IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 45, NO. 4, APRIL 1998 791

Theory of SiGe Waveguide AvalancheDetectors Operating at m

D. C. Herbert

Abstract— The potential performance of SiGe waveguideavalanche photodiodes is analyzed for operation at a wavelengthof 1.3 �m. It is found that response speeds in excess of 5 Gbit/swith gains of �40 should be readily achievable in the absenceof carrier trapping effects. Analysis of the electron initiatedavalanche current shows an initial low-noise fast pulse due toprimary ionization. This is followed by a noisy tail involvinghole initiated processes. Structures for future experimentalstudy are proposed.

Index Terms—Avalanche photodiodes, optical fibers, multi-quantum wells.

I. INTRODUCTION

T HERE IS now a growing interest in exploiting SiGe toextend the response of Si PIN and APD detectors to

wavelengths of interest for fiber-optic communications. It isenvisaged that for intra-city trunk routes, SiGe detectors oper-ating at 1.3 m which can be integrated with Si circuitry mayhave advantages over conventional III–V devices. Response atshorter wavelengths in the transmissive band of Si waveguidesis also of interest for various waveguide sensors, and opticalinterconnects.

Early work by Temkinet al. [1] indicated appreciable opticalabsorption at m by strained Si Ge withKesanet al. [2] then estimated the absorption constant to be

cm for a multiquantum well structure containingSiGe layers. This absorption constant, although

small compared to values obtainable from direct gap materials,is adequate to generate efficient gigabit response rates inwaveguide geometries. Theoretical estimates of the absorptionconstant have also been published by Navalet al. [3]. Mostwork in this field has used MBE growth, but recent workby Jalali et al. [4], [5] has successfully used rapid thermalchemical vapor deposition for high Ge concentration layers.

The CVD growth [4] demonstrated low dark currents andSplettet al. [6] using MBE growth have considered integrationof detectors and waveguides, again demonstrating low darkcurrents. Most work to date has used mesa structures, butSugiyamaet al. [7] have also demonstrated a planar processusing selective area epitaxy.

Manuscript received June 5, 1997; revised October 29, 1997. The reviewof this paper was arranged by Editor W. Weber.

The author is with the DERA Electronics Division, DERA, Malvern,Worcester, WR14 3PS U.K.

Publisher Item Identifier S 0018-9383(98)02282-5.

In the present paper, we focus on the potential performanceof avalanche photo diodes (APD) and argue that5 Gbit/sresponse should be readily achieveable with avalanche gainsof 40 if carrier trapping effects can be neglected. The ratioof electron and hole ionization coefficients is high in Si, lead-ing to high-speed, low-noise avalanche processes. It should,however, be noted that recent work on the InGaAsP/InAlAssuper lattice diodes [8] has demonstrated low noise avalancheperformance with low dark current, for multiplications up to

25, so that the main advantage of the SiGe device may befor low cost integration.

In previous work [9], we have argued that SiGe multi-quantum-wells (MQW) can be introduced into avalanche zoneswithout incurring a noise penalty. For APD the SiGe layersare used to absorb the radiation, and to avoid hole initiatedionization, it is advantageous to use doping profiles to obtainseparate electric fields across the MQW detection region andthe Si avalanche region. For high Ge concentration layers, thequantum wells can be quite deep (0.4 eV) so that particletrapping in the wells may become significant in limitingperformance. Jalaliet al. [4] indeed suggest that trappingeffects may have been observed in the bias dependence ofquantum efficiency. To minimize trapping, it is possible toincrease the electric field across the SiGe layers until ionizationstarts to be significant. Trapped holes should then have hightunneling escape rates. The high fields may however increasedark current, due to band to band tunneling, and in practicewe expect that some optimum field will exist.

It is also possible to reduce trapping by using step gradingof the SiGe layers to allow sequential tunneling of holesfrom the wells. These various features require experimentalstudy to provide data for detailed theoretical analysis, andwill be sensitive to material quality. In the present paper, weanalyze the evolution of avalanche current and noise for threestructures which we feel could repay a detailed experimentalstudy. The influence of carrier trapping will be analyzed infuture work when experimental data becomes available.

II. STRUCTURES

For simplicity, we assume an absorption constantof40 cm , following the work of Kessanet al. [2]. This requiresa length of waveguide equal to about 500m to absorbthe radiation. This can be reduced to 250m if one end isterminated with a mirror. If we assume a 20-m width ofwaveguide to facilitate coupling to optical fiber and an “I”region of 3 m for the PIN detector, then for a series resistance

0018–9383/98$10.00 1998 IEEE

792 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 45, NO. 4, APRIL 1998

TABLE IDEVICE LAYER STRUCTURES USED IN THESIMULATIONS

of 50 the 3 dB RC cutoff is 20 GHz and the diode willbe avalanche transit time limited.

We consider two double drift structures with a detectionzone consisting of 0.7 m of SiGe MQW in the center ofthe “I” region. A single drift structure with detection zoneadjacent to the P contact is also considered. The verticaldoping profiles for the three structures are given in Table I, andhave been chosen to engineer the electric field distributionsthrough the diodes in various ways. In structure ddapd7, asingle p-doped region is used to switch the electric field froma low to a high value. The low field value is chosen so that nophoto-current induced hole ionization occurs and the structurebehaves as a SAM (Separate absorption and multiplication)device. In structure ddapd6, two p-doped regions are used toincrease the field across the MQW region sufficiently to induceweak ionization, but maintain the main avalanche in the Siadjacent to the N contact. The single drift structure labeledapd8 in Table I has the SiGe MQW absorber placed adjacent to

Fig. 1. Energy relaxing path lengths (12) for Si and Ge.

the P contact layer with the avalanche zone having the samestructure as for the double drift diodes. The “I” region widthand transit time are reduced, but at the expense of capacitance,and simulations indicate the effect on the device speed. Byvarying the magnitude of the p-doping in the double driftstructures, the relative field values can be varied. It would bevaluable to have a series of experiments, varying the doping inthis way, and monitoring the effect on dark current, trappingand noise.

III. T HEORY

The basic avalanche theory for the Si/SiGe system hasalready been published [9]–[11] and only a brief summary isgiven here. By solving the hot carrier Boltzmann equation, theimportant nonlocal effects related to dead space and overshootare included. The theory is also found to give good agreementwith experiment for both GaAs [12]–[14] and Si [11] in thin p-i-n diodes where nonlocal effects can dominate the ionization.The ionization rates (I) are taken in the form

(1)

where denotes the lowest energy gap, is the particleenergy relative to the lowest bandedge, is the thresholdenergy, and is a constant, taken to be independent of theGe concentration. The exponent 4.3 is obtained by fitting thecalculated cross sections obtained by Kane [15]. Thresholdenergies and band gaps are taken from the work of Allamet al.[16]. The local ionization coefficients are obtained by adjustingthe phonon scattering rates to fit experimental data for Si andGe. The resulting energy relaxing path lengths (l2) are shownin Fig. 1. To describe the alloy, the transport parameters areinterpolated between the Si and Ge limits using theoreticalenergy gaps and thresholds in (1). Ionization in the strainedMQW layers is dominated by carrier heating in the thickerSi layers and by the band gaps and the threshold in the SiGe,and is insensitive to the interpolation used [9]. Some allowancefor tunneling in the quantum wells is included using previousmodels developed for GaAs/AlGaAs MQW structures [17].

To calculate the time evolution of avalanche current andnoise we use the semi-analytical trajectory method [18] to

HERBERT: THEORY OF SiGe WAVEGUIDE AVALANCHE DETECTORS 793

(a) (b)

(c) (d)

(e)

Fig. 2. Simulations for structure ddapd6. (a) Conduction band profiles for two values of multiplication. The SiGe MQW is positioned between the twoarrows. (b) Ionization coefficients�1 and �1: The position of the SiGe MQW is indicated by the pulsing of the ionization coefficients between 11 500and 18 500A: (c) Avalanche current as a function of time. At zero time the avalanche is initiated by an electron-hole pair generated at a random positionwithin the MQW detection zone. The calculation used 105 initiating pairs. (d) Development of the excess noise during an avalanche process for variousfinal multiplication values. (e) Excess noise factors.

solve the hot carrier Boltzmann equation, treating the ion-ization as an additional scattering mechanism. The device isdivided into a set of regions, where a region is defined as thedistance over which the potential drops by 52 meV .

Analytical solutions of the Boltzmann equation are constructedwithin each region, and these solutions are matched at theregion boundaries. To study noise, a sequence of solutions isgenerated for each of which a particle originates in one region,

794 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 45, NO. 4, APRIL 1998

(a) (b)

(c) (d)

Fig. 3. Simulations for structure ddapd7 (same rotation as Fig. 1). (a) Conduction band profiles for various values of multiplication. The SiGe MQWis positioned between the two arrows. (b) Ionization coefficients�1 and �1: The SiGe MQW is positioned between the two arrows. (c) Avalanchecurrent. (d) Development of excess noise during an avalanche.

and the corresponding ionization probability is determinedas a function of position. This yields a set of ionizationtrajectories , where labels the re-gion in which the initiating particle originates, areionization coefficients for electrons and holes, respectively,and is the local electric field. It should be noted that

are obtained by solving the Boltzmann equation for unitcurrent, with no allowance made for energy loss in ionizingcollisions. These ionization coefficients therefore differ fromthe conventional definition and show much smaller overshoot.After an ionization event, the particles switch to newtrajectories which are determined by both the position and theresidual kinetic energy.

After computing a full set of , random numbers areused with these probabilities to determine the positions andtimes of ionization events, for a given initiating particle. Theposition of the photo-generated initiating particle is chosenat random within the SiGe MQW. The particles are assumedto move at the saturated drift velocity, and after the initiatingparticle has reached the contact, each of the generated particlesis allowed to propagate and ionize. The procedure is repeated

until all particles have left the diode. Values of the multipli-cation from trials “ ” are stored and after typically 10trials, the excess noise factor is obtained from an ensembleaverage

(2)

The terminal current from the avalanche process is obtainedfrom the average number of particles which exist in the diodeat any given time.

IV. RESULTS

The conduction band profile for sample ddapd6 is shownin Fig. 2(a) for two values of multiplication and Fig. 2(b)shows the ionization coefficients for particles injectedfrom the contact regions. The large ratio is evident in theSi high field layer, and the pulsing of the weak ionizationin the SiGe layers is clear. The structure is designed togive a small ionization in SiGe, which is too weak to affectthe noise. Experimental measurements, varying the relative

HERBERT: THEORY OF SiGe WAVEGUIDE AVALANCHE DETECTORS 795

Fig. 4. Avalanche current for structure apd8.

field magnitudes are now required to study the influence ondark current and trapping. The time evolution of avalanchecurrent is shown in Fig. 2(c). For a multiplication of40,the avalanche lasts for about five transit times. For a 3-mdepletion region, the transit time is s so that apulse repetition rate of 7 Gbit/s should be achievable forthis structure. From the plots it is apparent that the avalanchehas a fast leading edge, which corresponds to the primaryelectron ionization. This is followed by a second peak and along tail which involves hole ionization. The time developmentof the excess noise is shown in Fig. 2(d). The-axis ischosen as multiplication rather than time, though they canclearly be interchanged using a multiplication versus timegraph. It is clear from these plots that for a given valueof multiplication on the -axis, the excess noise is reducedby increasing the electric field (or equivalently, the finalmultiplication). This implies that the long time tail of theavalanche current in Fig. 2(c) is very noisy, containing a highfraction of hole initiated ionization events. To achieve ultra-low-noise avalanche gain it is therefore desirable to applya very high electric field for a short time, possibly with aresonant circuit, or a quenching circuit. The steady state excessnoise factors are shown in Fig. 2(e).

Similar results are obtained for ddapd7. The conductionband profiles in Fig. 3(a) show the two field zones. The ioniza-tion coefficients in Fig. 3(b) demonstrate the SAM nature ofthis structure, and Fig. 3(c) shows that the avalanche processagain completes in about five transit times for multiplicationup to about 50 so that the response speed is very similar toddapd6. The evolution of noise in Fig. 3(d) also shows verysimilar features to ddapd6.

Finally in Fig. 4 we show the development of avalanche cur-rent for structure apd8. The computed ionization coefficientsand excess noise are similar to the other two structures, and arenot shown. The avalanche current shows that the response isslower in terms of transit time; however, the “I” region width(and transit time) has been reduced by about one third keepingthe avalanche zone the same. This implies that there is littlespeed advantage to be gained from removing the nonavalanch-ing drift region from the first two structures and the responsespeed is controlled by the width of the avalanche zone.

V. CONCLUSION

We conclude from these studies that a 5 Gbit/s avalanchephotodiode with a gain of 40 is feasible in the SiGe systemwith very simple fabrication. Detection at 1.3m requireshigh Ge concentration layers, with the consequent potentialfor trapping holes, and we propose a step graded structure tominimize the trapping. The noise calculations indicated thatthe short time initial pulse of ionization has very low noiseand the long time tail of an unquenched avalanche contributesthe major part of the excess noise.

For an unquenched avalanche we expect superior noiseperformance for the SiGe device when compared with III–Vmaterials. It should be noted, however, that recent work on theInGaAsP/InAlAs superlattices claims low noise performance,and a recent paper on thin GaAs p-i-n diodes [19] claims thatthe excess noise is greatly reduced in thin avalanche zones.Our own simulations on GaAs p-i-n diodes show that thenoise reduction in narrow avalanche zones is a consequenceof the dead space associated with each trajectory and isa general phenomenon [20]. The main electrical performanceadvantage of the SiGe APD derives from the low-noise, high-speed avalanche so that as narrower avalanche zones are usedto increase response speed, we can anticipate a reduction inthis advantage. The general cost advantages associated with Siintegration will, however, remain.

REFERENCES

[1] H. Temkin, T. P. Pearsall, J. C. Bean, R. A. Logan, and S. Luryi, “GeSistrained-layer superlattice waveguide photodetectors operating near 1.3micron,” Appl. Phys. Lett.vol. 48, pp. 963–965, 1986.

[2] V. P. Kesan, P. G. May, E. Bassous, and S. S. Iyer, “Integratedwavelength photodetectors using Si/SiGe multiple quantum wells forlong wavelength applications,” inIEDM ’90, 1990, pp. 637–640.

[3] L. Naval, B. Jalali, L. Gomelsky, and J. M. Liu, “Optimization ofSiGe/Si waveguide photodetectors operating at 1.3 micron,”J. Light-wave Technol.,vol. 14, pp. 787–797, 1996.

[4] B. Jalali, A. F. J. Levi, F. Ross, and E. A. Fitzgerald, “SiGe waveguidephotodetectors grown by rapid thermal chemical vapor deposition,”Electron. Lett.vol. 28, pp. 269–271.

[5] B. Jalali, L. Naval, and A. F. J. Levi, “Si-based receivers for opticaldata links,”J. Lightwave Technol.vol. 12, pp. 930–935, 1994.

[6] A. Splett, T. Zinke, K. Petermann, E. Kasper, H. Kibbel, H. J. Herzog,and H. Presting, “Integration of waveguides and photodetectors in SiGefor 1.3 micron operation,”IEEE Photon. Technol. Lett.vol. 6, pp. 59–61,1994.

[7] M. Sugiyama, T. Morikawa, T. Tatsumi, T. Hashimoto, and T. Tashiro,“A selective epitaxial SiGe/Si planar photodetector for Si-basedOEIC’s,” in IEDM, 1995, pp. 583–586.

[8] T. Kagawa, Y. Kawamura, and H. Iwamura, “InGaAsP-InAlAs super-lattice avalanche photodiodes,”IEEE J. Quantum Electron.vol. 28, pp.1419–1423, 1992.

[9] D. C. Herbert, C. J. Williams, and M. Jaros, “Impact ionization andnoise in SiGe multiquantum well structures,”Electron. Lett.vol. 32, pp.1616–1618, 1996.

[10] D. C. Herbert, “A model for transient impact ionization,”Compel II,pp. 413–418, 1992.

[11] , “Impact ionization in Si bipolar devices,”Electron. Lett.vol.31, pp. 334–335, 1995.

[12] , “Breakdown voltage in ultrathin pin diodes,”Semicond. Sci.Technol.vol. 8, pp. 1993–1998, 1993.

[13] S. A. Plimmer, J. P. R. David, D. C. Herbert, T. W. Lee, G. J. Rees,P. A. Houston, R. Grey, P. N. Robson, A. W. Higgs, and D. R. Wight,“Investigation of impact ionization in thin GaAs diodes,”IEEE Trans.Electron Devices, vol. 43, pp. 1066–1072, 1996.

[14] S. Millidge, D. C. Herbert, M. Kane, G. W. Smith, and D. R. Wight,“Non-local aspects of breakdown in pin diodes,”Semiconduct. Sci.Technol.vol. 10, pp. 344–347, 1995.

796 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 45, NO. 4, APRIL 1998

[15] E. O. Kane, “Electron scattering by pair production in silicon,”Phys.Rev.,vol. 159, p. 624, 1967.

[16] I. K. Czaijkowski, J. Allam, A. R. Adams, and M. A. Gell, “Impactionization thresholds in GeSi alloys and strained layers,”J. Appl Phys.vol. 71, pp. 3821–3826, 1992.

[17] D. C. Herbert, “Ionization in GaAs multilayers,”Semiconduct. Sci.Technol.vol. 10, pp. 405–411, 1995.

[18] , “Band structure engineering of hot carrier transport in SiGeheterojunction bipolar transistors,”Semiconduct. Sci. Techol.vol. 7, pp.44–50, 1992.

[19] C. Hu, K. A. Anselm, B. G. Streetman, and J. C. Campbell, “Noise char-acteristics of thin multiplication region GaAs avalanche photodiodes,”Appl. Phys. Lett.vol. 69, pp. 3734–3736, 1996.

[20] D. C. Herbert, “Avalanche noise in submicron pin diodes,”Electron.Lett. vol. 33, pp. 1257–1258, 1997.

D. C. Herbert received the B.Sc. degree in physicsin 1965, and the Ph.D. degree in mathematicalphysics in 1968, both from Imperial College, Lon-don, U.K. He held an S.R.C. research fellowship atBristol University, Bristol, U.K., for two years.

In 1970, he joined the Royal Radar Establish-ment (now the Defence Research Agency), Malvern,Worcester, U.K. Since then, he has worked on semi-conductor physics and device theory with particularinterests in bound exciton luminescence and hotcarrier transport problems. He has been a Visiting

Professor at the University of Newcastle Upon Tyne, Newcastle, U.K., since1984.