Effective Mass from Seebeck Coefficient. (9th February 2022) - Snyder, Gerald Jeffrey
Abstract: Engineering semiconductor devices requires an understanding of the effective mass of electrons and holes. Effective masses have historically been determined in metals at cryogenic temperatures estimated using measurements of the electronic specific heat. Instead, by combining measurements of the Seebeck and Hall effects, a density of states effective mass can be determined in doped semiconductors at room temperature and above. Here, a simple method to calculate the electron effective mass using the Seebeck coefficient and an estimate of the free electron or hole concentration, such as that determined from the Hall effect, is introduced m S ∗ m e = 0.924 ( 300 K T ) ( n H 10 20 cm − 3 ) 2 / 3 [ 3 ( exp [ | S | k B / e − 2 ] − 0.17 ) 2 / 3 1 + exp [ − 5 ( | S | k B / e − k B / e | S | ) ] + | S | k B / e 1 + exp [ 5 ( | S | k B / e − k B / e | S | ) ] ] here m S ∗ is the Seebeck effective mass, n H is the charge carrier concentration measured by the Hall effect ( n H = 1/ eR H, R H is Hall resistance) in 10 20 cm −3, T is the absolute temperature in K, S is the Seebeck coefficient, and k B / e = 86.3 μV K −1 . This estimate of the effective mass can aid the understanding and engineering of the electronic structure as it is largely independent of scattering and the effects of microstructure (grain boundary resistance). It is particularly helpful in characterizing thermoelectric materials. Abstract : The effective mass is a fundamental property of electronic structure and transport but has been difficult to measure experimentally. An experimental effective mass parameter, termed the Seebeck effective mass, is derived here from measurements of the Seebeck coefficient and charge carrier concentration. Analysis of the Seebeck effective mass is used to identify changes in electronic bandstructure directly from transport measurements.