Sheet resistivity calculation

A geometrical factor, k, can then simply be calculated from a ratio of these two voltages and the sheet resistance calculated from... 

Fig. 9.4. Typical loss of current density as a function of ZnO sheet resistance calculated for three values of the absorber bandgap (assuming air mass 1.5 illumination, redrawn with permission from [12])...

Fig. 9.6. Calculated optimum interconnect distance and resulting module efficiency as a function of ZnO sheet resistance. Calculations are based on the properties of a small area CIGSe-based cell with 14.4% efficiency. Reprinted with permission from [17]...

Figure 6.17. I-V curve for CuGaS2 thin film. The linear region below 3.0 x 10 5 amps was used to calculate sheet resistance.

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... 

The resistivity of the films was greater than 10" fl-cm (calculated from a reported sheet resistivity of >10 fi and an assumed thickness of 100 nm). 

The minimum length l and width id of a resistor are calculated from the given resistance R, the sheet resistance R in ohms per square, dissipated power P, and permissible power dissipation per square inch P by use of the formulas u> = /(P R)/P R and l = u>R/R. The capacitance of film capacitors is given by C = 0.225D(W — 1 )A/t, where C is the capacitance in picofarads. D the dielectric constant. N the number of plates, A die area in square inches, and / the dielectric thickness in inches. 

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... 

Fig. 8.12. Calculated active area (gray) and aperture area efficiencies (black) of a-Si 11/jLif- Si 11 tandem solar modules as function of cell width for different TCO sheet resistance values Rtco 5 0 (dashed), 10O (solid), and 20 0 (dotted)...

The most convenient way to determine the resistivity routinely is by the four point probe method as described by Valdes254. The resistivity can be calculated from the sheet resistance by ... 

In our day-to-day profiling at SSM, we depend primarily on comparisons with theory (as In Figure 7), or on comparisons between the known Ion Implant dosage and a dosage calculated by Integrating the dopant profile. For example. In Figure 8, the known Implant fluence was 2 x 10 cm 2 while the dosage calculated from the carrier concentration profile was 1.5 x 10 cm . we also frequently compare the measured sheet resistance of a layer with a Pg value calculated from the measured resistivity profile. 

The samples were fabricated on a bonded SOI wafer with a 60-70 tun thick SOI film, where the buried-oxide layer was 400 mn thick. The wafer was heavily doped with phosphorous 3.5 - 16 TO cm. The electrons were uniformly heated in the very long (up to 1500 pm) SOI film by applying heating current between the contacts, which were at the ends of the silicon film. The Joule heat was calculated by using the values of the sheet resistance of the film and of the electrical current. A He/" He dilution refrigerator was used for the measvuement in the temperature range between 50 mK and 500 mK. 

The calculated surface roughness contribution, resulting from ion bombardment, to the sheet resistance for the more reactive chromium is 166 fT/D. However, the measured sheet resistance is 370 O/n. Again, this value is about three times greater than prediaion. and values obtained on as-cured polymer and non-reacUve alumina substrate. This result is in agreement with thasc obtained on spuudcd films and presented above. 

Figure 14.10 Calculated curves of Internal transmission T/To versus sheet resistance Rs for ITO and highly conductive PEDOT PSS (Clevios PH 500 + 5 % DMSO)...

Using Equation 8.16, the equivalent sheet resistivity is calculated. 

By analogy with the above derivation of Eq. (23-7) for the general resistivity of bulk materials, this relationship for the sheet resistance can easily be obtained from a calculation of the differential resistance given by Eq. (23-8). In the case of thin films, the current paths can best be described as propagating rings, with an area of A— 2nxt, which after integration between s and 2s leads to... 

Surface conductivity of glass or of thin films on glass is often measured in terms of sheet resistance (ohms per square, or Q/D) using a four-point probe technique. Electrically contacting point probes are placed at the four comers of a square on the surface or the fihn. A current I is allowed to pass through two adjacent probes, and the potential difference V developed across the other two probes is measured. Sheet resistance in this arrangement is calculated as... 

Therefore, sheet resistivity at a desired thickness can be calculated using Eq. (8.35). For example, the sheet resistivity at 25 is given by ... 

From the above equations, the sheet resistivity of the fired paste can be calculated for a given resistor size. In the same way, the ratio of length to width, or aspect ratio, of a resistor for a required resistance value can theoretically be determined for a paste of known resistance. 

The conductivity of PEDOTPSS layers is usually determined by depositing uniform thin films onto a nonconductive substrate. The sheet resistance, is measured via four-point or two-point probes. The resistivity, p, or its inverse, the conductivity, o, are calculated by multiplying times the layer thickness, d, according to... 

Calculated relative luminous transmission ITO, PEDOT PSS and in situ PEDOT versus sheet resistance The layer thickness (d) is the parameter that determines and Y, d has... 

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