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SiGe HBTs based on hierarchical hydrodynamic noise simulation
Applied Surface Science 224 (2004) 350–353
Evaluation of compact noise modeling for Si/SiGe HBTs based on hierarchical hydrodynamic noise simulation M. Bartels*, B. Neinhu¨s, C. Jungemann, B. Meinerzhagen Institut fu¨r Theoretische Elektrotechnik und Mikroelektronik, Universita¨t Bremen, Otto-Hahn-Allee 1, Postfach 33 04 40, D-28334 Bremen, Germany
Abstract The hierarchical hydrodynamic (HD) noise simulation model used in this work allows to generate a complete small-signal noise representation of the device under test. This new noise model based on full-band Monte-Carlo (MC) generated local noise sources in conjunction with transfer function fields is currently the most accurate Si/SiGe HBT noise simulation technique with tolerable CPU requirements. This new efficient numerical noise model is verified by full-band Monte-Carlo device simulations and compared to two well-known compact noise models, the thermodynamic and the SPICE model. # 2003 Elsevier B.V. All rights reserved. PACS: 02.60; 72.70; 85.30 Keywords: Noise; Si/SiGe HBT; Hydrodynamic simulation; Compact noise models
these noise sources and exploits them in a Langevin-type equation system in conjunction with transfer function fields [4] for a detailed CPU-efficient noise analysis on the device level. Auto and cross correlation spectra of the terminal current noise and small-signal y-parameters are typical results of this analysis. Note that once the Monte-Carlo (MC) generated noise sources are available, the computation of the terminal current noise is about as fast as the evaluation of the y-parameters by ac analysis!
1. Hierarchical numerical noise modeling approach Our framework for the hierarchical numerical simulation of the noise properties of Si/SiGe HBTs comprises two major modules: 1. The full-band Monte-Carlo simulator ELWOMIS is applied in bulk-mode for the extraction of the local noise sources which are then stored in a data base structure for various configurations of the Si/ SiGe material system [1–3]. 2. From this data base, the classical numerical device simulator Galene III (solving the drift/ diffusion and the hydrodynamic equations) reads *
Corresponding author. Tel.: þ49-421-218-4689; fax: þ49-421-218-4434. E-mail address: [email protected] (M. Bartels).
The above approach yields a complete y-parameter noise representation of the device based on numerical simulation. Figures of merit used for noise characterization such as the minimum noise figure are usually defined based on input-referred noise sources in accordance with the A-parameter two-port representation. For a
0169-4332/$ – see front matter # 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2003.11.066
M. Bartels et al. / Applied Surface Science 224 (2004) 350–353
351
bipolar transistor in common-emitter mode, the noise source spectra of these input-referred sources SAfv;ig;fv;ig can be obtained from the terminal current short-circuit noise spectra SifB;Cg ;ifB;Cg [5] and the y-parameter representation in the following manner: SAv;v ¼
SiC ;iC jyCB j2
SAi;i ¼ SiB ;iB SAv;i ¼
þ
SvB ;vB |ffl{zffl}
;
additional term
2 ( ) y SiC ;iB yBB BB þ SiC ;iC 2Re ; yCB yCB
SiC ;iC yBB jyCB j2
(1)
SiC ;iB : yCB
(2)
(3)
The additional term in Eq. (1) is typically zero and will only be used for the definition of the SPICE model.
Fig. 1. Current noise spectral density versus dc-current extracted from Monte-Carlo (MC), hierarchical hydrodynamic (HD), and hierarchical drift/diffusion (DD) device simulation of an NþNNþ (electrons) and a PþPPþ (holes) structure.
3. Comparison with two compact noise models 2. Verification of the numerical noise model The hydrodynamic noise modeling approach is verified in Fig. 1 by comparison to full-band Monte-Carlo device noise simulations of 1D NþNNþ (for electrons) and PþPPþ structures (for holes), respectively. Each structure consists of a lowly-doped region with 0.4 mm length, doped at 2 1015 cm3 and additional 0.1 mm long contact regions on either side doped at 5 1017 cm3. In Fig. 1, terminal current noise spectra obtained from Monte-Carlo, hierarchical drift/diffusion (DD) and hierarchical hydrodynamic (HD) device simulations are shown. It can be clearly seen that especially the hierarchical hydrodynamic noise model reproduces the MC results very well.
The hierarchical HD noise model is compared to two compact noise models, the thermodynamic [6] and the SPICE model [5]. Both compact models rely on stationary terminal currents and ac parameters for parameter extraction. Table 1 summarizes how the noise source spectral densities are evaluated for these three different noise models. In case of the SPICE model, the base resistance rB(IC) has been extracted from the small-signal z-parameters as rB ðIC Þ ¼ RefzBB zBC g, just as described in [7] as an averaged value over the frequency range 0.1 – 0.1 GHz. Please note that for maximal consistency between the three noise models, the terminal currents and ac parameters needed for the compact models have been extracted from the hierarchical numerical device model. Furthermore please note, that there are two
Table 1 Noise source spectra used by the different models
SiB ;iB SiC ;iC SiC ;iB SvB ;vB y-parameters
Thermodynamic model
SPICE model
Numerical approach
2qjIB j þ 4kB T0 RefyBB g 2q|IC| 0 0 num.
2q|IB| 2q|IC| 0 4kBT0rB(IC) (rB: see text) num.
num. num. num. (not zero!) 0 num.
kB: Boltzmann constant, T0: lattice temperature, q: elementary charge, IB,C: dc bias currents, yð Þ; zð Þ: small-signal ac parameters. ‘‘num.’’: quantity obtained directly from numerical device simulation.
352
M. Bartels et al. / Applied Surface Science 224 (2004) 350–353
major differences between the hierarchical numerical noise model and the two compact noise models. In the hierarchical numerical noise model, 1. the cross correlation spectra are typically nonzero; and 2. all correlation spectra result directly from the hierarchical hydrodynamic noise simulation (indicated by ‘‘num.’’ in Table 1) as described in [2].
4. Results and discussion The investigated sample heterojunction Si/SiGe bipolar transistor has an HD-simulated maximum
Fig. 4. Optimum generator conductance, f ¼ 10 GHz, VCE ¼ 2 V, T ¼ 300 K.
Fig. 2. Minimum noise figure versus frequency, JC 1 mA/mm2, VCE ¼ 2 V, T ¼ 300 K.
cut-off frequency of fTMax 106 GHz at JC 3 mA/ mm2. All noise simulation results refer to VCE ¼ 2 Vand a lattice temperature of T ¼ 300 K. Figs. 2 and 3 show the simulated minimum noise figure versus frequency at JC 1 mA/mm2 and the simulated noise figure versus collector current at f ¼ 10 GHz, respectively. In Figs. 4–7, the three models are compared for the optimum generator admittance for noise matching, yG;opt :¼ gG;opt þ jbG;opt , the associated gain Gassoc and the noise resistance, RN at f ¼ 10 GHz, respectively. As a general trend it can be observed that the two compact models increasingly deviate from the
Fig. 3. Minimum noise figure, f ¼ 10 GHz, VCE ¼ 2 V, T ¼ 300 K.
Fig. 5. Optimum generator susceptance, f ¼ 10 GHz, VCE ¼ 2 V, T ¼ 300 K.
M. Bartels et al. / Applied Surface Science 224 (2004) 350–353
353
for important figures of merit. This comparison reveals substantial differences between the compact models and the hierarchical hydrodynamic noise model, which was successfully verified by full-band Monte-Carlo noise simulations on the device level. If numerical device simulation is applied to generate the parameters for the compact models, the generation of the hierarchical hydrodynamic noise model is just as time consuming as the generation of the compact models. Therefore hierarchical hydrodynamic noise simulation establishes an important new method for the generation of highly accurate small-signal compact noise models. Fig. 6. Associated gain, f ¼ 10 GHz, VCE ¼ 2 V, T ¼ 300 K.
References
Fig. 7. Noise resistance, f ¼ 10 GHz, VCE ¼ 2 V, T ¼ 300 K.
numerical approach for higher collector currents. This is most pronounced for yG;opt and Gassoc. This is mainly due to the assumption of zero cross correlation within the compact models, which has less justification for higher terminal currents.
5. Conclusion A comprehensive comparison of the new hierarchical hydrodynamic noise model with two frequently used noise compact models has been presented
[1] B. Neinhu¨ s, S. Decker, P. Graf, F.M. Bufler, B. Meinerzhagen, Consistent hydrodynamic and Monte-Carlo simulation of SiGe HBTs based on table models for the relaxation times, in: Proceedings of the IWCE, Notre Dame, Indiana, USA, May 1997, p. P27. [2] C. Jungemann, B. Neinhu¨ s, B. Meinerzhagen, Hierarchical 2-D DD and HD noise simulations of Si and SiGe devices. Part I. Theory, IEEE Trans. Electron Devices 49 (7) (2002) 1250– 1257. [3] C. Jungemann, B. Neinhu¨ s, S. Decker, B. Meinerzhagen, Hierarchical 2-D DD and HD noise simulations of Si and SiGe devices. Part II. Results, IEEE Trans. Electron Devices 49 (7) (2002) 1258–1264. [4] F. Bonani, G. Ghione, M.R. Pinto, R.K. Smith, An efficient approach to noise analysis through multidimentional physicsbased models, IEEE Trans. Electron Devices 45 (1) (1998) 261–269. [5] G. Niu, J.D. Cressler, S. Zhang, W.E. Ansley, C.S. Webster, D.L. Harame, A unified approach to RF and microwave noise parameter modeling in bipolar transistors, IEEE Trans. Electron Devices 48 (11) (2001) 2568–2574. [6] F. Herzel, P. Schley, B. Heinemann, U. Zillmann, D. Knoll, D. Temmler, U. Erben, Experimental verification and numerical application of the thermodynamic approach to high-frequency noise in SiGe HBTs, Solid-State Electron. 41 (1997) 387– 390. [7] S.P. Voinigescu, M.C. Maliepaard, J.L. Showell, G.E. Babcock, D. Marchesan, M. Schroter, P. Schvan, D.L. Harame, A scalable high-frequency noise model for bipolar transistors with application to optimal transistor sizing for low-noise amplifier design, IEEE Solid-State Circuits 32 (9) (1997) 1430–1439.
Evaluation of compact noise modeling for Si/SiGe HBTs based on hierarchical hydrodynamic noise simulation M. Bartels*, B. Neinhu¨s, C. Jungemann, B. Meinerzhagen Institut fu¨r Theoretische Elektrotechnik und Mikroelektronik, Universita¨t Bremen, Otto-Hahn-Allee 1, Postfach 33 04 40, D-28334 Bremen, Germany
Abstract The hierarchical hydrodynamic (HD) noise simulation model used in this work allows to generate a complete small-signal noise representation of the device under test. This new noise model based on full-band Monte-Carlo (MC) generated local noise sources in conjunction with transfer function fields is currently the most accurate Si/SiGe HBT noise simulation technique with tolerable CPU requirements. This new efficient numerical noise model is verified by full-band Monte-Carlo device simulations and compared to two well-known compact noise models, the thermodynamic and the SPICE model. # 2003 Elsevier B.V. All rights reserved. PACS: 02.60; 72.70; 85.30 Keywords: Noise; Si/SiGe HBT; Hydrodynamic simulation; Compact noise models
these noise sources and exploits them in a Langevin-type equation system in conjunction with transfer function fields [4] for a detailed CPU-efficient noise analysis on the device level. Auto and cross correlation spectra of the terminal current noise and small-signal y-parameters are typical results of this analysis. Note that once the Monte-Carlo (MC) generated noise sources are available, the computation of the terminal current noise is about as fast as the evaluation of the y-parameters by ac analysis!
1. Hierarchical numerical noise modeling approach Our framework for the hierarchical numerical simulation of the noise properties of Si/SiGe HBTs comprises two major modules: 1. The full-band Monte-Carlo simulator ELWOMIS is applied in bulk-mode for the extraction of the local noise sources which are then stored in a data base structure for various configurations of the Si/ SiGe material system [1–3]. 2. From this data base, the classical numerical device simulator Galene III (solving the drift/ diffusion and the hydrodynamic equations) reads *
Corresponding author. Tel.: þ49-421-218-4689; fax: þ49-421-218-4434. E-mail address: [email protected] (M. Bartels).
The above approach yields a complete y-parameter noise representation of the device based on numerical simulation. Figures of merit used for noise characterization such as the minimum noise figure are usually defined based on input-referred noise sources in accordance with the A-parameter two-port representation. For a
0169-4332/$ – see front matter # 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2003.11.066
M. Bartels et al. / Applied Surface Science 224 (2004) 350–353
351
bipolar transistor in common-emitter mode, the noise source spectra of these input-referred sources SAfv;ig;fv;ig can be obtained from the terminal current short-circuit noise spectra SifB;Cg ;ifB;Cg [5] and the y-parameter representation in the following manner: SAv;v ¼
SiC ;iC jyCB j2
SAi;i ¼ SiB ;iB SAv;i ¼
þ
SvB ;vB |ffl{zffl}
;
additional term
2 ( ) y SiC ;iB yBB BB þ SiC ;iC 2Re ; yCB yCB
SiC ;iC yBB jyCB j2
(1)
SiC ;iB : yCB
(2)
(3)
The additional term in Eq. (1) is typically zero and will only be used for the definition of the SPICE model.
Fig. 1. Current noise spectral density versus dc-current extracted from Monte-Carlo (MC), hierarchical hydrodynamic (HD), and hierarchical drift/diffusion (DD) device simulation of an NþNNþ (electrons) and a PþPPþ (holes) structure.
3. Comparison with two compact noise models 2. Verification of the numerical noise model The hydrodynamic noise modeling approach is verified in Fig. 1 by comparison to full-band Monte-Carlo device noise simulations of 1D NþNNþ (for electrons) and PþPPþ structures (for holes), respectively. Each structure consists of a lowly-doped region with 0.4 mm length, doped at 2 1015 cm3 and additional 0.1 mm long contact regions on either side doped at 5 1017 cm3. In Fig. 1, terminal current noise spectra obtained from Monte-Carlo, hierarchical drift/diffusion (DD) and hierarchical hydrodynamic (HD) device simulations are shown. It can be clearly seen that especially the hierarchical hydrodynamic noise model reproduces the MC results very well.
The hierarchical HD noise model is compared to two compact noise models, the thermodynamic [6] and the SPICE model [5]. Both compact models rely on stationary terminal currents and ac parameters for parameter extraction. Table 1 summarizes how the noise source spectral densities are evaluated for these three different noise models. In case of the SPICE model, the base resistance rB(IC) has been extracted from the small-signal z-parameters as rB ðIC Þ ¼ RefzBB zBC g, just as described in [7] as an averaged value over the frequency range 0.1 – 0.1 GHz. Please note that for maximal consistency between the three noise models, the terminal currents and ac parameters needed for the compact models have been extracted from the hierarchical numerical device model. Furthermore please note, that there are two
Table 1 Noise source spectra used by the different models
SiB ;iB SiC ;iC SiC ;iB SvB ;vB y-parameters
Thermodynamic model
SPICE model
Numerical approach
2qjIB j þ 4kB T0 RefyBB g 2q|IC| 0 0 num.
2q|IB| 2q|IC| 0 4kBT0rB(IC) (rB: see text) num.
num. num. num. (not zero!) 0 num.
kB: Boltzmann constant, T0: lattice temperature, q: elementary charge, IB,C: dc bias currents, yð Þ; zð Þ: small-signal ac parameters. ‘‘num.’’: quantity obtained directly from numerical device simulation.
352
M. Bartels et al. / Applied Surface Science 224 (2004) 350–353
major differences between the hierarchical numerical noise model and the two compact noise models. In the hierarchical numerical noise model, 1. the cross correlation spectra are typically nonzero; and 2. all correlation spectra result directly from the hierarchical hydrodynamic noise simulation (indicated by ‘‘num.’’ in Table 1) as described in [2].
4. Results and discussion The investigated sample heterojunction Si/SiGe bipolar transistor has an HD-simulated maximum
Fig. 4. Optimum generator conductance, f ¼ 10 GHz, VCE ¼ 2 V, T ¼ 300 K.
Fig. 2. Minimum noise figure versus frequency, JC 1 mA/mm2, VCE ¼ 2 V, T ¼ 300 K.
cut-off frequency of fTMax 106 GHz at JC 3 mA/ mm2. All noise simulation results refer to VCE ¼ 2 Vand a lattice temperature of T ¼ 300 K. Figs. 2 and 3 show the simulated minimum noise figure versus frequency at JC 1 mA/mm2 and the simulated noise figure versus collector current at f ¼ 10 GHz, respectively. In Figs. 4–7, the three models are compared for the optimum generator admittance for noise matching, yG;opt :¼ gG;opt þ jbG;opt , the associated gain Gassoc and the noise resistance, RN at f ¼ 10 GHz, respectively. As a general trend it can be observed that the two compact models increasingly deviate from the
Fig. 3. Minimum noise figure, f ¼ 10 GHz, VCE ¼ 2 V, T ¼ 300 K.
Fig. 5. Optimum generator susceptance, f ¼ 10 GHz, VCE ¼ 2 V, T ¼ 300 K.
M. Bartels et al. / Applied Surface Science 224 (2004) 350–353
353
for important figures of merit. This comparison reveals substantial differences between the compact models and the hierarchical hydrodynamic noise model, which was successfully verified by full-band Monte-Carlo noise simulations on the device level. If numerical device simulation is applied to generate the parameters for the compact models, the generation of the hierarchical hydrodynamic noise model is just as time consuming as the generation of the compact models. Therefore hierarchical hydrodynamic noise simulation establishes an important new method for the generation of highly accurate small-signal compact noise models. Fig. 6. Associated gain, f ¼ 10 GHz, VCE ¼ 2 V, T ¼ 300 K.
References
Fig. 7. Noise resistance, f ¼ 10 GHz, VCE ¼ 2 V, T ¼ 300 K.
numerical approach for higher collector currents. This is most pronounced for yG;opt and Gassoc. This is mainly due to the assumption of zero cross correlation within the compact models, which has less justification for higher terminal currents.
5. Conclusion A comprehensive comparison of the new hierarchical hydrodynamic noise model with two frequently used noise compact models has been presented
[1] B. Neinhu¨ s, S. Decker, P. Graf, F.M. Bufler, B. Meinerzhagen, Consistent hydrodynamic and Monte-Carlo simulation of SiGe HBTs based on table models for the relaxation times, in: Proceedings of the IWCE, Notre Dame, Indiana, USA, May 1997, p. P27. [2] C. Jungemann, B. Neinhu¨ s, B. Meinerzhagen, Hierarchical 2-D DD and HD noise simulations of Si and SiGe devices. Part I. Theory, IEEE Trans. Electron Devices 49 (7) (2002) 1250– 1257. [3] C. Jungemann, B. Neinhu¨ s, S. Decker, B. Meinerzhagen, Hierarchical 2-D DD and HD noise simulations of Si and SiGe devices. Part II. Results, IEEE Trans. Electron Devices 49 (7) (2002) 1258–1264. [4] F. Bonani, G. Ghione, M.R. Pinto, R.K. Smith, An efficient approach to noise analysis through multidimentional physicsbased models, IEEE Trans. Electron Devices 45 (1) (1998) 261–269. [5] G. Niu, J.D. Cressler, S. Zhang, W.E. Ansley, C.S. Webster, D.L. Harame, A unified approach to RF and microwave noise parameter modeling in bipolar transistors, IEEE Trans. Electron Devices 48 (11) (2001) 2568–2574. [6] F. Herzel, P. Schley, B. Heinemann, U. Zillmann, D. Knoll, D. Temmler, U. Erben, Experimental verification and numerical application of the thermodynamic approach to high-frequency noise in SiGe HBTs, Solid-State Electron. 41 (1997) 387– 390. [7] S.P. Voinigescu, M.C. Maliepaard, J.L. Showell, G.E. Babcock, D. Marchesan, M. Schroter, P. Schvan, D.L. Harame, A scalable high-frequency noise model for bipolar transistors with application to optimal transistor sizing for low-noise amplifier design, IEEE Solid-State Circuits 32 (9) (1997) 1430–1439.