Indium and Germanium - Semantic Scholar

Monte Carlo Simulation of Heavy Species (Indium and Germanium) Ion Implantation into Silicon Y. Chen a, B. Obradovic a, M. Morris b, G. Wang a, G. Balamurugan a , D. Li a, A. F. Tasch a, D.Kamenitsa c, W. McCoy c, S. Baumann d R. Bleier d, D. Sieloff b, D. Dyer b, P. Zeitzoff e a

Microelectronic Research Center, The University of Texas at Austin, Austin TX, 78712 b Motorola, Austin TX 78721 c Eaton Corporation, Boston MA 78758 d Evans Texas, Round Rock TX 78681 e Sematech, Austin TX 78702

Abstract Monte Carlo ion-implant models for germanium and indium implantation into singlecrystal silicon have been developed and are described in this paper. The models have been incorporated in the UT-MARLOWE ion implantation simulator, and have been developed primarily for use on engineering workstations. These models provide the required as-implanted impurity profiles as well as damage profiles, which can be used as inputs for transient enhanced diffusion simulation and subsequent multiple implant simulation. A comparison of simulation results with experimental data shows that the models predict both the impurity profiles and the damage profiles very successfully for a wide range of implant conditions. The damage profiles from germanium implant simulations have been used for subsequent multiple implant simulations and excellent agreement with experimental results has been achieved.

Introduction As integrated circuit devices scale into the deep sub-micron regime, ion implantation will continue to be the primary means of introducing dopant atoms into silicon. Different types of impurity profiles such as ultra-shallow profiles or retro-grade profiles are necessary for deep submicron devices in order to realize the desired device performance. In order to fulfill these requirements, heavy species implants are used more and more frequently. For example, germanium implantation has two major applications in deep submicron device fabrication: one is for pre-amorphization, a method of suppressing channeling tails and achieving shallow impurity profiles; the other application is to use a high dose germanium implant to form hetero-structure SiGe MOSFET[1-3]. Also, indium and antimony implants have been used to provide retrograde profiles in MOS devices. Through implantation of large mass atoms such as indium, very abrupt or retro-grade doping profiles can be achieved. The retrograde doping profiles can serve the needs of channel engineering in deep submicron MOS devices for punch-through suppression and threshold voltage control. In addition to retrograde profile and low coefficient of diffusion at high temperatures, indium has been shown [4] to have several other advantages compared to boron : indium implanted channel doping results in a lower silicon surface roughness and a higher channel mobility, resulting in better turn-off behavior and drive current in ultra-short-channel MOS devices. 1

The development of ion implant models for germanium and indium not only will facilitate the applications of indium and germanium implants, but also will provide a basis for modeling other heavy species implants into silicon. Previously, models have been developed and reported for boron, BF2, arsenic, phosphorus and silicon self implants[5-9]. Arsenic is the heaviest ion species for which ion implant models have been developed. Because germanium is very close to arsenic in mass, it is expected that the model parameters for germanium should be close to those of arsenic. Therefore, germanium modeling provides a case where the strength of the physical components of the previously developed models can be tested. With the success of indium modeling, which extends the range of the ion mass covered by our previous models, models for other species such as antimony may be generated by taking the approach of interpolation or extrapolation with a relatively small amount of effort. The objectives of modeling heavy species ion implants into single-crystal silicon are as follows: first we expect the models to accurately predict the as-implanted impurity profiles over a wide range of ion implant conditions; second, we expect the models to predict the damage profiles accurately. The damage profile prediction is very important for the following reasons: First, the defect dechanneling effect needs to be simulated so that the impurity profiles as a function of dose can be accurately predicted. Second, accurate damage profiles are needed so that the damage profiles can be used as inputs for transient enhanced diffusion (TED) simulation. Third, damage profiles are needed in the simulation of multiple implants, in which the existing damage from the initial implant has a large effect on the impurity and damage profiles of subsequent implants. As ions enter silicon, they give up their energy to the lattice atoms and finally come to rest at certain depths in the silicon. The energy loss of an ion can be divided into two components: nuclear stopping and electronic stopping. For Monte Carlo simulation, the nuclear stopping is treated with the binary collision approximation (BCA). The energy is also lost to the electronic cloud in two ways: one is due to the inelastic loss during a collision with silicon lattice atom and the other is inelastic loss between collisions. In all of the important modeling components, which include nuclear stopping, electronic stopping, damage generation and interaction, it is expected that heavy ions may exhibit some different behavior from the lighter ones. Before describing the models, the details are given for the experiments that were performed in order to provide experimental data for comparison with the prediction of the models.

Experimental Details For the development and verification of the models, a detailed experimental study was conducted to understand the germanium and indium profile dependence on key implant parameters such as energy, tilt/rotation angle, and dose. Over forty 150mm bare silicon wafers were implanted with germanium. An HF dip was performed before each implant in order to remove all native oxide and to suppress rapid re-growth of the native oxide prior to implantation. The energies used were 10keV, 20keV, 40keV and 80keV, and the

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doses ranged from 5 ×1012cm-2 to 2×1015 cm-2. The tilt/rotation angles ranged from 0o/0o to 6o/30o. The indium implants into bare silicon were performed over an energy range of 5-200keV, and included a similar range of doses and implant angles. The tilt angles were measured relative to the direction perpendicular to the [ 100] wafer surface. The rotation angle measures the rotation of the wafer about an axis perpendicular to the wafer surface. These two angles together determine the incident angle of the implant ion beam. The implants with tilt angles near 0o are not only highly sensitive to the tilt/rotation angles, but are also affected by the crystal cut-error, which is the angular deviation of the [ 100]direction in the crystal from the normal direction of silicon wafer. In order to correctly account for the crystal cut-error, samples from the 8 wafers with on-axis(0o tilt angle) implants were measured using X-ray Scitag Spectrostroscopy. The measured crystal cut-errors were used to calculate the real tilt/rotation angles relative to the [ 100] crystal orientation. In this way, the crystal cut errors are properly taken into account. The implanted wafers were then diced into 5mm×5mm and 10mm×10mm samples for damage and impurity profile measurements. Secondary Ion Mass Spectroscopy (SIMS) was used for the impurity profile measurements, and the Rutherford Backscattering Spectrometry (RBS) channeling technique was used for the damage profile measurements. The channeled RBS signals (yields) from each implant are compared with channeled RBS signals from virgin silicon and amorphous silicon. The yield versus energy profile is then transformed into a percentage amorphization versus depth profile.

Model Details 1. The Scattering Process  Time Integration BCA Model

An ion traveling through a silicon crystal experiences repulsive electric fields from several sources. The first comes from the screened Coulumb electric field of the nucleus of the silicon atoms. This gives rise to the nuclear stopping. The second source of stopping mechanism is the effect of polarization of electrons on the electric field, this gives rise to non-local electronic stopping. The third stopping force comes from the interaction of the electronic cloud of the ion with the more tightly bound electrons of the Si target atoms. The electrons can transfer a part of their momentum to the electrons of the targets, thereby causing a reduction of the overall energy of the ion; this gives rise to local electronic stopping.

The inter-atomic potential, which describes the electrostatic repulsion of the screened ion-target nuclei, is provided by the ZBL universal potential [10]. In this theory, the interatomic potential is considered to be a two-body center force potential:

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Z1Z 2 e 2 V (r )= Φ u ⋅ r where Φ u is the screening function and is given by:

(1)

Φ u = 0.1818e − 3.2 x + 0.5099e − 0.9423 x + 0.2802e − 0.4029 x + 0.02817e − 0.2016 x

(2)

r (3) 0.8854 ⋅0.529 / Z 10.23 + Z 20.23 Since the implant models simulate both implants into bare silicon and implants into silicon with an overlying layer of oxide, scattering will take place between indium and silicon, indium and oxygen, germanium and silicon, and between germanium and oxygen. The ZBL universal potential is used for calculation of the inter-atomic potential of all of the four kinds of scattering events. x=

(

(

))

Another major challenge in developing an accurate Monte Carlo model is obtaining a reliable and comprehensive electronic stopping model. Due to the silicon wafer’s crystal structure, the as-implanted profiles exhibit channeling tails[11]. The channeling component is mainly caused by ions traveling in a channel in the crystal structure. When this happens, the ions suffer much less nuclear stopping than do the ions in amorphous silicon. This significantly increase the importance of electronic stopping as an energy loss mechanism. For this reason, an accurate electronic stopping model is necessary. There are two parts of electronic stopping that need to be taken into account: the electronic loss between collision and the electronic loss during collision. First, the following expression is used to obtain the inelastic electronic loss between collisions[6]: 4πq 4 ⋅ρ (4) dE / dx = 2 2 L ε 0 mv Where v, m and Z1 are the velocity, mass and charge of ion in the silicon respectively, and ρ is the electron density at the position of the ion. 3  v  k (χ )  , v    f   L=   2mv 2  ln   2 2   h ω p + E g

v < vf

(5) 4  3  v 2   v  −   − (3 / 14 + χ / 3)  , v > v f 1/ 2   v  5 v f   f   Where χ 2 = 1 / πk f a0 . a0 is the Bohr radius. kf the Fermi wave number , and vf is the Fermi velocity.

(

)

Using a similar approach as that of Obradovic[12], in which Firsov’s theory of electronic stopping is used[13] for local electronic stopping, local electronic stopping models for

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germanium and indium implants into silicon are obtained. In Obradovic’s model, the forces acting on the ion and target during each collision due to electronic stopping are induced by the exchange of electrons between the incident ion and the target atom. By exchanging electrons, the ion and the target atom exchange momentum. Thus the force v due to electronic stopping is proportional to the relative velocity of the ion( Vion ) and the v target (Vt arg et ). The force is given by: v v v nv F = me (Vt arg et − Vion ) ⋅∫ dS (6) 4 where n is the electron density distribution, and v is the orbital velocity of the electrons. The integration is performed over a plane bisecting the line connecting the target and the ion. Traditional BCA[14-16] simulators have been very successful for ion implant simulation. However, a simplified approach has been taken for modeling the interaction between the ion and the target, namely, ignoring the coupling between the different stopping forces. The trajectory of the ion is computed using the inter-atomic potential, and the total electronic stopping energy loss during the collision is separately subtracted from the energy of ion after the collision. Even though this approach has been very successful in modeling moderate and high-energy ion implants into silicon[14-16], a more realistic model can extend its validity to low energies. For heavy species implants at low energies, the interaction time between ion and target is longer, therefore, the coupling between different stopping forces becomes more significant compared to the stopping forces. In this paper, Obradovic’s approach taking into consideration of all of the stopping forces, as well as the coupling between different forces, is adopted[12] throughout the energy range. In the models for germanium and indium implants, instead of using an asymptotic trajectory, the forces due to electronic stopping acting on the ion and target are computed along a realistic trajectory throughout the scattering event. By integration along a realistic trajectory, the coupling between the inter-atomic forces and the local electronic stopping forces is correctly accounted for. For each collision event, with the basic equations describing the forces on both the ion and the target, the trajectories of the ion and target are integrated over time. The integration is performed throughout the collision. The final trajectory and velocity of the ion and targets as well as the energy loss, are computed. This information is then saved as a set of scattering tables. Each scattering table is organized by energy and impact parameter, with each entry containing the velocity, path and energy loss of a scattering event for a specific energy and impact parameter. During the implant simulation, the scattering tables are loaded and the path of each ion scattering process is extracted from the scattering tables. Scattering events involving an energy and impact parameter in between the scattering table values are treated by interpolation. 2. Damage Modeling 1  Kinchin-Pease Model

The damage modeling is based on the previously developed damage models of UTMARLOWE for As, B and P[8, 17]. Two damage models have been developed for each species: One is a physically based damage model, which rigorously calculates the 5

damage formation and defect diffusion process during ion implantation. It is called the Kinetic Accumulation Dynamic Model (KADM), but is relatively CPU time consuming. The other damage model is a more computationally efficient model, and is called the Kinchin-Pease model. Both the KADM and Kinchin-Pease models have been developed for each species(In and Ge). An energetic ion implanted into single-crystal silicon can displace hundreds of secondary silicon atoms by direct or indirect collisions. A lattice atom is knocked out of its lattice site whenever it receives an energy greater than the displacement energy, leaving behind a vacancy at the lattice site and becoming an interstitial when it is finally brought to rest in the crystal. It is very CPU time consuming to follow every particle displaced from its original site even in a binary collision approximation (BCA) based code. When the extension of the subcascade initiated by the primary-knock-on-atom (PKA) is small compared to the ion range (i.e., when the implant energy is sufficiently low), the interstitials and the vacancies generated by a PKA can be assumed to be in the same local region where the collision occurs. Hence, the deposited energy in a local region, calculated by using the binary collision approximation between the PKA and the lattice atom, can be used to estimate the number of defects in that region. Using the modified Kinchin-Pease formula[18], this energy is converted into the number of point defects n: κE , (7) n = 2E d where κ=0.8 is a constant, and Ed is the displacement threshold energy, which is generally accepted as 15 eV.

Not all of the defects as calculated by Eq.(7) will survive, since some of the defects may recombine within the cascade as well as with the defects generated by previous cascades. The net increase in point defects due to the deposit of energy E after recombination is thus given by N ∆N = n ⋅ f rec (1 − ), (8) Nα where n is given by Eq.(7), N is the local defect density, and N α is the critical defect density for amorphization. This formula is similar to that of Hobler et al.[19] where the local defect density is denoted by Nv. However, there are some subtle differences. In their model, it is assumed that frec is the fraction of defects surviving the recombination within one recoil cascade. Also, recombination with point defects generated by previous cascades leads to a damage saturation density Nsat, a species dependent parameter. However, in our model frec represents the fraction of defects surviving both intra-cascade and inter-cascade recombination, instead of just the intra-cascade recombination. The factor (1 − N N α ) has been introduced because it is assumed that the energy is deposited on lattice atoms as well as on displaced atoms. Only the energy deposited on lattice atoms will contribute to an incremental increase in the number of defects. It should be noted that if the crystal should be amorphized, N=Nα and ∆n = 0 for any subsequent cascades, which implies that the defect density remains the same in the amorphous region. This is of course one of the characteristics of the amorphous state. Also, N α has a fixed value

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α N l for all species, where α is the percentage of the critical defect density with respect to the lattice density Nl. In the K-P model, the vacancy concentration and the interstitial concentration are always the same for computational simplicity, although they can differ in a more rigorous model such as the KADM Model. When the defect density reaches a critical value in a local region, amorphization will occur. For ion implantation with a sufficiently high dose, certain regions of the target can be completely amorphous. It is assumed that as the defect density at a certain region reaches a critical value, the crystal region undergoes a crystalline/amorphous phase transition, and this region is said to be amorphous. For all implant species, 10% of the lattice density is taken to be the critical density [20]. Once such an amorphous threshold is reached in a local region, the point defects formed in that region are no longer added to the point defect concentration, which has already been accounted for in Eq. (8). As is well known, the accumulated damage can effectively alter the subsequent ion trajectories. The probability that an implanted ion is traveling in a damaged region is given by N P =γ , (9) Nα where γis a constant, and N is the local defect density. It is found from ab initio calculations [21] that the dumbbell configuration has the lowest energy for a neutral interstitial silicon atom. In this configuration, two silicon atoms displace along the (110) direction by about one bond distance, sharing one single lattice site. If a projectile encounters an interstitial, the interstitial is assumed to be in a dumbbell configuration and a normal scattering event takes place. The separation between the two “split” atoms is taken as 2.76 Å, and for simplicity, the other atoms are assumed to remain in their lattice sites. A random configuration is used by Hobler et al. [19], wherein the interstitial is placed randomly in the plane perpendicular to the ion’s direction of motion within a sphere with a specified radius centered at the lattice site. In practice, this approach can be used without significantly changing the simulation results. However, this introduces another parameter, i.e., the radius of the distribution sphere of the interstitials. The basic assumption in the modified Kinchin-Pease model is that the trajectories of the secondary ions are much shorter compared with that of the primary ion. When an ion is implanted into a silicon crystal at higher energies, a large amount of kinetic energy can be transferred to a target atom in a single collision. This occurs more frequently for heavy species implants. The damage models are implemented in such a way that the silicon crystal is divided into many cells with a fixed volume. The energy loss in each collision is converted into a defect number in a local region( a single cell) according to Eq. (7). Therefore, if the deposit energy is too high, and the energy loss during a collision is deposited in a single cell, this local region can be totally amorphized as the result of a single collision. Although a high-energy impact may cause significant damage in a local region, amorphization of a local region due to a single collision is not realistic. In fact, when the deposited energy is larger than a certain value[22], the energy loss from

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electronic excitation would exceed the energy loss from all other sources, and the energy lost in this way will not cause as much damage as calculated by Eq. (7). For this reason, the cutoff energy was introduced into the damage models in order to account for this effect. Whenever the deposited energy E is more than Ecut-off, only Ecut-off is deposited and the number of defects is thus calculated. With Ecut-off being roughly the energy needed to amorphize the local region (125 unit cells) for boron implants, this local region cannot be amorphized due to one single collision since ∆N calculated from Eq. (8) is always less than N α . Because of the significant influence of damage on the impurity profiles at high energies, Ecut-off is adjusted for each species in order to obtain the best overall agreement between simulation results and experimental data. It’s value is approximately 3keV for the current local region size(125 cells). It should be noted, however, that this approach still effectively ignores the large amount of damage scattered in a deeper region, which is caused by the high kinetic energies of secondary Si atoms. A more physical approach would be to follow the secondary projectiles that receive high kinetic energies until their energies fall below a certain predefined value, and then replace them with the KinchinPease damage model. On the other hand, this increases the CPU time considerably. In order to keep the computational time at a reasonable minimum, the deposit energy cut-off approach is chosen for the energy range to which the K-P model is applied. 3. Damage Modeling 2  KADM Model Description

The Kinetic Accumulative Damage Model (KADM) was first developed by Tian [5]. In this model, the physical processes during ion implantation are divided into two phases due to different time scales. The first phase is defect production, while the second phase is defect diffusion and interaction during the time between incident ions. The first phase (displacement cascade) takes place in less than 1 pico-second, while the second phase happens shortly after the displacement cascade and lasts until the next ion comes to the same damage region. This phase lasts for approximately 0.1 millisecond or longer for typical dose rates. The algorithm of this damage model is as follows: For the first ion, the primary damage state is generated by the binary collision approximation (BCA) code. This damage information is then fed into a module, which simulates defect diffusion and reactions for an amount of time determined by the dose rate and the ion implanter scanning pattern. Subsequent ions are allowed to collide with the previous damage, and the damage thus generated is accumulated over the previous damage with near neighbor defect reactions being taken into account. The resulting (mobile) defects then diffuse and react for a certain amount of time, which again is determined by the dose rate and the scanning pattern. This cycle is repeated until all of the ions are implanted (simulated) for a given dose. The defect diffusion is simulated by a Monte Carlo algorithm which is based on defect hopping. The defect interactions are governed by "interaction rules", which include interstitial-vacancy recombination, clustering of same type of defects, defect-impurity complex formation, emission of mobile defects from clusters, surface effects, etc. Similar to the Kinchin-Pease model, a 10% critical defect density is assumed to be the ion beam induced amorphization threshold.

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Ion implantation simulators have traditionally used a super-ion approach, in which each simulated ion represents a large number of actual implanted ions. The model developed by Tian et al.[5] proposed that each simulated ion represent a real ion. The basic idea is to treat the ion implantation as implanting into an ensemble of implant windows. Assuming that the ions are uniformly distributed across the wafer, the number of ions implanted into each window can be calculated for a given dose. In principle, this is the number of ions required to do the simulation. More ions are used only to generate statistically significant profiles. This approach is termed “ion splitting” because of its splitting of the simulation ions into many different implant windows. Due to the fact that each ion cascade generates hundreds or even thousands of point defects, the number of ions required to generate the statistically significant damage profiles is much less than the number required to generate the impurity profiles. We can actually utilize this fact to advantage to reduce the CPU time considerably. The basic idea is to divide the simulation ions into “real” ions and “shadow” ions. The “real” ions generate full cascades, while the “shadow” ions are followed only when they travel through the damaged (by the “real” ions) crystal. The additional shadow ions provide the desired statistical significance in the computed impurity profile. The displaced silicon ions are not followed when the ``shadow'' ion is simulated. This approach allows us to obtain both the impurity profiles and damage profiles with comparable statistical significance at the same time. This technique of reducing the computational time is referred to as “shadowing”.

Simulation Results and Discussion The models for indium and germanium produce the impurity profiles and damage profiles as functions of depth. During each simulation, the interstitial/vacancy concentration profile is transformed into an amorphization percentage versus depth profile, in order to be able to compare with the RBS data. For each implant, the impurity profile is compared with the SIMS profile, and the damage profile is compared with the RBS profiles if the damage is significant enough to be detected by RBS measurements. The models have been tested over a wide range of implant conditions. Table 1 shows the range in which the impurity profiles have been validated, and Table 2 shows the range in which the damage profiles have been validated.

Species

Table 1. Range of Validation for Impurity Profiles Energy Range (keV) Tilt Angle Rotation Angle Dose Range(cm-2)

Indium

5-100

0°

0°

2×1012 - 2×1014

0°

0°

1×1012 - 1×1013

Germanium

110-200 through oxide 10-80

0°-7°

0°-30°

5×1012 - 2×1015

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Species Indium Germanium

Table 2. Range of Validation for Damage Profiles Energy Range (keV) Tilt Angle Rotation Angle Dose Range(cm-2) 5-100 0° 0° 2×1014 10-80 0°-7° 0°-30° 2×1013 - 2×1015

1. Germanium Implants Figure 1 illustrates the ability of the new germanium model to successfully predict the impurity profiles as a function of dose. As can be clearly seen, the germanium implant model can very successfully simulate the implant-induced dechanneling effect. As shown in the figures, both the Kinchin-Pease and the KADM damage models provide accurate as-implanted impurity profiles. Compared to the computationally efficient KP model, the KADM model is somewhat more accurate and provides more detailed damage information, as shown in Figure 2. The predicted and experimental tilt/rotation angle dependence of both the impurity and damage profiles are compared in Figure 3 at a dose of 1×1014 cm-2 and an energy of 80keV. It is can be seen that the predicted impurity profiles and the SIMS profiles are in excellent agreement, and that the predicted damage profiles and the RBS profiles are in very good agreement. It should also be noted that the cross-over of the damage profile at approximately 0.07 µm is correctly predicted. As indicated in the figure, the channeling effects and damage build up are closely related. Since the on-axis implant has more channeling, it not only exhibits a deeper impurity profile, but a deeper and wider damage profile as well. This is more pronounced for relatively higher energy implants. In addition, since the channeled ion suffers less scattering, the damage level of the on-axis implant is relatively lower than that of the off-axis implant, with all other implant conditions identical. For on-axis, relatively high energy implants, if the dose is appropriate, the formation of a buried amorphous layer can be observed. Because the amorphization transformation is not easy to capture, only the 1×1014cm-2-dose implant exhibits a buried layer for germanium 80keV implants, as shown in the figure. Figure 4 depicts the simulation results for both damage and impurity profiles as functions of energy compared with experimental data. Again, it is can be seen that the impurity profiles and the SIMS profiles are in excellent agreement, and that the predicted damage profiles and the RBS profiles are in very good agreement. As indicated by the damage profiles, the new germanium model can successfully simulate the effect that as the energy increases, the amorphization layer thickness increases accordingly. The predicted impurity and damage profiles are compared with SIMS and RBS data in Figure 5, for 80keV off-axis Ge implants at various doses. It is can be seen that the new germanium model can very effectively simulate the process of damage accumulation as the implant dose increase. The damage profiles also indicate the amorphization process takes place between the doses of 2×1013cm-2 and 1×1014cm-2. Generally, at all energies between 10keV and 80keV, the amorphization threshold is approximately 3 - 5×1013cm-2. The threshold is slightly lower for off-axis implants than for on-axis implants. Below this

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dose, the amorphization percentage is usually below 3~5%, which is in the same level as the noise of the RBS measurements. When the dose increases above this level, it can be observed from the RBS profiles that damage is building very quickly, and an amorphization layer is formed in the silicon. If the dose continues to increase, the amorphization layer thickness will increase slightly, as shown in the figure; the channeling tails cease to increase. This effect indicates that the amorphization and shut down of channels takes place within the same order of magnitude of dose. Pre-amorphization is a very important application for germanium implantation. Figure 6 shows a case of germanium pre-amorphization followed by boron implants. The boron implants are at a dose of 1×1014cm-2 , an energy of 35keV, and tilt/rotation angles of 0o/0o. This figure shows the effect of different implant doses of germanium on the subsequent boron implants. As the dose increases, the subsequent boron implant will “see” more and more damage, and thus the boron channeling tails are suppressed more and more. The new model successfully predicts this effect. Again, as shown in the figure, the predicted boron impurity profiles are in excellent agreement with the SIMS data. During the development of the germanium implantation model, the parameters derived were compared to those of the arsenic models. Since the ZBL universal potential is used for the inter-atomic potential, the only parameters that require adjustment are those related to the damage models. It turns out that the parameters for germanium are very close to those of arsenic. For example, in the Kinchin-Pease damage model, the parameter κ in Eq. (7) is 0.8 for arsenic and 0.83 that for germanium. The closeness of the parameters provides much confidence to extend the models to antimony with the indium implantation success. 2. Indium Implants The comparison of the predicted indium impurity profiles with SIMS data is shown in Figure 7. It can be seen from the figure that the channeling tail drops very slowly with depth. This phenomenon is due to the large atomic mass of indium. The new indium model accurately predicts this effect. Figure 8 shows the indium implants through a thin layer of oxide (90Å) at doses of 1×1012 cm-2 and 1×1013cm-2. At such low doses, the damage is not sufficient to block the channels. Therefore, the profiles of the two different doses are relatively proportional to each other. Again, in both figures, the predicted impurity profiles are in very good agreement with the SIMS profiles. Figure 9 shows the predicted indium implant damage profile as a function of energy compared with the RBS profiles. It can be seen that at different energies, at a dose of 2×1014 cm-2, amorphous layers are formed in the silicon. Again, the new indium model accurately predicts the amorphization thickness.

Conclusions New models for germanium and indium have been developed for the simulation of germanium and indium implants into single-crystal silicon. The models explicitly account

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for the stopping forces from different sources, as well as the coupling between the different stopping forces. Two previously developed damage models have been modified to simulate damage accumulation process and crystal amorphization at room temperature. The simulated impurity profiles and damage profiles have been compared with SIMS and RBS experimental profiles, respectively. It has been shown that the impurity profiles predicted by the new model are in excellent agreement with the SIMS profiles, and the damage profiles are in very good agreement with RBS profiles. The models have also been applied to multiple implants, and very good agreement with experimental results is achieved. The closeness of the germanium and arsenic parameters provides much confidence to extend the models to the simulation of the implantation of other heavy species.

Acknowledgements This work was supported in part by the Semiconductor Research Corporation, Motorola, Intel, AMD, Rockwell, and the Texas Advanced Technology Program.

References 1. Hong Jiang and R. G. Elliman, "Electrical properties of GeSi surface- and buriedchannel p- MOSFETs fabricated by Ge implantation", IEEE Transactions on Electron Devices, vol. 43, pp. 97-103, 1 1996. 2. C. R. Selvakumar and B. Hecht, "SiGe-channel n-MOSFET by germanium implantation", IEEE Electron Device Letters, vol. 12, pp. 444-6, 8 1991. 3. M. Yoshimi, et al., "Suppression of the floating-body effect in SOI MOSFET's by the bandgap engineering method using a Si/sub 1-x/Ge/sub x/ source structure", IEEE Transactions on Electron Devices, vol. 44, pp. 423-30, 3 1997. 4. P. Bouillon, F. Benistant, T.Skotnicky, and G. Guengan et. al., "Re-examination of indium implantation for a low power 0.1 micron technology", in International Electron Devices Meeting Technical Digest. pp. 897-900,. 1995. 5. S. Tian, S. J. Morris, M. Morris, B. Obradovic, and A. F. Tasch, "Monte Carlo Simulation of Ion Implantation Damage Process in Silicon", in International Electron Devices Meeting Technical Digest. pp. 713-716,. 1996. 6. S. J. Morris, B. Obradovic, S. H. Yang, and A. F. Tasch, "Modeling of boron, phosphorus, and arsenic implants into single-crystal silicon over a wide energy range (few keV to several MeV)", in International Electron Devices Meeting Technical Digest. pp. 721-724,. 1996. 7. G. Wang, S Tian, M. Morris, S. Morris, B. Obradovic, G. Balamurugan, and A. Tasch, "A computationally efficient ion implantation model: modified Kinchin-Pease model", in Microelectronic Device Technology, Austin, TX, USA: SPIE-Int. Soc. Opt. Eng. pp. 324-33,. 1997. 8. S. Tian, G. Wang, M. Morris, S. Morris, B. Obradovic, and A. Tasch, "A computationally efficient ion implantation damage model and its application to multiple implant simulations", in SISPAD '97. 1997 International Conference on

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Simulation of Semiconductor Processes and Devices. Technical Digest, Cambridge, MA, USA: IEEE; New York, NY, USA. pp. xii+353, 309-12,. 1997. 9. S. Tian, M. F. Morris, S. J. Morris, B. Obradovic, Wang Geng, A. F. Tasch, and C. M. Snell, "A detailed physical model for ion implant induced damage in silicon", IEEE Transactions on Electron Devices, vol. 45, pp. 1226- 38, 6 1998. 10. J.F Ziegler, J.P Bieresack, and U Littmark, "The stopping and range of ions in solid", , vol. 1, pp. 11. Robert Simonton and Al F. Tasch, Channeling Effects in ion implantation, in Ion Implantation Technology, J.F. Ziegler, Editor. 1992, North Holland. p. 119-233. 12. B.J. Obradovic, et al., "Low energy model for ion implantation of arsenic and boron into (100) single-crystal silicon", in Measurement, Characterization and Modeling of Ultra-Shallow Doping Profiles in Semiconductors. pp. p. 514, 49.1-9,. 1997. 13. O. B. Firsov, Soviet Physics JETP, vol. 36 (9), No. 5, pp. 1076 - 1080, Nov. 1959. 14. Mark T. Robinson and Ian.T torrens, "Computer simulation of atomic displacement cascades in solid in the binary-collision approximation", Physical Review B, vol. 9, pp. 5008-5024, 12 1974. 15. S. H. Yang, S. J. Morris, S. Tian, K. Parab, B. Obradovic, M. Morris, A. F. Tasch, and C. M. Snell, "An accurate Monte Carlo binary collision model for BF/sub 2/ implants into (100) single-crystal silicon", in Proceedings of 11th International Conference on Ion Implantation Technology,Austin, TX, USA: IEEE; New York, NY, USA. pp. xxvii+832, 547-50,. 1996. 16. M. Posselt, "Computer simulation of channeling implantation at high and medium energies", Nucl. Instrum. Methods Phys. Res. B, vol. B80-81, pt.1, pp. 28-32, 1993. 17. G Wang, Computationally Efficient Models for Monte Carlo Ion Implantation Simulation in Silicon, M.S. Thesis, The University of Texas at Austin, 1997. 18. M. J. Norgett, M. T. Robinson, and I. M. Torrens, "A Proposed Method of Calculating Displacement Dose Rates", Nucl. Eng. and Des., vol. 33, pp. 50-54, 1975. 19. G. Hobler, A. Simionescu, L. Palmestshofer, C. Tian, and G. Stingeder, "Boron Channeling Implantations in Silicon: Modeling of Electronic Stopping and Damage Accumulation", J. Appl. Phys., vol. 77, pp. 3697-3703, April 1995. 20. L. A. Christel, J. F. Gibbons, and T. W. Sigmon, "Displacement criterion for amorphization of silicon during ion implantation", J. Appl. Phys., vol. 52(12), pp. 7143-6, Dec. 1981. 21. J. Zhu, L. H. Yang, C. Mailhiot, Tomás Diaz de la Rubia, and G. H. Gilmer, "Ab initio pseudopotential calculations of point defects and boron impurity in silicon", Nucl. Instr. Meth. Phys. Res. B, vol. 102, pp. 29-32, 1995. 22. G. H. Kinchin and R. S. Pease, "The Displacement of Atoms in Solids by Radiation", Rep. Progr. Phys., vol. 18, pp. 1, 1955.

13

1021

1018

-3 UT-MARLOWE -KADM SIMS

dose: 2x1015 cm-2 5x1014 cm-2 1x1014 cm-2 2x1013 cm-2 5x1012 cm-2

1019

1017

1016 0.0

0.1

0.2

0.3

germanium concentration (cm

1020

)

Germanium Energy=40keV tilt=6o rotation=30o

Germanium Energy=40keV o o tilt=6 rotation=30

1020

dose: 15 -2 2x10 cm 14 -2 5x10 cm 14 -2 1x10 cm 2x1013cm -2 5x1012cm -2

1019

1018

UT-Marlowe KP

sims

1017

1016 0.0

0.1

depth (micron)

0.2

depth (micron)

Figure 1. Illustration of the ability of the new germanium model to accurately predict asimplanted impurity profiles for both the Kinchin-Pease and KADM damage models.

110 Germanium implant

100

energy=40keV tilt=6o rotation=30o

90

Percentage amorphization


-3

)

1021

80 70 60

dose=5x10 14cm-2 13 -2 dose=2x10 cm

50 40

RBS KADM damage Model Kinchin-Pease

30 20 10 0 0.00

0.05

0.10

0.15

0.20

Depth (µm)

Figure 2. Comparison of the damage profiles measured by RBS with both the KinchinPease and the KADM models. The KADM model can give somewhat more accurate damage profiles compared to the Kinchin-Pease model, and can provide more detailed information on the defects.

14

0.3

) -3


Ge ->Si energy=80keV dose=1x1014cm-2

1019

Model Prediction SIMS

tilt angle/rotation angle=0o /0o tilt angle/rotation angle=6o /30 o

1018

1017

1016 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

depth (µm) (a) 120

Ge->Si energy=80keV 14 -2 dose=1x10 cm

110


100

RBS Model Prediction

90 80 70 60 o

o

tilt/rotation angle=0 /0 tilt/rotation angle=6o/30o

50 40 30 20 10 0 0.00

0.05

0.10

0.15

0.20

0.25

0.30

Depth (µm)

(b) Figure 3. Simulation of the tilt/rotation angle dependence for both Ge impurity and damage profiles at an energy of 80keV and a dose of 1x10 14cm-2: (a) comparison with SIMS impurity profile and (b) comparison with RBS damage profiles. Note that the flat tails in the experimental RBS profiles are due to RBS background noise, and hence should be ignored. 15


-3

)

1021

Ge->Si dose=1x1014cm -2 tilt=6o rotation=30o

1020


energy=10keV energy=20keV energy=40keV energy=80keV

1019

1018

1017

1016 0.0

0.1

0.2

0.3

depth (µm) (a)

120

Ge->Si

110 100


RBS data Model Prediction

dose=1x1014 cm-2 tilt=6o rotation=30o

90 80

energy=80keV energy=40keV energy=20keV energy=10keV

70 60 50 40 30 20 10 0 0.00

0.05

0.10

0.15

0.20

Depth (µm) (b)

Figure 4. Simulation of the energy dependence for both the impurity and the damage profiles for germanium implants at a dose of 1x10 14cm -2 : (a) comparison with SIMS impurity profiles and (b) comparison with RBS damage profiles.

16

1021


-3

)

Ge->Si Energy=80keV o o tilt=6 rotation=30

1020

dose: 2x1015cm-2 5x1014cm-2 1x1014cm-2 2x1013cm-2 5x1012cm-2

1019


1018

1017

1016 0.0

0.1

0.2

0.3

0.4

depth (µm)

(a) 120

Ge->Si

110

energy=80keV tilt=6o rotation=30o


100

RBS data

Model Prediction

90 80 70 dose=2x1015cm-2 dose=5x1014cm-2 dose=1x1014cm-2 dose=2x1013cm-2

60 50 40 30 20 10 0 0.00

0.05

0.10

0.15

0.20

0.25

0.30

Depth (µm)

(b) Figure 5. The dependence of both the impurity and the damage profiles on dose is shown for germanium implants at a energy of 80keV and tilt/rotation angles=6 o/30o : (a) comparison with SIMS impurity profiles and (b) comparison with RBS damage profiles.

17

1020

B->Si Energy=35keV 14 -2 dose=1x10 cm o o tilt=0 rotation=0

concentration (cm -3)

1019

SIMS Model Prediction

1018

1017

1016

1015 0.0

Pre-amorphization w/o preamorphization 13 -2 with Ge 25kev 2x10 cm 14 with Ge 25kev 5x10 cm-2

0.1

0.2

0.3

0.4

0.5

0.6

depth (µm)

Figure 6. Illustration of the ability of the new germanium model to accurately simulate the dependence of boron implant profiles on pre-amorphization doses: the energy of the boron implant is 35keV. The tilt/rotation angles are 0 o/0o.

18

Indium concentration (cm -3)

1020

In->Si Energy=50keV tilt=0o rotation=0o

1019

SIMS Model Prediction 1018

dose: 2x1014cm-2 2x1012cm-2

1017

1016

1015 0.0

0.1

0.2

0.3

0.4

0.5

0.6

depth (µm)

(a)

Indium Energy=100keV o o tilt=0 rotation=0


1020

Model Prediction SIMS data

1019 dose=2x1014cm-2 dose=2x1012cm-2

1018

1017

1016

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

depth (µm) (b) Figure 7. Simulation of the dose dependence for the impurity profiles of indium on-axis implants. (a) Energy = 50keV. (b) Energy=100keV.

19

Indium Energy=140keV o o tilt=0 rotation=0 Implant through oxide of 9nm


1019

1018


dose=1x1013cm-2 12 -2 dose=1x10 cm

1017

1016

1015

0.0

0.1

0.2

0.3

0.4

0.5

depth (µm)

Figure 8. Illustration of the ability of the new indium model to accurately predict indium implants through oxide. The energy of the indium implants is 140keV, and the implants are through 9nm of oxide. The oxide was removed before the SIMS measurements. The depth =0 position corresponds to the Si and SiO 2 interface. UT-MARLOWE simulation of damage changing with energy 120 110


100

In->Si dose=2x1014 cm-2 o tilt=0 o rotation=0

90 80 70

energy=100keV energy=50keV energy=20keV

60 50 40

RBS data Model Prediction

30 20 10 0 0.00

0.05

0.10

0.15

0.20

Depth (µm)

Figure 9. The dependence of damage profiles on energy is shown for indium on-axis implants at a dose of 2×1014cm -2. 20