In the case of interstitial diffusion the impurity diffuses by squeezing between the lattice atoms and taking residence in the interstitial space between lattice sites. Since this mechanism does not require the presence of a vacancy, it proceeds much faster than substitutional diffusion Conventional dopants such as B, P, As, and Sb diffuse by the substitutional method. This is beneficial in that the diffusion process is much slower and can therefore be controlled more easily in the manufacturing process. Many of the undesired impurities such as Fe, Cu, and other heavy metals diffuse by the interstitial mechanism and therefore the process is extremely fast. This again is beneficial in that at the temperatures used, and in the duration of fabri unwanted metals can diffuse completely through the Si wafer Gettering creates trapping sites on the back surface of the wafer for these impurities that would otherwise remain in the silicon and cause adverse device effects Regardless of the diffusion mechanism, it can be formalized mathematically in the same way by introducing a diffusion coefficient, D(cm2/sec), that accounts for the diffusion rate. The diffusion constants follow an behavi ng to the E where Do is the prefactor, EA the activation energy, k Boltzmanns constant, and T the absolute temperature. Conventional silicon dopants(substitutional diffusers) have diffusion coefficients on the order of 10-to 10-12 at 1100@C, whereas heavy metal interstitial diffusers(Fe, Au, and Cu) have diffusion coefficients of 10- to 10 at this temperature The diffusion process can be described using Ficks Laws. Ficks first law says that the flux of impurity, F crossing any plane is related to the impurity distribution, N(x, t)per cm, by (23.8) dx in the one-dimensional case. Ficks second law states that the time rate of change of the particle density in turn is related to the divergence of the particle flux: an dF 239) Combining these two equations gives an aaN a-N (23.10) in the case of a constant diffusion coefficient as is often assumed This partial differential equation can be solved by separation of variables or by Laplace transform techniques for specified boundary conditions For a constant source diffusion the impurity concentration at the surface of the wafer is throughout the diffusion process. Solution of Eq (23. 10)under these boundary conditions, asst infinite wafer, results in a complementary error function diffusion profile: c2000 by CRC Press LLC
© 2000 by CRC Press LLC In the case of interstitial diffusion the impurity diffuses by squeezing between the lattice atoms and taking residence in the interstitial space between lattice sites. Since this mechanism does not require the presence of a vacancy, it proceeds much faster than substitutional diffusion. Conventional dopants such as B, P, As, and Sb diffuse by the substitutional method. This is beneficial in that the diffusion process is much slower and can therefore be controlled more easily in the manufacturing process. Many of the undesired impurities such as Fe, Cu, and other heavy metals diffuse by the interstitial mechanism and therefore the process is extremely fast. This again is beneficial in that at the temperatures used, and in the duration of fabrication processes, the unwanted metals can diffuse completely through the Si wafer. Gettering creates trapping sites on the back surface of the wafer for these impurities that would otherwise remain in the silicon and cause adverse device effects. Regardless of the diffusion mechanism, it can be formalized mathematically in the same way by introducing a diffusion coefficient, D (cm2 /sec), that accounts for the diffusion rate. The diffusion constants follow an Arrhenius behavior according to the equation: (23.7) where D0 is the prefactor, EA the activation energy, k Boltzmann’s constant, and T the absolute temperature. Conventional silicon dopants (substitutional diffusers) have diffusion coefficients on the order of 10–14 to 10–12 at 1100°C, whereas heavy metal interstitial diffusers (Fe, Au, and Cu) have diffusion coefficients of 10–6 to 10–5 at this temperature. The diffusion process can be described using Fick’s Laws. Fick’s first law says that the flux of impurity, F, crossing any plane is related to the impurity distribution, N(x,t) per cm3 , by: (23.8) in the one-dimensional case. Fick’s second law states that the time rate of change of the particle density in turn is related to the divergence of the particle flux: (23.9) Combining these two equations gives: (23.10) in the case of a constant diffusion coefficient as is often assumed. This partial differential equation can be solved by separation of variables or by Laplace transform techniques for specified boundary conditions. For a constant source diffusion the impurity concentration at the surface of the wafer is held constant throughout the diffusion process. Solution of Eq. (23.10) under these boundary conditions, assuming a semiinfinite wafer, results in a complementary error function diffusion profile: (23.11) D D E kT A = -È Î Í Í ˘ ˚ ˙ ˙ 0 exp F D N x = ¶ ¶ ¶ ¶ ¶ ¶ N t F x = ¶ ¶ ¶ ¶ ¶ ¶ ¶ ¶ N t x D N x D N x = Ê Ë Á ˆ ¯ ˜ = 2 2 N N x Dt (,) x t = Ê Ë Á ˆ ¯ 0 ˜ 2 erfc
Here, No is the impurity concentration at the surface of the wafer, x the distance into the wafer, and t the diffusion time. As time progresses the impurity profile penetrates deeper into the wafer while maintaining a constant surface concentration. The total number of impurity atoms/cm? in the wafer is the dose,Q,and continually increases with time Q Nadx 2N (23.12) For a limited source diffusion an impulse of impurity of dose Q is assumed to be deposited on the wafer surface. Solution of Eq.(23. 10)under these boundary conditions, assuming a semi-infinite wafer with no loss of impurity, results in a gaussian diffusion profile: (23.13) 2VDt In this case, as time progresses the impurity penetrates more deeply into the wafer and the surface concentration falls so as to maintain a constant dose in the wafer Practical diffusions Most real diffusions follow a two-step procedure, where the dopant is applied to the wafer with a short constant source diffusion then driven in with a limited source diffusion The reason for this is that in order to control the dose, a constant source diffusion must be done at the solid solubility limit of the impurity in the Si, which is on the order of 1020 for most dopants. If only a constant source diffusion were done, this would result in only very high surface concentrations. Therefore, to achieve lower concentrations, a short constant source diffusion to get a controlled dose of impurities in a near surface layer is done first. This diffusion is known as the predeposition or predep step. Then the source is removed and the dose is diffused into the wafer, simulating a limited source diffusion in the subsequent drive-in step. If the Dt product for the drive-in step is much greater than the Dt product for the predep, profile is very close to Gaussian. In this case the dose can be calculated by Eq (23.12)for the predep diffusion coefficient. This dose is then used in the limited source Eq (23. 13)to describe the final prof on the time and diffusion coefficient for the drive-in. If these Dt criteria are not met, then an integral solution exists for the evaluation of the resulting profiles [Ghandhi, 1968 Further profile considerations a wafer typically goes through many temperature cycles during fabrication, which can alter the impurity profile calculating a total Dt product r s that take place at different times and temperatures are accounted for by The effects of many thermal the diffusion that is equal to the sum of the individual process Dt products ∑ Here D, and t, are the diffusion coefficient and time that pertain to the ith process step Many diffusions are used to form junctions by diffusing an impurity opposite in type to the substrate. At the metallurgical junction, x,, the impurity diffusion profile has the same concentration as the substrate. For a junction with a surface concentration No and substrate doping N the metallurgical junction for a Gaussian x:=2 Dt In (23.15) c2000 by CRC Press LLC
© 2000 by CRC Press LLC Here, N0 is the impurity concentration at the surface of the wafer, x the distance into the wafer, and t the diffusion time. As time progresses the impurity profile penetrates deeper into the wafer while maintaining a constant surface concentration. The total number of impurity atoms/cm2 in the wafer is the dose, Q, and continually increases with time: (23.12) For a limited source diffusion an impulse of impurity of dose Q is assumed to be deposited on the wafer surface. Solution of Eq. (23.10) under these boundary conditions, assuming a semi-infinite wafer with no loss of impurity, results in a Gaussian diffusion profile: (23.13) In this case, as time progresses the impurity penetrates more deeply into the wafer and the surface concentration falls so as to maintain a constant dose in the wafer. Practical Diffusions Most real diffusions follow a two-step procedure, where the dopant is applied to the wafer with a short constant source diffusion, then driven in with a limited source diffusion. The reason for this is that in order to control the dose, a constant source diffusion must be done at the solid solubility limit of the impurity in the Si, which is on the order of 1020 for most dopants. If only a constant source diffusion were done, this would result in only very high surface concentrations. Therefore, to achieve lower concentrations, a short constant source diffusion to get a controlled dose of impurities in a near surface layer is done first. This diffusion is known as the predeposition or predep step. Then the source is removed and the dose is diffused into the wafer, simulating a limited source diffusion in the subsequent drive-in step. If the Dt product for the drive-in step is much greater than the Dt product for the predep, the resulting profile is very close to Gaussian. In this case the dose can be calculated by Eq. (23.12) for the predep time and diffusion coefficient. This dose is then used in the limited source Eq. (23.13) to describe the final profile based on the time and diffusion coefficient for the drive-in. If these Dt criteria are not met, then an integral solution exists for the evaluation of the resulting profiles [Ghandhi, 1968]. Further Profile Considerations A wafer typically goes through many temperature cycles during fabrication, which can alter the impurity profile. The effects of many thermal cycles that take place at different times and temperatures are accounted for by calculating a total Dt product for the diffusion that is equal to the sum of the individual process Dt products: (23.14) Here Di and ti are the diffusion coefficient and time that pertain to the ith process step. Many diffusions are used to form junctions by diffusing an impurity opposite in type to the substrate. At the metallurgical junction, xj , the impurity diffusion profile has the same concentration as the substrate. For a junction with a surface concentration N0 and substrate doping NB the metallurgical junction for a Gaussian profile is (23.15) Q N dx N Dt = = x t • Ú (,) 2 0 0 p N Q Dt x Dt (,) x t = exp – Ê Ë Á ˆ ¯ ˜ È Î Í Í ˘ ˚ ˙ ˙ p 2 2 ( ) Dt D ti i i tot = Â x Dt N N j B = Ê Ë Á ˆ ¯ ˜ 2 0 ln
and for a complementary error function profile is x ;=2v Dt erfc (23.16) ffected by the diffusion by using an oxide mask and making a cut in it where specific diffusion is to s are So far we have considered just vertical diffusion. In practical IC fabrication, usually only small Hence, we also have to be concerned with lateral diffusion of the dopant so as not to affect adjacent devices. Two-dimensional numerical solutions exist for solving this problem [Jaeger, 1988]; however, a useful rule thumb is that the lateral junction, y, is 0.8 Another parameter of interest is the sheet resistance of the diffused layer. This has been numerically evaluated for various profiles and presented as general-purpose graphs known as Irvin's curves For a given profile type, such as n-type Gaussian, Irvin's curves plot surface dopant concentration versus the product of sheet resistance and junction depth with substrate doping as a parameter. Thus, given a calculated diffusion profile one coul estimate the sheet resistivity for the diffused layer. Alternatively, given the measured junction depth and sheet resistance, one could estimate the surface concentration for a given profile and substrate doping. Most processing books [e.g. Jaeger, 1988] contain Irvin's curves Ion Implantation Diffusion places severe limits on device design, such as hard to control low-dose diffusions, no tailored profiles, and appreciable lateral diffusion at mask edges. Ion implantation overcomes all of these drawbacks and is an alternative approach to diffusion used in the majority of production doping applications today. Although many different elements can be implanted, IC manufacture is primarily interested in B, P, As, and Sb Ion Implant Technology A schematic drawing of an ion implanter is shown in Fig 23. 3. The ion source operates at relatively high voltage (20-25 kV) and for conventional dopants is usually a gaseous type which extracts the ions from a plasma The ions are mass separated with a 90 degree analyzer magnet that directs the selected species through resolving aperture focused and accelerated to the desired implant energy. At the other end of the implanter is the target chamber where the wafer is placed in the beam path. The beam line following the final accelerator and the target chamber are held at or near ground potential for safety reasons. After final acceleration the beam is bent slightly off axis to trap neutrals and is asynchronously scanned in the X and Y directions over the wafer to maintain dose uniformity. This is often accompanied by rotation and sometimes translation of the target The implant parameters of interest are the ion species, implant energy, and dose. The ion species can consist of singly ionized elements, doubly ionized elements, or ionized molecules. The molecular species are of interest in forming shallow junctions with light ions, i.e, B, using BF=. The beam energy is (23.17) where n represents the ionization state(1 for singly and 2 for doubly ionized species), q the electronic charge, and V the total acceleration potential (source acceleration tube)seen by the beam. The dose, Q, from the implanter is dt (23.18) where I is the beam current in amperes, A the wafer area in cm?, t, the implant time in sec, and n the ionization state c2000 by CRC Press LLC
© 2000 by CRC Press LLC and for a complementary error function profile is (23.16) So far we have considered just vertical diffusion. In practical IC fabrication, usually only small regions are affected by the diffusion by using an oxide mask and making a cut in it where specific diffusion is to occur. Hence, we also have to be concerned with lateral diffusion of the dopant so as not to affect adjacent devices. Two-dimensional numerical solutions exist for solving this problem [Jaeger, 1988]; however, a useful rule of thumb is that the lateral junction, yj , is 0.8xj . Another parameter of interest is the sheet resistance of the diffused layer. This has been numerically evaluated for various profiles and presented as general-purpose graphs known as Irvin’s curves. For a given profile type, such as n-type Gaussian, Irvin’s curves plot surface dopant concentration versus the product of sheet resistance and junction depth with substrate doping as a parameter. Thus, given a calculated diffusion profile one could estimate the sheet resistivity for the diffused layer. Alternatively, given the measured junction depth and sheet resistance, one could estimate the surface concentration for a given profile and substrate doping.Most processing books [e.g., Jaeger, 1988] contain Irvin’s curves. Ion Implantation Diffusion places severe limits on device design, such as hard to control low-dose diffusions, no tailored profiles, and appreciable lateral diffusion at mask edges. Ion implantation overcomes all of these drawbacks and is an alternative approach to diffusion used in the majority of production doping applications today. Although many different elements can be implanted, IC manufacture is primarily interested in B, P, As, and Sb. Ion Implant Technology A schematic drawing of an ion implanter is shown in Fig. 23.3. The ion source operates at relatively high voltage (ª20–25 kV) and for conventional dopants is usually a gaseous type which extracts the ions from a plasma. The ions are mass separated with a 90 degree analyzer magnet that directs the selected species through a resolving aperture focused and accelerated to the desired implant energy. At the other end of the implanter is the target chamber where the wafer is placed in the beam path. The beam line following the final accelerator and the target chamber are held at or near ground potential for safety reasons. After final acceleration the beam is bent slightly off axis to trap neutrals and is asynchronously scanned in the X and Y directions over the wafer to maintain dose uniformity. This is often accompanied by rotation and sometimes translation of the target wafer also. The implant parameters of interest are the ion species, implant energy, and dose. The ion species can consist of singly ionized elements, doubly ionized elements, or ionized molecules. The molecular species are of interest in forming shallow junctions with light ions, i.e., B, using BF2 +. The beam energy is E = nqV (23.17) where n represents the ionization state (1 for singly and 2 for doubly ionized species), q the electronic charge, and V the total acceleration potential (source + acceleration tube) seen by the beam. The dose, Q, from the implanter is (23.18) where I is the beam current in amperes, A the wafer area in cm2 , tI the implant time in sec, and n the ionization state. x Dt N N j B = Ê Ë Á ˆ ¯ ˜ - 2 1 0 erfc Q I nqA dt t I = Ú0
and Beam gaap Resolving Aperture Integrator F:° xam/③ lon Source H25kV FIGURE 23. 3 Schematic drawing of an ion implan As 1000 FIGURE 23. 4 Projected range for B, P, and As based on LSS calculations Ion Implant Profiles Ions impinge on the surface of the wafer at a certain energy and give up that energy in a series of electronic and nuclear interactions with the target atoms before coming to rest. As a result the ions do not travel in a straight line but follow a zigzag path resulting in a statistical distribution of final placement. To first order the ion distribution can be described with a gaussian distribution 2(△Rp)2 Re is the projected range which is the average depth of an implanted ion. The peak concentration, Np, occurs atR, and the ions are distributed about the peak with a standard deviation AR, known as the straggle. Curves for projected range and straggle taken from Lindhard, Scharff, and Schiott(LSS)theory [Gibbons et al., 1975] are shown in Figs. 23. 4 and 23.5, respectively, for the conventional dopants The area under the implanted distribution represents the dose as given by c2000 by CRC Press LLC
© 2000 by CRC Press LLC Ion Implant Profiles Ions impinge on the surface of the wafer at a certain energy and give up that energy in a series of electronic and nuclear interactions with the target atoms before coming to rest. As a result the ions do not travel in a straight line but follow a zigzag path resulting in a statistical distribution of final placement. To first order the ion distribution can be described with a Gaussian distribution: (23.19) Rp is the projected range which is the average depth of an implanted ion. The peak concentration, Np , occurs at Rp and the ions are distributed about the peak with a standard deviation DRp known as the straggle. Curves for projected range and straggle taken from Lindhard, Scharff, and Schiott (LSS) theory [Gibbons et al., 1975] are shown in Figs. 23.4 and 23.5, respectively, for the conventional dopants. The area under the implanted distribution represents the dose as given by: (23.20) FIGURE 23.3 Schematic drawing of an ion implanter. FIGURE 23.4 Projected range for B, P, and As based on LSS calculations. + – R R R C 25kV 0 to 175kV Ion Source C Acceleration Tube Focus Neutral Beam Trap and Beam Gate y-axis Scanner Neutral Beam Beam Trap Integrator Q x-axis Scanner 90° Analyzing Magnet Resolving Aperture C 1 2 3 4 5 + – Wafer in Process Chamber + – N N x R R x p p p ( ) exp ( ) ( ) = - È - Î Í Í ˘ ˚ ˙ ˙ 2 2 2 D Q = = N x dx Np Rp • Ú ( ) 2 0 p D
which can be related to the implant conditions by Eq (23.18 Implant doses can range from 100 to 108 per cm2 and can be controlled within a few percent. The mathematical representation of the implant profile just 2 presented really pertains to an amorphous substrate. Si wafers are crystalline and therefore present the opportunity 0.o1 for the ions to travel much deeper into the substrate by a process known as channeling. The regular arrangement of atoms in the crystalline lattice leaves large amounts of open space that appear as channels into the bulk when viewed from he major orientation directions, i. e, <110>,<100>, and <111>. Practical implants are usually done through a thin FIGURE 23.5 Implant straggle for B, P, and As oxide with the wafers tilted off normal by a small angle(typ- based on LSS calculations. ally 7 degrees)and rotated by 30 degrees to make the surface atoms appear more random. Implants with these conditions agree well with the projected range curves of Fig. 23.4, indicating the wafers do appear Actual implant profiles deviate from the simple Gaussian profiles described in the previous paragraphs Light ns tend to backscatter from target atoms and fill in the distribution on the surface side of the peak. Heavy atoms tend to forward scatter from the target atoms and fill in the profile on the substrate side of the pea This behavior has been modeled with distributions such as the Pearson Type-IV distribution [Jaeger, 1988] However, for implant energies below 200 keV and first-order calculations, the Gaussian model will more than Masking and Junction Formation Usually it is desired to implant species only in selected areas of the wafer to alter or create device properties, and hence the implant must be masked. This is done by putting a thick layer of silicon dioxide, silicon nitride, or photoresist on the wafer and patterning and opening the layer where the implant is desired. To prevent significant alteration of the substrate doping in the mask regions the implant concentration at the Si/mask interface, Xo, must be less than 1/10 of the substrate doping, No Under these conditions Eq.(23 19)can be solved for the required mask thickness as: 10N Rp +△R。2ln (23.21) NB This implies that the range and straggle are known for the mask material being used. These are available in the terature [Gibbons et al., 1975] but can also be reasonably approximated by making the calculations for Si. Sio2 is assumed to have the same stopping power as Si and thus would have the same mask thickness. Silicon nitride has more stopping power than Sio, and therefore requires only 85% of calculated mask thickness, whereas photoresist is less effective for stopping the ions and requires 1. 8 times the equivalent Si thickness Analogous to the mask calculations is junction formation. Here, the metallurgical junction, x;, occurs when ne opposite type implanted profile is equal to the substrate doping, NE Solving Eq (23. 19)for these conditions x=±△R,2l (23.22) Note that both roots may be applicable depending on the depth of the implant. c2000 by CRC Press LLC
© 2000 by CRC Press LLC which can be related to the implant conditions by Eq. (23.18). Implant doses can range from 1010 to 1018 per cm2 and can be controlled within a few percent. The mathematical representation of the implant profile just presented really pertains to an amorphous substrate. Silicon wafers are crystalline and therefore present the opportunity for the ions to travel much deeper into the substrate by a process known as channeling. The regular arrangement of atoms in the crystalline lattice leaves large amounts of open space that appear as channels into the bulk when viewed from the major orientation directions, i.e, <110>, <100>, and <111>. Practical implants are usually done through a thin oxide with the wafers tilted off normal by a small angle (typically 7 degrees) and rotated by 30 degrees to make the surface atoms appear more random. Implants with these conditions agree well with the projected range curves of Fig. 23.4, indicating the wafers do appear amorphous. Actual implant profiles deviate from the simple Gaussian profiles described in the previous paragraphs. Light ions tend to backscatter from target atoms and fill in the distribution on the surface side of the peak. Heavy atoms tend to forward scatter from the target atoms and fill in the profile on the substrate side of the peak. This behavior has been modeled with distributions such as the Pearson Type-IV distribution [Jaeger, 1988]. However, for implant energies below 200 keV and first- order calculations, the Gaussian model will more than suffice. Masking and Junction Formation Usually it is desired to implant species only in selected areas of the wafer to alter or create device properties, and hence the implant must be masked. This is done by putting a thick layer of silicon dioxide, silicon nitride, or photoresist on the wafer and patterning and opening the layer where the implant is desired. To prevent significant alteration of the substrate doping in the mask regions the implant concentration at the Si/mask interface, X0 , must be less than 1/10 of the substrate doping, NB. Under these conditions Eq. (23.19) can be solved for the required mask thickness as: (23.21) This implies that the range and straggle are known for the mask material being used. These are available in the literature [Gibbons et al., 1975] but can also be reasonably approximated by making the calculations for Si. SiO2 is assumed to have the same stopping power as Si and thus would have the same mask thickness. Silicon nitride has more stopping power than SiO2 and therefore requires only 85% of calculated mask thickness, whereas photoresist is less effective for stopping the ions and requires 1.8 times the equivalent Si thickness. Analogous to the mask calculations is junction formation. Here, the metallurgical junction, xj , occurs when the opposite type implanted profile is equal to the substrate doping, NB. Solving Eq. (23.19) for these conditions gives the junction depth as: (23.22) Note that both roots may be applicable depending on the depth of the implant. XR R N N p p p B 0 2 10 = + Ê Ë Á ˆ ¯ D ˜ ln XR R N N jp p p B = ± Ê Ë Á ˆ ¯ D ˜ 2 ln FIGURE 23.5 Implant straggle for B, P, and As based on LSS calculations