Subsections

• 4.1 Silicon-Germanium Alloys
  • 4.1.1 Modeling of Ion Implantation in SiGe Alloys
    • Crystalline Partner Selection Model
    • Nuclear and Electronic Stopping Power
  • 4.1.2 Simulation Results and Discussion
  
  
• 4.2 Strained-Si/SiGe Heterostructure
  • 4.2.1 Modeling of Biaxially Strained Silicon
  • 4.2.2 Ultra-Shallow Junction Formation
  
  
• 4.3 Germanium
  • 4.3.1 Modeling of Ion Implantation in Germanium
  • 4.3.2 Simulation Results and Discussion

4. Doping of Group-IV-Based Materials

2While the first transistor was developed in 1947 by using germanium as the semiconductor material and GaAs devices have demonstrated high switching speed, it is silicon which completely dominates the present semiconductor market. This development has arised due to the low cost of silicon CMOS technology. The fabrication processes and the device performance rely heavily on a number of natural properties of silicon, for instance, the availability of a good oxide. For alternative semiconductor materials much more expensive fabrication processes must be used, whereby the phenomenal yields achievable on a silicon CMOS line cannot be reached. One drawback of silicon is its relatively small carrier mobility. Since the device speed depends on how fast the carriers can be transported through the device channel under sustainable low operating voltages, silicon can be regarded as a relatively slow semiconductor. Today, it is commonly believed that a further improvement in the channel mobility beyond those that can be achieved with process-induced strain will be required in order to maintain continued commensurate device scaling. The higher carrier mobility offered by group-IV materials like SiGe compounds, germanium, and various heterostructures, for instance, biaxially strained silicon on relaxed SiGe, are required as new channel materials for bulk and on-insulator implementations [88,89,90].

While ion-implanted doping profiles are well studied in silicon for various dopant species and implantation conditions, such doping profiles are scarce in SiGe alloys as well as in pure Ge. An accurate and multi-dimensional simulation of ion implantation processes is required to optimize the doping profiles in these semiconductor materials for high-performance CMOS applications and optoelectronic devices. Since quantitatively predictive capabilities are a must for a Monte Carlo ion implantation simulator, the used models for implantations into silicon have been evaluated to extend the simulator to this wide class of materials on the basis of experimental results. For calibration purposes, a set of specifically selected experiments for arsenic and boron implantations into SiGe virtual substrates with different Ge content has been developed and carried out. Additional experimental results from other research groups obtained by arsenic and boron implantations into strained Si, relaxed SiGe layers with high Ge contents, and into Ge wafers have been included. The doping profiles in the investigated non-silicon materials are always compared to a reference doping profile in silicon, implanted under the same conditions. On the basis of these experiments various effects which influence the dopant distribution (e.g. Ge content in the alloy, damage accumulation, channeling effect) can be analyzed independently. The extended simulator is able to accurately predict the doping profiles in germanium and in SiGe alloys of arbitrary Ge content, and to estimate the produced point defects.

4.1 Silicon-Germanium Alloys

Silicon-germanium (SiGe) is a IV-IV compound semiconductor which offers enhanced carrier mobility and a higher dopant solubility compared to pure silicon. The remarkable potential of the SiGe material arises from the possibility to modify its properties by altering the composition. For instance, the band gap decreases from 1.12eV (pure silicon) to 0.66eV (pure germanium) at room temperature. The lattice parameter of the germanium crystal is 4.2% larger than that of silicon. Relaxed SiGe has a lattice parameter value which lies between those of the endpoint elements silicon and germanium depending on the Ge content in the alloy. Crystalline SiGe can be grouped into the two categories relaxed and strained. Strain engineering is used to enhance the carrier mobility for MOS transistors. By building different kinds of Si-SiGe heterostructures various properties for device design can be optimized. When silicon is epitaxially grown on SiGe, silicon forms a strained layer configuration up to a certain critical thickness. A strained SiGe layer can be grown on silicon in a similar way. A strained-Si/relaxed-SiGe structure produces tensile strain which primarily improves the electron mobility, while compressive strain obtained by a strained-SiGe/relaxed-Si structure boosts the hole mobility. Although the quality of SiGe virtual substrates or bulk wafers has steadily improved over the last years, the defect density is still too large to guarantee a reasonable yield in CMOS processing at present time [91].

4.1.1 Modeling of Ion Implantation in SiGe Alloys

The simulation of ion implantation in silicon with MCIMPL-II is based on gerneral physical models which are explained in Section 3. Nevertheless, some of the models used for the trajectory calculation have to be extended or the change of an empirical parameter value is sometimes required in order to extend the simulation capabilities to SiGe alloys [92,93,94]. Precise material data and many SIMS profiles are used for the investigation of ion implantation.

Crystalline Partner Selection Model

Silicon and germanium, which both crystallize in the diamond lattice structure, are completely miscible forming Si $_{1-\mathrm{x}}$Ge $_{\mathrm{x}}$ solids with $x$ ranging from 0 to 1. The most precise and comprehensive investigation of bulk lattice parameters and densities for Si $_{1-\mathrm{x}}$Ge $_{\mathrm{x}}$ alloys for x from 0 to 1 with Ge intervals of 5% has been carried out by Dismukes et al. [95]. We extended the target materials of the simulator MCIMPL-II from crystalline silicon to the class of Si $_{1-\mathrm{x}}$Ge $_{\mathrm{x}}$ alloys and germanium by adjusting the lattice parameter $a(x)$ of the crystalline model by

$$a(x) = 0.02733 x^2\! +\! 0.1992 x\! +\! 5.431\quad(\mathrm{\mathring{A}}) \qquad\mathrm{for}\quad\:\: 0\! \leq\! x\! \leq\! 1 .$$ (4.1)

While Vegard's law determines the Si $_{1-\mathrm{x}}$Ge $_{\mathrm{x}}$ lattice parameter only by a linear interpolation between the lattice parameters of the endpoint elements silicon and germanium, equation (4.1) takes the small departure from Vegard's law into account [96]. The parabolic relation (4.1) for the lattice parameter as a function of the Ge content $x$ is derived from measurement values in [95] and approximates the experimental data with a maximum deviation of about $10^{-3}\mathrm{\mathring A}$. The deviation from Vegard's law has been confirmed in a recent study on SiGe epitaxial layers on (100) silicon substrates analyzed by X-ray diffraction and Rutherford backscattering [97].

While the ion moves through the simulation domain, a local crystal model (as shown in Fig. 4.1) is built up around the actual ion position for searching the next collision partner. The selection of the target atom species for a collision event in Si $_{1-\mathrm{x}}$Ge $_{\mathrm{x}}$ targets is performed by probability $x$ for germanium and $1\!\! -\!\! x$ for silicon, respectively. This random choice of the atom species in the crystalline model is acceptable, because no ordering has been observed in bulk SiGe crystals and ordering mechanisms in epitaxial grown SiGe layers are still under investigation.

Figure 4.1: Local crystal model used for the simulation of ion implantation in Si, SiGe alloys of arbitrary Ge content $x$ , and pure Ge ( $0 \leq x \leq 1$).

Table 4.1: Approximation of SiGe material properties at 300K for ion implantation.

Properties	Si	Si$_{0.75}$Ge$_{0.25}$	Si$_{0.5}$Ge$_{0.5}$	Si$_{0.25}$Ge$_{0.75}$	Ge
Mass (amu)	28.09	39.2175	50.345	61.4725	72.6
Atomic density (cm$^{-3}$)	$5.02 \cdot 10^{22}$	$4.855 \cdot 10^{22}$	$4.712 \cdot 10^{22}$	$4.566 \cdot 10^{22}$	$4.418 \cdot 10^{22}$
Density (kg/m$^3$)	2329.11	3161.85	3939.23	4661.86	5326.69
Lattice constant $(\mathrm{\mathring A})$	5.431	5.4825	5.5374	5.5958	5.6575
Debye temperature (K)	640	573.5	507	440.5	374

Table 4.1 summarizes some important physical properties relevant for ion implantation in silicon, germanium, and Si $_{1-\mathrm{x}}$Ge $_{\mathrm{x}}$ alloys with $x \!= \!0.25$, $x \!= \!0.5$, and $x \!= \!0.75$. A linear interpolation between the endpoint elements silicon and germanium is used to derive the values for the average atomic mass and the Debye temperature in SiGe for different compositions. The values of the SiGe lattice parameter were calculated by using the quadratic approximation (4.1). The lattice parameter at a Ge concentration $x$, $a(x)$, determines the atomic density $N(x)$ for Si $_{1-\mathrm{x}}$Ge $_{\mathrm{x}}$ according to (4.2). Finally, the Si $_{1-\mathrm{x}}$Ge $_{\mathrm{x}}$ material density $\rho(x)$ is obtained by inserting equation (4.2) into equation (4.3) and by proportionately averaging over the atomic weights of silicon and germanium, $M_{Si}$ and $M_{Ge}$.
For the simulation with MCIMPL-II the properties of an arbitrary SiGe material segment can be uniquely defined in the input WSS file by specifying the three quantities molecular formula (composition), material density, and crystal orientation.

$$N(x) = \left(\frac{2}{\;a(x) }\right)^{\!3} \cdot 10^{24}\qquad(\mathrm{Atoms}/\mathrm{cm}^3) ,$$ (4.2)

$$\rho(x) = N(x) \Bigl[(1 - x) M_{Si}\; +\; x M_{Ge}\Bigr] \cdot amu \cdot 10^{6}\qquad(\mathrm{kg/m^3}) .$$ (4.3)

Thermal lattice vibrations in silicon are considered in the crystalline partner selection model by using the Debye model with a Debye temperature value of 490K, as described in Section 3.1.2. Table 4.1 shows that germanium has a smaller Debye temperature value of 374K which corresponds to a smaller average vibration amplitude of the 2.6 times heavier germanium atom. We found by a comparison of simulated and measured implanted profiles that the model parameter value of 490K used for the simulation of silicon can also be applied for SiGe targets of arbitrary composition and pure germanium. Note that the used parameter value of 490K is close to the average value of the theoretical Debye temperatures in silicon and in germanium.

Nuclear and Electronic Stopping Power

The total stopping process of the ions in the target solid is modeled as a sequence of alternating nuclear and electronic stopping processes, as explained in Section 3.1.2 and in Section 3.1.3. The inverse transformation of the scattering integral (3.8) leads, amongst others, to (4.4) which determines the scattering angle $\vartheta$ of the ion in the laboratory system. The scattering angle $\vartheta$ depends on the scattering angle $\Theta$ in the center-of-mass coordinate system, on the mass $M_1$ of the ion, and on the mass $M_2$ of the involved atomic nucleus of the SiGe target.

$$\tan \vartheta = \frac{\sin \Theta}{ \frac{M_{1}}{M_{2}}\; +\; \cos \Theta } .$$ (4.4)

From (4.4) it can be derived that if the ion is heavier than the target atom $(M_{1} > M_{2})$, a maximal scattering angle $\vartheta_{max} < 90^{ \mathrm{o}}$ exists according to

$$\sin \vartheta_{max} = \frac{M_{2}}{M_{1}} .$$ (4.5)

For instance, if an arsenic ion hits a silicon atom then $\vartheta_{max} \!= \!22^{ \mathrm{o}}$, and if the arsenic ion hits the heavier germanium atom, a larger maximal scattering angle $\vartheta_{max} \!= \!69^{ \mathrm{o}}$ is possible. Due to the fact that the angles of subsequent collisions have to be added up for a turn around from the incident direction, the backscattering probability for dopant ions increases with the germanium content in the alloy.

The electronic stopping process is calculated with the empirical Hobler model. The only physical parameter required for this model is the impact parameter which is determined when selecting a collision partner. Due to the fact that the model implies a dependence on the charge and the mass of the atoms of the target material, the electronic stopping power is averaged in the case of a compound material like SiGe. The electronic stopping power of SiGe is larger compared with silicon, which is caused by the higher electron density due to the electron-rich germanium atom [98]. The calibration of the model for Si $_{1-\mathrm{x}}$Ge $_{\mathrm{x}}$ targets was performed by arranging the Lindhard correction parameter $k_{corr}$ as a linearly rising function of the germanium fraction $x$. For the other three parameters of the model the values from crystalline silicon could be applied. We found the relations (4.6) and (4.7) by comparing simulated profiles with SIMS profiles, which determine the parameters $k_{As}(x)$ for arsenic and $k_{B}(x)$ for boron.

$$k_{As}(x) = 1.132 + 1.736 x ,$$ (4.6)

$$k_{B}(x) = 1.75 + 0.375 x .$$ (4.7)

It is difficult to calibrate the electronic stopping model based on SIMS depth profiles for a couple of reasons. First of all, ion implantation experiments from different research groups exhibit a wide variation in results. Ziegler compared 48 papers on the range distributions of boron implantations in silicon and found a factor of about 2 for the variation in experimental results [17]. With sputter-profiling techniques, the first $10 \!$-$\!20$nm of the dopant concentration profile cannot be measured correctly due to transient sputtering effects such as preferential sputtering and implantation of the incident ions, which changes the total sputtering yield and distorts the profiles somewhat. Furthermore, it is fundamentally difficult to measure arsenic profiles in SiGe due to the presence of a severe mass interference at $^{75}$As by $^{74}$GeH [99]. Therefore, it is not possible to characterize arsenic profiles in SiGe by SIMS analysis with a resolution larger than about three orders-of-magnitudes below the maximum arsenic concentration.

4.1.2 Simulation Results and Discussion

We have studied the implantation of arsenic as an n-type and boron as a p-type dopant in crystalline SiGe layers with different germanium content. Fig. 4.2 shows simulated and measured arsenic implant profiles in Si $_{1-\mathrm{x}}$Ge $_{\mathrm{x}}$ layers with a thickness of 150nm on a silicon substrate. All implantations were performed with an energy of 60 keV, a dose of $\mathrm{10^{11} cm^{-2}}$, a tilt of $\mathrm{7^{o}}$, and a twist of $\mathrm{15^{o}}$. Two effects of the germanium content on the dopant profiles can be observed. Firstly, with increasing germanium fraction there is a shift towards shallower profiles. Secondly, the germanium content produces a stronger decline of the dopant concentration compared to silicon. It has been pointed out by interpretation of (4.5) that the heavier germanium atom produces an increased backscattering probability for the ions. The electronic stopping power of Si $_{1-\mathrm{x}}$Ge $_{\mathrm{x}}$ increases with the germanium fraction $x$ and, therefore, causes a stronger decline of the concentration profiles. Fig. 4.3 demonstrates the successful calibration of the simulator for 38keV and 60keV arsenic implantations in Si$_{0.65}$Ge$_{0.35}$, using otherwise the same implantation conditions. The implanted boron profiles in SiGe layers with 53%, 63%, and 86% germanium content are very similar. Fig. 4.4 shows the simulated and measured result for a 20keV boron implantation into Si$_{0.47}$Ge$_{0.53}$. A native oxide of 1nm on the wafer surface was taken into account. Fig. 4.5 demonstrates again the effect of the germanium content on 5keV boron profiles. SiGe facilitates the forming of shallow junctions, but the trend to shallower profiles is non-linear.

Figure 4.2: Simulated 60keV arsenic concentration profiles in (100) SiGe layers with $x$ = 0, 20%, 50% compared to smoothed SIMS data.

Figure 4.3: Simulated 38keV and 60keV arsenic profiles in (100) Si$_{0.65}$Ge$_{0.35}$ layers compared to smoothed SIMS data.

Figure 4.4: Simulated 20keV boron implant profile in (100) Si$_{0.47}$Ge$_{0.53}$ using a dose of $6\cdot 10^{14}$cm$^{-2}$ and a tilt of $7^{\circ }$ compared to SIMS.

Figure 4.5: Simulated 5keV boron profiles in (100) SiGe with $x$ = 0, 20%, 40%, 60% using a dose of $10^{15}\!$cm$^{-2}$ and a tilt of $7^{\circ }$.

4.2 Strained-Si/SiGe Heterostructure

Despite scaling the channel lengths into the sub-50nm regime, carrier mobility continues to be a critical parameter in scaled MOS devices and carrier transport remains far from ballistic [90]. This is partly because the mobility is degraded by increased channel doping (as predicted by the ITRS roadmap in Table 1.1 in Section 1.3). Strained silicon provides an attractive platform for building high-performance CMOS applications due to mobility enhancements compared to unstrained silicon. It turned out that strain-induced enhancements persist even at high channel doping levels, studied up to a dopant concentration of $6 \cdot 10^{18}$cm$^{-3}$ [100]. There are two dominant methods, global and local stress, for introducing strain in the silicon surface channel. Both methods produce changes in the silicon bandstructure due to breaking of the crystal symmetry, and hence alter carrier scattering and effective masses. Global stress techniques employ epitaxial technology to generate a thin layer of strained silicon on a thick relaxed Si $_{1-\mathrm{x}}$Ge $_{\mathrm{x}}$ layer. Local stress relies on process techniques such as modifications to shallow trench isolation, high-stress nitride-capping layers around the gate, and selective epitaxial Si $_{1-\mathrm{x}}$Ge $_{\mathrm{x}}$ in the sourcs/drain regions [101]. These techniques are effective in small device geometries where it is possible to induce uniaxial strain in the channel by stressing the regions around the channel. However, it turned out that the improvement in electron mobility using biaxially tensile strained silicon on relaxed Si $_{1-\mathrm{x}}$Ge $_{\mathrm{x}}$ is larger than that obtained for local stress techniques [88].

Figure 4.6: Schematic illustration of the strained Si/relaxed SiGe system (left) and experimental data for the critical thickness of strained silicon (right).

Fig. 4.6 shows the strained-Si/relaxed-SiGe heterostructure which is used to investigate the impact of strain on ion implantation. Relaxed SiGe layers are epitaxially grown on (100) silicon substrates using a grading technique to obtain the desired Ge composition. Next a constant composition layer is grown to spatially separate the subsequently grown strained silicon layer from the misfit dislocations contained in the graded SiGe layer. When silicon is grown on SiGe, the lattice mismatch between the two materials can be accommodated by uniform lattice strain in sufficiently thin silicon layers [102]. If silicon is grown beyond its critical thickness, the strained crystal relaxes to its natural size and a high concentration of dislocations is introduced. Fig. 4.6 shows also typical experimetal data for the critical layer thickness which depends on growth rates, growth temperature, SiGe surface orientation, and mostly on the Ge concentration [96].

Figure 4.7: Crystal model for biaxially tensile strained silicon layers.

4.2.1 Modeling of Biaxially Strained Silicon

A strained silicon channel is formed by a silicon layer with a thickness smaller than the critical thickness, epitaxially grown on the (100) surface of a relaxed Si $_{1-\mathrm{x}}$Ge $_{\mathrm{x}}$ buffer layer. The silicon layer is under biaxial tensile strain and the so-called pseudomorphic interface is characterized by an in-plane lattice constant  $a_{\parallel}$ which remains the same throughout the heterostructure. By using the empirically determined parabolic relation (4.1) for the Si $_{1-\mathrm{x}}$Ge $_{\mathrm{x}}$ lattice parameter as a function of the Ge fraction $x$ we obtain for strained silicon

$$a_{\parallel}(x) = 0.02733 x^2\! +\! 0.1992 x\! +\! 5.431\quad(\mathrm{\mathring{A}}) .$$ (4.8)

The out-of-plane silicon lattice constant $a_{\perp}$, in the direction perpendicular to the interface plane, is reduced according to the continuum elastic theory [103],

$$a_{\perp}(x) = a_{\mathrm{Si}} \left[1 - \frac{2 C_{12}}{C_{11}}\... ...arallel}(x)}{a_{\mathrm{Si}}} - 1 \right)\right]\quad(\mathrm{\mathring A)} ,$$ (4.9)

where $a_{\mathrm{Si}}$ denotes the lattice constant of unstrained silicon, and $C_{11}$, $C_{12}$ are the elastic constants of silicon ( $C_{11} = 1.675$Mbar, $C_{12} = 0.650$Mbar at room temperature after [102]).

The constraints for the two lattice parameters in strained silicon are given by

$$a_{\perp}(x) < a_{\mathrm{Si}} < a_{\parallel}(x)\quad\quad\mathrm{for}\quad\:\: 0 < x < 1 .$$ (4.10)

The strain components parallel and perpendicular to the interface plane are then defined by

$$\varepsilon_{\parallel}(x)\! =\! \frac{a_{\parallel}(x) - a_{\mat... ...lon_{\perp}(x)\! =\! \frac{a_{\perp}(x) - a_{\mathrm{Si}}}{a_{\mathrm{Si}}} .$$ (4.11)

Fig. 4.7 shows the strained unit cell with the edge lengths  $a_{\parallel}$ and $a_{\perp}$, which can be used for the Monte Carlo simulation of ion implantation in strained silicon targets [104]. While the simulated ion moves through a strained silicon region, the strained crystal model from Fig. 4.7 is built up around the actual ion position for searching the next collision partner. The displacement energy of 15eV used for bulk silicon can be applied for strained silicon too. Due to the fact that the strained silicon lattice system is coherently aligned to the Si $_{1-\mathrm{x}}$Ge $_{\mathrm{x}}$ virtual substrate lattice, channeling ions can pass the interface between these two crystalline layers without being interrupted. While the implantation profiles in strained and unstrained silicon show only a very small difference at a given implantation energy, the penetration depth of ion-implanted dopants in relaxed Si $_{1-\mathrm{x}}$Ge $_{\mathrm{x}}$ is significantly reduced with increasing Ge fraction $x$, as demonstrated in Section 4.1. Thus the underlying Si $_{1-\mathrm{x}}$Ge $_{\mathrm{x}}$ layer helps to reduce the tail region of source/drain doping profiles in this heterostructure.

4.2.2 Ultra-Shallow Junction Formation

We study the implantation of boron as a p-type and arsenic as an n-type dopant in a silicon cap layer with a thickness of 12nm on a thick Si$_{0.8}$Ge$_{0.2}$ layer. Fig. 4.8 shows the simulated and experimental doping profile of a boron implantation with an energy of 400eV and a dose of $10^{15}\mathrm{cm}^{-2}$. Fig. 4.9 shows the arsenic implantation result, performed with an energy of 2keV and the same dose. The presented doping profiles demonstrate highly doped source/drain extension implants for a typical 65nm CMOS technology under the sidewall spacer, where lightly doped drain (LDD) structures used to be in previous technology generations.

Fig. 4.8 shows that the simulated boron profiles in strained and unstrained silicon are almost identically distributed, and the simulation result agrees well with the SIMS data. It is not possible to characterize arsenic concentration profiles in Si $_{1-\mathrm{x}}$Ge $_{\mathrm{x}}$ by SIMS analysis with a resolution larger than about three orders-of-magnitude due to similar atomic masses of arsenic and germanium [99]. As shown in Fig. 4.9 the Monte Carlo simulation can help to get a realistic continuation of the doping profile below the arsenic detection limit. The discrepancy between the predicted and measured doping profiles near the wafer surface may arise from a measurement error in this region. Feedback from industry revealed that this error can be eliminated by the deposition of amorphous silicon on the wafer before the SIMS measurement. Using this procedure, SIMS profiles show an increase in the near-surface region too. However, the simulation results in Fig. 4.9 demonstrate that the arsenic distribution in strained silicon has a slightly deeper penetration compared to unstrained silicon, which can be explained by a stress-induced volume dilation of the material. Strained silicon on Si$_{0.8}$Ge$_{0.2}$ has a strain  $\varepsilon_{\parallel}(0.2)\! \approx\! 0.75\%$ and approximately 99% of the atomic density of unstrained silicon.

Figure 4.8: Simulated 400eV boron implant profile in a 12nm thick strained silicon layer compared to SIMS measurement.

Figure 4.9: Simulated 2keV arsenic implant profile in strained silicon compared to SIMS data.

4.3 Germanium

Germanium has regained attention in the semiconductor industry for future silicon-compatible optoelectronic and advanced CMOS device applications. The carriers have lower effective masses and the intrinsic mobility is about two times higher for electrons and four times higher for holes in germanium compared to silicon, as shown in Table 4.2. Therefore, germanium offers the highest performance enhancement potential for channel engineering compared to bulk SiGe or strained silicon. On the one hand, the smaller band gap of germanium is advantageous to build photodetectors and, on the other hand, junctions made in a smaller band gap material will typically exhibit larger leakage currents.

In recent years, deep-submicron germanium MOS transistors have been processed in a silicon-like process flow by using either germanium oxynitride (GeO $_\mathrm{x}$N $_\mathrm{y}$) [105] or Hafnium oxide (HfO$_2$) based high-k dielectrics [106,107] as the gate insulator. The diffusion of the p-type dopant boron is suppressed while the diffusion of the n-type dopants phosphorus, arsenic, and antimony is increased in SiGe and germanium compared with silicon [108]. Thus, the formation of ultra-shallow junctions in germanium is facilitated for p-MOS transistors, while it becomes more challenging for n-MOS devices. It was found in [107] that the junction leakage is about four decades higher for germanium at a chip temperature of 110$^\circ$C compared with silicon. The reduction of the relatively large leakage current will be a key issue for Ge-CMOS technology to obtain devices with reasonably low $I_{off}$ current. It is reported in [105], that the leakage current of boron implanted p $^\mathrm{+}$/n junctions in germanium can be reduced down to the order of $10^{-4}$A/cm$^2$ with annealing at 400$^\circ$C, which is considered acceptable for device operation. Ge-rich Si $_{1-\mathrm{x}}$Ge $_{\mathrm{x}}$ alloys $(x \!> \!80\%)$ and germanium have been recognized as promising materials for photodetectors in fibre-optical transmission systems due to the high optical absorption coefficient for an operation at a wavelength of 1.3$\mu$m in the near infrared (NIR) regime [109,110]. The use of epitaxial Ge-on-Si technology allows the integration of germanium pin-photodiodes with CMOS circuits on a silicon chip to build optical communication receivers with low fabrication costs. Optical chip-to-chip communication solutions and even optical on-chip interconnects will be required to meet the challenges of differentiated, high-performance systems in the future.

Table 4.2: Important electronic properties of germanium vs. silicon at 300K [111].

Properties	Germanium	Silicon
Band gap (eV)	0.66	1.12
Electron mobility (cm$^2$/V-s)	3900	1500
Hole mobility (cm$^2$/V-s)	1900	450

Ion implantation is a crucial step for processing these device structures. An experimental and simulation study for introducing boron ions into (100) germanium wafers in the energy range from 5 to 40keV is presented in this section [112]. The successful calibration of the simulator MCIMPL-II for germanium is demonstrated by comparing the predicted boron profiles with SIMS data. A doping profile in germanium is shallower than in silicon for any given energy due to the larger nuclear and electronic stopping power. We found also that the produced crystal damage is significantly reduced in germanium, which is consistent with former experimental observations [113] indicating that boron-implanted germanium remains essentially crystalline.

4.3.1 Modeling of Ion Implantation in Germanium

The extended crystalline simulation model presented in Fig. 4.1 can be applied to germanium by using the maximum lattice parameter value $a(1) \!\!\!= \!\!\!5.6575\mathrm{\mathring{A}}$ and a probability of 100% for meeting a germanium atom at the next collision event. In a screened Coulomb collision the energy loss of the ion, $\Delta E$, is equal to the transferred energy to the recoil atom,

$$\Delta E = \frac{4 M_1 M_2}{(M_1 + M_2)^2} \cdot \sin^2 \frac{\Theta}{2} \cdot E_0 ,$$ (4.12)

where $M_1$ and $M_2$ are the masses of ion and target atom, $\Theta$ is the transformed scattering angle in the center-of-mass coordinates, and $E_0$ is the kinetic energy of the ion before the collision event. From this equation it can be derived that a smaller energy loss $\Delta E$ occurs in nuclear collisions in germanium due to the different masses between ion and atom. The transferred energy $\Delta E$ from a boron ion to a germanium atom is approximately the half (0.568-fold) compared to $\Delta E$ in silicon at a given scattering angle. Note that the difference in masses between boron and germanium leads also to a strong backscattering effect for the light boron ions.

Figure 4.10: Number of Frenkel pairs generated by a primary knock-on atom in Si and in Ge, assuming a displacement energy of 15eV and 30eV.

An advantage of the Monte Carlo simulation is that the used Kinchin-Pease model (as described in Section 3.1.4) allows to estimate the produced vacancies in the germanium crystal. Note that equal local concentrations of vacancies and interstitials are assumed, since the recoils themselves are not individually followed in our computationally fast simulation approach. However, a critical model parameter is the threshold displacement energy required for the ion to displace a target atom. A displacement energy $E_d$ of 15eV has become widely accepted for silicon. We fitted a value of $E_d\!\! =\!\!$30eV for germanium by comparison of simulated boron profiles with SIMS measurements. Fig. 4.10 shows the number of produced point defects for a damage cascade, calculated with the modified Kinchin-Pease model. The used value for the displacement energy in germanium is in good agreement with $E_d\!\! =\!\! 31$eV which was deduced by Mitchell in 1957 for germanium [114]. The larger $E_d$ value is responsible for the generation of significantly fewer point defects by a boron ion in germanium compared with silicon for any amount of transferred energy $\Delta E$ to the primary knock-on atom of a cascade. The reduced damage production by ion implantation in crystalline germanium is consistent with former experimental observations [113].

Figure 4.11: Comparison of the Monte Carlo simulation of ten boron trajectories in silicon and in germanium using an energy of 10keV and a tilt of 7$^\circ$.

The Lindhard correction parameter $k_L$ of the empirical electronic stopping model, which is explained in Section 3.1.3, has been calibrated to adjust the strength of the electronic stopping power for boron ions in germanium. We increased the empirical parameter value from $k_L\!\! = \!\!1.75$ for silicon to a value of 1.9 for germanium.

In the following simulation study, at least $10^6$ trajectories were calculated for a one-dimensional boron profile. Fig. 4.11 shows the visualization of ten arbitrarily selected boron trajectories in silicon and in germanium. This comparison demonstrates that the larger nuclear and electronic stopping power of germanium, in particular the stronger backscattering of boron ions in germanium, typically reduces the trajectory length.

4.3.2 Simulation Results and Discussion

Germanium has a larger nuclear and electronic stopping power for incoming ions due to the heavier atomic mass and higher electron density. For this reason, an implanted dopant profile in germanium is significantly shallower than in silicon and SiGe for any given implantation energy. Fig. 4.12 shows that the calibrated simulator can accurately reproduce the measured 20keV boron concentration profiles implanted with a dose of $6\cdot 10^{14}\mathrm{cm}^{-2}$ in amorphous and in crystalline germanium targets. The amorphization of germanium was performed by the implantation of $^{72}$Ge ions with an energy of 200keV and a dose of $10^{15}\mathrm{cm}^{-2}$. A channeling tail can be observed for the profile in crystalline germanium. Fig. 4.13 demonstrates a good agreement between the simulated and measured boron profiles implanted with a lower energy of 5keV and a lower dose of $3\cdot 10^{13}\mathrm{cm}^{-2}$. Fig. 4.14 compares simulated 20keV boron profiles in silicon and in germanium. We found the projected range $R_p$ of the boron distribution in Si$_{0.5}$Ge$_{0.5}$ at a depth of 65nm, which lies well within the boundaries defined by the projected ranges in germanium at 55nm and in silicon at 80nm. Table 4.3 summarizes simulated and measured $R_p$ and $\sigma_p$ parameters for boron implants in crystalline silicon, Si$_{0.5}$Ge$_{0.5}$, and germanium targets. The projected range $R_p$ is read off at the maximum concentration of a boron distribution and the provided straggling $\sigma_p$ is the average value of the left and right straggling values which are determined by 60% of the maximum boron concentration. The results in the table were obtained with an implantation dose of $10^{14}\mathrm{cm}^{-2}$ and a tilt of $7^{\circ }$.

Fig. 4.15 compares the simulated vacancy concentration profiles in silicon and in germanium associated with the 20keV boron implantations shown in Fig. 4.14. The vacancy maximum is not at the wafer surface, since the electronic stopping process dominates at high initial energies of the ions, when they enter the crystal. A boron ion enters most likely a channel at the surface and despite of the tilted incident direction it can stay at least a short distance inside a channel. The higher displacement energy of 30eV, the stronger backscattering of boron ions in germanium, and the smaller energy transfer $\Delta E$ from the ion to the primary recoil of a cascade are mainly responsible for the significantly smaller damage production in germanium. Privious experimental boron implantation results in germanium [113] performed up to a dose of $10^{14}\mathrm{cm}^{-2}$ within the energy range of 25-150keV revealed that 100% of the boron ions are immediately active after implantation without thermal annealing since boron-implanted germanium remains crystalline. This is a unique phenomenon, since an annealing step is required for every other dopant species implanted in silicon or germanium in order to activate a significant amount of dopants. Finally, Fig. 4.16 illustrates the dose dependence of 40keV boron profiles in germanium, which were simulated with the Kinchin-Pease model. It is obvious that the shape of the profiles is influenced by the damage accumulation in the crystal.

Table 4.3: Projected range and straggling parameters for boron distributions.

Cryst. Material	Si	Si$_{0.5}$Ge$_{0.5}$	Ge	Si	Si$_{0.5}$Ge$_{0.5}$	Ge
Energy (keV)	5	5	5	20	20	20
$R_p$ (nm)	18.91	15.44	14.32	79.52	65.32	55.27
$\sigma_p$ (nm)	14.16	12.56	12.16	37.42	36.33	39.38
SIMS $R_p$ (nm)	-	-	16.23	-	67.11	56.99
SIMS $\sigma_p$ (nm)	-	-	11.23	-	40.58	34.91

Figure 4.12: Simulated 20keV boron implantations in amorphous Ge and in (100) Ge using a dose of $6\cdot 10^{14}$cm$^{-2}$ and a tilt of $7^{\circ }$ compared to SIMS profiles.

Figure 4.13: Simulated 5keV boron profile in (100) Ge using a dose of $3\cdot 10^{13}$cm$^{-2}$ and a tilt of $7^{\circ }$ compared to SIMS measurement.

Figure 4.14: Comparison of simulated 20keV boron implant profiles in silicon and germanium using a dose of $6\cdot 10^{14}$cm$^{-2}$ and a tilt of $7^{\circ }$.

Figure 4.15: Comparison of produced vacancies for the 20keV boron implantations in silicon and germanium using a dose of $6\cdot 10^{14}$cm$^{-2}$ and a tilt of $7^{\circ }$.

The simulated point responses in crystalline silicon and germanium are shown in Fig. 4.17 and Fig. 4.18 to study quantitatively the lateral and vertical penetration of boron ions. The used two-and-a-half dimensional input geometry has a depth dimension of 40nm, and the slot width of the implantation window in an impenetrable mask is 8nm. A high-resolution mesh which consists of 33181 grid points and 144159 tetrahedrons is added to the input structure to resolve the implanted boron distribution. Boron is implanted with an energy of 10keV, a dose of $5\cdot 10^{15}\mathrm{cm}^{-2}$, and the ion beam is 7$^\circ$ tilted in such a way that the lateral component of the incident direction is parallel to the direction of view ($<\!010\!>$ direction). Therefore, the presented point responses are symmetric. Approximately 420000 simulated boron ions of a total number of 50 million ions can enter the substrate at the mask opening and contribute to the Monte Carlo result represented by the internal histogram cells.

The visualization of single trajectories in silicon and in germanium (as shown in Fig. 4.11) and in particular the comparison of the point responses indicate that the boron distribution in germanium is significantly reduced in the vertical direction, while the lateral profile is quite similar in silicon and germanium. Additionally, it can be observed that the channeling tail is closely centered around the $<\!\!100\!\!>$ axis in both cases. This demonstrates that in (100) silicon and in (100) germanium, axial channeling in the $<\!\!100\!\!>$ direction dominates by far over channeling in other directions.

Figure 4.16: Simulated 40keV boron implants in (100) Ge at doses of $5\cdot 10^{13}$, $5\cdot 10^{14}$, and $5\cdot 10^{15}$cm$^{-2}$ using a tilt of $7^{\circ }$.

As demonstrated in this study, the used physics-based simulation approach in combination with experimental results allows to get a comprehensive understanding of implantation-related phenomenons in germanium.

Figure 4.17: Simulated point response for a 10keV high-dose implantation of boron into crystalline silicon.

Figure 4.18: Simulated point response for a 10keV high-dose implantation of boron into crystalline germanium.