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Chapter 41CHAPTER 4: OxidationOxidation of silicon is an important process in VLSI. The typical roles of SiO2are:1. mask against implant or diffusion of dopant into silicon2. surface passivation3. device isolation4. component in MOS structures (gate oxide)5. electrical isolation of multi-level metallization systemsThere are several techniques to form oxide layers, namely thermal oxidation, wetanodization, chemical vapor deposition, and plasma oxidation. Of the fourtechniques, thermal oxidation tends to yield the cleanest oxide layer with theleast amount of interfacial defects.4.1 Theory of Oxide GrowthThe chemical reactions describing thermal oxidation of silicon in dry oxygen orwater vapor are:Si (solid) O2 (gas) SiO2 (solid)Si (solid) 2H2O (gas) SiO2 (solid) 2H2 (gas)During the course of the oxidation process, oxygen or water molecules diffusethrough the surface oxide into the silicon substrate, and the Si-SiO2 interfacemigrates into the silicon (Figure 4.1). Thermal oxidation of silicon results in arandom three-dimensional network of silicon dioxide constructed fromtetrahedral cells. Since the volume expands, the external SiO2 surface is notcoplanar with the original silicon surface. For the growth of an oxide ofthickness d, a layer of silicon equal to a thickness of 0.44d is consumed.
2Chapter 4Figure 4.1: Growth of SiO2.A model elucidating the kinetics of oxide growth has been developed by Dealand Grove. The model, which is generally valid for temperatures between 700oCand 1300oC, partial pressure between 0.2 and 1.0 atmosphere, and oxidethickness between 30 nm and 2000 nm for oxygen and water ambients, isschematically illustrated in Figure 4.2.Figure 4.2: Basic model for thermal oxidation of silicon.
3Chapter 4In steady state, the three fluxes, F1 (flux of oxidizing species transported from thegas phase to the gas-oxide interface), F2 (flux across the existing oxide towardthe silicon substrate), and F3 (flux reacting at the Si-SiO2 interface) must beequal. F1 can be approximated to be proportional to the difference inconcentration of the oxidizing species in the gas phase and on the oxide surface.F1 hG (CG - CS)(Equation 4.1)where hG is the gas-phase mass-transfer coefficient, CG is the oxidantconcentration in the gas phase, and CS is the oxidant concentration adjacent to theoxide surface. Substituting C P/kT into Equation 4.1,F1 (hG/kT)(PG - PS)(Equation 4.2)Henry's Law states that, in equilibrium, the concentration of a species within asolid is proportional to the partial pressure of that species in the surrounding gas.Thus,Co HPS(Equation 4.3)where Co is the equilibrium concentration of the oxidant in the oxide on the outersurface, H is the Henry's Law constant, and PS is the partial pressure of oxidant inthe gas phase adjacent to the oxide surface. Furthermore, we denote theequilibrium concentration in the oxide, that is, the concentration which would bein equilibrium with the partial pressure in the bulk of the gas PG by the symbolC*, andC* HPG(Equation 4.4)Hence,C* - Co H (PG - PS), andF1 (hG/HkT)(C* - Co) h (C* - Co)(Equation 4.5)where h hG/HkT is the gas-phase mass-transfer coefficient in terms ofconcentration in the solid.Oxidation is thus a non-equilibrium process with the driving force being thedeviation of concentration from equilibrium. Henry's Law is valid only in the
4Chapter 4absence of dissociation effects at the gas-oxide interface, thereby implying thatthe species diffusing through the oxide is molecular.The flux of the oxidizing species across the oxide is taken to follow Fick's Law atany point d in the oxide layer. Hence,F2 D(Co - Ci)/do(Equation 4.6)where D is the diffusion coefficient, Ci is the oxidizer concentration in the oxideadjacent to the SiO2/Si interface, and do is the oxide thickness.The chemical reaction rate at the SiO2/Si interface is assumed to be proportionalto the reactant concentration. Therefore,F3 kSCi(Equation 4.7)where kS is the rate constant.Under steady-state conditions, F1 F2 F3. Thus,h(C* - Co) D(Co - Ci)/do kSCiCi DCo/(kSdo D)(Equation 4.8)Ci C*/[1 kS/h kSdo/D], and(Equation 4.9)Co [(1 kSdo/D)C*]/[1 kS/h kSdo/D](Equation 4.10)When D is large, Equation 4.8 becomes Ci Co, implying that the oxidation rateis controlled by the reaction rate constant kS and by Ci ( Co), that is, a reactioncontrolled case. When D is very small, h(C* - Co) 0 kSCi. Therefore, C* Coand Ci 0. The latter case is called diffusion-controlled case, as the oxidationrate depends on the supply of oxidant to the interface.In order to calculate the oxide growth rate, we define N1 as the number of oxidantmolecules incorporated into a unit volume of the oxide layer. If oxygen is thereactant, N1 2.2 x 1022 atoms/cm3 because the density of SiO2 is 2.2 x 1022 cm-3.If water is used, N1 becomes 4.4 x 1022 cm-3 as two H2O molecules areincorporated into each SiO2 molecule. The differential equation for oxide growthis given by
5Chapter 4ksC * d (d o ) N1 kC s i kkd dt 1 s s ohD(Equation 4.11)With an initial condition of do(t 0) di, the solution of Equation 4.11 may bewritten as:do2 Ado B (t τ)(Equation 4.12)where A 2D [1/kS 1/h](Equation 4.13)B 2DC* / N1(Equation 4.14)τ (di2 Adi) / B(Equation 4.15)The quantity τ represents a shift in the time coordinate to account for the presenceof the initial oxide layer di. Solving Equation 4.12 for do as a function of timegivesdot 1 2A / 2 A / 4 B 1/ 2 1(Equation 4.16)For long oxidation times, i.e., t τ and t A2/4B, do2 Bt. B is thereforecalled the parabolic rate constant. For short times, i.e., (t τ) A2/4B, do [B/A](t τ), and B/A is referred to as the linear rate constant.
6Chapter 4Example 4.1In wet oxidation of silicon at 950oC, the following data are obtained:t (hour)do (oxide thickness in how how to graphically determine the linear and parabolic rate constants fromthese experimental data. Assume that τ 0 for wet oxidation.Solutiondo2 Ado B (t τ) and for wet oxidation, τ 0Bt AdoThus, a plot of do versus t/do will give B as the slope and A as the intercept.Rearranging the equation, d o t (hour)do (oxide thickness in o (µm)t/do (h/µm)0. om the plot, the slope of the line yields B 0.2 µm2/hThe intercept of the line yields A 0.50 µm.
7Chapter 44.2 Experimental FitsRate constants are usually obtained graphically based on experimental results.Table 4.1 and Table 4.2 list the experimental rate constants for wet and dryoxidation of silicon, respectively. The Deal-Grove model provides excellentagreement with experimental data. The only exception is for SiO2 films less thanabout 300Å thick grown in dry oxygen. In this case, an anomalously highoxidation rate is observed with respect to the model. However, a proposedmodification to the Deal-Grove model, assuming that although diffusion throughthe oxide is still by molecular oxygen or water, the oxidation of silicon occurs bythe reaction of a small concentration of atomic oxygen dissociated near the SiSiO2 interface, provides an excellent fit to the experimental data.Table 4.1: Rate constants for wet oxidation of silicon.Oxidationtemperature (oC)A ( m)Parabolic rate Linear rateconstantconstant2B ( m /h)B/A ( 70.20314.404.641.270.406 (h)0000Table 4.2: Rate constants for dry oxidation of silicon.Oxidationtemperature (oC)A ( m)Parabolic rate Linear rateconstantconstant2B ( m /h)B/A ( 450.0270.01170.00490.00111.120.300.0710.02080.0030 (h)0.0270.0760.371.409.0
8Chapter 44.3 Orientation DependenceThe rate of oxidation depends on the availability of reaction sites on the siliconsubstrates. Hence, as the surface areal density of atoms is dependent on crystalorientation, oxidation rates are expected to be orientation dependent. Oxidationon the 111 crystal plane has a higher rate because there are a higher number ofsurface atoms, i.e. reaction sites or chemical bonds, when compared to a 100 plane. Table 4.3 depicts some of the properties of different silicon crystal planes,whereas Table 4.4 and Figure 4.3 compare the oxidation rates obtained from the 100 and 111 planes. Note that since the parabolic rate constant, B, isdiffusion limited, it has very little dependence on the crystal orientation.Table 4.3: Calculated properties of silicon crystal planes.Area ofAvailableOrien- unit cell Si atoms Si bonds BondsBondsbonds, N N relative214-2tation (cm )in area in area available (10 cm ) (1014 cm-2) to 110 110 2a 242 111 1 / 2 3a 2 100 a 7
9Chapter 4Table 4.4: Rate constants for silicon oxidation in H2O (640 Torr).OxidationOrienotemperature ( C) tation A ( m)900950100010501100 100 111 100 111 100 111 100 111 100 111 ic rate Linear rateconstantconstantB/A ratio2B ( m /h)B/A ( m/h) 111 / 100 1.681.681.751.651.65Average 1.68Figure 4.3: Oxide thickness versus oxidation time for silicon in H2O at 640 Torr.
Chapter 4104.4 Effects of ImpuritiesAs aforementioned, the wet oxidation rate is substantially higher than that of dryoxidation. Hence, any unintentional moisture in the furnace accelerates theoxidation process. For instance, at 800oC, a 30 nm oxide film is grown in aperiod of 700 minutes if the ambient water content is less than 1 ppm, comparedto an oxide thickness of 37 nm if the moisture content is 25 ppm.Doping impurities are redistributed at the growing Si-SiO2 interface. If thedopant segregates into the oxide (e. g. boron), the bond structure in the silicaweakens, thereby permitting an enhanced incorporation and diffusivity of theoxidizing species through the oxide, resulting in a larger oxidation rate, asindicated in Figure 4.4. The oxidation process in this case is diffusion controlpredominant. However, impurities that segregate into the oxide but then diffuserapidly through it, such as gallium, indium, and aluminum, have no effect on theoxidation kinetics. For oxidation of phosphorus-doped silicon, a concentrationdependence is observed only at lower temperature, where the surface reactionbecomes important. This dependence may be the result of phosphorus beingsegregated into the silicon (Figure 4.5).Oxidation rates are also influenced by adventitious impurities.Highconcentrations of sodium influence the oxidation rate by changing the bondstructure in the oxide, thereby enhancing the diffusion and concentration of theoxidizing species in the oxide. Certain halogen species are intentionallyintroduced into the oxidation ambient to improve both the oxide and theunderlying silicon properties. For instance, chlorine is instrumental in convertingcertain impurities in the silicon to volatile chlorides, resulting in a reduction inoxidation-induced stacking faults.
Chapter 411Figure 4.4: Oxidation of boron-doped silicon in wet oxygen as a function oftemperature and boron concentration.Figure 4.5: Oxidation of phosphorus-doped silicon in wet oxygen as a functionof temperature and phosphorus concentration.
Chapter 44.512High Pressure Oxidation, Plasma Oxidation, and Rapid ThermalOxidationAs stated in Equation 4.14, the parabolic rate constant, B, is proportional to C*which in turn is proportional to the partial pressure of the oxidizing species in thegas phase. Oxidation in high pressure thus produces a substantial acceleration inthe growth rate, as illustrated in Figure 4.6 and Figure 4.7. Thermal oxidelayers can therefore be grown at low temperature in run times comparable totypical high temperature in order to reduce dopant diffusion and suppressoxidation induced defects.Anodic plasma oxidation has all the advantages associated with the high-pressuretechnique and also offers the possibility of growing high-quality oxides at evenlower temperatures. Plasma oxidation is a low-pressure process usually carriedout in a pure oxygen discharge. The plasma is sustained either by a highfrequency or DC discharge. Placing the wafer in the uniform density region ofthe plasma and biasing it slightly negatively against the plasma potential allows itto collect active charged oxygen species. The oxidation rate typically increaseswith higher substrate temperature, plasma density, and substrate dopantconcentration.Figure 4.6: Oxide thickness versus oxidation time for pyrogenic steam at 900oCfor 100 and 111 silicon and pressures up to 20 atmospheres.
Chapter 413Figure 4.7: Oxide thickness versus oxidation time for 100 silicon oxidized indry O2 at 900oC and 1, 5, 10, and 20 atmospheres.Rapid thermal oxidation (RTO) is increasingly used in the growth of thin, highquality dielectric layers. The primary issues that differentiate RTO fromconventional thermal oxidation are the more complex chamber design, radiationsource, as well as temperature monitoring. From the point of view of oxidegrowth kinetics, RTO may be influenced by both thermally activated processesand a non-thermal, photon-induced process involving monatomic O atomsgenerated by UV and creating a parallel oxidation reaction that dominates atlower temperature.RTO growth kinetics exhibit activation energies differing from those measuredin conventionally grown oxides. In the initial stage (on the order of 20seconds), the RTO growth rate is linear followed by nonlinear growth. Theduration of the linear region is hardware dependent, particular the heatingsource.
14Chapter 44.6 Oxide PropertiesA silicon dioxide layer can provide a selective mask against the diffusion ofdopant atoms at elevated temperature, a very useful property in IC processing.For it to work, the dopant diffusion rate in the oxide must be slow with respect tothat in silicon, so that the dopant does not diffuse through the oxide in themasked region into the silicon. The masking oxide thickness must also be largeenough to prevent it from reaching the silicon substrate. Table 4.5 lists thediffusion constants of the common dopants in silicon. The often used n-typeimpurities as well as boron have very small diffusion coefficients in oxide andare compatible with oxide masking. However, this is not true for gallium,indium, and aluminum.Table 4.5: Diffusion constants in SiO2.DopantsDiffusion constants at 1100oC (cm2/s)B3.4 x 10-17 to 2.0 x 10-14Ga5.3 x 10-11P2.9 x 10-16 to 2.0 x 10-13As1.2 x 10-16 to 3.5 x 10-15Sb9.9 x 10-17Various charges and traps exist in thermally grown oxide films. If a charge ispresent close to the Si/SiO2 interface, it can induce a charge of the oppositepolarity in the underlying silicon, thereby affecting the ideal characteristics of thedevice, such as the threshold voltage of a MOS capacitor. Figure 4.8 shows thegeneral types of charges that can exist in a thermal oxide film. Interface-trappedcharges (Qit) can interact with the underlying silicon. These charges originatefrom structural defects related to the oxidation process, metallic impurities, andbond-breaking processes. A low temperature hydrogen anneal at 450oCeffectively neutralizes most interface-trapped charges. Values of 1010/cm2-eVand lower have been observed. Fixed oxide charges (Qf) are located in the oxidewithin approximately 3 nm of the SiO2 / Si interface. Qf cannot be charged or
15Chapter 4discharged easily. Its density ranges from 1010 cm-2 to 1012 cm-2, depending onthe oxidation and annealing conditions and orientation (Qf 111 is larger thanQf 100 ). Mobile ion charges (Qm) are attributed to alkali ions such as Na, K,and Li, as well as negative ions and heavy metals. Densities range from 1010 cm-2to 1012 cm-2 or higher and are related to the processing materials, chemicals,ambient, or handling. Common techniques employed to minimize Qm includecleaning the furnace tube in a chlorine ambient, gettering with phosphosilicateglass (PSG), and using masking layers such as silicon nitride. Oxide-trappedcharges (Qot) may be positive or negative, due to holes or electrons being trappedin the bulk of the oxide. Densities range from 109 cm-2 to 1013 cm-2. They canbe annealed out by low-temperature treatment.Figure 4.8: Charges in thermally oxidized silicon.
Chapter 4164.7 Dopant Redistribution at the InterfaceDuring thermal oxidation, the interface advances into the silicon substrate, anddoping impurities will redistribute at the interface until its chemical potential isthe same on each side of the interface. The ratio of the equilibrium concentrationof the impurity in silicon to that in SiO2 at the interface is called the equilibriumsegregation coefficient. Two additional factors that influence the redistributionprocess are the diffusivity of the impurity in the oxide (if large, the dopant candiffuse through the oxide rapidly, thereby affecting the profile near the Si - SiO2interface) and the rate at which the interface moves with respect to the diffusionrate.
/Si interface, and d o is the oxide thickness. The chemical reaction rate at the SiO 2 /Si interface is assumed to be proportional to the reactant concentration. Therefore, F 3 k S C i (Equation 4.7) where k S is the rate constant. Under steady-state conditions, F 1 F 2 F 3. Thus, h(C* - C o) D(C o - C i)/d o k S C i C i DC o /(k S d o
