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A Refined Step-Recovery Technique for Measuring Minority Carrier

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A Refined Step-Recovery Technique for Measuring Minority Carrier IEEE TRANSACTIONS ON ELECTRON DEVlCES, VOL. ED-18,NO. 3, MARCH 1971 151 A Refined Step-RecoveryTechnique for Measuring Minority Carrier Lifetimes and Related Parameters in Asymmetric b-n Tunction Diodes Absfracf-Minority-carrier lifetimein a forward-biased asym- nature of therecombination processes [4], orelectro- metrical p-n junction diode can be measured by observing the time luminescent junctions [2]. Krakauer [SI has considered response of the diode to a sudden reversing step voltage. An ap- proximate but general theory for p-n junctions with almost arbitrary the response of a quiescent junction toa large sinusoidal impurity gradients is developed, and its results are within about 25 excitation for the special caseof 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- siderthe transient response of aninitially forward- mental technique is described which is suitable for measuring life- biased junction to a sudden reversing step. This tran- 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 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- from the experiment are in the form of an oscilloscope trace, which termining lifetime as a function of injection level. provides an immediate qualitative and semiquantitative indicationof The step recovery phenomenon was first studied by the minority-carrier lifetime and the penetration length for the in- Pel1 [6], Laxand Neustadter [7], andKingston [8], jected carriers. A graphical presentation of the theoretical results leads quickly toa more precise quantitative evaluation of these who developed physical and theoretical descriptions for parameters. In addition, the technique can be used to measure an the storage time T, and therecovery time T, in an ideal average junction depletion capacitance and the device series resis- step junction. For conventional germanium and silicon tance. p-njunctions, this abrupt approximation is usually reasonable,since the impurity profile between the n- INTRODUCTION and p-sides of thejunction usually becomes uniform HE effectivelifetime andpenetration depth of within a distance from the junction which is much less minoritycarriers 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 semiconductordevices, such as transistors, one diffusion length exists in many other semiconduc- lasers, “cold-cathode” emitters, etc. Through the years, tors, particularly the 111-V compounds where lifetimes avariety of techniqueshave been developed for the areon the order of lo-* to s anddiffusion lengths determination of minority lifetimes, each of which has are often less than a micron. For such junctions, the itsparticular advantages and disadvantages and re- abrupt approximation would not be valid, and a graded quiresits specific assumptionsand approximations. impurity profile should be considered. Moll, Krakauer, Suchtechniques include the external generation of and Shen [9] and Moll and Hamilton [lo] have treated excess carriers near a reverse-biased junction [l],fre- junctions with an exponentially graded and p-i-n ap- quency response and delay time measurements on elec- proximation, respectively. Particularly desirable, how- troluminescentdiodes [2], andanalyses of thesmall- ever, would be a lifetime measurement procedurewhich signalimpedance [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-njunction to a large-signalsinusoidal or step recovery technique to p-n junctions with nearly arbi- excitation.This approach is appropriate forasym- trary impurity distributions, and develops an approxi- metricp-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 dicularto the junction [l],knowledge of the specific is especially well-suited for measuring very short life- times (25XlO-’O s) under a wide range of ambient conditions. With this procedure, the step-recovery tech- Manuscript received October 16, 1970. ‘The researchreported herein was partially sponsoredby the National aeronautics and Spacenique and its interpretation is found to be remarkably Administration,Langley Research Center, Hampton, Va., under Contract NAS-12-2091, and RCA Laboratories, Princeton, N. J. straightforward. In most cases, a pairof closely related The authors are with RCA Laboratories, Princeton, N. J. 08540. measurements recorded on a single oscilloscope photo- j 52 IEEE TRANSACTIONS ON ELECTRON DEVICES, MARCH 1971 graph is sufficient determineto notonly the minority t carrierlifetime and penetration length, but also the no diode’s series resistance and average depletion capaci- E tance. A cursory examination of the oscilloscope photo- n wa graph allows an immediate qualitative and semiquan- a a titativeevaluation of theseparameters. Furthermore, s n1 byanalyzing the photograph with the aid of simplea Wn I-u chartcontained in this paper, one can refine there- W -J sultsandincrease accuracythe of quantitativethe DISTANCE INTO LIGHTLY-DOPEDMORE determinationswithinabout to 25 percent.way,this In MATERIAL,X - it is practical to carry out a series of important junction Fig. 1. Density of injected minority carriers for times (t) after the lneasurements Over a wide range of temperature and in- reversingpulse teaches the diode. Theshaded area indicates the charge remaining at the end of the storage time (T8).The dotted jection levels to obtain an extensive characterization of lines indicateour straight-line approximations. the junctions of interest. THEORYOF JUNCTION BEHAVIORvalue. Then, ‘with TI,the average capacitance C is de- fined by the relation TI/R. In the extreme case of QualitativeDescription C= an ideal stepjunction in which thedepletion width Minority-carrierdensity profiles for a crosssection builds up from zero to a final value corresponding to a cutting through the plane of the junction are indicated final capacitance C,, one can show [9] that C=2.17 Cf. by solid lines in Fig. 1. Carriers have been injected into Thusour “average” capacitance is somewhat higher the more lightly doped material to the right of the junc- thanthe final open-circuitvalue of thejunction de- tion. The length L is the average “penetration length” pletionCapacitance. Although the actual depletion of thesecarriers. This length is stronglyaffected by capacitancevaries with applied voltage, for our de- impuritygradients in the regionoccupied bythe in- velopment, we will approximate it by a constant jectedcarriers. For meaningful results, the built-in capacitance C whose value is determined in the above field due to such gradients must be either zero or di- fashion. rected so as to retard injection. (An injection-enhancing A current source is appropriate for representing the “drift” field pullscarriers away from the junction, extraction of the remaining minority carriers for t> T,, where they cannot be retrieved by a reversing poten- since the extraction process is controlled by diffusion, tial.) For an ideally abrupt step junction [6]-[8] with and is thereforeindependent of the reversevoltage zero built-in field, thepenetration length equals the across the depletion layer. By assuming a constant dis- classical“diffusion length.” For a “graded”junction tance from the junction edge to the point of maximum [9]-[lO] the penetration length is shortened by a re- minoritycarrier density, wewill showlater that the tarding field. current source decays exponentially in time, with a time The top solid curve in Fig. 1 indicates the minority- constant equal to the recovery time T,. carrier density profile before a reversing voltage is ap- The ratio of forward to reverse bias current IF/IR plied. Upon application of a reversing voltage, the den- determines the density profile at t = T,, and therefore sity at the junction starts dropping, and it continues toaffects the magnitude of both T, and T,. A relatively drop throughout a period of time defined as the storage largereverse current shortens the storage time T, by period [9]. During this period the excess carriers avail- extractingthe carriers quickly and by producing a able at the junction make it effectively a short circuit density profile at t = T, which is skewedtoward the PI. junction.With such a profile, most of the previously When the carrier densityat the junctionreaches zero injected carriers are still present. During the recovery at t = T, (storage time), a reverse-biased depletion layer period, the densityprofile at t = T, determines the initial begins to form. The voltage across the diode builds up rate at which the remaining carriers are extracted. (A rapidlyand approaches its steady-state value. The profile crowdedclose to the junction produces a high voltagebuildup is retardedby the time required to extraction rate.) When selecting the time constant for charge
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