Semiconductor Manufacturing Plasma Processes

Plasma processes are foundational to modern semiconductor fabrication—nearly 40-50% of all processing steps in advanced chip manufacturing involve plasma in some form.

1. What is Plasma in Semiconductor Manufacturing?

In semiconductor manufacturing, plasma refers to a partially ionized gas containing:

• Free electrons ($e^-$)
• Positive ions ($\text{Ar}^+$, $\text{Cl}^+$, etc.)
• Neutral atoms and molecules
• Highly reactive radicals ($\text{F}^{\bullet}$, $\text{Cl}^{\bullet}$, $\text{O}^{\bullet}$)

Plasma Characteristics

These are typically "cold" or non-equilibrium plasmas:

The electron temperature is related to thermal energy by:

$$T_e [\text{eV}] = \frac{k_B T}{e} \approx \frac{T[\text{K}]}{11600}$$

Debye Length

The characteristic shielding distance in plasma:

$$\lambda_D = \sqrt{\frac{\varepsilon_0 k_B T_e}{n_e e^2}} = 743 \sqrt{\frac{T_e [\text{eV}]}{n_e [\text{cm}^{-3}]}} \text{ cm}$$

For typical process plasmas: $\lambda_D \approx 10-100 \text{ μm}$

Plasma Frequency

The characteristic oscillation frequency of electrons:

$$\omega_{pe} = \sqrt{\frac{n_e e^2}{m_e \varepsilon_0}} \approx 9000 \sqrt{n_e [\text{cm}^{-3}]} \text{ rad/s}$$

2. Major Plasma Processes

2.1 Plasma Etching

The most critical plasma application—removes material in precisely defined patterns.

2.1.1 Reactive Ion Etching (RIE)

Combines chemical attack from radicals with directional ion bombardment.

Key Mechanism - Ion-Enhanced Etching:

$$\text{Etch Rate}_{total} >> \text{Etch Rate}_{chemical} + \text{Etch Rate}_{physical}$$

The synergistic enhancement factor:

$$\eta = \frac{R_{ion+neutral}}{R_{ion} + R_{neutral}}$$

Typically $\eta = 5-20$ for common etch processes.

Common Chemistries:

• Silicon etching:
• $\text{SF}_6 \rightarrow \text{SF}_x + \text{F}^{\bullet}$ (isotropic)
• $\text{Cl}_2 \rightarrow 2\text{Cl}^{\bullet}$ (anisotropic with sidewall passivation)
• $\text{HBr} \rightarrow \text{H}^{\bullet} + \text{Br}^{\bullet}$ (high selectivity)

• Silicon dioxide etching:
• $\text{CF}_4 + \text{O}_2 \rightarrow \text{CF}_x + \text{F}^{\bullet} + \text{CO}_2$
• $\text{C}_4\text{F}_8 \rightarrow \text{CF}_2 + \text{C}_2\text{F}_4$ (polymerizing)
• $\text{CHF}_3$ (selective to Si)

• Metal etching:
• $\text{Cl}_2/\text{BCl}_3$ for Al, W
• $\text{Cl}_2/\text{O}_2$ for Ti, TiN

Silicon Etch Reaction:

$$\text{Si}_{(s)} + 4\text{F}^{\bullet} \xrightarrow{\text{ion assist}} \text{SiF}_{4(g)} \uparrow$$

Oxide Etch Reaction:

$$\text{SiO}_2 + \text{CF}_x \xrightarrow{\text{ion bombardment}} \text{SiF}_4 \uparrow + \text{CO}_2 \uparrow$$

2.1.2 Deep Reactive Ion Etching (DRIE)

Creates high-aspect-ratio structures using the Bosch process.

Bosch Process Cycle:

1. Etch step (typically 5-15 seconds): $$\text{SF}_6 \rightarrow \text{SF}_5^+ + \text{F}^{\bullet} + e^-$$ $$\text{Si} + 4\text{F}^{\bullet} \rightarrow \text{SiF}_4 \uparrow$$

2. Passivation step (typically 2-5 seconds): $$\text{C}_4\text{F}_8 \rightarrow n\text{CF}_2 \rightarrow (\text{CF}_2)_n \text{ polymer}$$

Achievable Parameters:

• Aspect ratio: $> 50:1$
• Etch depth: $> 500 \text{ μm}$
• Sidewall angle: $90° \pm 0.5°$
• Scallop size: $< 50 \text{ nm}$ (optimized)

2.1.3 Atomic Layer Etching (ALE)

Provides angstrom-level precision through self-limiting reactions.

Two-Step ALE Cycle:

1. Surface modification (self-limiting): $$\text{Surface} + \text{Reactant} \rightarrow \text{Modified Layer}$$

2. Modified layer removal (self-limiting): $$\text{Modified Layer} \xrightarrow{\text{ion/thermal}} \text{Volatile Products} \uparrow$$

Example - Silicon ALE with Cl₂/Ar:

• Step 1: $\text{Si} + \text{Cl}_2 \rightarrow \text{SiCl}_x$ (surface chlorination)
• Step 2: $\text{SiCl}_x + \text{Ar}^+ \rightarrow \text{SiCl}_y \uparrow$ (ion-assisted removal)

Etch per Cycle (EPC):

$$\text{EPC} \approx 0.5 - 2 \text{ Å/cycle}$$

Total Etch Depth:

$$d = N \times \text{EPC}$$

where $N$ = number of cycles.

2.2 Plasma-Enhanced Chemical Vapor Deposition (PECVD)

Deposits thin films at lower temperatures than thermal CVD.

Temperature Advantage:

$$T_{PECVD} \approx 200-400°\text{C} \quad \text{vs} \quad T_{thermal CVD} \approx 700-900°\text{C}$$

Deposition Rate Model (simplified):

$$R_{dep} = k_0 \exp\left(-\frac{E_a}{k_B T}\right) \cdot f(n_e, P, \text{flow})$$

Where plasma activation effectively reduces $E_a$.

Common PECVD Films

Silicon Dioxide:

$$\text{SiH}_4 + \text{N}_2\text{O} \xrightarrow{\text{plasma}} \text{SiO}_2 + \text{H}_2 + \text{N}_2$$

or using TEOS:

$$\text{Si(OC}_2\text{H}_5)_4 + \text{O}_2 \xrightarrow{\text{plasma}} \text{SiO}_2 + \text{CO}_2 + \text{H}_2\text{O}$$

Silicon Nitride:

$$3\text{SiH}_4 + 4\text{NH}_3 \xrightarrow{\text{plasma}} \text{Si}_3\text{N}_4 + 12\text{H}_2$$

Film composition varies: $\text{SiN}_x\text{H}_y$ where $x \approx 0.8-1.3$

Film Properties (Typical):

High-Density Plasma CVD (HDP-CVD)

Simultaneous deposition and sputtering for gap fill.

Deposition-to-Sputter Ratio:

$$D/S = \frac{R_{deposition}}{R_{sputter}}$$

Optimal gap fill: $D/S \approx 3-5$

Gap Fill Mechanism:

• Deposition occurs everywhere
• Sputtering preferentially removes material from corners/top
• Net result: bottom-up fill

2.3 Physical Vapor Deposition (Sputtering)

Argon ions bombard a solid target, ejecting atoms.

Sputter Yield

Number of target atoms ejected per incident ion:

$$Y = \frac{3\alpha}{4\pi^2} \cdot \frac{4M_1 M_2}{(M_1 + M_2)^2} \cdot \frac{E}{U_s}$$

Where:

• $M_1$ = ion mass
• $M_2$ = target atom mass
• $E$ = ion energy
• $U_s$ = surface binding energy
• $\alpha$ = dimensionless function of mass ratio

Typical Sputter Yields (500 eV Ar⁺):

Ionized PVD (iPVD)

Ionizes sputtered metal atoms for directional deposition.

Ionization Fraction:

$$f_{ion} = \frac{n_{M^+}}{n_{M^+} + n_M}$$

Modern iPVD: $f_{ion} > 70\%$

Bottom Coverage Improvement:

$$\text{BC} = \frac{t_{bottom}}{t_{field}}$$

iPVD achieves BC > 50% in features with AR > 5:1

2.4 Plasma-Enhanced Atomic Layer Deposition (PEALD)

Uses plasma as one of the reactants in the ALD cycle.

Standard ALD Cycle:

1. Precursor A exposure (self-limiting) 2. Purge 3. Precursor B exposure (self-limiting) 4. Purge

PEALD Advantage:

Plasma provides reactive species at lower temperatures:

$$\text{O}_2 \xrightarrow{\text{plasma}} 2\text{O}^{\bullet}$$

vs thermal:

$$\text{H}_2\text{O} \xrightarrow{T > 300°C} \text{OH}^{\bullet} + \text{H}^{\bullet}$$

Example - HfO₂ PEALD:

• Step 1: $\text{Hf(NMe}_2)_4 + \text{Surface-OH} \rightarrow \text{Surface-O-Hf(NMe}_2)_3 + \text{HNMe}_2$
• Step 2: $\text{Surface-O-Hf(NMe}_2)_3 + \text{O}^{\bullet} \rightarrow \text{Surface-HfO}_2\text{-OH}$

Growth per Cycle (GPC):

$$\text{GPC} \approx 0.5-1.5 \text{ Å/cycle}$$

Film Thickness:

$$t = N \times \text{GPC}$$

3. Plasma Sources

3.1 Capacitively Coupled Plasma (CCP)

Two parallel plate electrodes with RF power (typically 13.56 MHz).

Sheath Voltage:

$$V_{sh} \approx \frac{V_{RF}}{2}$$

Ion Bombardment Energy:

$$E_{ion} \approx eV_{sh} = \frac{eV_{RF}}{2}$$

For $V_{RF} = 500\text{ V}$: $E_{ion} \approx 250\text{ eV}$

Plasma Density:

$$n_e \propto P_{RF}^{0.5-1.0}$$

Typical: $n_e \approx 10^9 - 10^{10} \text{ cm}^{-3}$

Limitations:

• Ion flux and energy are coupled
• Lower density than ICP

3.2 Inductively Coupled Plasma (ICP)

RF coil induces plasma currents.

Power Transfer:

$$P_{plasma} = \frac{V_{ind}^2}{R_{plasma}}$$

Where induced voltage:

$$V_{ind} = -\frac{d\Phi}{dt} = \omega \cdot N \cdot B \cdot A$$

Key Advantage - Independent Control:

• Source power ($P_{source}$) → Ion flux ($\Gamma_i$)

$$\Gamma_i \propto n_e \propto P_{source}^{0.5-1.0}$$

• Bias power ($P_{bias}$) → Ion energy ($E_i$)

$$E_i \propto V_{bias} \propto \sqrt{P_{bias}}$$

Typical Parameters:

3.3 Electron Cyclotron Resonance (ECR)

Microwave power (2.45 GHz) + magnetic field.

Resonance Condition:

$$\omega = \omega_{ce} = \frac{eB}{m_e}$$

At 2.45 GHz: $B_{res} = 875 \text{ G}$

Advantages:

• Very high density: $n_e > 10^{12} \text{ cm}^{-3}$
• Low pressure operation: $< 1 \text{ mTorr}$
• Efficient power coupling

3.4 Remote Plasma

Plasma generated away from substrate—only radicals reach wafer.

Radical Flux at Wafer:

$$\Gamma_r = \Gamma_0 \exp\left(-\frac{L}{\lambda_{mfp}}\right) \cdot \exp\left(-\frac{t}{\tau_{recomb}}\right)$$

Where:

• $L$ = distance from plasma
• $\lambda_{mfp}$ = mean free path
• $\tau_{recomb}$ = recombination lifetime

Benefits:

• No ion bombardment damage
• Gentle surface treatment
• Ideal for cleaning and selective processes

4. Plasma Sheath Physics

The sheath is the region between bulk plasma and surfaces.

4.1 Sheath Formation

Electrons are faster than ions:

$$v_e = \sqrt{\frac{8k_BT_e}{\pi m_e}} >> v_i = \sqrt{\frac{8k_BT_i}{\pi m_i}}$$

Result: Surfaces charge negatively, forming a positive space-charge sheath.

4.2 Bohm Criterion

Ions must reach sheath edge with minimum velocity:

$$v_{Bohm} = \sqrt{\frac{k_B T_e}{m_i}}$$

Ion flux to surface:

$$\Gamma_i = n_s \cdot v_{Bohm} = n_s \sqrt{\frac{k_B T_e}{m_i}}$$

Where $n_s \approx 0.61 n_e$ at sheath edge.

4.3 Child-Langmuir Law

Ion current density through collisionless sheath:

$$J_i = \frac{4\varepsilon_0}{9} \sqrt{\frac{2e}{m_i}} \cdot \frac{V^{3/2}}{d^2}$$

4.4 Sheath Thickness

$$s = \frac{\sqrt{2}}{3} \lambda_D \left(\frac{2V_s}{T_e}\right)^{3/4}$$

For $V_s = 100\text{ V}$, $T_e = 3\text{ eV}$: $s \approx 10-100 \text{ μm}$

4.5 Ion Angular Distribution

Without collisions (low pressure):

$$\theta_{max} \approx \arctan\sqrt{\frac{T_i}{eV_s}}$$

Typically $\theta_{max} < 5°$ — highly directional!

With collisions (high pressure):

$$\theta \propto \frac{s}{\lambda_{mfp}}$$

Collisions broaden the angular distribution, reducing anisotropy.

5. Etch Process Metrics

5.1 Etch Rate

$$R = \frac{\Delta d}{\Delta t} \quad [\text{nm/min}]$$

Typical values:

• Si in $\text{SF}_6$: $200-1000$ nm/min
• $\text{SiO}_2$ in $\text{CF}_4$: $50-200$ nm/min
• Poly-Si in $\text{Cl}_2$: $100-500$ nm/min

5.2 Selectivity

Ratio of etch rates between two materials:

$$S_{A:B} = \frac{R_A}{R_B}$$

Critical Selectivities:

5.3 Anisotropy

$$A = 1 - \frac{R_{lateral}}{R_{vertical}}$$

• $A = 1$: Perfectly anisotropic (vertical sidewalls)
• $A = 0$: Perfectly isotropic (hemispherical profile)

5.4 Uniformity

$$U = \frac{R_{max} - R_{min}}{2 \cdot R_{avg}} \times 100\%$$

Target: $U < 3\%$ across 300mm wafer.

5.5 Aspect Ratio Dependent Etching (ARDE)

Etch rate decreases with aspect ratio:

$$R(AR) = R_0 \cdot f(AR)$$

Knudsen Transport Model:

$$\frac{R(AR)}{R_0} = \frac{1}{1 + \frac{AR}{K}}$$

Where $K$ is a chemistry-dependent constant (typically 5-20).

6. Process Control Parameters

6.1 RF Power

Source Power (ICP coil or CCP top electrode):

• Controls plasma density: $n_e \propto P^{0.5-1.0}$
• Controls radical production
• Typical: $100-3000$ W

Bias Power (substrate electrode):

• Controls ion energy: $E_i \propto \sqrt{P_{bias}}$
• Controls anisotropy
• Typical: $0-500$ W

6.2 Pressure

Effects:

Mean Free Path:

$$\lambda = \frac{k_B T}{P \cdot \sigma}$$

At 10 mTorr, 300K: $\lambda \approx 5 \text{ mm}$

6.3 Gas Flow and Chemistry

Residence Time:

$$\tau_{res} = \frac{P \cdot V}{Q}$$

Where $Q$ = flow rate (sccm), $V$ = chamber volume.

Dissociation Fraction:

$$\alpha = \frac{n_{dissociated}}{n_{total}}$$

Higher power → higher $\alpha$

6.4 Temperature

Wafer Temperature Effects:

• Reaction rates: $k \propto \exp(-E_a/k_BT)$
• Desorption rates
• Selectivity
• Film stress (PECVD)

Typical range: $-20°C$ to $400°C$

7. Advanced Topics

7.1 Pulsed Plasmas

Modulate RF power on/off with period $T_{pulse}$.

Duty Cycle:

$$D = \frac{t_{on}}{t_{on} + t_{off}} = \frac{t_{on}}{T_{pulse}}$$

Benefits:

• Narrower ion energy distribution
• Reduced charging damage
• Better selectivity control

Ion Energy Distribution (IED):

• CW plasma: Bimodal distribution
• Pulsed plasma: Controllable, narrower distribution

7.2 Plasma-Induced Damage

Charging Damage:

$$V_{gate} = \frac{Q_{accumulated}}{C_{gate}} = \frac{(J_e - J_i) \cdot t \cdot A}{C_{gate}}$$

When $V_{gate} > V_{BD}$ → oxide breakdown!

Mitigation:

• Pulsed plasmas
• Neutral beam sources
• Process optimization

UV Damage:

VUV photons ($E > 9$ eV) can break Si-O bonds.

$$\text{Si-O} + h u \rightarrow \text{defects}$$

7.3 Loading Effects

Macro-loading:

$$R = R_0 \cdot \frac{1}{1 + \frac{A_{etch}}{A_0}}$$

More exposed area → lower etch rate (radical consumption).

Micro-loading:

Local pattern density affects local etch rate.

$$\Delta R = R_{isolated} - R_{dense}$$

7.4 Profile Control

Sidewall Passivation Model:

$$\theta = \arctan\left(\frac{R_{lateral}}{R_{vertical}}\right) = \arctan\left(\frac{R_V - R_P}{R_V}\right)$$

Where:

• $R_V$ = vertical etch rate
• $R_P$ = passivation deposition rate

Ideal Vertical Profile: $R_P = R_{lateral}$ on sidewalls

8. Equipment and Monitoring

8.1 Chamber Components

• Chuck/Pedestal: Temperature-controlled substrate holder
• Electrostatic chuck (ESC) for wafer clamping
• He backside cooling for thermal contact

• Gas Distribution:
• Showerhead or side injection
• Mass flow controllers (MFCs): $\pm 1\%$ accuracy

• Pumping System:
• Turbo-molecular pump: base pressure $< 10^{-6}$ Torr
• Throttle valve for pressure control

• RF System:
• Generator: 13.56 MHz, 2 MHz, 60 MHz common
• Matching network: L-type or $\pi$-type

8.2 In-Situ Monitoring

Optical Emission Spectroscopy (OES):

Monitor plasma species by emission lines:

Endpoint Detection:

$$\text{EPD Signal} = \frac{I_{product}}{I_{reference}}$$

Endpoint when signal changes (product species decrease).

Interferometry:

Film thickness from interference:

$$2nd\cos\theta = m\lambda$$

Real-time thickness monitoring during etch/deposition.

9. Challenges at Advanced Nodes

9.1 Feature Dimensions

At 3nm node:

• Gate length: $\sim 12$ nm ($\sim 50$ atoms)
• Fin width: $\sim 5-7$ nm
• Metal pitch: $\sim 20-24$ nm

Precision Required:

$$\sigma_{CD} < 0.5 \text{ nm}$$

9.2 New Architectures

Gate-All-Around (GAA) FETs:

• Requires isotropic etching for channel release
• Selective removal of SiGe vs Si
• Inner spacer formation

3D NAND:

• $> 200$ stacked layers
• High aspect ratio etching ($> 60:1$)
• Memory hole etch: $> 10$ μm deep

9.3 New Materials

10. Key Equations

Plasma Parameters

$$\lambda_D = \sqrt{\frac{\varepsilon_0 k_B T_e}{n_e e^2}}$$

$$v_{Bohm} = \sqrt{\frac{k_B T_e}{m_i}}$$

$$\Gamma_i = 0.61 \cdot n_e \cdot v_{Bohm}$$

Etch Metrics

$$S_{A:B} = \frac{R_A}{R_B}$$

$$A = 1 - \frac{R_{lateral}}{R_{vertical}}$$

$$U = \frac{R_{max} - R_{min}}{2R_{avg}} \times 100\%$$

Process Dependencies

$$n_e \propto P_{source}^{0.5-1.0}$$

$$E_i \propto \sqrt{P_{bias}}$$

$$R \propto \Gamma_i \cdot f(E_i) \cdot [X^{\bullet}]$$