1. 7.1 Fundamentals of BJT Operation (Qualitative Analysis)
Figure 7—1
External control of the current in a reverse-biased p-n junction: (a) optical generation; (b) junction I–V characteristics as a function of EHP generation; (c) minority carrier injection by a hypothetical device.

2. Common Base Configuration
Figure 7—2
A p-n-p transistor: (a) schematic representation of a p-n-p device with a forward-biased emitter junction and a reverse-biased collector junction; (b) I–V characteristics of the reverse-biased n-p junction as a function of emitter current.

3. Figure 7—3
Summary of hole and electron flow in a p-n-p transistor with proper biasing: (1) injected holes lost to recombination in the base; (2) holes reaching the reverse-biased collector junction; (3) thermally generated electrons and holes making up the reverse saturation current of the collector junction; (4) electrons supplied by the base contact for recombination with holes; (5) electrons injected across the forward-biased emitter junction.

4. 7.2 Amplification with BJTs
Neglect saturation current at the collector and recombination in the transition regions.
iC=BiEp
B is the base transport factor
 is the emitter injection efficiency
total emitter current
 is the total current transfer ratio or the common-base current gain
No amplification between iE and iC

5. - Electron injection across the emitter junction (iEn) and electron recombination in the base
must be included to account for the base current iB
(7-4)
- Neglect the collector saturation current
(7-5)
(7-6)
 is the base-to-collector current amplification factor or the common-emitter current gain
Since  is near unity,  can be large for a good transistor
Can iB control iC?

6. Example of an amplification circuit
Figure 7—4
Example of amplification in a common-emitter transistor circuit:
biasing circuit;
addition of an a-c variation of base current ib to the d-c value of IB, resulting in an a-c component ic.

7. 7.3 BJT Fabrication (please read this section)
Figure 7—5
Process flow for double polysilicon, self-aligned npn BJT: (a) n+ buried layer formation; (b) n epitaxy followed by LOCOS isolation; (c) base/emitter window definition and (optional) masked “sinker” implant (P) into collector contact region; (d) intrinsic base implant using self-aligned oxide sidewall spacers; (e) self-aligned formation of n+ emitter, as well as n+ collector contact.

8. 7.4 Minority Carrier Distributions and Terminal Currents
- In sections 7.1 and 7.2, we related BJT terminal currents iB, iC, and iE with various factors
, , , and B. And we have seen that current amplification is possible between base current
iB and collector current iC.
In this section we will find the mathematical expressions for iB, iC, and iE
- We first make several assumptions in order to simplify the calculations
Hole transport in the base region is by diffusion only; drift is negligible.
The emitter injection efficiency is  = 1, which means the emitter current is made up entirely of holes; No electron injection from base to emitter (component 5 in Fig. 7-3 is zero)
The collector saturation current is negligible (component 3 in Fig.7-3 is negligible)
The entire device is of uniform area A.
All current and voltages are at steady state.

9. 7.4.1 Solution of the Diffusion Equation in the Base Region
Figure 7—6
Simplified p-n-p transistor geometry used in the calculations.

10. - The excess hole concentration at the left-hand side of the base ∆pE and the corresponding
concentration on the collector side of the base ∆pC are found from Eq, (5-29):
- If the emitter junction is strongly forward biased (VEB>>kT/q), and the collector junction is
strongly reverse biased, (VCB<<0), then
- These will serve as the boundary conditions when we solve for p(xn) using the diffusion
equation.

11. - Excess hole concentration p(xn) in the base can be solved with the diffusion equation we
introduced in Chapter 4.
- The solution of this equation is
C1 and C2 can be solved with the appropriate boundary conditions
- Assume the collector junction is strongly reverse biased and the equilibrium hole
concentration is negligible compared with ∆pE

12. Figure 7—7
Sketch of the terms in Eq. (7—14), illustrating the linearity of the hole distribution in the base region. In this example, Wb/Lp = 1/2

13. 7.4.2 Evaluation of the Terminal Currents
- Excess hole concentration p(xn) in the base has a nearly linear distribution from 0 to Wb,
but it can not be perfectly linear, why?
- Now we have found out the distribution of p(xn), we can calculate terminal currents from
the gradient of the p(xn) at each edge of the base:
- The hole component of the emitter current is
- Similarly the collector current is (neglecting reverse saturation current)
- Substitute parameters C1 and C2, we have

14. - Write the equations in terms of hyperbolic functions: