Chapter 1 - Introduction

1.1 - Motivation

Step recovery diodes (SRDs) have remained extremely useful in wave-shaping applications in the three and a half decades since they were first presented [Boff60], [Moll62]. No other device rivals their combination of fast switching speed and ease of use. Figure 1.1 shows the typical circuit configurations for SRD pulse sharpening. In both circuits, the SRD is initially biased with a constant forward bias current I_BIAS, which stores charge in the SRD. When the voltage source V_IN rises, reverse biasing the SRD, the SRD conducts for a short period of time, removing the stored charge. This keeps the voltage across the diode very low. Then the stored charge is abruptly exhausted, and the SRD switches to a high-impedance, high-voltage state, resulting in a sharpening of the output voltage waveform.

Figure 1.1 - Standard step recovery diode pulse sharpening circuits.

Unfortunately, conventional step recovery diodes are somewhat limited in their maximum breakdown voltages. Most commercially available SRDs have breakdown voltages of less than 100V, since the switching times tend to increase rapidly with rated voltage. Table 1.1 surveys commercial offerings, and illustrates this problem. Table 1.1 lists the three main figures of merit that are used in this thesis to evaluate SRDs: the operating voltage, V_OP (which, except for the A8.6 and MA44952, is taken to be V_BR), the time-rate-of-change during the step recovery, given approximately by V_OP/t_R, and the maximum effective carrier lifetime τ_EFF. Table 1.1 contrasts the commercial offerings with the experimental SRDs discussed in this thesis, and clearly shows the desirable fast switching speeds and long lifetimes of the experimental diodes.

It is of great interest to extend the voltage range of SRDs, to allow their use in high-voltage pulse generators.

This thesis considers methods of designing high-voltage SRDs, for operation from several hundreds of volts to several kilovolts. One entirely new method is presented, and results from fabricated devices are reported. A second (previously proposed) method is also considered in detail. The existing design theory is shown to be incomplete, and is greatly extended by the work presented here. This new theory is compared to experimental results obtained elsewhere, and to simulations presented here.
Table 1.1 - Commercially Available SRDs. Note the rapid increase in switching time with breakdown voltage. (The data for the last four diodes are measured values, the other data was obtained from the manufacturers' data books.)

1.2 - New Approaches for Step Recovery Diodes

Traditional SRDs are constructed with an epitaxial p-i-n structure [Moll69]. The middle i-layer is kept quite narrow, so that all of the charge injected by a forward bias is stored close to the two junctions. This ensures that most of the stored charge is removed while the voltage that has accumulated across the expanding space charge regions is low. In other words, the narrow width ensures that the dynamic punch-through voltage is low relative to the operating voltage. After punch-through occurs, a significant electric field exists throughout the entire i-layer and any remaining mobile carriers are rapidly swept out, causing the voltage across the diode to "snap" to its final value.

The abrupt-epitaxial structure with an intrinsic layer has some drawbacks. During the removal of the stored charge, the space-charge regions in the i-layer consist solely of mobile carriers. No fixed charge is present to compensate the mobile carriers. As a result, the electric field gradients will be relatively steep, thus requiring a narrow i-layer to achieve a low punchthrough voltage. Also, the abrupt junction will have a relatively low breakdown voltage, compared to graded junctions.

For these reasons, this thesis considers two different approaches for designing SRDs. Each approach focuses on a different aspect of the SRD, and the two approaches are in a sense "orthogonal". These two approaches are believed to be the only practical methods currently available for designing high-voltage, single-device SRDs.

The first approach attempts to reduce the steep electric field gradients by using a diffused doping profile. One advantage of this is obvious: higher breakdown voltages can be obtained with a diffused profile. Also, by using a diffused profile, a lower punch-through voltage can be obtained (under certain conditions). The reason for this is that rather than developing steep, narrow electric field profiles at the junctions, lower, wider, electric field profiles develop due to the charge-compensating effect of the doping.

It is well known that in theory [Benda67] and experiment [Chud95b], [Appendix B], diffused high-voltage power diodes will have a "snappier" reverse recovery transient than epitaxial diodes. However, snappiness in power diodes has generally been treated as an undesirable phenomena, rather than as a useful wave-shaping effect [Roul90]. Indeed, virtually all modern power diodes are constructed with epitaxial structures to guarantee a smooth reverse transient. This thesis considers the snappiness of diffused power diodes as a useful effect, and for the first time presents a design theory and experimental results for the use of these diodes as high voltage SRDs. These new diodes are termed "wide-field step recovery diodes", or WFSRDs for short.

The second approach focuses on keeping the stored charge near the (abrupt) diode junctions. In traditional SRDs the forward bias is nearly steady-state, and the diodes rely on a narrow i-layer to keep the charge in close proximity to the junctions. Grekhov has proposed a new SRD, called the "drift step recovery diode" (DSRD), that uses pulsed forward biasing [Grek85], [Grek89], [Belk94]. If the duration of the pulse is much less than the carrier lifetimes, the carriers will be concentrated very close to the junctions. This has produced some very fast switching. 1700 V transitions into 50 Ω have been reported with less than 2 ns transition times [Grek85]. (The concept of pulsed biasing to achieve concentrated charge injection has also been demonstrated in very-high-power thyristor-like devices [Grek83], [Gorb88].)

However, only two design equations are presented in [Grek85], one being:

(1.1)

which relates the reverse current density J_R to the lightly-doped layer doping N_D. The other is:

(1.2)

which limits the forward bias pulse width to a fraction of the base transit time.

By assuming that the diode is operated at voltages near the breakdown voltage V_BR, one can write:

(1.3)

where A is the cross-sectional area and R_L is the load resistance (generally 50 Ω). Also, the breakdown voltage is a function of the doping. In mathematical terms,

(1.4)

By combining the design equation (1.1) with (1.3) and (1.4), one can determine the optimum values of A and N_D for a given V_BR. However, this information is not sufficient to design the diode structure or to choose the ideal biasing conditions. In particular, the optimum lightly-doped layer width can not be predicted (and hence, through (1.2), neither can the maximum storage time), nor can the ideal forward biasing current level.

By considering in detail the nature of the forward transient in the DSRD, new results are developed in this thesis that allow these important parameters to be derived.

1.3 - Remarks on the Philosophy Adopted in This Study

Before beginning to discuss the theoretical aspects of this thesis, it is important to first note the approach taken by this author. The SRDs discussed in this thesis have been studied and developed for the intended application of waveshaping in pulse generators. As such, the primary goal of this thesis is to develop relatively simple (or at least easily computable) expressions for engineering purposes, rather than exact descriptions of the underlying physics.

Given the practical orientation of this thesis, some effort is also devoted to considering the fact that the step-recovery effects described here already occur (unintentionally) in some commercial devices. The properties of these non-optimized diodes are considered, since they may prove to be more economical than custom-built devices, and since they provide insight into the step recovery mechanism.

Most of the common simplifying assumptions in diode physics, such as the low-injection, high-injection, or abrupt-junction assumptions will not apply here, and as such, computer simulations were used as a primary tool in this study. In particular, many diode simulations were run using MEDICI, a powerful large-signal semiconductor simulator. Insofar as the physical diode structures were described accurately to the simulator, the simulations are believed to take into account all significant effects (e.g., the variation of lifetimes with injection level, concentration-dependent mobilities, etc.). All simulated structures used conservative gridding, at the expense of longer computation time, to ensure accuracy.

Since the WFSRD is an entirely new device, working devices have been fabricated and tested for this thesis in order to validate the design theory. In the case of the DSRD, experimental results have been presented elsewhere so devices have not been fabricated. Instead, the new theoretical results are compared to the reported results, and to computer simulations.

1.4 - Main Contributions

This thesis examines two methods of obtaining high-voltage SRDs. The following contributions are related to the first method:

• A new step-recovery mechanism is proposed, which relies upon a diffused doping structure. Methods of optimizing this structure are provided.

• A new method of estimating the breakdown voltage of diffused rectifiers is presented. This empirical method has a wide range of applicability.

• This new step-recovery phenomenon is shown to be present in certain obsolete commercially-produced diffused ultrafast rectifiers. The limitations imposed by the fact that these diodes are not optimized for use as SRDs are discussed.

• Optimized diodes based on this new effect are fabricated and demonstrated for the first time. These diodes are shown to exhibit very long lifetimes and extremely fast switching speeds, making them highly desirable for pulse sharpening applications.

The contributions described in points 1 and 4 have been summarized and accepted for publication [Chud96a].

The following contributions are related to the second method:

• The existing design theory for DSRDs is shown to be inadequate for designing an optimal device. A new, more complete design theory is proposed, which uniquely specifies an optimum device for a given operating voltage.

• A new expression is derived for the evolution of the charge carrier densities in a pin diode during the forward transient. The new expression is considerably more compact than the conventional one.

Portions of the contributions described in points 5 and 6 have been summarized and accepted for publication (subject to minor revision) [Chud96b].

The following contributions are related to instrumentation and measurement issues:

• A new, simple, low cost method of measuring C-V curves at kilovolt voltages, for the purposes of determining doping profiles, is presented. This contribution has been summarized in [Chud95a].

• A new high-speed pulse amplifier configuration was developed for use in reverse-recovery t_RR measurements. This contribution has been summarized in [Chud95b].

1.5 - Organization

Chapter 1 is the introduction. Chapter 2 is a review of diode reverse transient physics, including both SRDs and power rectifiers.

Chapters 3 to 6 deal with the new diffused step recovery diode. Chapter 3 discusses experimental results from commercially available diodes. It is shown that some (but relatively few) obsolete ultrafast rectifiers can be used as high voltage SRDs, but with definite limitations. From high-voltage C-V measurements, it is shown that all of the diodes that act as SRDs have a diffused structure. As a prelude to developing a full design theory for the diffused high voltage SRDs, Chapter 4 presents a new method of estimating the breakdown voltage of diffused rectifiers. Chapter 5 develops the switching theory for the WFSRDs, and uses these results and those of Chapter 4 to propose a design for a 300 V WFSRD. The fabrication method for this diode is documented in Chapter 6. Experimental results are presented in Chapter 7.

Chapter 8 discusses the existing design theory for DSRDs. It is shown that by examining the nature of the forward bias transient, a new design theory can be developed that permits a more optimal design. These results are compared to previously reported experimental results, and to simulations.

Chapter 9 contains the concluding remarks.

Appendix A discusses the instrumentation developed to allow C-V measurements to be made at kilovolt voltages.

A very fast, medium-voltage dc-coupled non-linear pulse amplifier circuit is presented in Appendix B. This pulse amplifier configuration is shown to be very useful for making fast reverse-recovery lifetime measurements.

Appendix C examines the relationship between the maximum electric field at breakdown, E_C, with the breakdown voltage V_BR from a theoretical standpoint. This compliments the empirical discussion presented in Chapter 4.

Appendix D discusses the relationship between the WFSRD switching time and the carrier lifetimes.