Experimental Determination of Effective Minority Carrier Lifetime in HgCdTe Photovoltaic Detectors Using Optical and Electrical Methods

This paper presents experiment measurements of minority carrier lifetime using three different methods including modified opencircuit voltage decay (PIOCVD) method, small parallel resistance (SPR) method, and pulse recovery technique (PRT) on pn junction photodiode of the HgCdTe photodetector array.The measurements are done at the temperature of operation near 77K. A saturation constant background light and a small resistance paralleled with the photodiode are used to minimize the influence of the effect of junction capacitance and resistance on theminority carrier lifetime extraction in the PIOCVD and SPRmeasurements, respectively. The minority carrier lifetime obtained using the two methods is distributed from 18 to 407 ns and from 0.7 to 110 ns for the different Cd compositions. The minority carrier lifetime extracted from the traditional PRT measurement is found in the range of 4 to 20 ns for x = 0.231–0.4186. From the results, it can be concluded that the minority carrier lifetime becomes longer with the increase of Cd composition and the pixels dimensional area.


Introduction
Minority carrier lifetime is an important characteristic to evaluate the quality of photovoltaic material and the performance of the photoelectronic devices [1].The basic theory of minority carrier recombination through recombination centers was put forth in 1952 [2].Even though many techniques have been developed in order to determine the minority carrier lifetime for Si-based or Ge-based devices, the carrier lifetime for the HgCdTe photovoltaic infrared focal plane array (IRFPA) photodetector [3][4][5][6] is still a puzzling question, especially for the pn junction devices.This is because the instability of HgCdTe material, in which the characteristics may change during the formation process of device, results in the differences between the actual and design parameters such as carrier concentration and the junction depth and so forth.These issues have many uncertainties effects on the minority carrier lifetime in the pn junction device.
Previous studies results show that the lifetime obtained is widely distributed in the range of ns∼s [7] for different testing techniques, Cd composition, active junction area, and growth conditions.Since the investigation of the carrier lifetime is beneficial to understand the recombination mechanism, the measurements must be carried out on the actual devices to extract the minority carrier lifetime.Here, on the junction type HgCdTe IRFPA, we compare minority carrier lifetimes measured by PIOCVD method [8,9], SPR method [10], and PRT [11] for a series of Cd compositions and the pixels dimensional area.

Device Description and Experimental Setup
The Hg 1−x Cd x Te photovoltaic array detector was grown by MBE epitaxy on GaAs substrates.An ion implantation was fabricated on the p-type HgCdTe layer through B + ion implantation to form the n + region.The acceptor and donor concentration were   ≈ 8 × 10 15 cm −3 and   ≈ 1 × 10 17 cm −3 , respectively.The n + heavy-doping area was 50 × 50 m 2 or 28 × 28 m 2 .A ZnS film was evaporated on the surface as a passivation layer.The metal contacts were deposited on either side of the n-on-p junctions in preparation for photovoltaic measurements.The sample was mounted in a liquid nitrogen-cooled Dewar for measurements and the temperature was close to 77 K.
The transient photovoltage of the photodetector was stimulated by the incident laser pulse, which was generated by an optical parametric oscillator (OPO) and difference frequency generator (DFG) pumped with a picosecond Nd:YAG pulsed laser.The laser pulse duration was 30 ps and the repetition rate was 10 Hz.An Oriel THL (tungsten halogen lamp, Oriel 63355) was used as the bias light source to stimulate the steady-state photovoltage.The nanosecond electric pulses in the PRT measurement were generated by an Agilent 33250A.The sample under test was connected via BNC coaxial cable in series with a 50 Ohm matched load resistance.An Agilent Infiniium 54832B oscilloscope was used to record the optical and electrical methods signals obtained.

Lifetime Measurement Techniques and Results Discussions
3.1.Photo-Induced Open-Circuit Voltage Decay Method.Theoretically, when the HgCdTe photodiode is excited by the pulsed laser, the photoresponse shows a rapid increase and slow decay process.As it has been analyzed in the previous report [8,9], however, the decay curve profiles are dominated by the RC discharge time constant and trap energy level capture effects on excess carrier's relaxation.In order to minimize the effects of the equivalent junction capacitor and the carrier traps in the HgCdTe photodiode, a constant background illumination has been introduced in the traditional OCVD method, which can be called photo-induced open-circuit voltage decay (PIOCVD) method.
The composition of Hg 1−x Cd x Te in our experiments is  = 0.231 ( Eg ∼ 8.6 m),  = 0.305 ( Eg ∼ 4.6 m),  = 0.343 ( Eg ∼ 3.7 m), and  = 0.418 ( Eg ∼ 2.9 m).The detectors were processed into 50 × 50 m 2 area of planar structures.By increasing the bias light intensity, the steadystate photovoltage will saturate the junction potential barrier of the photodiode.When the steady-state photovoltage does not increase with the rising of the background intensity, the photogenerated carriers recombination will dominate the decay time constant, which is related to the minority carrier lifetime.In agreement with this picture, photovoltage transient decay can be fitted by a one-order exponential function.
Figure 1 shows the situation that the DC photovoltage has been saturated.The photovoltage transient decay time constant can be determined from the best fit to the experiment, and consequently the minority carrier lifetime is obtained.The results show that the minority carrier lifetime is in the range of 18∼407 ns for  Cd = 0.231∼0.4186at 77 K.With the Cd composition increasing, the minority carrier lifetimes show an increasing tendency.By comparing the lifetime values of different pixels in one-component array, it is found that there are some distinctions between the different pixels, which can be attributed to the nonuniformity of the HgCdTe  material or due to the fabrication process variations of the detector.

Small Parallel Resistance Method.
In order to minimize the effects of the equivalent junction, we can parallel a small resistance in the load circuit of the photodiode in the transient photovoltage measurement, which is called the small parallel resistance (SPR) method [10].In this situation, the load resistance combines with the junction series resistance to parallel with the junction shunt resistance.Although all these resistances contribute to the RC discharge time constant and impact the photovoltage decay curve, the influence of the junction shunt resistance on the RC constant can be minimized because the load resistance and the junction series resistance are much less than the junction shunt resistance.Thus, the delay effect of the RC discharging process on the photovoltaic decay curve is weakened and the time constant will be dominated by the minority carrier recombination, consequently.
The dependence of bias light intensity on the photovoltage decay profile in SPR is very different from that in the PIOCVD measurement.Figure 2 is the photovoltage of the HgCdTe photodiode illuminated by laser pulses with different bias light intensity when a 50 Ω resistance has been connected in the load circuit.Since the bias light illuminating nearly does not influence the transient photovoltage curves, RC discharging can be excluded from the photovoltage decay process; therefore, the minority carrier lifetime can be correlated to the decay time constant.The area size measured in the experiment is 50 × 50 m 2 and 28 × 28 m 2 .The oneorder exponential function can fit well with the experiment indicating that transient photovoltage decay is an exponential characteristic, which is shown in Figure 3. Thus, the photogenerated minority carrier lifetime can be extracted.Using this method, we measured the minority carrier lifetimes for different Cd components and different area dimensions of the HgCdTe photodiode.They show that the carrier lifetime is in the range of 0.7∼110 ns at 77 K.The lifetime becomes longer with the increase of Cd composition that is consistent with the PIOCVD measurement result.The results also show that the minority carrier lifetime decreases with decreasing area because of perimeter surface recombination effects, which coincides with previous works [12,13].[11] is a widely used method to determine the minority carrier lifetime in the pn junction diodes, which was developed in 1954.When the photodiode is rapidly switched from forward into reverse bias, the excess minority carriers which remained from forward bias injection must recombine  before current flow through the diode can drop to near zero [14].There are two different decay phases which can be distinguished in the reverse current signals: one is the constant recovery current component and the other one is the reverse current dropping to near zero subsequently.Figure 4 shows the reverse recovery current transient recorded on the device as a function of varying initial reverse bias.The average minority carrier lifetime  can be calculated from   and the ratio of forward current to reverse current, which is shown in Figure 5.

Pulse Recovery Technique. The pulse recovery technique (PRT)
The active area of the devices used in this experiment is 50 × 50 m 2 and 28 × 28 m 2 .The lifetime distributes in the range of 4 to 30 ns for  Cd = 0.231∼0.419at 77 K.The  results also show that the value of the lifetime becomes longer with the increase of Cd composition.This is also consistent with the PIOCVD and SPR measurement results.

Results Discussions.
From the above discussion, we measured the HgCdTe photodiode with different Cd compositions and the pixels dimensional area using the three different techniques including PIOCVD, SPR, and PRT.The minority carrier lifetime extracted from these methods is summarized and shown in Figure 6.It is clear that no matter which kind of experiment methods is adopted the minority carrier lifetime values obtained from these methods show the same increasing trend with the increase of Cd compositions.The values of the minority carrier lifetime show the increase with the increase of Cd composition.On the other hand, the minority carrier lifetimes extracted from the three methods are unequal.For example, the carrier lifetime obtained from PIOCVD is sometimes bigger than the ones from PRT.This is because the RC effect cannot be avoided in a pn junction photodiode no matter in what bias-light conditions in PIOCVD measurement.Since the RC discharging process delays the photovoltage decay cure, the minority carrier lifetime is bigger than the real values.In addition, the entire region of the device is in a high-injection condition, and the minority carrier lifetimes are larger than low injection [1], consequently.For the PRT measurements, recombination theory dictates that the minority carrier lifetime will be affected seriously by the surface recombination.
Particularly, for the thin base region photovoltaic device, its dominance effect is even more pronounced.The effective minority lifetime profile can be given by including both surface recombination and diffusion of carriers: where  is the simple thickness perpendicular to the surface plane,  is the surface recombination velocity, and  is the diffusion coefficient.This equation describes the effective carrier lifetime as a function of depth due to the surface recombination and diffusion of carriers within the sample to the surface.In this reason, the measured value is smaller than the base region value.Another correlate point to be cleared up is the influence of pixels dimensional area on the minority carrier lifetime measurement.Form Figure 6, one can see that the minority carrier lifetime of HgCdTe photodiode with the pixels dimensional area of 2500 m 2 is larger than that with the pixles dimension area of 784 m 2 in the SPR measurements.Because the HgCdTe IRFPA was fabricated to the planar junction structure, the active area is related to the junction area.Large decrease in the lifetime with decreasing device size suggests that surface recombination plays an important role in limiting effective device minority carrier lifetime which may be interpreted as the effect of specific surface area on the minority carrier lifetime [15].The smaller the pixel dimension area is, the larger the specific surface area is, and the greater the effect of surface recombination is, consequently.

Conclusion
In summary, the work described in this paper presented the two kinds of minority carrier lifetime optical measurement methods including the PIOCVD method and the SPR method and the electrical method based on PRT.In the optical measurement method, a constant bias light illumination and a small resistance parallel in the load circuit were used to minimize the junction RC discharging process, respectively.The measurement results of the three methods show that the values of the minority carrier lifetime will increase with the increase of Cd compositions.It also shows that the lifetime of PIOCVD is larger than that of PRT, which can be attributed to the RC discharging effect in PIOCVD and strong surface recombination effect in PRT.The experiment methods and the conclusion of this paper will have significance for the HgCdTe device design and optimization.

Figure 1 :
Figure 1: Photovoltaic transient profile of the HgCdTe photodiode illuminated by the laser pulses and the saturate bias light intensity.

Figure 4 :Figure 5 :
Figure 4: Reverse recovery current transient recorded on the diode as a function of varying initial reverse bias.

Figure 6 :
Figure 6: The variation of the extracted lifetime values with Cd composition using three experimental methods.