Comment on the measurement of bandgap narrowing from the minority-carrier current in heavily doped emitters

A New Solution for Minority-Carrier Injection into the Heavily Doped Emitter of Silicon Devices

“…We first construct an approximated analytical solution for u r y [or J S y, based on the assumption that the function CyY N s , given in (9) or in (10), is replaced by CN s . CN s is assumed to be y-independent, but it is a function of the surface impurity density N s , now defined by…”

“…In addition, this constant C S is an empirical parameter, determined by a particular functional dependence of the minority-carrier lifetime tN. This approach [4] or the similar one [7,10,12] may be questionable because CN is a function of y and N s .…”

Apparent Band-Gap Narrowing and Its Data Derived from the Measurements of Minority-Carrier Current Density in Heavily Doped Emitters of Silicon Devices

“…Note in (1) that, if using the definition coth P = (ep + e-')/(ePe-'), the Gummel integral P ( N s ) can be shown to be a function of X , [5], Further, under the transparent emitter condition: P(N,) < 1 or W < L&), needed for an interpretation of measured values of &O,h(e) [2 to 41, (1) can be approximated by In addition, as developed in I, the above expressions (1) and (3) have been obtained, based on the two following assumptions:…”