.55 Torr of Ch was discharged 102 i 1 1 r 0.00 0.05 0.10 0.15 0.20 0.25 Pressure of Cl Atom (Torr) 103 Table 3.8 The values of kci at different total pressures (0.20, 0.50, 2.55 Torr) and several temperatures 104 T P d 2 discharged (°C) (Torr) (^m/min/Torr) 91 0.20 34( ± 5) 0.50 34( ± 3) 2.55 33( ± 4) 100 0.50 42( ± 4) 110 0.50 57( ± 5) 132 0.20 114( ± 16) 0.50 118( ± 10) 2.55 115( ± 16) 156 0.50 224( ± 23) Figure 3.15 A n Arrhenius plot of kci 106 3.6 Crystallographic Etching and Surface Morphology The etching of GaAs(lOO) by both atomic and molecular chlorine displays very clear crystallographic effects. Fig. 3.16(a) and 3.17(a) show top views of the Si 3 N4 striped masks oriented to the [Oil] and [Oil] directions. Fig. 3.16(b)and 3.16(c) show SEM photographs of the cross sections of channels etched by CI2, while Fig. 3.17(b) and 3.17(c) show those resulting from Cl atom etching. A mesa with inward sloping walls shown in Fig. 3.16(b) and 3.17(b) was obtained with the mask stripes parallel to the [Oil] direction and a mesa with outward sloping walls shown in Fig. 3.16(c) and 3.17(c) was obtained with the mask stripes parallel to the [Oil] direction in both C l 2 and Cl etching processes. Both the inward sloping planes and the outward sloping planes which form are {111}A planes indicating that the etching proceeds rapidly until it reaches {111}A planes. These two types of sloping planes are formed when the etch rates on the {111 }B, {110} and {100} planes are much faster than the {111}A planes. This was verified by experiments with some GaAs{ll l}A and GaAs{lll}B faced chips. 6 cm2 of unpolished (111) GaAs was obtained from Dr. F. Weinberg. This (111) GaAs piece was first chemically polished in a B r 2 / C H 3 O H mixture and then mechanically polished by a polishing wheel with Alumina powder whose size was progressively varied between 2 and 0.06 |um. A dot of Ga was used as a mask and removed after etching for Tencor surface profilometry. At T = 126°C and the pressure of CI2 = 0.50 Torr, the measured etch rates of {lll}AGaAs and {HlJeGaAs is 0.0294 |um/min and 1.65 fim/min, respectively, while the measured etch rates with a Cl atom pressure = 0.21 Torr are 12.7 |um/min and 20.6 |am/min, respectively. Because of the limited amount of sample 92 further experiments could not be performed. MacFadyen explained the difference in etch rates between {111}A and {111 }B planes on the basis that the removal of the triply bonded surface atom is rate controlling and this atom is different on these two surfaces. Similar 93 crystallographic etching was observed in wet Br/CH 3OH and H 2 S O 4 -92 55 H 2 O 2 - H 2 O systems and chlorine plasma etching systems. In the temperature range from 75°C to 150°C the surface morphology after etching was rough, with a surface variation of about 3 to 4% of the etch depth after C l 2 etching and 6 to 8 % after Cl etching. These variations could occur in distances less than 1 jam across the wafer. Etching by CI2 at temperature above 160°C produced shiny surfaces but no great change in the % surface height variation given above. It would appear, therefore that the "shine" is due to surface regularities at a dimension below that which the 54 profilometer samples. Donnelly et al. reported a change from rough to smooth at 125°C in a CI2 plasma. It is not clear how they judged the surface morphology. 3.7 On the Significance of Dislocations An important but unanswered question is the effect of dislocations (line defects) on the etch rates. Certainly, in the etching of {111} faces triangular pits develop due to dislocations and this can 94 be detected by a carefully chosen etchant . However, {111} faces usually have only one dangling bond and are very unreactive. It is not clear whether etching is more rapid at such defects on a (100) face since this face has 2 dangling bonds and is intrinsically much more reactive. According to Johnson and Matthey the dislocation level varies by a factor of 5 across the wafer. However we did not observe any variation in etch rates for samples cut from different regions of the wafer. Furthermore we could not detect a measurable difference in the etch rate for a Si doped GaAs sample (doping concentration is 2 x 10 cm" ) which the supplier informs us has a dislocation density which is an order of magnitude higher than the undoped sample. We are therefore led to conclude that dislocations do not appear to affect the bulk etch rates of GaAs(lOO) that we report in this thesis. The average value of dislocation density quoted by Johnson and Matthey in fact corresponds to only about 1 dislocation for 40 (im in any direction across the wafer, a much larger scale than that of the observed surface roughness after etching, which is therefore probably not dislocation-related. 109 Figure 3.16 A top view of schematic diagram of Si3N4 mask pattern (a) and SEM photographs of channels etched in the (100) plane of GaAs by Ch. Etching conditions: (b) total etch time = 3.02 min., pressure of Ch = 2.57 Torr, and T= 91°C (c) total etch time = 14.2 min., pressure of Ch = 0.72 Torr, and T = 91°C 110 I l l Figure 3.17 A top view of schematic diagram of S13N4 mask pattern (a) and SEM photographs of channels etched in the (100) plane of GaAs by CI and CI2. Etching conditions : (b) pressure of CI2 = 0.44 Torr, pressure of CI = 0.13 Torr, T = 132°C, and total etch depth = 7.70 Jim (c) pressure of CI2 = 0.40 Torr, pressure of CI = 0.20 Torr, T = 91°C, and total etch depth = 2.30 pm 112 Chapter 4 Discussion and Error Analysis 4.1 The C l 2 Reaction 4.1.1 The "Low Pressure Rate Constant" ki The value of the activation enthalpy for ki (24.0 kcal), which is 95 approximately half of the bond energy of Cl-Cl (58 kcal), and the first order dependence of the etch rates on the pressure of C l 2 lead us to propose that the rate controlling step is the dissociative adsorption of CI2 on the "surface (Sf)" as previously represented by Eq. 4.1. Cl 2 + S f k l » 2C1 ( S ) (4.1) with k! = 5.8 x 10<13 ± %< 2 4 - 0 ± 2.8)xl03/RT M m m i n - i T o r r - l A step which is similar to reaction 4.1 was proposed by Eyring and 96 97 Laidler for the interaction of H2 on tungsten. Kondratiev estimated the activation energy for the C l 2 adsorption reaction from 98 the rate of heterogeneous generation of chlorine atoms on glass. The value of 25 kcal which Kondratiev estimated is close to the value 99 of -20 kcal reported for this reaction on a Pyrex vessel. These estimated and observed activation energies are within experimental error of the activation enthalpy for ki (24.0 kcal) observed in this study. It is therefore not unreasonable to propose that reaction 4.1 is the rate determining step at low pressure. However this reaction could be energetically endothermic, neutral or exothermic process depending on the strength of the bond which the Cl atoms make to the surface. The nature of Sf and C1(S) will be considered in more detail in section 4.3. 4.1.2 The "High Pressure Limiting Rate Constant" k 2 In view of the magnitude of the activation enthalpy for k 2 (14.2 kcal) the rate limiting reaction at high pressures could be the desorption of GaCh which is the less volatile product of the GaAs/Cl 2 reaction. The heat of vaporization of GaCl3(l) (as the dimer Ga2CLj) is 11.4 kcal mole-!100 and the heat of sublimation of GaCl3(s) is 17 kcal mole1- As mentioned in section 1.5 Donnelly et al . 5 4 rejected the possibility of a rate controlling product-desorption step because the evaporation rate of GaCl3(l) which they calculated was several orders of magnitude larger than the observed etch rate. To see whether the agreement is better if a heat of "vaporization" of 14.2 kcal (i.e. the activation enthalpy for k2) is used, we repeated the calculation. It should be noted however that the equilibrium vapor is actually the dimer (Ga2Cl6) and the calculation therefore determines the Ga2Cl6 evaporation rate. The evaporation rate of GaCb can be calculated by where R e is the rate of evaporation, P* is the equilibrium vapor pressure of the gas over the solid, a is the evaporation coefficient, M is the mass of the molecule and other symbols have their usual significance. The vapor pressure of GaCb can be calculated from the Clausius-Clapeyron equation103 Langmuir's expression. 102 (4.2) P*(T) = Cexp(-AH/RT) (4.3) where C is a constant of integration. A value of 1.4 x 10 Torr is used for C. This is the value for the GaCb dimer because no information is available for the monomer. Substituting for A H with the activation enthalpy (14.2 kcal) which we obtained, P* for GaCl 3 is 0.42 Torr at 91°C. Assuming the evaporation coefficient (a) is 1 104 which is typically between 0.1 and 1 , at this temperature Eq. 4.2 predicts a maximum GaCb removal rate 0.045 g crabs'1, which corresponds to an etch rate of 4244 |Lim/min for GaAs. This calculated evaporation rate is more than 104 times bigger than the observed etch rate with C l 2 (0.39 jum/min at 91°C). Even with the larger activation enthalpy assumed in these calculations we are forced to the same conclusion as Donnelly et al.. It is difficult to see how GaCl3 desorption can be rate controlling in this system. Nevertheless 63 Balooch et al. , in their more recent modulated beam study of this reaction, interpreted their results to indicate that a "gallium-chloride rich" scale exists on the surface and that removal of this scale limits the etch rate. Balooch et al. assumed that this scale was GaCl3(S) in order to account for the ion enhance rates which they observed. Ameen and Mayer105calculated a binding energy of 16.1 kcal for GaCb on GaAs(100) surface in their investigation of ion-assisted GaAs(100) etching by Cl 2 . In their work the GaCl 3 was the observed gallium containing etch product and its binding energy was obtained from fitting the waveform of the GaCl 2 + signal from their time-of-flight mass spectrometer. However they also found a value of 23 kcal for the binding energy of AsCb to the surface. This is inconsistent with the observation of Balooch et al. who observed rapid surface loss of AsCb and a formation of a GaCl3 scale on the surface. It is also inconsistent with a smaller value of 7 kcal for the binding energy of AsCb reported by O'Brien et al . . 1 0 6 Although the results of the molecular beam studies described above are consistent with a GaCh species adsorbed on the surface they do not prove that such a species actually exists on the surface during the etching process. These workers were led to this conclusion because an acceleration of the etching by ions is most easily explained if the ions desorb a product thus freeing the surface for further reaction. They prefer to ignore the effect that ion bombardment has on the surface concentrations of the etchant, because such interaction could affect the etching in very complex ways. However, it is possible, and in fact quite probable, that the ion bombardment affects the reactivity of the etchant with the surface. Therefore there remains the possibility that the interpretation of the molecular beam experiments in terms of product desorption is incorrect. The ions could well be acclerating the reactions of intermediate on the surface to produce volatile products. An alternative interpretation of k 2 is that this rate limiting step at high pressures is associated with the reaction of the surface adsorbed intermediate (C1(S)) formed in equation 4.1. This rate limiting step could be the reaction which forms either 54 GaCb or AsCb. However the evidence from Auger analysis and from molecular beam experiments63'64 indicates that the reacting surface is gallium rich i.e. the rate controlling step is the removal of the Ga layer on a (100) surface. This is consistent with our observations that the (111)R face is more reactive than the (111)A face (see section 3.6). In order to satisfy the kinetic requirements the reaction is written: C l ( s ) k l » GaCl3(g) + S f (4.4) with k 2 = 1.5 x 10(8 ± 0.6)e-(14.2 ± 1.7)xl03/RT ^ m m i p - i The reaction may of course occur in several steps with only the one that is 1st order in C1(S) rate controlling. 4.2 The Cl Atom Reaction A very significant observation from our Cl-atom studies is that the etch rate can exceed the high pressure limiting rate measured for the CI2 reaction at any given temperature. For example at 91 °C the limiting high pressure rate is 0.39 |um/min with CI2. With CI atoms an etch rate of 7 jam/min is measured at the same temperature when Pci2 is only 0.40 Torr. This observation provides a strong argument against the identification of the rate limiting step at high pressures (k2) with product desorption in the CI2 reaction. It might be argued that perhaps CI atoms can accelerate the desorption of the product. A similar mechanism was proposed by Flamm and Donnelly6'1 0 7 for the desorption of the etch product S1F2 in the Si + F reaction. Si s r _r F K t o , (4.5) sr Si b u l k si si / \ / \ / \ / \ According to their mechanism, the reaction of an F atom with the Si-Si bond results in breaking the bonds and producing SiF2(g). They 108 claimed that the mechanism is supported by both ESCA and g infrared emission studies which show that there remains a fluorinated silicon surface after Si is etched in a fluorine plasma. In an analogous manner the CI atom can assist the desorption of GaCb as shown in reaction 4.6. CI GaCl3(g) + ASL (4.6) The kinetic consequences of the occurrence of reaction 4.6 would be (a) a lack of additivity of the CI and CI2 etch rates and (b) a higher order dependences on Pci for the reaction under some conditions. Neither was observed in our experiments. 118 A less contrived explanation is possible if, as proposed in the last section, k 2 is identified with the reaction of an adsorbed chlorine atom to form an easily volatilized product. This reinforces our earlier conclusion that the C l 2 etching reaction contains the following two steps C l 2 + S f k l > 2C1 ( S ) (4.1) with k! = 5.8 x 10< 1 3 ± V 2 4 0 ± 2.8)xl0 3/RT | U m m i n - i T o r r - l C l ( s ) k 2 > G a C l 3 ( g ) + S f (4.4) with k 2 = 7.9 x 10<7 ± 0.5)c-(13.7 ± 1.6)xl0 3/RT ^ m i n - i while the only step which we can observe in the C l atom etching is Cl(g) + Ga surface ^ GaCl 3 (g) (4.7) kci = 8.7xl0( 6 ± ° - 7 ) e - ( 9 0 ± 1.2)xlO?/RT ^ m m i n - i T o r r - i In view of the difference in activation enthalpy between 4.4 and 4.7 reaction 4.7 is probably occurr ing through a E l e y - R i d e a l mechanism (i.e. without prior adsorption). T o determine what fraction of the collisions of the C l atoms with the surface results in reaction it is useful to calculate a quantity called the sticking coeffcient. This quantity is defined as the ratio of the rate of reaction to the rate of impingement Ri . The rate of impingement is calculated by the Hertz-Knudson equation. 1 1 0 Ri = / ? (4.8) V27rmkT 119 where P and m are the pressure and mass of the atom or molecule and k is the Boltzman constant. At 100°C and P C i = 0.056 Torr, R{ = 1.7xl019 atoms cm"2 s"1. The experimental etch rate at this temperature and pressure is 2.2 |Lim/min. Converting this to the same units as Ri we obtain 8.0xl016 atoms cm"2 s"1. Dividing this by the impingement rate Ri yields a sticking coefficient of 4.7xl0"3. The sticking coefficient for the Cl/GaAs reaction increases to 0.023 at 156°C. These are not unreasonable values for gas-solid reactions. 4.3 The Complete Mechanism The arguments presented in the last two sections lead us to propose the following complete mechanism for the combined atomic and molecular reactions with GaAs. From the magnitude of the preexponential and the activation enthalpy of ki ( it is not clear how many steps reaction 3.1 involves. However it is possible that the rate-controlling reaction is preceded by a step in which rapid partial chlorination occurs to satisfy the "free valencies" of Ga and As without breaking the bonds which hold these atoms to the surface. Such a step has been proposed by Repinski and coworkers in their studies of the halogenation of group 90,91 IV semiconductors. ' According to their ellipsometric data this step is fast and irreversible. Although we have no direct evidence for such a process, we include it in the following complete mechanisms. C l 2 + Ga surface rapid» (Ga-Cl x ) ( s ) (4.9) Since there are two dangling bonds on each Ga atom one might expect that this rapid surface chlorination process adds two Cl atoms to each Ga-site. However, as can be seen in Fig. 1.6(d), two dangling bonds point to a site that is normally occupied by a single As atom and there is not sufficient space to accomodate two chlorine atoms. Consequently, unless there is some rotation of these bond directions (due to d-orbital involvement?), only one CI atom can be associated with each surface Ga atom. Since this question can not be answered unequivocally we write the surface halide formed in equation 4.9 as (Ga-Clx)(S) where x is probably between 1 and 2. This process is followed by the steps represented below. Cl 2 + (Ga-Cl x) ( s ) ^ 2C1 ( S ) (4.10) C l ( s ) — - GaCl3(g) + (Ga-Cl x) ( s ) (4.11) Cl(g) + Ga surface ^ GaCl3(g) (4.7) Assuming a steady state for C1(S) and [Ga surface] = [(Ga-Clx)(S)] + [C1(S)L which is equivalent to S c = Sf + S c used in section 3.4, the rate law resulting from this mechanism becomes (derivation of Eq. 4.12 is in Appendix 8) k i p c i 2 E.R. = r  2— + kciPci (4.12) When there are no CI atoms present equation 4.12 becomes the same as equation 3.9 which we showed was consistent with our results for etching by C l 2 alone. E H . . . k ' P c ' 2 (3.9) At low C l 2 pressures i.e. where kiPci2 << k2> equation 4.12 reduces to E.R. = kiPCi 2 + kciPci (4.13) At high C l 2 pressures i.e. where kiPci2 >> k2, equation 4.12 becomes E.R. = k2 + kciPci (4.14) In equations 4.12, 4.13, and 4.14 the etching by Cl and C l 2 are simply additive and hence consistent with our experimental results. This is not the case if product desorption is the rate limiting step. 4.4 Conclusion The etching of the (100) face of a GaAs crystal by atomic and molecular chlorine has been studied over the pressure range from 0.09 to 99.0 Torr and the temperature range from 25°C to 160°C. The reaction with C l 2 was found to obey the complex rate law: kiPci 2 Etch Rate = r — (3.9) ^ + 1 The rate controlling reactions proposed to explain this rate law were the following: C l 2 + (Ga-CLJ ( B ) 2C1 (S ) (4.10) C l ( s ) — — * GaCl3(g) + (Ga-Cl x) ( s ) (4.11) where, for the rate controlling reaction at low pressures (Eq. 4.10), ki = 5.8 x 10<13 ± V 2 4 - 0 1 2.8)xl03/RT m m i n - i T o r r - l and for the rate controlling reaction at high pressures (Eq. 4.11), k2 = 7.9 x 10(7 ± 0.5)e-(13.7 ± 1.6)xl03/RT m m i n - l The reaction of chlorine atoms was found to obey the first order rate law: Etch Rate = kciPci (3.10) with kci = 8.7xl0(6 ± 0-7)e-(9.0 ± 1.2)xl03/RT ^ m i n - i T o r r - i These fundamental rate parameters have not previously been determined. 4.5 Error Analysis The error limits of the etch rate constants for CI and C l 2 etching which are shown in Table 3.8 and 3.4, respectively, were estimated as follows. (1) Uncertainty in etch rate : The errors in etch rates calculated from mass spectrometric data were in the measured C l 2 flows (2-3%), the pressures of C l 2 and standard ASCI3 (3-4%), and the surface area of the GaAs sample (8-10%). The sum of all these errors ranged from 13 to 17%. Surface roughness was the major error source in etch rates measured by surface profilometry. The error in surface roughness which was estimated from the maximum range of values of this quantity was 4% in CI2 etching and 8% in CI etching. The maximum errors in the measured CI2 pressures and flows were 3 and 2%, respectively, and the uncertainty in the measured temperatures was ± 1°C in this study. (2) Error from data scattering : Because the etch rate constant was obtained from a least squares analysis of data points, the magnitude of data scattering was calculated from the confidence limit of the etch rate constant(obtained from the slope of the fitted line) with 90% probability. (3) Uncertainty in the pressure of CI atoms : The error in Pci was calculated by a standard propagation of errors method using errors in the fluctuation of glow intensity during the titration (2%), the pressure of NOC1 at the end point (7-8%), and the measured flows (2%). The error resulting from the correction of the chlorine atom pressure along the tube (3%) was also included by estimating the uncertainties in the values of kr and k w used for calculation. The largest error came from the error in measuring the pressure of NOC1 at the end point. The upper limit obtained by summing all these errors was 15%. The error limits for the activation enthalpy and the pre-exponential which are shown in equation 3.6, 3.7, and 3.12 were estimated from the errors in the etch rate constants and uncertainties in the measured temperatures described above. Fig. 4.1 which is an Arrhenius plot for kci for the Cl-atom etching shows the error bars for ln(etch rate) and 1/T. From the maximum and minimum slope fitted with these error bars, the errors in the slope (i.e. activation enthalpy) and in the intercept (i.e. pre-exponential) were estimated. 124 Figure 4.1 Errors in In kci and 1/T The dotted lines show the minimum and maximum slope fitted by these error bars. 1 2 5 126 Appendix 1 Circuit diagram of cadmium sulfide photodetector r. + photocell amplitude set 10 K + to chart recorder 1.5 V Appendix 2 Procedure for silicon nitride mask deposition (1) A wafer was degreased and cleaned in hot trichloroethylene, aceton, and isopropyl alcohol. ( for 10 minutes in each solution) (2) Si3N4 plasma was deposited on the wafer under the following conditiond: S1H4 flow = 380 seem, N H 3 flow = 42.5 seem, H 2 flow = 500 seem, temperature = 300°C, RF power = 100 watts, deposition time = 2.5 minutes. (3) The wafer was patterned with a photoresist by the following procedures. a, . Photoresist (Shipley's 1400-30 photoresist) was spin-deposited on the wafer with the speed 4700 rpm for 35 seconds. b. The deposited photoresist was baked at 95°C for 25 minutes. CL The photoresist was exposed to UV light(Hg vapour, 320 nm) for 27 seconds with a stripe-shape mask on. d. The photoresist was baked at 95°C for 25 minutes again. e. The pattern was developed in 50 % MF-312 developer. (4) Si3N4 layer unpatterned was etched with bufferred HF solution (mixture of 28 ml HF, 170 ml H 2 0 , and 113 g NH 4F) and then the wafer was rinsed with D.I. water. (5) The residual photoresist was removed with aceton, then the wafer was rinsed with hot aceton and isopropyl alcohol several times and finally N 2 blow-dried. 1 2 8 Appendix 3 Derivation of equation 2.9 HeNe Laser | GtAs The difference in optical path (L) L = (AB + BC) - AD = (AB + BC) - 2ABsin28 = 2AB(1 - sin29) s 2dcos6 for constructive interference nX « 2dcos9 (n = 1,2,3 ) when 8 = 0 nX«2d Appendix 4 Kinetic analysis of experimental data for heterogeneous reactions The kinetics of reactions which occur in a single phase are treated in a number of standard text books. The same can not be said for heterogeneous reaction, especially those involving gas-solid processes. The following discussion is therefore an attempt to establish a fundamental set of equations and units which will not only be correct but convenient and practical for experimentalists. Consider first a unimolecualr reaction of a surface species S Q producing a gaseous product P(g) represented by equation A4.1 S 0 k a * P(g) (A4.1) The rate law for such an elementary step is given by = ka'So (A4.2) where the dP(g)/dt is the rate of formation of product P(g) in units of "number of species" per unit time. Chemists would normally write the units of dP(g)/dt as molecules sec"1 (physicists often normally suppress the "molecules" and write the units as s"1). In the field of semiconductor etching the most convenient and universally used unit is the minute"1. From a practical point of view we are more interested in the depth of an etch rate i.e. the rate at which the etching is occuring over a specific area. Such a specific rate can be obtained by dividing both sides by the surface area S in units of cm2 and by the atom or molecule density in the solid D in units of molecules (or atoms) cm"3. The left hand side then becomes equal to the etch rate in units of cm sec'^or \xm min"1 which is more commonly used unit in the field of semiconductor etching) c p ( c m \ _ dP(g)/dt/ (molec/sec) \ • ' " SD V(cm2Xmolec/cm3)' _ J k a £ o / (sec-^Cmolec) \ _ ~ SD V(cm2)(molec/cm 3)/ " K a K M ' 3 ) where S Q / S (molec/cm2) is a constant for a given face of a given solid which is referred to as the number density of sites on the surface with notation D s (6.3xl014 molec/cm2 for the (100) face of GaAs) and D is the molecular (or atomic) density of the solid (2.2xl0 2 2 molec/cm3 for GaAs). We then can incorporate this (ka'S0/SD) with ka' to yield an "etch rate constant" ka with units of cm sec"1 or jam min"1 for convenience. Since a true first order reaction rate constant should have units of time"1 we will refer to the rate constants with units of jLim min"1 as "etch rate constants" to differentiate them from "reaction rate constants". Similarily for a second order reaction e.g. Cl2(g) + S c k b > products (A4.4) we will use an etch rate constant with units of pm min-1 Torr 1 . This is related to the conventional reaction rate constant with units of min"1 Torr"1 through equation A4.5 ^ J ^ f c v s ) ( M 5 ) for the reasons discussed early in the case of a first order reaction. 131 Appendix 5 Steady state analysis of the Cl2/GaAs reaction (3.1 and 3.2) mechanism If the reaction consists of the following elementary steps (where Sf, Sc, and SG are defined in section 3.4 and ki^min"1 Torr"1), k-iXmin"1 Torr"1), and k2,(min"1) are conventional reaction rate constants) Cl 2 + S f S c (A5.1) K - i S c — p r o d u c t + S f (A5.2) The rate of formation of the product is given by A J S ^ = VS< (A5.3) Assuming a steady state for Sc, then ^ = ki'PcfeSf - k.!'Sc - k2'Sc - 0 (A5.4) If Sf = S 0 - S c (for reasons discussed on page 75), then equation A5.4 becomes ^ = ki'Pc^So - Sc) - k_i'Sc - k2'Sc * 0 (A5.5) Therefore S c is given by ki'P C i 2 S 0 ^"ki 'Pc ia + k.i" +k2' (A5.6) 132 Substituting for S c in equation A5.3 with equation A5.6 the rate of product formation becomes d[product] k 2'ki'Pci 2S 0 {AJ. I) dt k!'Pci 2 + k.j 1 +k2' As shown in Appendix 4 for convenience the etch rate (E.R.) is defined as B * ^ ^ (A5.8, where S0/S is number density of sites on the surface and D is density of the solid. The units of etch rate are etch depth/time. We have chosen these to be |um/min for convenience and for confirmity with current usage in plasma etching. For reasons discussed in Appendix 4 the corresponding rate constants (without primes) have the additional unit of depth (|im) and will be called "etch rate constants" to differentiate them from the more conventional "reaction rate constants". Eq. A5.7 then becomes Eq. A5.9 k 2 k i P C i 2 E.R. = 7—z ^ , ' . (A5.9) kiPci , + k_i +k2 Dividing the numerator and denominator of Eq. A5.9 by l/(k_i + k2) yields Eq. 3.3 E R = _ k r M ^ k 2 (33) Appendix 6 Steady state analysis of the Cl2/GaAs reaction (3.9 and 3.10) mechanism If the reaction consists of the following elementary steps (where Sf and C1(S) are defined in section 3.4 and ki' (min"1 Torr"1) and k2' (min"1) are conventional reaction rate constants) Cl 2 + S f k l ' 2C1 {S ) (A6.1) C l ( s ) ** product +S f (A6.2) The rate of formation of the product is given by = k 2 ' [Cl ( s ) ] (A6.3) Assuming a steady state for C1(S), then = 2k1'Pci2Sf - k2'[Cl(s)] - 0 (A6.4) If Sf = S 0 - [C1(S)] (for reasons discussed on page 75), then equation A6.4 becomes = 2k1 ,Pci2S0 - 2ki'Pci2[Cl(s)] - k2'[C\(s)] - 0 (A6.5) Therefore [C1(S)] is given by 2 k i ' P c i 2 S 0 W = 2 k l ' P c i / + k 7 ( A 6 6 ) Substituting for [C1(S)] in A6.3 with Eq. A6.6 the rate of the product formation becomes 134 d[product] _ 2k2'ki'Pci2S0 dt ^ k V P c u + kz' ( A 6 , 7 ) For the reasons described in Appendix 4 we define "etch rate" (in units of |um min"1) by E.R. ( A 6 . 8 ) where S = surface area and D = solid density. Etch rate constants (unprimed) are then related to the reaction rate constants (primed) by the relationships: k! = ^ a n d k 2 = ^ (A8.10) where SG/S is number density of sites on the surface. The additional factor of 2 in k! arises from the stoichiometric relationship between reaction sites and product molecules in equations A6.1 and A6.2. Eq. A6.7 then becomes k 2 k i P C i 2 E.R. = — -\r (A6.10) k i P C i 2 + k 2 Dividing the numerator and denominator of Eq. A6.10 by k 2 yields Eq. 3.11 135 Appendix 7 Estimating upper limit for reverse reaction 3.9 In order to estimate the possible contribution of the reverse reaction in the dissociation adsorption of C l 2 on the GaAs which is represented by the following mechanism (where Sf and C1(S) are defined in section 3.4 and ki', k_i', and k2' are conventional reaction rate constants) k ' Cl 2 + S f T - ^ 7 » 2C1 ( S ) (A7.1) C l ( s ) product +S f (A7.2) we first assumed the steady state for C1(S) = 2k1'Pci2Sf - 2k.i'[Cl ( s )]2 - k2'[Cl(s)] - 0 (A7.3) If Sf = S 0 - [C1(S)] (for reasons discussed on page 75), then equation A7.3 becomes 2k1'Pci2(S0 - [Cl(s)])- 2k.1'[Cl ( s )]2 - k 2 ,[Cl ( s )] « 0 (A7.4) If the fraction of the reverse reaction contribution (F) is defined by Eq (A7.5) F . ( A 7 . 5 ) Eq. A7.4 can be transformed to Eq. A7.6 k2'[Cl ( s )](l + F) + 2k1'PCi2[Cl (s )] = 2k1 ,Pci2S0 (A7.6) or solving for [C1(S)] is represented by Eq. A7.7 136 2krP Ci 2S 0 [Cl(s)]= k 2 . ( 1 + F ) + 2 k 1 ' P C i 2 ( A 7 - 7 ) For the reasons described in Appendix 4 and 6 etch rate constants (unprimed) are related to the reaction rate constants (primed) by the relationships: 2ki'S0 MSo ,A_B, ki = S D and k2 = S D (A7.8) where SQ/S is the number density of sites on the surface and D is the solid density. Eq. A7.8 then becomes W k 2 ( l ^ k . P c u <A7-9> or in its linear form ( A 7 , 0 ) k 2[Cl ( s )] k i P C i 2 k 2 Substituting with F = k_i[Cl(S)]/k2 and E.R. = k2[Cl(S)] equation A7.10 becomes Eq. A7. l l 1 f 1 k ^ 1 1 ER \ k i k i k 2 2 / P c i 2 k 2 v ' Eq. A7. l l can be rearranged into a different linear equation ( l k - k l ) P < * =r: + ^ E . R . (A7.12) k i k ! k 2 2 A plot of the left hand side (L.H.S.) of Eq. A7.12 against E.R. yields slope (k.j/kik22) which is related to F by the equation F " fe)kI E R ( A 7 1 3 ) Using a value of 0.17 pm min for the maximum etch rate measured and values of k 2 = 0.19 (see Table 3.4) and 0.20 (i.e. the maximum value of k 2 in the quoted error range) we obtain values of F = 0 and 0.03 respectively.at 76°C. This indicates a maximum contribution from the back reaction equal to 3% of k 2 which is well within the experimental error for the measurements. 138 Appendix 8 Steady state analysis of the combined Cl/Cl 2/GaAs reaction mechanism If the reaction consists of the following elementary steps (where (Ga-Clx)(S) and C1(S) are defined in section 4.1, 4.2, and 4.3 and ki^min"1 Torr"1), k^Xmin"1), and kciXmin"1 Torr"1) are conventional reaction rate constants) C l 2 + (Ga-Cl x) ( s ) k l ' » 2C1 ( S ) (A8.1) C l ( s ) * GaCl3(g) + (Ga-Clx) ( s ) (A8.2) Cl(g) + Ga surface ^ GaCl3(g) (A8.3) The rate of formation of the product GaCl 3 is given by d[GaCl3] d t = k2'Cl(S) + kci'Pci[Ga surface] (A8.4) Assuming a steady state for C1(S)( then = 2k1,PCi2[(Ga-Clx) (s)] - k2'[Cl (s)] - 0 (A8.5) If [(Ga-Clx)(S)] = [Ga surface] - [C1(S)] (for reasons discussed on page 75), then equation A8.5 becomes = 2k1'PCi2[Ga surface] - 2k 1'P c l 2[Cl ( s )] - k2'[Cl ( s )] « 0 (A8.6) Therefore [C1(S)] is given by 2ki'Pci2[Ga surface] [ C 1 ( S ) ] = 2krP C i 2 + k 2' (A8.7) 139 Substituting for [Cl ( s )] in A8.4 with Eq. 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