Ion Implantation Ion implantation is currently the method of choice for introduction of dopant species into semiconductor substrates for state-of-the-art integrated circuit fabrication. Indeed, this process affords much better control of the impurity concentration profile for shallow and/or low dose doping than is possible using classical non-implanted diffusion processes. To understand why this is so, one need only consider conventional furnace doping. In the case of a constant source, the surface concentration is effectively at the solubility limit during the entire process. Typically, this concentration is quite high which makes this method unsuitable for very low doses. Similarly, in the case of an instantaneous source generated by conventional pre-deposition, the dopant surface concentration is, again, effectively at the solubility limit. Furthermore, since dose cannot be controlled directly, i.e., surface concentration, not dose, is determined by the solubility limit at a given temperature, small process variations, e.g., in time or temperature, can cause relatively large variations in dose. Also, an additional complication may arise because after a pre-deposition, all of the dopant atoms are effectively on the surface of the substrate. In this situation, dose control can become difficult because dopant can evaporate from the substrate surface during a subsequent high temperature drive process. (This problem can be remedied by use of a “cover oxide” or other judicious modification of process conditions.) In contrast, ion implantation is not subject to any of these limitations. First of all, very small amounts of dopant can be accurately measured and precisely introduced into the silicon wafer. Moreover, dose rather than concentration is measured directly during ion implantation. Secondly, dopant atoms are deposited at some depth below the surface of the semiconductor and, therefore, they are much less easily lost during any subsequent diffusion drive (or other heat treatment). Conceptually, ion implantation is extremely simple. Dopant containing source gases, e.g., arsine (AsH3), phosphine (PH3), diborane (B2H6), etc., are initially ionized in an electrical discharge within a vacuum chamber or “source”. A high voltage power supply is used to “extract” atomic ions from the discharge. These extracted ions are then sorted according to mass by dispersion in a strong magnetic field, i.e., by magnetic mass spectrometry. The desired ions are then selected and electrostatically accelerated through a final high voltage stage to the desired energy. Typical acceleration energies range from a few thousand to a few hundred thousand electron-volts. The resulting pure, monoenergetic ion beam enters the “end station” and strikes the wafer (or target). Since the beam cross section is typically much smaller than the wafer diameter, to obtain a uniform dose, electrostatic deflection of the beam to “scan” the wafer is required. In addition, mechanical motion of the wafer stage can also be used to augment electrostatic scanning and to average out directional effects. Implanted dose is controlled by directly measuring beam current (using a “Faraday cup” or some other device) and integrating over time. Modern ion implanters can easily achieve doses below 1011 cm2. This is far lower than is achievable using conventional doping methods. Of course, the nature of the interaction of an ion beam with a crystalline solid is strongly dependent on the incident ion kinetic energy. At very low energy, ions do not penetrate the target crystal and are just deposited on the surface, i.e., so-called ion beam deposition or ion beam plating. At higher energy, the impinging ions deposit kinetic energy just in the first few surface layers. This causes sputtering which scatters atoms of the crystalline solid from the surface into the ambient and, thence onto surrounding surfaces. (Indeed, this is the underlying physical process for physical vapor deposition (PVD) of thin films.) At still higher energy, ions penetrate the surface and come to rest inside the crystal. This is, of course, ion implantation. At the highest energies, impinging ions penetrate very deeply and can be applied to sophisticated analytical techniques, e.g., Rutherford back-scattering (RBS). Obviously, a collateral effect of penetration of ions into a crystalline solid is the creation of damage and disorder within the crystal lattice. Therefore, an important aspect of ion implantation processes requires control and/or elimination of these effects. (Indeed, ion implantation of species such as argon (Ar), silane (SiH4), or germane (GeH4), etc., can be used intentionally to damage or amorphize the crystal for gettering or other purposes.) Elementary Hard Sphere Collision Dynamics As asserted previously, for ion kinetic energies in the range of a few thousand electron-volts to several hundred thousand (or even several million) electron-volts, ions impinging on a solid surface penetrate into the interior and then come to rest. (At kinetic energies above several million electron-volts, ions can completely pass through the solid and, also nuclear reactions may occur which induce radioactivity!) Obviously, when impinging ions penetrate a crystalline solid, they must collide with atoms inside the solid and lose energy. Furthermore, since kinetic energies of implanted ions are much higher than atomic bond energies of the solid, ion-atom collisions can generally be treated as isolated collisions between free particles, i.e., atomic binding energy can be neglected. In the simplest picture, these collisions can be viewed as collisions between two hard spheres (i.e., one treats ions and atoms as “billiard balls”). Although the actual ion-atom interaction is much more complicated, this simplistic approach provides at least a qualitative insight into the form of observed implant concentration profiles. (Of course, a hard sphere collision is only a simplified approximation to a real physical process; however, if collision energy is relatively large, a hard sphere approximation often gives quite reasonable results.) To describe hard sphere collisions, one first defines a vector, vi, as incident velocity of an implanted ion and a second vector, vi , as the resulting ion velocity after collision with a silicon atom. The initial silicon atom velocity vector, vs, is taken to be zero since it is reasonable to consider silicon atoms as initially at rest within the crystal lattice. The recoil velocity vector, vs , of a silicon atom is, of course, its velocity after it is struck by an implanted ion. Other parameters which characterize a collision between an ion and a silicon atom are impact parameter, b, which is the “center-to-center miss distance” (by definition, if b vanishes the collision is “dead center”) and scattering angle, , which is the deflection angle of the incident ion due to the collision. Of course, as in any two-body collision, total momentum must be conserved, therefore: m v m v m v i i i i s s Here, mi is ion mass and ms is the mass of a silicon atom. (Of course, masses are unchanged by collision.) Likewise, kinetic energy must also be conserved, hence: m v2 m v2 m v2 i i i i s s 2 2 2 (Here, vi, vi , and vs are just defined as the magnitudes of vi, , and , respectively.) From these two conditions, the characteristics of the collision are completely determined. Within this context, the geometry of a collision of two hard spheres is illustrated by the following figure: tangent plane vi (edge on) kˆ vi i b vˆ s vˆ | | vs Fig. 65: Geometry of a collision between two hard spheres Clearly, when two hard spheres collide, the entire interaction occurs as an instantaneous impulse just at the moment they “touch”. Furthermore, this impulse is directed along a line connecting the centers of the two spheres.vi This direction defines the apse of the collision and is characterized by a unit vector, kˆ , which by definition “points” outward from the center of the silicon atom at the moment of contact. Thus, if G is defined as a scalar quantity that correspondsvs to impulse strength, then incident, scattered, and recoil velocities are formally related as follows: G G v v kˆ ; v kˆ i i m s m i s Clearly, these expressions trivially satisfy momentum conservation. Thus, to determine G, one substitutes these two expressions into the formula for energy conservation to obtain the result: 2 2 2 2 ˆ G G mivi mivi 2Gvi k mi ms 2 Obviously, mivi can be subtracted from both sides, hence: 1 1 m m 2v kˆ G G i s i m m m m i s i s One explicitly solves for the impulse strength in terms of a dot product taken between the incident ion velocity and the apse unit vector: m m G 2 i s v kˆ m m i i s As one intuitively might expect, G depends on atomic masses, incident ion velocity ˆ magnitude, and the apse angle, . (Clearly, cos is just vi k divided by vi.) The quantity, mims /(mi+ms), often appears in the classical mechanics of binary collisions and is called reduced mass. Accordingly, one can substitute for G to obtain expressions for the scattered ion velocity and the recoil velocity of a silicon atom: m m v v 2 s v kˆkˆ ; v 2 i v kˆkˆ i i m m i s m m i i s i s Clearly, the dot product, is just determined by the geometry of the collision. One observes from the collision geometry that can be decomposed into components parallel and perpendicular to incident ion velocity as follows: kˆ sin vˆ cosvˆ | | kˆ ˆ Here, v| | is a unit vector parallel to vi and vˆ is a unit vector perpendicular to vi. The sine of the angle, , is just the ratio of impact parameter to the combined radii of the ion and silicon atom, .