Quantitative mobility spectrum analysis for magnetic field dependent hall and resistivity data
First Claim
1. A method comprising:
- providing an isotropic sample of semiconductor material;
sequentially exposing said sample to a plurality I of preselected magnetic fields Bi, i=1, 2, . . . , I; and
for each said Bi ;
(a) measuring the Hall coefficient RH(i) and electrical resistivity ρ
i corresponding to said Bi ;
(b) using said RH(i), said ρ
i, and said Bi to determine elements σ
xx(i) and σ
xy(i) of the conductivity tensor of said sample at said Bi,(c) using said σ
xx(i) and σ
xy(i) to make estimates of the magnitudes Sxx(i) and Sxy(i) of the conductivity-mobility spectrum of said sample;
wherein said method further comprises;
using said Bi '"'"'s, said σ
xx(i) '"'"'s and σ
xy(i) '"'"'s, and said estimates of Sxx(i) and Sxy(i) for mathematically iterating the values of Sxx(i) and Sxy(i) ;
wherein said iterating is done effective to cause, upon any value of said Sxx(i) becoming negative, to reset said Sxx(i) to a preselected non-negative value.
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Abstract
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.
7 Citations
7 Claims
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1. A method comprising:
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providing an isotropic sample of semiconductor material; sequentially exposing said sample to a plurality I of preselected magnetic fields Bi, i=1, 2, . . . , I; and for each said Bi ; (a) measuring the Hall coefficient RH(i) and electrical resistivity ρ
i corresponding to said Bi ;(b) using said RH(i), said ρ
i, and said Bi to determine elements σ
xx(i) and σ
xy(i) of the conductivity tensor of said sample at said Bi,(c) using said σ
xx(i) and σ
xy(i) to make estimates of the magnitudes Sxx(i) and Sxy(i) of the conductivity-mobility spectrum of said sample;wherein said method further comprises; using said Bi '"'"'s, said σ
xx(i) '"'"'s and σ
xy(i) '"'"'s, and said estimates of Sxx(i) and Sxy(i) for mathematically iterating the values of Sxx(i) and Sxy(i) ;wherein said iterating is done effective to cause, upon any value of said Sxx(i) becoming negative, to reset said Sxx(i) to a preselected non-negative value.
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2. An apparatus comprising:
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means for providing an isotropic sample of semiconductor material; means for sequentially exposing said sample to a plurality I of preselected magnetic fields Bi, i=1, 2, . . . , I; and means, for each said Bi, for; (a) measuring the Hall coefficient RH(i) and electrical resistivity p, corresponding to said Bi ; (b) using said RH(i), said ρ
i, and said Bi to determine elements σ
xx(i) and σ
xy(i) of the conductivity tensor of said sample at said Bi ;(c) using said σ
xx(i) and σ
xy(i) to make estimates of the magnitudes Sxx(i) and Sxy(i) of the conductivity-mobility spectrum of said sample;wherein said apparatus further comprises; means for using said Bi '"'"'s, said σ
xx(i) '"'"'s and σ
xy(i) '"'"'s, and said estimates of Sxx(i) and Sxy(i) for mathematically iterating the values of Sxx(i) and Sxy(i) ;wherein said iterating is done effective to cause, upon any value of said Sxx(i) becoming negative, to reset said Sxx(i) to a preselected non-negative value.
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3. A method comprising:
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providing an isotropic sample of semiconductor material; sequentially exposing the sample to a plurality I of preselected magnetic fields Bi, i=1, 2, . . . , I, and for each Bi ; (a) measuring the Hall coefficient RH(i) and electrical resistivity ρ
i corresponding to the Bi ;(b) using the RHi, the ρ
i, and the Bi to determine elements σ
xx(i) and σ
xy(i) of the conductivity tensor of the sample at the Bi ;(c) using the σ
xx(i) and σ
xy(i) to make estimates of the magnitudes Sxx(i) and Sxy(i) of the conductivity-mobility spectrum of the sample;wherein the method further includes; using the Bi '"'"'s, the σ
xx(i) '"'"'s, and σ
xy(i) '"'"'s, and the estimates of Sxx(i) and Sxy(i) for mathematically iterating the values of Sxx(i) and Sxy(i) ;wherein the iterating comprises recursively iterating the Sxx(i) and Sxy(i) according to;
##EQU10## where μ
i is the ith mobility point. - View Dependent Claims (4)
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5. A method comprising:
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providing an isotropic sample of semiconductor material; sequentially exposing the sample to a plurality I of preselected magnetic fields Bi, i=1, 2, . . . , I, and for each Bi ; (a) measuring the Hall coefficient RH(i) and electrical resistivity ρ
i corresponding to the Bi ;(b) using the RH(i), the ρ
i, and the Bi to determine elements σ
xx(i) and σ
xy(i) of the conductivity tensor of the sample at the Bi ;(c) using the σ
xx(i) and σ
xy(i) to make estimates of the magnitudes Sxx(i) and Sxy(i) of the conductivity-mobility spectrum of the sample;wherein the method further includes; using the Bi '"'"'s, the σ
xx(i) '"'"'s, and σ
xy(i) '"'"'s, and the estimates of Sxx(i) and Sxy(i) for mathematically iterating the values of Sxx(i) and Sxy(i) ;wherein the iterating includes recursively iterating the Sxx(i) and Sxy(i) according to;
##EQU11## where ω
x and ω
y are damping parameters selected to be between 0 and 1 and where μ
i is the ith mobility point. - View Dependent Claims (6, 7)
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Specification