CHAPTER 4: P-N JUNCTION Part I

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

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)

BASIC FABRICATION STEPS Oxidation Lithography Diffusion & Ion Implantation Metallization

THERMAL EQUILIBRIUM Most important characteristic of p – n junction: it allows 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.

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

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.

BAND DIAGRAM Depletion region Fermi level position Figure 4.4. (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.

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)

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)

Figure 4.5. (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.

Figure 4.6. Built-in potentials on the p-side and n-side of abrupt junctions in Si and GaAs as a function of impurity concentration.

DEPLETION REGION To solve Poisson’s equation eq. (3), it 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.

(a) (b) Figure 4.7. Approximate doping profiles. (a) Abrupt junction. (b) Linearly graded junction.

ABRUPT JUNCTION (4) and (5) Total depletion layer width W is given by 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 exists at x = 0: (6)

ABRUPT JUNCTION (cont.) Figure 4.8. (a) Space charge distribution in the depletion region at thermal equilibrium. (b) Electric-field distribution. The shaded area corresponds to the built-in potential.

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)

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).

Figure 4.9. (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.

ABRUPT JUNCTION (cont.) Fig. 4.10 – 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)

Figure 4-10. 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.

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)

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)

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

Figure 4.12. Built-in potential for a linearly graded junction in Si and GaAs as a function of impurity gradient.

EXERCISE 1 For a Si linearly graded junction at room temperature with an impurity gradient of 1020cm-4, calculate the built in potential. Where , and

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.

Figure 4.13. (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.

Notice Test 1 will be on Wednesday 13/8/2008 in K. Perlis (DKP1) at 8.30pm-9.30pm