What Is an Etch Iep Endpoint Algorithm

An etch Interferometric Endpoint algorithm (etch IEP endpoint algorithm)—also known as an in situ reflectometry fringe-tracking algorithm—is a computational framework that translates sinusoidal optical interference oscillations into real-time etch depth, instantaneous etch rate, and sub-nanometer recipe termination triggers during dry etching. Unlike bulk Optical Emission Spectroscopy (OES) algorithms that look for step transitions when clearing onto a stopping layer, IEP algorithms must continuously track periodic interference fringes ($I(t) \propto \cos(\Delta\phi)$) through non-stationary plasma noise, surface roughening damping, and chamber vibrations. Modern IEP endpoint algorithms combine Hilbert transforms, quadrature demodulation, nonlinear Levenberg-Marquardt sine fitting, and predictive Kalman filtering to extract the instantaneous optical phase angle $\phi(t)$ in real time, enabling sub-2nm stopping accuracy for blind silicon recesses, gate-all-around nanosheet cavity formation, and FinFET fin height trims. At a high level, how an etch IEP endpoint algorithm processes raw reflectometry signals and triggers tool interrupts looks like this:

A few principles are essential for understanding how etch IEP endpoint algorithms operate, why simple peak-valley counting is inadequate for sub-3nm nodes, and how advanced quadrature demodulation extracts sub-fringe depth precision:

The limitation of integer fringe counting mandates phase-space tracking. When a laser beam of wavelength $\lambda_0$ reflects from a thinning film of refractive index $n$, the distance between adjacent peaks or valleys is quantized:

For silicon ($n \approx 3.88$ at 670 nm), $\Delta d_{\text{extrema}} \approx 43.2\text{ nm}$; for $SiO_2$ ($n \approx 1.46$), $\Delta d_{\text{extrema}} \approx 114.7\text{ nm}$. If an algorithm simply increments an integer counter every time a peak or valley is reached, it cannot terminate at an intermediate specification such as a 27.5 nm recess. An advanced IEP algorithm converts the 1D intensity wave $I(t)$ into a 2D continuous phase space $(\phi(t))$:

By extracting the continuous instantaneous phase $\phi(t)$ in radians, depth is calculated as a continuous linear variable:

Because the phase $\phi(t)$ is continuous, the algorithm can terminate at any arbitrary fraction of a fringe, achieving sub-2nm depth resolution.

Quadrature demodulation and Hilbert transforms. To determine phase $\phi(t)$ from a single intensity signal $I(t)$ in real time without future data lookahead, algorithms apply a digital Hilbert transform or lock-in quadrature demodulation:
1. *In-Phase Component $I_N(t)$:* The normalized, zero-mean intensity signal: $I_N(t) = \cos(\phi(t))$.
2. *Quadrature Component $Q(t)$:* The $90^\circ$ phase-shifted analytic signal: $Q(t) = \mathcal{H}\{I_N(t)\} = \sin(\phi(t))$.
3. *Phase Angle:* The instantaneous four-quadrant phase angle is extracted instantaneously via:

Plotting $Q(t)$ versus $I_N(t)$ generates a circular Lissajous trajectory in the complex plane. As the wafer etches, the trajectory traces a continuous spiral; its angular velocity corresponds directly to instantaneous etch rate ($d\phi/dt \propto \text{Rate}$).

Kalman filtering and amplitude damping compensation. During harsh reactive ion etching, several physical non-idealities degrade the pure sine wave:
1. *Surface Roughening & Amplitude Damping:* As plasma ions bombard the surface, microscopic roughness increases. This scatters specular laser photons diffusely, causing the amplitude $A(t)$ of the Lissajous circle to shrink inwards over time.
2. *Plasma Emission Light Interference:* Broadband plasma glow leaks through the optical bandpass filter, creating a dynamic DC offset $I_{\text{DC}}(t)$.
To maintain continuous phase lock through these distortions, an extended Kalman filter (EKF) tracks a four-dimensional state vector $\mathbf{x} = [I_{\text{DC}}, A, \phi, \omega]^T$, where $\omega = d\phi/dt$ is the instantaneous fringe angular frequency. By dynamically balancing process covariance against sensor noise, the Kalman filter projects the trajectory forward with high confidence, predicting the exact millisecond the target depth will be reached even if plasma noise momentarily obscures several samples.

Multi-wavelength spectroscopic reflectometry algorithms. In modern sub-3nm gate-all-around architectures, wafer features are multi-layered (e.g., repeating stacks of $Si / Si_{0.7}Ge_{0.3}$ nanosheets). Single-wavelength laser reflectometry produces complex beating patterns where multiple film boundaries interfere simultaneously. Modern IEP tools replace single diodes with broad-band xenon-flash or LED spectrometers collecting 200–1000 nm spectra. The IEP algorithm runs real-time Rigorous Coupled-Wave Analysis (RCWA) or Fresnel matrix solvers, performing nonlinear least-squares regression between the measured reflectance spectrum $R_{\text{meas}}(\lambda)$ and modeled physical parameters $R_{\text{model}}(\lambda, d_{\text{recess}})$, yielding absolute recession depths with sub-nanometer accuracy across heterogeneous stacks.

Read an etch IEP endpoint algorithm through a *digital-phase-ruler* lens: by transforming non-linear, damped sinusoidal interference waves into a pristine, continuously unwrapped linear depth vector, the algorithm grants process engineers the power to stop an etching plasma within a single atomic layer of its programmed specification.