Years ago, I found myself on the campus of the state university in Minneapolis, and at the wrong time of year to be there – in January. The occasion was a meeting with Aldert (not Albert) van der Ziel, by then a very retired E.E. professor who was a leading expert on electrical noise. Aldert showed up wearing the appropriate attire for the cold winter in Minnesota and we trudged slowly up the stairwell of the building in which he retained a presence, past what looked like a high-voltage laboratory and into a spacious office – or was it another laboratory? – with a large Faraday cage and long wooden tables with many books, journals, and papers. Aldert proceeded to dig into his “piling system” for a reference to whatever we were discussing; it wasn’t noise.
Well into his seventies, Aldert moved and talked slowly but his countenance reflected a youthful mind. I knew of him in another connection than his pioneering work on noise. He had published a landmark paper in the IEEE Proceedings (Vol. 54, pp. 411 – 412, MAR66) with D. Agourdis on “The Cutoff Frequency Falloff in UHF Transistors at High Currents”. This effect appears in the EM3 model of the BJT and can be seen on the plot of fT (IC ) in BJT specifications. Transistor speed increases with current because (in the hybrid-π BJT model) fT = β x fβ and fβ = 1/2 x π x rπ x C π , where
Incremental emitter resistance, re and hence rz decrease linearly with current while the emitter-junction diffusion charge, and hence C π , most often increase at a lower rate with current. fT increases until the current is so high that the BJT enters the high-level injection region of operation, where the minority carrier concentration is comparable to the majority carriers. In other words, in a collector made of p material, the injected n carriers (electrons) from the base concentrate at the edge of the junction and diffuse into the p material with a concentration that is comparable to the hole concentration in the p material from doping. Under high-level injection, the exponent in the junction v-i equation changes from the medium-level value of VBE /VT to VBE /2 x VBE and instead of having a junction-voltage change of about 60 mV/decade of current, it becomes 120 mV/dec.
As BJT modeler Ian Getreu has catalogued in his classic compendium on BJT models, Modeling the Bipolar Transistor , (at lulu.com) there are two base-widening effects. One is 1D (the Kirk effect) and the other is 2D, as described by van der Ziel and Agourdis. It is a fine point as to which effect dominates. The Kirk effect is accompanied by space-charge-limited current flow and effective base widening, as the effective edge of the collector junction retreats because of carrier polarity reversal. As the base effectively widens, carrier transit time across it increases and fT decreases. Neither the 1D or 2D models explain the total observed BJT behavior. No wonder this effect is in the most refined level of BJT modeling, the Ebers-Moll 3 model. (The Gummel-Poon model also includes it.)
Van der Ziel is better known for such works as his 1970 Prentice-Hall book, Noise: Sources, Characterization, Measurement . Yet my visit to van der Ziel was not primarily to discuss base widening effects or the physical sources of noise. I came to know of van der Ziel, not from his involvement in electrical engineering but from our mutual participation in an organization (The American Scientific Affiliation) that is largely a forum for discussing science and technology from a larger viewpoint – indeed, from the largest viewpoint of our shared worldview.
What was on my mind in particular to discuss with van der Ziel was an issue that was a tumultuous 20th-century conflict, the creation-evolution controversy. Van der Ziel became involved with this issue by looking at it from his background in electrical noise theory which involves statistical randomness that can be characterized in various ways. Accidental in discussion of wider issues is not the same in meaning as random in stochastic process theory. Accidental is the opposite of purposive while random , in the sciences, has a more limited meaning: an absence of knowledge of causes. Because we do not know the detailed micro-level activity it can only be characterized in its broader features through the statistics of probability theory. Random in probability theory means not having prior (a priori ) knowledge of the outcomes of events. At an atomic level, there are a multitude of events, and statistical characterization can be successfully applied. In the argument over biological origins, one of the main features of the dispute is whether the mechanisms of macro-evolution (not the ordinary micro-kind that can be observed to happen to bacteria, for instance) are capable of being characterized in the same way that noise can be characterized as a random process.
Biologists talk about this aspect of evolution using words like chance which is also a word from probability theory and is thus limited in its meaning to that which is within the scope of scientific scrutiny. Some antievolutionists cite this reliance by biologists upon chance as evidence that Neo-Darwinian theory lacks adequate causal mechanisms for its support as a scientific explanation. While the theory is not claimed to be complete – biologists are only now beginning to seriously understand life scientifically – if the number of mutational or environmentally selective events is large enough over the eons to be statistically significant, it seems that recourse to the kind of process characterization that is applied to electrical noise might also be applied to it, though the events are historical and not subject to repeated experiment in the laboratory. Perhaps it might be better to categorize evolutionary theory as a theory of natural history, like paleontology, archaeology, or much of geology, which themselves evolved from the experimental sciences. Nobody seems to deny that historic evidence in geological columns is scientifically admissible. In an extreme sense, all data, once recorded, is history, and thus the evidence of experimental science is all historical.
It is well-known that the creation-evolution controversy has been driven by certain theological theories that clash with biological ones. How this becomes sorted out is best left to groups like the ASA of which van der Ziel and myself were members. With an obviously Dutch name like van der Ziel, one might expect that Aldert was from a Dutch Reformed background, writing books with titles like The Natural Sciences and the Christian Message , but he was Lutheran instead. Although I could not tell how this influenced his view of the creation-evolution debate, I could see that his understanding of natural stochastic processes impelled him to address the aspect of randomness in Neo-Darwinian theory as an expanded application of a concept he understood from electronics. In the usual working environment, engineers tend to focus on engineering, yet all have some larger view of reality and to many it is important.
Did van der Ziel settle this never-ending controversy? Of course not; yet his mental involvement with stochastic processes was sufficiently intensive to spill over into other aspects of his wider thinking.