CHAPTER 4: P-N P N JUNCTION Part 2. M.N.A. Halif & S.N. Sabki

Transcription

1 CHAPTER 4: P-N P N JUNCTION Part 2

2 Part 2 Charge Storage & Transient Behavior Junction Breakdown Heterojunction

3 CHARGE STORAGE & TRANSIENT BEHAVIOR Once injected across the junction, the minority carriers recombine with the majority carriers and decay exponentially with distance. These minority-carrier distributions lead to current flow and to charge storage in the p-n junction. It will effect on junction capacitance, and the transient behavior of the p-n junction due to sudden charge of bias.

4 MINORITY CHARGE STORAGE The charge of injection minority carriers/area stored in the neutral n-region can be found by integrating the excess holes in the neutral region: Q p ( exp[ qv / ] 1) = ql p kt p no A similar expression may be obtained for the stored electrons in the neutral p-region. The number of stored minority carriers depends on both diffusion length and the charge density at the boundary of the depletion region. Thus, the stored charge in terms of the injected current: Q p = L D 2 p p J p ( x ) = τ J ( x ) n Eq. (2) the amount of stored charges is the product of the current & lifetime of the minority carriers. This is because of the injection of holes that diffuse farther into the n-region before recombining if their lifetime is longer; thus more holes are stored. p p n (1) (2)

5 DIFFUSION CAPACITANCE The depletion-layer capacitance when the junction is reverse biased. Forward biased there is an additional significant contribution to junction capacitance from the rearrangement of the stored charges in the neutral regions called diffusion capacitance, C d, where 2 Aq L p C = p no d exp( qv / kt ) (3) kt diffusion capacitance of the stored holes in the neutral n-region, where A is the device cross-section area. In many applications, p-n junction may represented by an equivalent circuit. In addition to diffusion capacitance C d, and depletion capacitance C j, conductance must be included into account for current through the device.

6 DIFFUSION CAPACITANCE (Cont.) For ideal diode the conductance can be obtained from: qa G = J + J s ) kt qi kt ( (4) The diode equivalent circuit is shown in Fig. 4.21, C j stands for the total depletion capacitance.

7 Figure Small-signal equivalent circuit of a p-n junction.

8 TRANSIENT BEHAVIOR For switching applications, the forward to reverse bias transitions must be nearly abrupt & the transient time short. Fig. 4.22(a) forward current I F flows through a p-n junction. At t = 0, switch S is suddenly thrown to the right & an initial reverse current I R ~ V/R flows. Under the forward-bias condition, the stored minority carriers in the n-region for a p+-n junction is given by Q p I F = τ pj p = τ p (5) A I F is the total forward current and A device area. The turn-off time is the length of time required to remove the total stored charges Q p : t off = Q I p A R, ave Where I R,ave average current flowing during the turn-off period. = I F τ p (6) I R, ave

9 TRANSIENT BEHAVIOR (cont.) Figure Transient behavior of a p-n junction (a) Basic switching circuit. (b) Transient response of the current switched from forward bias to reverse bias.

10 TRANSIENT BEHAVIOR (cont.) The turn-off depends on both ratio of forward to reverse currents & the lifetime of the minority carriers. Fig normalized transient time versus the ratio of forward to reverse current. For fast switching devices the lifetime of the minority carriers must be reduced recombination-generation centers that have energy levels located near mid-bandgap, i.e gold in Si.

11 Figure Normalized transient time versus the ratio of forward current to reverse current.

12 JUNCTION BREAKDOWN When large reverse voltage is applied to p-n junction junction breakdown and conducts a very large current. Two important breakdown mechanisms are: (i) Tunneling effect (ii) Avalanche multiplication Avalanche breakdown imposes an upper limit on the reverse bias for most diodes. Avalanche breakdown also limits: (a) The collector voltage of a bipolar transistor (Chapter 5) (b) The drain voltage of a MOSFET (Chapter 6) Avalanche multiplication: (a) Generate microwave power as in an IMPATT diode (Chapter 8) (b) Detect optical signals as in an avalanche photodetector (Chapter 9)

13 TUNNELING EFFECT High electric is applied to p-n junction (in reverse direction) valence electron can make the transition from the valence band to the conduction band. (in Fig. 4.24(a)). Tunneling electron penetrates through the energy bandgap. Tunneling occurs only if the electric field is very high. Typical for Si and GaAs 10 6 V/cm. To achieve high field doping concentration for both p- and n- regions must be > 5 x cm -3. The breakdown mechanism for Si and GaAs junction with breakdown voltages < 4E g /q. For junction with breakdown voltage ~ 6E g /q the breakdown mechanism is the results of avalanche multiplication. At 4E g /q < V < 6E g /q : the breakdown is mixture of both avalanche multiplication & tunneling.

14 TUNNELING EFFECT (cont.) Figure Energy band diagrams under junction-breakdown conditions. (a) Tunneling effect (b) Avalanche multiplication.

15 AVALANCHE MULTIPLICATION Similar to the Avalanche Process in Chapter 3. To derive the breakdown condition, I no incident at the left hand side of the depletion width W (Fig. 4.25). Electron current In may increase if the electric field is high enough to initiate the avalanche multiplication. It will increase with distance through the depletion region to reach value M n I n at W, where M n multiplication factor and defined as I n ( W ) (7) M n = Similar, the hole current Ip increase from x = W to x = 0. Total current is constant at steady-state. The incremental current: di n dx + I no ( x x ) I = α I p n n p (8) Where α n and α p electron and hole ionization rates respectively.

16 AVALANCHE MULTIPLICATION (cont.) Figure Depletion region in a p-n junction with multiplication of an incident current.

17 AVALANCHE MULTIPLICATION (cont.) If α n = α p = α, and M n, thus α dx = Voltages in depletion region are defined from the solution of Poisson s equation. For one-sided abrupt junction: W 0 1 (9) V B (breakdown voltage) = E C 2 W = ε E s 2qN 2 C B (10) For linearly graded junction: V B = 2ECW 3 = 4E 3 N B background doping of the lightly doped side, ε s semiconductor permittivity and a impurity gradient. 3 / 2 C 2ε s aq 1/ 2 (11)

18 AVALANCHE MULTIPLICATION (cont.) Figure Critical field at breakdown versus background doping for Si and GaAs one-sided abrupt junctions.

19 AVALANCHE MULTIPLICATION (cont.) Fig GaAs has higher breakdown voltage than Si for a given N B or a, mainly because of its larger bandgap. Larger bandgap must be sufficient K.E to be gained between collisions. The inset of Fig space charge distribution of a diffused junction with linear gradient near the surface & constant doping inside the s/c. For a large a and low N B, the breakdown voltage of the diffused junction is given by the abrupt junction results shown on the bottom line of Fig For a <<<, and N B >>>, V B is given linearly graded junction results indicated by the parallel lines in Fig Fig & 4.28 assumed that s/c layer is thick enough to support the reverse bias depletion layer width W m at breakdown.

20 AVALANCHE MULTIPLICATION (cont.) Figure Avalanche breakdown voltage versus impurity concentration for onesided abrupt junction and avalanche breakdown voltage versus impurity gradient for linearly graded junction in Si and GaAs. Dash-dot line indicates the onset of the tunneling mechanism.

21 AVALANCHE MULTIPLICATION (cont.) Figure Breakdown voltage for diffused junctions. Inset shows the space charge distribution.

22 AVALANCHE MULTIPLICATION (cont.) Figure Breakdown voltage for p + -π-n + and p + -v-n + junctions. W is the thickness of the lightly doped p-type (π) or the lightly doped n-type (v) region.

23 If W << W m (Fig. 4.29) device will punched through: the depletion layer may reach the n n+ interface prior to breakdown. The breakdown voltage V B for the punch-through diode: When n-type region reduced to 20µm, the punch-through will occur first, thus = = m m m B B W W W W W V V 2 2 E inset) 4.29 in Fig. area (shaded C ' V W W W W V V m m B B ' = = = (12) AVALANCHE MULTIPLICATION (cont.) AVALANCHE MULTIPLICATION (cont.)

24 AVALANCHE MULTIPLICATION (cont.) Fig the calculated results for Si one-side abrupt junction. The solid line represents the plane junction. As the junction radius r j <<<, the V B <<< dramatically, especially for spherical junctions at low impurity concentration.

25 Figure Breakdown voltage versus impurity concentration for one-sided abrupt doping profile with cylindrical and spherical junction geometries, where r j is the radius of curvature indicated in Fig

26 HETEROJUNCTION Heterojunction junction formed between two dissimilar s/c. Fig. 4.31(a) Two s/c are assumed to have different E g, ε s, work function qφ s, and different electron affinities qχ. qφ s energy required to remove an electron from E F to position outside the material, called vacuum level. qχ - energy required to removed an electron from the bottom of E C to vacuum level. The difference energy of the cond. band edges in two s/c: and = q χ (13) ( ) E C ( ) C 2 χ 1 EV = Eg 1 + qχ1 Eg2 qχ 2 = E g E (14) Energy band different, E g = E g1 E g2

27 HETEROJUNCTION (Cont.) Fig. 4.31(b) equilibrium band diagram of an ideal abrupt heterojunction formed between these s/c. Assumed that there is a negligible number of generation-recombination at two interface (for two dissimilar s/c). It is valid only when heterojunction are formed between s/c with closely matched with lattice constant. There are 2 basic requirements in the construction of energy band diagram: (i) EF must be the same on both sides of the interface in thermal equilibrium. (ii) The vacuum level must be continuous & parallel to the band edge. The total built-in potential: V = V + V (15) bi b 1 b 2

28 HETEROJUNCTION (Cont.) V bk = ε N ε ( V V ) l l bi 1 N 1 + ε 2 N 2 (16) k = 1, l = 2, and if k = 2, l = 1 N 1 and N 2 doping concentration in s/c 1 and 2 respectively. Depletion width are: x k = 2ε1ε qn f 2N l ( Vbi V ) ( ε N + ε N ) (17) For k = 1, l = 2, and f = 1, and if k = 2, l = 1, and f = 2

29 Figure (a) Energy band diagram of two isolated semiconductors. b) Energy band diagram of an ideal n-p heterojunction at thermal equilibrium.

30 SUMMARY Part 2 of p-n junction covered from charge storage & transient behavior with the sub-discussion of minority carrier, diffusion capacitance, transient behavior, then a junction breakdown in a focused of avalanche multiplication and finally the heterojunction. A limiting factor of the p-n junction operation is junction breakdown especially due to avalanche multiplication. Some equations of breakdown condition for p-n junction has been derived from the factor of doping concentration & device geometry. A related device is the heterojunction formed between two dissimilar s/c.

31 Make everything as simple as possible, but not simpler Albert Einstein

32 Want to Be Genius? Tathagat Avatar Tulsi 15 years old Lev Davidovich Landau Enter University at age 14, Finish PhD at age 19, Professor at age 27 Died at age 60. Graduated 1 st degree in Physics at 10 Became the youngest in the world to complete his M.Sc at age 12. On course to get his doctorate at the Indian Institute of Science (IISc), before he turns 17.

33 Genius using bicycle. The institute's youngest alumnus is in a hurry to complete his PhD and turn professor by 17. Colin Maclaurin of Scotland became a professor at 19 in the 18th Century. Tulsi's PhD thesis is on identifying roomtemperature superconductors. "I will love to win a Nobel Prize. It has a place in my dream but that is not my main aim in life," he says. World is watching Tulsi what about you??? The young scientist cycles to work