Mott, Nevill Francis
MOTT, NEVILL FRANCIS
(b. Leeds, United Kingdom, 30 September 1905; d. Cambridge, United Kingdom, 8 August 1996)
condensed-matter physics, metals, amorphous semiconductors, glasses.
For the whole of a working life of over sixty years, Mott was the unquestioned leader of English condensed-matter physicists. At the universities of Bristol and Cambridge in England his intuitive appreciation of promising research fields attracted a circle of students and colleagues. His prolonged and searching analysis of electrical conduction in disordered systems earned him a Nobel Prize in Physics in 1977 that he shared with John H. Van Vleck and Philip W. Anderson. He was knighted in 1962 and made a Companion of Honour in 1995.
Early Years at Cambridge Mott’s parents, Charles Francis Mott and Lilian Mary Reynolds, had both worked as research students of J. J. Thomson, Cavendish Professor of Physics at Cambridge University, and he grew up expecting a life in physics, with Cambridge as the center of choice. He studied mathematics at St. John’s College, Cambridge, graduating in 1927, at the very time that Werner Heisenberg, Erwin Schrödinger, and others in continental Europe were revolutionizing physics with the development of quantum mechanics. With no local experts at hand, except the reclusive Paul Dirac, he taught himself German so as to read about the new techniques from the original papers. A half year with Niels Bohr in Copenhagen was immensely valuable, and he returned having solved several problems in atomic physics and satisfied himself that a career in theoretical physics was feasible. He predicted that when alpha particles were scattered by helium nuclei, the identity of the two particles, together with the fact that they obeyed Bose statistics, would cause twice as many to be observed at a deflection of forty-five degrees than would be expected from Ernest Rutherford’s classical theory. Verification of the prediction elicited Rutherford’s praise and confirmed his career decision. A paper reconciling the wave picture of α-particle emission with the sharply localized tracks observed in cloud-chamber photographs is still cited as a valuable contribution to the interpretation of quantum mechanics.
In 1930, after returning to Cambridge from a one-year lectureship at Manchester, England, Mott married Ruth Eleanor Horder. They had two daughters, Elizabeth and Alice. His wife, Ruth, a classical scholar and harpsichordist,
complemented Mott’s enduring friendship for all his colleagues and students by the welcome she gave to their wives and families. Their contented life together ended only with his death.
The Move to Bristol Mott’s commitment to nuclear physics ended in 1933 when he accepted, still only twenty-eight years old, the offer of a professorship in theoretical physics at Bristol University. A fine new laboratory had just been built and Arthur M. Tyndall, the talented head of the department, had begun to gather a research team. On arrival, Mott found staff members already engaged in problems concerning metals: Herbert Skinner was measuring with precision the spectra of x-rays from light elements, while Clarence Zener and Harry Jones had begun theoretical studies of metallic conduction. Mott’s enthusiastic leadership welded these and others into a group that later could be recognized as one of the earliest pioneering groups of solid-state physics. Until the outbreak of World War II, its members were largely involved with electrons in metals, though after Ronald Gurney’s arrival in 1936 their interests expanded to include electrical conduction and other properties involving defects and impurities in otherwise nonconducting crystals and in semiconductors.
Such problems, though they were being studied experimentally by Robert W. Pohl and his students in Göttingen, were not to the taste of many leading continental theorists—Wolfgang Pauli dismissed them as “dirty physics.” Nevertheless the foundations had been laid, in more ideal form, by Arnold Sommerfeld and his younger followers, especially Hans Bethe, Felix Bloch, and Rudolf Peierls; following Schrödinger’s formulation of quantum mechanics, they had shown how electrons could move as freely through a crystal lattice as light waves through glass, though their behavior is modified by the atomic structure. The electron wavelength is comparable to the spacing of atoms so that something akin to Bragg reflection of x-rays affects the dynamics strongly, and in each direction of motion there are forbidden, as well as allowed, bands of energy. Since, according to the Pauli exclusion principle, each permitted state may be occupied by only one electron, there may be solids in which the electrons are sufficient to fill a particular allowed band, with none left over. As a small electric field cannot change the state of electrons in filled bands, such solids are insulators. In other solids, the metals, there are partially filled bands and a current is produced easily. In the lowest state of the metal, at absolute zero, all states up to a certain maximum energy, the Fermi level, are filled; this energy is large enough that at ordinary temperatures, few electrons are thermally affected and the sharp distinction between filled and empty states is only slightly blurred. Between insulators and metals there are the semiconductors, where the forbidden range of energy above the top filled band is sufficiently small that some electrons may be thermally excited into the next empty (conduction) band to produce an electrical conductivity that gets better as the temperature is raised.
Bloch’s original exposition of this viewpoint assumed, against all probability, that the strong Coulomb interactions between electrons were not significant; it might be expected that they would collide and exchange energy so frequently as to vitiate, through the action of the Heisenberg uncertainty principle, the idea of a well-defined Fermi level. This is a question that Skinner attacked experimentally with his delicate studies of x-ray spectra; the sharp boundary to the spectrum at the high-energy end indicated an equally sharp cutoff to the energy spectrum of the electrons in the light metals he used. In consultation with Mott and Jones, he concluded that an excited electron just above the Fermi level could not readily be scattered by the other electrons; each could only do so if it found a vacant state into which to move—another consequence of the exclusion principle—and the shortage of available states would make the scatterings very improbable. The assumption of independent particles is therefore a good starting point.
The first of Mott’s major books from Bristol, The Theory of the Properties of Metals and Alloys (1936), for which Jones was coauthor, starts from here and attempts bravely to explain how different crystal structures and electron concentrations give each metal its peculiar character. Not everything has stood up to subsequent experiment and analysis, but it was the first book in English to apply quantum mechanics to metals and was very influential in introducing this branch of physics to the next generation of researchers. It also illustrates a characteristic of the new Bristol school, the fusing of experiment with theory, each team member keeping steadily in mind the general physical picture and, wherever possible, subordinating minor details to the overall grasp of processes. This attitude can be recognized in all Mott’s work from then on. He may indeed, as he said, have regretted not having studied mathematics more deeply as a student, but his colleagues, especially the experimenters, did not count this a fault.
Insulators and Semiconductors The Coulomb interaction between electrons, which apparently plays a minor role in metals, becomes a major issue in the imperfect insulating crystals that interested Mott and Gurney and were the subject of the next important book from the Bristol school, Electronic Processes in Ionic Crystals (1940). To a great extent they had to rely on experimental results from elsewhere, especially from Pohl’s group, whose investigations of color centers in the alkali halides supplied their first topic. A vacant halide site in the crystal behaves as a positive charge, attracting an electron into a hydrogen-like orbit. Because of the relative permittivity of the crystal, and the lattice field that lowers the electron’s effective mass, it is only loosely bound and is a strong absorber of visible light; this gives the crystal its characteristic deep color.
Mott and Gurney then turned to matters of technical importance, the photographic process and semiconducting rectifiers, to the understanding of which they made significant innovations. They paid particular attention, in their discussion of the action of light on silver bromide, to the effects of gross overexposure. A small crystal of silver bromide eventually becomes totally opaque, seemingly being converted into a grain of metallic silver. Unlike the alkali halides, silver bromide is an ionic conductor—an interstitial silver ion may wander, albeit slowly, through the lattice. When an incident photon dislodges an electron from a silver atom, both electron and ion begin to migrate. The faster-moving electron attaches itself to any speck of silver it finds, and the charged speck attracts the interstitial silver ion so that in due course the speck is larger by one atom. Mott and Gurney pointed out that there is no space for growth of the speck within a perfect lattice, but the surface of the bromide crystal or micro-cracks are suitable sites. When, later, the prevalence of dislocations was appreciated, they were seen also to play an important part in the process. All this, however, involves far more photons than are needed when the photographic plate is to be developed. They comment at some length on what development involves, but at the time of writing there were many outstanding mysteries. The value of their contribution is not that it completed, but that it initiated, a sound understanding of a difficult subject.
The treatment by Mott and Gurney of semiconducting rectifiers must be seen in the light of what was then known. Only later, through the work of Karl Lark-Horovitz and his colleagues working at Purdue University in Indiana during the war, were germanium and silicon purified to such a degree that there was no doubt they were semiconductors. Until then the only semiconductor rectifiers in use were the cat’s whisker rectifiers of early radio sets (already superseded by thermionic diodes) and the power-handling rectifiers made by oxidizing the surface of a copper sheet and pressing metallic contacts against the outer oxide surface layer. It was copper oxide, along with other compounds, that Alan Wilson had in mind when he explained semiconductors as insulators with only a very small energy gap, so that thermal excitation sufficed to produce conduction electrons and leave conducting holes in the otherwise filled valence band. In addition, impurities may behave as excess positive charges (donors) with a weakly bound electron that can readily be excited into the conduction band, or as negative charges (acceptors) with a weakly bound hole—that is to say, an electron can readily be attracted from the valence band.
Mott’s theory of the copper oxide rectifier, formulated independently by Walter Schottky, relies on the impurity sites associated with an excess of oxygen in the oxide layer to equalize the Fermi energy in the copper and its oxide. When, however, two metals are joined, equalization is achieved by a double layer of charge at the junction, and electrons are copiously available to provide charges. In copper oxide, on the other hand, only the sparse defects can serve, and when they give up their weakly bound charges to leave an insulating layer, it is too thick to allow passage of a current. In this layer there is a potential gradient that only thermally excited electrons can surmount. A potential difference applied from outside can either increase the gradient and inhibit electrical conduction, or, in the reverse sense, lower it and enhance the conductivity. This explanation of the rectifying process accords well with experiment and can be taken over with minor adjustment to describe the modern semiconducting p-n junction.
Postwar Bristol and Cambridge Like its predecessor, Mott and Gurney’s book broke new ground and would have had as great an immediate impact but for the outbreak of war and cessation of academic research. In 1945 Mott returned to Bristol, assured of soon succeeding Arthur M. Tyndall as head of the department. The prewar team had largely disbanded, but new staff soon renewed the old harmony of theory and experiment, albeit with a shift of emphasis to dislocations and their role in metallic deformation, work-hardening, and fatigue. Mott was in charge—along with Frank Nabarro, Charles Frank, and others, including Jacques Friedel, Mott’s future brother-in-law—of a formidable team whose achievements somewhat overshadowed his own, occupied as he was with heavier departmental duties. Among the group’s many outputs, Frank’s theory of the leading part played by dislocations in crystal growth is outstanding for originality and elegance. Mott’s twenty years at Bristol were for him the happiest of a long and happy life. When, in 1954, he was invited to succeed Sir Lawrence Bragg as Cavendish Professor in Cambridge, it was only reluctance to disappoint his still-living parents that persuaded him to accept.
The strength of metals was still very much in Mott’s mind in 1954 when he moved to the Cavendish chair of physics at Cambridge and found an active group similarly engaged. Peter Hirsch’s direct observation, in an electron microscope, of moving dislocations pleased him, but his concern to make changes in the department, along with his involvement with the Pugwash Conferences on Science and World Affairs and with other public issues, reduced his personal research for some years. During his time at Cambridge, Bragg had given enthusiastic support to Max Perutz and John Kendrew in their heroic determination of protein structure, and more guarded support to Francis Crick and James Watson’s elucidation of the double helix of DNA. These researches had established the Cavendish (as the department of physics is generally known) at the center of the new science of molecular biology; Mott, though persuaded of the importance of this subject, quickly saw that the laboratory did not have space for both its group and the solid-state theoreticians he was determined to assemble. In the event, having been rehoused (with his help) in a new laboratory of its own, the molecular biology group grew enormously beyond anything the Cavendish could have coped with.
Outside physics, Mott saw a real need to make substantial changes in the university, especially in the organization of science courses for students, which ranged from mathematics to medicine; aided by other science professors, he made great progress. In the belief that it would give him a foothold beyond the Cavendish, he accepted the mastership of Gonville and Caius College (1959–1966) but eventually became impatient with the internal maneuverings of the fellows and resigned. By that time, however, he had attained an authority among the university’s scientists that led to his chairing a committee on the development of high-level industrial research in the city of Cambridge. The committee’s recommendations, and the seed corn supplied by the richest college, Trinity, overcame the city’s reluctance and resulted in the creation of Cambridge Science Park, which has since served as a model for many similar ventures in the United Kingdom.
The Mott Transition During this period Mott continued thinking about electrons in solids. He had never forgotten how J. H. de Boer and E. J. W. Verwey, at a Bristol meeting in 1937, pointed out that the electrons in nickel oxide, NiO, were too few to completely fill the energy bands as described by the independent-electron theory; yet NiO was an insulator. Peierls had immediately pointed to the Coulomb interaction as the reason, and it was already appreciated that this interaction depended strongly on electron density. Rather paradoxically, it is in dilute electron gases that the effect is most pronounced; thus, electrons can move freely enough, and almost independently, to conduct electricity in a solid or liquid metal, but in the vapor of the same material, mercury, for example, they are strictly confined to their atoms. Returning to this problem in Cambridge, Mott realized that dilute impurities in semiconductors provided an almost ideal model. Hellmut Fritzsche and coworkers in Chicago had produced, by slow neutron bombardment, carefully controlled mixtures of donor and acceptor centers in otherwise highly purified crystals of germanium; transmutation of germanium to arsenic creates a donor, and of germanium to gallium an acceptor. These two are in a fixed proportion determined by the cross section of germanium for the two transmutations, but the total number is controllable by the neutron dosage.
It is convenient at this point to pretend that the donors outnumber the acceptors, so that the account may proceed more easily, without significant change, in terms of electrons rather than holes. At zero temperature all the acceptor levels are filled and a fraction of the donors are deprived of electrons. Electrical conduction in such a system can take place only by quantum mechanical tunneling of an electron from an occupied to an unoccupied site. In a real material the inevitable tiny variations of environment make for variations of energy level on otherwise identical sites. As a result the temperature must be raised to permit thermally assisted transfer between sites. This mechanism, hopping conduction, involves transitions between neighbors or, at lower temperatures, more distant sites. For the latter process Mott used rather simple arguments (later verified more rigorously by others) to show that the conductivity should vary as exp(–C/T¼); this prediction was borne out by experiment and later shown to be relevant to conduction in amorphous films of germanium and silicon.
As the density of centers increases, for example by heavier neutron dosage, it must be expected that hopping conduction will be replaced by metallic conduction as the electron states become delocalized in a narrow donor impurity band, but the physics involved has proved highly controversial. In Mott’s view, at a certain critical concentration there would be an abrupt transition, like a phase change. A low concentration of free electrons would form a weak screen around positive charges, reducing the Coulomb attraction of a bound electron and facilitating the hopping, so that more free electrons would be available. At some concentration the process would become inherently unstable; all electrons on donor sites would become free, forming a half-filled band with weak metallic properties. Mott did not present his reasoning with mathematical rigor but, typically for his innovative ideas, with a certain reliance on intuition. His estimated critical concentration, however, was in excellent agreement with experiment, and what was soon known and widely discussed as the Mott transition became, if not an article of faith, at any rate an attractive hypothesis.
At about the same time as the birth of the Mott transition, Philip W. Anderson, working at Bell Telephone Laboratories in New Jersey, was conceiving an alternative point of view and, following a different tradition, presenting it in such a difficult and detailed mathematical form as to delay its immediate discussion, let alone enthusiastic acceptance. He showed that randomly distributed scattering centers, which at low concentrations limit the free path of electrons in metals without preventing their motion, at higher concentrations may confine them to localized states and prevent conduction at zero temperature without invoking Coulomb interactions between electrons. For intermediate degrees of disorder the localized states lie near the extremities of electron bands; if the Fermi level shifts from extended to localized states, the material changes from a conductor to an insulator. Mott early appreciated the importance of the Anderson transition and the consequent development of the concept of mobility edges in amorphous semiconductors. The new ideas from Mott and Anderson led to an outpouring of learned papers from solid-state theorists.
From about 1966, Mott found himself in a position to leave departmental and outside problems in other willing hands and devote himself to attempts to resolve the controversies he, along with Anderson and others, had started. He retired as department head in 1971 but remained in the department for another twenty-five years until two days before his death, never losing his enthusiasm for physics. He was awarded the Nobel Prize in Physics in 1977, along with Anderson and Van Vleck, for fundamental theoretical studies of magnetic and disordered systems. In his Nobel Prize address he paid tribute to Anderson’s contributions—a typically generous acknowledgment of a development that considerably influenced his views on disordered systems. Unlike many late Nobel laureates he continued to publish until the end; more than 100 of his papers, of at least 320 in total, appeared after 1977. They covered a range of related problems in disordered systems—liquid metals, solutions of alkali metals in liquid ammonia, and especially amorphous semiconductors and glasses. With Mott at the center of a large and fluctuating group that included Edward A. (Ted) Davis and Michael Pepper, and with many other laboratories joining in the elucidation of these difficult problems, a vast literature developed and was reduced to order in the last of his collaborative books, Mott and Davis’s Electronic Processes in Non-crystalline Materials (1971, 1979), the two editions of which had wide circulation in several languages.
The Last Years The discovery in 1986, by J. Georg Bednorz and K. Alexander Müller, of high-temperature superconductivity initiated an explosion of research into which Mott was willingly drawn. With A. S. Alexandrov he developed, and championed in the face of many mutually incompatible alternative theories, an explanation in terms of spin-polaron pairs. None of the then-contending theories had, at Mott’s death in 1996, found general support; nor had they ten years later, at the time of this writing. Whatever the permanent value of Mott’s proposals, it was heartening to all who knew him to see the survival at so late a date of the intellectual excitement that had driven him from his earliest days.
In 1998 Davis edited Nevill Mott: Reminiscences and Appreciations, a collection of ninety essays by Mott’s friends and colleagues that gives an overview of his wide-ranging interests and powers of invention but, above all, shows the devotion he inspired in all who could penetrate the apparently austere shell that quite thinly enclosed a warm, amusing, and generous man.
Unpublished letters and manuscripts are in the archives of the University of Cambridge. A microfiche listing published papers is to be found in Biographical Memoirs of Fellows of the Royal Society, London 44 (1998).
WORKS BY MOTT
“The Wave Mechanics of a-Ray Tracks.” Proceedings of the Royal
Society of London, series A, 126 (1929): 79–84.
With H. S. W. Massey. The Theory of Atomic Collisions. Oxford: Clarendon Press, 1933.
With H. Jones. The Theory of the Properties of Metals and Alloys. Oxford: Clarendon Press, 1936. With R. W. Gurney. “The Theory of the Photolysis of Silver Bromide and the Photographic Latent Image.” Proceedings of the Royal Society of London, series A, 164 (1938): 151–167.
“The Theory of Crystal Rectifiers.” Proceedings of the Royal Society of London, series A, 171 (1939): 27–39.
With R. W. Gurney. Electronic Procesess in Ionic Crystals. Oxford: Clarendon Press, 1940.
With W. D. Twose. “The Theory of Impurity Conduction.” Advances in Physics 10 (1961): 107–163.
“Conduction in Non-Crystalline Materials III: Localized States in a Pseudogap and Near Extremities of Conduction and Valence Bands.” Philosophical Magazine 19 (1969): 835–852.
With E. A. Davis. Electronic Processes in Non-crystalline Materials. and ed. Oxford: Clarendon Press, 1979.
Editor. “The Beginnings of Solid State Physics.” Proceedings of the Royal Society of London, series A, 371 (1980): 3–177. A collection of articles about the history of solid-state physics.
A Life in Science. London: Taylor and Francis, 1986. A short autobiography.
With A. S. Alexandrov, eds. Sir Nevill Mott: 65 Years in Physics (Selected Papers). Singapore: World Scientific, 1995.
Anderson, Philip W. “Absence of Diffusion in Certain Random Lattices.” Physical Review 109 (1958): 1492–1505.
Davis, E. A., ed. Nevill Mott: Reminiscences and Appreciations.
London: Taylor and Francis, 1998.
Hoddeson, Lillian, Ernest Braun, Jürgen Teichmann, et al., eds. Out of the Crystal Maze: Chapters from the History of Solid State Physics, 1900–1960. New York: Oxford University Press, 1992. The first attempt to write a comprehensive history of solid-state physics.
Pippard, A. Brian. “Sir Nevill Francis Mott, C.H.” Biographical Memoirs of Fellows of the Royal Society (London) 44 (November 1998): 313–328.