USA As Represented by Secretary of the Navy

Lorenzo Faraone

Jerry R Meyer

Igor Vurgaftman

Filbert J Bartoli

Craig A Hoffman

Jaroslav Antoszewski

Jaroslaw Antoszewski

David Redfern

Jeffrey R Lindenmuth

The present invention is a method for determining a carrier conductivity-rier mobility spectrum for a semiconductor sample, having the steps of: exposing the semiconductor sample to a range K of discrete magnetic fields k=1,2, . . . K; for each field obtaining a Hall coefficient R.sub.H and a resistivity .rho., and calculating from R.sub.H (B.sub.k) and .sigma.(B.sub.k) experimental conductivity tensor components .sigma..sub.xx.sup.k (exp) and .sigma..sub.xy.sup.k (exp), and slopes of these conductivity tensor components .sigma.'.sub.xx.sup.k (exp) and .sigma.'.sub.xy.sup.k (exp); selecting a trial carrier conductivity-carrier mobility spectrum s.sub.i corresponding to a plurality I of carrier mobilities .mu..sub.i, i=1,2, . . . I; for each B.sub.j, using this trial carrier conductivity-carrier mobility spectrum to calculate conductivity tensor components .sigma..sub.xx.sup.j and .sigma..sub.xy.sup.j, and slopes of the conductivity tensor components .sigma.'.sub.xx.sup.j and .sigma.'.sub.xy.sup.j ; for each B.sub.j, calculating errors .DELTA..sub.xx.sup.j .ident..sigma..sub.xx.sup.j (exp)-.sigma..sub.xx.sup.j, .DELTA..sub.xy.sup.j .ident..sigma..sub.xy.sup.j (exp)-.sigma..sub.xy.sup.j, .DELTA.'.sub.xx.sup.j (exp)-.sigma.'.sub.xx.sup.j, and .DELTA.'.sub.xy.sup.j .ident..sigma.'.sub.xy.sup.j (exp)-.sigma.'.sub.xy.sup.j, and calculating therefrom a total weighted squared error .chi..sub.j.sup.2 ; for each B.sub.j and at least a subset of .mu..sub.i, calculating an optimum change to said trial carrier conductivity-carrier mobility spectrum .delta.s.sub.ij, and calculating therefrom a modified total weighted squared error .chi..sub.ij.sup.2 ; for each B.sub.j, determining a minimum carrier mobility point .mu..sub.iminj whose corresponding change .delta.s.sub.ij that yields the lowest weighted squared error .chi..sub.ij.sup.2 ; for each B.sub.j and at least a subset of .mu..sub.i, changing the carrier conductivity-carrier mobility spectrum by not more than .delta.s.sub.ij.

Quantitative mobility spectrum analysis of magnetic-field dependent hall

A method and apparatus for producing the conductivity-mobility spectrum of an isotropic semiconductor material, and hence infer the mobility and concentration of carriers in the material. Hall voltage and material conductivity are measured at a plurality of magnetic field strengths, values of the spectrum estimated for each field strength, and the estimates numerically iterated to produce convergent values for the spectrum. In one embodiment, interim selected values of the spectrum are prevented from going negative, which increases the precision of the ultimate convergent values. In another embodiment, the iteration equations employ damping factors to prevent over-correction from one iteration to the next, thus preventing convergent instabilities. The preferred iteration is the Gauss-Seidel recursion.

Quantitative mobility spectrum analysis for magnetic field dependent

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Mt. Lawley, WA, United States of America

Lorenzo Faraone