1. ECE 4211_Lecture L4_Week 4-1 02072017 F. Jain
P-n and n-p junction summary: Slide 1, p. 186 Heterojunctions: slides 2-14, Chapter 2, pp Fabrication and characterization of p-n junctions: slides15- 18, pp Application of p-n junction Chapter 3A:slides 19-26, pp Bipolar Junction Transistors Chapter 3B: slides 26-40, pp

2. Heterojunctions: Single and double heterojunctions
Single heterojunctions: Energy band diagrams for N-AlGaAs – p-GaAs and P-AlGaAs/n-GaAs heterojunctions under equilibrium
Fig. 35 (P. 163). Energy band diagram per above calculations. N-p heterojunction.
Fig. 36.(p. 163) Energy band diagram for a p-n heterojunction.

3. Energy band diagram: Double Heterojunction
Fig. 39. A forward biased NAlGaAs-pGaAs-P-AlGaAs double heterojunction diode.
Fig. 42 Energy band diagram of a NAlGaAs-pGaAs-PAlGaAs double heterostructure diode.

4. Built-in Voltage in Heterojunctions
Fig. 33. Energy band diagram line up before equilibrium.

5. Built-in Voltage in Heterojunctions

6. Built-in Voltage in Heterojunctions Cont.

7. 2.9.3.2. Built-in Voltage Method II: Gauss' Law
(145)

8. 2.9.4. Forward-Biased NAlGaAs-pGaAs Heterojunction
Fig.34 Carrier concentrations in an n-p heterojunction
Electron diffusion from N-AlGaAs to the p-GaAs side,
Hole diffusion from pGaAs to the N-AlGaAs,
(73)
(162)
(161)
(164)

9. I-V Equation
Next we substitute the values of npo and pNo in Eq. 107
(170)

10. I-V Equation and Current Density Plot
Here, we have used the energy gap difference DEg=Eg2-Eg1. From Eq. 174 we can see that the second term, representing hole current density Jp which is injected from p-GaAs side into N-AlGaAs, and it is quite small as it has [exp-(DEg/kT)] term.
As a result, J ~ Jn(xp), and it is
Fig. 38B Current density plots.

11. Fig .41. Minority carrier concentrations in p-GaAs and in p-AlGaAs.
Carrier Confinement in lower energy gap layer in double heterojunctions
Fig .41. Minority carrier concentrations in p-GaAs and in p-AlGaAs.
Thus, the addition of P-AlGaAs at x=xp+d forces the injected electron concentration quite small. That is, it forces all injected carrier to recombine in the active layer. This is known as carrier confinement.

12. Photon confinement in higher index of refraction layer (lower energy gap layer) forming a waveguide region between two wider energy gap and lower index layers (p.170)
When electron and holes recombine in the GaAs layer, they produce photons.
AlGaAs layers have lower index of refraction than GaAs layer. As a result it forms a natural waveguide.
In the laser design example, we have mentioned various methods for the calculation of modes in such a slab waveguide. Also we need to calculate the confinement factor G of the mode. Confinement factor also determines the JTH. Generally, the confinement factor becomes smaller as the thickness of the active layer becomes narrower. This also depends on the index of refraction difference between the active and the cladding layers.

13. 2.9.8 Double heterojunction with a quantum well
By reducing the thickness of p-GaAs layer to Å, we obtain a quantum well double heterostructure as shown schematically in Fig. 42B, page 173.
AlxGa1-xAs
GaAs
∆EV
∆EC
V(z) z
-EG
-EG+∆EV
∆Ec = 0.6∆Eg
∆Ev = 0.4∆Eg
Fig. 42 B GaAs quantum well with finite barriers produced by AlGaAs layers.

14. diffusion of p- impurities in n-Si,
2.8. Fabrication of Diodes
Interfacing of an n- and a p-type semiconductor forms a p-n junction (or diode). Experimentally, this is done by one of the following methods including:
diffusion of p- impurities in n-Si,
ion implantation of donor atoms in p-Si (generally this is followed by annealing to eliminate the damage to the lattice caused by high energy implantation), and
epitaxial growth (depositing a p- layer on n-type substrate). In the case of diffusion or ion implantation, the impurity or dopant concentration is higher in the top layer than the substrate.

15. Diffusion from an infinite source: Predeposition p.143
Fig The impurities distribution during predeposition. Note the increasing junction depth as a function of predeposition duration.

16. Junction depth measurements
Figure (a) Sample before Diffusion (Width polished side up)
(b) Sample after Diffusion (p-type)
(c) Sample after back etch of p-Si diffused Layer.
Figure 25. Dicing and Mesa Formation

17. Electrical Characterization of p-n diodes
Figure 26. (a) Left: Circuit connections for current source and voltage meter. (b) Right: Sample after Diffusion (p-type)
Figure 27. C-V measurements
Figure 29. Solar cell measurements

18. Chapter 3A Applications of p-n junctions
3.1. Bipolar Junction Transistors (BJTs) 198
3.2 Semiconductor Controlled Rectifiers (SCRs) 199
3.3 Triacs
3.4 LEDs & LASERs
3.5 Solar cells, Photodiodes and CCD/MOS Imaging
3.7 Field-Effect Transistors FETs using source and drain regions forming p-n or n-p junctions
BJTs

19. P-n-p-n or Silicon Controlled Rectifiers (SCRs)

20. Triacs or two Silicon Controlled Rectifiers (SCRs) in parallel
Fig. 3 Equivalent representation of a triac modeled as two SCRs in parallel.

21. LEDs
Fig. 6. A typical LED encased in an epoxy dome.

22. Lasers
Fig. 7. AlGaAs-GaAs DH (double heterostructure) laser structure.

23. Fig. 8B V-I characteristics of a p-n junction solar cell.
Solar cells
Fig. 8A Voltage polarity and direction of current flow in a p-n junction solar cell.
Fig. 8B V-I characteristics of a p-n junction solar cell.

24. 3.5.3. p-n Photodiodes and p-i-n Avalanche Photodiodes (APDs)

25. FETs
Fig. 16B. N-channel FET.
Fig. 16A. p-channel FET.

26. N-p-n BJT as fabricated using p-Si substrate
Figure 5. Cross-section and Top view of a n-p-n transistor

27. P-n-p BJTs current flow (ECE 4211 2/7/17 F. Jain)
Fig. 1C. Details of currents in a p-n-p transistor operating in the active mode.
C1 and C2 are to be determined using boundary conditions
(16)

28. Minority Carrier Distribution in the Base
C1 and C2 are to be determined using boundary conditions
(26)
(27)
31)

29. BJT parameters

30. BJT parameters: base transport factor aT
Base transport factor relation
The second term in ICP dominates under forward basing and it simplifies to
Here also the second term in IEP dominates under forward basing and it simplifies to
The base transport factor (ratio of ICP to IEP ) is aT
If the ratio of junction areas is similar, aT

31. P-n-p BJT injection efficiency
Emitter-base junction current injection efficiency relation
(6)
We know the relation for IEP
IEN is obtained by knowing the minority electron n(x) or excess election concentration dn(x) on p-side like in p-n diodes
Here also the dominant second term in IEP simplifies to
The injection efficiency (ratio of IEP to IE ) is g
Using tanh(W/Lp)= W/Lp, it simplifies to

32. P-n-p BJT Collector Current
P-n-p BJT Current Gain
Common base current gain relation assuming collection efficiency to be unity.
(45)
Common emitter current gain relation at DC or low frequencies
bo = ao/(1-ao)
P-n-p BJT Collector Current
Collector current is made of two parts: 1) Hole current ICP and we know the expression
and 2) electron current due to reverse biased base-collector junction ICN
(43)
(15)
(44)

33. Common emitter P-n-p BJT: Current relationships
ICN is also referred as ICBO, i.e. the reverse current flowing when IE=0 (in common base).
(46)
(50)
(51)

34. Base width modulation: Early effect
When VEC is increased or VCE is made more negative, it causes VCB to be more reverse-biased. This results in an increase in the depletion width of the base-collector junction. As a consequence the width W of the neutral base region decreases.
This causes increase in the base transport factor and the current gain. As a result there is slope in the current voltage characteristics shown in Fig. 3A

35. 3B.3 Breakdown of Base-Collector Junction : Punch-through

36. 3B.4 Saturation Effects : Kirk Effect/ Base Pushout
As the collector current IC (or IEP component of IC) increases the condition pn(W)=0 is no longer true. In fact, pn(W) increases with an increase in IC. Under high injection conditions, the minority hole concentration may even become comparable to the doping in the base. The increased hole concentration affects the base-collector junction. The junction starts decreasing in width. Alternatively, the base width W starts increasing. This is known as base push-out(expand) or Kirk effect. This results in reduction of βo values at high IC levels.

37. 3B.5 Large Signal Model: Ebers-Moll Model
Fig. 4. The interaction between the two diodes by having αRIR and αFIF current sources

38.   Ebers-Moll Model

39. 3B. 6 Design of a Bipolar Junction Transistor
Design specifications: Design an n-p-n transistor with a common emitter gain, bo = The device cross-section and a typical layout is given in Fig. 5. The cut-off frequency fa = wa/2p value in GHz is also provided.
Starting substrate is an epitaxial wafer with a 10 Ohm-cm n-Si epitaxial layer on p-Si substrate. Epi thickness is not known. Given for guideline purposes are the following device parameters:
Figure 5. Cross-section and Top view of a n-p-n transistor