Peter T. Landsberg

Lifetime broadening of a parabolic band edge of a pure semiconductor at various temperatures

Abstract In doped and in highly excited semiconductors many-body effects produce a shrinkage of the band gap. However, the Coulomb interactions between the conduction band electrons also cause a spreading of the conduction band edge and similar effects occur at the valence band edge. This effect is estimated here by considering the lifetime of an electron vacancy in the conduction band. Owing to the Coulomb interaction induced electron collisions (“Auger effect”) this lifetime is finite and broaders the state considered. The broadening is estimated theoretically for the simple model of a single parabolic band at non-zero temperature, and experimental evidence is presented from related studies showing that the effect can be observed. The spreading out of levels considered here corresponds to the imaginary part of the self energy (the real part is normally calculated as the main energy band narrowing). The results imply that under high excitation conditions the imaginary part can be a significant fraction of the real part.

The band-band Auger effect in semiconductors

Abstract Theoretical and experimental work on the band-band Auger effect is discussed with special reference to recent work.

The connection between carrier lifetime and doping density in nondegenerate semiconductors

It is assumed that there exists a temperature Tf at which dominant recombination centers in the form of electrically neutral, mechanical defects (e.g., vacancies) are frozen into a semiconductor matrix. For this process we assume an Arrhenius‐type law with an activation energy. From this assumption there follows by standard semiconductor statistics the doping dependencies of (a) the defect concentration and (b) the minority carrier lifetimes. The analysis can in principle be applied to any defect in any semiconductor which satisfies the above assumptions, provided the cross sections and related data are known. For the case of silicon we have deduced a set of parameters to fit the optimal experimental lifetimes. Assuming the unknown defects to have two charge states, neutral and negative, it is inferred that the levels lie near midgap and have recombination coefficients of order 10−9 cm3 s−1.

Effects of surface states and of excitation on barrier heights in a simple model of a grain boundary or a surface

The model of a grain boundary (or of a surface) used here employs parallel quasi‐Fermi levels but does not require the depletion approximation. Shockley–Read–Hall recombination via the surface states (including Auger effects) is utilized and the resulting surface trap occupation is displayed as a generalization of the well‐known Fermi–Dirac distribution function. This enables one to cover equilibrium and steady‐state conditions in one treatment. The barrier height has been given as a function of bulk doping, surface energy level density, and also as a function of excitation intensity. The latter is determined by the separation between the quasi‐Fermi levels and can be due to incident light or carrier injection. A number of experimental curves have been fitted satisfactorily on the basis of the theory. Among the conclusions, we note that there is a maximum (with respect to doping) in the barrier height, and that illumination reduces the barrier height. The effect of the energetic position of the surface st...

Effect of the capture coefficient in deep‐level transient spectroscopy measurements

Underlying the conventional deep‐level transient spectroscopy (DLTS) method is the assumption of an exponential capacitance transient to the equilibrium state as a result of the thermal emission rate of free carriers from a filled trap energy level. This exponential capacitance transient may prove to be a good approximation for specific cases but, in general, the transient capacitance decay to the equilibrium state following a capture pulse is nonexponential. In this study nonexponential capacitance transients are shown to be encouraged by the presence of the free‐carrier tail which spills over abundant free mobile carriers into the space‐charge region thus negating the abrupt junction depletion approximation and favoring both capture and emission of carriers. An upper limit for this effect is obtained here by assuming the carrier concentration in the relevant part of the space‐charge region which one has in the neutral region. This reduces the thermal emission rate by several orders of magnitude from wha...

Some maximal thermodynamic efficiencies for the conversion of blackbody radiation

Two efficiency formulas are derived for the conversion of blackbody radiation and their relationship is briefly discussed. It enables one to give an analytical expression for the entropy generation rate, obtained previously by microscopic considerations.

Nonparabolicity as a tool in band-gap engineering

A new analytical, but still approximate, formula for the threshold energy of electron‐electron‐hole impact ionization is given for the case of parabolic valence and conduction bands of the simple Kane type. It is shown for the first time that impact ionization in this system can be ‘‘switched off’’ if the ratio of electron to hole effective mass is large enough. The condition for this to happen is given by a new formula which is exact within this model.

Equivalent circuits for recombination-generation processes in semiconductors: A unified approach

Abstract It is shown how, by use of irreversible thermodynamics and semiconductor statistics, one can derive resistance and capacitance matrices as well as current generator vectors. They become elements of an equivalent circuit for recombination-generation processes. These results are readily obtained for small departures from a nonequilibrium steady state (which is taken as reference state) provided quasi-Fermi levels exist. The circuit elements are found in terms of electron (and hole) concentrations in various levels and the transition probabilities between them. From the general results thus obtained many specific circuit elements already in the literature can be obtained, notably some early ones due to C.T. Sah.

On the work done in changing the state of a black hole

We examine the process of slowly lowering a charged particle to the event horizon of a static charged black hole and then allowing it to be absorbed by the black hole. This process is examined both using the laws of black-hole thermodynamics and using general relativity. The work done in this process is calculated. In addition, we calculate the change in the mass, charge, and area of the black hole. We find that the area (i.e., entropy) is left unchanged.

Capture‐to‐emission ratios for multivalent traps

It is shown that a formula recently given for the ratio of emission to capture coefficient of a trap, en/cn=Nc  exp(−ΔG/kT), holds with only minor modifications also for traps which can capture several electrons. Auger effects and impact ionization can also readily be included.