Selective Epitaxial Growth Advanced

# Selective Epitaxial Growth: Kinetics, Facet Engineering & Channel Strain

In advanced CMOS manufacturing (FinFET, Gate-All-Around Nanosheet, and Complementary FET nodes), Selective Epitaxial Growth (SEG) is the indispensable chemical vapor deposition (CVD) process used to fabricate strain-engineered, ultra-low-resistance embedded source and drain (S/D) junctions. By co-flowing gaseous semiconductor precursors with chemical etchants, epitaxy proceeds with atomic registry exclusively upon the exposed crystalline silicon seed while suppressing nucleation entirely on surrounding amorphous dielectric hardmasks and spacers ($\text{SiO}_2$, $\text{Si}_3\text{N}_4$, $\text{SiCOH}$).

Embedded epitaxy fulfills two vital physical functions at the leading edge:
1. Uniaxial Channel Strain Engineering: Epitaxially growing lattice-mismatched alloy crystals—such as compressive $\text{Si}_{1-x}\text{Ge}_x$ ($x = 0.35\text{ to }0.55$) in pMOS and tensile $\text{Si:CP}$ in nMOS—exerts channel stresses exceeding $1.8\text{ to }2.5\,\text{GPa}$, lifting band degeneracy and enhancing carrier mobility by $> 2.5\times$.
2. Ultra-Low Specific Contact Resistivity: Maximizing in situ dopant incorporation beyond solid solubility ($N_A > 2 \times 10^{21}\,\text{cm}^{-3}$ for boron, $N_D > 3 \times 10^{21}\,\text{cm}^{-3}$ for phosphorus) reduces the Schottky barrier tunneling width, driving specific contact resistivity below the sub-$1\,\text{nm}$ target of $\rho_c < 1.0 \times 10^{-9}\,\Omega\cdot\text{cm}^2$.

Selective Epitaxial Growth Kinetics & Selectivity Window chemical surface dynamics, nucleation incubation delay, and HCl flow balance 1. CHEMICAL REACTION & SURFACE SELECTIVITY Crystalline Si Seed Incubation Time: τ_seed ≈ 0 Dielectric Mask (SiN/SiO₂) HCl Etches Subcritical Clusters Precursor Chemistry (DCS + HCl Co-Flow): Deposition: SiH₂Cl₂(g) ⇌ Si(s) + 2 HCl(g) Etching: Si(s) + 2 HCl(g) ⇌ SiCl₂(g) + H₂(g) Critical Nucleation Radius Formulation: r* = 2 · γ_surf · Ω / [ k_B T · ln(S) ] • On dielectric masks, chemical binding energy is low, leading to a massive critical cluster radius r*. • Adatoms arriving on mask remain isolated and are volatilized by HCl before reaching r* (τ_etch < τ_inc). Selective Window Requirements: • Growth Temperature: 600°C to 750°C (RP-CVD) • Reactor Pressure: 10 to 100 Torr (Reduced Pressure) • Carrier Gas: Ultra-pure H₂ (removes surface oxides) • HCl/DCS Ratio: Maintained between 0.8 and 1.4 to avoid poly-nucleation or net silicon etching. 2. THE SELECTIVE EPITAXIAL PROCESS WINDOW HCl / Precursor Flow Ratio Rate (nm/min) Zero Rate Growth on Si Seed Nucleation on Mask SELECTIVE WINDOW Process Regime Analysis: • Non-Selective Regime (Low HCl / Flow < 0.8): Deposition exceeds etch rate on both surfaces. Unwanted polycrystalline nodules deposit on dielectric spacers. • 100% Selective Regime (Flow = 0.8 to 1.4): Net growth on crystalline Si > 0; net nucleation on mask ≤ 0. Perfect self-aligned source/drain filling with zero mask defects. • Etch Dominant Regime (Excess HCl / Flow > 1.4): Chlorine etching outpaces precursor deposition. Net cavity recession occurs; crystal silicon substrate is etched. • In Situ Pre-Bake: High-temp H₂ anneal (750°C–800°C) strips native sub-monolayer SiO₂ before gas flow initiates.

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## 1. Selective Epitaxial Reaction Thermodynamics & Kinetic Window

Selective Epitaxial Growth balances two simultaneous, reversible surface reactions: heterogeneous precursor decomposition and chemical halide etching.

In reduced-pressure chemical vapor deposition (RP-CVD) reactors, the primary silicon precursor is Dichlorosilane ($\text{SiH}_2\text{Cl}_2$, DCS) and the primary germanium source is Germane ($\text{GeH}_4$), co-injected with anhydrous Hydrochloric Acid ($\text{HCl}$) gas:

$$\begin{aligned} \text{Deposition Reaction: } & \text{SiH}_2\text{Cl}_2(g) \xrightarrow{\Delta, \text{surface}} \text{Si}(s) + 2\text{HCl}(g) \\ \text{Halide Etching Reaction: } & \text{Si}(s) + 2\text{HCl}(g) \rightleftharpoons \text{SiCl}_2(g) + \text{H}_2(g) \end{aligned}$$
Facet Engineering, Channel Strain Field & Contact Resistance crystallographic faceting angles, valence band splitting, and Schottky tunneling FACET CRYSTALLOGRAPHY & STRAIN Gate / Fin Silicon Bulk (100) Substrate Si₀.₆Ge₀.₄ {111} Facet Si₀.₆Ge₀.₄ {311} Flat Top σ_xx > 2.0 GPa (Compressive) Growth Velocity Anisotropy: R(100) > R(110) > R(311) ≫ R(111) • Slowest {111} plane sets the self-limiting diamond boundary. • Angle relative to (100) plane: θ = arccos(1/√3) = 54.74° Facet Engineering Solutions: • Adjusting Ge% and temperature forces transition from sharp {111} tips to rounded {311}/{110} flat tops. • Prevents spacer pinch-off and expands contact landing area to drastically lower contact resistance R_contact. • In Situ Boron Doping: Electrically active N_A > 2 × 10²¹ cm⁻³ BAND SPLITTING & CONTACT RESISTIVITY Uniaxial Compressive Strain (pMOS Valence Band): Heavy Hole (HH) Lower effective mass m_h* Light Hole (LH) ΔE_v > 120 meV Lifts band degeneracy; suppresses inter-band scattering. Quantum Tunneling Contact Resistivity (WKB): ρ_c ∝ exp[ ( 4π · √m* · Φ_B ) / ( ℏ · √N_active ) ] Doping Concentration Scaling Impact: • At N_active = 5 × 10²⁰ cm⁻³: ρ_c ≈ 2.5 × 10⁻⁸ Ω·cm² • At N_active = 1.5 × 10²¹ cm⁻³: ρ_c ≈ 2.0 × 10⁻⁹ Ω·cm² • Target (Leading Edge): ρ_c < 8.0 × 10⁻¹⁰ Ω·cm² • High in situ boron/phosphorus incorporation narrows the depletion barrier width to < 1.5 nm, enabling field emission quantum tunneling directly through the contact silicide interface.

### 1.1 The Nucleation Incubation Phenomenon
When reactant gases encounter an exposed substrate, adatoms must coalesce into a stable cluster exceeding the thermodynamic critical radius $r^*$:

$$r^* = \frac{2 \gamma_{surf} \Omega}{k_B T \ln(S)}$$

Where:
- $\gamma_{surf}$ is the surface free energy of the nucleating cluster.
- $\Omega$ is the atomic volume.
- $S = P / P_{eq}$ is the precursor chemical supersaturation ratio.

On crystalline silicon seed areas, incoming silicon and germanium adatoms encounter epitaxial lattice sites where chemical bonding is strong ($\text{Si--Si}$ bond energy $\approx 3.25\,\text{eV}$), so the incubation time is essentially zero ($\tau_{seed} \approx 0$).

Conversely, on amorphous dielectric mask surfaces ($\text{SiO}_2$ or $\text{Si}_3\text{N}_4$), adatom binding is weak and physisorption-dominated. The incubation time $\tau_{mask}$ required to form a supercritical nucleus is on the order of tens to hundreds of seconds. By maintaining an $\text{HCl}$ partial pressure such that the etch rate of subcritical adatoms exceeds their arrival rate on dielectric surfaces ($\tau_{etch} < \tau_{mask}$), no nucleation occurs on the mask while steady epitaxial growth proceeds on the silicon seed.

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## 2. Facet Crystallography & Growth Anisotropy

During selective epitaxy in recessed source/drain cavities, growth proceeds with marked anisotropy depending on the surface orientation:

$$R(100) > R(110) > R(311) \gg R(111)$$
+----------------------------------------------------------------------------------------------------+
|                               CRYSTALLOGRAPHIC FACET HIERARCHY IN SEG                              |
+--------------------+--------------------+--------------------+-------------------------------------+
| CRYSTAL PLANE      | RELATIVE VELOCITY  | SURFACE BOND STATE | FACET MORPHOLOGY & CHARACTERISTICS  |
+--------------------+--------------------+--------------------+-------------------------------------+
| (100) Plane        | 1.00 (Fastest)     | 2 dangling bonds   | Standard planar bottom seed growth; |
|                    |                    | per surface atom   | rapid vertical growth profile       |
+--------------------+--------------------+--------------------+-------------------------------------+
| (110) Plane        | 0.70 to 0.85       | 1 dangling bond    | Sidewall fin planes; steady lateral |
|                    |                    | per surface atom   | epitaxial expansion                 |
+--------------------+--------------------+--------------------+-------------------------------------+
| (311) Plane        | 0.40 to 0.55       | Stepped terrace    | Stable transitional facet; ideal for|
|                    |                    | morphology         | rounded contact pad capping         |
+--------------------+--------------------+--------------------+-------------------------------------+
| (111) Plane        | 0.15 to 0.25       | 1 dangling bond    | Slowest growing; forms self-limiting|
|                    | (Slowest)          | tightly packed     | diamond facets at 54.74° angle      |
+--------------------+--------------------+--------------------+-------------------------------------+

The $\{111\}$ plane represents the densest atom packing in diamond cubic lattices. Because its growth rate is the slowest, it acts as a self-limiting boundary. If unmanaged, epitaxial growth forms sharp diamond-shaped tips.

Foundries employ Facet Engineering—tuning the $\text{HCl} / \text{DCS}$ ratio, temperature ($650^\circ\text{C}\text{ to }720^\circ\text{C}$), and reactor pressure (typically $20\text{ to }40\,\text{Torr}$)—to promote $\{311\}$ and $\{110\}$ facet growth, flattening the top of the epitaxy into an elevated box-like profile. This prevents spacer pinch-off and triples the contact landing area for subsequent middle-of-line (MOL) contact plug formation.

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## 3. Uniaxial Channel Strain Mechanics ($\text{Si}_{1-x}\text{Ge}_x$)

In pMOS transistors, replacing relaxed silicon in the source/drain recesses with epitaxial $\text{Si}_{1-x}\text{Ge}_x$ exerts intense uniaxial compressive strain along the channel transport direction ($[110]$ orientation on a $(100)$ wafer).

### 3.1 Lattice Parameter & Stress Calculation
Germanium has a larger lattice constant than silicon:
- $a_{\text{Si}} = 5.431\,\text{Å}$
- $a_{\text{Ge}} = 5.658\,\text{Å}$

According to Vegard's law, the relaxed lattice constant of the $\text{Si}_{1-x}\text{Ge}_x$ alloy is:

$$a_{\text{SiGe}}(x) = (1 - x) a_{\text{Si}} + x a_{\text{Ge}} - 0.00188 x(1 - x)$$

For a typical pMOS alloy with $x = 0.45$ ($45\%\,\text{Ge}$):

$$a_{\text{SiGe}}(0.45) \approx 5.532\,\text{Å} \implies \epsilon_{mismatch} = \frac{a_{\text{SiGe}} - a_{\text{Si}}}{a_{\text{Si}}} \approx \mathbf{+1.86\%}$$

When constrained by the rigid silicon substrate, this lattice mismatch creates a longitudinal compressive stress in the channel:

$$\sigma_{xx} = \frac{E_{Si}}{1 - \nu_{Si}^2} (\epsilon_{xx} + \nu_{Si} \epsilon_{yy}) \approx -\mathbf{2.1\,\text{GPa}}$$

### 3.2 Valence Band Degeneracy Lifting
In unstrained silicon, the valence band maximum consists of degenerate Heavy Hole (HH) and Light Hole (LH) bands at the $\Gamma$-point. Under compressive uniaxial stress ($\sigma_{xx} < 0$):
1. Band Splitting: The degeneracy is lifted by $\Delta E_v > 120\,\text{meV}$, shifting the top band above the bottom band.
2. Effective Mass Reduction: The top band curvature sharpens, reducing the in-plane effective mass from $m_h^* \approx 0.49\,m_0$ down to $m_h^* \approx 0.18\,m_0$.
3. Scattering Suppression: Because $\Delta E_v \gg k_B T$ ($25.9\,\text{meV}$ at room temperature), inter-band optical phonon scattering is suppressed, delivering a $2.5\times\text{ to }3.0\times$ increase in pMOS hole mobility.

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## 4. Specific Contact Resistivity ($\rho_c$) & In Situ Doping

At advanced nodes where contact area per transistor shrinks below $15\,\text{nm} \times 15\,\text{nm} \approx 2.25 \times 10^{-12}\,\text{cm}^2$, source/drain series resistance ($R_{ext}$) dominates the total device on-resistance ($R_{on}$).

The specific contact resistivity $\rho_c$ across the silicide/semiconductor interface is governed by quantum field emission (tunneling):

$$\rho_c \propto \exp\left( \frac{4 \pi \sqrt{m^* \epsilon_s} \cdot \Phi_B}{\hbar \sqrt{N_{active}}} \right)$$

Where:
- $\Phi_B$ is the effective Schottky barrier height ($0.15\text{ to }0.20\,\text{eV}$ for $\text{TiSi}_x / \text{SiGe}$).
- $N_{active}$ is the electrically active dopant concentration.

Through optimized in situ doping during selective epitaxy—co-flowing diborane ($\text{B}_2\text{H}_6$) or boron trichloride ($\text{BCl}_3$) for pMOS, and phosphine ($\text{PH}_3$) for nMOS—foundries achieve active concentrations exceeding $N_A, N_D > 2.5 \times 10^{21}\,\text{cm}^{-3}$.

This ultra-dense doping narrows the electrostatic depletion space-charge layer thickness ($W_{dep} \propto 1/\sqrt{N}$) to less than $1.2\,\text{nm}$, enabling direct quantum mechanical tunneling and achieving record-low contact resistivities:

$$\rho_c \le \mathbf{8.0 \times 10^{-10}\,\Omega\cdot\text{cm}^2}$$

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