Oldwig von Roos

Quantification of the effects of generation volume, surface recombination velocity, and diffusion length on the electron‐beam‐induced current and its derivative: Determination of diffusion lengths in the low micron and submicron ranges

A systematic and quantitative analysis is carried out to investigate the effects of the shape (point, cube, Gaussian) and size of the generation volume, the surface recombination velocity, and the diffusion length on the electron‐beam‐induced current (EBIC) and its derivative (DEBIC). Thick homogeneously doped samples exhibiting diffusion lengths in the low micron and submicron range are considered. The results are presented in computed EBIC curves as a function of scanning distance and of the ratio true diffusion length/effective diffusion length. Using these curves, we show (1) a simple and yet rigorous method for the determination of the true diffusion length, taking into consideration all of the factors cited above, (2) a method for the rapid determination of the surface recombination velocity, (3) the condition under which the source shape becomes insignificant, and (4) a new value for the lower limit of the diffusion length which can be determined by the EBIC technique.

Influence of radiative recombination on the minority-carrier transport in direct band-gap semiconductors

When radiative (band to band) lifetimes and nonradiative (multiphonon via flaws) lifetimes become comparable, as is the case for GaAs, the customary diffusion equation for minority carriers under low level injection conditions must be augmented by terms originating from photon transport. Using the generalized van Roosbroeck–Shockley relation between absorption and emission as well as radiative transfer theory, the relevant equations for free carrier transport are derived. Subsequently, it is shown that the influence of the reabsorbed recombination radiation on carrier transport while unimportant at low doping levels becomes important for n‐type GaAs at high doping levels. We also determine the external luminescence flux taking due account of multiple emission and absorption events inside the sample.

Analysis of the interaction of an electron beam with a solar cell—II☆

Abstract In continuation of previous work, the short circuit current I SC generated by a collimated electron beam impinging on an N - P junction (solar cell) is investigated in a configuration in which the beam scans the front surface of a solar cell crossing the ohmic contact strips. The analysis employs Fourier and Wiener-Hopf techniques and shows that even in the idealized case of uniform doping in both the N -material and the P -material the scanning electron beam gives little information about junction parameters (diffusion lengths, surface recombination velocities etc.). A recently proposed method for measuring the surface recombination velocity by means of changing the beam energy is inapplicable for shallow junctions (junction depth ≈ 0.1 μ m). The reason for this state of affairs is the fact that the radius of the beam-semiconductor interaction volume is larger than or comparable to the characteristic lengths, junction depth, depletion layer width and diffusion length of minority carriers in the N -material. The uncertainties of the distribution in space of excess carriers generated by the electron beam prevent an accurate determination of junction parameters. If, however, the ohmic contact on the back surface of a solar cell is partially removed, scanning across the free surface toward the ohmic contact yields useful information about the bulk diffusion length.

Analysis of the interaction of an electron beam with back surface field solar cells

In this paper the short circuit current ISC induced by the electron beam of a scanning electron microscope in a back surface field solar cell will be determined theoretically. It will be shown that, in a configuration used previously for solar cells with an ohmic back surface, the ISC gives a convenient means for estimating the back surface recombination velocities and thus the quality of back surface field cells. Numerical data will be presented applicable to a point source model for the electron–hole pair generation.

Recombination lifetimes and surface recombination velocities of minority carriers in n‐p junctions. A new method for their determination by means of a stationary amplitude‐modulated electron beam

When a well‐collimated electron beam of an electron microscope impinges on the free surface of an n‐p junction, a short circuit ISC will be generated. If the primary beam current is amplitude modulated sinusoidally in time, the ISC exhibits a characteristic coherent phase shift with respect to the modulated primary beam. This phase shift depends on the minority‐carrier lifetime, doping level, and the position of energy levels of recombination centers within the band gap. For solar‐grade material with their long lifetimes the influence of energy‐level positions is negligible, but for short‐lifetime material (switching devices) the dependence of the phase shift on the energy levels of the recombination centers is critical. In this paper it is shown that the measurement of the phase shift at two different beam‐modulation frequencies allows for the determination of the lifetime and surface recombination velocity in solar‐grade material (solar cells).

An EBIC equation for solar cells

Abstract When an electron beam of a scanning electron microscope (SEM) impinges on an N-P junction, the generation of electron-hole pairs by impact ionization causes a characteristic short circuit current I SC to flow. The I SC , i.e. EBIC (electron beam induced current) depends strongly on the configuration used to investigate the cells response. In this paper we consider the case where the plane of the junction is perpendicular to the surface. An EBIC equation amenable to numerical computations is derived as a function of cell thickness, source depth, surface recombination velocity, diffusion length, and distance of the junction to the beam-cell interaction point for a cell with an ohmic contact at its back surface. It is shown that the EBIC equation presented here is more general and easier to use than those previously reported. The effects of source depth, ohmic contact, and diffusion length on the normalized EBIC characteristic are discussed.

Analysis of the photo voltage decay (PVD) method for measuring minority carrier lifetimes in P‐N junction solar cells

When the diffusion length of minority carriers becomes comparable or even larger than the thickness of a P‐N junction solar cell, the characteristic decay of the photogenerated voltage becomes a mixture of contributions with different time constants. The minority carrier recombination lifetime τ and the time constant l2/D, where l is essentially the thickness of the cell and D the minority carrier diffusion length, determine the signal as a function of time. It is shown that for ordinary solar cells (N+‐P junctions), particularly when the diffusion length L of the minority carriers is larger than the cell thickness l, the excess carrier density decays according to exp(−t/τ−π2Dt/4l2), τ being the lifetime. Therefore, τ can be readily determined by the photo voltage decay (PVD) method once D and l are known. For ideal back‐surface‐field (BSF) cells (N+‐P‐P+ junctions) under the same circumstances the excess number density of carriers decays purely exponentially as exp(−t/τ). However most BSF solar cells are...

On the determination of diffusion lengths by means of angle-lapped p-n junctions

A standard procedure for determining the minority carrier diffusion length by means of SEM consists of scanning an angle-lapped surface of a p-n junction and measuring the resulting short circuit current as a function of beam position. The present paper points out that the usual expression linking the short circuit current induced by the electron beam to the angle between the semiconductor surface and the junction plane is incorrect. The correct expression is discussed and it is noted that, for angles less than 10 deg, the new and the old expression are practically indistinguishable.

Recombination-generation currents in degenerate semiconductors

Abstract The classical Shockley-Read-Hall theory of free carrier recombination and generation via traps is extended to degenerate semiconductors. A concise and simple expression is found which avoids completely the concept of a Fermi level, a concept which is alien to non-equilibrium situations. Assumptions made in deriving the recombination generation current are carefully delinated and are found to be basically identical to those made in the original theory applicable to nondegenerate semiconductors.

Destruction of Metastable Helium Atoms in Binary Collisions

A calculation of the cross section for the reaction He′+He′=He+He++e (destruction of the metastable 23S state by ionization) has been performed by means of the perturbed stationary state method. The cross section obtained is of the order of magnitude 10—18 cm2 at room temperature and increases slowly with decreasing kinetic energy of the colliding particles. The magnitude of the cross section fits well with a tentative scheme which considers processes of the type A′+B=A+B++e as being intermediate between true resonance collisions and nonresonance collisions. It disagrees by 4 orders of magnitude with experimental findings [A. V. Phelps and J. P. Molnar, Phys. Rev. 89, 1202 (1953)]. The reason for this discrepancy is not known.