grow a thin(=45 A)oxide in a relatively short time. To achieve the thicknesses of SiO2 used in integrated circuit hnology(100 A to 2 um)alternative steps must be taken. Thermal oxidation is an extension of the natural oxide growth at an elevated temperature( 800 to 1200oC). The temperature is usually selected out of compro- mise,i.e, it must be high enough to grow the oxide in a reasonable time and it must be as low as practical to minimize crystal damage and unwanted diffusion of dopants already in the wafer. The Oxidation process Thermal oxidation is usually accomplished by placing wafers in a slotted quartz carrier which is inserted into a quartz furnace tube. The tube is surrounded by a resistance heater and has provisions for controlled flow of an inert gas such as nitrogen and the oxidant. a vented cap is placed over the input end of the tube. The gas flows in the back end of the tube, over the wafers, and is exhausted through the vented cap. The wafer zone has a flat temperature profile to within 1/2C and can handle up to 50 parallel stacked wafers. Modern furnaces are computer controlled and programmable Wafers are usually loaded, in an inert environment, ramped to temperature, and switched to the oxidant for a programmed time. When the oxidation is complete the gas is switched back to the inert gas and the temperature is ramped down to the unload temperature. All these mplications in the process are to minimize thermal stress damage to the wafers and the procedures can vary onsiderably. Detailed discussions of the equipment and procedures can be found in references[Sze, 1983] The two most common oxidizing environments are dry and wet. As the name implies, dry oxides are grown in dry O2 gas following the reaction Si+o et oxides were originally grown by bubbling the dry oxygen gas through water at 95C. Most"wet"oxides today are accomplished by the pyrogenic reaction of H, and o, gas to form steam, and are referred to as steam oxidations. In either case the reaction is essentially the same at the wafer: Si+H2O→SiO2+2H2 (23.2) The oxidation process can be modeled as shown in Fig. 23. 1 The position Xo represents the Si/SiO, interface which is a moving Oxide Silicon boundary. The volume density of oxidizing species in the bulk NG gas, N, is depleted at the oxide surface, Ns, due to an amount, No, being incorporated in the oxide layer. The oxidizing species then diffuses across the growing oxide layer where it reacts with the silicon at the moving interface to form SiO,. FG represents the flux of oxidant transported by diffusion from the bulk gas to the oxide surface. The oxidizing species that enters the Sio iffuses across the growing SiO, layer with a flux, For. A reaction takes place at the Si/SiO, interface that consumes some or all of NI the oxidizing species, as represented by the flux, Fr. In steady state these three flux terms are equal and can be used to solve for the concentrations N, and No in terms of the reaction rate and diffusion coefficient of the oxidizing species This in turn specifies the flux terms which can be used in the FIGURE 23. 1 Model of the oxidation process solution of the differential equation dx F for the oxide growth, x In this equation No is the number of oxidant molecules per unit volume of oxide. An excellent derivation of the growth equation is given in Grove [1967]. Here we give the result which can be c 2000 by CRC Press LLC© 2000 by CRC Press LLC grow a thin (≈45 Å) oxide in a relatively short time. To achieve the thicknesses of SiO2 used in integrated circuit technology (100 Å to 2 µm) alternative steps must be taken. Thermal oxidation is an extension of the natural oxide growth at an elevated temperature (800 to 1200°C). The temperature is usually selected out of compro￾mise, i.e., it must be high enough to grow the oxide in a reasonable time and it must be as low as practical to minimize crystal damage and unwanted diffusion of dopants already in the wafer. The Oxidation Process Thermal oxidation is usually accomplished by placing wafers in a slotted quartz carrier which is inserted into a quartz furnace tube. The tube is surrounded by a resistance heater and has provisions for controlled flow of an inert gas such as nitrogen and the oxidant. A vented cap is placed over the input end of the tube. The gas flows in the back end of the tube, over the wafers, and is exhausted through the vented cap. The wafer zone has a flat temperature profile to within 1/2°C and can handle up to 50 parallel stacked wafers. Modern furnaces are computer controlled and programmable. Wafers are usually loaded, in an inert environment, ramped to temperature, and switched to the oxidant for a programmed time. When the oxidation is complete the gas is switched back to the inert gas and the temperature is ramped down to the unload temperature. All these complications in the process are to minimize thermal stress damage to the wafers and the procedures can vary considerably. Detailed discussions of the equipment and procedures can be found in references [Sze, 1983]. The two most common oxidizing environments are dry and wet. As the name implies, dry oxides are grown in dry O2 gas following the reaction: Si + O2 → SiO2 (23.1) Wet oxides were originally grown by bubbling the dry oxygen gas through water at 95°C. Most “wet” oxides today are accomplished by the pyrogenic reaction of H2 and O2 gas to form steam, and are referred to as steam oxidations. In either case the reaction is essentially the same at the wafer: Si + H2O → SiO2 + 2H2 (23.2) The oxidation process can be modeled as shown in Fig. 23.1 The position X0 represents the Si/SiO2 interface which is a moving boundary. The volume density of oxidizing species in the bulk gas, NG, is depleted at the oxide surface, NS, due to an amount, N0, being incorporated in the oxide layer. The oxidizing species then diffuses across the growing oxide layer where it reacts with the silicon at the moving interface to form SiO2. FG represents the flux of oxidant transported by diffusion from the bulk gas to the oxide surface. The oxidizing species that enters the SiO2 diffuses across the growing SiO2 layer with a flux, Fox. A reaction takes place at the Si/SiO2 interface that consumes some or all of the oxidizing species, as represented by the flux, FI. In steady state these three flux terms are equal and can be used to solve for the concentrations NI and N0 in terms of the reaction rate and diffusion coefficient of the oxidizing species. This in turn specifies the flux terms which can be used in the solution of the differential equation: (23.3) for the oxide growth, x. In this equation Nox is the number of oxidant molecules per unit volume of oxide. An excellent derivation of the growth equation is given in Grove [1967]. Here we give the result which can be represented by: FIGURE 23.1 Model of the oxidation process. dx dt F Nox =