IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-18, NO. 3, MARCH 1971 A Refined Step-Recovery Technique for Measuring Minority carrier Lifetimes and related Parameters in asymmetric p-n Junction Diodes RAYMOND H. DEAN, MEMBER, IEEE, AND CHARLES J NUESE metrical p-n junction diode can be measured by observing the time nature of the recombination processes [4], or electro- Abstract-Minority-carrier lifetime in a forward-biased response of the diode to a sudden reversing step voltage. An ap ther nescent junctions [2]. Krakauer [5]has considered impurity gradients is developed, and its results are within about 25 excitation for the special case of an exponentially graded percent of those previously obtained for the special cases of ideal impurity profile in the junction. In this paper we con step and exponentially graded junctions. A relatively simple experi- sider the transient response of an initially forward mental technique is described which is suita ble for measuring life- biased junction to a sudden reversing step. This tran are facilitated by the fact that the test diode is mounted at the end sient technique is ideally suited for a one-port measure of a single coaxial line which can be arbitrarily long. The raw data ment scheme, like the one we will describe, and for de- om the experiment are in the form of an oscilloscope trace, which termining lifetime as a function of injection level ovides an immediate qualitative and semiquantitative indication of The step recovery phenomenon was first studied by ie minority-carrier lifetime and the penetration length for the in- Pell [6], Lax and Neustadter [7], and Kingston [8] leads quickly to a more precise quantitative evaluation of these who developed physical and theoretical descriptions for arameters. In addition, the technique can be used to measure an the storage time T. and the recovery time f, in an ideal average junction depletion capacitance and the device series resis- step junction. For conventional germanium and silicon p-n junctions, this abrupt approximation is usually reasonable, since the impurity profile between the and p-sides of the junction usually becomes uniform HE effective lifetime and penetration depth of within a distance from the junction which is much less minority carriers injected across a forward- than a diffusion length. However, the possibility of an biased p-n junction play an important role in a impurity gradient extending to a significant fraction of variety of semiconductor devices, such as transistors, one diffusion length exists in many other semiconduc- lasers, cold-cathode"emitters, etc. Through the years, tors, particularly the Ill-V compounds where lifetimes a variety of techniques have been developed for the are on the order of 10-8 to 10-10 s and diffusion lengths determination of minority lifetimes, each of which has are often less than a micron. For such junctions, the its particular advantages and disadvantages and re- abrupt approximation would not be valid, and a graded quires its specific assumptions and approximations. impurity profile should be considered. Moll, Krakauer Such techniques include the external generation of and Shen [9] and Moll and Hamilton [10] have treated excess carriers near a reverse-biased junction [1, fre- junctions with an exponentially graded and p-i-n ap quency response and delay time measurements on elec- proximation, respectively. Particularly desirable, how troluminescent diodes 2, and analyses of the small- ever, would be a lifetime measurement procedure which signal impedance [3] and steady-state I-V character- could treat junction profiles intermediate to the step istics [4]of p-n junctions and graded junctions considered previously. Another approach is to make use of the time response The present paper treats the application of the step of a p-n junction to a large-signal idal or step recovery technique to p-n junctions with nearly arbi excitation. This approach is appropriate for asym- trary impurity distributions, and develops an approxi metric p-n junctions biased to intermediate current mate, but general, theory for such junctions. In addition levels. It does not require access to a surface perpen- a particular experimental procedure is described which dicular to the junction [1, knowledge of the specific is especially well-suited for measuring very short life- times(25x10-10 s)under a wide range of ambient script received October 16, 1970. The resear oratories, Princeton, NIEEE TRANSACTIONS ON ELECTRON DEVlCES, VOL. ED-18, NO. 3, MARCH 1971 151 A Refined Step-Recovery Technique for Measuring Minority Carrier Lifetimes and Related Parameters in Asymmetric b-n Tunction Diodes Absfracf-Minority-carrier lifetime in a forward-biased asym￾metrical p-n junction diode can be measured by observing the time response of the diode to a sudden reversing step voltage. An ap￾proximate but general theory for p-n junctions with almost arbitrary impurity gradients is developed, and its results are within about 25 percent of those previously obtained for the special cases of ideal step and exponentially graded junctions. A relatively simple experi￾mental technique is described which is suitable for measuring life￾times down to less than 1 ns. Measurements at extreme ambients are facilitated by the fact that the test diode is mounted at the end of a single coaxial line which can be arbitrarily long. The raw data from the experiment are in the form of an oscilloscope trace, which provides an immediate qualitative and semiquantitative indication of the minority-carrier lifetime and the penetration length for the in￾jected carriers. A graphical presentation of the theoretical results leads quickly to a more precise quantitative evaluation of these parameters. In addition, the technique can be used to measure an average junction depletion capacitance and the device series resis￾tance. INTRODUCTION HE effective lifetime and penetration depth of minority carriers injected across a forward￾biased p-n junction play an important role in a variety of semiconductor devices, such as transistors, lasers, “cold-cathode” emitters, etc. Through the years, a variety of techniques have been developed for the determination of minority lifetimes, each of which has its particular advantages and disadvantages and re￾quires its specific assumptions and approximations. Such techniques include the xternal generation of excess carriers near a reverse-biased junction [l], fre￾quency response and delay time measurements on elec￾troluminescent diodes [2], and analyses of the small￾signal impedance [3] and steady-state I-V character￾istics [4] of p-n junctions. Another approach is to make use of the time response of a p-n junction to a large-signal sinusoidal or step excitation. This approach is appropriate for asym￾metric p-n junctions biased to intermediate current levels. It does not require access to a surface perpen￾dicular to the junction [l], knowledge of the specific Manuscript received October 16, 1970. ‘The research reported herein was partially sponsored by the National aeronautics and Space Administration, Langley Research Center, Hampton, Va., under Contract NAS-12-2091, and RCA Laboratories, Princeton, N. J. The authors are with RCA Laboratories, Princeton, N. J. 08540. nature of the recombination processes [4], or electro￾luminescent junctions [2]. Krakauer [SI has considered the response of a quiescent junction to a large sinusoidal excitation for the special case of an exponentially graded impurity profile in the junction. In this paper we con￾sider the transient response of an initially forward￾biased junction to a sudden reversing step. This tran￾sient technique is ideally suited for a one-port measure￾ment scheme, like the one we will describe, and for de￾termining lifetime as a function of injection level. The step recovery phenomenon was first studied by Pel1 [6], Lax and Neustadter [7], and Kingston [8], who developed physical and theoretical descriptions for the storage time T, and the recovery time T, in an ideal step junction. For conventional germanium and silicon p-n junctions, this abrupt approximation is usually reasonable, since the impurity profile between the n￾and p-sides of the junction usually becomes uniform within a distance from the junction which is much less than a diffusion length. However, the possibility of an impurity gradient extending to a significant fraction of one diffusion length exists in many other semiconduc￾tors, particularly the 111-V compounds where lifetimes are on the order of lo-* to s and diffusion lengths are often less than a micron. For such junctions, the abrupt approximation would not be valid, and a graded impurity profile should be considered. Moll, Krakauer, and Shen [9] and Moll and Hamilton [lo] have treated junctions with an exponentially graded and p-i-n ap￾proximation, respectively. Particularly desirable, how￾ever, would be a lifetime measurement procedure which could treat junction profiles intermediate to the step and graded junctions considered previously. The present paper treats the application of the step￾recovery technique to p-n junctions with nearly arbi￾trary impurity distributions, and develops an approxi￾mate, but general, theory for such junctions. In addition, a particular experimental procedure is described which is especially well-suited for measuring very short life￾times (25 XlO-’O s) under a wide range of ambient conditions. With this procedure, the step-recovery tech￾nique and its interpretation is found to be remarkably straightforward. In most cases, a pair of closely related measurements recorded on a single oscilloscope photo-