Gummel number

The Gummel number ( English gummel number ) is in the semiconductor integrated circuit technique is a measure of the emitter efficiency . It provides information about the current gain in bipolar transistors . This quantity was named after Hermann Gummel , who also indicated a possibility of its experimental determination with the Gummel plot , which was also named after him . ${\displaystyle G_{\mathrm {B} }}$

Definition and application

The Gummel number is defined as the integral over the dopant concentration in the base of a transistor .

${\displaystyle G_{\mathrm {B} }=\int _{0}^{W}N_{\mathrm {B} }(x)\mathrm {d} x}$

Here, the width of the quasi-neutral base region and the i. a. inhomogeneous basic doping. ${\displaystyle W}$ ${\displaystyle N_{\mathrm {B} }(x)}$

The Gummel number is required to calculate the collector current of bipolar transistors ( Gummel-Poon model ), in which, due to an inhomogeneous basic doping, not only diffusion but also the drift in the electric field caused by the dopant gradient contribute to the current transport. Typical values ​​are around 10 ¹² dopant atoms per square centimeter.

literature

• Kurt Hoffmann: System integration: from transistor to large-scale integrated circuit . Oldenbourg Wissenschaftsverlag, 2006, ISBN 3-486-57894-4 , p. 95 f .

Individual evidence

1. ↑ László Palotas: electronics engineers . Vieweg + Teubner Verlag, 2003, ISBN 3-528-03915-9 , pp. 24 ( limited preview in Google Book search).
2. ↑ Kurt Hoffmann: System integration: From the transistor to the large-scale integrated circuit . Oldenbourg Wissenschaftsverlag, 2006, ISBN 3-486-57894-4 , p. 95 f .