Effects of Phosphorus Doping and Postgrowth Laser Annealing on the

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Effects of Phosphorus Doping and Post-Growth Laser Annealing on the Structural, Electrical, and Chemical Properties of Phosphorus-Doped Silicon Films Minhyeong Lee, Hwa-Yeon Ryu, Eunjung Ko, and Dae-Hong Ko ACS Appl. Electron. Mater., Just Accepted Manuscript • DOI: 10.1021/acsaelm.8b00057 • Publication Date (Web): 25 Feb 2019 Downloaded from http://pubs.acs.org on February 26, 2019

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ACS Applied Electronic Materials

Effects of Phosphorus Doping and Post-Growth Laser Annealing on the Structural, Electrical, and Chemical Properties of Phosphorus-Doped Silicon Films Minhyeong Lee, Hwa-Yeon Ryu, Eunjung Ko, and Dae-Hong Ko∗ Department of Materials Science and Engineering, Yonsei University, Seoul 03722, Republic of Korea E-mail: [email protected]

Abstract Phosphorus has low solubility in silicon but non-equilibrium incorporation of phosphorus exhibits unusual high strain and low contact resistance for advanced Si-based metal-oxidesemiconductor field-effect transistors. Despite recent technological breakthroughs, the origin of tensile strain and electrical deactivation in P-doped Si films is not yet fully understood. Here, by using a combination of experiments and first-principles calculations, we investigate the effect of non-equilibrium phosphorus incorporation into Si lattices and subsequent annealing on structural, electrical, and bonding properties of P-doped Si films. Quantitative structural analyses reveal that the high tensile strain is generated by the incorporation of P into Si substitutional sites irrespective of the distribution of P atoms. More importantly, we found that advanced post-growth annealing lead to significantly enhanced electrical properties, while keeping the same physical states without loss of induced strain. To explore the reason for improved performances, we conducted the comprehensive theoretical calculations that present the

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contributions of dopant incorporation and vacancy formation to structural, chemical, and electrical properties, thereby providing atomic insights into the underlying physical mechanism of the electrical deactivation. Our findings indicate that the tensile strain can be controlled by manipulating the number of substitutionally incorporated P atoms and electrical properties may be enhanced by reducing the vacancy concentration using advanced post annealing processes or low temperature growth conditions.

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KEYWORDS: phosphorus doping, tensile stress, dopant activation, epitaxial growth, phosphorusdoped silicon, density functional theory

INTRODUCTION One of the most important requirements for successful semiconductor applications is the extremely high concentration of impurity doping, 1,2 which leads to significant improvements in electrical, structural, and optical properties. 3–5 In particular, enhanced carrier mobility and drive current have been achieved by incorporating Si1−x Gex and Si1−x Cx into the source/drain (S/D) region in metaloxide-semiconductor field-effect transistors (MOSFETs). 6,7 Si materials doped with phosphorus have recently attracted much attention as a promising candidate for use in photovoltaic, electrochemical, and quantum computing devices as well as advanced Si-based MOSFETs owing to their remarkable properties. 2,8–15 Despite intrinsic physical limitations such as low equilibrium solubility of P in Si (< 0.6%) 16 and the lattice mismatch between Si and P (9.0%), 17,18 high-quality Si films doped with concentrations of P over the solid solubility limit have been grown successfully as a result of significant efforts to overcome serious technical problems such as P surface segregation and defect generation during growth, thus enhancing overall device performance. 19,20 For example, incorporating a considerable number of P atoms into substitutional Si host sites in the S/D region provides high tensile strain in the Si channel regions, thereby increasing the electron mobility. 19–22 More importantly, subsequent laser annealing of highly P-doped Si films increases the active dopant concentration, which significantly improves electrical properties such as ultra-low contact resistivity to meet the requirements for future Complementary MOS technology. 11,23 Despite recent breakthrough, several key issues of their remarkable features are not fully understood as follows: (1) Since a P atom has five valence electrons, the one extra electron that remains weakly bound may contribute to electrical activation. 17 However, when the concentration of P is larger than its solid solubility limit in Si, the electrical deactivation in which a considerable number of P atoms do not emit free carriers has been identified in highly P-doped Si materials,

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which is similar to previous reports on other group V elements such as As and Sb. 9,24–26 For heavily P-doped Si materials including thin films and nanocrystals, the donor-vacancy model has been suggested to understand the mechanism. 11,26–29 However, previous studies have looked at the deactivation mechanism of Si doped with impurities mainly from a thermodynamic standpoint. More crucially, no unified and clear picture of how films grown in non-equilibrium states are initially electrical inactive and then become more active after subsequent laser annealing has emerged due to insufficient experimental and theoretical results. (2) Fundamental understanding of the physical and chemical characteristics in highly P-doped Si materials, such as the lattice parameter, bond length, and bond angle, is still lacking; moreover, it is challenging to precisely control and predict the dopant profile and atomic configuration of the dopant in host materials. 1,30 For other group IV alloys such as Si1−x Gex , Si1−x Cx , Si1−x−y Gex Cy , and Ge1−x Snx , the dependence of the lattice parameters and the elastic constants on the composition has been extensively studied by using X-ray diffraction (XRD). 31–37 Moreover, the lattice parameters of Si films doped with arsenic and boron were already reported. 4,38,39 However, the fundamental physical properties such as the lattice parameter and elastic properties of Si films with high concentrations of P dopant are not yet fully understood. Previous studies were limited to alloys with very low P concentrations or primarily focused on analysis of the relaxed lattice parameter. 18,21 Since P atom does not exist in the form of a diamond structure in nature and its concentration becomes higher than the solid solubility limit in Si ( 5 × 1020 atoms/cm3 , the free-carrier concentration increases with more P, with maximum value in one sample of P 5 at. %. After that, it decreases with increasing P, as shown in Figure 4a. We presume that the increase the number of donor-vacancy complexes with the increase of P concentration induces the decrease of the active carrier concentration in the P concentration ranges over 5%. The ratio (ne /Nd ) is less than 1 at high levels of P dopant (Nd > 1 × 1021 atoms/cm3 ), indicating that not all incorporated P atoms are electrically active, which is well known to be a critical issue in semiconductor physics. 63 Moreover, this observation about P-doped Si is in good agreement with the results of P-doped Ge and Sb-doped Si film. 64,65 Here,

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we highlight two very important points in the experimental results for electrical properties: (1) We have obtained the highest free-carrier concentration (1.5 × 1021 atoms/cm3 ) in a Si:P epitaxial film that underwent DSA. (2) Even though most of P atoms in the Si:P samples at high concentration are well incorporated into the substitutional Si sites, electrical deactivation has been confirmed in which a considerable number of P atoms do not emit free carriers. The increase in active P concentration resulting from DSA process decreases Hall mobility due to greater ionized impurity scattering (Figure 4b). 66 Finally, the resistivities of Si:P films are calculated from the equation ρ = 1/neµ, where ρ is the resistivity of the films, n is the free-carrier concentration, e is the elementary charge and µ is the Hall mobility. 67 Due to the increase in active P concentration, the resistivities of all the annealed Si:P samples decrease, as seen in Figure 4c. Using the laser annealing method, the lowest resistivity is significantly reduced to 0.25 mΩ⋅ cm without any dopant diffusion confirmed in Figures 3a and 3b. Although device performance is substantially enhanced from heavy P doping and subsequent laser annealing, 11,23 the mechanism of dopant incorporation and electrical activation remains poorly understood. 11,29 It is crucial for both fundamental studies and practical applications of P-doped Si to fully understand the origin of electrical deactivation and find a way for improving the material properties. Considering that donor-vacancy complexes can be a cause of the electrical deactivation by referring to the literature of group V elements, we will investigate the effect of vacancies on the electrical properties of P-doped Si and present a strategy that improves fundamental properties and device performance by adjusting the number of vacancies in the next theoretical investigations.

Modelling P-doped Silicon and First-principles Calculations. Thorough understanding of the role of dopants and intrinsic defects such as vacancies and interstitials in Si:P is of crucial importance to practical applications as well as fundamental studies of P-doped Si materials. Although the donor-vacancy model has been suggested to explain electrical deactivation of heavily P-doped Si materials, a previous study has looked at the phenomenon from a thermodynamic standpoint. 28 Therefore, little is known about the role of P atoms and the 18


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formation of vacancies in terms of structural and bonding characteristics in P-doped Si films. To get more insights into a deeper understanding of fundamental bonding and structure in P-doped Si, we present theoretical results of Si:P under various phosphorus and vacancy conditions (See Experimental Section and Figure S8). In the first step, optimized structures for isolated (random) Si:P with different P concentrations (6.25, 12.50, and 18.75%) using LDA functionals are shown in Figure 5a-c. Moreover, the bond distributions for the first nearest neighbor (1NN) distances between Si and P atoms are given in Figure 5a-c. As intuitively expected results, the number of Si-Si bonds decreases (from 128 to 80) and the number of Si-P bonds increases (from 0 to 48) as P concentration increases (Table 3). The supercell parameters (< a >SC ) are calculated from : < a >SC =

√ 3

V 2

, where V is the

volume of the supercell (64 atoms). To understand the bonding properties both macroscopically √

and microscopically, we extracted two parameters (SC and BD ). Clearly, SC (=

3 4

SC ) derived from the calculation of the supercell is in excellent agreement with BD (the mean bond length) obtained from the average of the Si-Si and Si-P bond lengths (see Table 3 and Figure S10). In addition, the bond analyses exhibit structural distortion caused by the substitutional incorporation of smaller P dopant into the Si host lattices, which causes a decrease in Si-P and Si-Si bond lengths to decrease with greater P concentrations. These results are intuitively understandable in terms of the diamond structure and agree well with previously reported results on random GeSn alloys. 36 Table 3: Summary of the average of the Si-Si and Si-P bond lengths and the number of Si-Si and Si-P bonds. P at. % SC (Å) 0 2.340 6.25 2.328 12.50 2.315 18.75 2.305

BD (Å) Si-Si (Å) Si-P (Å) 2.340 2.340 (na : 128) n/a 2.328 2.328 (n: 112) 2.326 (n: 16) 2.316 2.323 (n: 96) 2.295 (n: 32) 2.306 2.319 (n: 80) 2.289 (n: 48) a n is the number of bonds

Furthermore, we obtained the lattice parameters of isolated (random alloys) Si:P for several discrete P concentrations and compared them with the values of other alloys such as SiGe and Si:C 19



(a)

(b)

P 6.25 % : 𝑎𝑆𝐶 = 5.376 Å 𝑏

𝑆𝐶

𝑏

𝑆𝐶

𝑏

= 2.328 Å

6

𝑁𝑆𝑖−𝑆𝑖 = 112 𝑏𝑆𝑖−𝑆𝑖 = 2.328 Å

4

𝑁𝑆𝑖−𝑃 = 16 𝑏𝑆𝑖−𝑃 = 2.326 Å

2

𝐵𝐷

= 2.316 Å

6

𝑁𝑆𝑖−𝑆𝑖 = 96 𝑏𝑆𝑖−𝑆𝑖 = 2.323 Å

4 𝑁𝑆𝑖−𝑃 = 32 𝑏𝑆𝑖−𝑃 = 2.295 Å

2

𝑏

Si-Si Si-P

8

# of bonds

8

𝑆𝐶

= 2.305 Å

10

𝑏

Si-Si Si-P

𝐵𝐷

= 2.306 Å

Si-Si Si-P

8 6

# of bonds

𝐵𝐷

P 18.75 % : 𝑎𝑆𝐶 = 5.323 Å

= 2.315 Å

10

𝑏

4

𝑁𝑆𝑖−𝑆𝑖 = 80 𝑏𝑆𝑖−𝑆𝑖 = 2.319 Å

2

𝑁𝑆𝑖−𝑃 = 48 𝑏𝑆𝑖−𝑃 = 2.289 Å

0 2.24 2.26 2.28 2.30 2.32 2.34 2.36 2.38

0 2.24 2.26 2.28 2.30 2.32 2.34 2.36 2.38

0 2.24 2.26 2.28 2.30 2.32 2.34 2.36 2.38

Bond length (Å )

Bond length (Å )

Bond length (Å )

(d)

(e)

5.48

(f)

2.38 Experiment DFT (LDA) DFT (GGA-PBE) Vegard’s law

5.46

2.36

d 0 (Å )

5.44 5.42 5.40 5.38

0.0050 Experiment DFT (LDA) DFT (GGA-PBE) Vegard’s law

2.34

2.32

Experiment DFT (LDA) DFT (GGA-PBE)

0.0025

a ( Å )

# of bonds

(c)

P 12.50 % : 𝑎𝑆𝐶 = 5.346 Å

= 2.328 Å

10

a 0 (Å )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.0000

-0.0025

5.36 5.34

0

2

4

6

8

10

P concentration (%)

12

2.30

0

2

4

6

8

10

12

P concentration (%)

-0.0050

0

2

4

6

8

10

12

P concentration (%)

Figure 5: Bond distribution analysis and lattice parameters for isolated Si:P using DFT calculations. (a-c) Structural and bond distribution analysis of isolated Si:P with different P concentrations (6.25, 12.50, and 18.75%). P and Si atoms are shown as red and white spheres, respectively. (d) Relaxed lattice parameters calculated by LDA (blue filled squares) and GGA-PBE (blue open squares) as a function of P concentrations compared with experimental values determined by XRD (red solid circles) and Vegard’s law (black solid circles). (e) Comparison of average bond lengths as a function of P concentrations. (f) Absolute values of calculated and measured deviation of the relaxed lattice parameters in Si:P from Vegard’s law.

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shown in Figure S9a and S9b. This result can be well understood to be a result of the incorporation of smaller P atoms into Si lattices. The relaxed lattice parameters calculated by LDA are less than the experimental values by 0.5%, while those calculated by GGA are greater than the experimental ones by 0.7% (Figure 5d). These results are in accordance with previous theoretical analyses, which report equilibrium lattice constants of silicon: underestimation by LDA and overestimation by GGA-PBE, compared to the experimental values. 68,69 Based on the results of Figure 5d, SC obtained using both LDA and GGA is compared with experimental values in Figure 5e. Since the optimized structure is also a diamond cubic crystal doped with phosphorus, we have found that SC exhibits the same trend as the relaxed lattice parameters and is in excellent agreement with BD obtained from microscopic analysis. Since there has been little work for the lattice parameters of highly P-doped Si, we have extracted additional deviation parameters from Vegard’s law to validate our findings. Figure 5f represents absolute values of the calculated and measured deviation of the relaxed lattice parameters in Si:P from Vegard’s law (Table 4). In contrast to the small negative deviation from Vegard’s law observed by XRD, the calculation using LDA and GGA-PBE show small positive deviations from the law. Considering the approximation to the lattice parameter of P in the form of a diamond structure and the uncertainty of the experiment and calculations, the absolute values of the deviation (< ±0.005 Å) indicates that our experiments and calculations are considered to be reliable up to P 12.5% (Figure 5f). Consequently, we have confirmed the effect of incorporating P into substitutional Si lattices on the lattice parameters using a combination of XRD and first-principles calculations. To fully interpret the physical origin of the high tensile strain in heavily P-doped Si films, however, we turn our attention to addressing the other important factor such as the vacancy formation that can affect the lattice constants, thus providing direct evidence for the unusual experimental behavior and properties in P-doped Si. In addition, we address the issue of the experimentally identified electrical deactivation in as-grown Si:P samples. Since electrical deactivation is one of the most critical issues directly related to the performance of electrical devices, considerable effort has been devoted to understanding the mechanism of electrical degradation in materials doped

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Table 4: Measured and calculated relaxed lattice parameters of Si:P. P% 0 2.0 3.5 4.0 4.6 5.0 6.2 100

Experiment (XRD) a(Vegard) a(measured) 5.431 5.431 5.421 5.419 5.414 5.411 5.412 5.410 5.409 5.407 5.407 5.404 5.401 5.401 4.942 n/a

Calculation (LDA) P% P/(Si+P) a(Vegard) a(calculated) 0 0/64 5.403 5.403 1.56 1/64 5.395 5.395 3.13 2/64 5.388 5.388 4.69 3/64 5.380 5.381 6.25 4/64 5.372 5.375 7.81 5/64 5.365 5.367 9.38 6/64 5.357 5.360 10.94 7/64 5.350 5.354 12.50 8/64 5.342 5.348 100 64/64 4.914 n/a

with impurities. The reported literature has confirmed that as the concentration of dopant increases above the solid solubility limit, the concentration of the free-carrier formed by the substitutional incorporation of the dopant into host lattice saturates and finally decreases. 24,42,65 In particular, for Si-based materials doped with common n-type dopants (As and Sb), two models (donor-vacancy complex and donor pair (DP) defect models) have been suggested to understand the deactivation mechanism. 9,24–26 It has been reported experimentally and theoretically that the Asn V (n ≥ 2) complexes, which has a low formation energy and thus is energetically favorable, might be responsible for the electrical deactivation in highly As-doped Si (Nd > 1 × 1020 atoms/cm3 ). For heavily Pdoped Si materials including thin films and nanocrystals, although no unified and clear picture explaining the deactivation mechanism has emerged due to insufficient experimental and theoretical results, the donor-vacancy model has been suggested to explain the mechanism. 11,27–29 First, to determine a thermodynamically stable structure in heavily P-doped Si, we have calculated the formation energy of Si, Si with V, Pn , and Pn V, which is one conventional method in the literature. Our results using both LDA and GGA-PBE functionals demonstrate that P4 V has the lowest energy and thus is the most energetically favorable structure for Si:P, which is consistent with previous reports (Figure S11 and Table S1). 28,29 In addition to a thermodynamic approach, we will explore the effect of vacancy formation on structural and electrical properties using theoretical calculations. First, we investigated the lattice parameters of different P configurations (Pn , Pn V, and Pn V+I), 22


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(a)

(b)

30

𝑎𝑆𝐶 = 5.374 Å 𝑏 𝑆𝐶 = 2.327 Å 𝑏 𝐵𝐷 = 2.327 Å

25

Si-Si Si-P

𝑁𝑆𝑖−𝑆𝑖 = 112 𝑏𝑆𝑖−𝑆𝑖 = 2.330 Å

10

𝑁𝑆𝑖−𝑃 = 16 𝑏𝑆𝑖−𝑃 = 2.311 Å

# of bonds

# of bonds

15

(c)

25 20

20

15 10

𝑎𝑆𝐶 = 5.368 Å 𝑏 𝑆𝐶 = 2.325 Å 𝑏 𝐵𝐷 = 2.331 Å

0 2.26

𝑁𝑆𝑖−𝑆𝑖 = 112 𝑏𝑆𝑖−𝑆𝑖 = 2.337 Å

𝑁𝑆𝑖−𝑃 = 12 𝑏𝑆𝑖−𝑃 = 2.279 Å

2.28

2.30

2.32

2.34

2.36

0 2.26

2.38

2.28

(e)

5.50

P1 V

5.44

P3 P3V

5.36

P4V

Experiment

Si64 P1

P1V

V

P3

2

4

2.36

P concentration (%)

P4 V

10

Si-Si Si-P

𝑁𝑆𝑖−𝑆𝑖 = 115 𝑏𝑆𝑖−𝑆𝑖 = 2.349 Å

𝑁𝑆𝑖−𝑃 = 15 𝑏𝑆𝑖−𝑃 = 2.300 Å

2.38

0 2.26

2.28

2.30

2.32

2.34

2.36

2.38

Bond length (Å )

DFT_Random (LDA) DFT_Pn (LDA) DFT_PnV (LDA)

DFT_Random (GGA-PBE) DFT_Pn (GGA-PBE) DFT_PnV (GGA-PBE)

P2

P3

P4

P1V P3V

2.34

P4

6

15

𝑎𝑆𝐶 = 5.382 Å 𝑏 𝑆𝐶 = 2.331 Å 𝑏 𝐵𝐷 = 2.343 Å

P2V

P1 V

2.32

P4 V

Experiment

Si64

P2V

P3V

0

2.34

P2

P2 V

2.36

P4

P1V

5.42

5.38

Si64

P1

P2

20

2.38

DFT_Random (GGA-PBE) DFT_Pn (GGA-PBE) DFT_PnV (GGA-PBE)

P2V

5.40

2.32

d 0 (Å )

5.46

Si64

DFT_Random (LDA) DFT_Pn (LDA) DFT_PnV (LDA)

2.30

Bond length (Å )

(d)

25

5

Bond length (Å )

5.48

Si-Si Si-P

5

5

a 0 (Å )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


# of bonds

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P1V

P3

P3V

0

P4

P2V

2

4

P4V

6

P concentration (%)

Figure 6: Comparison of bond distribution analyses and lattice parameters in various Si:P structures using DFT calculations. (a-c) Bond distribution analysis of P4 , P4 V, and P4 V+I. (d) Relaxed lattice parameters of various structures such as isolated (random alloys), Pn , and Pn V as a function of P concentration. (e) Comparison of average bond lengths in various Si:P structures.

23



allowing us to clarify the role of substitutional P dopant as well as vacancy formation in lattice parameters. Figure 6a-c shows the bond distribution analysis of the optimized structures depicted in Figure S8. In the P4 structure shown in Figure 6a, the total mean bond length (BD = 2.327 Å) from a microscopic view has the same value as the average bond length (SC ) calculated from the supercell parameter. However, compared to the value of isolated (random) Si:P alloys at the same concentration (6.25%), the mean bond length of the Si-P bond in P4 is decreased by 0.015 Å and that of the Si-Si average bond is increased by 0.002 Å, which can be understood as a structural distortion caused by the placement of four P atoms. Importantly, the parameters (< a >SC = < a >BD = 5.374 Å) in P4 (P 6.25%) are in good agreement with those of (< a >SC = 5.376 Å and < a >BD = 5.377 Å) in isolated (random) Si:P (P 6.25%). Next, by substituting Si with V in the center of tetragonal P4 , the structure of P4 V is optimized and its bond distribution is analyzed in Figure 6b. As a Si atom in the tetragonal P4 is removed, the coordination number of the P atom in P4 V is reduced from 4 to 3, thus structural distortion is also observed in Figure 6b and Figure 7a,d. It is noted in Figure 6b that the mean bond length of the Si-P bond in P4 V is decreased by 0.032 Å and that of the average Si-Si bond is increased by 0.007 Å, compared to the value of P4 . More importantly, it has been found that the supercell parameter (< a >SC ) of P4 V is reduced by 0.006 Å (LDA) and 0.003 Å (GGA-PBE) compared to that of P4 due to the removal of the Si atom (Figure 6). With most energetically favorable structure (P4 V), the effect of the vacancy formation on the lattice parameter is greatly reduced, and thus the lattice parameters of P4 and P4 V are similar. Furthermore, the value is too small to explain the high tensile strain observed in highly P-doped Si film. Therefore, we have concluded that the high tensile strain experimentally observed in Si:P is generated by not the formation of a vacancy but by the substitutional incorporation of smaller P atoms into Si host lattices. Previous documents have described that the tensile strain observed in Si:P can be understood by the lattice mismatch between P4 V complexes (a = 5.027Å, c = 4.998 Å) 70 and Si (a = 5.431 Å) using Vegard’s law. 19,20,22 However, as shown in our theoretical results of Figure 5, the strain is generated due to the covalent radii difference between Si and P when the smaller P atoms are incorporated into the substitutional

24


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Si sites even if P4 V is not formed. To confirm our theoretical results that conflicts with previous reports, 11,20,22,29 which argue that the formation of the donor-vacancy complex (P4 V) is responsible for creating the stress, we have assessed the impact of vacancy formation on the relaxed lattice parameter for possible structures such as Pn and Pn V (0 ≤ n ≤ 4) using additional calculations with both LDA and GGA-PBE functionals. Figure 6d provides clues to identify the role of vacancies in various structures and sheds new light on the origin of the high tensile strain in P-doped Si films. Surprisingly, we confirmed that the relaxed lattice parameter in the form of Pn (0 ≤ n ≤ 4) is strongly influenced by the environment around V. When a vacancy is formed in bulk Si (Si64 ), the lattice parameter of (Si63 +V) decreases by 0.031 Å and 0.021 Å compared to the reference (Si64 ) in the calculation using LDA and GGA-PBE functionals. However, when the vacancy is generated around the P atom, the influence of vacancy formation on the lattice parameter is greatly reduced as the number of P atoms increases (Figure 6d). Finally, when the number of P atoms around V increases to 4, it is confirmed that the lattice parameter of P4 V is reduced by 0.006 Å (LDA) and 0.003 Å (GGA-PBE) compared to P4 , which has been ascribed to structural distortion (analyzed in more detail in Figures 7a and 7d). Although it appears that there is a non-linear variation in the change of lattice parameter from P2 V to P3 V, Figure S12 shows that differences in lattice parameters between Pn and Pn V except P2 in GGA decrease linearly as the number of nearby P atoms surrounding a vacancy increases, indicating that the effect of the vacancy formation on the change of lattice parameter is reduced as the number of surrounding P atoms increases. As a result, with most energetically favorable structure (P4 V), the effect of the vacancy formation on the lattice parameter is greatly reduced, and thus the lattice parameters of P4 and P4 V are similar. In other words, it is found in Figure 6d-e that if the number of incorporated P atoms is the same, the lattice parameter at the fixed distances in P2 , P3 , and P4 structures is similar to that of randomly distributed Si:P system, which can support the results of a previous study 48 describing induced strain as the pure difference between the covalent radii between Si and P. While the similarity of lattice parameters of P4 and P4 V is consistent with previous literature, 48 we have found the following differences: the lattice parameters obtained with the structure of with a vacancy given

25



in Figure 6d-e decreases compared to the case without vacancy, but the previous literature shows that the lattice parameter slightly increases when vacancy is present, 11 which requires additional theoretical researches to be fully understood. These findings in Figures 5a and 6a demonstrate that the high tensile strain experimentally observed in Si:P is generated by not the formation of a vacancy but by the substitutional incorporation of smaller P atoms into Si host lattices, regardless of the distribution of P atoms such as random alloys or Pn (2 ≤ n ≤ 4). This theoretical description is also supported by our XRD results, where the measured strain linearly increases with greater total substitutionally incorporated P compositions, irrespective of the electrically active P concentration, as seen in Figure 2 and Figure S4. Our explanation of the straining mechanism shows that the strain can be tuned by adjusting the number of substitutionally incorporated P atoms, thus helping the design of highly P-doped Si materials. The effect of vacancy formation on the lattice parameters has been discussed in previous figures. In the final part of this paper, we address the structural and bonding characteristics at the atomic level to discover the nature of electrical deactivation in highly P-doped Si films. Since a P atom has five valence electrons and exists as a four-fold coordination in the P4 structure, the one extra electron that remains weakly bound can contribute to electrical conduction. 17 On the other hand, in a configuration of P4 V, the P atom in a three-fold coordination has one lone pair of two electrons. Consequently, the significant difference in the active P concentration between as-grown and DSA Si:P samples has been attributed to different chemical environments, such as the presence or absence of a lone pair related to electrical neutrality. Considering that local bonding has a significant effect on the molecular geometry, we predict that the molecular geometry of P4 V will be identified differently from P4 due to the non-bonding electron pair. In order to investigate the effect of the vacancy formation on the electrical properties in highly P-doped Si films, we employed the valence-shell electron-pair repulsion (VSEPR) theory and the electron localization function (ELF) analyses as a guide to predict the shapes and bonding properties of molecules. As a result, we found that the structure of P4 V including a vacancy has a trigonal-pyramidal structure and has a one-lone (non-bonding) electron pair that causes the electrical deactivation, while P4 has four tetrahedrally

26


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(a)

(b)

(c)

(e)

(f)

Si(2) Si(4)

108.908° 2.311 Å

P(2)

P(1) Si(1)

Si(3)

109.471°

110.029°

P(3)

2.311 Å

P(4)

(d) Si(2) 104.567° 2.279 Å

Si(4)

P(2)

P(1)

v

Si(3)

P(3)

P(4)

Figure 7: Structure and bond characteristics of P4 and P4 V. (a,d) The structure and bond parameters including bond length and angle of P4 and P4 V, respectively. (b,e) 3D representation of ELF isosurface with ELF = 0.88 for P4 and P4 V, respectively. (c,f) 2D cross-section in the (101) plane containing a vacancy as well as P atoms for P4 and P4 V, respectively.

27



covalent bonding pairs at an angle of (109.468°) from each other. In Figure 7a, the molecular structure (SiP4 ) centered on Si (1) has four Si-P bonds with same bond length (2.311 Å and angle (109.471°), indicating that the structure is an ideal tetrahedron (Figure S13, and Table S2). For PSi4 centered on P (1), P (2), P (3) and P (4), we also found a general tetrahedron structure with the same bond length (2.311 Å) and average angle (109.468°) (Figure 7a, Figure S13a, and Table S2). On the other hand, as expected in the P4 V structure where one Si atom is replaced by a vacancy, structural distortion from the P4 with tetrahedron has been observed (Figure 7d, Figure S13b, and Table S3). The structural change from tetrahedral (AX4 coordination) in P4 to trigonal-pyramidal (AX3E coordination) in P4 V caused by the vacancy formation can be understood in terms of the VSEPR theory, which predicts molecular structures by the number of bonding-pairs and lone-pairs in the valence-shell of the central atom. Both bond lengths (2.279 Å) and angles (104.567°) of P4 V decreases compared to those of P4 (2.311 Å and 109.468°) due to the greater electron repulsions caused by one lone pair of two electrons in the nonbonding region, as clearly seen in Figure 7e,f. Moreover, the lone pair of two electrons around the P atom that significantly affects structural and electrical properties has been directly visualized by using the ELF, which allows finding an electron in the neighborhood of an electron located at a given point and with the same spin (Figure 7b-f). ELF can be used as a measure of Pauli repulsion and electron localization ranging between 0 and 1 (See Experimental Section). Figure 7b,e show three-dimensional (3D) representations of an ELF isosurface with ELF = 0.88 for the atomic configurations (P4 and P4 V) when electron-pair repulsion between the pairs in valence shells minimize. Similar to the CH4 (methane) molecule, P4 has four tetrahedrally covalent bonding pairs at an angle of (109.468°) from each other. In contrast, similar to the ammonia (NH3 ) molecule, the P4 V structure (trigonal-pyramidal with an angle (104.567°)) has three bonding pairs and one lone (non-bonding) electron pair. Direct observation of the lone (non-bonding) electron pair in our P4 V structure using ELF clearly shows that the vacancy plays a critical role in determining the structural and electrical properties of P-doped Si materials. Likewise, the dissimilar bonding characteristics of P4 and P4 V are clearly confirmed and illustrated in the two-dimensional (2D) cross section in the (101) plane containing a vacancy and

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P atoms (Figure 7c,f). In the presence of a vacancy in the center of the P4 V seen in Figure 7f, the 2D image shows an electron localization value close to 1, indicating that the non-bonding lone pair that could be the origin of electrical deactivation is formed by the vacancy, which is in consistent with the 3D view shown in Figure 7e. We also confirmed that the calculation results for the charge density are consistent with the ELF information (Figures S14 and S15). The 3D and 2D ELF results show that the structure of P4 V including a vacancy has a trigonal-pyramidal structure and has a one-lone (non-bonding) electron pair that causes the electrical deactivation, while P4 has four tetrahedrally covalent bonding pairs at an angle of (109.468°) from each other. Furthermore, our results of electrical deactivation with a donor-vacancy complex in highly P-doped Si films can be understood in the same context with previous published experimental result that vacancy decreases after laser annealing and active P increases. 29 In addition, it has been experimentally confirmed by positron annihilation spectroscopy (PAS) measurement that lower vacancies are formed in highly P-doped Si at lower temperatures. 26 Finally, our comprehensive study implies that if we can grow Si:P films under conditions that can reduce the vacancy concentrations (e.g. at low temperatures) we can increase the free-carrier concentration, thereby ultimately improving the semiconductor device performance.

CONCLUSIONS In summary, we report a broad range of experimental and theoretical investigations that reveal the origin of the unresolved issues of P-doped Si materials: high tensile strain and electrical deactivation, which are of both fundamental and practical importance in applications from advanced MOSFETs to photovoltaic devices. Our experimental findings not only clarify the straining mechanism, which is also supported by theoretical analyses, but also help to establish the fundamental physical and chemical properties in P-doped Si materials. Moreover, our theoretical descriptions unveil the role of vacancies on electrical deactivation experimentally observed in heavily P-doped Si and provide critical cues for tailoring the material properties and device performance of P-doped

29



Si materials. Our results imply that it is important to reduce the non-bonding lone pair due to the presence of vacancy in P4 V, as it experimentally proved to cause electrical inactivation and deteriorate electrical properties. Our systematic study will shed more light on evaluating of dopant incorporation and the resulting electrical behavior, thus opens up a new avenue to understanding and designing doped semiconductor materials for novel electronic and photovoltaic devices.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsaelm.8b. Schematic illustration of our approach (Figure S1); TEM images of as-grown Si0.938 P0.062 on Si (001) substrates (Figure S2); the schematic diagram of Si:P films in two different states (Figure S3); structural analyses using XRD (Figure S4-10); theoretical analyses (Figure S11-15 and Table S1-3) (PDF)

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] (D.-H.Ko).

Present address E.K is currently at SK Hynix Inc., Icheon 17336, Republic of Korea

ORCID Minhyeong Lee: 0000-0001-6322-5897 30


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Dae-Hong Ko: 0000-0002-5198-0163

Author Contributions M.L. and D.-H.K conceived this work. M.L., H.-Y.R, E.K, and D.-H.K designed the research. M.L. performed all experiments and first-principle calculations. All authors discussed the results. M.L. and D.-H.K wrote and edited the manuscript. All authors have given approval to the final version of the manuscript.

Notes The authors declare no competing financial interest.

Acknowledgement This work was supported by the Brain Korea 21 Plus Projects through the National Research Foundation (NRF) funded by the Ministry of Education of Korea.

References (1) Erwin, S. C.; Zu, L.; Haftel, M. I.; Efros, A. L.; Kennedy, T. A.; Norris, D. J. Doping Semiconductor Nanocrystals. Nature 2005, 436, 91–94. (2) Fukata, N. Impurity Doping in Silicon Nanowires. Adv. Mater. 2009, 21, 2829–2832. (3) Méndez, H.; Heimel, G.; Opitz, A.; Sauer, K.; Barkowski, P.; Oehzelt, M.; Soeda, J.; Okamoto, T.; Takeya, J.; Arlin, J.-B.; Balandier, J.-Y.; Geerts, Y.; Koch, N.; Salzmann, I. Doping of Organic Semiconductors: Impact of Dopant Strength and Electronic Coupling. Angew. Chem. Int. Ed. 2013, 125, 7905–7909.

31



(4) Ovsyannikov, S. V.; Gou, H.; Karkin, A. E.; Shchennikov, V. V.; Wirth, R.; Dmitriev, V.; Nakajima, Y.; Dubrovinskaia, N.; Dubrovinsky, L. S. Bulk Silicon Crystals with the High Boron Content, Si1−x Bx : Two Semiconductors Form an Unusual Metal. Chem. Mater. 2014, 26, 5274–5281. (5) Lundstrom, M. Moore’s Law Forever? Science 2003, 299, 210–211. (6) Ghani, T.; Armstrong, M.; Auth, C.; Bost, M.; Charvat, P.; Glass, G.; Hoffmann, T.; Johnson, K.; Kenyon, C.; Klaus, J.; Mclntyre, B.; Mistry, K.; Murthy, A.; Sandford, J.; Silberstein, M.; Sivakumar, S.; Smith, P.; Zawadzki, K.; Thompson, S.; Bohr, M. A 90nm High Volume Manufacturing Logic Technology Featuring Novel 45nm Gate Length Strained Silicon CMOS Transistors. IEDM Tech Dig. 2003, 11.6, 978–980. (7) Ang, K. W.; Chui, K. J.; Bliznetsov, V.; Du, A.; Balasubramanian, N.; Li, M. F.; Samudra, G.; Yeo, Y.-C. Enhanced Performance in 50 nm N-MOSFETs with Silicon-Carbon Source/Drain Regions. IEDM Tech Dig. 2004, 7.8, 1069–1071. (8) Velusamy, T.; Mitra, S.; Macias-Montero, M.; Svrcek, V.; Mariotti, D. Varying Surface Chemistries for p-doped and n-doped Silicon Nanocrystals and Impact on Photovoltaic Devices. ACS Appl. Mater. Interfaces 2015, 7, 28207–28214. (9) Moon, C.-Y.; Lee, W.-J.; Chang, K. J. Formation of Dopant-Pair Defects and Doping Efficiency in B- and P-doped Silicon Nanowires. Nano Lett. 2008, 8, 3086–3091. (10) Domi, Y.; Usui, H.; Shimizu, M.; Kakimoto, Y.; Sakaguchi, H. Effect of Phosphorus-Doping on Electrochemical Performance of Silicon Negative Electrodes in Lithium-Ion Batteries. ACS Appl. Mater. Interfaces 2016, 8, 7125–7132. (11) Rosseel, E.; Dhayalan, S.; Hikavyy, A.; Loo, R.; Profijt, H. B.; Kohen, D.; Kubicek, S.; Chiarella, T.; Yu, H.; Horiguchi, N.; Mocuta, D.; Barla, K.; Thean, A. V.-Y.; Bartlett, G.; Margetis, J.; Bhargava, N.; Tolle, J. Selective Epitaxial Growth of High-P Si:P for Source/Drain Formation in Advanced Si nFETs. ECS Trans. 2016, 75, 347–359. 32


Page 32 of 47

Page 33 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(12) Cho, E.-C.; Park, S.; Hao, X.; Song, D.; Conibeer, G.; Park, S.-C.; Green, M. A. Silicon Quantum Dot/Crystalline Silicon Solar Cells. Nanotechnology 2008, 19, 245201. (13) Perego, M.; Bonafos, C.; Fanciulli, M. Phosphorus Doping of Ultra-Small Silicon Nanocrystals. Nanotechnology 2010, 21, 025602. (14) Wang, X.; Hagmann, J. A.; Namboodiri, P.; Wyrick, J.; Li, K.; Murray, R. E.; Myers, A.; Misenkosen, F.; Stewart, M. D.; Richter, C. A.; Silver, R. M. Quantifying Atom-Scale Dopant Movement and Electrical Activation in Si:P monolayers. Nanoscale 2018, 10, 4488–4499. (15) McKibbin, S.; Scappucci, G.; Pok, W.; Simmons, M. Epitaxial Top-Gated Atomic-Scale Silicon Wire in a Three-Dimensional Architecture. Nanotechnology 2013, 24, 045303. (16) Trumbore, F. A. Solid Solubilities of Impurity Elements in Germanium and Silicon. Bell Syst. Tech. J. 1960, 39, 205–233. (17) Pearson, G. L.; Bardeen, J. Electrical Properties of Pure Silicon and Silicon Alloys Containing Boron and Phosphorus. Physical Review 1949, 75, 865. (18) Celotti, G.; Nobili, D.; Ostoja, P. Lattice Parameter Study of Silicon Uniformly Doped with Boron and Phosphorus. J. Mater. Sci. 1974, 9, 821–828. (19) Ye, Z.; Chopra, S.; Lapena, R.; Kim, Y.; Kuppurao, S. High Tensile Strained In-Situ Phosphorus Doped Silicon Epitaxial Film for nMOS Applications. ECS Trans. 2012, 50, 1007–1011. (20) Li, X.; Dube, A.; Ye, Z.; Sharma, S.; Kim, Y.; Chu, S. Selective Epitaxial Si:P Film for nMOSFET Application: High Phosphorous Concentration and High Tensile Strain. ECS Trans. 2014, 64, 959–965. (21) Weeks, K. D.; Thomas, S. G.; Dholabhai, P.; Adams, J. Characterization and Analysis of Epitaxial Silicon Phosphorus Alloys for Use in n-Channel Transistors. Thin Solid Films 2012, 520, 3158–3162.

33



(22) Rosseel, E.; Profijt, H. B.; Hikavyy, A.; Tolle, J.; Kubicek, S.; Mannaert, G.; L’abbé, C.; Wostyn, K.; Horiguchi, N.; Clarysse, T.; Parmentier, B.; Dhayalan, S.; Bender, H.; Maes, J. W.; Mehta, S.; Loo, R. Characterization of Epitaxial Si:C:P and Si:P Layers for Source/Drain Formation in Advanced Bulk FinFETs. ECS Trans. 2014, 64, 977–987. (23) Yu, H.; Schaekers, M.; Rosseel, E.; Peter, A.; Lee, J.-G.; Song, W.-B.; Demuynck, S.; Chiarella, T.; Ragnarsson, J.-Å.; Kubicek, S.; Everaert, J.; Horiguchi, N.; Barla, K.; Kim, D.; Collaert, N.; Thean, A. V.-Y.; De Meyer, K. 1.5×10−9 Ω⋅ cm2 Contact Resistivity on Highly Doped Si:P using Ge Pre-Amorphization and Ti Silicidation. IEDM Tech Dig. 2015, 21.7, 592–595. (24) Chadi, D. J.; Citrin, P. H.; Park, C. H.; Adler, D. L.; Marcus, M. A.; Gossmann, H.-J. FermiLevel-Pinning Defects in Highly n-Doped Silicon. Phys. Rev. Lett. 1997, 79, 4834. (25) Voyles, P. M.; Muller, D. A.; Grazul, J. L.; Citrin, P. H.; Gossmann, H.-J. L. Atomic-Scale Imaging of Individual Dopant Atoms and Clusters in Highly n-Type Bulk Si. Nature 2002, 416, 826–829. (26) Ranki, V.; Saarinen, K. Formation of Thermal Vacancies in Highly As and P doped Si. Phys. Rev. Lett. 2004, 93, 255502. (27) Takamura, Y.; Jain, S. H.; Griffin, P. B.; Plummer, J. D. Thermal Stability of Dopants in Laser Annealed Silicon. J. Appl. Phys. 2002, 92, 230–234. (28) Chen, R.; Trzynadlowski, B.; Dunham, S. T. Phosphorus Vacancy Cluster Model for Phosphorus Diffusion Gettering of Metals in Si. J. Appl. Phys. 2014, 115, 054906. (29) Dhayalan, S. K.; Kujala, J.; Slotte, J.; Pourtois, G.; Simoen, E.; Rosseel, E.; Hikavyy, A.; Shimura, Y.; Iacovo, S.; Stesmans, A.; Loo, R.; Vandervorst, W. On the Manifestation of Phosphorus-Vacancy Complexes in Epitaxial Si:P Films. Appl. Phys. Lett. 2016, 108, 082106.

34


Page 34 of 47

Page 35 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(30) Björk, M. T.; Schmid, H.; Knoch, J.; Riel, H.; Riess, W. Donor Deactivation in Silicon Nanostructures. Nat. Nanotechnol. 2009, 4, 103–107. (31) Dismukes, J. P.; Ekstrom, L.; Paff, R. J. Lattice Parameter and Density in Germanium-Silicon Alloys. J. Phys. Chem. 1964, 68, 3021–3027. (32) Kelires, P. C. Short-Range Order, Bulk Moduli, and Physical Trends in c-Si1−x Cx Alloys. Phys. Rev. B 1997, 55, 8784–8787. (33) Berti, M.; De Salvador, D.; Drigo, A. V.; Romanato, F.; Stangl, J.; Zerlauth, S.; Schäffler, F.; Bauer, G. Lattice Parameter in Si1−x Cx Epilayers: Deviation from Vegard’s Rule. Appl. Phys. Lett. 1998, 72, 12–15. (34) De Salvador, D.; Petrovich, M.; Berti, M.; Romanato, F.; Napolitani, E.; Drigo, A.; Stangl, J.; Zerlauth, S.; Mühlberger, M.; Schäffler, F.; Bauer, G.; Kelires, P. C. Lattice Parameter of Si1−x−y Gex Cy Alloys. Phys. Rev. B 2000, 61, 13005–13013. (35) Chizmeshya, A. V. G.; Bauer, M.; Kouvetakis, J. Experimental and Theoretical Study of Deviations from Vegard’s Law in the Snx Ge1−x System. Chem. Mater. 2003, 15, 2511–2519. (36) Beeler, R.; Roucka, R.; Chizmeshya, A. V. G.; Kouvetakis, J.; Menéndez, J. Nonlinear Structure-Composition Relationships in the Ge1−y Sny /Si(100) (y

Effects of Phosphorus Doping and Postgrowth Laser Annealing on the

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