Chapter 3 - Experimental Evidence from Commercial Devices

3.1 - Introduction

Most of the theory outlined in the previous chapter assumes that the pin or psn structures have abrupt doping boundaries. Virtually all reverse transients studies have been restricted to abrupt boundary devices, due to the simple mathematical boundary conditions that these devices offer. This structure is in fact the optimum structure for low voltage SRDs [Moll69] since it concentrates the stored charge in a narrow layer where it is easily removed. Power rectifiers on the other hand, often take advantage of the higher breakdown voltages possible with diffused junctions, which are poorly approximated by abrupt boundaries. (However, as noted before, there has been a move to power rectifiers with abrupt junctions, to reduce the stored charge.) Experimental evidence from several obsolete rectifiers presented below indicates that certain diffused structures can exhibit good step recovery characteristics. Computer simulations, presented later, have confirmed this. While previous theories predict qualitatively that voltage development across a diffused rectifier may occur with a period of slow voltage development followed by a rapid step-recovery-diode-like transient, no studies have predicted that the entire voltage swing (i.e. 10% - 90%) can occur via the step recovery transient.

3.2 - Experimental Observations With Commercial Diodes

As mentioned above, certain commercially produced power rectifiers have been observed to exhibit step-recovery action. It is important to note that this phenomenon was not intentional, that is, the diodes were not specified to exhibit step recovery. Most rectifiers specify only t_RR, rather than ts and t_R, so it is generally impossible to judge a rectifier's step recovery action without experimentation. This step-recovery action was observed by this author in the course of proprietary pulse generator research and development before this thesis began, but has not been satisfactorily explained previously.

Figure 3.1 shows a typical SRD circuit, with ideal waveforms. This circuit is typically used in a pulse generator to sharpen the pulse fall time using low-voltage SRDs. The diode is normally forward biased by a DC current through the two inductors. Initially, the intrinsic region of the pin SRD is swamped with electrons and holes, providing a high conductivity path through the diode. When the input pulse reaches the diode the diode initially stays in conduction, so the output voltage follows the input voltage. However, in a good SRD, the stored charge in the intrinsic layer will quickly fall and the electric fields will suddenly increase, as discussed earlier. The diode will then develop the full reverse voltage across it, and act as an open circuit, so the output voltage will fall to zero.

This section reports the results of tests where the SRD of Figure 3.1 is replaced with a commercially available power rectifier. In this test voltages much higher than those used in normal SRD applications were used. Specifically,

• V_max = 300V (thus I_R = 6 A)
• V_bias = varied to obtain best waveform, see Table 3.1
• R = 50 Ω
• L = 200 μH
• C = 0.1 μF

For these tests, a specially modified Avtech avalanche-transistor-based pulse generator was used as the signal source. The unit was modified so that the output stage of the pulse generator was replaced with the sharpening stage of Figure 3.1, and the distance between the Avtech output and the sharpening circuit was kept as small as possible, to minimize the possibility of undesirable transmission line reflections. The purpose of this sharpening stage is to reduce the fall time (and pulse width) of the input pulse (see Figure 1.1). Figure 3.2 shows the output waveform with no sharpening stage added (thus it is essentially the input waveform when the sharpening stage is added, if reflections are ignored).

Figure 3.1 - Step Recovery Test Circuit

A wide range of commercially produced diodes were tested. All of those that exhibited step recovery action, and a small fraction of the comparable diodes that did not are listed in Table 3.1. Interestingly, the breakdown voltages of most of the diodes were extremely conservatively rated.

Table 3.1 - Results of Experiments on Commercially Produced Diodes

Figure 3.2 - Output of pulse generator (158 V/div, 5 ns/div)

Figure 3.3 - Output pulse when sharpened with diode 13. (158 V/div, 5ns/div)

Figure 3.4 - Doping profile of diode 13. Note the very wide epitaxial layer, bounded by a highly doped substrate.

Figure 3.5 - Output pulse when sharpened with diode 103. (158 V/div, 5ns/div)

Figure 3.6 - Doping profile of diode 103. Note the moderately wide epitaxial layer, bounded by a highly doped substrate.

Figure 3.7 - Output pulse when sharpened with diode 100. (158 V/div, 5ns/div)

Figure 3.8 - Doping profile of diode 100. Note the moderately wide epitaxial layer, bounded by a highly doped substrate.

Figure 3.9 - Output pulse when sharpened with diode 47. (158 V/div, 5ns/div). Note the SRD-like pulse sharpening.

Figure 3.10 - Doping profile of diode 47. Note the diffused profile.

Figure 3.11 - Output pulse when sharpened with diode 89. (158 V/div, 5ns/div). Note the SRD-like pulse sharpening.

Figure 3.12 - Doping profile of diode 89. Note the diffused profile.

Figure 3.13 - Output pulse when sharpened with diode 88. (158 V/div, 5ns/div). Note the SRD-like pulse sharpening.

Figure 3.14 - Doping profile of diode 88. Note the diffused profile.

Figures 3.3, 3.5, etc., show two distinct types of diode transient behavior. The diodes numbered 13, 103, and 100 show no step recovery response. The voltage outputs, and hence the diode impedances, change quite gradually. In contrast diodes 47, 88, and 89 show step responses, where the diode initially conducts, and the output looks quite similar to the input. Then the diodes switch off rapidly, and the output voltages have fall times on the order of 2 ns. These diodes, which are not optimized for step recovery operation, already show better performance than the M/A-COM diode MA44750 listed in Table 1.1!

(All oscilloscope measurements in this thesis were performed using a Tektronix S4 sampling head in a 7S11 sampling unit, with a 7T11 time base, in a 7704 mainframe. The S4 sampling head has a bandwidth of 14 GHz. Where applicable, all rise and fall times measurements are 10%-90% values.)

Tellingly, two of the three diodes that were tested and exhibited step recovery were obsolete, all were fast rectifiers, and one (diode 88) was rated as an extremely fast rectifier. This, for reasons explained in section 2.2.2, strongly suggests that these diodes are ps_pn diffused rectifiers. One part of this hypothesis is easily confirmed using C-V measurements.

For each of the diodes listed in Table 3.1, C-V plots were obtained using the circuit described in Appendix A. This novel C-V profiling instrument allowed measurement over the entire reverse bias range, which ranged down to -1400V for some diodes. From these C-V profiles, the effective doping profile N_eff(W) was plotted for each diode, using [Moll64]

(3.1)

where

(3.2)

and

(3.3)

In these equations, W_DR represents the width of the depletion region, x₁ and x₂ represent the location of the edges of the depletion region, C is the measured capacitance and V is the applied bias. Hence, knowing the variation of C with V allows N_eff(W_DR) to be plotted against W_DR. For each diode, the cross-sectional area was estimated by visual inspection using a microscope.

These doping profiles clearly show that the diodes that exhibit high-voltage step recovery also have diffused doping profiles, and those that do not show step recovery were epitaxially grown. These findings show that step recovery diodes can be made to operate at voltages significantly higher than those that have been developed previously, through the use of diffused-type profiles rather than the textbook abrupt profile.

3.3 - Usefulness of Commercial Diodes as High-Voltage SRDs

While several of the commercial diodes presented above do exhibit step recovery, their actual usefulness is somewhat limited. This is for two reasons. First, most of the diodes that exhibit this effect are now obsolete, probably reflecting the declining use of diffused profiles. Second, all of the diodes found to exhibit this effect were found to be fast or ultrafast rectifiers, meaning that the carrier lifetimes in the diodes have deliberately been made small. This is highly undesirable for pulse sharpening applications, as it increases the forward bias required to obtain a storage time of reasonable duration. For instance, Table 3.1 indicates that diode 88 was biased with 500 mA of current. This is a relatively large current to handle. The diodes presented in Chapter 7 are shown to require bias currents that are at least an order of magnitude smaller for comparable storage times. However, these problems are somewhat mitigated by the fact that these commercial diodes are quite cheap, when available.

Table 3.2 lists the main figures of merit for the diodes of Table 3.1 that displayed step-recovery action, compared to the experimental diodes presented later. The effective lifetime, _EFF, is calculated from the formula:

(3.4)

where t_S is the diode storage time (i.e. the reverse conduction time, which is equal to the output pulse width in the waveforms presented above). This formula is based on a simple charge-control model [Neud89], [Moll62]. It should be noted that in this model the lifetime is not directly linked to any physical parameter like carrier lifetimes or transit times, so it is an "effective" lifetime. More rigorous formulas or numerical approaches for calculating diode storage time are available [King54], [Lax54], [Ko61], [Kuno64], [Bend67], [Rauh90], [Darl95], but equation (3.4) has the advantage of simplicity, and it allows direct comparison with the lifetime values presented in manufacturers' data books [HP90].

Table 3.2 clearly shows the superiority of the optimally-designed diodes over those that show parasitic step recovery, on the basis of both speed and particularly effective lifetime.

Table 3.2 - Figures of merit for the diodes displaying step recovery action.