Introduction Amorphous arrangement of atoms means that there is a possibility that multiple Si atoms will be connected Amorphous arrangement of atoms means that there is a possibility that multiple Si atoms will be connected Thin ‘wires’ of Si within SiO 2 layer enables leakage currents to flow Thin ‘wires’ of Si within SiO 2 layer enables leakage currents to flow When films get this thin, quantum mechanical effects including tunneling become important When films get this thin, quantum mechanical effects including tunneling become important Finite probability that an electron can penetrate through an energy barrier Finite probability that an electron can penetrate through an energy barrier Tunneling is usually undesirable, but some devices are now built using this phenomenon (nonvolatile memory) Tunneling is usually undesirable, but some devices are now built using this phenomenon (nonvolatile memory)

Basic Concepts Oxide grows by diffusion of oxygen/H 2 O through the oxide to the Si/SiO 2 interface Oxide grows by diffusion of oxygen/H 2 O through the oxide to the Si/SiO 2 interface Thus, a new interface is continuously growing and moving into the Si wafer Thus, a new interface is continuously growing and moving into the Si wafer The process is known as: The process is known as: Dry oxidation when oxygen only is used. Dry oxidation when oxygen only is used. Wet oxidation when water vapor (with or without oxygen) is used. Wet oxidation when water vapor (with or without oxygen) is used.

Basic Concepts

The process involves an expansion The process involves an expansion the density of an equal volume of Si occupies less space than a volume of oxide containing the same number of Si atoms the density of an equal volume of Si occupies less space than a volume of oxide containing the same number of Si atoms Nominally, the oxide would like to expand by 30% in all directions; but it cannot expand sideways because it is constrained by the Si atoms Nominally, the oxide would like to expand by 30% in all directions; but it cannot expand sideways because it is constrained by the Si atoms Thus, there is a 2.2  expansion in the vertical direction Thus, there is a 2.2  expansion in the vertical direction In figure 6-4, note the growth of the LOCOS (Local Oxidation of Silicon) oxide above the surface In figure 6-4, note the growth of the LOCOS (Local Oxidation of Silicon) oxide above the surface Also note the “bird’s beak” of oxide under the nitride layer – a stress-induced rapid growth of oxide Also note the “bird’s beak” of oxide under the nitride layer – a stress-induced rapid growth of oxide

Basic Concepts

If there are shaped surfaces where oxide must grow, this expansion may not be so easily accommodated If there are shaped surfaces where oxide must grow, this expansion may not be so easily accommodated The oxide layers are amorphous (i.e., there is only short range order among the atoms) The oxide layers are amorphous (i.e., there is only short range order among the atoms) There are no crystallographic forms of SiO 2 that match the Si lattice There are no crystallographic forms of SiO 2 that match the Si lattice The time required for transformation to a crystalline form at device temperatures is very very long The time required for transformation to a crystalline form at device temperatures is very very long

Basic Concepts The oxide that grows is in compressive stress The oxide that grows is in compressive stress This stress can be relieved at temperatures above 1000 o C by viscous flow This stress can be relieved at temperatures above 1000 o C by viscous flow There is a large difference in the TCE (thermal coefficient of expansion) between Si and SiO 2 There is a large difference in the TCE (thermal coefficient of expansion) between Si and SiO 2 This increases the compressive stresses in the oxide and results in tensile stresses in the Si near its surface This increases the compressive stresses in the oxide and results in tensile stresses in the Si near its surface Si is very thick while the oxide is very thin Si is very thick while the oxide is very thin Si can usually sustain the stress Si can usually sustain the stress Since the wafer oxidizes on both sides, the wafer remains flat; if you remove the oxide from the back side, you will see a warping of the wafer Since the wafer oxidizes on both sides, the wafer remains flat; if you remove the oxide from the back side, you will see a warping of the wafer The stress can be measured by measuring the warp of the wafer The stress can be measured by measuring the warp of the wafer

Basic Concepts The electrical properties of the Si/SiO 2 interface have been extensively studied The electrical properties of the Si/SiO 2 interface have been extensively studied To first order, the interface is perfect To first order, the interface is perfect The densities of defects are 10 9 – /cm 2 as compared to Si atom density of /cm 2 The densities of defects are 10 9 – /cm 2 as compared to Si atom density of /cm 2 Most defects are associated with incompletely oxidized Si Most defects are associated with incompletely oxidized Si Deal (1980) suggested a nomenclature that is now used to describe the various defects Deal (1980) suggested a nomenclature that is now used to describe the various defects

Defect Nomenclature

There are four type of defects There are four type of defects 1. Q f is the fixed oxide charge. – It is very close (< 2 nm) to the Si/SiO 2 interface – Surface concentration of 10 9 –10 11 /cm 2 – Related to the transition from Si to SiO 2 – Incompletely oxidized Si atoms – Positively charged and does not change under normal conditions

Defect Nomenclature 2. Q it is the interface trapped charge – Appears to incompletely oxidized Si with dangling bonds – Located very close to the interface – Charge may be positive, neutral, or negative – Charge state may change during device operation due to the trapping of electrons or holes – Energy levels associated with these traps are distributed throughout the forbidden band, but there seem to be more near the valence and conductions bands – Density of traps is 10 9 —10 11 cm -2 eV -1

Defect Nomenclature 3. Q m is the mobile oxide charge – It is not so important today but was very serious in the 1960’s – It results from mobile Na + and K + in the oxide – Shift in V TH is inversely proportional to C OX and thus, as oxides become thinner, we can tolerate more impurity

Defect Nomenclature 4. Q ot is charge trapped anywhere in the oxide – Broken Si-O bonds in the bulk oxide well away from the interface – by ionizing radiation or by some processing steps such as plasma etching or ion implantation – Metal ions from surface of Si or introduced during growth – Fe, Mn, Cr, Cu – Normally repaired by a high-temperature anneal – They can trap electrons or holes – This is becoming more important as the electric field in the gate oxide is increased – They result in shifts in V TH

Defect Nomenclature All four types of defects have deleterious effects on the operation of devices All four types of defects have deleterious effects on the operation of devices High temperature anneals in Ar or N 2 near the end of process flow plus an anneal in H 2 or forming gas at the end of process flow are used to reduce their effect High temperature anneals in Ar or N 2 near the end of process flow plus an anneal in H 2 or forming gas at the end of process flow are used to reduce their effect

Manufacturing Methods Furnace capable of 600 – 1200 o C with a uniform zone large enough to hold several wafers Furnace capable of 600 – 1200 o C with a uniform zone large enough to hold several wafers Gas distribution system to provide O 2 and H 2 O Gas distribution system to provide O 2 and H 2 O Generally, H 2 is burnt with O 2 at the entrance of the furnace to create water vapor Generally, H 2 is burnt with O 2 at the entrance of the furnace to create water vapor TCA or HCl may be used to remove metal ions TCA or HCl may be used to remove metal ions Control system that holds the temperatures and gas flows to tight tolerances (  0.5 C) Control system that holds the temperatures and gas flows to tight tolerances (  0.5 C)

PRODUCTION FURNACES Commercial furnace showing the furnace with wafers (left) and gas control system (right). Commercial furnace showing the furnace with wafers (left) and gas control system (right).

PRODUCTION FURNACES Close-up of furnace with wafers. Close-up of furnace with wafers.

PRODUCTION FURNACES

Models The first major model is that of Deal and Grove (1965) The first major model is that of Deal and Grove (1965) This lead to the linear/parabolic model This lead to the linear/parabolic model Note that this model cannot explain Note that this model cannot explain the effect of oxidation of the diffusion rate the effect of oxidation of the diffusion rate the oxidation of shaped surfaces the oxidation of shaped surfaces the oxidation of very thin oxides in mixed ambients the oxidation of very thin oxides in mixed ambients The model is an excellent starting place for the other more complicated models The model is an excellent starting place for the other more complicated models

CHEMICAL REACTIONS Process for dry oxygen Process for dry oxygen Si + O 2  SiO 2 Si + O 2  SiO 2 Process for water vapor Process for water vapor Si + 2H 2 O  SiO 2 + 2H 2

OXIDE GROWTH Si is consumed as oxide grows and oxide expands. The Si surface moves into the wafer. Si is consumed as oxide grows and oxide expands. The Si surface moves into the wafer. 54% 46% SiO 2 Silicon wafer Original surface

MODEL OF OXIDATION Oxygen must reach silicon interface Oxygen must reach silicon interface Simple model assumes O 2 diffuses through SiO 2 Simple model assumes O 2 diffuses through SiO 2 Assumes no O 2 accumulation in SiO 2 Assumes no O 2 accumulation in SiO 2 Assumes the rate of arrival of H 2 O or O 2 at the oxide surface is so fast that it can be ignored Assumes the rate of arrival of H 2 O or O 2 at the oxide surface is so fast that it can be ignored Reaction rate limited, not diffusion rate limited Reaction rate limited, not diffusion rate limited

Deal-Grove Model of Oxidation Fick’s First Law of diffusion states that the particle flow per unit area, J (particle flux), is directly proportional to the concentration gradient of the particle. Fick’s First Law of diffusion states that the particle flow per unit area, J (particle flux), is directly proportional to the concentration gradient of the particle. We assume that oxygen flux passing through the oxide is constant everywhere. F 1 is the flux, C G is the concentration in the gas flow, C S is the concentration at the surface of the wafer, and h G is the mass transfer coefficient

J Distance from surface, x N NoNo NiNi Silicon dioxide Silicon SiO 2 Si XoXo

Deal-Grove Model of Oxidation Assume the oxidation rate at Si-SiO 2 interface is proportional to the O 2 concentration: Assume the oxidation rate at Si-SiO 2 interface is proportional to the O 2 concentration: Growth rate is given by the oxidizing flux divided by the number of molecules, M, of the oxidizing species that are incorporated into a unit volume of the resulting oxide: Growth rate is given by the oxidizing flux divided by the number of molecules, M, of the oxidizing species that are incorporated into a unit volume of the resulting oxide:

Deal-Grove Model of Oxidation The boundary condition is The boundary condition is The solution of differential equation is The solution of differential equation is

Deal-Grove Model of Oxidation x ox : final oxide thickness x i : initial oxide thickness B/A : linear rate constant B : parabolic rate constant

There are two limiting cases: There are two limiting cases: Very long oxidation times, t >>  Very long oxidation times, t >>  x ox 2 = B t x ox 2 = B t Oxide growth in this parabolic regime is diffusion controlled. Oxide growth in this parabolic regime is diffusion controlled. Very short oxidation times, (t +  ) << A 2 /4B Very short oxidation times, (t +  ) << A 2 /4B x ox = B/A ( t +  ) x ox = B/A ( t +  ) Oxide growth in this linear regime is reaction- rate limited. Oxide growth in this linear regime is reaction- rate limited.

Deal-Grove Model of Oxidation