IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 54, NO. 8, AUGUST 2007 2051

Effect of Dead Space on Low-Field AvalancheMultiplication in InP

L. J. J. Tan, J. S. Ng, Member, IEEE, C. H. Tan, Member, IEEE, M. Hopkinson, andJ. P. R. David, Senior Member, IEEE

Abstract—A systematic study of avalanche multiplication be-havior in InP has been performed on a series of diodes withavalanche region widths w ranging from 2.50 to 0.08 µm. The localmodel for impact ionization is found to increasingly overestimatethe multiplication at low electric fields as w decreases due to thepresence of dead space. The suppression of the multiplication canbe modeled accurately by applying a simple correction for theinjected carrier dead space to the local model, which enables themultiplication to be accurately predicted over a wide range ofavalanche region widths.

Index Terms—Breakdown, dead space, heterojunction bipolartransistors, impact ionization, multiplication.

I. INTRODUCTION

IMPACT ionization, which occurs at high electric fieldsin semiconductors, often limits the maximum voltage that

can be applied in a device. For example, impact ionizationevents initiated by electrons in the InP collector of doubleheterojunction bipolar transistors (DHBTs) can limit the powerperformance of these devices due to the hole feedback effect[1], which causes breakdown in DHBTs even at very lowcollector multiplication factor.

In the conventional local model for impact ionization, wherethe ionization behavior of carriers depends solely on the localelectric field, avalanche multiplication can be calculated ifthe electric field profile, carrier injection profile, and impactionization coefficients (α for electrons and β for holes) areknown [2]. However, in submicrometer structures such as thatin the collector region of a DHBT, the effects of nonlocal carriertransport on avalanche multiplication can become significant.It has been shown in other submicrometer III–V materials [3],[4] that the conventional local model significantly overestimatesavalanche multiplication at low multiplication factors (M < 2).This effect was attributed to the dead space d, i.e., the minimumdistance a carrier must travel to acquire sufficient energy fromthe electric field to initiate an impact ionization event. Althoughmodern InP DHBTs have more complex structures than thesimple p-i-n studied in this brief, a reduced multiplication factorcan also be expected in DHBTs.

Early works on determining InP ionization coefficients wereperformed by Cook et al. [5], Armiento and Groves [6], and

Manuscript received November 15, 2006; revised March 19, 2007. Thereview of this brief was arranged by Editor Y.-J. Chan.

The authors are with the Department of Electronic and Electrical En-gineering, The University of Sheffield, S1 3JD Sheffield, U.K. (e-mail:j.p.david@sheffield.ac.uk).

Digital Object Identifier 10.1109/TED.2007.900010

Umebu et al. [7] using diodes with several micrometer thickavalanche regions. Since the carrier dead space was relativelyinsignificant in these diodes, the ionization behavior of thecarriers can be assumed to be purely field dependent, whichenables the ionization coefficients to be deduced from Me andMh, i.e., the multiplication due to pure injection of electronsand holes, respectively. More recently, Yuan et al. measuredMh and hole-initiated excess noise factors Fh in a series ofsubmicrometer InP diodes [8]. Saleh et al. [9] later obtaineda set of ionization coefficients and threshold energies, whichcharacterize dead spaces, for electrons and holes by fittingto the experimental data in [8]. However, since no Me andelectron-initiated excess noise factors Fe data were availablein [8], the parameters in [9] obtained for electrons may notbe accurate, potentially affecting predictions for breakdownbehavior in n-p-n DHBT devices. Furthermore, the field rangecovered by Yuan et al. [8] was limited to between 390 and620 kV/cm.

In this brief, pure Me and Mh were measured from a se-ries of InP diodes with avalanche region widths ranging from2.50 to 0.08 µm, which covers a large electric field rangefrom 180 to 950 kV/cm. Using the experimental data, weassess the accuracy of local model predictions for avalanchemultiplication at low electric fields and determine the magni-tude of the dead space using a simple dead space correctiontechnique.

II. STRUCTURE DETAILS

The p+-i-n+ and n+-i-p+ wafers consisted of an i-InPavalanche region of width w and sandwiched by n+ and p+

InP cladding layers. A further p+-n+ wafer was also grown.A total of one p+-n+, seven p+-i-n+, and two n+-i-p+ diodeswere characterized in this brief. Their structural details aresummarized in Table I. Circular mesa devices of 25-, 50-, 100-,and 200-µm radius with annular top contacts for optical accesswere fabricated from the wafers using standard lithographyand wet etching. Capacitance–voltage (C–V ) characteristicswere measured and modeled by solving Poisson’s equation toestimate the doping densities in the p+ and n+ cladding regions,the unintentional doping density in the i-region ni, and thei-region width. The extracted values are also shown in Table I.Secondary ion mass spectroscopy (SIMS) was also performedon w = 0.13 and 0.25 µm diodes, and the deduced dopingprofiles were found to be similar to those obtained from simplethree-region C–V fitting.

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2052 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 54, NO. 8, AUGUST 2007

TABLE ISTRUCTURAL DETAILS OF THE InP DIODES USED IN THIS BRIEF

III. EXPERIMENTAL TECHNIQUE

Pure injection of electrons into the avalanche regions ofp+-i-n+ devices was produced by illuminating the top of thedevices with 542- or 633-nm wavelength light from He–Nelasers focused to a small spot. Multiplication factors werereproducible when the laser spot was focused onto differentareas of the device, indicating that the multiplication and hencebreakdown were uniform over the diode area. The absorptioncoefficients of InP at these wavelengths were such that <1%of the light reaches the avalanche region, which results inessentially pure electron injection for all p+-i-n+ devices. Theresultant photocurrent was measured as a function of reversebias V . Similar measurements were performed on the n+-i-p+

devices to give Mh.To distinguish photocurrent from dark current, phase-

sensitive detection techniques were used, and the multiplicationfactor was given by the ratio of measured photocurrent tothe injected photocurrent. Further details of the measurementtechnique are given in [10].

IV. RESULTS

Fig. 1 shows the typical dark current characteristics for InPdiodes with radius of 100 µm. For diodes with wide avalancheregions, the dark current densities remain below the microam-pere per square centimeter level before increasing rapidly withreverse biases close to the avalanche breakdown voltage (BV).Dark current densities below these levels are dominated bysurface leakage of the unpassivated devices. The avalanche BVhere is arbitrarily defined as the voltage when the dark currentreaches 0.1 mA. BVs of several devices from the same waferwere found to vary by less than 0.1 V and are also givenin Table I. Dark currents for the p+-n+, w = 0.08 µm, andw = 0.13 µm diodes exhibited undesirably large dark current

Fig. 1. (From right to left) Reverse dark current characteristics of 100-µmradius diodes with nominal w of 2.50, 1.20, 0.80, 0.60, 0.55, 0.49, 0.25, 0.13,and 0.08 µm, and a p+-n+ junction.

Fig. 2. Measured (symbols) M − 1 versus reverse bias with (◦) Me forp-n and p-i-n diodes as well as (�) Mh for n-i-p diodes. Fittings using thelocal model (solid lines) with and (dashed lines) without the simple dead spacecorrection are also shown. The diodes have nominal w as described in Fig. 1,but the w = 0.49 µm diode is left out for clarity.

even at low reverse bias. This was attributed to significant band-to-band tunneling current at high electric fields (> 600 kV/cm).

Fig. 2 shows M(V ) − 1 for the InP diodes with radius of100 µm. Measurements were performed on other sized devices,but the multiplication was found to be independent of devicesize. Data for the w = 0.49 µm diode, which are not very dis-similar to those of the w = 0.55 µm diode, are omitted in Fig. 2for clarity. A vertical logarithmic axis is used to clearly showthe onset of avalanche multiplication. Multiplication factors assmall as 1.001 were measured reliably. Multiplication factorsof up to 10 were measured in all except for the p+-n+ andthe w = 0.08 µm diodes. This was due to the high tunnelingcurrents present in these devices. The multiplication for thesetwo diodes appears to saturate at higher values, and this againmay be due to the very high dark tunneling currents in thesedevices.

V. DISCUSSION

Predictions from the local model using the published coeffi-cients of [5] and our experimental data are compared in Fig. 2.

TAN et al.: EFFECT OF DEAD SPACE ON LOW-FIELD AVALANCHE MULTIPLICATION IN InP 2053

The values of w were adjusted to within ±5% of the values ob-tained from C–V measurements to fit the experimental M(V )at large gains. Since the ionization coefficients of Cook et al. donot cover the electric field range for the p+-n+, w = 0.08 µm,and w = 0.13 µm diodes near breakdown, the coefficients wereextrapolated beyond electric fields of 770 kV/cm.

As shown in Fig. 2, the local model using the ionizationcoefficients of [5] is able to accurately predict M(V ) fordevices with w > 0.5 µm at all reverse biases. However, themultiplication of narrower diodes at low biases is overesti-mated. The disagreement arises from using the local modelto predict multiplication in narrow avalanche regions wheredead space effects are significant. Both the C–V fitting andthe SIMS analysis show similar abrupt electric field profiles inthese structures, which suggest that the reduction in avalanchemultiplication was not due to a soft or gradual change in theelectric field profile but rather due to the presence of dead spaceeffects.

A simple dead space correction technique can be applied tothe local multiplication model to account for this dead space.This technique, which accounts for the dead space experiencedby just the injected carriers (rather than all the carriers), hasbeen used successfully to fit the avalanche multiplications ofsubmicrometer Si [10] and InAlAs [4] diodes. The multiplica-tion due to pure electron injection Me is given by [10]

Me = 1 +

x∫

0

(Ne(x′) + Nh(x′)) dx′

where Ne(x) and Nh(x) are the number of ionization events perunit length at x initiated by electrons and holes, respectively.For ideal p+-i-n+ structures with uniform electric field profile,this reduces to [10]

Me =α exp [de(β − α)] − β

α exp [w(β − α)] − α

where de is the electron dead space. Mh can be obtained in asimilar manner by replacing α and de with β and dh. The deadspace can be approximated using the ballistic approximationd = (Eth/q�), where Eth is the effective ionization thresholdenergy, q is the electron charge, and � is the electric field. Thiscorrection works because at low multiplication factors, impactionization events initiated by secondary carriers (whose deadspaces are not accounted for in this technique) are rare. Thecorrection has little effect at higher multiplications (close tobreakdown) compared to the local model because at these highelectric fields, the dead space becomes relatively insignificantcompared to the device avalanche width. This simple deadspace correction only yields satisfactory results for multiplica-tion factors but not for excess noise factors. It should be notedthat the different wafers have different unintentional dopingni, which results in different electric field gradients in thehigh-field region. However, this is not expected to affect thedead space.

Since the p+-n+ and w = 0.08 µm diodes do not have con-stant electric field profiles (see Table I), a closed-form solutionis impossible. Instead, we use numerical methods described

Fig. 3. (◦) Experimental and predicted voltages calculated using the localmodel (solid lines) with and (dashed lines) without the simple dead spacecorrection, which is required to achieve a Me of 1.01 for the p-i-n diodes usedin this brief. (Insert) Percentage of dead space to avalanche region width at Me

of 1.01 for the p-i-n diodes.

in [11] to solve for Me and Mh with the impact ionizationcoefficients of Cook et al. [5]. Effective threshold energies of2.8 eV for electrons and 3.0 eV for holes were found to give thebest agreement with the experimental M(V ). Although thesethreshold energies have been used as a fitting parameter, whenused in conjunction with the coefficients of Cook et al. [5],these threshold energies are comparable with those reported forother III–V materials [12], [13].

The multiplication factors determined by the local modelwith and without the simple dead space correction are com-pared in Fig. 2. The correction has negligible or marginal effecton the predicted multiplication for the w = 2.50, 1.25, and0.80 µm diodes, as expected, because for these diodes the deadspace is negligible compared to the avalanche region width.However, the impact of the correction becomes more significantas the avalanche region width decreases to below 0.50 µm. Withthe correction, accurate predictions of multiplication factors foreven the narrowest device have been achieved. Predicted BVshowever for the p+-n+ and the w = 0.08 µm diodes disagreewith the experimental values, possibly due to errors in theextrapolated ionization coefficients of Cook et al. at very highelectric fields and high dark tunneling currents.

Fig. 3 plots the applied voltage required to achieve Me of1.01 for the p+-i-n+ diodes used in this brief. Since no i-regionwidth is associated with the p+-n+ diode, we assume a valueof 0.05-µm p+-i-n+ diode, which would achieve Me of 1.01for the same applied voltage. The predictions using the localmodel with and without the simple dead space correction arecompared to the experimental values in Fig. 3. The predictionswith the correction agree well with the experimental valuesfor all widths. However, the predictions without the simpledead space correction show increasing disagreement as theavalanche regions become narrower. This is highlighted in theinsert graph of Fig. 3, which shows the percentage of deadspace to avalanche region width at Me of 1.01. The dead spacebecomes a significant fraction of the avalanche region width

2054 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 54, NO. 8, AUGUST 2007

as the avalanche region < 0.5 µm. In very narrow avalancheregions (< 50 nm), a 100% increase in applied voltage can betolerated as compared to the local model predictions.

VI. CONCLUSION

The presence of dead space has been demonstrated to sup-press the multiplication in thin submicrometer InP avalanchingstructures. The local model has been shown to underestimatethe voltage that can be applied before the onset of appreciablemultiplication. A simple correction for the carrier dead spaceapplied to the local model with published ionization coefficientsenables even small multiplication factors to be accurately pre-dicted in narrow InP avalanche regions, such as collectors ofDHBTs.

REFERENCES

[1] W. Liu, Handbook of III–V Heterojunction Bipolar Transistors.Hoboken, NJ: Wiley, 1998, pp. 287–293.

[2] G. E. Stillman and C. M. Wolfe, “Avalanche photodiodes,” in Semicon-ductors and Semimetals, vol. 12, R. K. Willardson and A. C. Beer, Eds.New York: Academic, 1977, pp. 291–293.

[3] D. J. Massey, J. P. R. David, C. H. Tan, B. K. Ng, G. J. Rees, D. J. Robbins,and D. C. Herbert, “Impact ionization in submicron silicon devices,”J. Appl. Phys., vol. 95, no. 10, pp. 5931–5933, May 2004.

[4] Y. L. Goh, D. J. Massey, A. J. R. Marshall, J. S. Ng, C. H. Tan,W. K. Ng, G. J. Rees, M. Hopkinson, J. P. R. David, and S. K. Jones,“Avalanche multiplication in InAlAs,” IEEE Trans. Electron Devices,vol. 54, no. 1, pp. 11–16, Jan. 2007.

[5] L. W. Cook, G. E. Bulman, and G. E. Stillman, “Electron and holeimpact ionization coefficients in InP determined by photomultiplicationmeasurements,” Appl. Phys. Lett., vol. 40, no. 7, pp. 589–591, Apr. 1982.

[6] C. A. Armiento and S. H. Groves, “Impact ionization in (100)-oriented,(110)-oriented and (111)-oriented InP avalanche photodiodes,” Appl.Phys. Lett., vol. 43, no. 2, pp. 198–200, Jul. 1983.

[7] I. Umebu, A. N. M. M. Choudhury, and P. N. Robson, “Ionization coeffi-cients measured in abrupt InP junctions,” Appl. Phys. Lett., vol. 36, no. 4,pp. 302–303, Feb. 1980.

[8] P. Yuan, C. C. Hansing, K. A. Anslem, C. V. Lennox, H. Nie,A. L. Holmes, B. G. Streetman, and J. C. Campbell, “Impact ionizationcharacteristics of III–V semiconductors for a wide range of multiplicationregion thickness,” IEEE J. Quantum Electron., vol. 36, no. 2, pp. 198–204,Feb. 2000.

[9] M. A. Saleh, M. M. Hayat, P. P. Sotirelis, A. L. Holmes, J. C. Campbell,B. E. A. Saleh, and M. C. Teich, “Impact ionization and noise characteris-tics of thin III–V avalanche photodiodes,” IEEE Trans. Electron Devices,vol. 48, no. 12, pp. 2722–2731, Dec. 2001.

[10] D. J. Massey, G. J. Rees, and J. P. R. David, “Temperature dependenceof impact ionization in submicron silicon devices,” IEEE Trans. ElectronDevices, vol. 53, no. 9, pp. 2328–2334, Sep. 2006.

[11] M. M. Hayat, W. L. Sargeant, and B. E. A. Saleh, “Effect of dead space ongain and noise in Si and GaAs avalanche photodiodes,” IEEE J. QuantumElectron., vol. 28, no. 5, pp. 1360–1365, May 1992.

[12] S. A. Plimmer, J. P. R. David, R. Grey, and G. J. Rees, “Avalanchemultiplication in AlxGa1−xAs (x = 0 to 0.60),” IEEE Trans. ElectronDevices, vol. 47, no. 5, pp. 1089–1097, May 2000.

[13] C. H. Tan, R. Ghin, J. P. R. David, G. J. Rees, and M. Hopkinson, “Theeffect of dead space on gain and excess noise in In0.48Ga0.52P p+-i-n+ diodes,” Semicond. Sci. Technol., vol. 18, no. 8, pp. 803–806,Aug. 2003.

L. J. J. Tan received the B.Eng. degree in electronic and electrical engineeringfrom the University of Sheffield, Sheffield, U.K., in 2003. He is currentlyworking toward the Ph.D. degree in electronic and electrical engineering at theUniversity of Sheffield. His Ph.D. thesis is on InP-based avalanche photodiodesand Geiger-mode avalanche photodiodes.

J. S. Ng (M’99) received the B.Eng. and Ph.D. degrees from the University ofSheffield, Sheffield, U.K., in 1999 and 2003, respectively.

Between 2003 and 2006, she was with the National Centre for III–V Tech-nologies, University of Sheffield, where she was responsible for material anddevice characterization. She is currently a Royal Society University ResearchFellow at the University of Sheffield. Her research interests are avalanchephotodiode, Geiger-mode avalanche photodiode, and material characterization.

C. H. Tan (M’95) received the B.Eng. and Ph.D. degrees in electronic engi-neering from the University of Sheffield, Sheffield, U.K., in 1998 and 2002,respectively.

He is currently a Lecturer in the Department of Electronic and Electrical En-gineering, University of Sheffield. His research activities include experimentaland theoretical investigation of excess noise, breakdown and jitter in Si andIII–V APDs and SPADs, design of high-speed APDs and HPTs, and infraredphotodetectors.

M. Hopkinson received the B.Sc. degree from the University of Birmingham,Birmingham, U.K., in 1985 and the Ph.D. degree from The University ofSheffield, Sheffield, U.K., in 1990.

After an initial postdoctoral position at the University of Warwick, Coventry,U.K., he returned to the University of Sheffield in 1990 to begin work on III–Vmaterials by molecular beam epitaxy. In 2000, he was with Marconi OpticalComponents. In 2002, he returned to the University of Sheffield to becomea Senior Research Scientist and later a Professor within the Department ofElectronic and Electrical Engineering. His research interests are the field ofcompound semiconductor materials and their applications within the fieldof optoelectronics.

J. P. R. David (SM’96) received the B.Eng. and Ph.D. degrees in electronicengineering from the University of Sheffield, Sheffield, U.K.

In 1985, he was with the Central Facility for III–V semiconductors inSheffield, where he was responsible the characterization activity. In 2001, hewas with Marconi Optical Components (now Bookham Technologies). Heis currently a Professor at the University of Sheffield. His research interestsinclude piezoelectric III–V semiconductors and impact ionization in analogueand single-photon avalanche photodiodes. He was an IEEE Lasers and Electro-Optics Society (LEOS) Distinguished Lecturer from 2002 to 2004.