Voltage sharing effect and interface state calculation of

Voltage sharing effect and interface state calculation of a wafer-bonding Ge/Si avalanche photodiode with an interfacial GeO2 insulator

layer Shaoying Ke, Shaoming Lin, Xin Li, Jun Li, Jianfang Xu, Cheng Li, and Songyan Chen*

Semiconductor Photonics Research Center, Department of Physics, Xiamen University, Xiamen 361005, China *[email protected]

Abstract: The tunneling effect and interface state in the p-Ge/GeO2/p-Si structure of a wafer-bonding Ge/Si avalanche photodiode (APD) are investigated. It is found that the thin interfacial GeO2 layer (1-2 nm) formed by the hydrophilic reaction at the wafer-bonding interface significantly affects the performance of the Ge/Si APD. With the increase of the GeO2 thickness, the dark current of the Ge/Si APD decreases enormously due to the blocking effect of this GeO2 layer. Owing to the carrier accumulation in Ge layer under illumination condition, the voltage sharing effect of the GeO2 layer (thicker) becomes serious, leading to the absence of the electric field in Ge layer. The photon-generated electrons at Ge/GeO2 interface can be captured and released by the interface states at certain reverse bias. This can adjust the avalanche current of the Ge/Si APD. The stronger interface recombination induced by the larger interface state density (ISD) results in the decrease of the electric field in Ge layer. This increases the transit time of carriers, which in turn decreases the 3dB-bandwidth. Due to the drastic increase of the dark current (larger ISD), the gain of the Ge/Si APD decreases.

©2016 Optical Society of America

OCIS codes: (040.1345) Avalanche photodiodes (APDs); (040.5160) Photodetectors; (060.2330) Fiber optics communications.

References and links 1. W. S. Zaoui, H. W. Chen, J. E. Bowers, Y. Kang, M. Morse, M. J. Paniccia, A. Pauchard, and J. C. Campbell,

“Frequency response and bandwidth enhancement in Ge/Si avalanche photodiodes with over 840 GHz gain-bandwidth-product,” Opt. Express 17(15), 12641–12649 (2009).

2. N. Duan, T. Y. Liow, A. E. J. Lim, L. Ding, and G. Q. Lo, “310 GHz gain-bandwidth product Ge/Si avalanche photodetector for 1550 nm light detection,” Opt. Express 20(10), 11031–11036 (2012).

3. Y. Kang, H. D. Liu, M. Morse, M. J. Paniccia, M. Zadka, S. Litski, G. Sarid, A. Pauchard, Y. H. Kuo, H. W. Chen, W. S. Zaoui, J. E. Bowers, A. Beling, D. C. McIntosh, X. Zheng, and J. C. Campbell, “Monolithic ermanium/silicon avalanche photodiodes with 340 GHz gain-bandwidth product,” Nat. Photonics 3(1), 59–63 (2009).

4. R. E. Warburton, G. Intermite, M. Myronov, P. Allred, D. R. Leadley, K. Gallacher, D. J. Paul, N. J. Pilgrim, L. J. M. Lever, Z. Ikonic, R. W. Kelsall, E. Huante-Ceron, A. P. Knights, and G. S. Buller, “Ge-on-Si single-photon avalanche diode detectors: design, modeling, fabrication, and characterization at wavelengths 1310 and 1550 nm,” IEEE Trans. Electron. Dev. 60(11), 3807–3813 (2013).

5. Z. Lu, Y. Kang, C. Hu, H. D. Liu, and J. C. Campbell, “Geiger-mode operation of Ge-on-Si avalanche photodiodes,” IEEE J. Quantum Electron. 5(47), 731–735 (2011).

6. N. A. DiLello and J. L. Hoyt, “Impact of post-metallization annealing on Ge-on-Si photodiodes passivated with silicon dioxide,” Appl. Phys. Lett. 99(3), 033508 (2011).

7. V. A. Shah, A. Dobbie, M. Myronov, and D. R. Leadley, “Effect of layer thickness on structural quality of Ge epilayers grown directly on Si (001),” Thin Solid Films 519(22), 7911–7917 (2011).

8. Z. Zhou, C. Li, H. Lai, S. Chen, and J. Yu, “The influence of low-temperature Ge seed layer on growth of high-quality Ge epilayer on Si (100) by ultrahigh vacuum chemical vapor deposition,” J. Cryst. Growth 310(10), 2508–2513 (2008).

#254465 Received 24 Nov 2015; revised 23 Dec 2015; accepted 4 Jan 2016; published 25 Jan 2016 © 2016 OSA 8 Feb 2016 | Vol. 24, No. 3 | DOI:10.1364/OE.24.001943 | OPTICS EXPRESS 1943

9. S. Huang, C. Li, Z. Zhou, C. Chen, Y. Zheng, W. Huang, H. Lai, and S. Chen, “Depth-dependent etch pit density in Ge epilayer on Si substrate with a self-patterned Ge coalescence island template,” Thin Solid Films 520(6), 2307–2310 (2012).

10. C. Chen, C. Li, S. Huang, Y. Zheng, H. Lai, and S. Chen, “Epitaxial growth of germanium on silicon for light emitters,” Int. J. Photoenergy 2012, 1–8 (2012).

11. M. T. Currie, S. B. Samavedam, T. A. Langdo, C. W. Leitz, and E. A. Fitzgerald, “Controlling threading dislocation densities in Ge on Si using graded SiGe layers and chemical-mechanical polishing,” Appl. Phys. Lett. 72(14), 1718–1720 (1998).

12. H. C. Luan, D. R. Lim, K. K. Lee, K. M. Chen, J. G. Sandland, K. Wada, and L. C. Kimerling, “High-quality Ge epilayers on Si with low threading-dislocation densities,” Appl. Phys. Lett. 75(19), 2909–2911 (1999).

13. F. Gity, K. Y. Byun, K.-H. Lee, K. Cherkaoui, J. M. Hayes, A. P. Morrison, C. Colinge, and B. Corbett, “Characterization of germanium/silicon p-n junction fabricated by low temperature direct wafer bonding and layer exfoliation,” Appl. Phys. Lett. 100(9), 092102 (2012).

14. K. Y. Byun, I. Ferain, P. Fleming, M. Morris, M. Goorsky, and C. Colinge, “Low temperature germanium to silicon direct wafer bonding using free radical exposure,” Appl. Phys. Lett. 96(10), 102110 (2010).

15. R. Loo, G. Wang, L. Souriau, J. C. Lin, S. Takeuchi, G. Brammertz, and M. Caymax, “High quality Ge virtual substrates on Si wafers with standard STI patterning,” J. Electrochem. Soc. 157(1), H13–H21 (2010).

16. H. C. Luan, D. R. Lim, K. K. Lee, K. M. Chen, J. G. Sandland, K. Wada, and L. C. Kimerling, “High-quality Ge epilayers on Si with low threading-dislocation densities,” Appl. Phys. Lett. 75(19), 2909–2911 (1999).

17. K. Y. Byun, P. Fleming, N. Bennett, F. Gity, P. McNally, M. Morris, I. Ferain, and C. Colinge, “Comprehensive investigation of Ge-Si bonded interfaces using oxygen radical activation,” J. Appl. Phys. 109(12), 123529 (2011).

18. Q.-L. Li, Q. Xie, Y.-L. Jiang, G.-P. Ru, X.-P. Qu, B.-Z. Li, D. W. Zhang, D. Deduytsche, and C. Detavernier, “Annealing induced hysteresis suppression for TiN/HfO2/GeON/p-Ge capacitor,” Semicond. Sci. Technol. 26(12), 125003 (2011).

19. D. Kuzum, T. Krishnamohan, A. Nainani, Y. Sun, P. A. Pianetta, H. S. P. Wong, and K. C. Saraswat, “High-mobility Ge N-MOSFETs and mobility degradation mechanisms,” IEEE Trans. Electron Dev. 58(1), 59–66 (2011).

20. M. Gogna, E. Suarez, P. Y. Chan, F. Al-Amoody, S. Karmakar, and F. Jain, “Nonvolatile silicon memory using GeOx-cladded Ge quantum dots self-assembled on SiO2 and lattice-matched II-VI tunnel insulator,” J. Electron. Mater. 40(8), 1769–1774 (2011).

21. Q. C. Zhang, J. C. Kelly, and D. R. Mills, “Possible high absorptance and low emittance selective surface for high temperature solar thermal collectors,” Appl. Opt. 30(13), 1653–1658 (1991).

22. C. Liu, C. Wang, X. Chen, and Y. Yang, “Analysis of direct current performance on N-polar GaN-based high-electron-mobility transistors for next-generation optoelectronic devices,” Opt. Quantum Electron. 47(8), 2479–2488 (2015).

23. P. J. Price and J. M. Radcliffe, “Esaki tunneling,” IBM J. Res. Develop. 3(4), 364–371 (1959). 24. A. M. Kiefer, D. M. Paskiewicz, A. M. Clausen, W. R. Buchwald, R. A. Soref, and M. G. Lagally, “Si/Ge

junctions formed by nanomembrane bonding,” ACS Nano 5(2), 1179–1189 (2011). 25. J. Tersoff, “Schottky barrier heights and the continuum of gap states,” Phys. Rev. Lett. 52(6), 465–468 (1984). 26. A. Dimoulas, P. Tsipas, A. Sotiropoulos, and E. K. Evangelou, “Fermi-level pinning and charge neutrality level

in germanium,” Appl. Phys. Lett. 89(25), 252110 (2006). 27. D. Kuzum, J. H. Park, T. Krishnamohan, H. S. P. Wong, and K. C. Saraswat, “The effect of donor/acceptor

nature of interface traps on Ge MOSFET characteristics,” IEEE Trans. Electron. Dev. 58(4), 1015–1022 (2011). 28. D. Kuzum, K. Martens, T. Krishnamohan, and K. C. Saraswat, “Characteristics of surface states and charge

neutrality level in Ge,” Appl. Phys. Lett. 95(25), 252101 (2009). 29. J. R. Weber, A. Janotti, P. Rinke, and C. G. Van de Walle, “Dangling-bond defects and hydrogen passivation in

germanium,” Appl. Phys. Lett. 91(14), 142101 (2007). 30. P. Tsipas and A. Dimoulas, “Modeling of negatively charged states at the Ge surface and interfaces,” Appl.

Phys. Lett. 94(1), 012114 (2009). 31. L. Livadaru, J. Pitters, M. Taucer, and R. A. Wolkow, “Theory of nonequilibrium single-electron dynamics in

STM imaging of dangling bonds on a hydrogenated silicon surface,” Phys. Rev. Lett. 84(20), 205416 (2011). 32. P. Broqvist, A. Alkauskas, and A. Pasquarello, “Defect levels of dangling bonds in silicon and germanium

through hybrid functionals,” Phys. Rev. B 78(7), 075203 (2008). 33. M. B. Haider, J. L. Pitters, G. A. DiLabio, L. Livadaru, J. Y. Mutus, and R. A. Wolkow, “Controlled coupling

and occupation of silicon atomic quantum dots at room temperature,” Phys. Rev. Lett. 102(4), 046805 (2009). 34. L. Livadaru, P. Xue, Z. Shaterzadeh-Yazdi, G. A. DiLabio, J. Mutus, J. L. Pitters, B. C. Sanders, and R. A.

Wolkow, “Dangling-bond charge qubit on a silicon surface,” New J. Phys. 12(8), 083018 (2010). 35. L. Livadaru, J. Pitters, M. Taucer, and R. A. Wolkow, “Theory of nonequilibrium single-electron dynamics in

STM imaging of dangling bonds on a hydrogenated silicon surface,” Phys. Rev. B 84(20), 205416 (2011).

1. Introduction

Ge/Si avalanche photodiodes (APDs) are widely used in optical communications. They can provide significant sensitivity improvements owing to the internal avalanche gain. Recently, lots of works focus on the improvement of the gain, bandwidth, and gain-bandwidth product of the epitaxial Separate-Absorption-Charge-Multiplication (SACM) Ge/Si APDs [1–3]. The


Ge/Si APDs with the bandwidth-gain-product of 845 GHz and 310 GHz have been achieved at the wavelength of 1310 [1] and 1550 nm [2], respectively, which can be applied to high-speed near-infrared detection.

Very recently, some groups attempt to apply the Ge/Si APDs for single-photon detection. Warburton et al. [4] have proposed a Ge/Si single photon avalanche photodiode (SPAD) with thicker Si avalanche layer (1 μm). The single photon detection efficiency (SPDE) of 4% at 1310 nm, the dark count rate (DCR) of 106-107 Hz, and the noise quivalent power (NEP) of 1 × 10−14 WHz-1/2 at 100 K were obtained. For the longer wavelength of 1550 nm, the SPDE of ∼0.15% at 6% excess bias and the NEP of 5 × 10−12 WHz-1/2 with a jitter of 420 ps were achieved at 125 K. As we all know that the DCR is an important factor that significantly affects the sensitivity of the SPAD. It was demonstrated that the high dark current of the epitaxial Ge/Si APD can be responsible for the high DCR due to the narrow band gap of Ge and the high-density threading dislocations (TDs) in Ge layer [5]. In addition, it was proposed in previous literatures [6] that the surface recombination of the cylindrical Ge side walls can also contribute to the dark current. It suggested that directly epitaxial growth of Ge on Si leads to the formation of high-density TDs (108-109 cm−2) in Ge film due to the vertical spread of dislocation loops induced by the 4.2% lattice mismatch [7]. The TDs act as the acceptor-like defects (midgap state) in the Ge film and promote the bulk recombination. This indicates that the TDs in Ge film can increase the dark current of the APD. Different methods are proposed to weaken the strain-relief effect in Ge layer. Such as the low-temperature seed layer growth [8,9], Ge/SiGe multiple quantum well isolation [10], graded SiGe buffer layer growth [11,12], and Ge/Si direct wafer bonding [13,14].

The graded SiGe buffer layer can significantly decrease the TD density (2.1 × 106 cm−2) due to the smaller strain accumulated in each SiGe buffer layer, but it requires a thickness of 10 μm. This is not suitable for fabricating high-speed photodetectors. The seed layer growth can confine the TDs to a ~100 nm thick low-temperature Ge layer, leading to the low TD density in upper high-temperature Ge layer. On the other hand, the Ge/SiGe quantum well on the Ge seed layer can bend the dislocation line formed at the Ge/Si interface. Therefore, this recipe can prevent the sequential penetration of the TDs. Nevertheless, the TD density in this low-temperature Ge layer is demonstrated to be 1~2 × 1010 cm−2 [15], this is still too high for achieving high-performance detectors. Luan et al. [16] combined this twe step growth with the selective area growth (SiO2 square window) and annealing process to decrease the TD density. The selective-grown Ge layer (1 μm) with the average TD density of 2.33 × 106 cm2 is achieved after cyclic thermal annealing. However, this method is unsuitable for large area fabrication. Of more important, with the development of the wafer bonding and smart cut techniques, the high-quality Ge thin film with several micrometers can be stripped off from the bulk Ge and be directly bonding with Si. This can be expected to reduce the dark current (recombinantion through TDs) of the Ge/Si APD.

In order to enhance the single-photon detection ability of the Ge/Si APDs, the Ge/Si direct wafer bonding seems to be the most promising candidate. However, lots of reports [13,14,17] proposed that there is a thin GeO2 insulator layer (1~2 nm) at the Ge/Si interface after the Ge/Si direct wafer bonding. It is well known that it is difficult to achieve direct wafer bonding of Ge to Si wafer due the large lattice mismatch and coefficient of thermal expansion. A novel recipe called “free radical exposure” prior to direct wafer bonding can generate a more hydrophilic surface. This is very important for the direct bonding due to the fact that the increase of the hydroxyl groups can give rise to more hydrophilic reactions at the bonded interface. The formation of the native GeO2 layer at the interface after the Ge/Si wafer bonding can be described using the following two equations: Ge-OH + OH-Si = Ge-O-Si + H2O and Ge + 2H2O = GeO2 + 2H2. This thin GeO2 layer can relieve the strain accumulated at the Ge/Si interface and achieve perfect wafer bonding.

In this paper, we theoretically study the dependence of the GeO2 thickness and the interface state at both sides of GeO2 layer on the properties of the wafer-bonding Ge/Si APD. The abnormal I-V curve of the APD with thicker GeO2 and the difference of electric field in


the APD under dark and illumination condition are well clarified. A detailed understanding of the effect of the interface state on the 3dB-bandwidth is also gained.

2. Parameter settings

The simulated cylindrical Ge/Si APD with 30 μm in diameter is shown in Fig. 1(a). A thin GeO2 insulator layer is inserted between p-Ge absorption layer and p-Si charge layer. The parameters of the GeO2 material are user-defined, which are permittivity: 5.5 [18], energy gap: 5 eV [19], affinity: 1 eV [20], and refractive index: 1.6 [21]. In order to simulate the surface recombination of the side walls (passived by Si3N4 material) of the cylindrical device structure, the surface recombination velocity of 1 × 107 cm/s at the side walls is also set in the program. The conduction and valence-band offset at Ge/Si interface are calculated to be ~3 and ~1.5 eV, respectively. Thus, the tunneling current is dominant at the Ge/Si interface of the wafer-bonding Ge/Si APD.

The running of the program is based on the Poisson’s equation, continuity equations, and transport equations [22]. Poisson’s equation associates variations in electrostatic potential with local charge densities. The continuity equations and the transport equations describe the transport processes, generation processes, and recombination processes of carriers. Based on these three equations, a non-local quantum barrier tunneling model is introduced to simulate the tunneling effect at the Ge/Si interface with a defined special tunneling region covering the GeO2 layer. The calculation of the tunneling current is based on a formula [Eq. (1)], which was introduced by Price and Radcliffe [23]. Where mt is the transverse effective mass, ml the longitudinal effective mass, Efl and Efr the quasi-Fermi levels on either side of the barrier. It formulates the Schrodinger equation in the effective mass approximation and can calculate the tunneling probability of carrier through the potential barrier. The semi-classical Wentzel-Kramers-Brillouin (WKB) approximation [24], which is used commonly to simulate the quantum tunneling effect and can simplify the iteration calculation, is introduced to solve the Schrodinger equation. The formula is given by Eq. (2). Where k is the wave vector of the electron within the barrier and the integration limits are the classical turning points at the barrier’s edges, d the barrier width.

Fig. 1. (a) Schematic cylindrical 30 μm-diameter wafer-bonding Ge/Si APD with Ge/GeO2 and GeO2/Si interface states. (b) Band diagram of the GeO2 interface and interface state levels at both sides of GeO2.

( ) ( ) ( )( )2 3

1 /2 4 ln

2 1 /Fr

t l t

Fl

exp E E kTqkTJ m m m T E dE

h exp E E kTπ + − = +

+ − (1)


( ) ( )0

2 d

T E exp k x dx

≅ −

(2)

In order to simulate the effect of the interface state between semiconductor and insulator on the properties of the wafer-bonding Ge/Si APD, two interfaces (Ge/GeO2 and GeO2/Si interface) at both sides of GeO2 should be taking into account. In this work, a 1 nm thick Ge and Si layer with different trap densities are added at Ge/GeO2 and GeO2/Si interface, respectively, to calculate the interface states. Of more importance, the energy level location and the trap type of the defined traps should be identified firstly. For Ge surface, it was demonstrated theoretically [25] and experimentally [25,26] that the charge neutrality level (CNL) is ~0.1 eV away from the valence band edge. In NMOS device (p-Ge/GeO2) [27], the Fermi level lies above the CNL, causing a large negative charge at the interface. That is, the acceptor-like states are located below the Fermi level and ionized to be negatively charged [27,28]. Besides, several recent theory calculations [29,30] consistently reveal that instead of the bond distortion, Ge atom displacement, and Ge adatom formation, the dangling bonds (DBs) are probably the best candidate to form the acceptor-like interface states at p-Ge/GeO2 interface. It was also predicted that the charged acceptor and donor DB states of Ge are located in close proximity of the valence band (Eacc = Ev + 0.11 eV, Edon = Ev + 0.05 eV).

For Si surface, the DB can be in three different states: negative state DB− (acceptor-like) which holds two localized electrons, neutral state DB0 which holds one localized electron, and positive state DB+ (donor-like) which holds one localized hole [31,32]. It suggested previously that the acceptor and donor levels of Si DBs are 0.84 and 0.26 eV above the valence band edge (Eacc = Ev + 0.84 eV, Edon = Ev + 0.26 eV), respectively [28,30]. In addition, Livadaru et al. [33–35] indicated that the state type of the Si DBs is related to the doping type of the Si bulk. It was proposed that for highly-doped n-type Si, the high Fermi level allows two electrons to be localized at each DB, thus the DB site is negatively charged. However, the p-type doping of Si renders the DB site to be positively charged, corresponding to one hole in the DB state. According to the structure of the wafer-bonding Ge/Si APD, the acceptor DB states (p-Ge/GeO2) with a level at Ev + 0.11 eV and the donor DB states (GeO2/p-Si) with a level at Ev + 0.26 eV are setting in the program. The simulated band diagram and trap energy level at Ge/GeO2 and GeO2/Si interface of the wafer-bonding Ge/Si APD are plotted in Fig. 1(b).

3. Simulation results

The effect of the GeO2 thickness on the carrier transport process is investigated firstly. In this part, the interface state at the Ge/Si interface is not taking into account. The interfacial layer thickness is in the range of 0-2.4 nm. The simulation results are shown in Fig. 2. One obvious feature is that with the increase of the GeO2 thickness, the dark and total currents at lower bias extremely decrease. Especially, the total current (1 × 10−5 A) of the APD with 1 nm thick GeO2 layer is four orders of magnitude larger than that (1 × 10−9 A) of the APD with 2.4 nm thick GeO2 layer under 10 V reverse bias. This indicates that the photocurrent largely decreases with the increase of the GeO2 thickness. It was demonstrated [31] that the electron tunneling probability is inversely proportional to the quantum barrier thickness. Thus, with the increase of the GeO2 thickness, the electron tunneling probability decreases, leading to the decrease of the tunneling current. Another factor that may induce the decrease of the photocurrent is the accumulation of carriers in Ge layer causing by the voltage sharing of GeO2 under illumination conduction (discussed next). On the other hand, it is also shown that with the increase of the GeO2 thickness, the current of the APD under Geiger model (>28 V) largely decreases, especially for the dark current. This results from the decreased avalanche current in Si layer induced by the decreased tunneling electrons. It is worth nothing that the decrease of the avalanche current signifies the weakening of the APD signal. That is, the SPDE of the wafer-bonding Ge/Si SPAD may decrease with the increase of the GeO2 thickness. One special feature in Fig. 2 is that when the GeO2 thickness increases to 2.4 nm,


the calculation of the total current cannot converge (>22.5 V). The detail explanation is given as follow.

Fig. 2. I-V curves of the wafer-bonding Ge/Si APDs with different GeO2 thickness at different reverse bias.

During the electric filed simulation, a feature of particular interest is that when the GeO2 thickness increases to 2.4 nm, the electric fields in the wafer-bonding Ge/Si APDs under dark and illumination condition are very different, as shown in Fig. 3(a). One can see that in dark condition, the Ge layer is totally covered by the electric field and the field covering the GeO2 layer is small. However, under illumination condition, the electric field in Ge layer is absent and that in GeO2 layer becomes very large. This is a special phenomenon. It is also found that under dark condition, the electric fields in the APDs with different GeO2 thickness are changeless. Nevertheless, when the GeO2 thickness exceeds 2 nm, the electric field in Ge layer decreases and that in GeO2 layer increases with the increase of the GeO2 thickness under illumination condition (no shown here). This behavior can also be described in Fig. 3(b). One can observe that the carriers accumulate in the Ge layer gradually with the increase of the GeO2 thickness due to the voltage sharing of GeO2 and the decreased electron tunneling possibility. Inset (left hand) in Fig. 3(a) shows the carrier concentration in the wafer-bonding Ge/Si APD under dark and illumination condition. One obvious feature is that the carrier concentration in Ge layer largely increases under illumination condition (carrier accumulation). It suggests that under illumination condition, lots of photon-generated carriers are formed in the Ge layer, leading to the decrease of the resistivity of Ge layer. As a result, due to the voltage sharing (in series) of the Ge and GeO2 layer, the applied bias (electric field) undertaken by the GeO2 layer increases and that undertaken by Ge layer decreases. In addition,due to the absence of the electric field in Ge layer, the number of the electrons reaching the Si layer by tunneling process is reduced, leading to the increase of the resistivity of Si layer. Thus, the electric field in Si layer under illumination condition is stronger than that under dark condition. This can also be responsible for the enormous decrease of the photocurrent at lower bias discussed above. The right-hand side of the inset in Fig. 3(a) presents the hole ionization coefficient at the Ge/GeO2 interface of the Ge/Si APD with 2.4 nm thick GeO2 layer under illumination condition. It surprises that the maximum value of the hole ionization coefficient in the Ge region is ~6 × 105 cm−1. This is enough to trigger the pre-breakdown of the APD. Thus, the total current of the APD with 2.4 nm thick GeO2 layer is largely increased when the applied bias exceeds 22.5 V.


Fig. 3. (a) Electric field of the wafer-bonding Ge/Si APD under dark and illumination condition at 22.5 V reverse bias, inset on the left-hand side is the related carrier concentration and that on the right-hand side is the hole ionization coefficient under illumination condition. (b) Carrier concentration in Ge layer of the APD with different GeO2 thickness at 22.5 V reverse bias.

In order to simulate of the dependence of the APD performance on the interface state, 1 nm thick Ge and Si thin layer with different interface state densities (ISDs) are inserted at Ge/GeO2 and GeO2/Si interface, respectively. The I-V curves of the Ge/Si APDs (0.5 nm thick interfacial GeO2 layer) with ISDs from 5 × 1015 to 5 × 1018 cm−3 are calculated, as shown in Fig. 4 (a). A light source with an optical input power of −20 dBm and a wavelength of 1310 nm is set to simulate the photoresponse of the APD. One can see that with the increase of the ISD, the dark current increases gradually. When the ISD exceeds 5 × 1016 cm−3, the breakdown voltage tends to decrease and the dark current starts to deviate from the ideal state (no defect) at higher bias near breakdown voltage, leading to the extreme increase of the dark current. It is well known that the semiconductor/insulator interface exhibits crystal flaws, i.e. dangling bonds at material surface. These interface defects, whose associated energy level locates in the forbidden gap, can exchange charge with the conduction and valence bands through the capture and emission of the electrons. Thus, these defects can significantly affect the electrical characteristics of the device. Figure 4(b) shows the recombination rates at Ge/GeO2 and GeO2/Si interface of the wafer-bonding Ge/Si APDs with different ISDs. As expected, with the increase of the ISD, the recombination rate increases at both sides of GeO2. Upon increasing the ISD to 5 × 1017 cm−3, the recombination effect becomes serious, leading to the tremendous increase of the dark current.

One special feature in Fig. 4(a) is that the total current at lower bias decreases with the increase of the ISD. That is, the photocurrent of the APD decreases with the increase of the ISD. To our knowledge, the photon-generated electrons are formed in Ge absorption layer under illumination condition and are swept to the Ge/GeO2 interface immediately under certain reverse bias. It is suggested that high-density interface states are located at Ge/GeO2 interface. The photon-generated electrons (accumulating at Ge/GeO2 interface), which have not yet tunneled through the GeO2 layer, can be captured by these defects. In addition, the electrons tunneling through the GeO2 barrier can also be captured by the interface states at GeO2/Si interface. This leads to the decrease of the electrons, which in turn weakens the avalanche multiplication effect in Si layer. Thus, the photocurrent decreases with the increase of the ISD at lower bias (0-18 V). However, the total current increases with the increase of the ISD at higher bias (18-27 V). It is shown that the dark current is enormously increased at higher bias. In addition, with the increase of the applied bias, the electrons, which are captured by the interface states, are gradually released with the increase of the applied bias. This leads to the increase of the photocurrent of the APD at high bias.


Fig. 4. (a) I-V curves of the wafer-bonding Ge/Si APDs with different ISDs at different reverse bias. (b) Recombination rates at Ge/GeO2 and GeO2/Si interface of the APDs with different ISDs.

Note in Fig. 4(b) that the recombination rate at Ge/GeO2 interface is almost one order of magnitude larger than that at GeO2/Si interface. This indicates that the carrier recombination at Ge/GeO2 interface dominantly affects the performance of the Ge/Si APD. This feature can be explained as follow. Before the simulation of the interface state, the acceptor interface state with a level at Ev + 0.11 eV and the donor interface state with a level at Ev + 0.26 eV are setting at p-Ge/GeO2 and GeO2/p-Si interface in the program, respectively. Thus, we believe that the stronger recombination at p-Ge/GeO2 is associated with the acceptor state type and the deeper energy level.

Fig. 5. 3dB-BWs of the wafer-bonding Ge/Si APDs with different ISDs at different reverse bias.

The dependence of the 3dB-bandwidth (BW) on the ISD is plotted in Fig. 5. It is worth nothing that the 3dB-BW decreases tremendously with the increase of the ISD at certain bias before breakdown. However, it is changeless with the increase of the ISD after breakdown. This is an interesting phenomenon. It was demonstrated that the 3dB-BW of the APD is significantly affected by three factors, which are transit time (ttr), RC time constant (tRC), and avalanche build-up time (ta). The relationship can be given by Eq. (3), which is associated with the three individual bandwidths (ftr, fRC, and fa). In this work, during the comparison of


the APDs with different ISDs, no extra resistance or capacitance is added, thus the tRC cannot contribute to the BW drop with ISD before breakdown.

( ) ( ) ( ) ( ) ( ) ( )

3 2 2 2 2 2 2

1 1

1 1 1dB

RC tr a RC tr a

BWf f f a t b t c t

= =+ + ⋅ + ⋅ + ⋅

(3)

Fig. 6. (a) Electric fields of the wafer-bonding Ge/Si APDs with different ISDs. (b) Enlarged image of the electric field in GeO2 layer.

In order to give a detail insight into this abnormal BW drop, the electric fields of the Ge/Si APDs with different ISDs under 25 V reverse bias are mapped in Fig. 6(a). One can observe that with the increase of the ISD, the electric field in Ge absorption layer decreases. It is also shown in Fig. 6(b) that with the increase of the ISD, the electric field in GeO2 layer increases. This can be attributed to the increase of the charge concentration at the Ge/GeO2 and GeO2/Si interface induced by the interface recombination. As a result, due to the voltage sharing effect (in series) of the GeO2 layer and Ge layer, the electric field in Ge layer is affected by the electric field in GeO2 layer.

Fig. 7. (a) Electron and hole velocity (inset) versus ISD in Ge layer. (b) Gain of the wafer-bonding Ge/Si APD with different ISDs at different reverse bias.

It is discussed above that the 3dB-BW is affected by the ttr in Ge absorption layer. On the other hand, the ttr is determined by the carrier velocity in Ge layer. The effect of ISD on the carrier velocity under 25 V reverse bias is investigated, as shown in Fig. 7(a). One obvious


feature is that with the increase of the ISD, the carrier velocity in Ge layer decreases. This is in good agreement with the electric field in Ge layer analyzed above. This indicates that with the increase of the ISD, the ttr in Ge layer increase due to the decrease of the carrier velocity, resulting in the decrease of the 3dB-BW before breakdown. Here, another factor ta is not taken into account. In order to further clarify the 3dB-BW drop with ISD before breakdown, the gains of the Ge/Si APDs with different ISDs are also plotted in Fig. 7(b). It is found that the gain of the APD at lower bias (22-25 V) increases with the increase of the ISD. As discussed above, the photocurrent increases with the increase of the ISD at certain bias (>22 V) due to the release of the captured electrons at the interface. Thus, the gain of the APD increases. This indicates that the ta in this bias range increases with the increase of the ISD, leading to the tremendous BW drop at lower bias (22-25 V). After breakdown, the electric field in Ge layer is high enough to render the carrier velocity to reach maximum, the capture effect of the interface states is weakened at high voltage. Therefore, the BW is almost unchanged with the increase of the ISD after the breakdown of the Ge/Si APD. On the other band, as shown in Fig. 7(b), the gain of the APD under the bias near breakdown voltage decreases with the increase of the ISD. This can be ascribed to the tremendous increase of the dark current when the ISD is high enough.

4. Conclusion

We study the transport characteristic and interface state of a wafer-bonding Ge/Si APD. With the increase of the GeO2 thickness, the photocurrent of this APD decreases tremendously at lower bias due to the decrease of the tunneling possibility and the carrier accumulation in Ge layer. The photoelectric effect in Ge layer under near-infrared illumination and the blocking effect of the GeO2 layer lead to the accumulation of photon-generated carriers in Ge layer, which decreases the resistivity of the Ge layer and increases the electric field in GeO2 layer. With the increase of the ISD, the dark current increases tremendously due to the increase of the interface recombination rate, leading to the decrease of the APD gain. The photocurrent decreases at lower bias is the result of the capture effect of the electrons by the interface state and that increases at higher bias can be attributed to the release of the captured electrons. The decreased electric field in Ge layer with the increase of the ISD can be responsible for the decrease of the 3dB-BW (transit time) at lower bias.

Acknowledgments

This work was supported by the Key Project of Natural Science Foundation of China under Grant number 61534005 and the National Science Foundation of China (NSFC) under Grant number 61474081 and National Basic Research Program of China (973 Program) under Grant number 2013CB632103.


Documents

Voltage sharing effect and interface state calculation of