Frequency Response Optimization of Dual Depletion InGaAs/InP PIN Photodiodes

Transcription

1 PHOTONIC SENSORS / Vol. 6, No. 1, 216: 63 7 Frequency Response Optmzaton of Dual Depleton InGaAs/InP PIN Photododes J. M. Torres PEREIRA and João Paulo N. TORRES * Insttuto de Telecomuncações, Insttuto Superor Técnco-Unversdade de Lsboa, Lsboa, Portugal * Correspondng author: João Paulo N. TORRES E-mal: joaotorres@st.utl.pt Abstract: The frequency response of a dual depleton p--n (PIN) photodode structure s nvestgated. It s assumed that the lght s ncdent on the N sde and the drft regon s located between the N contact and the absorpton regon. The numercal model takes nto account the transt tme and the capactve effects and s appled to photododes wth non-unform llumnaton and lnear electrc feld profle. Wth an adequate choce of the devce s structural parameters, dual depleton photododes can have larger bandwdths than the conventonal PIN devces. Keywords: PIN photododes; dual depleton; frequency response; modelng Ctaton: J. M. Torres PEREIRA and João Paulo N. TORRES, Frequency Response Optmzaton of Dual Depleton InGaAs/InP PIN Photododes, Photonc Sensors, 216, 6(1): Introducton The photodode s one of the most mportant devces n an optcal communcaton system. The p--n (PIN) structure s wdely used because t has good frequency response, low nose, and hgh senstvty. For long wavelength applcatons, the materals most commonly used are: InP, for the N and P contact regons, and In.53 Ga.47 As, for the near ntrnsc absorpton regon [1]. The choce of ths partcular ternary semconductor s determned by ts hgh absorpton coeffcent n the 1. µm 1.6 µm wavelength range, because t s lattce matched to InP. Expermental work and theoretcal work have shown that there s an upper lmt for the PIN photodode s bandwdth, whch has resulted from the nterplay between the transt tme and the capactve effects [2, 3]. Addtonally, the bandwdth-quantum effcency product s nearly constant for a wde range of absorpton regon lengths, takng values of the order of tens of GHz. The conventonal PIN photodode s therefore not sutable for the last generaton communcaton systems wth hgh bt rate. In order to ncrease the devce s bandwdth and the bandwdth-quantum effcency product, the capactve effects should be reduced. Towards ths goal, a new structure has been proposed whch s bascally a PIN structure wth an addtonal layer of ntrnsc InP next to the absorpton layer of InGaAs [4]. In fact, the smaller permttvty of InP, compared wth that of InGaAs, s responsble for a decrease n the structure s total capactance. Some prelmnary work has shown that better bandwdths may be obtaned wth ths structure and they depend on the locaton of the drft layer, relatve to the contacts, and on the drecton of the ncdent lght [5]. It was reported that the best structures have the drft layer placed next to the N contact and the lght should be ncdent on the N sde. The publshed results assume that the photo Receved: 11 November 215 / Revsed: 8 December 215 The Author(s) 215.Ths artcle s publshed wth open access at Sprngerlnk.com DOI: 1.17/s Artcle type:regular

2 64 Photonc Sensors generated carrers move wth ther drft saturaton velocty n the absorpton and drft regons. In ths work, a very general model s used whch enables us to compute the devce s bandwdth for any electrc feld profle n the absorpton and drft regon,.e, for spatal varyng carrer s veloctes. The results may be used to optmze the devce s bandwdth regardng ts dmensons and bas voltage. 2. Devce structure The structure under nvestgaton s shown n Fg. 1. It conssts of two hghly doped p + and n + contacts of InP, one regon of ntrnsc InP (D) wth length d, placed next to the n + contact, and the other regon of lghtly doped In.53 Ga.47 As (A) wth length a. The lght, ncdent on the n + sde, beng n the wavelength range 1. µm 1.6 µm, s only absorbed by the ternary semconductor because the photon energy s lower than the energy band gap of InP. Under normal operaton, the devce s reverse based n such a way that the electrc feld extends over the absorpton and drft regons, A and D layers, respectvely, and s responsble for the transport of the optcal generated electrons to the n + contact and holes to the p + contact. Φ n + InP InP In.53Ga.47As D d n d+x 1 A d+x d+ a Fg. 1 Schematc of the photodode structure under nvestgaton. 3. Modelng The frequency response of the dual depleton PIN photodode s computed by consderng the transt tme and the capactve effects. The transt tme effects are assocated wth the transport, by the electrc feld n the absorpton and drft regons, of the optcal generated electrons and holes. These p + InP x effects depend manly on the carrer s drft velocty and the length of the absorpton and drft regons. The capactve effects are due to the juncton capactance and other parastc capactances related to the contact pad and package. By reducng the length of the devce, the transt tme decreases, and the capactance ncreases. Therefore, for short devces, the bandwdth s manly dependent on the capactve effects, whereas, for long devces, t s transt tme lmted. There wll be an optmum length where the bandwdth reaches a maxmum. Around ths maxmum, both the capactve and the transt tme effects play mportant roles. 3.1 Transt tme effects Regardng the transt tme effects, the frequency response s calculated by combnng the coeffcents derved from a matrx formulaton, followng the analytcal soluton of the contnuty equatons n the drft and absorpton regons [6]. The analytcal solutons can be obtaned only for constant drft carrer veloctes,.e., when the electrc feld s constant. In general, ths s not the case, and therefore a new approach has been mplemented, whch enables us to treat stuatons nvolvng arbtrary electrc feld profles [7]. In ths case, the partcular regon s dvded nto several layers, wth each layer beng assgned a constant electrc feld. Thus, t s possble to obtan analytcal solutons for each of these layers, and by combnng the coeffcents of every layer, t s possble to calculate the frequency response of the whole structure. The accuracy of the results depends on the number and sze of the layers. In ths work, the electrc feld s assumed to be constant n the drft regon and to vary lnearly n the absorpton regon. The contnuty of the dsplacement vector at the boundary of the two regons establshes the relatonshp between the correspondng electrc felds. It s also assumed, n our dervaton, that dffuson and trappng of carrers are neglgble and the lght ntensty s not hgh enough to cause

3 J. M. Torres PEREIRA et al.: Frequency Response Optmzaton of Dual Depleton InGaAs/InP PIN Photododes 65 saturaton or screenng effects. In the frequency doman, the electron and hole current denstes n the th layer, J p (x,ω) and J n (x,ω), respectvely, obey the followng contnuty equatons [7]: ω djn ( x, ω) Jn ( x, ω) = + G ( x, ω) vn dx (1) ω djp ( x, ω) Jp ( x, ω) = + G ( x, ω) v dx (2) p where v n and v p are the electron and hole drft veloctes, respectvely, and G (x,ω) refers to the electron-hole optcal generaton rate gven by ( x d ) G ( x, ω) =. (3) α ( x d ) qαφ1 e ( d x a + d) The parameter α s the absorpton coeffcent, q s the magntude of the electron charge, φ 1 s the ampltude of the snusodal nput optcal flux component, and a s the wdth of the absorpton regon. By solvng the contnuty (1) and (2), the th layer may then be represented by a set of lnear response coeffcents T, S, R and D. The quanttes T, S are related to the electron and hole current denstes through the equatons J p( x) J p( x 1) = T + S (4) Jn( x) Jn( x 1) wth Tpp Tpn Sp T = and S =. (5) Tnp Tnn Sn The matrx T s called the current transfer matrx, and the vector S represents the contrbuton to the current due to the optcal sources. The quanttes R and D are obtaned from the equaton J p( x 1) T p( ω) = S + D (6) Jn( x 1) where p(ω) s called the partal electrode current gven by p( ω) = J n( x, ω) + J p( x, ω) dx. (7) The quantty D s a scalar related to the optcal T sources whereas R = Rp R n determnes the proportonalty between the left-hand termnal currents and p(ω). The four lnear response coeffcents may be used now to compute the correspondng response coeffcents of the multlayer structure by followng a smple set of rules: T+ 1, = T+ 1T S+ 1, = S+ 1 + T+ 1S (8) T T T R = R T + R + 1, + 1 T + 1, = R+ 1 S D D D where subscrpts (), (+1), and (+1, ) refer to the th layer, (+1)th layer, and the unon of the two layers, respectvely. The frequency response s obtaned from [6] I ( ω) = δ ( ω) ( a + d) (9) where the response scalar δ (ω) s gven by δω ( ) = D RS n n Tnn. (1) The quanttes D, R n, S n, and T nn, for the multlayer structure, are obtaned by repeated applcaton of (8). Solvng (1) and (2) usng (3) and by relatng the current denstes as n (4), we are able to obtan T and S. For the drft regon, ωτ dp e TD = ωτ S D = (11) dn e and for the th layer of the absorpton layer, ωτp e T = ωτ n e (12) f ( ωτ α α x ) p S = qαφ e 1 f ( ωτ α n ) wth τ dn = d /v dn, τ dp = d /v dp, τ n = /v n, τ p = /v p, and f(θ)=(1 e θ )/θ beng τ dn, τ n, τ dp, τ p the electron and hole transt tme n the drft and th layer. The quanttes R and D are obtaned from (6) takng nto account (7). For the drft regon, f ( ωτ ) dp R D = d DD = (13) f ( ωτ dn ) and for the th layer of the absorpton layer,

4 66 Photonc Sensors R = f f D qαφ e ( ωτ p ) ( ωτ ) 2 α ( x) = 1 ( α ) f ( ωτ ) f ( α ) f ( ωτ p ) f n. α + ωτ n α ωτ p n (14) In the drft regon, the electron and hole veloctes, for each electrc feld value, are taken or extrapolated from a table obtaned from typcal InP velocty-feld plots [8]. For the InGaAs, the electron and hole drft veloctes are related to the electrc feld by two emprcal expressons [9]: γ γ vn( E) = ( µ ne+ βv n E )/1 ( + βe ) (15) v ( E) = v tanh µ E/ v ( ) p p p p where µ n and µ p are the electron and hole mobltes, v n and v p are the electron and hole saturaton veloctes,.e., the drft veloctes for hgh electrc felds, and β and γ are adjustng constants, β = (m/v) 2.5 ; γ =2.5 (Fg. 2). Drft velocty ( 1 5 m/s) Electron Hole In.53Ga.47As 5 1 Electrc feld (MV/m) Fg. 2 Electron and hole drft veloctes versus electrc feld for In.53Ga.47As. The electrc feld n the absorpton regon may be expressed by [1] 2U d U1 U d Ex ( ) = 2 ( x d ) + a a (16) ( U1 > Ud ; x d) wth U 2 / ( 2 d = qn a ε n), U d s called the punch-through voltage, U 1 s the reverse bas voltage n the absorpton regon, N s the resdual donor concentraton n the absorpton regon, and ε n s the InGaAs electrc permttvty. A typcal electrc feld profle along the drft and the absorpton regon s shown n Fg. 3. t=3µm U 1=1V a/ t=.7µm Fg. 3 Electrc feld profle along the photodode structure. 3.2 Capactve effects The capactve effects are ncluded n the model by usng the small sgnal equvalent crcut of the PIN photodode [2], as shown n Fg. 4. It conssts of a seres resstance R S, a leakage resstance R d, a load resstance R L, a juncton capactance C 1, and a parastc capactance C p. The juncton capactance takes nto account the capactances due to the drft, C D, and the absorpton, C A, regons and may be wrtten as CD CA A A C1 = wth CD = εd ; CA = εn (17) C + C D A d a where A s the cross sectonal area of the devce, and ε D and ε n are the electrc permttvtes of InP and In.53 Ga.47 As, respectvely. R S I 1 R d C 1 C p Fg. 4 Equvalent crcut model of the PIN photodode consderng the seres and leakage resstance. The current source I 1 s drectly related to the transt tme lmted frequency response gven by (9), and the output current I may be expressed as I = HRC I1 where H RC s the transfer functon assocated wth the capactve effects whch, neglectng R d, may be wrtten as R L I

5 J. M. Torres PEREIRA et al.: Frequency Response Optmzaton of Dual Depleton InGaAs/InP PIN Photododes 67 H RC 1 = 2 ω RRCC + ω( C R + R + RC ) + 1. ( ) L S p 1 1 L S L p (17) The frequency response of the devce may then be obtaned by the product of (9) and (17) [2]. 4. Results and dscusson The smulatons use the materal parameters from Table 1. the best frequency response s obtaned for devces wth an absorpton regon wth a length that s about half of the total length. For larger absorpton regon lengths, the frequency response s determned by the transt tme effects, whereas for shorter absorpton regon lengths, the capactve effects become domnant. In both cases, a 3-dB bandwdth decrease s observed. Table 1 Materal parameters at 3 K. Parameters Unts In.53 Ga.47 As InP Absorpton coeffcent (α) (λ = 1.3 µm) m Electron saturaton velocty (v nl) m/s Hole saturaton velocty (v pl) m/s Electron moblty (µ n ) m 2 V 1 s Hole moblty (µ p ) m 2 V 1 s 1.42 Electrc permttvty (ε) F/m 14.1 ε ε The photododes are assumed to have an absorpton regon wth a donor concentraton N = 1 21 m 3. The devces are assgned an area of m 2, a parastc capactance of F, and a load resstance of 5 Ω [2]. In the calculatons, the absorpton regon s dvded nto 4 layers. Frequency response (db) t=3 µm U 1=1 V a/ t=.2 a/ t=.5 a/ t= f f Fg. 5 Frequency responses for t =3 µm, U 1 =1 V, and several values of a / t, f = 1 GHz. The frequency responses are represented n Fgs. 5 and 6 and show the expected behavor of a low pass flter. The normalzaton frequency f s taken as 1 GHz. For a fxed total length of 3 µm (Fg. 5), Fg. 6 Frequency responses for a / t =.5, U 1 =1 V, and several values of t, f = 1 GHz. In Fg. 6, when the rato a / t =.5, the frequency response s better when the total length decreases from 3 µm to 1 µm whch means that, n ths case, the frequency response s manly transt tme lmted, and for smaller a, the transt tme decreases. Fgure 7 shows the 3-dB devce s bandwdth, B, as a functon of the rato a / t, for a bas voltage across the absorpton regon U 1 =1 V and several values of the total length t. Ths bas voltage value s chosen to ensure that both the drft and the absorpton regons are fully depleted. For t 1 µm, the curves have a maxmum for a certan value of a / t, whch means that the ncluson of a drft regon ncreases the bandwdth compared wth the value obtaned for the conventonal PIN devce ( a / t 1). A observed decrease n bandwdth for devces wth t > 1 µm shows that the transt tme effects are domnant. For very short devces, t =.5 µm, there s no vsble maxmum because the bandwdth s determned by the capactve effects. It s mportant to nvestgate how the bandwdth

6 68 Photonc Sensors relates to the responsvty and f the optmzed double depleton structure s better than the conventonal PIN structure. 29 GHz and s obtaned for a devce 1 µm long wth an absorpton regon wdth about half of that length. Fg. 7 Bandwdth versus a / t. In the calculatons of the responsvty, the reflectvty at the nterfaces s neglected, whch assumes that an antreflecton coatng has been deposted on the n + contact. In ths case, the responsvty may be wrtten as ( μm ) ( 1 a e α ) ( A/W ) λ S = (18) whch shows that, for a fxed wavelength, the responsvty ncreases wth the length of the absorpton regon. Therefore, there s a compromse between the bandwdth and responsvty. The plot bandwdth-responsvty s shown n Fg. 8. It can be seen that for the dual depleton structure, wth the total length of 1 µm, the bandwdth s always hgher than the one obtaned for the PIN devce wth the same responsvty. The results show that for an optmzed devce the dual depleton structure s better than the PIN structure wth a responsvty that s less than.7 A/W. It can be seen that for the maxmum bandwdth of 29 GHz, the responsvty s around.47 A/W. Fgure 9 shows the maxmum bandwdth versus total length for devces wth bas voltages U 1 = 6 V and U 1 = 1 V. The bandwdth values n Fg. 9, for U 1 = 1 V, correspond to the maxmum of the curves shown n Fg. 7, for several values of t. The absolute bandwdth maxmum s seen to be about Fg. 8 Bandwdth versus responsvty for dual depleton structures wth several t and for the conventonal PIN structure. By decreasng the voltage from 1 V to 6 V, the bandwdth only changes when t >1 µm, because below ths value, t s manly dependent on the capactve effects. The observed hgher bandwdth values, for lower voltages, may be explaned n terms of the carrer velocty-electrc feld type of dependence for these materals (Fg. 2). Ths fgure shows that lower electrc feld values, wthn a certan range, are responsble for hgher electron veloctes and therefore lower transt tme. Fg. 9 Maxmum bandwdth versus total length for U 1 = 6 V and U 1 = 1 V. Fgure 1 shows the maxmum bandwdth versus total length for devces wth several cross-sectonal areas. It s observed that when the area changes from 1 µm 2 to 1 µm 2, the optmzed bandwdth may change from 22 GHz up to 58 GHz due to a decrease n the devce s juncton capactance [3].

7 J. M. Torres PEREIRA et al.: Frequency Response Optmzaton of Dual Depleton InGaAs/InP PIN Photododes 69 Bmax (GHz) µm 2 1 µm 2 1 µm t (µm) U 1 = 6 V These results show a clear mprovement compared wth those for the conventonal PIN [3]. Fg. 1 Maxmum bandwdth versus total length for several areas, U 1 = 6 V. The contour plot of the constant bandwdth, related to a and d, for U 1 = 6 V and A = 5 µm 2, s shown n Fg. 11. From ths fgure, t s seen that the maxmum bandwdth of about 29 GHz may be obtaned for devces approxmately 1 µm long wth a.5 µm absorpton regon length. For the same length, f the area of the devce s decreased, the capactance also decreases, and an ncrease n the devce s bandwdth s expected [3]. Fg. 11 Contour plot of the constant bandwdth, related to a and d, for U 1 = 6 V and A = 5 µm 2. The contour plot of Fg. 12, obtaned for A = 1 µm 2 and U 1 =6 V, ndcates that the bandwdth of 58 GHz may be obtaned for a devce approxmately.5 µm long wth a.25 µm absorpton regon length. Fg. 12 Contour plot of the constant bandwdth, related to a and d, for U 1 = 6 V and A = 1 µm Conclusons The numercal smulaton of the frequency response of dual depleton InGaAs/InP PIN photododes shows that, for a fxed total length of the devce, there s a value of the absorpton length that maxmzes ts bandwdth. Ths value s seen to be a consequence from the nterplay between the transt tme n the drft and absorpton regon and the capactve effects. For short devces, the maxmum bandwdth s seen to be mostly ndependent of bas voltage because the capactve effects are domnant. The bandwdth may be optmzed by an adequate choce of the absorpton and drft regon lengths. The optmzed bandwdth values range from 22 GHz up to 58 GHz when the cross-sectonal area of the devce decreases from 1 µm 2 to 1 µm 2, and they are obtaned for t = 1 µm, a =.5 µm and t =.5 µm, a =.25 µm, respectvely. The optmzed dual depleton structure s seen to have a larger bandwdth than the conventonal PIN structure wth the same responsvty.

8 7 Photonc Sensors Open Access Ths artcle s dstrbuted under the terms of the Creatve Commons Attrbuton 4. Internatonal Lcense ( lcenses/by/4./), whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded you gve approprate credt to the orgnal author(s) and the source, provde a lnk to the Creatve Commons lcense, and ndcate f changes were made. References [1] T. P. Pearsall, Ga.47 In.53 As: a ternary semconductor for photodetector applcatons, IEEE Journal of Quantum Electroncs, 198, 16(7): [2] Y. G. Wey, K. Gboney, J. Bowers, M. Rodwell, P. Slvestre, P. Thagarajan, et al., 11 GHz GaInAs/InP double heterostructure p--n photodetectores, Journal of Lghtwave Technology, 1995, 13(7): [3] C. M. C. Fernandes and J. M. T. Perera, Bandwdth modelng and optmzaton of PIN photododes, n 211 IEEE Internatonal Conference on Computer as a Tool (EUROCON), Lsbon, pp. 1 4, 211. [4] F. J. Effenberger and A. M. Josh, Ultrafast, dual-depleton regon, InGaAs/InP p--n detector, Journal of Lghtwave Technology, 1996, 14(8): [5] C. C. Fernandes and J. T. Perera, Frequency response analyss of dual depleton PIN photododes, n the 12th Portuguese-Spansh Conference on Electrcal Engneerng (XIICLEEE), Ponta Delgada, pp. 1 4, 211. [6] J. N. Hollenhorst, Frequency response theory for multlayer photododes, Journal of Lghtwave Technology, 199, 8(4): [7] J. M. T. Perera, Modellng the frequency response of p+inp/n-ingaas/n+inp photododes wth an arbtrary electrc feld profle, COMPEL The Internatonal Journal for Computaton and Mathematcs n Electrcal and Electronc Engneerng, 27, 26(4): [8] C. Hammar and B. Vnter, Calculaton of the velocty-feld characterstc of n-inp, Sold State Communcaton, 1972, 11(5): [9] M. Dentan and B. D. Cremoux, Numercal smulaton of the nonlnear response of a p--n photodode under hgh llumnaton, Journal of Lghtwave Technology, 199, 8(8): [1] J. B. Radunovc and D. M. Gvozde, Nonstatonary and nonlnear response of a p--n photodode made of a two-valley semconductor, IEEE Transacton on Electron Devces, 1993, 4(7):