Abstract
Amplifying a signal typically requires an intervening effect or party as illustrated by the analogy in Fig. 3.1a. Similar comments apply to switching (Fig. 3.1b). In the early twentieth century vacuum tube triodes (Fig. 3.1c) began replacing the earlier mechanical and electromechanical amplifying/switching devices, as discussed in Chap. 1. Such triodes were the first all-electronic amplifiers and switches.
“This thing’s got gain!”
W. H. Brattain, Bell Laboratories 1947
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Notes
- 1.
The term triode follows the naming convention of diodes and here refers to the three different paths in such devices. Tetrode and pentode, etc., vacuum tubes were also developed, containing 4 and 5 terminals, etc., respectively.
- 2.
Important early work using point-contact devices and circuits for radio signal detection and amplification was due to Eccles and Losev (often spelt Lossev).
- 3.
A large part of this early effort was devoted to developing field effect devices, which, although unsuccessful at the time, allowed important insights that led to the first transistors. Field effect transistors are covered in Chap. 4.
- 4.
J. Bardeen and W. H. Brattain, Phys. Rev. 74, 230 (1948).
- 5.
W. Shockley, Bell Syst. Tech. J. 28, 435 (1949).
- 6.
The term “bipolar” is used to describe devices that depend on both types of carriers (e.g., the pn diode or BJT). “Unipolar” devices on the other hand usually refer to devices that mainly rely on majority carriers for their operation (e.g., Schottky diodes and MOSFETs).
- 7.
Although most of the discussion in this chapter focuses on npn transistors, the corresponding equations for pnp transistors will have the same form but with the current directions and voltage polarities reversed.
- 8.
The doping gradient means that the band edges must be sloped in thermal equilibrium, which leads to the built-in electric field described by Eq. (3.5).
- 9.
This result arises by integrating both sides of Eq. (3.7) and using the junction law, Eq. (2.44).
- 10.
Cf. footnote of Eq. (2.37), where U is given by the integrand in Eq. (3.15).
- 11.
For a long emitter x E is replaced by L p .
- 12.
Equations (3.27) assume a short emitter and collector.
- 13.
Recall the emitter current is negative or opposite in sign to the collector current under forward-active bias.
- 14.
J. M Early, Proc. IRE 40, 1401 (1952).
- 15.
V t is usually referred to as the “thermal voltage.”
- 16.
See Eq. (2.45).
- 17.
For example, if large numbers of electrons are swept through the base–collector junction under forward-active bias there will be a significant average negative charge added to the fixed charges in the depletion layer. Qualitatively, this results in a net charge increase in the negative side of the depletion layer and a net decrease in the positive side, which means the depletion width on the p-side (−x p) becomes smaller and leads to an increase in the base width, x B, at large collector currents, known as the Kirk effect (C. T. Kirk, IRE Trans. Electron Devices ED-9, 164 (1962).
- 18.
This makes sense intuitively since the motion of a hole corresponds to the movement of many electrons in the valence band (see Appendix A) and thus has a larger “inertia” compared to the free electrons in the conduction band.
- 19.
A smaller band gap in the emitter means that the intrinsic carrier concentration will increase, which leads to an increase in the amount of holes injected into the emitter of an npn transistor and thus lowers the emitter injection efficiency.
- 20.
This problem may be somewhat difficult and/or lengthy.
References
Muller, R.S., Kamins, T.I.: Device Electronics for Integrated Circuits, 3rd edn. Wiley, New York (2003)
Leaver, K.D.: Microelectronic Devices, 2nd edn. Imperial College Press, London (1997)
Sze, S.M., Lee, M.K.: Semiconductor Devices Physics and Technology, 3rd edn. Wiley, New York (2012)
Ng, K.K.: Complete Guide to Semiconductor Devices, 2nd edn. Wiley Interscience, New York (2002)
Schilling, D.L., Belove, C.: Electronic Circuits: Discrete and Integrated. McGraw-Hill, New York (1968)
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Problems
Problems
-
1.
Gummel numbers. Assume the data in Fig. 3.5 was measured on an idealized npn transistor structure with a base width x B = 0.75 μm. Find the Gummel number for this transistor. (Hint: use an iterative solution.)
-
2.
Asymmetric transistor structure. Find β F for an npn bipolar transistor structure with abrupt step junctions having emitter doping N dE = 2 × 1018cm− 3, base doping N aB = 1017cm− 3, and collector doping N dC = 1016cm− 3. The emitter width is 5 μm, the base width is 0.5 μm, the collector width is 20 μm, and A = 10− 4cm2. Assume also that τ n = 10− 7 s in the base, τ p = 10− 7 s in the collector, and τ p = 10− 8 s in the emitter. Calculate α R for this transistor and use it to determine the ratio of the Ebers–Moll model parameters, I F0/I R0.
-
3.
Ebers–Moll equations. (1) Use the Ebers–Moll model to calculate the voltage present on the base–emitter junction of an npn BJT when the base is open-circuited and a reverse bias exists on the base–collector junction. What is the collector current? Assume α R = 0.70, I R0 = 10− 13 A, and I CB0 = 3.14 × 10− 14 A. (2) Use the Ebers–Moll model to calculate the voltage present on the base–emitter junction of an npn BJT when the emitter is open-circuited and a reverse bias is placed on the base–collector junction. Assume α F = 0.985.
-
4.
Bipolar transistor design Footnote 20. Assuming an npn bipolar transistor structure with abrupt step junctions and 1 μm emitter width, design the doping levels and base width such that the dc current gain is 100 and the punchthrough voltage is 100 V. τ n = 10− 6 s in the base and τ p = 5 × 10− 8 s in the emitter.
-
5.
Bipolar transistor frequency limit. If the cutoff frequency of a silicon npn bipolar transistor is determined solely by the collector transit time, design the doping levels so that the BJT will operate up to 10 GHz for V BC = −10 V.
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Papadopoulos, C. (2014). Bipolar Transistors. In: Solid-State Electronic Devices. Undergraduate Lecture Notes in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8836-1_3
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