Spreading Resistance Profiling (SRP) is a destructive electrical depth profiling technique that mechanically bevels a silicon sample at a shallow angle to geometrically magnify the vertical depth scale, then steps two tungsten carbide probes in micrometer increments along the beveled surface to measure local resistivity as a function of depth — translating the resulting resistance-versus-position data into net active carrier concentration profiles with depth resolution of 5-20 nm and dynamic range spanning six orders of magnitude in doping concentration.
What Is Spreading Resistance Profiling?
- Bevel Preparation: The sample is mechanically lapped at a very shallow angle (0.1-5 degrees, typically 1-2 degrees) using a diamond abrasive on a precision lapping fixture. A 2-degree bevel magnifies the vertical depth scale by 1/tan(2°) ≈ 29x — so 1 µm of vertical depth becomes 29 µm of bevel length, enabling micrometer probe steps to resolve nanometer depth increments.
- Probe Configuration: Two tungsten carbide (WC) probes with hemispherical tips (radius 1-5 µm) are pressed onto the beveled surface under controlled force (5-30 g). The spreading resistance between the two probes is measured by applying a small voltage (5-50 mV) and recording the current, from which resistance R is calculated.
- Spreading Resistance Physics: When current flows through a small circular contact of radius a into a semi-infinite conductor of resistivity ρ, the current spreads hemispherically from the contact and the resistance is R = ρ/(4a). For two contacts (source and sense), R_spreading = ρ/(2a). By solving for ρ from R and the known contact radius (calibrated against standard resistivity samples), local resistivity is obtained at each probe position.
- Carrier Concentration Extraction: Resistivity ρ = 1/(q μ n) where μ is carrier mobility and n is carrier concentration. Using the known relationship between mobility and concentration (Sze-Irvin curves, empirically calibrated for electrons and holes vs. doping), carrier concentration is extracted from measured resistivity at each depth step.
Why SRP Matters
- Net Active Carrier Measurement: SRP measures the electrically active net carrier concentration directly — the quantity that actually controls transistor behavior. Unlike SIMS (which counts all atoms), SRP sees only carriers that contribute to conduction. A boron-doped sample with 50% activation shows SIMS [B] = 2 x 10^20 cm^-3 but SRP p = 10^20 cm^-3 — the difference is the inactive, clustered boron fraction.
- Six-Decade Dynamic Range: SRP measures carrier concentrations from 10^14 cm^-3 (lightly doped background) to 2 x 10^20 cm^-3 (degenerately doped source/drain) in a single scan, capturing the full profile from junction background through the peak implant concentration. This range is difficult to achieve in a single SIMS analysis without multiple primary beam conditions.
- Junction Depth Determination: The junction depth x_j appears as the depth at which the SRP profile changes conductivity type — the measured resistance minimum (where p-type transitions to n-type) corresponds to the metallurgical junction where net doping changes sign. SRP defines x_j with 5-10 nm precision.
- Abruptness Measurement: The steepness of the dopant profile at the junction edge (abruptness, dN/dx at x_j) determines short-channel effect suppression in MOSFETs. SRP directly measures this gradient, verifying whether millisecond annealing (spike anneal, laser anneal) produced the required abrupt junction.
- Historical Significance: SRP was the primary depth profiling technique for silicon process development from the 1970s through the early 1990s, when SIMS became more accessible. The entire database of ion implant range-straggle parameters and diffusion models was built on SRP measurements. TCAD simulators still use SRP data as reference for shallow junction process calibration.
SRP Limitations and Artifacts
Carrier Spilling:
- At abrupt junctions, the electric field at the junction sweeps majority carriers from both sides into the junction region (the depletion approximation fails), creating an apparent broadening of the profile in SRP that is not present in SIMS. This carrier spilling effect overestimates junction depth by 5-20 nm for abrupt profiles and is a well-known systematic artifact in SRP of MOSFET source/drain structures.
Bevel Preparation Artifacts:
- Non-uniform bevel angle (taper) from lapping non-uniformity introduces depth scale errors. Surface damage from lapping creates a thin damaged layer (1-5 nm) that can alter surface conductivity near the bevel start.
- Bevel surface preparation (cleaning, etching) affects probe contact resistance and reproducibility.
Contact Resistance:
- The WC probe-silicon contact is not an ideal ohmic contact — it is a metal-semiconductor contact with resistance that depends on surface states, probe conditioning, and applied force. Probe conditioning (touching reference samples repeatedly) stabilizes contact geometry, but contact resistance variation is the primary source of measurement noise.
Resolution Limit:
- The finite probe size (1-5 µm radius) and bevel angle set a minimum depth resolution of approximately 5-20 nm. Features shallower than this are averaged over the probe contact area, smearing the apparent profile. For junctions below 10 nm depth (as required at advanced nodes), SRP has been largely superseded by SIMS and atom probe tomography.
Spreading Resistance Profiling is mechanical magnification of the invisible — physically grinding a ramp through the nanometer-scale doping architecture of a semiconductor device and walking two tiny probes down that ramp to directly measure the electrical carrier concentration that controls transistor behavior, providing the ground-truth active doping profile against which all other measurements and simulations are compared.