Four-point probe

Four-point probe is the most commonly used method to measure sheet resistance for metal films in silicon processing. Given known resistivities of each material, the film thickness can be obtained. Table VI lists the resistivities for the films often used in the back-end interconnect processes. The theory in four-point prohe originally comes from Ohm s law  

Resistivities for the Commonly Used Materials IN A Metal CMP Process 

PVD physical vapor deposition. CVD chemical vapor deposition. 

A schematic for the four-point probe measurements is shown in Fig. 22. For an infinite sheet wafer (film on an unbounded wafer), the sheet resistance is 

If a single metal film is deposited on an oxide, the sheet resistance measurement results can by easily interpreted and converted to the thickness. In practice, however, this is not usually the case. For example, in W CVD, the tungsten is not directly deposited on oxide due to high residual stress and unreliable adhesion. A titanium (Ti) layer must be first deposited as a glue layer. In addition, to prevent the fluorine in the CVD-precursor WFg from directly reacting with Ti (a strong catalytic reaction will occur), a barrier layer of titanium nitride (TiN) must be deposited on top of the Ti. As a result, we have a trilayer film of W on TiN on Ti on oxide, as shown schematically in Fig. 21. This poses some problems in accuracy in the four-point probe measurements. Based on the resistivities in Table VI, the 

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Diffusivities of various elements ate determined experimentally. Dopant profiles can be determined. The junction depth can be measured by chemically staining an angle-lapped sample with an HE/HNO mixture. The -type region of the junction stains darker than the n-ty e region. The sheet resistivity can also be measured using a four-point probe measurement. These two techniques ate used for process monitoring. 

One problem with methods that produce polycrystalline or nanocrystalline material is that it is not feasible to characterize electrically dopants in such materials by the traditional four-point-probe contacts needed for Hall measurements. Other characterization methods such as optical absorption, photoluminescence (PL), Raman, X-ray and electron diffraction, X-ray rocking-curve widths to assess crystalline quality, secondary ion mass spectrometry (SIMS), scanning or transmission electron microscopy (SEM and TEM), cathodolumi-nescence (CL), and wet-chemical etching provide valuable information, but do not directly yield carrier concentrations. 

Sheet resistance (Rs) is defined by p = Rst, where p is resistivity and t is film thickness. For CuGaS2 thin-film samples, Rs was determined using the four-point probe method53 and calculated from current-voltage data (Fig. 6.17) using... 

This section deals with the electrodes in the electrochemical set-up, with special emphasis on the silicon electrode and its semiconducting character. An electrochemical cell with its complete electrical connections, as shown in Fig. 1.3 a and b, is similar to the well-known four-point probe used for applying a defined bias to a solid-state device. The two tines that supply the current are connected to... 

The most typical way to measure the in-plane electrical conductivity of a diffusion layer is through the use of the four-point probe method. A small current is applied across the sample material a separate set of voltage measuring probes that are in touch with the material are used to measure the resulting voltage drop in order to calculate the resistance. With these values, the in-plane resistivity, p, can be calculated with the following equation [9,233] ... 

Fig. 22. Schematic of a four-point probe setup. The djs value and its correction factor are typically provided by the equipment company.

Solid State Properties. Most likely as a result of the limited intermoleeular interactions of these complexes in the solid state, little investigation of their solid-state properties have been reported. However, the electrical conductivity of pressed pellets of 17 have been measured via four-point probe to give a room temperature value of 10 S cm. This relatively low value is likely a result of the lack of significantly strong t-stacking as observed in the X-ray structure. 

It is frequently important to determine electrode resistance to account for any contributions to iR drop and circuit rise time due to the electrode itself. Two general strategies are available for this purpose. One strategy for accurately determining p is to use a four-point probe (see Fig. 11.2) for the measurement [6]. This device supplies a controlled current to be passed through the film via... 

Figure 11.2 Arrangement of a four-point probe on a rectangular sample. Note that the dimensions a, d, and s must be specified to calculate a specific value for the resistance. [From Ref. 9.]...

Emissive spectral features were consistent with those previously reported for CdS Te (6-13) and confirmed (Roessler s correlation, (12)) that the Te concentration was <100 ppm. TheA,5x5xl mm samples had resistivities of A,2 ohm-cm (four point probe method) and were oriented with the 5x5 mm face perpendicular to the c-axis. Samples were first etched with 1 10 (v/v) Br2/MeOH and then placed in an ultrasonic cleaner to remove residual Br2. The electrolyte was either sulfide, 1M 0H /1M S2-, or polyselenide, typically 5M 0H /0.1M Se2 /0.001M Se22- short optical pathlengths (<0.1 cm) were used to make the latter essentially transparent for A >500 nm. Electrode and electrolyte preparation as well as electrochemical and optical instrumentation employed have been described previously (8). Electrolytes were magnetically stirred and blanketed under N2 during use. 

To minimize the current flow through the sample, an ac four-point probe technique was used to monitor the conductivity of the sample with a lock-in amplifier (Stanford Research Systems, model SR 830 DSP). The lock-in amplifier enabled us to measure very low voltages without noise problems. 

Sheet resistance can be measured with a four-point probe. The probes may be in line or in a square pattern, as shown in Figure 9. In either configuration, a constant current I is passed through two of the probes, and the voltage difference between the other two is read. Provided the conducting layer is thin (t < 0.60 d), the sheet resistance can be calculated from... 

Figure 9 Four-point probes to measure sheet resistance, (a) in-line (b) square.

Smits, F.M., Measurement of sheet resistivities with the four point probe. 

An alternative method to TLM is the four-point probe, which consists of introducing into the conducting channel two additional electrodes [45, 46]. The current remains the same all along the channel and the voltage drop between these two additional electrodes is not affected by the contact resistance, thus giving access to the true channel resistance. Moreover, as shown in Fig. 1.14, the contact resistance at each side of the channel can now be estimated independently. 

A variety of experimental measurements can be used to determine free carrier densities (and thus dopant levels) in semiconductors. Four-point probe resistivity measurements are the most common because they are relatively painless, nondestructive, and can be performed on thin wafers. There is more to them than meets the eye, however. 

Typically, one works with thin, round semiconductor wafers, ranging in size from 5 inches to less than a quarter inch in diameter, and measures their resistivities using a four-point probe setup. Suppose you use a four-point probe to measure the resistivity of an n-type (p-doped) Si sample. A micrometer tells you that the average thickness ( ) of the 30-inch diameter wafer is 0.408 mm. The spacing on the probe is 0.050 inch. You collect the following current-voltage data at room temperature ... 

The resistivity of a free-standing bulk sample was measured by depositing Pt electrodes by FIB and by employing the four point probe method [8], The resistivity of the bulk was 10 - 15 Q cm. The carrier concentration was estimated to be less than 1016 cm 3 by the plasmon-coupled mode in the Raman spectrum. These electrical measurements show that the crystal is of relatively high purity. 

Four-point probe measurements are very reliable, but the technique has limitations, because, as more highly resistive materials are examined, the... 

Hall voltage was measured by a four-point probe method for the samples shaped like a cross, using dc current and dc magnetic field. 

By the process described above, a plasma film could be obtained that had high enough electrical conductivity to allow direct electrodeposition of copper. The bulk resistivity of film measured by a four-point probe was 2.6 x 10 " ohm-cm for the copper-containing polymer film when deposition was stopped after 18 min at HOW. This value is critical if a uniform electrolytic deposit is to be obtained. For safety, deposition was carried out until a total film thickness of 150nm was obtained, giving a nearly pure metallic layer thick enough to allow subsequent electroplating. 

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