Comparison of the current characteristics of photodiodes formed on CdHgTe filmsgrown by molecular-beam and liquid-phase epitaxy for the 8–12-�m spectral range

E. V. Andreeva, Zh. V. Gumenyuk-Sychevskaya,a� Z. F. Tsibri , and F. F. Sizov

Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine

V. S. Varavin, V. V. Vasil’ev, S. A. Dvoretski , and N. N. Mikha lov

Institute of Semiconductor Physics, Siberian Section, Russian Academy of Sciences, Novosibirsk�Submitted August 8, 2009�Opticheski� Zhurnal 76, 42–48 �December 2009�

This paper presents a comparison of the dark currents and differential resistance of photodiodes,obtained using p-type cadmium-mercury telluride �CdHgTe� layers doped with boron ions, grownby molecular-beam epitaxy �MBE� and liquid-phase epitaxy �LPE�. The volt-ampere responsesfor diodes on CdHgTe layers with composition x=0.215, grown by MBE and LPE �x�0.222�are characterized by various saturation currents �reverse bias −0.25 V� of 1–2 and 5–10 nA,even though the band gap is greater for the latter. In this case, the maximum differential resis-tance is 4�109 and 5�107 � for diodes based on MBE and LPE layers, respectively. The ex-perimental data are compared with the calculated values. Numerical modelling showed that, forMBE structures with low biases, the dark current is limited by the diffusion current and by theShockley-Read-Hall current outside the n-p junction, whereas, in LPE structures, there is a sub-stantial contribution of currents through traps in the depletion region. © 2009 Optical Society ofAmerica.

INTRODUCTION

Some of the fundamental physical characteristics of IRphotodiodes used in multielement �array-type or linear� pho-todetector devices �PDDs� with silicon readout circuits arethe current-transport processes through the p-n junction�dark current� that determine the differential resistance.These characteristics of the photodiodes at the operatingtemperatures �77 K� in the long-wavelength region of the IRspectrum �8–12 �m� must be matched with the parametersof modern silicon integrated readout circuits, in which theresistance of the input devices is greater than 108 � for eachof the photodiodes and the charge capacity of the accumula-tor cells is about 2�107 electrons �e−�. The signal-accumulation time will be determined by the time that ittakes the storage capacitors of the silicon readout circuit tobe filled by the charge-carrier current generated by the radia-tion flux. For the 8–12-�m spectral sensitivity range and acold stop, a PDD with f number F /2, the accumulation timesfor CdHgTe-based photodiodes with an area of 25�25 �m2 and accumulator charge N�2�107e− equal ��20 �s at a background temperature of 300 K.

To implement long signal-accumulation times, it is nec-essary to ensure that the charge-carrier conditions in the pho-todiodes only result from the diffusion current, which deter-mines the limiting electric characteristics. There are alsoadditional current-flow channels that reduce the quality ofthe photodiodes.

This paper is devoted to a comparison of the currentparameters of photodiodes in the 8–12-�m spectral range,obtained on heteroepitaxial layers �HELs� of p-type CdHgTegrown by molecular-beam epitaxy �MBE� and CdHgTe lay-ers grown by liquid-phase epitaxy �LPE� with similar param-eters of ion doping with boron. The volt-ampere responses

767 J. Opt. Technol. 76 �12�, December 2009 1070-9762/2009/

�VARs� of the photodiodes have been measured, and they arecompared with the values obtained by modelling current-transport processes on the basis of the balance equations ofcarriers on donor-type trapping levels in the band gap, takinginto account two current mechanisms: tunnelling through thetraps and Shockley-Read-Hall �SRH� generation/recombination. Other substantial current mechanisms �with-out the participation of traps� were regarded as additive.Moreover, the literature data on such photodiodes fabricatedby LPE were analyzed.

EXPERIMENT

The VARs and differential resistance of CdxHg1−xTe �x�0.215� photodiodes obtained by boron implantation weremeasured at a temperature of 77 K. The photodiodes wereformed in p-type variband CdHgTe MBE HELs, obtained byMBE on �013� GaAs substrates, followed by thermal anneal-ing �Fig. 1a�. The composition of the CdHgTe MBE HELsvaried from x�0.35 at the boundary with the CdTe bufferlayer to x�0.215 in the photosensitive layer with thicknessd�8–11 �m, and then a broad- band variband layer of up tox�1 was grown on the surface of the structure. As the thick-ness of the photosensitive layers varied within these limits,the long-wavelength boundary of photosensitivity varied by���0.3 �m for a constant chemical composition of thelayer.1 A photograph of the cross section of the layers of aCdHgTe /CdZnTe heterostructure grown by LPE is shown inFig. 1b.

The n-type regions were formed by implanting boronions with an energy of 50 keV and a dose of3�1013 cm−2.2,3 The n-p junctions form as a result of thediffusion of interstitial mercury from the near-surface layerand their annihilation with mercury vacancies,4,5 as a result

767120767-06$15.00 © 2009 Optical Society of America

of which an n+-n−-p profile appears, with the n+ layer about1 �m deep from the surface and the n-p junction at a depthof from 2 to 4 �m.3 It is shown in Ref. 6 that a donor levelassociated with interstitial mercury lies at �0.65–0.75�Eg

from the top of the valence band, where Eg is the band gap.

10 µm

(а)

20 мкм

(b)

FIG. 1. Photograph of the cross sections of heterostructures: �a�HgCdTe /CdTe ZnTe /GaAs, grown by MBE; �b� HgCdTe /CdZnTe, grownby LPE.

–4

–8

4

0

Bias, V

Dar

kcu

rren

t,n

A

0– 0.2 – 0.1– 0.3– 0.5 – 0.4

diode 1

diode 2

diode 3

diode 4

(а)

FIG. 2. Experimental �symbols� and calculated �curves� VARs �a� and the deCd Hg Te photodiodes �x�0.215, � �11.5 �m� at T=77 K. The values

x 1−x co

768 J. Opt. Technol. 76 �12�, December 2009

The VARs of the photodiodes were measured by a mi-croprobe method in liquid-nitrogen vapor. Typical VARs andthe dependences of the differential resistance on the biasvoltage for photodiodes based on CdHgTe MBE HELs areshown in Fig. 2, and those based on LPE in Fig. 3. Thevarious symbols designate the experimental values, and thesolid curves show the calculated values. The mean dark cur-rents of the MBE photodiodes, determined from measure-ments of thirty diodes at a temperature of T=77 by randomsampling with a reverse bias of −200 mV did not exceed1–2 nA �for a diode area of 27.5�10−6 cm2�; the differen-tial resistance of the photodiodes was 4�109 �. The darkcurrent is more than an order of magnitude less than thephotocurrent caused by radiation at a background tempera-ture of 300 K, and therefore such photodiodes make it pos-sible to implement a noise equivalent temperature differenceof NETD�9 mK, close to the limiting possible value forlinear PDDs with time-delay and storage with an F /2 coldstop and storage charges of the silicon readout circuits ofN�2�107 electrons.

The dark current in the working region of typical goodLPE photodiodes was about 5–10 nA for a diode area of27.5�10−6 cm2, while the differential resistance was about5�107 �. It can be seen from Fig. 3a that the dark currentbegins to increase sharply when the bias voltage is more than−0.3 V.

MODELLING THE CURRENT TRANSPORT IN n+-n−-pPHOTODIODES AND COMPARING THE CALCULATEDVALUES WITH THE EXPERIMENTAL DATA

The main dark-current mechanisms in CdHgTe photo-diodes are diffusion current, interband tunnelling, Auger re-combination, tunnelling through traps, and the SRH recom-bination process. The last two mechanisms are caused byprocesses of current transport through trap levels in the bandgap. The contribution of each mechanism depends on thedegree of filling of such traps. Taking these processes intoaccount independently of each other can give a significant

Bias, V0–0.2 –0.1–0.3–0.5 –0.4

5

6

8

10

7

9

logR

diode 1

diode 2

diode 3

diode 4

(b)

ences of the logarithm of the differential resistance �b� of a sample of MBEe parameters used for the modelling are shown in Table I.

pendof th

768Andreeva et al.

ers u

increase of the currents through the traps. Consequently, it isnecessary to take into account the carrier balance on eachtrap, and this is successfully used in the approximation of thebalance equations of Ref. 8 to describe the current character-istics of photodiodes based on the ternary compoundscadmium-mercury-tellurium and tin-lead-tellurium.9–11

Briefly, the essence of the method of balance equationsis as follows: a free carrier in the field of a p-n junction canbe captured at a localized trapping center

• when an electron tunnels from the conduction band to anunoccupied center;

• when a hole tunnels from the valence band to a centeroccupied by an electron, followed by recombination at thecenter;

• when an electron from the valence band is thermally gen-erated at an empty trap;

• when a hole recombines with an electron on a trap;• and also when a carrier is emitted from a trap by the re-

verse processes.

The probability of each of these processes is determinedby the occupancy of the trap. Moreover, depending on thecoordinate along the transition and the external electric fieldapplied to the p-n junction, some of these processes are al-lowed, while some are forbidden.8 Two approximations wereused to obtain the recombination rate through the traps: aconstant field in the barrier �abrupt p-n junctions� and a con-stant quasi-Fermi level in the barrier �for a forward or asmall reverse bias voltage�. The generation-recombinationcurrent density is obtained by integrating the recombinationrates along the p-n junction. The final expression for thecurrent takes many different forms, depending on the rela-tionship between the band gap Eg, the placement of the traplevel Et�x�, and the applied potential difference q�V0−V�.Moreover, integrals that have no analytical solution are ob-tained in the equations, and this prevents a formula for thecurrent from being obtained in closed form. Therefore, theproblem is solved numerically. The free parameters of themodel are the concentration N of trapping centers, the en-

0

50

–50

–100

–150

Bias, V

Dar

kcu

rren

t,n

A

0–0.2–0.6 –0.4

(а)

1

2

FIG. 3. Experimental �1� and calculated �2� VARs �a� and dependences of�co�10.4 �m� at T=77 K, A=2.75�10−15 cm2. The values of the paramet

t

769 J. Opt. Technol. 76 �12�, December 2009

ergy Et of these centers, the donor and acceptor concentra-tions Nd and Na, and the lifetimes of the carriers on the traps,�p and �n. It was assumed that the capture cross sections areidentical on the traps for electrons and holes, and therefore�p=�n.

Other dark currents, such as interband tunnelling, diffu-sion current, Auger recombination, SRH generation/recombination in quasi-neutral regions, and radiative recom-bination, are regarded as additive and independent of eachother. The largest contribution comes from the diffusioncomponent, the SRH mechanism in the quasi-neutral p re-gion, the Auger-1 process in the n+ region, and interbandtunnelling. The tunnelling through traps and interband tun-nelling in the Wentzel-Kramers-Brillouin model are consid-ered in the kp approximation, which takes into account thenonparabolic nature of the dispersion law.11 Interband tunnel-ling, like tunnelling from traps, strongly depends on the “ge-ometry” of the transition and, consequently, on Na, Nd, andV. In this case, the impurity concentrations obtained whenfitting the calculated curves must satisfy the values of thediffusion and tunnelling currents for small and large reversebias voltages, respectively.

The currents associated with SRH generation-recombination in the quasi-neutral n and p regions are sub-stantial at small biases and are comparable in magnitude withthe diffusion currents �in the approximation of infinitely widen and p regions�.

Auger recombination is negligible in the depletion re-gions. According to the data in Ref. 12, the Auger-7 processcan make a substantial contribution in the p regions. It fol-lows from the review in Ref. 13 that the Auger-1 process issubstantial at T=77 K in n-type regions for an electron con-centration n greater than 1015 cm−3. There is no single opin-ion concerning which recombination dominates in p-typelayers—Auger, SRH, or radiative. However, the lifetimesthat have been calculated from phenomenological formulas14

for the carrier concentrations obtained from experiment forMBE diodes are about 10−7 sec for Auger-1 and about10−8 sec for Auger-7, and this is far less than the lifetimes

Bias, V0–0.2–0.6 –0.4

6

8

7logR

(b)

1

2

garithm of the differential resistance �b� of an LPE photodiode �x�0.222,sed for the modelling are shown in Table I.

the lo

769Andreeva et al.

that we obtained on the basis of modelling the experimentaldark currents. The calculated values of the recombinationcurrents with such a lifetime will significantly exceed thoseobtained in experiment.

Based on the values of the parameters shown in Table I,the solid curves in Figs. 2 and 3 show the results of calcula-tions based on the proposed model for photodiodes obtainedby MBE and LPE, respectively. Good agreement can be seenbetween the experimental data and the parameters of themodel shown in Table I. For small reverse biases, the darkcurrent is added up from the diffusion current and the SRHrecombination current. There are virtually no tunnelling cur-rents with such biases. The donor and acceptor concentra-tions Nd and Na and the carrier lifetimes �pv and �nv in thedepletion region, as well as the trap concentration Ntv outsidethe depletion region, are found by fitting this section of thecurves �see Table I�.

The tunnelling processes become stronger at large valuesof the reverse bias voltage. Interband tunnelling and tunnel-ling through traps strongly depend on the parameters of thep-n junction and consequently on the donor and acceptorconcentrations. These concentrations, found by fitting the pa-rameters, must satisfy the diffusion currents at small biasesand tunnelling currents at large biases.

The trap level in the band gap has an energy of Et

=0.7Eg above the top of the valence band and concentrationof centers of Nt= �1.0–5.5��1015 cm−3 comparable with thedonor concentration Nd= �1.1–1.8��1015 cm−3 in the n− re-gion. The acceptor concentration in the p layers is Na

�1016 cm−3. Thus, the photodiodes studied here, followingthe parameters obtained from the model for describing theexperimental results, had an n−-p type junction. The modelwith such input parameters gives the following concentra-tions and mobilities at T=77 K:

TABLE I. Values of the parameters that were used tCdxHg1−xTe photodiodes �x�0.215, �co�10.3 �m�the valence band, Na is the acceptor concentration, Nconcentration in the p-n transition region, Nvt is the trand �pv are the times spent by an electron and a holethe film.

Parameter

Name Designation

Trap energy relative to thetop of the valence band

Et

Acceptor concentration Na, cm−3

Donor concentration in the n region Nd, cm−3 1Trap concentration in thep-n junction region

Nt, cm−3

Trap concentration in thevolume of the film

Nvt, cm−3

Time spent by an electron and ahole in the p-n junction regionand in the volume of the film

�n, sec�p, sec�nv, sec�pv, sec

Eg is the band gap.

770 J. Opt. Technol. 76 �12�, December 2009

ni = 1.2 � 1013 cm−3, pp0 = 1016 cm−3,

nn0 = �1.4 − 1.8 � 1015 cm−3�;

�n = 1.2 � 105 cm2/�V sec�,

�p = 5 � 102 cm2/�V sec� ,

which coincides with the data of Ref. 3 for similar boron-implantation regimes. Thus, MBE diodes have low carrierconcentrations in the n region because of compensation ofthe mercury vacancies by interstitial mercury, generated inthe near-surface region by the implanted boron. The longlifetimes in this structure are associated with the presence ofa variband potential. The charge-carrier lifetimes obtained inthe depletion-layer region and in the quasi-neutral regionwere rather high: �0.7–2.0��10−6 sec and �5–10��10−6 sec, respectively, but similar to the carrier lifetimescalculated in Ref. 15 for the given variband structure. More-over, since Na�Nd, the n-p junction shifts into the n region,where high values of the carrier lifetimes and low concentra-tions of the recombination centers are observed because ofthe compensation of mercury vacancies.

The electron concentrations in the n region are some-what higher in an LPE structure than in an MBE structure. Inthis case, the concentrations of the trapping centers are anorder of magnitude higher and the lifetimes an order of mag-nitude lower in the depletion region and are also lower byabout 3 orders of magnitude in the quasi-neutral regions. Inall probability, this is associated with the presence of a varib-and potential in the MBE structure. The increase of the ef-fective carrier lifetime in the presence of the n+ region on thesurface of the structure and the increase in x and the band

del the dark VARs and the differential resistance of2 and 3�. Et is the trap energy relative to the top ofe donor concentration in the n region, Nt is the trapncentration in the volume of the film, and �n, �p, �nv,trap in the p-n junction region and in the volume of

Diodes

E1 MBE2 MBE3 MBE4 LPE

g 0.7Eg 0.7Eg 0.7Eg 0.7Eg

16 1016 1016 1016 1016

1015 1.8�1015 1.6�1015 1.4�1015 2.1�1015

015 1015 5.5�1015 1.5�1015 6�1015

014 0.5�1014 1014 5�1014 2�1015

0−6 2�10−6 0.7�106 0.8�10−6 2�10−7

0−6 2�10−6 0.7�106 0.8�10−6 2�10−7

0−6 10−5 5�10−6 7.5�10−6 6�10−7

0−6 10−5 5�10−6 7.5�10−6 6�10−7

o mo�Figs.

d is thap coon a

MB

0.7E

10.4�

3�1

1�1

2�12�16�16�1

770Andreeva et al.

gap close to the substrate and the surface are explained bythe decrease in the influence of surface recombination be-cause of the built-in electric field.

In order to convince ourselves of the advantages of theMBE method, we shall analyze the data from photodiodesgrown by the LPE method by other companies with exten-sive experience in that area. A discussion of the results ofRef. 16 was published earlier in Ref. 8, in which layers ofCdxHg1−xTe �x�0.222� were grown by LPE on CdZnTe sub-strates and were passivated from above with CdTe layers bythe MBE method. Diodes were formed by implanting B withan energy of 160 keV and a dose of 2.5�1014 cm−2 throughthe CdTe layer and had the shape of a circle 20–30 �m indiameter with differential resistance 105–106 �. However,subsequent annealing in nitrogen vapor at a temperature of120 °C for 1.5–3 h or at 150 °C for 1 h made it possible toreduce the dark current by an order of magnitude and toincrease the differential resistance to 2�106–2�107 �; thisis 2 orders of magnitude worse than our data obtained fordiodes on MBE CdHgTe.

Reference 18 showed the VARs and differential resis-tance of LPE CdHgTe photodiodes optimized at a wave-length of ��10.5 �m, with a pixel size of 50�50 �m: thesaturation currents are of the order of 500 nA, the maximumdifferential resistance at a reverse bias greater than 0.12 V isapproximately 4�107 �, and R0�8�105 �. Reference 19shows values of R0= �0.8–1.2��107 �, and this is some-what lower than our data for MBE photodiodes.

The results given in the literature give no possibility ofmodelling the parameters of the photodiodes, because theoriginal data are inadequate.

Thus, according to our data, photodiodes based on CdH-gTe MBE HELs with variband layers have higher parametersthan those of photodiodes based on LPE structures.

CONCLUSION

This paper has presented a comparison of the dark cur-rents and the differential resistance at a temperature of T=77 K of IR photodiodes obtained by implanting boron ionsfor the 8–12-�m spectral range on the basis of CdHgTeMBE vacancy HELs and epitaxial structures grown by theLPE method. The experimental data of the current transportof the photodiodes were modelled by the balance equationsfor the carriers at donor-type trap levels in the band gap withan energy of 0.7Eg, taking into account two current mecha-nisms: tunnelling through the traps and SRH generation/recombination. Other substantial current mechanisms �with-out the participation of traps� were regarded as additive. Withreverse biases less than −0.25 V, both types of structures hadfairly similar dark currents �1–2 nA for MBE structures and5–10 nA for LPE structures� and substantially different dif-ferential resistances �4�109 and 5�107 �, respectively�.For MBE structures at low biases, the dark current is limitedby the diffusion current and the SRH-type current outside then-p junction, and, in LPE structures, the contribution of thecurrents through the trap in the depletion region is essential.With reverse biases greater than −0.25 V, the dark currentsof the photodiodes were determined by tunnelling and by

771 J. Opt. Technol. 76 �12�, December 2009

thermal generation from the trap levels. Interband tunnelling,as well as other recombination mechanisms, make virtuallyno contribution at the biases used here. It is shown that thestructures studied here have characteristics limited in prac-tice by the diffusion mechanism of current transport for idealdiodes. Such characteristics make it possible to implementPDDs in the background-limited regime.

A comparison of the characteristics of the two types ofstructures �see Table I� shows that the electron concentra-tions in the n region are somewhat larger in an LPE structurethan in MBE structures. In this case, the concentrations oftrapping centers are higher by an order of magnitude, whilethe lifetimes in the depletion region are an order of magni-tude lower, while they are lower by 3 orders of magnitude inthe quasi-neutral regions. The variband potential in a CdH-gTe HEL with an MBE structure makes it possible to in-crease the effective lifetime by reducing the influence of sur-face recombination. The ion-implantation regimes make itpossible to obtain an n+-n−-p-type structure with an n-p junc-tion displaced into the n region, where high values of thelifetime of the carriers and low concentrations of the recom-bination centers are observed because of the compensation ofthe mercury vacancies.

a�Email: gumenjuk@isp.kiev.ua

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