DEAN AND NUESE: STEP-RECOVERY TECHNIQUE FOR MEASURING PARAMETERS IN ASYMMETRIC P-n JUNCTION DIODES fraction of the diodes tested gave values of L/Lp sig nificantly less than unity attests to the need for a theory such as ours which includes the effects of unknown im purity CONCLUSIONS An efficient Ital technique has been de veloped for carrying out step-recovery measurements of very short lifetimes. The outstanding feature of this that only one electrical line is contact the test diode, and the distance from the diode to the measuring equipment may be arbitrarily long. This simplicity makes it possible to minimize stray circuit reactances for definitive high-speed measure ments, It also facilitates subjecting the test diode trace for p*n GaAs Time scale is 2 ns wide range of ambient conditions, including temper oltage scale is 0.5 v/di ature. The raw data from the experiment provide an im The recovery in the high-current experiment is more mediate qualitative and semiquantitative indication of complicated because it is the sum of two exponentials. the key parameters, and a large amount of informa Fortunately, the coefficients of the exponentials are tion is available in a single oscilloscope display. The such that the sum can be approximated by a single various features on the oscilloscope display have been exponential having a time constant equal to the sum of quantitatively characterized reaches 1/e of its final value in a time given by oigy' the time constants of the two original expo Using simple heuristic arguments based on the key numerical evaluation of (19)shows that the recovery physical phenomena in the experiment, we have de- veloped an approximate theory which makes direct use of the salient features in a typical oscilloscope display. t=T1+(1+b)T The results are presented in an easy-to-use graphical where 8 has a maximum value of +0.17 at T/T, =1.75 form, and fit closely the results of more rigorous deriva and approaches zero in the two limits of large and small tions previously done by others, in the appropriate Ti/Tr. Thus, with an error of les than 20 percent(which limits. The present technique is more general, however,, tends to cancel the previous errors), one can evaluate t, and provides more information from a single experi- as the difference between the times required for the volt- ment than could have been obtained previously. In age to reach 1/e of their final values in the high- and formation conveyed includes series resistance, depletion low-current experiments described above. In the limit of capacitance, injected-carrier lifetime, and the effect of small series resistance, one has R,<<Ro, and the de- ossible impurity gradients or recombination in termination becomes especially simple. The time be- homogeneities on the penetration length of the injected tween the two curves measured 1/e of the way from the arriers steady-state value to zero is simply ( T,+T,). This AcknOWledgment determination is depicted in Fig 4 The technique we have described has been used to The authors are indebted to A. M. Garofalo and measure lifetime and penetration length in a large J J. Gannon for experimental assistance number of GaAs and GaAs-P2 p-n junctions, a typical oscilloscope trace is shown in Fig. 5. Results of these REFERENCES measurements will be published later, but some general [11 H: Higuchi and H. Tamura, Measurement of the lifetime of observations are in order here. Series resistances deter roscope, mined from the step-recovery oscilloscope trace are (21 Oku, The average depletion capacitance determined from the step-recovery oscilloscope trace is typically slightly higher than the depletion capacitance measured on a bridge with the bias voltage equal to the steady-state (515. M. Krakauer, "Harmonic ge lifetimes range between 1 and 60 ns and values of L/Lp (6]E,M.61962, pp. 1665-1676p recovery diode, "Proc.IRE,vol voltage in the step-recovery measurement. Measured range between 0.25 and 1.00. The fact that a reasonable of pulsed reverse characteristic 1953 pDEAN AND NUESE: SmP-RECOVERY TECHNIQUE FOR MEASURINO PARAMETERS IN ASYMMETRIC p-n JUNCTION DIODES 157 Fig. 5. Typical oscilloscope trace for p+-n GaAso,&Po,l~ diode. Time scale is 2 ns/div. Voltage scale is 0.5 V/div. The recovery in the high-current experiment is more complicated because it is the sum of two exponentials. Fortunately, the coefficients of the exponentials are such that the sum can be approximated by a single exponential having a time constant equal to the sum of the time constants of the two original exponentials. A numerical evaluation of (19) shows that the recovery reaches l/e of its final value in a time given by t’ = TI + (1 + S)TT where 6 has a maximum value of +0.17 at T1/Tr= 1.75 and approaches zero in the two limits of large and small T1/TT. Thus, with an errorf less than 20 percent (which tends to cancel the previous errors), one can evaluate T, as the difference between the times required for the volt￾age to reach l/e of their final values in the high- and low-current experiments described above. In the limit of small series resistance, one has R, < <Rot and the de￾termination becomes especially simple. The time be￾tween the two curves measured lle of the way from the steady-state value to zero is simply (T8+ TT). This determination is depicted in Fig. 4. The technique we have described has been used to measure lifetime and penetration length in a large number of GaAs and GaAsl-,P, p-n junctions. A typical oscilloscope trace is shown in Fig. 5. Results of these measurements will be published later, but some general observations are in order here. Series resistances deter￾mined from the step-recovery oscilloscope trace are typically about 30 percent higher than the saturation resistance indicated on a forward-biased I-V curve. The average depletion capacitance determined from the step-recovery oscilloscope trace is typically slightly higher than the depletion capacitance measured on a bridge with the bias voltage equal to the steady-state voltage in the step-recovery measurement. Measured lifetimes range between 1 and 60 ns and values of L/LD range between 0.25 and 1.00. The fact that a reasonable fraction of the diodes tested gave values of LILD sig￾nificantly less than unity attests to the need for a theory such as ours which includes the effects of unknown im￾purity grading. CONCLUSIONS An efficient experimental technique has been de￾veloped for carrying out step-recovery measurements of very short lifetimes. The outstanding feature of this technique is that only one electrical line is required to contact the test diode, and the distance from the diode to the measuring equipment may be arbitrarily long. This simplicity makes it possible to minimize stray circuit reactances for definitive high-speed measure￾ments. It also facilitates subjecting the test diode to a wide range of ambient conditions, including temper￾ature. The raw data from the experiment provide an im￾mediate qualitative and semiquantitative indication of the key parameters, and a large amount of informa￾tion is available in a single oscilloscope display. The various features on the oscilloscope display have been quantitatively characterized. Using simple heuristic arguments based on the key physical phenomena in the experiment, we have de￾veloped an approximate theory which makes direct use of the salient features in a typical oscilloscope display. The results are presented in an easy-to-use graphical form, and fit closely the results of more rigorous deriva￾tions previously done by others, in the appropriate limits. The present technique is more general, however, and provides more information from a single experi￾ment than could have been obtained previously. In￾formation conveyed includes series resistance, depletion capacitance, injected-carrier lifetime, and the effect of possible impurity gradients orrecombination i￾homogeneities on the penetration length of the injected carriers. ACKNOWLEDGMENT The authors are indebted to A. M. Garofalo and J. J. Gannon for experimental assistance. REFERENCES minority carriers in semiconductors with a scanning electron H. Higuchi and H. Tamura, “Measurement of the lifetime of m~croscope,” Japan. J. Appl. Phys., vol. 4, 1965, p. 316. T. Nakano and T. Oku, (‘Temperature dependence ofrecombina￾tion lifetime in gallium arsenide electroluminescent diodes,” Japan. J. Appl. Phys., vol. 10, 1967, p. 1212. and recombination in P-A’ junctions and P-N junction char￾C.-T. Sah, R. N. Noyce, and W. Shockley, “Carrier generation acteristics,” Proc. IRE, vol. 45, Sept. 1957, pp. 1228-1243. W. Shockley, ‘(The theory of P-N junctions in semiconductors and P-N junction transistors,” Bell Syst. Tech. J., vol. 28, 1949, p. 435. S. M. Krakauer, ‘Harmonic generation, rectification, and life￾time evaluation with the step recovery diode,” Proc. I=, vol. 50, July 1962, pp. 1665-1676. E. M. Pell, “Recombination rate ;,n germanium by observation of pulsed reverse cliaracteristic, Phys. Rev., vol. 90, 1953, p. 278