An equivalent circuit model for uni-traveling-carrier photodiode

The Journal of China Universities of Posts and Telecommunications September 2009, 16(Suppl.): 40–44 www.buptjournal.cn/xben

An equivalent circuit model for uni-traveling-carrier photodiode LI Xiao-jian1 ( ), ZHANG Ye-jin2, LI Guo-yu1, TIAN Li-lin1 1. Institute of Microelectronics, Tsinghua University, Beijing 100084, China 2. Institute of Semiconductors, Chinese Academy of Science, Beijing 100083, China

Abstract

In this paper, an equivalent circuit model of uni-traveling-carrier photodiode (UTC-PD) is developed. According to the feature of UTC-PD, hole continuity equation is ignored and only electron continuity equation is introduced, which decreases the complexity of the model. The model is based on a simplified structure and can well express the feature of UTC-PD. Several direct current (DC) and alternating current (AC) analyses are performed to test the model, and the results from the model agree well with that of numerical simulation. Keywords photodiode, UTC, circuit model, InGaAs/Inp

1

Introduction

Since its appearance in 1997 [1], UTC-PD has drawn attention of researchers and scientists world widely. Because only electrons are active in the transportation, UTC-PD has a wider bandwidth and can give a higher operation current than the conventional devices like PIN-PD. A large number of experiments have been done for the investigation of UTC-PD [2–4]. Many researches which include finding new materials, designing new structures and optimizing the structure parameters have been done to improve the performance of UTC-PD [5–7]. Now this new device has already been used in industry field. With the scale of microwave photonics system getting larger and the structure of it getting more complex, difficulty for system design increases greatly. The CAD tools and accurate circuit models have become essential for designers. However, modeling for UTC-PD hasn’t been well developed. Ref. [8] has once developed a circuit model of near-ballistic uni-traveling-carrier photodiodes (NBUTC-PD) using experimental results (S parameters). In this paper, a UTC-PD circuit model is derived by directly solving the electron continuity Received date: 29-06-2007 Corresponding author: LI Xiao-jian, E-mail: [email protected] DOI: 10.1016/S1005-8885(08)60360-X

equation. Numerical simulations, which solve the Poisson’s equation and electron/hole continuity equations self-consistently, have been done for comparison. Our work is based on the previous work of Refs. [9,10].

2 Modeling 2.1

Typical UTC-PD

For demonstration, a typical structure of UTC-PD is shown in Fig. 1 with its energy band [2] which is under reverse bias voltage. UTC-PD mainly contains the following layers: the barrier layer which makes all the electrons collected by the collection layer, the absorption layer where light emitted electron-hole pairs generate, the spacer layer which smoothes the energy band, the cliff layer which controls the potential profile and the collection layers which collects the electrons generated in absorption layer. Since the electron-hole pairs are generated in absorption layer and reverse bias voltage will prevent holes from diffusing into the collection layer, the transportation is dominated by electrons. Thus UTC-PD is faster than conventional photodiodes.

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LI Xiao-jian, et al. / An equivalent circuit model for uni-traveling-carrier photodiode

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setup the UTC-PD circuit model as shown in Fig. 3. In the circuit model, Na, Nb, Nc are the three ports. Pin is the optical input power, and Vb is the reverse bias voltage. Id and Ie are dark current and diffusion current through the pn junction, respectively. Rd is the parallel parasitic resistance. Cs is the parasitic capacitance. Cj=İ0İsA/Wc represents the capacitance brought by i collection layer (where A is the device area). Rs is the series parasitic resistor. Rt and Ct are artificial components used for imitating the electron transit time in p absorption layer.

Fig. 1 A typical structure of UTC-PD and its energy band structure

2.2

(a) Simplified structure of UTC-PD

Circuit model

The structure we used for modeling is shown in Table 1 which is reported by Ref. [11]. For the convenience of modeling, we first simplified the structure of UTC-PD to Fig. 2(a). It can be considered that UTC-PD only consist of two layers, one is the p doped InGaAs absorption layer (p absorption layer) and the other is the nondoped (or sometimes n- doped) InP collection layer (i collection layer). The functions of other layers are realized by setting relative model parameters. Wa and Wc are the width of absorption layer and collection layer, respectively.

(b) Equivalence form Fig. 2 Simplified structure of UTC-PD and its equivalence form

Fig. 3 Equivalent circuit model of UTC-PD

Table 1 Structure of InGaAs-InP UTC-PD reported in Ref. [11] Layers p InGaAs contact p InGaAsP blocking p InGaAs absorption i InGaAs spacer i InGaAsP spacer i InP spacer n InP cliff n InP collection n InP subcollector n InGaAs contact

Thickness/nm 50 20 220 8 16 6 7 263 50 10

Doping/cm–3 3h1019 2h1019 1018 1015 1015 1015 1018 1016 5h1018 1019

Eg/eV 0.76 0.89 0.76 0.76 1.00 1.35 1.35 1.35 1.35 0.76

In this model, the total current is calculated at x=Wa. The major point of UTC-PD is that only electrons contribute to the total current. So we can assume that, except the dark current, the total current through the pn junction all comes from the diffusion current of minority carriers in p absorption layer. We also assume that the i collection layer is intrinsic that we can treat it as a capacitance. Depending on those assumptions, we can convert Fig. 2(a) to Fig. 2(b) [11]. From Fig. 2(b), we can

2.3

Diffusion current

Because the diffusion current includes only the electron current, we can just solve the electron continuity equation without dealing with the hole continuity equation. Then since we set a parameter ĭ in the model to represent the potential variation of p absorption layer (which is mainly affected by cliff layer), the Poisson’s equation can also be avoided. In the calculation, we didn’t use the conventional boundary condition, n(Wa)=0, since the electron diffusion velocity in InGaAs will easily reach the thermal velocity and n(x) will not reduce to 0 at x=Wa [9]. To meet the reality, we use the thermionic emission boundary which suggests that the current at pn junction is dominated by the thermionic emission velocity vth [9], and vth is mainly affected by the spacer layers. The time independent electron continuity equation we

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solved is w 2n wn n De 2  vd (1)   G exp(D x) 0 wx wx W and the boundary condition [9] we used in the calculation is ­ § wn ·  vd n ¸ 0 ° q ¨ De ¹x 0 ° © wx Je ® (2) ° q § D wn  v n · ( ) q v v nW   th d a ° ¨© e wx d ¸¹ x Wa ¯ where De is the electron diffusion coefficient; n is the electron density; vd=–ȝeĭ/Wa, ĭ is the potential variation of absorption layer; IJ is the lifetime of electron; Į is the optical absorption coefficient of the absorption layer; vth is the thermionic emission velocity of electrons at pn junction; Gexp(Įx) is the generation rate of electron-hole pairs caused by the optical input, and G can be expressed as Pin (1  R ) (3) G AhQ where R is the reflection coefficient and Q is the frequency

of the input light. From Eqs. (1) and (2), we can get the following solution. The electron density distribution is n( x) n0 > exp(D x)  A0 exp(O1 x)  B0 exp(O2 x) @ (4) and the diffusion current at pn junction is § wn · J e (Wa ) q ¨ De  vd n ¸ w x © ¹ x Wa qn0 > ( DeD  vd )exp(DWa ) 

( DeO1  vd ) A0 exp(O1Wa )  ( DeO2  vd ) B0 exp(O2Wa ) @

(5)

The derived parameters used in Eqs. (4) and (5) are defined as

n0

GW exp(DWa ) 1  vdDW  DeD 2W

O1

§ v · vd 1  ¨ d ¸  2 De 2 D D W e © e¹

O2

§ v · vd 1  ¨ d ¸  2 De 2 D D W e © e¹

(8)

A0

1 Z3 C0 Z6

Z2 Z5

(9)

B0

1 Z1 C0 Z 4

Z3

(6)

2

(7)

2

Z6

where C0 and Z1–Z6 are Z 2 Z1 C0 Z5 Z4

2009

Z1

DeO1  vd

(12)

Z2

DeO2  vd

(13)

Z3

DeD  vd

(14)

Z4

( DeO1  vth )exp(O1Wa )

(15)

Z5

( DeO2  vth )exp(O2Wa )

(16)

Z6

( DeD  vth )exp(DWa )

(17)

2.4

Dark current

The dark current includes two parts. When bias voltage Vb is low, the diffusion current of minority carriers in p absorption layer dominates. With Vb increasing, the tunneling current gradually takes the leadership. In this model, we use a combinational expression to represent the dark current. ª § V  V0 · º (18) J d J 0 «1  T exp ¨ » ¨ mE ¸¸ » g ¹¼ © ¬« where J0 is the diffusion current [12], T is the temperature, Eg is the bandgap, V0 (in units of V) and m are fitting parameters. The latter term of Eq. (18) is the tunneling term. §Dn D p · J 0 q ¨ e p0  p n 0 ¸ (19) ¨ Ln Lp ¸¹ © where Dp is the hole diffusion coefficient, Ln /Lp are the electron and hole diffusion length in InGaAs/InP. To calculate J0 we need to get np0 (electron density in p absorption layer) and pn0 (hole density in i collection layer) first. § qV · np0 N D exp ¨  bin ¸ (20) © kT ¹ pn 0

§ qV · N A exp ¨  bip ¸ © kT ¹

(21)

where ND/NA are the donor and acceptor concentration in InP/InGaAs. It should be noted that electrons and holes do not face the same potential barrier (Vbi) in this heterostructure device. In this model, we mainly consider the band-to-band tunneling effects. The tunneling term is semi-empirical that we considered both the conventional expression and the simulation results.

3 Simulation (10)

(11)

Optoelectronic integrated circuit (OEIC) simulator is used for the simulation of the equivalent circuit model of UTC-PD. For comparison, the same structure has been simulated numerically in the commercial software Taurus (for DC and

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LI Xiao-jian, et al. / An equivalent circuit model for uni-traveling-carrier photodiode

transient simulations) and Crosslight Apsys (for AC simulations). The structure parameters [13] are listed in Table 1. The constants and other parameters used in the simulation are listed in Table 2.

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simulation using circuit model is well agreed with that of numerical simulation. As we can see, UTC-PD keeps a good linearity of the optical input power up to 10 mW.

Table 2 Constants and parameters used in simulation Parameter De/(cm2·s–1) IJ/ps Į/cm–1 vth/(m·s–1) ȝe/(cm2·V–1·s–1) ĭ/mV R A/ȝm2 Ȝ/ȝm Rd/ȍ Rt/ȍ Cs/ȝF NA/cm–3

Value 103 100 2 800 2.5h105 4 000 25 0.7 2 500 1.55 107 107 0 1018

Parameter T/K V0/V m Eg/eV Dp/(cm2·s–1) Ln/ȝm Lp/ȝm Vbin/eV Vbip/eV Rs/ȍ Ct/ȝF Wc/nm ND/cm–3

Value 300 12 0.25 1.35 6 2.27 1.32 0.96 1.615 5 10 263 1016

Fig. 5 Transient analysis

We simulate the dark current first. In the test, we apply a reverse bias from 0 to 12 V to UTC-PD without any optical input. The result is presented in Fig. 4. As we can see, simulation using circuit model agrees with numerical simulation. The current is dominated by the minority diffusion at lower Vb. With Vb increasing, the tunneling current gradually takes the leadership.

Fig. 6 DC analysis

Result of AC analysis is shown in Fig. 7. In this test, a 1 mW DC bias and a 1 ȝW AC signal is applied to the device. 3 dB bandwidth gets to 17.5 GHz. A higher bandwidth can be obtained after more optimization.

Fig. 4 Dark current of UTC-PD as a function of reverse bias

Then the transient analysis is executed using our model. A light pulse is input from the end of UTC. The width of the pulse is 200 ps and its rising and falling time are both 1 ps. The peak power is 1 mW. The result is shown in Fig. 5. Simulation using circuit model gives both the rising and falling times of 21 ps, while in numerical simulation both times are 23 ps. The DC analysis result is presented in Fig. 6. In this test, we sweep the light intensity from 0 to 10 mW. The result of

Fig. 7 AC analysis

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Conclusions

In this paper, a circuit model of UTC-PD is developed. In this model, hole continuity equation is ignored; so the complexity of circuits is decreased. However, the results from our simplified model agree well with that using commercial software.

5.

6.

Acknowledgements 7.

This work was Supported by the National Natural Science Foundation of China (60736002), and the Hi-Tech Research and Development Program of China (2007AA03Z408).

References 1. Ishibashi T, Shimizu N, Kodama S, et al. Uni-traveling carrier photodiodes. Proceedings of Ultrafast Electronics and Optoelectronics (UEO’97), Mar 17, 1997, Incline Village, NV, USA. 1997: 166–168 2. Shimizu N, Watabnabe N, Furuta T, et al. InP-InGaAs Uni-traveling-carrier photodiode with improved 3-dB bandwidth of over 150 GHz. IEEE Photonics Technology Letters, 1998, 10(3): 412–414 3. Ito H, Furuta T, Kodama S, et al. InP/InGaAs uni-travelling-carrier photodiode with 310 GHz bandwidth. Electronics Letters, 2000, 36(21): 1809–1810 4. Shi J W, Yu Y S, Wu C Y, et al. Highspeed, high-responsivity, and

8.

9.

10. 11. 12. 13.

2009

high-power performance of near ballistic unitraveling-carrier photodiode at 1.55ȝm wavelength. IEEE Photonics Technology Letters, 2005, 17(9): 1929–1931 Raring J W, Skogen E J, Wang C S, et al. Design and demonstration of novel QW intermixing scheme for the integration of UTC-type photodiodes with QW-based components. IEEE Journal of Quantum Electronics, 2006, 42(2): 171–181 Jun D H, Kang I H, Song J I. A modified UTC-PD having high speed and efficiency characteristics utilizing a frequency compensation. Proceedings of International Semiconductor Device Research Symposium (ISDRS’03), 2003, Dec 10–12, Washington DC, USA. Piscataway, NJ, USA: IEEE, 2003: 86–87 Shi J W, Li Y T, Pan C L, et al. Bandwidth enhancement phenomenon of a high-speed GaAs-AlGaAs based unitraveling carrier photodiode with an optimally designed absorption layer at an 830 nm wavelength. Applied Physics Letters, 2006, 89(5): 053512/1–053512/3 Wu Y S, Shi J W, Chiu P H. Analytical modeling of a high-performance near-ballistic uni-traveling-carrier photodiode at a 1.55 ȝm wavelength. IEEE Photonics Technology Letters,2006, 18(8): 938–940 Ishibashi T, Kodama S, Shimizu N, et al. High-speed response of uni-traveling carrier photodiodes. Japanese Journal of Applied Physics: Part 1, 1997, 36(10): 6263–6268 Chen W, Liu S. PIN avalanche photodiodes model for circuit simulation. IEEE Journal of Quantum Electronics, 1996, 32(12): 2105–2111 Ishibashi T, Furuta T, Fushimi H, et al. InP/InGaAs uni-traveling carrier photodiodes. IEICT Transactions on Electronics, 2000, E83-C(6): 938–949 Anderson B L, Anderson R L. Fundamentals of semiconductor devices. New York, NY, USA: McGraw-Hill Higher Education, 2006 Rahman S M M , Hjelmgren H, Vukusic J, et al. Hydrodynamic simulations of unitraveling-carrier photodiodes. IEEE Journal of Quantum Electronics, 2007, 43(11): 1088–1094