Patent Number: 048048526
Section: description

EMBODIMENT OF FIG. 1 Referring to the embodiment of FIG. 1, the basic technique of the invention is uniquely applied to acomodate the 1/R dependence of a spinning disc scanning an ion beam 2 entering at 180.degree. magnet 8 of constant and uniform magnetic field strength at position 7, (hereafter, position 7 will mean the centroid of the beam and may be referred to as the magnet entry point). In order to take into account the fact that the areal density of the ions in the energy-modulated, magnetically deflected beam is directly proportional to the displacement of he beam, and to accomodate the 1/R dependence, the energy of the ions of charge q is modulated by an accelerations gap 3 in which the voltage, V, varies linearly with time in a triangular wave form as shown in the inset to FIG. 1. (We emphasize that the energy modulation is not used as a possible means of controlling the beam intensity on the basis of sensed ion beam current. In the present invention, the ion beam current is assumed to be kept constant by methods well known in the art, not discussed here.) The energy versus time profile over one period T can be written (using in every instance throughout the differential function "d" even when describing discrete changes in quantities that occur in the illustrated incremental implementation of the invention): EQU E=q(dV/dt)t+E.sub.o, o.ltoreq.t.ltoreq.T/2 EQU E=q(dV/dt) (T-t)+E.sub.o, T/2.ltoreq.t.ltoreq.T (1a) the energy change per unit time is constant, of magnitude k.sub.1 ; that is, EQU dE/dt=q dV/dt=k.sub.1, o.ltoreq.t.ltoreq.T/2 EQU dE/dt=q dV/dt=31 k.sub.1, T/2.ltoreq.t.ltoreq.T (1b) The intensity of particles in the ion beam 2, dN/dt=I, is constant, so that the number of particles per unit energy interval is also constant: EQU dN/dE=(dN/dt)(dt/dE)=I/k.sub.1 (2) where the sign of k.sub.1 has been dropped since it has no significance, for present purposes. The magnetic field produced by the magnet 8 in this embodiment is also constant in value throughout its gap 28 and is directed out of the plane of FIG. 1. The magnetic field H produces a force on the ions causing the ions to move in the arc of a circle of radius r which depends on the energy, E, the strength of the magnetic field, H, the ion's mass, m, and charge, q, according to the well-known relationship, EQU (H.sup.2 r.sup.2 q.sup.2)/2m=E (3a) The bend of the particle trajectores by the magnetic field is 180.degree., so the distance x=2r, where x is the distance along the face of the magnet 8 from the point where the beam of energy E enters the magnet. Thus Equation 3a can be written in terms of x EQU (H.sup.2 x.sup.2 q.sup.2)/8m=E (3b) The radius of the trajectory of an ion of a given mass and ionic charge, which moves in a constant and uniform magnetic field, varies as the square root of the energy. Ions entering the magent at point 7, perpendicular to the face of the magnet, represented schematically at 8a, will be bent, according to equation 3, through 180.degree. so as to emerge perpendicular to the magnet face into region 13. It is the unique property of a 180.degree. deflection magnet of constant strength that all parallel rays entering the magnet gap perpendicular to the magnet entry face will emerge, after the 180.degree. deflection, again parallel and perpendicular to the magnet exit face. Such rays suffer no focusing by the fringe field on entering or leaving the magnet. This unique property is illustrated in FIG. 1a, which shows a beam of finite width entering the magnet face from point 7a to 7b; point 7 is the mean of the finite beam. The ions of lowest energy are bent through the smallest arc indicated by trajectories 9a and 9b; the corresponding trajectories of the highest modulation energy are indicated by 10a and 10b. Trajectory 9a which entered the magnet gap at point 7a, leaves the magnet gap at point 11a; trajectory 10a which also entered the magnet gap at point 7a leaves the magnet gap at point 12a. The bundle of rays of lowest energy leave the magnet from positions 11a to 11b; those of highest energy leave from points 12a to 12b; and all rays are parallel to each other. The rate of change of the position x with respect to E is found directly from Equation 3b. For convenience of later use, we write the invese of this ratio, EQU dE/dx=(H.sup.2 q.sup.2 x)/4m=k.sub.2 x (4) where k.sub.2 is a constant for a given ion in a uniform magnetic field that is constant in time. From Equations 2 and 4 we see that the intensity of the ions as a function of distance x along the exiting surface, dN/dx, varies directly with the distance x. EQU dN/dx=(dN/dE)(dE/dx)=(I k.sub.2 /k.sub.1)x (5) This is the desired intensity distribution to compensate for the radial dependence of area in a spinning disc. To make the compensation precise it is necessary for the disc to be properly positioned with respect to the magnet entry point 7, and the ratio of wafer size to the position of the waver on the disc must have a proper relationship with the positions 11 and 12 of the beam exiting the magnet position. The requirements can be readily realized in practice as the following derivation shows. We begin the analysis with the condition for uniform implantation on the rotating disc. We require, at all points of the wafer, a constant implant dose density, dN/dA, where N is the number of ions implanted and A is the area. Without loss of generality we will take dN to be the number of ions implanted in one revolution of the disc, dA to be the area the beam strikes in one revolution, and dt, in Equations 1 and 2 to be the time for one revolution of the disc. Thus dN/dt is again the particle beam current, assumed constant. If the beam has a radial extent dr, then in one revolution, EQU dN/dA=(1/2.pi.r) dN/dr (6) To obtain a constant dose density dN/dA, it is necessary for dN/dr to vary linearly with r in order to cancel the radial dependence in the denominator of Equation 6. To effect that cancellation, it is necessary that the center 21 of the rotating disc 20 be positioned so that x, the exiting distance from 7 along the magnet face, corresponds to r, the radial distance of the beam with respect to the disc. That is, EQU x=k.sub.3 r (7) where k.sub.3 is a constant. Thus EQU dN/dr=(dN/dx)(dx/dr)=k.sub.3 dN/dx. (8) Substituting Equation 5 into Equation 8 yields the desired dose implanted per unit increment of radius on the wafer EQU dN/dr=Ik.sub.3 k.sub.2 /k.sub.1 x. (9) Finally, combining Equation (9) with Equation (6) gives the dose per unit area per revolution of the disc, ##EQU1## which is a constant, independent of the radius. Thus, the simple linear voltage scan at the input to the magnet 8 results in a uniform ion implantation over the entire diameter of the wafer. It must be appreciated that certain broader aspects of the present invention can be adapted to workpieces which move under the beam in almost any manner. To emphasize this important point, consider the expanded equation for the dose per unit area, dn/dA, on the workpiece. We write, using notations above, EQU dN/dA=(dN/dt)(dt/dE)(dE/dx)(dx/dr)(dr/dA) (11) which can be simplified, according to the above discussion EQU dN/dA=(k.sub.2 Ix/k.sub.1)(dt/dE)(dx/dr)(dr/dA). (12) The ratio dx/dr, which is the ratio of the rate of change of the coordinate of the beam with respect to the magnet, to that of the beam with respect to the wafer, and dr/dA, the rate of change of the radial coordinate of the wafer with respect to its area, will depend on the specific geometry of the implanter components. For every product function (dx/dr)(dr/dA) it is always possible to track (x)(dx/dr)(dr/dA) by the appropriate function of voltage modulation dV/dt so that (dN/dA) is a constant independent of time. The voltage wave form on the demodulator will again be the same as that on the modulator but with opposite phase. Two examples will make the point clear. A. Linear wafer motion. If the wafers are moved under the beam linerly in the direction orthogonal to the direction of the beam scan, i.e., the wafers are stationary with respect to the scan direction, then a linearly modulated wave form would result in a non-uniform implant density of the beam energizing from the magnet. It is emphasized that this non-uniformity occurs when the beam intensity, in particles per second, is constant. That is, for a constant beam intensity a modulation of equal voltage increments in equal time increments would lead to an implant dose density which increases linearly with x, the distance from the magnet entry point. To produce an implant which is uniform across the wafer the modulation voltage wave form is varied as the square of the time. In differential form, dV/dt=CV.sup.1/2 between the limits of V.sub.min and V.sub.max. B. Rotational wafer moton, generally. Rotational motion of the wafer-holding disc, where the disc, whose surface is parallel to the magnet face as in FIG. 1 and FIG. 2, rotates about an axis a distance D from the point of entry on the magnet of the centroid of the beam. A special solution to this problem is described below in terms of a post-acceleration lens designed as an image inverter. A more general solution is to vary the wave form on the modulator so that dV/dt=x/(D-x), where x is again the distance between the entrance point 7 and the exit point 11 or 12, FIG. 2, of the beam relative to the magnet. (It will be appreciated that in all these applications, the 180.degree. magnet deflection of FIG. 1 results in parallel rays emerging perpendicular to the magnet face for all rays of a finite beam which enter the magnet perpendicular to the magnet face, see e.g. FIG. 1a.) Two additional provisions may be made to accommodate the needs of the industry. First, the semiconductor industry at present generally requires that the beam have a higher energy han one would want to use in the scanning apparatus described above; that is, a final acceleration of the beam is generally desired to meet the needs of ion implantation. Second, the semiconductor industry at present also generally desires that the beam energy be homogeneous, to at least a few percent for most industrial implants; that is, the large energy spread of the modulated beam usually must be demodulated out. Both these needs can be readily taken care of: To compensate for the change in energy caused by the scanning potential 3 it is only necessary to place a deceleration gap 14 following the exit from the magnet. The gap electrodes are connected so that the acceleraton at the input to the magnet results in a corresponding decelleration at the output; that is, electrode 15 should be connected to electrode 4 and electrode 16 should be connected to electrode 5. The shift in energy caused by the finite transit time of the ions through the magnet is negligible. Post-acceleration is a standard element in ion-implantation systems. In the method described here, it is preferred to use an acceleration lens 18 which is wide in the scan direction but fairly narrow in the direction perpendicular to the scan. Experience shows that such an oval lens can be designed to focus only in the narrow direction, i.e., perpendicular to the plane of the paper, so as to preserve the directionality, in the plane of the paper, of the beam through the lens. Thus the beam emerging from the magnet in region 13 will travel through region 17 with little deflection in the plane of the paper; trajectory 10, which strikes the wafer 19 at position 23, will do so at the same angle as trajectory 9 strikes the wafer at its corresponding point 22. In respect of accommodating the 1/R dependence which results when a target wafer is swept past the beam on the arc of circle of radius R whose rotational axis is parallel to the beam, it should be appreciated that certain features of this invention are of special emphasis for easy implementation with presently available techniques. These features are: (1) A magnetic deflection which satisfies Equation 4 and where the beam emerges perpendicular to the magnet face at all energies. (2) A voltage modulation of the beam, as, for example, in Equation 1, in which the voltage increments are carried out in equal time increments, in order to produce a beam density out of the magnet which varies linearly with the total deflection. (3) A rotating carrier whose axis of rotation is positioned to cause the 1/R variation of area on the wafer to correspond to the 1/R variation in the deflection of the beam. These features allow significant flexibility in choosing key parameters such as the magnet and carrier sizes and the modulation period. It should be noted that the ratio dx/dr is constant if the carrier plane is at a fixed angle to the magnet face, they need not be parallel as shown in FIG. 1. It should also be noted that the ratio x/R can be considered a constant even for a broad beam entering the magnet provided that the beam profile in the x direction be symmetric and that the centroid, that is, the mean position satisfy Equation 7. It should also be noted that the final acceleration lens 18 can be an inverting compound electrostatic lens which transforms the ray emerging from point 11 to position 23 and the ray emerging from point 12 into position 22. If such a lens is used then the center axis A of the disc 20 must be on the opposite side from that shown (i.e. axis of rotation 21 must be spaced to the right of wafer 19, shown in the figure, the same distance as the centroid of the beam 7 is to the left of the wafer); such a geometry may have practical advantages. In the presently preferred embodiment, however, the axis of rotation is aligned with the centroid of the beam entering the magnet and a non-inverting acceleration lens is used. Also we note that it is not necessary to have a demodulation lens 14 and the gap which that implies in order to produce ions of constant energy impinging on the wafers. The energy of the beam may be made constant by modulating the post-acceleration lens 18 with the sample amplitude but with opposite phase to that of the modulator, both modulator 3 and post-accelerator 18 acting as accelerators at all times. This is illustrated schematically in FIG. 3, described below. EMBODIMENT OF FIG. 2 Referring now to FIG. 2, the embodiment of FIG. 1 is adapted for implantatin of 8 inch wafers held on a 48 inch diameter spinning disc. These dimensions correspond to those used in the NV20 ion implanter, the latest model at Eaton Corporation, and the one used for implanting the largest wafers presently in production. We further assume that arsenic, of mass 75 and unit charge, +1, is to be implanted into the silicon wafers at 200 keV of energy. These parameters represent the most difficult tests for present ion implanters. A schematic of the essential elements is shown in FIG. 2. The entire system is assumed to be under vacuum according to standard practice. Fixing the wafer dimension, fixes the magnet deflection. To scan an 8 inch wafer with a one inch diameter beam requires a total deflection of 9 inches so as to overscan the edges. If we place the wafers at a mean radius of 19.5 inches from the center of the disc, we can implant 13 wafers at one loading. The wafers on the disc have a minimum radius of 15.5 inches and a maximum radius of 23.5 inches. Thus the minimum diameter of the magnetic deflection must be 15 inches and the maximum must be 24 inches; that is x(min), the distance from point 7 to point 11 must be 15 inches and the distance from point 7 to point 12 must be 24 inches. If we fix the magnetic field at 1 Tesla, a reasonable value for a gap which need not be more than 2 inches, then Equation 3 gives us the minimum and maximum energies of the arsenic ions entering the magnet at point 7. The minimum energy is 23.5 kev and the maximum energy is 60 keV, resulting in magnetic radii of 7.5 inches and 12 inches respectively, or a net scan of 2(12-7.5)=9 inches. The energy of the ion beam entering the modulation gap will therefore be 23.5 keV and the total modulation of the voltage will have an excursion of 60 keV minus 23.5 keV or 36.5 keV. A 23.5 keV source system is well within the standards of the industry. The source system 1 would consist of an ion source 24, in which ions are extracted at a potential of 25.5 keV; a small 2 keV decelleration voltage 25 is used to suppress the electrons in the source. The resulting beam of 23.5 keV is analysed by the magnet 26 to produce a pure beam of homogeneous ions for input into the modulation gap 3. At this gap the energy of the beam is modulated by variable voltage source 27. The excursion time for a back-forth radial scan will depend on the size of the beam, the disc rotation frequency, and the number of revolutions desired per radial increment of beam diameter. The overall criterion is the need for a desired uniformity of implant. Typical numbers for present implanters are in excess of ten revolutions of the disc for every radial increment of one beam diameter. If we assume a beam diameter of 1 inch, and a disc frequency of 1000 rpm, both nominal values for present implanters, then we have 10 revolutions in 0.01 minute, and need a radial speed of 1 inch per 0.01 minutes. Thus a full back-forth scan of 18 inches will take 0.18 minutes or 10.8 seconds. This is to be compared with typical mechanical scan rates of more than a minute per back-forth scan. Although advantageously much faster (e.g. for better uniformity of dose) than typical mechanical scan rates, the modulation can be done quite slowly from the point of view of electromagnetic devices and permits use of a stepped voltage profile such as is shown in FIG. 4. For illustration purposes we show the steps applied by variable voltage source 27 as being 2 keV, but in practice one would use a stepping voltage of only a few hundred volts to produce a beam displacement on the wafer of about 0.1 inches per disc revolution. The total power into the scanning system is small even for intense beams, and, in any case, most of this power is extracted back out of the system during the deceleration phase. The beam will exit from the magnet in a back and forth scan in which the beam moves a smaller increment per unit time when at the larger values of x than it does at the smaller values of x. To show this relationship we consider the results of the modulated voltage specimen of FIG. 4 with voltage increments of 2 keV. In FIG. 4a, the energy of each beam is plotted as a function of the distance from the magnet entry point, x, for the parameters of the illustrative embodiment. The smaller linear increments per unit of time imply a greater current density. This is shown explicitly in FIG. 4b where the inverse of the increments in x, labelled as dN/dX, the particles per unit length, is plotted as a function of the exiting distance x. The electrodes of the demodulation gap 14 have an elliptical profile, about 10 inches by 2 inches; the gap size can be less than 1 inch. The beam exiting from the demodulation gap will have a constant energy of 23.5 keV. The post-acceleration lens present a special design problem, since this lens must accelerate each beam by 176.5 keV to produce a 200 keV implant and it must do so without focusing in the scan direction. On the other hand, any designer of a high-energy implanter must face the problem of designing a special acceleration lens and there are no fundamental problems to doing so. The design is straightforward to those experienced in the field since the lens is long and narrow and such lenses inherently have little focus in the long direction. It is also worth noting that since the beam is being scanned slowly back and forth across the acceleration gap, one can add features which cannot be considered in more conventional acceleration systems; in particular, it is practical to consider putting in a time-dependent correction lens if there is distortion of the beam in the acceleration tube as a function of the sweep position. It is instructive to look at the actual numbers for the scanning profiles shown in FIGS. 4, 4a, and 4b, using the parameters of the illustrative embodiment and assuming an arsenic current of 10 milliamperes in the one inch beam. In Table 1, we show in successive columns as a function of the arsenic energy into the magnet, the distance x (equivalent to twice the bending radius), the increment in x between successive increments in energy, the inverse of those increments, the latter being directly proportional to the density of the ions leaving the magnet into space B. The last column is the dose per square inch during one pass which is directly proportional to the product of the increments in x, column 3, times the weighted mean value of the x values of column 2 for that increment. The values of column 4 are directly proportional to the density of the ions emerging from the magnet. Multiplying this measure of particle density by the mean value of x is equivalent to multiplying the particle density by the radius value of the wafer on the disc. Column 5 is the forementioned product multiplied by the appropriate constants for the parameters used in this illustration to yield the expected density of ions implanted per square inch in a single scan of the wafer. The constancy of the values of column 5 is a test of the essential idea of this aspect of the invention. The method does indeed compensate for variations due to radial changes on the rotating disc. TABLE 1 ______________________________________ 3 5 1 2 X(E.sub.i) - 4 dN/dA E X(E) X(E.sub.i-1) [X(E.sub.i) - X(E.sub.i-1)].sup.-1 IONS/ KeV inches inches 1/(inches) square inch ______________________________________ 23.5 15.1 25.5 15.7 0.628 1.591 2.95 .times. 10.sup.14 27.5 16.3 0.604 1.655 2.95 29.5 16.89 0.583 1.716 2.95 31.5 17.455 0.563 1.776 2.95 33.5 18.00 0.546 1.833 2.95 35.5 18.530 0.530 1.888 2.95 37.5 19.045 0.515 1.942 2.95 39.5 19.546 0.501 1.992 2.95 41.5 20.035 0.489 2.046 2.95 43.5 20.512 0.477 2.096 2.95 45.5 20.978 0.466 2.145 2.95 47.5 21.434 0.456 2.193 2.95 49.5 21.881 0.447 2.239 2.95 51.5 22.318 0.438 2.285 2.95 53.5 22.748 0.430 2.327 2.95 55.5 23.169 0.421 2.374 2.95 57.5 23.583 0.414 2.417 2.95 59.5 23.989 0.406 2.461 2.95 ______________________________________ EMBODIMENT OF FIG. 3 We refer now to FIG. 3 which employs a post accelerator and no decelerator. We assume an energy of 24 keV from the ion source and a desired energy of 200 keV for the implanted ions. We further assume for illustration that the modulation voltage form is a symmetric triangle wave whose amplitude varies from zero to 36 keV. The acceleration voltage on the post-accelerator 18a varies with the same triangular wave form as shown in FIG. 3, but with opposite phase so that the voltage excursion is from 176 keV to 140 keV. Specifically, when the modulator 3 has zero voltage, the ions enter and leave the magnet with an energy of 24 keV and get further accelerated by 176 keV by the post accelerator 18a. When the modulator 3 is at 36 keV, the ions enter and leave the magnet with an energy of 60 keV (24 keV+36 keV) and get further accelerated by 140 keV by the post-accelerator 18a. By tracking the wave forms on the modulator and post-accelerator together with the same period, using a common control circuit 42, one ensures that the particles in the beam being implanted into the wafer will always have a uniform energy of 200 keV. A disadvantage of this scheme is that one needs to vary the voltage of both the modulator and the post-accelerator when they are under load, rather than, as in FIGS. 1 and 2, vary the voltage of the modulator and demodulator which are under no load when coupled together. There are however compensating advantages to the scheme shown in FIG. 3: First, one reduces the system by one component with attendant savings in space and hardware. Second, the demodulator gap, which here need not be employed, is a potentially strong source of damaging x-ray radiation, just as are the modulator and post-accelerator. Third, each of the gaps is a region of unneutralized beam, since the neutralizing electrons in the beam are swept out by the positive potentials at the gaps. Thus, each of the gaps results in beam spreading, so-called beam blow-up, which can be severe if intense ion beams are used. For this reason, getting rid of the demodulator gap may well offset the technical disadvantage of dealing with modulated gaps under load. EMBODIMENT OF FIG. 5 It should be noted that to enjoy benefits of the invention (e.g. essentially parallel ion trajectories into the target and uniformity of particle density per unit area) the deflection angle of the beam in the analyzer magnet need not be 180.degree. as has been used in the preceding embodiments. First, the needs of an industrial implanter may be satisfied with angular deflections of, for example, 170.degree. if, even when ion beams of finite width are used, the resulting deviations from parallelism of the ions implanted into the wafer do not produce non-uniformities which exceed tolerance limits. Second, analyzing magnet systems following energy modulation can be designed which produce a bending much smaller than 180.degree., the deflection being proportional to E.sup.1/2 (Equation 3) while preserving, to a good approximation, the requirement that all ions move essentially parallel to each other when impinging on the wafer. That is, while the preferred embodiment of a 180.degree. magnet deflection is unique in preserving the parallelism of ion trajectories of beams of finite width, other designs may approximate the needs of industry with possible savings and cost. To preserve the constancy of the dose per unit area on the workpiece, the voltage modulation will have to be tailored, according to Equation 11, for the magnet design used. One possible example is shown in FIG. 5. The beam of ions 2 is assumed to enter the magnet 38 at point 7, perpendicular to the magnet face 39, as before. The exit face 41 of the magnet is at an angle .theta. with respect to the direction of the beam 2; the plane of the magnet face 41 passes through point 7. The total deflection in the analyzing magnet 38 is 2.sup..theta., and rays, of different energy entering at point 7, emerge parallel to one another at an angle of .theta. with respect to the magnet face 41. It should be recognized that FIG. 5 represents a generalization of the scheme of FIGS. 1, 2, and 3 (in which .theta. equals 90, all rays exit at 90.degree. from the magnet face, and the total deflection is 180.degree.). Unlike the case of the 180.degree. magnet, under such conditions, a beam of finite width entering the magnet face with beam centroid at point 7 results in a diverging beam emerging from the magnet face (though it will be appreciated that in the present state of the art the widths of the ion beams may be made so small as to result in negligible divergence from parallelism). Moreover, the fringe field acts as a sector lens on the ions, causing ions of different energies, even though they exit in parallel paths, to have different asymptotic direction. If the resulting divergence from parallelism is unacceptable for obtaining the desired uniformity of dose on the workpiece, it may be possible to compensate for the non-parallelism by the addition of an optical system, 40, shown as dotted lines. Also shown schematically for illustrative purposes, are a demodulator 14, a post-accelerator 18, and a wafer 19 on a rotating disc. The axis A--A' of the rotating disc points to the entrance point 7 as in FIGS. 1 and 2. OTHER ROTATING EMBODIMENTS In other embodiments, for instance, the rate of voltage scan on modulator 3 can be chosen from a wide range of speeds, including sweep speeds that are very fast, and the speed of mechanical scan in the orthogonal direction can be markedly decreased from that mentioned in the above embodiments. In other embodiments, instead of a spinning disc, a generally planar conveyer can be employed, which at the region of implant, turns about a circular arc, the center of which is aligned according to the same principles as employed for the disc described above. X-Y SCANNING, EMBODIMENT OF FIG. 6 Indeed, it should also be noted that the complete scan of an ion beam on a semiconductor wafer may be accomplished by applying the technique of magnetic scanning of an energy-modulated beam twice in succession so that both orthogonal motions needed to obtain a uniform implant dose are accomplished by electromagnetic scanning of a beam of ions which are implanted at a fixed angle into the workpiece. In this use of the basic invention there would be no mechanical motion while the wafer is being implanted. The essentials of the orthogonal magnetic scanning are illustrated in FIG. 6 with two independent 180.degree. systems. The first stage of the scan is the same as described above. It consists of an ion source 1 and a voltage modulator 3 to modulate the energy of the ion beam 2 which enters the magnet 8 at a fixed mean point 7. The beam exits from the magnet 8 into region 13 at positions which scan a range from point 11 to point 12 as determined by the parameters of the magnetic and ion energy. The second, independent stage of scanning, employs a second modulator 29 followed by a second scanning magnet 30. The magnetic field gap 31 of magnet 30 must be orthogonal to that of the magnetic gap 28 of magnet 8 and the gap of magnet 30 must be wide enough to encompass the full scan from point 11 to point 12 of the ion beam of finite size. The voltage range impressed on the modulator 29 is such that the scan produced in magnet 30 has the desired range of spatial values. It is then straightforward to arrange the modulation wave forms and values so as to produce a scan over the full face of a wafer placed under the scanning beam exiting from magnet 30, for example, the raster scan 36 produced by modulation ranges such that when the ions are deflected to position 11 by magnet 8, they are further scanned from position 34 to 35 by magnet 30, and when the ions are deflected to position 12 by magnet 8, they are further scanned from positions 33-32 by magnet 30, see FIG. 6a. For the ion beam exiting from magnet 30 to implant a wafer with a uniform dose we further require that the voltage wave forms on modulators 3 and 29 have a special time dependence, as discussed above, namely that the time spent at each voltage vary as the square root of that voltage. To obtain ions of higher energy than exit from magnet 30, it is necessary to have a post-accelerator 18 as before. This post accelerator will have an oval or circular gap large enough to accept the full two dimension scan of the beam. The energy of the ions exiting from the magnet 30 has been modulated twice, producing a scan 36. In the illustration above, the total energy variation during the full scan of a wafer will not exceed the maximum energy added by the first modulator 3. To obtain a homogeneous energy of the ions implanting the wafer one again has two choices. The first choice is to demodulate the energy with a demodulation gap 14; the deceleration in the gap must precisely track the sum of the accelerations in modulator 3 and modulator 29. The second choice is to vary, as a function of time, the amount of acceleration in the post-acceleration stage 18 so that the algorithmic sum of all accelerations is a constant independent of time. The optic design of the post-accelerator alone or the post-accelerator and the demodulator can be implemented in a manner to result in an inverted (or even a non-inverted) image of the rays exiting from the magnet 30 to correct distortion or the post-accelerator may be followed by a time-dependent correction lens system to correct distortion introduced by the post accelerator. It should be noted that FIG. 6 is an illustration of just one possible arrangement to achieve a full two-dimensional scan using the invention. Orthogonal scans in which each of the orthognal bends of the ion paths is considerably less than 180.degree. are possible. In particular, orthogonal scans in which each bend is 90.degree. (as illustrated in FIG. 5 for a scan in one direction) could effect a considerable saving in magnet size. For simplicity of explanation, the embodiments shown herein employ a source of a single specie. In practce ion sources usually emit multiple species and a source analyzer, usually magnetic, is used to select the one specie desired. In practice one may use a separate analyzing magnet prior to the scanning magnet described though under special conditions it may be possible to use the same magnet both for selection of the specie and for scanning.