02. Resistivity Sheet Resistance

02. Resistivity Sheet Resistance - D.K. Schroder,...

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Unformatted text preview: D.K. Schroder, Semiconductor Characterization Resistivity Sheet Resistance Four-point Probe Semiconductor Resistivity Wafer Mapping van der Pauw Eddy Current Modulated Photoreflectance Conductivity Type D.K. Schroder, Semiconductor Characterization Graphs and Plots x x y 17 10 4 . 6 1 = 10-4 10-2 10 10 2 10 14 10 16 10 18 10 20 y x 50 100 150 200 5 10 19 1 10 20 y x When two variables, e.g ., resistivity and doping density, vary over many orders of magnitudes (decades) it is best to plot log - log D.K. Schroder, Semiconductor Characterization Graphs and Plots n x y = n x d y d Slope = = ) (log ) (log 2000 4000 6000 8000 10000 2 4 6 8 10 y x 10-4 10-3 10-2 10-1 10 10 1 10 2 10 3 10 4 0.1 1 10 y x-4-3-2-1 1 2 3 4-1-0.5 0.5 1 logy logx What is n ? x n x y x y n n log log log = = = D.K. Schroder, Semiconductor Characterization Graphs and Plots 1 / x x Ke y = 1 1 3 . 2 1 10 ln 1 ) (log x x dx y d Slope = = = = 10 ln ln log y y recall 1 10 100 2 4 6 8 10 y x 20 40 60 80 100 2 4 6 8 10 y x What are K and x 1 ? 10 ln / log log ; / ln ln 1 1 x x K y x x K y + = + = D.K. Schroder, Semiconductor Characterization Two terminal Voltage and current measured at same contact points DUT C W equ DUT C W R R R R I R R R V + + = + + = 2 2 ) 2 2 ( V I R W DUT R W 2-Terminal R C R C DUT equ DUT R R I R V = = Four terminal Voltage and current measured at different contact points V I R W DUT R W 4-Terminal R C R C 2-Terminal or 4-Terminal Measurements? D.K. Schroder, Semiconductor Characterization Four Point Probe The four point probe is used to determine the resistivity and sheet resistance s t I I V Why are four probes better? D.K. Schroder, Semiconductor Characterization Kelvin Measurements Kelvin measurements refer to 4-probe measurements Two probes: 2 R Probe +2 R Contact +2 R Spreading Four probes: R Semicond V I I R Probe R Contact R Spreading Current I I V R Semicond D.K. Schroder, Semiconductor Characterization Four Point Probe Derivation of the basic four point probe equation I P A =2 r 2 r = = 2 1 2 1 1 1 2 2 2 r r I V r I r I V I I r 1 r 2 r I V r dr I dV r I A I J dr dV J IR V r V 2 2 2 ; ; 2 2 = = = = = = = D.K. Schroder, Semiconductor Characterization Four Point Probe For four in-line probes I I s s s 1 2 3 4 cm I V s = 2 s I s s s s I V V V V s s I V s s I V 2 1 2 1 2 1 1 2 1 2 1 2 ; 2 1 1 2 3 2 23 3 2 =...
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02. Resistivity Sheet Resistance - D.K. Schroder,...

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