Emitter Effects in Shallow Bipolar Devices: Measurements and Consequences

Empirical determination of the energy band gap narrowing in highly doped n+ silicon

“…Alternatively, the p 0 n 0 product can be expressed by means of an apparent BGN DE app g in conjunction with Boltzmann statistics, 19 where DE app g is based on electronic measurements by several researchers. 4,[19][20][21][22][23] Fig . 3 shows the p 0 n 0 product as a function of the ionized dopant concentration in n-type silicon calculated with Eqs.…”

“…8 The continuous lines represent this work's Fermi-Dirac based empirical BGN expression (blue) and the Boltzmann-based apparent BGN empirical expression (red). Electronic measurements by del Alamo et al, 19 Mertens and Van, 20 Neugroschel, 21 Possin et al, 22 and Wieder 23 have been corrected with Klaassen's 37 mobility model and n i ¼ 9:65 Â 10 9 cm À3 . Photoluminescence measurements from Wagner and Alamo.…”

An improved formulation of the temperature dependence of the Gummel-Poon bipolar transistor model equations

“…The empirical formula, derived by Slotboom et al [7], is used in this paper since this formula was obtained by the characteristic of current-voltage from the electrical measurement. Also Wieder [25] found that it was satisfactory to use this formula to fit the experimental results with the exception of using a different value for constant No, because n-type material was used. After a more valid assumption, described by Fermi-Dirac statistics, was made for the density of the majority-carrier band in the high doping level, Mertens et al [26] indicated that the bandgap narrowing is not only a function of impurity concentration but also temperature dependent, and the temperaturedependence formula is added to the previous bandgap narrowing.…”

“…where No= 1 x 10 17 for p-type and No= 1.5 x 10 17 for n-type material semiconductors Figure 3 presents the discrepancies of the bandgap-narrowing data, which were obtained from electrical measurements of Slotboom et al [7], Wieder [25], Mertens et al [26], and Neugroschel et al [20], from the luminescence measurement of Dumke [28], and from the theory of Fossum et al [29] who implied that the bandgap narrowing occurred above dopant concentrations equal to 10 1 9 cm-3. In the next section, the effective mass for electrons and holes dependence of temperature will be discussed.…”

Effect of Bandgap Narrowing on Performance of Modern Power Devices

“…Different techniques have been adopted to measure the BGN Manuscript but they refer to specific materials (i.e., epitaxial layer [2]), specific device properties (e.g., β in a bipolar transistor [3]), or they employ approximations (e.g., low injection, uniform doping [4], [5]). The effect of BGN on the performance of the bipolar junction transistors is well known and has been intensively analyzed in the past [6], [7].…”