Determination of germanium ionization coefficients from small-signal IMPATT diode characteristics

Small-signal measurements of germanium IMPATT diode admittance in the frequency range from 2 to 8 GHz were taken for various current densities. These measurements were compared with the small-signal admittances calculated using the model developed by Gummel, Scharfetter, and Blue [1], [2]. Values for the ionization coefficients and saturated velocities for electrons and holes used for the calculations have been chosen to secure reasonable agreement between theory and experiment for the diode avalanche voltage, the frequencies at which the small-signal susceptance and conductance cross zero, and the slope and general shape of the admittance versus frequency curves. The calculated small-signal admittance characteristics of the n
⁺
-p-p
⁺
mesa diode investigated are quite sensitive to the saturated hole velocity and the field dependence of the ionization rates. For the operating junction temperature, the velocity which gives the best fit is resolvable to about 5 percent. The best fit velocity is in agreement with published values. However, the ionization coefficients determined give a substantially smaller dependence of ionization rate on electric field than was obtained by Miller [3]. The coefficients obtained can be fitted by Baraff's theoretical model [4] using a low value for r, the normalized ionization cross section, in order to obtain the small dependence on field. The values of the ionization rates determined here,
\alpha_{p}=2.15 \times 10_{5} \exp
(
-7.10 \times 10_{5}
V.cm
^-1
/E) cm
^-1
\alpha_{n}=4.90 \times 10_{5} \exp
(
-7.90 \times 10_{5}
V.cm
^-1
/E) cm
^-1
are believed to be generally applicable to impact ionization effects in germanium semiconductor devices.