1. Chapter 4 Static Characteristics 4.1 Intuitive Picture 4.2 Collector Current Density and Current Gain 4.3 Output Conductance 4.4 Equivalent Circuit Model

2. 4.1 Intuitive Picture An ideal,graded-base SiGe HBT with constant doping in the emitter, base, and collector region.  Ge content is linear graded from 0% near the metallurgical emitter-base junction to some maximum value of Ge content near the metallurgical collector-base junction,and then rapidly ramped back down to 0% Ge.  Observe in Fig 4.1 that a Ge-induced reduction in base bandgap occurs at EB edge of the quasi-neutral base, and at the CB edge of the quasi-neutral base.  This grading of the Ge across the neutral base induces a built-in quasi-drift field in the neutral base that will impact minority transport. Fig 4.1:Energy band diagram for a Si BJT and graded- base SiGe HBT,both biased in forward active mode in low-injection.

3. The Fermi level must realign itself such that it is fixed in energy to its previous (Si) value,and further, that it must be constant (flat) if the system is in equilibrium. This grading of the Ge across the neutral base induces a built-in quasi-drift field in the neutral base that will impact minority carrier transport Induced drift field will positively influence the minority electron transport through the base.The injected electrons diffuse across the base, and sweep into the electric field of the CB junction,yielding a useful collector current. The density of back-injected holes will be small compared to the forward-injected electron density,and hence a finite current gain ß ∝ n/p results. Fig 4.2:Illustration of bandgap changes induced by the introduction of Ge into the base region of an n-p-n SiGe HBT.

4. The potential barrier to injection of electron from emitter into the base is decrease.Intuitively, this will ylied expontentially more electron injection for the same applied V BE,tanslating into higher collector current and higher current gain.We can trade the higher gain induced by the Ge band offset for a higher base doping level. The present of a finite Ge content in the CB junction will positively influence the output conductance of the transistor,yielding higher Early voltage.

5. 4.2 Collector Current Density and Current Gain 4.2.1 Jc in SiGe HBT 4.2.2 Relevant Approximations 4.2.3 Other SiGe Profile Shapes 4.2.4 Implication and Optimization Issue for ß

6. Jc in SiGe HBT Fig 4.3 Schematic doping and Ge profile used in the derivation. Fig 4.4 Schematic base bandgap in a linearly graded SiGe HBT.

7. Generalized Moll-Ross collector density relation: With the condition:

8. We can get the expression With the condition:

9. We obtain the final expression where Fig 4.5 Comparison of current-voltage characteristic of a comparably constructed SiGe HBT and Si BJT.

10. The current gain issue Fig 4.6 Measure and calculated current gain ratio as a function of reciprocal temperature for a comparably constructed SiGe HBT and Si BJT. 1000/T

11. Relevant Approximations First:we can assume that △ E g,Ge (grade)  kT Second:weak Ge grading

12. Fig 4.7 Theoretical calculation of the current gain ratio as a function of Ge profile shape.

13. Other SiGe Profile Shapes Fig 4.8 schematic representation of the hybrid Ge trapezoidal profile.  Trapezoids profile

14. Fig 4.9 current gain ratio as a function of reciprocal temperature for varying ξ values.Noted that the integrated Ge content is not fixed in this case. Fig 4.10 current gain ratio as a function of reciprocal temperature for varying ξ values.Noted that the integrated Ge content is held fixed in this case.

15. Implication and Optimization issue for ß The present of Ge in the base region will enhance J C at fixed V BE over a comparably constructed Si BJT. The J C enhancement depends exponentially ob the EB boundary value of Ge-induced band offset,and linearly on the Ge grading across the base.  A box Ge profile is better for current gain enhancement than a triangular Ge profile.  The Ge-induced J C enhancement is thermally Activated (exponentially dependent on the reciprocal temperature),and thus cooling will produce a strong magnification of the enhancement.

16. 4.3 Output Conductance 4.3.1 V A Trade-offs in Si BJTs 4.3.2 V A in SiGe HBTs 4.3.3 Relevant Approximations 4.3.4 Current Gain-Early Voltage Product 4.3.5 Other SiGe Profile Shapes 4.3.6 Implication and Optimization Issue for V A and ß V A

17. VA Trade-offs in Si BJTs Basically Definition And than Q b (0) is the total base charge at V CB =0V,C cb is the base depletion capacitance. Where { W b (0) is the neutral base width at V CB =0 W m is the metallurgical base width  bi is the CB junction built-in voltage { Where

18. Fig 4.12 Schematic representation impact of the Early effect. Fig 4.11 Schematic representation of the Early effect. Increasing collector concentration degrades V A. Increasing base concentration increasing V A. Increasing base concentration degrades ß. Increasing base concentration degrades f T due to the reduction in the minority electron mobility. It is inherently difficult to simultaneous obtain high V A,high ß,and high f T.

19. V A in SiGe HBTs  Basically Definition for HBT  And than  If the nib is position-independent,there is no V A enhancement due to Ge.If n ib is position- dependent,V A will depend exponentially on the difference in bandgap between x=W b and that region in the base where n ib is smallest.

20. Fig 4.13 Dependence of VA on both N dc + and N ab - for a Si BJT. Fig 4.14 Measured and calculated Early voltage ratio as a function of reciprocal Temperature for a comparably constructed SiGe HBT and Si BJT.

21. Relevant Approximations Fig 4.15 Theoretical calculations f of the VA ratio and ß VA ratio as a function of Ge profile shape. we can assume that △ E g,Ge (grade) ≫ kT we can assume that △ E g,Ge (grade) ≪ kT

22. Current Gain-Early Voltage Product Fig 4.16 Current gain-Early voltage product ratio as a function for a comparable SiGe HBT And Si BJT.  One conventionally defines a figure-of-merit for analog circuit design:the so-call “ßVA” product.In a conventional Si BJT,it is not favorably impacted by conventional scaling. For a SiGe HBT,however,both ß and VA are decoupled from the base profile,and can be Independent tuned by changing the Ge profile shape.pppppppppppppppppppp

23. Other SiGe Profile Shapes  Trapezoids profile

24. Implication and Optimization issue for VA and ß VA Unlike J C,only the presence of a large Ge content at the CB side of the neutral base than at the EB side of the neutral base will enhance V A over a comparably costructed Si BJT. This V A enhancement depends exponentially on the Ge grading cross the base. A triangular Ge profile is better for Early voltage enhancement than a box Ge profile is,everything else being equal. The Ge-induced V A enhancement is thermally activated,and thus cooling will produce a strong magnification of the enhancement. Putting any Ge into base region of a device will exponentially enhance this key analog figure-of-merit,a highly favorable scenario given the discussion above of inherent difficulties of achieving high ßV A in a Si BJT. A reasonable compromise Ge profile design that balance the dc optimization needs of ß,V A,and ßV A would be a Ge trapezoid,with a small Ge content at the EB junction,and a large Ge content at the CB junction.

25. 4.4 Equivalent Circuit Model 4.4.1 Basic Ebers-Moll Model 4.4.2 Transport Version 4.4.3 Small-Signal Equivalent Circuit Model

26. Basic Ebers-Moll Model A fundamental assumption in this modal is that the overall transistor operation can be viewed as a superposition of both the forward and the reverse mode operation. Fig 18 The basic Ebers-Moll for a bipolar transisitor.

27. Transport Version

28. Small-Signal Equivalent Circuit Model

49. 4.5 Avalanche Multiplication 4.5.1 Carrier Transport and Terminal Current 4.5.2 Forced-V BE Measurement of M-1 4.5.3 Forced-I E Measurement of M-1 4.5.4 Effects of Self-Heating 4.5.5 Impact of Current Density 4.5.6 Si Versus SiGe

50. Carrier Transport and Terminal Current Simple analysis shows that the minimum threshold energy for impact ionization is 1.5E g Fig 21 The avalanche multiplication process in a bipolar transistor under normal operation. ……….

51. Forced-V BE Measurement of M-1 Fig 4.22 Force V BE setup for M-1 measurement.

52. Forced-I E Measurement of M-1 At high J C and V CB,self-heating and thermal runaway occur.. Fig 4.22 Force I E setup for M-1 measurement.

55. Effects of Self-Heating

56. Impact of Current Density

57. Si Versus SiGe Fig 28 M-1 versus V CB comparison between SiGe HBTs with different Ge profile Fig 27 Simulated depth profile of carrier temperature at V BE =0.7V and VCB=5.

58. 4.6 Breakdown Voltage 4.6.1 BV CBO 4.6.2 BV CEO 4.6.3 Circuit Implication

59. BV CBO Fig 29 An example of M-1 versus V CB fitting using the Miller equation..

60. BV CEO Fig 4.30 An illustration of the avalanche multiplication process with an open base..

61. Circuit Implication