STRAINED n-SI CRYSTAL LATTICE IN THE PRESENCE OF PHOSPHORUS IMPURITY

Abstract

The successful application of heterojunctions in various devices is due to the ability of epitaxy technology to grow semiconductor materials with a well-matched lattice structure on top of each other practically without traps at the interface. Therefore, it is relevant to study (investigate) the characteristics (parameters, behavior) of semiconductor materials caused by deformations of the crystal lattice and deformation changes in their properties in the presence of impurities. This can provide important information in modeling heterostructures and successful application of heterojunctions (strained heteroepitaxy) in creating various devices with predicted properties. In the development of electronic devices, the main attention is paid to the three most-important semiconductors: silicon (Si), germanium (Ge) and gallium arsenide (GaAs). Silicon has been studied extensively and widely used in commercial electronics products. The paper presents the results of research for undeformed and uniaxially deformed (Х ≤ 1.2 GPa) along [100] Si n-type crystals with a concentration of NP donor phosphorus (Р) impurity of 2.4 · 1013 cm-3 and 2.3 · 1015 cm-3. We studied the longitudinal (Х || j [100]) and transverse (Х ⊥ j [100]) piezoresistance in the temperature range 78 ÷ 300 K.
When the crystal lattice of n-Ge and n-Si crystals is deformed, the mobility anisotropy parameter K is an important characteristic. For sufficiently pure n-Ge crystals, the set of curves ρX/ρ0 = f(Х) for different temperatures in the case of Х || j || [111] is characterized in the temperature range T > 120 K by essentially a single plateau ρ∞/ρ0 value, which determines the value of the mobility anisotropy parameter. For the correct determination of the parameter K in n-Si in such cases, the experimental data on the longitudinal piezoresistance must be supplemented with the results of measurements of the transverse piezoresistance. The work aims to comprehensively investigate the features of changes in electrophysical parameters during crystal lattice deformation, which distinguish germanium and n-type silicon, associated with the inadequacy of scattering mechanisms in these crystals for strained heteroepitaxy.
The values of K determined by different methods for a crystal with a donor impurity concentration of 2.3 · 1015 cm-3 differ significantly. This is due to the fact that at a donor impurity concentration NP > 1015 cm-3 in silicon crystals, due to the expansion of the spectrum of impurity states, the phosphorus impurity is not completely ionized at T = 78 K. In the case of undeformed n-Si crystals with NP = 2.4 · 1013 cm-3 up to 100 K ρ ~ T1.66. With increasing temperature due to the appearance of intervalley scattering ρ ~ T2.3. In the case of deformed crystals with complete exclusion of f-transitions (Х = 1.2 GPa) no breaks are observed on the ()Tρρ=∞|| and ()Tρρ=⊥∞ curves and at the same time ρ ~ T1.66. Based on the ||∞ρ and ⊥∞ρ values, we obtained the value of the carrier mobility anisotropy parameter K = 5.1 ± 0.1. In the case of undeformed n-Si crystals with an impurity concentration NP = 2.3 · 1015 cm-3, the temperature dependence of ρ has a complex character. At low temperatures (T > 78 K), its form is determined not only by intervalley scattering of electrons on acoustic lattice vibrations, but also by their scattering on ionized impurities with an increase in the concentration of charge carriers n in the conduction band due to thermal ionization of impurity states (which manifest themselves in n-Si at NP > 1015 cm-3). Only in the high temperature region (T > 230 K) does the slope of the ρ(T) dependence approach 2.3. In the case of deformed crystals with NP = 2.3 · 1015 cm-3 at X = 1.2 GPa, the last factor affecting the value of ρ disappears due to the deformation reduction of the ionization energy of the impurity when the deformation axis is oriented along the [100] direction (n = const) in the temperature range 78 ÷ 300 K. Based on the ||∞ρ and ⊥∞ρ values, it is possible to reliably determine the parameter K, and accordingly, Kτ at any temperature. In the case of NP = 2.3 · 1015 cm-3 at 78 K, Kτ = 1.2 ± 0.1. From a comparison of the scattering anisotropy parameters for n-Si crystals with impurity concentrations of 2.4 · 1013 cm-3 and 2.3 · 1015 cm-3, it is seen that when scattering on impurity ions, the parameter Kτ is significantly larger than in intervalley acoustic scattering. Analysis of the Kτ = Kτ(Т) dependence indicates a decrease in the contribution to the anisotropy of impurity scattering and an increase in the relative contribution of scattering on acoustic lattice vibrations with increasing temperature.
It was found that in n-Si crystals at 78 K, the values of the parameters of the anisotropy of electron mobility and scattering at low concentrations of the donor impurity (2.4 · 1013 cm-3), i.e. under conditions of dominance of scattering on acoustic phonons, as in n-Ge, can be reliably determined from the data of the longitudinal piezoresistance only. At concentrations of the doping impurity that provide mixed scattering (2.3 · 1015 cm-3), as well as with increasing temperature, for the correct determination of the parameter K in n-Si, measurements of both the longitudinal and transverse piezoresistance in the saturation region of the ρ = ρ(X) curves are necessary.