Spreading resistance profiling
Spreading resistance profiling, also known as spreading resistance analysis, is a technique used to analyze resistivity versus depth in semiconductors. Semiconductor devices depend on the distribution of carriers within their structures to provide the desired performance. The carrier concentration can be inferred from the resistivity profile provided by SRP.
History
The fundamental relationship is usually attributed to James Clerk Maxwell. In 1962, Robert Mazur and Dickey developed a practical 2-probe system using a pair of weighted osmium needles.In 1970, Solid State Measurements was founded to manufacture spreading resistance profiling tools and in 1974, Solecon Labs was founded to provide spreading resistance profiling services. In 1980, Dickey developed a practical method of determining p- or n-type using the spreading resistance tool. Improvements have continued but have been challenged by the ever-shrinking dimensions of state-of-the-art digital devices. For shallow structures, the data reduction is complex. Some of the contributors to the data reduction are Dickey, Schumann and Gardner, Choo et al., Berkowitz and Lux, Evans and Donovan, Peissens et al., Hu, Albers, and Casel and Jorke.
Theory of operation
If a voltage is applied between two probe tips providing electrical contact to an infinite slab, the resistance encountered within the slab is, where:- ' is the measured resistance in ohms,
- ' is the resistivity of the slab in ohm-cm, and
- is the radius of the contact area in cm.
Instrumentation
A bias of 5mV is applied across the probe tips. The measured resistance can range from 1-ohm to one billion ohms. A "log R" amplifier or electrometer is used to measure the resistance.Mechanical
[Image:Probes on bevel.jpg|thumb|right| Figure 1 Illustration of the probing of a beveled piece of silicon. (Typically, 60 to 100 or more measurements are made.)|500px]The modern SRP has two tungsten carbide probe tips placed about 20 um apart. Each tip is mounted on a kinematic bearing to minimize "scrubbing". The probes are lowered very gently onto a beveled piece of silicon or germanium. Although the loading of the probe tips may be as little as 2 g., the pressure is in excess of one million pounds per sq inch causing a localized phase transformation in the silicon to "beta-tin" producing a nearly ohmic contact. Between each measurement, the probes are raised and indexed a pre-determined distance down the bevel. Bevels are produced by mounting the sample on an angle block and grinding the bevel with typically a 0.1- or 0.05-micrometre diamond paste. Bevel angles, chosen to fit the depth of interest, can range from ~ 0.001 to 0.2 radians. Care must be used to produce a smooth, flat bevel with minimum rounding of the bevel edge.
Detection limits
The instrument range is typically from one ohm to one billion ohms. This is adequate for the entire resistivity range in single-crystal silicon.Calibration
Calibration standards have been produced by NIST. A set of 16 standards ranging from about 0.0006 ohm-cm to 200 ohm-cm have been produced for both n- and p-type and for both and crystal orientations. For high resistivity the resistivity value must extrapolated from the calibration curve.Applications
The tool is used primarily for determining doping structures in silicon semiconductors. Deep and shallow profiles are shown in Figure 2.[Image:Deep and Shallow SR profiles portrait.jpg|thumb|center| Figure 2 The shallow profile on the left, the deep profile on the right. Carrier concentration is plotted against depth. Regions with a net electron concentration are denoted as "n" (or n-type). Regions with a net hole concentration are denoted as "p".|900px]