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The role of high-injection effects on the transient ion beam induced current response of high-speed photodetectors
Nuclear Instruments and Methods in Physics Research B 219–220 (2004) 1015–1021 www.elsevier.com/locate/nimb
The role of high-injection effects on the transient ion beam induced current response of high-speed photodetectors Jamie Stuart Laird a, Toshio Hirao a, Shinobu Onoda b, Tomihiro Kamiya
a,*
a Department of Materials Development, Severe Environment Materials Laboratory, Takasaki Radiation Chemistry Research Establishment, Japan Atomic Energy Research Institute (JAERI), 1233 Watanuki-machi, Takasaki, Gunma 370-1292, Japan b Graduate School of Engineering, Tokai University, 1117 Hiratsuka, Kanagawa 259-1292, Japan
Abstract High-speed photodetectors are the primary cause of increasing bit error rates (BER) in optic fiber communication system used in radiation hard environments such as space. MeV heavy ions passing through the collection volume of a photodetector generate a single event transient which upon passing to the decoding electronics causes spurious noise (increasing the BER). The time-resolved (or transient) ion beam induced current response of a photodetector is largely influenced by high-injection effects such as space-charge screening that perturb the electric-field distribution leading to drastic alterations in carrier velocity distributions, local mobilities and charge collection characteristics. Here, we examine the transient response of a Si p–i–n photodetector irradiated with 15 MeV O and 11 MeV C ions and discuss the role of high-injection effects with the aid of Technology Computer Aided Design (TCAD) software. Ambipolar diffusion was found (experimentally and theoretically) to dominate charge transport for high-injection levels present for most heavy ions. Light ions also experience similar conditions, but over a much shorter period. 2004 Elsevier B.V. All rights reserved. Keywords: Transient ion beam induced current; Time resolved ion beam induced current; Si p–i–n photodiode; GHz photodetectors; TCAD; Photodiode; Ambipolar diffusion; SET; BER
1. Introduction High-speed photodetectors are the primary source of increasing bit error rates (BER) in optical communication systems used in radiation hard environments [1]. MeV ions passing through the collection volume of a photodetector generate a transient current or single event transient (SET) which passes to decoding electronics increasing the * Corresponding author. Tel.: +81-27-356-9346/346-9320; fax: +81-27-346-9687. E-mail addresses: [email protected] (J.S. Laird), [email protected] (T. Kamiya).
BER. They cannot be filtered since they contain frequency components common with that of the receiver signal. The thin absorption region of photodetectors makes them particularly susceptible to MeV heavy ions (generated by proton induced nuclear reactions or high-energy recoils). Designing possible mitigation schemes for BER restoration requires the ability to measure (or reliably simulate), their transient response. There appear to be two paradigms for approaching the problem theoretically. One based on solving the Poisson equation, continuity equations and transport models self-consistently, is the backbone of the ‘‘TCAD’’ based approach [2]. The
0168-583X/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2004.01.206
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J.S. Laird et al. / Nucl. Instr. and Meth. in Phys. Res. B 219–220 (2004) 1015–1021
other approach uses theories based on Shockley– Ramo–Gunn theory [3,4] and Laplacian methods to derive the form of the SET for more specific situations [5–8]. These approaches lead to reasonable interpretation but do not fully describe carrier dynamics with non-uniform electron–hole pair (EHP) distributions (large lateral and longitudinal gradients in EHP density distributions) where Fermi–Dirac statistics must be applied. These high densities coupled with the fact that all relevant parameters depend on this density, lead to large perturbations of the above models requiring the possible use of correction factors. To examine the response in detail we use TCAD to examine high- and low-injection regimes and their transition point for different device conditions (bias) and
EHP distributions (LET and width). It was found that under ultra high-injection, the static electric field is distorted to the point where the transient response is predominantly determined by the dynamics of the EHP plasma, which for most of the collection time can be described by ambipolar diffusion. Measurements in a Si p–i–n device with 11 MeV C and 15 MeV O confirm these findings.
2. Experimental To examine the role of high-injection, we measure and simulate the response to heavy ions with the same approximate range but different average LET. Here the model of Kobetich and Katz [9]
Fig. 1. (a) DUT mounted on TIBIC chip carrier and its external connection to the bias-T. (b) DUT cross-section and equivalent circuit connected to the 50 X transmission line and DSO.
J.S. Laird et al. / Nucl. Instr. and Meth. in Phys. Res. B 219–220 (2004) 1015–1021
was used for track structure estimates for 11 MeV C and 15 MeV O. Although these results are not used in TCAD, for reasons pointed out in [10], they do illustrate that both ion tracks have the same functional form and end of range (EOR) to within ±0.1 lm. Differences in the SET are due to differences in initial carrier densities or energy-loss (pC/lm), which for 11 MeV C and 15 MeV O are 50 and 75 fC/lm, respectively [11]. 2.1. Device structure and fabrication The device under test (DUT) was a Si p–i–n photodiode used for communication modules operating near 1.5 GHz at )10 V. Shown in Fig. 1 is cross-sectional view of the DUT and its TIBIC mounting configuration (top) as well as its equivalent circuit (bottom). Use of a chip carrier avoids most parasitic elements such as inductance and capacitance and is important for examining highspeed devices where large RC time constants result in transient fall-times characteristic of the circuit, not the charge collection [12]. Capacitance voltage (CV) measurements are typically employed to measure doping profiles [13]. Here, the i-layer complicates matters due to its capacitive offset and a combination of CV and TIBIC was used to determine an approximate doping profile. Crosssectional samples were produced by a diamond saw and cleaned with a 30 keV Ga focused ion beam. Combining cross-sectional TIBIC results and CV data gave an approximate doping and thickness of 1 · 1014 cm3 and 15 lm, respectively [14]. Note the aim is not to verify TCAD simulation [10] but to make general interpretations, and approximate device structures should suffice.
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A 15 MeV O beam was focused to a spot size of 1 lm and (200 · 200) lm2 scans performed over the DUT at biases ranging from 0 to )20 V. Sparse sampling (4 lm steps), combined with single ion switching ensured damage levels remained minimal (2500 ions/bias). Previous experiments on the same device revealed that this level of damage does not interfere significantly with interpretation [18]. The same procedure was repeated for 11 MeV C. After averaging over the scan to increase the SNR, the SET bias dependence was extracted as indicated in Fig. 2. Note the clear distinction between two separate phases, which we term, somewhat prematurely, the low-field or ambipolar phase (A) and high-field or bipolar phase (B) with respective durations of tA and tB . Here, tOA > tCA and tOB < tCB . The rise-time for O is longer than that for C.
2.2. Transient ion beam induced current The system for time resolved (or transient) ion beam induced current measurements [15,16] has been discussed in detail elsewhere [17]. The DUT was mounted on a double-ended stripline chip carrier and launched onto 50 X transmission lines into 40 GHz bias tees (see Fig. 1(a)). To reduce damage, a single shot 3 GHz TDS 694C Digital Storage Oscilloscope (DSO) was used (overall system response time was 141 ps).
Fig. 2. Measured SET bias dependencies for 11 MeV C and 15 MeV O indicating the ambipolar (A) and bipolar (B) phases.
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Fig. 3. Simulated SET’s for 0.2 and 0.01 pC/lm with 0.1 lm waists on a linear-log and log-linear scale.
2.3. Technology computer aided design ISE TCAD 8.5 was used for all of the following simulations [19]. The simulated device had a pþ doping layer (B) with a peak level of 2 · 1019 cm3 and an erf distribution width of 0.2 lm. An i–n doping of 1 · 1014 cm3 and thickness of 15 lm was used. Uniform nþ doping of 2 · 1019 cm3 was assumed for the substrate. No load was simulated and the recharge time for recombination at electrodes depends on dielectric relaxation times (sd ¼ q e). sd is bias invariant and defines the ‘‘intrinsic’’ RC time constant of the material (characteristic time for carrier density changes [20]). Here, si=n 50 ps (dominant) and spþ ;nþ 1 fs assuming low-field mobilities at room temperature. Models assumed in all simulations are (1) Fermi-statistics, (2) band-gap narrowing (BGN) in the pþ and nþ base, (3) carrier velocity saturation (Canali model
[21]), (4) doping dependent mobilities, (5) SRH and Auger recombination (not addressed here) and (6) carrier–carrier (e–h) scattering [19]. All simulations assume an exponential ion track with waists ranging from 0.1–0.5 lm. All simulated tracks had a range of 10 lm and the LET was varied from 0.01–0.2 pC/lm. A Gaussian (5 ps FWHM) was assumed for initial track generation. The bias dependence of the simulated SET for 0.2 and 0.01 pC/lm is shown in Fig. 3.
3. TCAD results and discussion 3.1. Initial stage (1st peak) For times t < sd the EHP plasma represents a near-infinite reservoir of charge compared to the static charge (and density) stored on the device
J.S. Laird et al. / Nucl. Instr. and Meth. in Phys. Res. B 219–220 (2004) 1015–1021
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Fig. 4. Transient (a) potential and (b) electric-field distribution along the ion track for the case of )10 V bias and an LET and waist of 0.2 pC/lm and 0.1 lm, respectively. The scale on the upper left graph applies to all left graphs (volts). The scale on the right graph is kV/cm.
area S, Qs ¼ CV ¼ SðV Vbi =2ees N Þ1=2 where N is the doping concentration. Holes directly under the pþ contact (subtending a large solid angle) are rapidly extracted (traveling at near thermal velocities into the pþ region) resulting in an ultrafast response which follows the incident pulse shape (Gaussian 5 ps FWHM) until the electrode charge Qs can no longer supply charge for recombination, defined as the onset of a spacecharge limited current (SCLC) [22], tSCLC . Hence we suggest the 1st peak current, ifp (and the integrated charge at tSCLC ) is proportional to the initial static surface charge density, Qs . Indeed, the height of the 1st peak in the current was confirmed to be uncannily linear with V 1=2 for both the 0.01 and 0.2 pC/lm cases for V > 5 V. Measuring this peak (challenging) may lead to local probing of the device capacitance (Fig. 4). 3.2. Secondary stage (ambipolar phase) Local Qs is exhausted (recharging with a time constant sRC > sn ) and the surface field is small due to the high conductivity of the column. A
displacement current quickly redistributes carriers to create a dipolar field at the EHP plasma edges that opposes the external field and maintains charge neutrality (as indicated by their density and difference shown in Fig. 5). Nearly all of the potential drops from near the ion EOR (defined as the electron extraction (EE) edge) to the nþ interface. The surface to hole extraction (HE) edge (top of the plasma) is completely void of majority carriers. They were rapidly extracted prior to SCLC and cannot be replaced since the dipolar field and pþ regions are reflective to electrons [23]. At the same time, large gradients in carrier densities cause a large change in the quasi-electron and hole Fermi levels resulting in lateral fields. Electrons are pushed further into the i-region due to the weak (but non-zero field in the plasma) and out, due to the lateral fields. As expected, holes move in the opposite sense: they move up the column and out (the lateral field is opposite near the surface). Both the electron and holes on the outer skin of the plasma terminate the external field, which must meet the edge at close to 90 (by definition of a highly conducting column).
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Fig. 5. The relative (a) electron and (b) hole densities (on the same scale) along the ion track as well as their difference (c). The difference indicates the excess charge responsible for the dipolar field. The dashed lines indicates the time dependence of the EH plasma edges (EE and HE). A log scale is used to indicate the HE near the top surface.
Another way of viewing this; which is why the authors believe it to be the charge density and not the total charge [22] that matters, is that holes move further away from the SCL region to find electrons with which to terminate. By charge neutrality, the same consideration applies to electrons terminating at the depletion edge. Laser studies on the same device indicate no presence of SC effects even though the injected charge (delivered over almost 1500 times the area) is almost twice that of 15 MeV O [14]. Electrons and holes extracted from the plasma edges EE and HE do so with equal rates to maintain charge neutrality in the plasma. The current at the top (equal to the bottom) is a function of the ambipolar coefficient Da ¼ ðDn Dp Þ=Dn þ Dp and the distance from 0 to HE [23]. Depending on the bias, this process continues for several ns, by which time most of the charge is collected.
for )20 V). For high-injection, carriers attain saturation velocities due to the dipolar field and no bias dependence is observed for sB . This is still under investigation.
3.3. Final stage (bipolar stage)
4. Conclusion
The EH distribution have weakened to levels where the dipolar field cannot maintain charge neutrality and rapid collection occurs with the original static high-field (5 kV/cm at the surface
SET’s induced by MeV heavy ions in Si p–i–n devices were found to be dominated by SC screening and ambipolar diffusion. Increasing ion LET increases the average plasma density, extend-
3.4. Dependence on LET For the higher LET of 15 MeV O compared to 11 MeV C, the density dependence of the ambipolar diffusion coefficient Da [24] (reducing with increased density) combined with carrier flow being an ensemble motion [23] i.e. ‘‘traffic flow like’’, resulting in a lengthening of the ambipolar phase and a reduced relaxation rate as noted in the measurement data where tOA > tCA . Before tSCLC , a fraction of the charge was collected, resulting in a different HE edge entering the ambipolar phase.
J.S. Laird et al. / Nucl. Instr. and Meth. in Phys. Res. B 219–220 (2004) 1015–1021
ing the collection time well beyond that predicted by low-injection drift. This may have serious ramifications for modeling the heavy-ion response and BER rates for photodetectors used in space. References [1] P.W. Marshall, C.J. Dale, M.A. Carts, K.A. Label, IEEE Trans. Nucl. Sci. NS-41 (6) (1994) 1958. [2] P.E. Dodd, IEEE Trans. Nucl. Sci. 43 (2) (1996) 561. [3] S. Ramo, Proc. IRE 27 (1939) 584. [4] W. Shockley, J. Appl. Phys. 9 (1938) 635. [5] Z. Li, H.W. Kraner, Nucl. Phys. B (Proc. Supp.) 32 (1993) 398. [6] J.D. Eskin, H.H. Barrett, H.B. Barber, J. Appl. Phys. 85 (2) (1999) 647. [7] E. Vittone, F. Fizzotti, A.L. Giudice, C. Paolini, C. Manfredotti, Nucl. Instr. and Meth. B 161–163 (2000) 446. [8] C. Manfredotti, F. Fizzotti, A.L. Guidice, M. Jaksic, Z. Pastuovic, C. Paolini, P. Olivero, E. Vittone, Mater. Sci. Eng. B 102 (2003) 193. [9] E.J. Kobetich, R. Katz, Phys. Rev. 170 (2) (1968) 391. [10] J.S. Laird, T. Hirao, S. Onoda, H. Mori, H. Itoh, IEEE Trans. Nucl. Sci. 49 (3) (2002) 1389. [11] J.F. Ziegler, SRIM, 2003.
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[12] R.S. Wagner, J.M. Bradley, N. Bordes, C.J. Maggiore, D.N. Sinha, R.B. Hammond, IEEE Trans. Nucl. Sci. NS34 (6) (1987) 1240. [13] P. Blood, J.W. Orton (Eds.), The Electrical Characterisation of Semiconductors: Majority Carrier and Electron States, Academic Press, 1992. [14] J.S. Laird, T. Hirao, S. Onoda, H. Itoh, IEEE Trans. Nucl. Sci. (December 2003). [15] I. Nashiyama, T. Hirao, T. Kamiya, H. Yutoh, T. Nishijima, H. Sekiguti, IEEE Trans. Nucl. Sci. 40 (6) (1993) 935. [16] H. Schone, D.S. Walsh, F.W. Sexton, B.L. Doyle, P.E. Dodd, J.F. Aurand, N. Wing, Nucl. Instr. and Meth. B 158 (1999) 424. [17] J.S. Laird, T. Hirao, H. Mori, S. Onoda, T. Kamiya, H. Itoh, Nucl. Instr. and Meth. B 181 (2001) 87. [18] S. Onoda, T. Hirao, J.S. Laird, H. Mori, H. Itoh, T. Wakasa, T. Okamoto, Y. Koizumi, Nucl. Instr. and Meth. B 206 (2003) 444. [19] ISE TCAD Manual 8.5, 2003. [20] J.D. Jackson, Classical Electrodynamics, J. Wiley, 1975. [21] C. Canali, G. Majni, R. Minder, G. Ottaviani, IEEE Trans. Electron Dev. 22 (1975) 1045. [22] Z.H. Cho, M.K. Watt, M. Slapa, P.A. Tove, IEEE Trans. Nucl. Sci. 22 (1975) 229. [23] L.D. Edmonds, IEEE Trans. Nucl. Sci. 44 (3) (1997) 1448. [24] M. Rosling, H. Bleichner, P. Jonsson, E. Nordlander, J. Appl. Phys. 76 (5) (1994) 2855.
The role of high-injection effects on the transient ion beam induced current response of high-speed photodetectors Jamie Stuart Laird a, Toshio Hirao a, Shinobu Onoda b, Tomihiro Kamiya
a,*
a Department of Materials Development, Severe Environment Materials Laboratory, Takasaki Radiation Chemistry Research Establishment, Japan Atomic Energy Research Institute (JAERI), 1233 Watanuki-machi, Takasaki, Gunma 370-1292, Japan b Graduate School of Engineering, Tokai University, 1117 Hiratsuka, Kanagawa 259-1292, Japan
Abstract High-speed photodetectors are the primary cause of increasing bit error rates (BER) in optic fiber communication system used in radiation hard environments such as space. MeV heavy ions passing through the collection volume of a photodetector generate a single event transient which upon passing to the decoding electronics causes spurious noise (increasing the BER). The time-resolved (or transient) ion beam induced current response of a photodetector is largely influenced by high-injection effects such as space-charge screening that perturb the electric-field distribution leading to drastic alterations in carrier velocity distributions, local mobilities and charge collection characteristics. Here, we examine the transient response of a Si p–i–n photodetector irradiated with 15 MeV O and 11 MeV C ions and discuss the role of high-injection effects with the aid of Technology Computer Aided Design (TCAD) software. Ambipolar diffusion was found (experimentally and theoretically) to dominate charge transport for high-injection levels present for most heavy ions. Light ions also experience similar conditions, but over a much shorter period. 2004 Elsevier B.V. All rights reserved. Keywords: Transient ion beam induced current; Time resolved ion beam induced current; Si p–i–n photodiode; GHz photodetectors; TCAD; Photodiode; Ambipolar diffusion; SET; BER
1. Introduction High-speed photodetectors are the primary source of increasing bit error rates (BER) in optical communication systems used in radiation hard environments [1]. MeV ions passing through the collection volume of a photodetector generate a transient current or single event transient (SET) which passes to decoding electronics increasing the * Corresponding author. Tel.: +81-27-356-9346/346-9320; fax: +81-27-346-9687. E-mail addresses: [email protected] (J.S. Laird), [email protected] (T. Kamiya).
BER. They cannot be filtered since they contain frequency components common with that of the receiver signal. The thin absorption region of photodetectors makes them particularly susceptible to MeV heavy ions (generated by proton induced nuclear reactions or high-energy recoils). Designing possible mitigation schemes for BER restoration requires the ability to measure (or reliably simulate), their transient response. There appear to be two paradigms for approaching the problem theoretically. One based on solving the Poisson equation, continuity equations and transport models self-consistently, is the backbone of the ‘‘TCAD’’ based approach [2]. The
0168-583X/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2004.01.206
1016
J.S. Laird et al. / Nucl. Instr. and Meth. in Phys. Res. B 219–220 (2004) 1015–1021
other approach uses theories based on Shockley– Ramo–Gunn theory [3,4] and Laplacian methods to derive the form of the SET for more specific situations [5–8]. These approaches lead to reasonable interpretation but do not fully describe carrier dynamics with non-uniform electron–hole pair (EHP) distributions (large lateral and longitudinal gradients in EHP density distributions) where Fermi–Dirac statistics must be applied. These high densities coupled with the fact that all relevant parameters depend on this density, lead to large perturbations of the above models requiring the possible use of correction factors. To examine the response in detail we use TCAD to examine high- and low-injection regimes and their transition point for different device conditions (bias) and
EHP distributions (LET and width). It was found that under ultra high-injection, the static electric field is distorted to the point where the transient response is predominantly determined by the dynamics of the EHP plasma, which for most of the collection time can be described by ambipolar diffusion. Measurements in a Si p–i–n device with 11 MeV C and 15 MeV O confirm these findings.
2. Experimental To examine the role of high-injection, we measure and simulate the response to heavy ions with the same approximate range but different average LET. Here the model of Kobetich and Katz [9]
Fig. 1. (a) DUT mounted on TIBIC chip carrier and its external connection to the bias-T. (b) DUT cross-section and equivalent circuit connected to the 50 X transmission line and DSO.
J.S. Laird et al. / Nucl. Instr. and Meth. in Phys. Res. B 219–220 (2004) 1015–1021
was used for track structure estimates for 11 MeV C and 15 MeV O. Although these results are not used in TCAD, for reasons pointed out in [10], they do illustrate that both ion tracks have the same functional form and end of range (EOR) to within ±0.1 lm. Differences in the SET are due to differences in initial carrier densities or energy-loss (pC/lm), which for 11 MeV C and 15 MeV O are 50 and 75 fC/lm, respectively [11]. 2.1. Device structure and fabrication The device under test (DUT) was a Si p–i–n photodiode used for communication modules operating near 1.5 GHz at )10 V. Shown in Fig. 1 is cross-sectional view of the DUT and its TIBIC mounting configuration (top) as well as its equivalent circuit (bottom). Use of a chip carrier avoids most parasitic elements such as inductance and capacitance and is important for examining highspeed devices where large RC time constants result in transient fall-times characteristic of the circuit, not the charge collection [12]. Capacitance voltage (CV) measurements are typically employed to measure doping profiles [13]. Here, the i-layer complicates matters due to its capacitive offset and a combination of CV and TIBIC was used to determine an approximate doping profile. Crosssectional samples were produced by a diamond saw and cleaned with a 30 keV Ga focused ion beam. Combining cross-sectional TIBIC results and CV data gave an approximate doping and thickness of 1 · 1014 cm3 and 15 lm, respectively [14]. Note the aim is not to verify TCAD simulation [10] but to make general interpretations, and approximate device structures should suffice.
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A 15 MeV O beam was focused to a spot size of 1 lm and (200 · 200) lm2 scans performed over the DUT at biases ranging from 0 to )20 V. Sparse sampling (4 lm steps), combined with single ion switching ensured damage levels remained minimal (2500 ions/bias). Previous experiments on the same device revealed that this level of damage does not interfere significantly with interpretation [18]. The same procedure was repeated for 11 MeV C. After averaging over the scan to increase the SNR, the SET bias dependence was extracted as indicated in Fig. 2. Note the clear distinction between two separate phases, which we term, somewhat prematurely, the low-field or ambipolar phase (A) and high-field or bipolar phase (B) with respective durations of tA and tB . Here, tOA > tCA and tOB < tCB . The rise-time for O is longer than that for C.
2.2. Transient ion beam induced current The system for time resolved (or transient) ion beam induced current measurements [15,16] has been discussed in detail elsewhere [17]. The DUT was mounted on a double-ended stripline chip carrier and launched onto 50 X transmission lines into 40 GHz bias tees (see Fig. 1(a)). To reduce damage, a single shot 3 GHz TDS 694C Digital Storage Oscilloscope (DSO) was used (overall system response time was 141 ps).
Fig. 2. Measured SET bias dependencies for 11 MeV C and 15 MeV O indicating the ambipolar (A) and bipolar (B) phases.
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Fig. 3. Simulated SET’s for 0.2 and 0.01 pC/lm with 0.1 lm waists on a linear-log and log-linear scale.
2.3. Technology computer aided design ISE TCAD 8.5 was used for all of the following simulations [19]. The simulated device had a pþ doping layer (B) with a peak level of 2 · 1019 cm3 and an erf distribution width of 0.2 lm. An i–n doping of 1 · 1014 cm3 and thickness of 15 lm was used. Uniform nþ doping of 2 · 1019 cm3 was assumed for the substrate. No load was simulated and the recharge time for recombination at electrodes depends on dielectric relaxation times (sd ¼ q e). sd is bias invariant and defines the ‘‘intrinsic’’ RC time constant of the material (characteristic time for carrier density changes [20]). Here, si=n 50 ps (dominant) and spþ ;nþ 1 fs assuming low-field mobilities at room temperature. Models assumed in all simulations are (1) Fermi-statistics, (2) band-gap narrowing (BGN) in the pþ and nþ base, (3) carrier velocity saturation (Canali model
[21]), (4) doping dependent mobilities, (5) SRH and Auger recombination (not addressed here) and (6) carrier–carrier (e–h) scattering [19]. All simulations assume an exponential ion track with waists ranging from 0.1–0.5 lm. All simulated tracks had a range of 10 lm and the LET was varied from 0.01–0.2 pC/lm. A Gaussian (5 ps FWHM) was assumed for initial track generation. The bias dependence of the simulated SET for 0.2 and 0.01 pC/lm is shown in Fig. 3.
3. TCAD results and discussion 3.1. Initial stage (1st peak) For times t < sd the EHP plasma represents a near-infinite reservoir of charge compared to the static charge (and density) stored on the device
J.S. Laird et al. / Nucl. Instr. and Meth. in Phys. Res. B 219–220 (2004) 1015–1021
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Fig. 4. Transient (a) potential and (b) electric-field distribution along the ion track for the case of )10 V bias and an LET and waist of 0.2 pC/lm and 0.1 lm, respectively. The scale on the upper left graph applies to all left graphs (volts). The scale on the right graph is kV/cm.
area S, Qs ¼ CV ¼ SðV Vbi =2ees N Þ1=2 where N is the doping concentration. Holes directly under the pþ contact (subtending a large solid angle) are rapidly extracted (traveling at near thermal velocities into the pþ region) resulting in an ultrafast response which follows the incident pulse shape (Gaussian 5 ps FWHM) until the electrode charge Qs can no longer supply charge for recombination, defined as the onset of a spacecharge limited current (SCLC) [22], tSCLC . Hence we suggest the 1st peak current, ifp (and the integrated charge at tSCLC ) is proportional to the initial static surface charge density, Qs . Indeed, the height of the 1st peak in the current was confirmed to be uncannily linear with V 1=2 for both the 0.01 and 0.2 pC/lm cases for V > 5 V. Measuring this peak (challenging) may lead to local probing of the device capacitance (Fig. 4). 3.2. Secondary stage (ambipolar phase) Local Qs is exhausted (recharging with a time constant sRC > sn ) and the surface field is small due to the high conductivity of the column. A
displacement current quickly redistributes carriers to create a dipolar field at the EHP plasma edges that opposes the external field and maintains charge neutrality (as indicated by their density and difference shown in Fig. 5). Nearly all of the potential drops from near the ion EOR (defined as the electron extraction (EE) edge) to the nþ interface. The surface to hole extraction (HE) edge (top of the plasma) is completely void of majority carriers. They were rapidly extracted prior to SCLC and cannot be replaced since the dipolar field and pþ regions are reflective to electrons [23]. At the same time, large gradients in carrier densities cause a large change in the quasi-electron and hole Fermi levels resulting in lateral fields. Electrons are pushed further into the i-region due to the weak (but non-zero field in the plasma) and out, due to the lateral fields. As expected, holes move in the opposite sense: they move up the column and out (the lateral field is opposite near the surface). Both the electron and holes on the outer skin of the plasma terminate the external field, which must meet the edge at close to 90 (by definition of a highly conducting column).
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Fig. 5. The relative (a) electron and (b) hole densities (on the same scale) along the ion track as well as their difference (c). The difference indicates the excess charge responsible for the dipolar field. The dashed lines indicates the time dependence of the EH plasma edges (EE and HE). A log scale is used to indicate the HE near the top surface.
Another way of viewing this; which is why the authors believe it to be the charge density and not the total charge [22] that matters, is that holes move further away from the SCL region to find electrons with which to terminate. By charge neutrality, the same consideration applies to electrons terminating at the depletion edge. Laser studies on the same device indicate no presence of SC effects even though the injected charge (delivered over almost 1500 times the area) is almost twice that of 15 MeV O [14]. Electrons and holes extracted from the plasma edges EE and HE do so with equal rates to maintain charge neutrality in the plasma. The current at the top (equal to the bottom) is a function of the ambipolar coefficient Da ¼ ðDn Dp Þ=Dn þ Dp and the distance from 0 to HE [23]. Depending on the bias, this process continues for several ns, by which time most of the charge is collected.
for )20 V). For high-injection, carriers attain saturation velocities due to the dipolar field and no bias dependence is observed for sB . This is still under investigation.
3.3. Final stage (bipolar stage)
4. Conclusion
The EH distribution have weakened to levels where the dipolar field cannot maintain charge neutrality and rapid collection occurs with the original static high-field (5 kV/cm at the surface
SET’s induced by MeV heavy ions in Si p–i–n devices were found to be dominated by SC screening and ambipolar diffusion. Increasing ion LET increases the average plasma density, extend-
3.4. Dependence on LET For the higher LET of 15 MeV O compared to 11 MeV C, the density dependence of the ambipolar diffusion coefficient Da [24] (reducing with increased density) combined with carrier flow being an ensemble motion [23] i.e. ‘‘traffic flow like’’, resulting in a lengthening of the ambipolar phase and a reduced relaxation rate as noted in the measurement data where tOA > tCA . Before tSCLC , a fraction of the charge was collected, resulting in a different HE edge entering the ambipolar phase.
J.S. Laird et al. / Nucl. Instr. and Meth. in Phys. Res. B 219–220 (2004) 1015–1021
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