Anatoly Grinberg

It is with great sadness that we announce the passing of our beloved friend and colleague Anatoly Grinberg. Anatoly passed away in Israel on 22 October 2021 at the age of 89. He was a theoretical physicist who made many great contributions to the physics of semiconductors and semiconductor devices. His scientific life spanned both Russia (A. F. Ioffe Institute in Saint Petersburg) and the US, where he had emigrated in the mid 1980s and joined Bell Laboratories in Murray Hill, New Jersey.

Perhaps Grinberg’s greatest contribution was his prediction and theory of the photon drag effect (PDE) in semiconductors. His 1970 theory of this effect is a classical work that has stimulated a number of experimental investigations. The PDE owes its existence to the momentum of light. The small photon momentum q transferred into a semiconductor electron system gives rise to a current made up of four large components, whose sum under “normal” conditions is proportional to q and is therefore small. For example, the current of excited particles with momentum k + q is balanced by that of “holes” left behind in the ground sub-band at momentum k. Nontrivial phenomena arise when the balance between these currents is destroyed, e.g., when the momentum relaxation times are different in the ground and the excited sub-band, so that the net current is dominated by one of the four components and is proportional to the typical electron momentum k rather than q. Grinberg predicted (1974) the resonant PDE in optical transitions between valence bands in germanium under conditions of resonance with optical phonons. The characteristic feature of the resonant PDE is the dependence of the current direction on the photon energy. These effects were subsequently observed by several groups.

Grinberg returned to the PDE in 1988 when he was already in the US. He published a comprehensive analysis of the PDE in light absorption between sub-bands of two-dimensional electron gas in quantum wells. The predicted effect was experimentally verified by a German group (Wieck et al., 1990), showing an exceptionally good agreement with Grinberg’s prediction—complete with the change in current direction with incident photon energy.

Another fundamental contribution by Grinberg is his series of theoretical studies (1976–78) of deep impurity centers (single- and multi-charge) in semiconductors. His picture of the effect of a short-range potential on the asymptotic behavior of the wave function permitted the description of both the photoionization of the deep centers and of their scattering of electrons. We can only mention such contributions by Grinberg as his prediction of the acoustomagnetic effect (1965) and the anomalous photoconductivity effect in magnetic fields (1960).

While at Bell Laboratories, Grinberg focused his interests on the physics of novel semiconductor devices. His contributions are very broad in their topics and fascinating in substance; we can only briefly go over the most important ones. Grinberg contributed a number of excellent papers devoted to various fundamental aspects of the physics of a 2D electron gas (2DEG). He presented a new variational theory for the 2DEG ground sub-band, which gives one of the best and simplest analytical expressions for the wave function, and calculated the image force exerted by a 2DEG on a test charge. He also formulated and explained a “Richardson constant paradox,” which appears in problems involving thermionic current between media of different effective electronic masses. Grinberg was the principal force behind collaborative papers on the theory of hot-electron injection in real-space-transfer devices, the theory of space- charge-limited current in unipolar semiconductor structures, and an analytical theory of the many-body effects on screening in 2DEG.

In 1990 Grinberg presented a definitive model of the mysterious fine-structure oscillations in current-voltage characteristics of heterojunction diodes, whose period corresponds to the optical phonon energy, as first observed by Hickmott et al. (1984) in an external magnetic field B, and then by Eaves et al. (1985) at B = 0. The effect had not been understood until Grinberg introduced his model, based on the assumption that the only tangible scattering mechanisms in the active region of these diodes are due to optical phonons and charged impurities. He showed that, under this restriction, a new conserved quantity arises: the reduced differential current.
This gives a constructive way of determining the carrier mobility that varies periodically with applied voltage and gives rise to the observed current oscillations. The calculated oscillations were in good quantitative agreement with experiments.

In 1992 Grinberg published a study of the diffusion transport of minority carriers in a short base of heterojunction bipolar transistors (HBT), based on an exact solution of the Boltzmann transport equation. His solution became the gold standard for validating subsequent approximate approaches modelling minority-carrier transport for important applications. Another important contribution to the HBT theory were his studies of thermionic injection of minority carriers followed by transport of their nonequilibrium ensembles across the base. He analyzed in detail the ballistic versus diffusive modes of minority-carrier transport that can take place depending on the injection energy, base width, and the intensity of scattering. These studies led to the invention (1993) of the so-called “coherent transistor,” which has gain peaks at frequencies well above the conventional cutoffs for power and current gains.

Everybody who had the privilege of interacting with Anatoly Grinberg was impressed by his profound insight and his ability to simplify complex problems by isolating their most essential aspects. Those of us who were fortunate to be his friends and collaborators will always remember this most charming, most unpretentious man with a great sense of humor.

Anatoly is survived by his daughters, Anna Kramer of New York and Vera Goncharova of Saint Petersburg.