Hall scattering constant in n‐type silicon

Abstract

The factor relating the Hall cocfficient to carrier concentration has been determined in n-type silicon by combining optical measurements of the carrier concentration at infrared frequencies with conventional dc Hall effect measurements. Interpreting this factor in terms of electronic charge, mobility anisotropy and the usual scattering constant, the latter is found to reach values much greater than unity, especially a t 77 OK, when with a doping level of 2.6 x 1017 0111-3 a value of 7.3 is obtained. IntrodiictionThe purpose of this short papcr is to communicate new experimental values for the Hall scattering constant in n-type silicon. It is found to be particularly large a t 77 O K for specimens dopcd = 1018 ~m -~.A recent paper [l] by the authors showed how, in semiconductors, thc concentration and effective mass of conduction band electrons can be determined from measurements of the infrared free carrier Faraday effect and dispersion. I n fact, observation of these t w o phenomena yields values of m2 Nlm; and m Nlm,, respectively, where N is the carrier concentration, mF and mR arc relevant effective mass parameters, and m is the electron mass. For multivalley conduction band states, such as those pertaining to silicon, Here mL and mT are the longitudinal and transverse effective masses corresponding to the ellipsoidal energy surfaces. Values obtained for N and mT in this way are not sensitive to R since it is large. Actually K has been taken to bc 4.3, the room-temperature value deduced from experimental observations of the stress dependence of Faraday rotation [2]. This is close to that found from low-temperature cyclotron resonance experiments [3].It is prudent to observe both the Paraday effect and dispersion to find N a t room temperature because the effective mass has not been measured by an independent experiment a t such a high temperature. At low temperatures (c.g., 77 OK), however, it is only necessary to observe the Faraday rotation since m, can be calculated from the accurate cyclotron resonance data available.11 pliysica (b) 4R/l

On the calculation of Hall factors for the characterization of electronic devices

“…With a further increase of doping concentration, the Hall factor decreases and, for doping concentrations exceeding 10 20 cm -3 , the Hall factor approaches the theoretical value of r H = 0.87 [11]. This value of r H results from r H0 = 1 in (12) with the anisotropy of the electron mass in silicon taken into consideration. It is important here to point out that a value of r H0 = 1 indicates that the semiconductor has already become degenerate.…”

“…The results of this calculation are shown in Fig. 3 in comparison with the measurements reported in the literature for Si [9][10][11][12][13].…”

“…Keeping in mind that the Hall factor is r H0 = 1.18 for the limiting case of exclusive acoustic phonon scattering and r H0 = 1.93 for the exclusive case of ionized impurity scattering, one expects also an increase of the Hall factor with doping concentration. On the other hand, several groups found experimentally that the Hall factor in n-type silicon increases with donor concentrations but only until a doping level of about 3×10 18 cm -3 [9][10][11][12][13]. With a further increase of doping concentration, the Hall factor decreases and, for doping concentrations exceeding 10 20 cm -3 , the Hall factor approaches the theoretical value of r H = 0.87 [11].…”

“…For Si, SiC and Ge, the Hall mass factor a 0 takes values of 0.87, 0.98 and 0.785, respectively. Using ( 6) - (11), and assuming the concurrent action of different scattering mechanisms, the Hall factor can be easily determined and corrected with the anisotropy model given in (12).…”

Plasma edge reflection study of the conduction band effective mass in n‐type silicon

“…The corresponding value of the scattering constant r has been taken to be 1 . 7 (10). The results a r e shown in Table 1.…”