Impact ionization in thick multiplication regions is adequately described by models in which the ionization coefficients are functions only of the local electric field. In devices with thin multiplication lengths, nonlocal effects become significant, necessitating new models that account for the path that a carrier travels before gaining sufficient energy to impact ionize. This paper presents a new theory that incorporates history-dependent ionization coefficients, and it is shown that this model can be utilized to calculate the low-frequency properties of avalanche photodiodes (APD's) (gain, noise, and breakdown probability in the Geiger mode) and the frequency response. A conclusion of this work is that an ionization coefficient is not a fundamental material characteristic at a specific electric field and that any experimental determination of ionization coefficients is valid only for the particular structure on which the measurement was performed.

A new look at impact ionization-Part I: A theory of gain, noise, breakdown probability, and frequency response

For Part I see R.J. McIntyre, ibid., vol.46, no.8, pp.1623-31 (1999). In Part I, a new theory for impact ionization that utilizes history-dependent ionization coefficients to account for the nonlocal nature of the ionization process has been described. In this paper, we will review this theory and extend it with the assumptions that are implicitly used in both the local-field theory in which the ionization coefficients are functions only of the local electric field and the new one. A systematic study of the noise characteristics of GaAs homojunction avalanche photodiodes with different multiplication layer thicknesses is also presented. It is demonstrated that there is a definite "size effect" for thin multiplication regions that is not well characterized by the local-field model. The new theory, on the other hand, provides very good fits to the measured gain and noise. The new ionization coefficient model has also been validated by Monte Carlo simulations.

A new look at impact ionization-Part II: Gain and noise in short avalanche photodiodes

Avalanche noise measurements have been performed on a range of homojunction GaAs p/sup +/-i-n/sup +/ and n/sup +/-i-p/sup +/ diodes with "i" region widths, /spl omega/ from 2.61 to 0.05 /spl mu/m. The results show that for /spl omega//spl les/1 /spl mu/m the dependence of excess noise factor F on multiplication does not follow the well-established continuous noise theory of McIntyre [1966]. Instead, a decreasing noise factor is observed as /spl omega/ decreases for a constant multiplication. This reduction in F occurs for both electron and hole initiated multiplication in the thinner /spl omega/ structures even though the ionization coefficient ratio is close to unity. The dead-space, the minimum distance a carrier must travel to gain the ionization threshold energy, becomes increasingly important in these thinner structures and largely accounts for the reduction in noise.

Avalanche multiplication noise characteristics in thin GaAs p/sup +/-i-n/sup +/ diodes

We demonstrate an impact-ionization-engineered structure for the multiplication region of avalanche photodiodes. By enhancing the control of the impact-ionization position, the structure achieved high gain, low dark current, and very low noise.

Avalanche photodiodes with an impact-ionization-engineered multiplication region

Light falling on a photodetector produces an output current that fluctuates. The noise in this signal arises from two sources: randomness in the photon arrivals and randomness in the carrier multiplication process intrinsic to the photodetector. A general formula is derived for the variance of the photodetector output current in terms of parameters characterizing these two sources of randomness (the photon-number variance-to-mean ratio for the light and the excess noise factor for the detector). An important special case of this formula illustrates that the output-current variance is directly proportional to the detector excess noise factor when the number of photons at the input to the detector is Poisson distributed. Explicit expressions for excess noise factors are provided for three kinds of photodetectors: the double-carrier conventional avalanche photodiode, the double-carrier superlattice avalanche photodiode, and the photomultiplier tube. The results for the double-carrier superlattice device are new; it is shown that even a small amount of residual hole ionization can lead to a large excess noise factor. Comparisons are drawn among the detectors in terms of their noise properties.

Excess noise factors for conventional and superlattice avalanche photodiodes and photomultiplier tubes

It is shown that the standard theories of avalanche statistics for two-carrier impact ionization by Tager, McIntyre, and Personick only deal with processes for which the number of possible ionizations is very large. On the contrary, it is believed that in many modern devices the number N of possible ionizations is finite and perhaps even very small ( N = 1-5 ). A complete theory for this case is developed, using a new statistical approach, referred to as the "method of recurrent generating functions." The rather complex detailed expressions so obtained contain as special cases the result for N = 1 given by Lukaszek et al., and the results of the above mentioned standard theories for N = \infin these theories thus retain asymptotic validity. Computer plots of the new results indicate that the standard theories overestimate the noise of the avalanche process; this may explain exceedingly low noise data, as reported recently by Goedbloed and Smeets. Finally, for the asymptotic case a complete evaluation is made of the distribution for the output particle population. Previous results by McIntyre are fully corroborated.

Theory of carrier multiplication and noise in avalanche devices&#8212;Part II: Two-carrier processes

A critical discussion is given of existing methods for the computation of noise in single injection space−charge−limited (SCL) devices: the salami method, the Langevin method, and the impedance field method. In addition, a new method is set forth, which in one form (finite volume divisions Δ3r) presents a lumped network description of noise and electrical parameters, whereas in another form (Δ3r→0) it presents a continuous media transport picture which is characterized by a transfer impedance tensor. The first form ties in with a modified salami method, whereas the second form is the substratum from which the more global impedance field formulas can be derived. A necessary and sufficient condition under which the noise is expressible as generalized Nyquist noise is obtained. For the simplest device, the thermal electron trap−free insulator, this is applied to one−dimensional as well as some three−dimensional geometries.

Noise in single injection diodes. I. A survey of methods

The noise of single injection diodes of varying degrees of complexity is studied: the trap−free insulator, the trap−free semiconductor, structures with traps, and three−dimensional insulators. Where possible, results for hot as well as thermal carriers are derived. The one−dimensional results are consistently obtained with the transfer impedance method and the emphasis is on results valid in the entire characteristic [Ohmic, space−charge−limited (SCL), and mixed conduction]. Agreement with other work in limiting current regimes is generally observed. For devices with traps explicit new formulas for the trapping noise are obtained.

A. Friedmann

Papers

Theory of carrier multiplication and noise in avalanche devices—Part II: Two-carrier processes

Noise in single injection diodes. I. A survey of methods

Noise in single injection diodes. II. Applications

A. Friedmann

Papers

Theory of carrier multiplication and noise in avalanche devices&#8212;Part II: Two-carrier processes

Noise in single injection diodes. I. A survey of methods

Noise in single injection diodes. II. Applications

Theory of carrier multiplication and noise in avalanche devices—Part II: Two-carrier processes