# Junction Diodes. Tim Sumner, Imperial College, Rm: 1009, x /18/2006

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1 Junction Diodes Most elementary solid state junction electronic devices. They conduct in one direction (almost correct). Useful when one converts from AC to DC (rectifier). But today diodes have a wide range of applications from LEDs, photodiodes, a variety of sensors and in optical communication 1

2 The Diode Symbol The Diode Symbol: Current flows from Anode to Cathode Current Flow Anode Cathode This is how they look : Anode (Higher V) Cathode (Lower V) 2

3 The Diode Characteristics In Reverse Bias it draws significantly less current till it reaches the breakdown voltage In the Forward Bias Region the diode draws current if V anode = V cathode V 3

4 Forward Bias Characteristics In forward bias the diode draws current according to: I(V)= I S {e (V/nV T ) -1} I S is called Saturation Current V is the Diode Voltage V T = KT/q = 25.2 mv at T=20 C 0 K = Jules/Kelvin (Boltzmann s constant ) q = Cb n = 2 for discrete components n = 1 for diodes within ICs 4

5 Voltage Drop vs Current One can solve for V(I): I(V)= I S {e (V/nV T ) -1} to get V 2 -V 1 = nv T ln(i 2 /I 1 ) or V 2 -V 1 = 2.3 nv T log(i 2 /I 1 ) Conclusion: A factor of 10 in current results to 60 mv in voltage drop (n=1) or 120 mv n=2 5

6 Temperature Dependence (1N4001 in forward bias) Both I S and the exponent are temperature dependent in mv I(V)= I S {e (V/nV T ) -1} In fact most of the temperature dependence comes from I S Rule : -2 mv per 0 C C C 80 0 C C 0 0 C C C C 6 ma

7 Diodes in reverse bias In reverse bias the V<0 and as it becomes more negative the exponential term vanishes I(V)= I S {e (V/nV T ) -1} I R = - I S hence the name saturation. I S = A In practice the reverse current is much larger, of the order of na, because of leakage effects which dominate and have different temperature dependence. Rule of thumb: I S doubles every 5 0 C In reality I R doubles every 10 0 C (leakage) 7

8 Exercise 1-I: 1 Simple Rectifier Input Output I Only the positive part of the signal (shown in red) goes through But the output is hardly DC. 8

9 Exercise 1-II: 1 Add 5µF Capacitor XSC1 A B G T D1 1N4001GP Ripple V2 6V 50Hz 0Deg C2 5uF R1 5.5kohm Input: AC Output : DC + ripple Assume a output current of I out = 1 ma When the supply voltage is below ~ V out 0.7 the diode stops conducting and the capacitor discharges through the load resistor What capacitor do I need for 1% ripple noise ( = 55 mv)? 9

10 Exercise 1-III: 1 Calculating C This calculation is only valid when RC>>T Notice that when C = 5µF this approx. is not valid. 10

11 Exercise 1-1 IV: C =363.6 µf The output is almost DC XSC1 A B TG D1 V2 6V 50Hz 0Deg 1N4001GP C uF R1 5.5kohm DC Coupling 2 V/Div The resulting ripple is 45.3 mv ~ 1% The capacitor required is large!!!! DC Coupling AC Coupling 11

12 Exercise 1-VI: 1 Average Diode Current Average Current 752 ma 12

13 Exercise 1-VII: 1 Maximum Diode Current Maximum Current 1.5 A 13

14 Exercise 1-1 V: Bridge Supply The Signals without the capacitor DC Coupling 2 V/Div The Diode Bridge utilises both the positive and the negative part of the AC pulse. Hence, rectifying such a signal is easier and a smaller capacitor (half as big) does the same job. 14

15 Exercise 1-1 VI: Bridge Supply The Signals With the capacitor DC Coupling DC Coupling 2 V/Div AC Coupling: 20mV/div Since the output of the bridge rectifier has a period which is half the period of the one diode rectifier we need a filter capacitor which is half as large. The ripple voltage is shown to be 37 mv (even better than before). 15

16 Exercise 2: AND Gate VCC 5V XSC2 G 1000ohm R2 A B T Input 0 D2 1N4009 Input 1 D1 OutPut 1N4009 XFG2 Diodes in an AND gate configuration. One input disconnected (floats) The output (red) is 0.7 Volts shifted from the input (blue) 16

17 Clipping Circuits with Diodes In-Put Out-Put Often one needs to limit the range of some input analogue pulse or even to clip spikes on a digital signal. This can easily be done with a diode and a voltage source 17

18 Voltage Doubling Circuits XSC3 XSC2 XSC1 A B G T A B G T A B T G C1 D1 100uF 1N4001GP V1 10V 50Hz 0Deg D2 1N4001GP C2 100uF R1 10kohm 1mohm R3 1mohm R2 A XSC4 G T B D2 is Charging C1 here C1 Charges during the first half of the reverse phase. C1 is in series with the source during the forward phase. Hence it doubles the output voltage. The output voltage will approach to 2*V1-2*V D 18

19 Voltage Doubling Circuits XSC3 XSC2 XSC1 A B G T A B G T A B G T C1 D1 100uF 1N4001GP V1 10V 50Hz 0Deg D2 1N4001GP C2 100uF R1 10kohm 1mohm R3 R2 XSC4 1mohm G A B T The First step is about 5 Volts (V/2) The charge stored in the cap. each time can be calculated. Hence, the time it takes to stabilize can also be calculated 19

20 Voltage Doubling Circuits Here is the proof that the first step is V/2 The next step can be calculated: V D 0.7 Volts but you need the diode equation in order to calculate the current and then the charge 20

21 Appendix I: Semiconductors For those of you who are interested to see how the diodes and in general the semiconductors work. For the students who are not taking the Instrumentation course. 21

22 Semiconductor Physics I A semiconductor diode is a pn-junction. Next: Silicon properties; electron and hole carriers What us a p-type and what is an n-type semiconductor Electrical properties of semiconductors 22

23 Semiconductor Physics II Silicon Lattice Bound electrons Silicon atoms are held in place by 4 covalent bonds. At sufficiently low Temperature there are no free electrons or holes (carriers) At room temperature some bonds brake (thermal excitation) and n free electrons and p holes are created. n = p = n i Si Si Si Hole Si Si Si Si Si Si Silicon atoms Free Electron 23

24 Semiconductor Physics III The number of carriers n i is obviously temperature dependent: n i2 = BT 3 e (-E G /KT) (proof in App. II) B= K -3 cm -6 E G = 1.12 ev (Si) K = ev/k At 300 K n i = to be compared with Si-Atoms/cm 3 The semiconductor conductivity rises with temperature 24

25 Semiconductor Physics IV Energy Bands Metals have no gap between the conduction band and the last bound band. Insulators have a large gap Semiconductors have a small gap ~ 1eV At T>0 thermally excited electrons move to the conduction band leaving holes behind. This is why the conductivity rises with Temperature 25

26 Semiconductor Physics III Diffusion Current The net current created by thermal excitation is of course zero because the motion is random and the silicon carrier density is uniform. But suppose that the carrier density is made non-uniform. In this case the thermal excitation results to the Diffusion Current: I D. Where p, n are the hole and electron densities 26

27 Semiconductor Physics IV Drift Velocity and Current The carriers (electrons/holes can also drift under the influence of an electric field E. The Drift velocity is proportional to the Electric field but different for electrons and holes: The constant µ p is the mobility for electrons and µ n the mobility for holes 27

28 Semiconductor Physics V Drift Current Density For Si the electron mobility is 1350 cm 2 /Vs and the hole mobility is 480 cm 2 /Vs. From first year physics one can calculate that the current density due to the drift velocity is: 28

29 Doped Semiconductors (VI) Doped semiconductors come either as n- or p-type (electrons or holes are predominately the carriers) Introducing small Phosphorus ( which has 5 valence electrons) impurities generates an n-semiconductor since one electron remains free. Hence Phosphorus is a Donor. Boron has three valence electrons. Introducing Boron in Si will crate holes because the Boron takes one electron from Si to form covalent bonds in the Si lattice. Hence Boson is an Acceptor. Donor Acceptor 29

30 Doped Semiconductors (VII) The donor electrons occupy energy states just below the conductivity band The holes created by the acceptors occupy energy states which are just above the zone with the bounded electrons. 30

31 Doped Semiconductors (VIII) The carriers created via implant of impurities are called majority carriers. In general carriers can always be created via thermal excitation. Therefore there are always also minority carriers. In a p-type semiconductor the majority carriers are the holes and the minority carriers are the electrons. In an n-type semiconductor the majority carriers are electrons and the minority carriers are holes Electron and hole densities obey : N-type n n0 =N D n n0 p n0 =n 2 i p n0 = n i2 /N D P-type p p0 =N A n p0 p p0 =n 2 i n p0 = n i2 /N A Notation: n n0 / p n0 = number of electrons/holes in n-type Semiconductor at thermal equilibrium N D = number of donors n p0 /p p0 = number of electrons/holes in p-type Semiconductor at thermal equilibrium N A = number of acceptors 31

32 pn-junction in open circuit (VII) As discussed before n-type of carriers will diffuse towards p-type and p-type of carriers will diffuse towards n-type creating I D. There they will recombine. This will leave + charges in the n-region and charges in the p-region mostly close to the junction. Therefore a carrier-depleted region is created close to the junction. This charge creates a field that eventually stops the process. In addition minority carriers (thermally excited holes from n-type region or electrons from the p-type region) will through the depletion region. This will crate I S (drift current). Since no net current is flowing through the diode we have : I D = I S The Junction potential is given by: V 0 =V T ln(n A N D /n i2 ) I D = I S 32

33 Depletion Region Depth (VIII) The charges from both sides of the depletion region are equal. Therefore: qx p AN A = qx n AN D x n /x p = N A /N D where x p, x n are the depths of each side of the depletion region and A is the area. The depletion region total depth is simply W dep =x p + x n : W dep = [(2ε s /q)(1/n A + 1/N D )V 0 ] 1/2 X p X n For Silicon: ε s = F/cm W = µm 33

34 pn-junction in reverse bias (IX) In reverse bias the n-side of the junction is connected to the + and the p-side to the of a source. The external field has the same direction with the depletion region field resulting to a stronger field in the depletion region. The depletion region grows as more holes are transported to the n-side and more electrons in the p-side No current flows except of a small I S I D leakage current. I = I S - I D I 34

35 The Depletion Capacitance (X) V R 35

36 The Depletion Capacitance (XI) 36

37 The Diode in Forward Bias XII Majority carriers are supplied on both sides. They neutralize some of the uncovered bound charge. The depletion layer narrows and the depletion voltage reduces The diffusion current grows I = I D - I s 37

38 The Diode in Forward Bias XIII The Saturation current can then be calculated 38

39 Diffusion Capacitance Diode display a capacitance also in forward bias. Results to a transit time τ T 39

40 Appendix II: Number of Carriers in Semiconductors Fermi Statistics is used to calculate the number of electron and hole carriers in a semiconductor. The explicit calculation is shown 40

41 Appendix II: Number of Carriers in a Semiconductor 41

42 Appendix II: II 42

43 Appendix II: III 43

44 Appendix II: IV 44

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