Bipolar Junction Transistor Models

1. Bipolar Junction Transistor Models Professor K.N.Bhat Center for Excellence in Nanoelectronics ECE Department Indian Institute of Science Bangalore-560 012 Email: knbhat@gmail.com

2. Bipolar Junction Transistor Modeling • Topics for presentation: • Merits of BJT • BJT types and structures • Current components ,current gain and breakdown voltage • Ebers –Moll model for BJT and Breakdown voltage • BJT with non uniform base region doping • Cut off frequency and effect of base spreading resistance • Heterojunction Bipolar Transistor and models

3. Comparative Merits of FETs and BJTs Parameter FETs BJTs Cut-Off Freq and Transit time Channel Length dependent Base Width dependent Practically constant (diode cut in voltage) and depends on the Eg of the semiconductor Strongly depends upon doping concentration and thickness of the channel layer Threshold Voltage

4. Comparative Merits of FETs and BJTs Parameter FETs BJTs charge storage reduces Switching Speed Charge Storage Effects Minimum – Device is basically fast Trans- Conductance gm Depends on (VGS- VTh), µn, W, Cox or Cs and L Highest in BJT per unit area. Depends upon collector current which exponentially depends on VBE/VT

5. BJT types • Alloy Junction – Uniform base (germanium and silicon transistors) • Planar Junction Transistor-graded base (Silicon transistors) • Heterojunction Bipolar Transistor-Uniform base and graded base (Transistors using Compound semiconductors- Silicon/ silicon Germanium , AlGaAs/ GaAs)

6. Alloy Junction Transistor

7. Planar Junction diode

8. Planar Junction Transistor

9. Monolithic Transistors without Isolation

10. BJT in Integrated Circuit with Isolation

11. Bipolar Junction Transistor (Uniformly doped regions) Current Components WE is base transport factor is Emitter efficiency

12. Carrier Density Distribution (BJT biased in Active region)

13. Common Base Characteristics

14. Common Emitter Characteristics Change due to Early effect

15. Base width Modulation (Early Effect) Output resistance is reduced

16. Current gain of narrow base transistors High when total emitter doping is high

17. Collector –Base Junction Breakdown Voltage , BVCBO • Junction breakdown takes place when the carrier multiplication factor ‘M’ becomes infinite. • ‘M’ depends upon the initiating carrier and is related to the applied voltage, V and the breakdown voltage BVCBO. n=6 for PNP transistor n=4 for NPN transistor

18. Maximum sustaining voltage BVCES in the Common emitter configuration At VCES , IC tends to infinity. This is possible when tends to infinity because in CE mode IB is constant

19. In high Voltage transistors the is deliberately made small to achieve VCES as close to BVCBO as possible

20. Ebers –Moll Equations for BJT Transistor Operating modes: 1.Normal mode -active , saturation and cut off . 2. Inverse mode – emitter as collector and collector as emitter EBERS –MOLL model gives a set of equations encompassing all the four operating regions of operation in circuit simulations

21. Transistor operating in Normal Mode or Forward active mode

22. Transistor operating in Inverse Mode or Reverse active mode

23. Transistor operating in Saturation Mode

24. Ebers Moll Equations Valid for all combinations of VEB and VCB Here we have

26. NPN-Transistor having Non-uniformly doped Base P-region (graded base ) Base Region

27. The doping gradation gives rise to an electric field E(x) which arises to counter the diffusion of holes. E(x) aids the flow of electrons in the x direction In thermal equilibrium

28. Carrier transport is by drift and diffusion in Graded base transistor • Velocity of carriers is three to four times higher compared to transistors with uniformly doped base region • Transit time of carriers , • Cut off frequency, • Smaller base width is required for higher cutoff frequency

29. Base spreading resistance depends upon base region doping concentration NA and base width W

30. Need for modifications in BJT For high speed, WB should be reduced . This increases rbb’ affecting the maximum operation frequency, fm , at which power gain is unity . fm is given by

31. Conflicting Requirements for fT and fm • Cutoff frequency fT can be increased by reducing base width ‘W’. This increases and lowers fm • To improve fm , should be reduced

32. r bb’ is the base spreading resistance and is proportional to the sheet resistance which varies inversely as total integrated doping concentration (= NAW) in the base region. NA should be increased when WB is reduced so that rbb’ does not increase . It leads to (1) increase in CTE , (2) reduction in β and (3) fall in DnB These conflicting requirements are met using an emitter region of wider band gap material. This BJT is the Heterojunction Bipolar Transistor (HBT)

33. First HBT in the history of BJT n-AlGaAs / p-GaAs / n+GaAs HBT B AlGaAs E n p GaAs n GaAs n+ collector C Possible because of the lattice match between GaAs and AlGaAs Heterojunction Bipolar Transistor (HBT)

34. For PNP transistor we have seen Similarly for NPN transistor , we have

37. n-AlGaAs / p-GaAs / n+GaAs HBT E 0.2m n+ > 1018/cm3 GaAs EmitterAlGaAs 0.3m ND =5x1017/cm3 B 0.15m GaAs base P=1018/cm3 0.5m GaAs collector n=1018/cm3 N+GaAs substrate C

38. AlGaAs /GaAs /GaAs HBTs fabricated at BELL Labs showed the following: • very low values of  =30 • Higher values of  were observed in Devices with larger areas. • The  increased from 30 t0 about 1800 when the surface of the base region was passivated by chemical treatment to saturate the dangling bonds with sulfur . But the  values were unstable . • Several approaches have been used to stabilize the . The most successful one has been chemical treatment with (NH4)2Sx and protect with PECVD silicon nitride

39. Silicon Germanium HBT (SiGe HBT) WB p SiGe n Si n- Si n+ Si • Band gap of Si1-xGex depends upon x. • Strained layer Si1-xGex without dislocations can be realized with thin layers of base

40. Strained Layer Epitaxy for Lattice mismatched materials Possible means of growing lattice – mismatched materials.

41. Solid Line : Calculated thickness above which it becomes energetically favorable to form misfit dislocations in strained layer GeSi grown on Si Points: experimental data for low temperature MBE growth. Dashed Line : Trend calculated for simple model of kinetically limited defect formation

42. Calculations showing the diagrammatic effect of strain upon semiconductor band gaps Unstrained Gex Si1-x Strained Gex Si1-x on Unstrained Gex/2 Si1-x/2 Strained Gex Si1-x on Unstrained Si Strained Si on Unstrained Gex Si1-x

43. Benefits of SiGe HBT over Si BJT • Collector Currents IC is larger for a given VBE

44. Benefits of SiGe HBT over Si BJT (Contd….) • IC increase improves  • IC increase decreases the emitter charging time. This improves the switching speed.

45. Effect of grading the band gap in the Base Region n p n 0 x WB E Eg(0) Eg(x) Eg(WB) Eg(x) = Eg(0) - Eg(x)

46. Electric Field due to bandgap gradation is given by . For a linear gradation For = 0.15 eV and WB = 0.1 m Electric Field = 0.15/10-5 = 15 KV / cm Cut off frequencies up to 200GHz have been achieved

47. Summary • BJTs are still popular for achieving better driving capability particularly when the load is capacitive. • Ebers Moll model enables us to estimate the currents for all modes of BJT operation. • Base region can be reduced and doping concentration in the base can be increased with HBTs. • Base region with graded doping and graded band gap lead to higher cut of frequencies due to reduction in transit time as a result of the built in electric field