1. CHAPTER 4: P-N JUNCTION
Part I

2. SUB-TOPICS IN CHAPTER 4:
Basic Fabrication Steps
Thermal Equilibrium Condition
Depletion Region
Depletion Capacitance
I-V Characteristics
Charge Storage & Transient
Behavior
Junction Breakdown
Heterojunction

3. CHAPTER 4: Part 1 Basic Fabrication Steps (EMT 261)
Thermal Equilibrium Condition
Depletion Region (recall your EMT 111)
I – V Characteristics (recall your EMT 111)

4. BASIC FABRICATION STEPS
Oxidation
Lithography
Diffusion & Ion Implantation
Metallization

5. THERMAL EQUILIBRIUM
Most important characteristic of p – n junction: they allow current to flow easily in ONE direction.
FORWARD BIAS – +V at p-side, current I increase rapidly (mA).
REVERSE BIAS – no I flows initially, I small (A) – at critical point, I suddenly increases – “junction breakdown”.
Refer to Fig. 4.3.

6. Figure 4.3 I - V characteristics of a typical Si p-n junction.
FORWARD BIAS
REVERSE BIAS
I(A)
Figure I - V characteristics of a typical Si p-n junction.

7. BAND DIAGRAM
Fig. 4.4(a) and 4.4(b) – p and n-type of s/c materials before and after junction is formed, respectively.
Fermi level, EF, in p and n-type is near valance band and conduction band respectively.
When they are joined together, large carrier concentration gradients at the junction cause carrier diffusion. (recall your basic knowledge in EMT 111).
The combination valence & cond. band of p and n-type (Fig. 4.4 b) – lower side shows that the hole diffusion current flows from left to right, and hole drift current is in opposite direction.
Note: electron diffuse from RIGHT to LEFT, while DIRECTION OF ELECTRON CURRENT IS OPPOSITE.

8. BAND DIAGRAM Depletion region Fermi level position
Figure (a) Uniformly doped p-type and n-type semiconductors before the junction is formed. (b) The electric field in the depletion region and the energy band diagram of a p-n junction in thermal equilibrium.

9. EQUILIBRIUM FERMI LEVELS
The unique space charge distribution and the electric potential  is given by Poisson’s equation:
(1)
All donors and acceptors are ionized.
In regions far away from the metallurgical junction, charge neutrally is
maintained and space charge density is zero, where (d2/dx2) = 0,
and ND – NA + p – n = 0.
The total electrostatic potential different between the p-side and the n-side
neutral regions at thermal equilibrium is called the built-in potential Vbi:
(2)

10. EQUILIBRIUM FERMI LEVELS (cont.)
Fig. 4.5(c), we have a narrow transition region – space charge of impurity ions is partially compensated by the mobile carriers.
Depletion region / space charge region – depleted region where the mobile carrier densities are zero.
For typical p-n junction of Si & GaAs – width of each transition region << width of the depletion region, thus neglected the transition region & represent the depletion region by the rectangular distribution in Fig. 4.5(d).
xp and xn – depletion layer widths of the p- and n-sides with p = n = 0, thus
Where , and n from eq(2). Both of these variables (electrostatic potential) are plotted in Fig. 4.6 as a function of the doping concentration of Si and GaAs.
The electrostatic potential of GaAs is higher than Si because of intrinsic concentration ni.
(3)

11. Figure (a) A p-n junction with abrupt doping changes at the metallurgical junction. (b) Energy band diagram of an abrupt junction at thermal equilibrium. (c) Space charge distribution. (d) Rectangular approximation of the space charge distribution.

12. Figure Built-in potentials on the p-side and n-side of abrupt junctions in Si and GaAs as a function of impurity concentration.

13. DEPLETION REGION
To solve Poisson’s equation (eq.3), needs the impurity distribution. In this section there are two important cases:
(i) The abrupt junction
(ii) The linearly graded junction
Fig. 4.7(a) – Abrupt junction: p-n junction formed by shallow diffusion or low-energy ion implantation.
Fig. 4.7(b) – Linearly graded junction: either deep diffusion or high-energy ion implantations – impurity distribution varies linearly across the junction.

14. (a)
(b)
Figure Approximate doping profiles. (a) Abrupt junction. (b) Linearly graded junction.

15. ABRUPT JUNCTION
Space charge distribution is shown in Fig. 4.8(a), at depletion region, free carriers are totally depleted, so Poission’s equation
(4)
and
(5)
Total depletion layer width W is given by
The maximum field Em that exist at x = 0:
(6)

16. ABRUPT JUNCTION (cont.)
Figure (a) Space charge distribution in the depletion region at thermal equilibrium. (b) Electric-field distribution. The shaded area corresponds to the built-in potential.

17. ABRUPT JUNCTION (cont.)
At two region (-xp  x < 0, and 0 < x  xn) – gives the total potential variation called built-in potential Vbi:
(7)
Total depletion layer width as a function of the built-in potential:
(8)
When the impurity concentration on one side of an abrupt junction >> of the
other side – the junction is called one-side abrupt junction (Fig. 9(a)).
Fig. 4.9(b) – space charge distribution of one –sided abrupt p+-n junction
with NA >> ND. The depletion layer width of p-side << the n-side (xp << xn),
and W can be simplified to:
(9)

18. ABRUPT JUNCTION (cont.)
The field decreases to 0 at x = W, thus
Integrating Poisson’s equation with the boundary condition of zero potential in the neutral p-region or (0) = 0, the potential distribution may be written as:
(10)
(11)
shown in Fig. 4.9(d).

19. Figure (a) One-sided abrupt junction (with NA >> ND) in thermal equilibrium. (b) Space charge distribution. (c) Electric-field distribution. (d) Potential distribution with distance, where Vbi is the built-in potential.

20. ABRUPT JUNCTION (cont.)
Fig – depletion layer width & energy band diagram of p-n junction under various biasing conditions.
Fig. 4.10(a) – the total electrostatic potential across the junction = Vbi. The different potential energy from p-side to the n-side = qVbi.
Apply +ve voltage VF to the p-side – forward biased (Fig. 4.10(b)). The total electrostatic across the junction decrease by VF, and replaced with Vbi – VF. Thus forward bias REDUCED the depletion layer width.
Fig. 4.10(c), by applying VR at n-side – reverse-biased. The total electrostatic across the junction increases by VR with Vbi + VR. Thus, reverse bias INCREASES the depletion width layer.
The depletion layer width:
Where NB – lightly doped bulk concentration, and V = +ve (forward bias) and V = -ve (reverse bias). W varies as the square root of the total electrostatic potential difference across the junction.
(12)

21. Figure Schematic representation of depletion layer width and energy band diagrams of a p-n junction under various biasing conditions. a) Thermal-equilbrium condition. (b) Forward-bias condition. (c) Reverse-bias condition.

22. LINEARLY GRADED JUNCTION
For Fig. 4.11(a), it shows the impurity distribution for linearly graded function for thermal equilibrium, then the Poisson’s equation is
where a – impurity gradient (cm-4).
The electric-field distribution in Fig. 4.11(b) represents by
The built-in potential:
Depletion layer: at
(13)
(14)
(15)
(16)

23. LINEARLY GRADED JUNCTION
Since the values of the impurities concentrations at edge of depletion region (-W/2 and W/2) are the same and equal to aW/2, thus the built-in potential for linearly graded junction may be expressed as
(17)

24. Figure 4-11. Linearly graded junction in thermal equilibrium
Figure Linearly graded junction in thermal equilibrium. (a) Impurity distribution. (b) Electric-field distribution. (c) Potential distribution with distance. (d) Energy band diagram.

25. Figure Built-in potential for a linearly graded junction in Si and GaAs as a function of impurity gradient.

26. EXERCISE 1
For Si linearly graded junction with an impurity gradient of 1021cm-4, the
depletion layer width W = 0.35m. Find the maximum field and built-in voltage at room temperature.

27. DEPLETION CAPACITANCE
Basically, the junction depletion layer capacitance/area is defined as Cj = dQ/dV, where dQ – incremental change in depletion layer/unit area for an incremental change in the applied voltage dV. From Fig. 4.13, the depletion capacitance/area is given by
(18)
with unit F/cm2.

28. Figure (a) p-n junction with an arbitrary impurity profile under reverse bias. (b) Change in space charge distribution due to change in applied bias. (c) Corresponding change in electric-field distribution.

29. C – V CHARACTERISTICS
Eq(18) for depletion capacitance/area is the same as for a parallel-plate capacitor, where spacing between two plates represents the depletion width. It’s valid for any arbitrary impurity distribution.
For one-sided abrupt junction:
(19)

30. EXERCISE 2
For Si one-side abrupt junction with NA = 1019cm-3, and ND = 1015cm-3, calculate the capacitance at zero and reverse bias of 2V at room temperature.

31. EVALUATION OF IMPURITY DISTRIBUTION
For the p+ - n junction with an arbitary impurity distribution, the corresponding charge in applied voltage (shaded area) in Fig. 4.14(c) is
The expression for the impurity concentration at the edge of the depletion region:
For linearly graded junction, the depletion layer capacitance is
(20)
(21)
(22)

32. Figure (a) p+-n junction with an arbitrary impurity distribution. (b) Change in space charge distribution in the lightly doped side due to a change in applied bias. (c) Corresponding change in the electric-field distribution.

33. VARACTOR
Varactor (variable reactor) – the p-n junction that employ the voltage-variable properties of reverse-biased.
Reverse-biased depletion capacitance is given by
where for linearly graded junction, n = 1/3, and abrupt junction, n = ½.
Fig – shows 3 p+ - n doping profiles with the donor distribution ND(x) given by B(x/x0)m. B and x0 – constants. m = 1 (for linearly graded junction) and m = 0 (for abrupt junction), and m = -3/2 (for hyperabrupt junction).
The hyperabrupt profile – from epitaxial growth techniques
(23)

34. Figure Impurity profiles for hyperabrupt, one-sided abrupt, and one-sided linearly graded junctions.

35. VARACTOR (cont.)
By solving Poisson’s equation with the appropriate boundary conditions, therefore
From eq. Cj above, thus n = 1/(m+2), and for hyperabrupt junction, n > ½, and m = negative number.
When this varactor is connected to an inductor L in a resonant circuit, the resonant frequency varies linearly with the voltage applied to the varactor, where
(24)
for n = 2
(25)

36. I – V CHARACTERISTICS
By applying voltage to a p-n junction – it may disturb the precise balance between diffusion current & drift current of electrons and holes.
From Fig. 4.16: -
Forward Bias: the applied voltage reduces the electrostatic potential across the depletion region (middle of Fig. 4.16(a)). Drift current is reduced in comparison to the diffusion current - enhanced hole diffusion from p-side to n-side and electron diffusion from n-side to p-side.
Reverse Bias: the applied voltage increases the electrostatic potential across the depletion region (middle of Fig. 4.16(b)). Greatly reduced the diffusion currents – resulting small reverse current.
Note: minority carrier densities at the boundaries (-xp and xn) increase substantially above their equilibrium values under forward bias and decrease for reverse bias.

37. Figure Depletion region, energy band diagram and carrier distribution. (a) Forward bias. (b) Reverse bias.

38. IDEAL CHARACTERISTICS
Ideal I-V characteristics are derived based on:
(a) The depletion region has abrupt boundaries/outside the boundaries – the s/c is assumed to be neutral.
(b) Carriers densities at the boundaries are related by the electrostatic potential difference across the junction.
(c) The majority carrier densities are changed negligibly at the boundaries of neutral regions by the applied bias.
(d) Neither generation nor recombination current exists in the depletion region, and the electron and hole currents are constant throughout the depletion region.
In ideal case, the expression for the built-in potential may be rewrite as
(26)
Where nno and ppo – equilibrium electron densities in the n and p sides
respectively

39. IDEAL CHARACTERISTICS (cont.)
The mass action law nnoppo = ni2, and by rearrange eq (26), thus
Electron & hole density at two boundaries of the depletion region are related through the electrostatic potential difference Vbi at thermal equilibrium.
When forward bias : Vbi – VF. While for reverse bias: Vbi + VR, thus for both cases:
where nn and np – are the nonequilibrium densities at the boundaries of the depletion region in the n and p sides respectively (+V – forward bias, and –V for reverse bias).
and
(27)
(28)

40. IDEAL CHARACTERISTICS (cont.)
For low injection condition, nn ~ nno, thus
at x = -xp
(29)
and
at x = xn
(30)
THESE EQUATIONS ARE THE MOST IMPORTANT BOUNDARY CONDITIONS
FOR THE IDEAL I-V CHARACTERISTICS.

41. IDEAL CHARACTERISTICS (cont.)
Fig – illustrated the injected minority carriers recombine with the majority carriers as minority carriers move away from the boundaries. Electron and hole currents shown in the bottom of Fig
Hole diffusion current will decay exponentially in the n-region with diffusion length Lp, and electron diffusion behave the same as hole diffusion but at p-region with Ln.
The total current is constant throughout the devices and represents ideal diode equation (Generally for Ge p-n junction):
(31)
Where Js – saturation current density, and defined as
(32)
The ideal I-V characteristic is shown in Fig. 4.18(a) and (b) for Cartesian and
semilog plots.

42. Figure Injected minority carrier distribution and electron and hole currents. (a) Forward bias. (b) Reverse bias. The figure illustrates idealized currents. For practical devices, the currents are not constant across the space charge layer.

43. Figure 4-18. Ideal current-voltage characteristics. (a) Cartesian plot
Figure Ideal current-voltage characteristics. (a) Cartesian plot. (b) Semilog plot.

44. GENERATION-RECOMBINATION & HIGH-INJECTION EFFECTS
For Si and GaAs p-n junction the ideal equation (eq. 31) can give qualitative agreement because of generation or recombination of carrier in the depletion region.
For reverse bias case with large values of ni, i.e Ge, the diffusion current dominates at T = 300K, and the reverse current follows the ideal diode equation, but if ni <<<, i.e Si and GaAs the generation current in the depletion region may dominate, and the total reverse current for p+ - n junction (for NA >> ND and for VR > 3kT/q):
(33)
And g – generation lifetime, and for simple case n = p = o,
the rate of electron hole-pair generation, G is
(34)

45. GENERATION-RECOMBINATION & HIGH-INJECTION EFFECTS (cont.)
For forward bias, concentration of both electrons and holes exceed their equilibrium values. The carriers will attempt to return to their equilibrium values by recombination – the dominant generation-recombination processes in the depletion region are the capture processes.
The total forward current (for pno >> npo, and V > 3kT/q) is
(35)
Generally, the experimental results can be represented empirically by
(36)
- ideality factor. Ideal diffusion current dominant with  = 1,
and for recombination current dominant,  = 2.

46. GENERATION-RECOMBINATION & HIGH-INJECTION EFFECTS (cont.)
Fig – measurement of forward characteristics of a Si and GaAs p-n junction at T = 300K. At low current levels, recombination current dominates and  = 2, while at higher current levels, diffusion current dominates with  = 1.
For higher current levels, it increases more gradually with forward current and caused by two effects: series resistance & high injection.
For series resistance effect: at low- and medium current levels, IR drop across the neutral regions and it usually compared with kT/q (I – forward current, R – series resistance).
This IR drop reduces the bias across the depletion region, the current becomes
(37)

47. Figure Comparison of the forward current-voltage characteristics of Si and GaAs diodes at 300 K. Dashed lines indicate slopes of different ideality factors η.

48. EXERCISE 3
From Si p-n junction diode in example 5 (Sze, pg.109) and assume g = p = n , calculate the generation density for a reverse bias of 5V.

49. TEMPERATURE EFFECT
Temperature has a profound effect on device performance. Both forward and reverse case, the magnitude of the diffusion and the recombination-generation currents depend strongly on temperature.
Forward bias:
The ratio of hole diffusion current to the recombination is given by
The ratio depends on both temperature and the s/c bandgap.
From Fig. 4.20(a), the ideal diode equation will be followed over a wide range of forward biases as the temperature increases. The temperature dependence of saturation current density Js, where
(38)
(39)

50. TEMPERATURE EFFECT (cont.)
Reverse bias:
The ratio of diffusion current to the generation is given by
The ratio is proportional to the ni, as the temperature increases, the diffusion current dominates.
Fig. 4.20(b) – at low temperature, the generation current dominates and reverse current varies as (VR)1/2 for an abrupt junction (i.e W ~ (VR)1/2). As T > 175oC, the current demonstrates a saturation tendency for VR  3kT/q, at which point the diffusion current becomes dominates.
(40)

51. Figure Temperature dependence of the current-voltage characteristics of a Si diode. (a) Forward bias. (b) Reverse bias.

52. CONCLUSION OF PART 1
The p-n junction is the basic building block for other s/c devices. Understanding of junction theory serve as the foundation to understanding other s/c devices.
Modern p-n junctions are fabricated using “planar technology”.
When p-n junction is formed – the uncompensated –ve ions (NA-) on the p-side and uncompensated +ve ion (ND+) on n-side. Thus, depletion region formed at the junction.
At thermal equlibrium, the drift current (due to the electric field) balanced by diffusion current (due to concentration gradients of the mobile carriers).
When +V applied to p-side – large current will flow through the junction, while when –V applied virtually no current flows.
Practical devices depart from ideal characteristics because of carrier generation & recombination in the depletion layer, high injection under forward bias and series-resistance effect.

53. ~ Ahmed Zewail ~ 1999 Chemistry Nobel Laureate
“There is a beauty and IMPORTANCE in understanding fundamental science & not everything we do has to have immediate applications”
~ Ahmed Zewail ~
1999 Chemistry Nobel Laureate

54. “An education isn't how much you have committed to memory, or even how much you know. It's being able to differentiate between what you do know and what you don't”
~ Anatole France ( ) ~

55. Next Lecture: p-n junction (part 2)