The Effect of Uniaxial Stress on the Donor Polarizabilities of Phosphorus and AntimonyDoped Silicon.
Abstract
This thesis reports piezocapacitance measurements on high purity Si, Si:P and Si:Sb with a uniaxial tensile stress along either the {100} or the {110 } axis and an electric field along the {001} axis from T = 4.2 K to 1.1 K. Dielectric constant values were obtained from the capacitance data after applying various corrections. The donor concentrationdependence of the dielectric constant was investigated for Si:P from N(,D) = 6.8 x 10('16) cm('3) to. N(,D) = 1.9 x 10('18) cm('3). The high purity Si data was essential for extracting the donor contribution to the dopedSi data. A value of 11.40 (+OR) 0.06 is obtained for the static dielectric constant (epsilon)(,h)(T (>) 0) of pure Si. The variation of (epsilon)(,h,zz) is linear with the applied stress (sigma)(,s) along the {110} axis up to. 610 Kg cm('2), with (1/(epsilon)(,h,zz))(DELTA)(epsilon)(,h,zz)/(DELTA)(sigma)(,s)(110) = (3.37 (+OR) 0.07) x 10('7) Kg('1) cm('2). For the temperature variation of (epsilon)(,h), a value of (1/(epsilon)(,h))d(epsilon)(,h)/dT = (1.12 (+OR) 0.05) x 10('4) K('1) is obtained at T = 4.2 K, which decreases as T (>) 0 K. A minimum in the stressdependent dielectric constant (epsilon)(N(,D),x(,100)) data (x is the reduced valley strain along either the {100} or the {110 } axis) was always observed for every sample stressed along a {100} axis. Except possibly at T = 4.2 K, a minimum in (epsilon)(N(,D),x(,100)) was not observed for the samples stressed along the axes. The values of the stressdependent donor polarizability (alpha)(,D)(x) were calculated from the (epsilon)(N(,D),x) data employing the. ClausiusMossotti relationship. The stressdependent behavior of (alpha)(,D)(x) and the corresponding (epsilon)(N(,D),x) are very similar. The magnitudes of the initial slopes (beta)(,100) and (beta)(,110) of (alpha)(,D) (x)/(alpha)(,D)(0) and the positions of the minimum x(,100)('min) are characteristic of the particular donor. For P donor, (beta)(,100) = 0.13 (+OR) 0.01, x(,100)('min) (DBLTURN) 0.6 (+OR) 0.1 and for the Sb, (beta)(,100) = 0.07 (+OR) 0.01 and x(,100)('min) =. 0.9 (+OR) 0.2 in the dilute N(,D) region. While (beta)(,100) and (beta)(,110) are insensitive to the variation of N(,D), x(,100)('min) seems to decrease slightly with increasing N(,D). In general, the effects due to the valley repopulation and the variation of the Bohr radius with stress are not adequate in explaining the stressdependent data quantitatively. The data, however, can be fit to the theory if the valleyorbit coupling parameter (DELTA)(,c) is written as a power series in x. A simple extrapolation procedure was employed to obtain the zerostress (alpha)(,D)(N(,D)) as T (>) 0 K. The values of (alpha)(,D)(N(,D),x = 0) obtained for the dilute limit are (1.2 (+OR) 0.2) x 10('5) (ANGSTROM)('3) for P and (1.9 (+OR) 0.6) x 10('5) (ANGSTROM)('3) for Sb. The (alpha)(,D)(N(,D),x = 0) data show an enhancement with increasing N(,D), but the enhancement is smaller than the value inferred from the data of other. workers. The Bohr radii inferred from the dilute limit (alpha)(,D)(N(,D),x = 0) and a theory of (alpha)(,D)(N(,D) = 0) are 14.8 (ANGSTROM) for P and 17 (ANGSTROM) for Sb. These lead to values for the Mott criterion of 0.23 (+OR) 0.01 and 0.25 (+OR) 0.01 for Si:P and Si:Sb respectively. The stressdependent AC conductivity data (sigma)(x) of samples with dilute N(,D) are consistent with the corresponding stressdependent (alpha)(,D)(x) data. A qualitative explanation is given for the (sigma)(x) behavior of the samples with large N(,D). The frequencydependent data at both small and large values of N(,D) are also briefly discussed.
 Publication:

Ph.D. Thesis
 Pub Date:
 1981
 Bibcode:
 1981PhDT........45T
 Keywords:

 Physics: Condensed Matter