Submitted by
BEFIN SKARIA DEPARTMENT OF PHYSICS
St. Peters University
CONTENTS Chapter 1 – Diode Characteristics
1.1 Introduction
1.2 Intrinsic Semiconductors
1.3 Extrinsic Semiconductors
1.3 (a) N-type Semiconductors
1.3 (b) P-type Semiconductors
1.4 Majority & Minority Carriers
1.5 P-N Junction Diodes
1.6 Forward Biasing
1.7 Reverse Biasing
1.8 Types of Diodes
1.9 Diode Equation
Chapter 2 – Diode as a Temperature Temperature Sensor
2.1 Introduction
2.2 Theory
2.3 Constant Current Source
Chapter 3 – Diffusion Capacitance 3.1
Junction Capacitance
3.2
Theory
3.3
Diffusion Capacitance
Observations Conclusion
CONTENTS Chapter 1 – Diode Characteristics
1.1 Introduction
1.2 Intrinsic Semiconductors
1.3 Extrinsic Semiconductors
1.3 (a) N-type Semiconductors
1.3 (b) P-type Semiconductors
1.4 Majority & Minority Carriers
1.5 P-N Junction Diodes
1.6 Forward Biasing
1.7 Reverse Biasing
1.8 Types of Diodes
1.9 Diode Equation
Chapter 2 – Diode as a Temperature Temperature Sensor
2.1 Introduction
2.2 Theory
2.3 Constant Current Source
Chapter 3 – Diffusion Capacitance 3.1
Junction Capacitance
3.2
Theory
3.3
Diffusion Capacitance
Observations Conclusion
Bibliography
CHAPTER – 1 DIODE CHARACTERISTIC
1.1 INTRODUCTION In electronics, a Diode is a two-terminal electronic component with asymmetric conductance; it has low (ideally zero), resistance to current flow in one- direction and high (ideally infinite) resistance in the other. Diodes were the first semiconductor electronic devices. The first semiconductor diodes called cat’s whisker diodes, developed around 1906 where made of mineral crystals such as galena. Today most diodes are made of silicon but other semiconductors such as germanium or selenium are sometimes used. A semiconductor diode, the most common type today is a crystalline piece of semiconductor material with a P-N junction connected to two electrical terminals. The most common function of a diode is to allow an electric current to pass in one direction called forward direction. While blocking current in the opposite direction (Reverse direction). By explaining the concepts of semiconductors, the band structure consists of valance band and conduction bond. The energy band occupied by the valance electrons is called valance band. It is the highest occupied band. If valance electrons acquire sufficient energy to overcome their binding energy, they will leave the valance bond. Such electrons are called free electron. The energy band occupied by these free electrons are called conduction band. Depending upon electrical properties material can be classified as insulators, conductors and semiconductors.
Semiconductors are materials whose electrical conductivity lies between those of insulators and conductors. The conductivity of semi conductor increases with temperature. At room temperature they have partially filled valance and conduction bands with a narrow energy gap between them. Eg. Germanium and silicon.
Semiconductors are two types:
1.2 INTRINSIC SEMICONDUCTORS A semiconductor in an extremely pure form is known as intrinsic semiconductor. Germanium (32G73) and Silicon (14Si28) are commonly
used
intrinsic
semiconductors.
At
sufficiently
low
temperature there is no free electron in a semiconductor are not free to wonder about as they are in metals, but rather are trapped in a bond between two adjacent ions. Electron – hole pairs As the atmospheric temperature, the ambient temperature increases some of the electrons acquire enough heat energy to break away from the valance bond and move to the conduction band. When an electron breaks away from the covalent bond and becomes free, a vacancy is left behind in the valance bond. This vacancy is termed as hole. Thus in a semiconductor electrons and holes are produced in pairs by thermal agitation.
1.3EXTRINSIC SEMICONDUCTOR The conductivity of an intrinsic semiconductor can be increased by adding a little amount of suitable impurities. The process of adding impurity to a semiconductor is known as doping. The amount of impurity added is extremely small; say 1 to 2 atoms of impurity for 10 6 atoms of semi conductor. Depending upon the type of impurity added extrinsic semiconductors are of two types.
1.3 (a) N-type Semiconductor
When pentavalent impurity atoms like arsenic, antimony, phosphorous, or bismuth having five valance electrons are added to Germanium or Silicon, covalent bonds are established between the atoms of germanium or Silicon and the impurity. Four of the five electrons of each impurity atom from covalent bonds with four of the Germanium or Silicon atoms. The 5 thelectron is free to wander within the crystal. The presence of these five electrons increases the conductivity of the crystal. Such crystals with excess free electrons is called N-type semiconductors.
1.3(b) P-type semiconductors
In P-type semiconductor, if trivalent impurity atoms like Boron, Indium, aluminum, or Gallium have three valance electrons are introduced into Germanium or Silicon; covalent bonds are established between the atoms of Germanium or Silicon and the impurity. The three valance electrons of the impurity atoms form covalent bonds with three of neighboring Germanium or Silicon atoms. This deficiency is known as hole. Due to thermal agitations the covalent bonds of an adjacent atom may break and an electron thus released may fill the hole. Thus a new hole is formed. So the hole moves from one place to another.
1.4 MAJORITY CARRIERS AND MINORITY CARRIERS In an N-type semiconductor since the free electrons out number the holes, electrons are called majority carriers and the holes minority carriers. But in the case of P-type semiconductor, holes outnumber free electrons, Hence here holes are called the majority carriers and free electrons the minority carriers.
1.5 P-N JUNCTION DIODES
P
N
Junction Diode
Symbol
If one side of a semiconductor crystal is doped with acceptor impurity atoms and the other side of the same crystal is doped with donor impurity atoms a P-N junction is formed. A P-N junction is known as a semiconductor diode or crystal diodes. When a P type semiconductor is properly joined to an N type semiconductor. We get PN junction diode. The contact surface of two types of extrinsic semiconductors is called PN junction. When P-N junction is formed. Majority carrier from the P region and that of N region will immediately cross each other across the junction by diffusion. At the junction each electron will recombine with a hole releasing a certain amount of energy. This process is called electron hole pair recombination. The recombination process will now create a thin layer of immobile ions of the junction. This layer is called depletion layer. The width of the depletion layer depends on the doping level, the heavier the doping the thinner is depletion layer.
1.6 FORWARD BIASING When a P-N junction is forward based, the positive potential drives, the holes from the P-region and negative potential
drives the electrons from the N-region towards the junction. Thus they recombine and stimulate current flow from P to N side across the junction. This process reduces the width of the depletion layer and causes a reduction in electrical resistance of the crystal. The current continues as long as the forward potential is maintained.
1.7 REVERSE BIASING When the PN junction is reversed biased the holes in the Pregion migrates towards the negative terminal of the external power source and the electrons in the N-region migrate to the positive terminal. This creates a widening of the depletion layer and an increase of resistance prevents the electron – hole recombination at the junction. Hence no current will flow across the junction as long as it reverse biased.
1.8 Types of Diodes There are several types of P_N-junction diodes which emphasize, either a different physical aspect of diode often by geometric scaling, doping level, choosing the right electrodes. 1.
Silicon Diodes A Silicon diode is a semiconductor that has positive and negative polarity, and can allow electrical current to flow in one direction while restricting it in another. The element Silicon, in its pure form acts as an electrical insulator. To enable it to conduct electricity, minute amount of other elements in a process known as doping-are added to it. When a Silicon diode is made it has both positive and negative side and a connection between the two known as the P-N junction. The two differently charged sides are a result of different elements being added to the Silicon.
2.
Germanium Diodes Germanium diodes are part of an electrical circuit and conduct electrical signal through the diode travelling in one direction only. Diodes such as the germanium diode are constructed out of a semiconductor material and impurities are added to the Germanium so it will allow the right amount of current to pass through, Though not as popular as the Silicon diode, a germanium diode does have certain advantages over Silicon, less energy lost in a Germanium diode as the current passes through as compared to the loss in a Silicon diode. This makes it an ideal choice for dealing with signals caused by small currents where a large loss of energy could disrupt the signal.
1.9 DIODE EQUATION As the mechanisms of diffusion and mobility of the carriers are affected by the lattice vibrations in crystals, they are related to the temperature in the form of Einstein’s relation,
---(1)
Where, is the diffusion constant for holes De is the diffusion constant for electrons
Is the charge mobility K is the Boltzman constant T is the temperature in Kelvin
V T = The net hole current density across the junction
Jn =
nE–eDh
– (2)
Where P – hole density
- Conc. of hole w.r to distance x - Conc. of electrons w.r to distance x Similarly the net electron current density
Je = ne E + eDe
Where n = electron density
For an unbiased PN junction the net hole current across the junction is zero. Now Jn = 0, and Je = 0 When Jn = 0, equ (2) becomes
Pe E - e = 0
= = (-Edx) Integrating,
∫
= -
∫
= ∫ ∫ = V B, the potential barrier = V B But
log = V B
= exp [ V B] = exp [ V B]
From eq (1) = V T
Pn = Ppexp[-] Similarly by putting Je = 0 we get
--(3)
= exp[-] By Law of mass action
=
2
where
is
the electron density in intrinsic
semiconductor
= much below
room temperature conc. percentage ionization of the
donor level can be expected and for the n – material
= N , the donor atom density and D
Pn = Similarly for P- material
Pp = N A , the acceptor atom density
= Now eqn. – (3) becomes
= N exp [ A ]
= 2.303 x log
Let the PN junction be subjected to forward voltage +ve. The barrier potential becomes (Vb-V). The reduced barrier potential allows increased rate of diffusion of holes from P-region to N-region. Those
current across the forward biased junction is due to the minority carriers. Hence an expression for the Diode current is obtainable by calculating the increase in the minority carrier density on the application of a forward bias. The hole density increase to
+ = Pp exp []
= Pp exp [ ] exp [ ]
-- (4)
Subtracting eq 3 from 4
= Pp exp [] exp () – 1] Similarly
= exp [] exp [ ]
The hole current in flowing from p to n region, Where, A is the cross sectional area of junction
is the drift velocity of holes )-1]
Or,
)
Where
)-1]
Similarly electron current,
Where,
is the drift velocity of electrons
The total current I=
()
--(5)
For forward bias,
( )
--(6)
For reverse bias,
If V>> , the exponential term becomes negligible small compared to unity. Now equation (5) becomes,
)-1]
--(7)
, T is expressed in Kelvin.
Where
Equation (7) gives the relation between current I and voltage V across the pn junction.
)-1]
Where the factor =1 for Ge, and =2 for Si.
CHAPTER – 2 DIODE AS A TEMPERATURE SENSOR
2.1 Introduction Temperature sensor is devices used to measure the temperature of a medium. There are mainly two kinds of temperature sensors) 1. Contact Sensors 2. Non-contact Sensors A temperature sensor is a device typically a thermocouple or RTD that provides for temperature measurement through an electrical signal. A thermocouple (T/C) is made from two dissimilar metals that generate electrical voltage in direct proportion into charges in temperature. An RTD (Resistance temperature defector) is a variable resistor that will change its electrical resistance in direct proportion to charges in temperature in a precise, repeatable and nearly linear manner. +
-
+ -
The charge of biasing voltage (forward or reverse) changes the width of the depletion region and the current through the diode. As the rise is temperature in capable of bringing more and more electron from the valance bond to the conduction based of the
semiconductor material of the diode, the current through th PN junction charges. All these information are contained in the diode equation.
)-1] Neglecting one we get,
)] Where I is the diode current through the forward biased PN
junction at temperature T (in Kelvin scale) and biasing voltage V. , e, k and n denote the reverse saturation current, electronic charge, Boltzman’s constant and ideality factor respectively. The ordinary semiconductor diode may be used as a temperature sensor. The diode is the lowest cost temperature sensor and can produce more than satisfactory results if you are prepared to undertake a two point calibration and provide a stable excitation current. Almost any Silicon diode is ok. The forward biased voltage across a diode has a temperature efficient of about 2.3mv and in reasonably linear. One advantage of the diode as a temperature sensor is that it can be electrically robust to voltage spikes induced by lightning strike. This is particularly true if power diodes (eg. IN4001) and is used to limit power dissipation during high peak currents. To improve the performance of the diode as a temperature sensor, two diode voltages (v1 and v2) can be measured at different currents (I1 and I2), typically selected to be about 1:10 ratio. The absolute temperature can be calculated from the equation:
T=
The result is in Kelvin’s (k). This is the method employed by most integrated circuit temperatures sensors and explain why some output a signal proportional to absolute temperature.
2.2 Theory P-N junction diode have negative co-efficient of resistance ie, as temperature increases resistance of diode decreases, when a diode is forward biased the width of depletion region decreases and current began to flow through it. The diode current include contribution from recombination current and diffusion current. As rise in temperature is capable of bringing more and more electrons from valance bond to conduction band of semiconductor material of diode current through P-N junction changes. The relation between current I passing through the diode at temperature, T and biasing voltage is given by diode equation.
)-1]
--(1)
Where the reverse saturation current, e is is the electronic charge, k- Boltzmann constant and s is the ideality factor. Taking logarithm,
--(2)
--(3)
(since, e= )
As T varies the variation of lnI is very small. Hence ln I is taken as constant for variation of T from room temperature to C or 303K to 403K. Therefore if T is kept constant,
Multiplying by T we get, V=
--(4)
i.e., if v is plotted against T we get a straight line. Thus curve is called calibration graph as they can be used for measurement of unknown temperature.
2.3 Constant current source Constant current source can source a current that is fixed by circuit elements. In constant source circuit in fig(1) the base emitter junction of the transistor is stiffly biased by a sensor diode. Since base voltage is a constant.
CHAPTER – 3 DIFFUSION CAPACITANCE
3.1 Junction Capacitance We know that the depletion layer is between p and n region. When it is reverse biased, the diode act as a capacitor. The p and n region are then like the plates of a capacitor and depletion layer like the dielectric. The external circuit can change this capacitor by removing the valence electrons from the p side and adding free electrons to n side. The diode capacitance is called the junction capacitance which refers to the transition from p type to n type material.
3.2 Theory As a p-n diode is forward biased, the minority carrier distribution in the quasi – neutral region increases dramatically. In addition, to preserve quasi- neutrality, the majority carrier density increases by the same amount. This effect leads to an additional capacitance called the diffusion capacitance. The diffusion capacitance is calculated from the change with voltage, where the charge, DQ is due to the excess carriers. Unlike a parallel plate capacitor, the positive and negative charge is not partially separated. Instead, the electrons and holes are separated by the energy band gap. Nevertheless, these voltage dependent charges yield a capacitance just as the one associated with a parallel plate capacitor. The total capacitance of the junction equals the sum of the junction capacitance and the diffusion capacitance. For reverse biased voltages and small forward bias voltage, one finds that the
junction capacitance is dominant. As the forward bias voltage is further increased the diffusion capacitance increases exponentially and eventually becomes larger than the junction capacitance. When p-n junction is forward biased, the depletion capacitance of the junction increases due to the decrease on the width of depletion layer. In addition, due to the motion and storage of minority carriers on either side of the junction, a capacitance known as the storage or diffusion, capacitance is introduced. The storage or diffusion capacitance takes into account of the capacitive effects of the carrier injected into each side of the junction when it is forward biased. The introduction of the diffusion capacitance leads to the restriction of the diode at high frequency operations. The diffusion capacitance is important at low frequencies and forward biased conditions. In a forward biased p-n junction diode electron density and hole density co exist in the neutral n region. When the forward bias changes due to the ac component voltage the minority carrier concentration also changes. This charge dQ is alternately being charged and discharged through the junction as the voltage across the junction changes. This charge is stored minority carriers as a function of the change in voltage is the diffusion capacitance. If the change in the number of holes stored per unit area of the n layer is dQp. When the applied forward bias changes by dV, the diffusion capacitance due to the scored holes on the n side is -- (1)
The diffusion (storage) capacitance per unit area due to electrons on the p side is, -- (2) In a forward biased diode the two capacitors Cp and C. behave as if they are connected in parallel to each other. Hence the total diffusion capacitance per unit area in the junction is -- (3)
3.3 Diffusion Capacitance For the diode IN4007 try with C = 0.01, 0.02, 0.03 etc. Capacitance
Width of the split trace
Cd
Cd + C
Cd + C + C Cd + C + C + C
1)
Cd =
2)
Cd =
3)
Cd =
PROJECT METHOD The change of biasing voltage changes the width of the depletion region and the current through the diode. We know that the diode current include contributions from generation recombination current and diffusion current. As the rise in temperature is capable of bringing more and more electrons from the valance band to the conduction bond of the semiconductor material of the diode, the current through the P-N junction changes. From the diode equation we can see that diode current depends on absolute temperature. As a project we undertake the work of studying how the diode voltage varies with temperature for a given forward biased voltage due to represent it. Graphically for doing this project we need a DC o/p regulator, diodes (Silicon, Germanium), resistance of 3.3ohm and a digital multimeter. Made the forward current at a constant value. Voltage across the diode at room temperature is found by using multimeter. Then the temperature of the diode is varied by heating it by beeping it in an oil bath. The voltage across the diode is noted at each temperature beeping the forward current constant. Then plot the graph with temperature T along x-axis and voltage across the diode along y-axis. We got a straight line. For each value of the applied voltage v, we get a straight line. These graphs are called calibration graphs as they can be used for the measurement of unknown temperature say, the melting point of wax.
The simplest for the determination of diffusion capacitance is to use the principle of formation of lissajous figure o a CRO. By adjusting the rheostat, a fixed voltage is applied to the diode and resistor. The horizontal and vertical gain controls of the CRO are adjusted to get the diode pattern on the screen. Here the splitting of horizontal area is due to diffusion capacitance
and vertical area is
due to transition capacitance . When the capacitance value of the capacitor connected becomes equal to the diffusion capacitance and the width get doubled. The experiment is repeated with the capacitors of diffusion capacitance.
OBSERVATIONS
V-I Characteristics Silicon
Germanium
Voltage
Current
Voltage
Current
(Volts)
(mA)
(Volts)
(mA)
0
0
0
0
.1
.1
.1
.2
.2
.2
.2
.5
.3
.3
.3
1.2
.4
.5
.4
2
.5
2
.5
2.9
.6
10.7
.6
3.8
.8
20.7
.8
6
V-I Characteristics (Constant Voltage) Silicon V = 6
V= 6.4
V=7
V = 7.4
Temp
Current
Temp
Current
Temp
Current
Temp
Curr:
(K)
(mA)
(K)
(mA)
(K)
(mA)
(K)
(mA)
30
10.5
30
11.3
30
12
30
12.4
35
10.6
35
11.4
35
12.1
35
12.4
40
10.9
40
11.5
40
12.2
40
12.5
45
11.1
45
11.6
45
12.3
45
12.6
Germanium V = 6
V = 6.4
V=7
V = 7.4
Temp
Current
Temp
Current
Temp
Current
Temp
Curr:
(K)
(mA)
(K)
(mA)
(K)
(mA)
(K)
(mA)
30
10.5
30
11.3
30
12
30
12.4
35
10.6
35
11.4
35
12.1
35
12.4
40
10.9
40
11.5
40
12.2
40
12.5
45
11.1
45
11.6
45
12.3
45
12.6
Temperature Sensor of Diode Diode-Silicon Const. Current=6.8mA Temperature
(
Mean Rising
Falling (mV)
30
678
668
680
35
664
670
666
40
642
646
644
45
628
632
630
50
601
610
608
55
598
602
600
60
580
584
582
65
562
566
564
70
546
550
548
75
536
540
538
80
518
522
520
Temperature Sensor of Diode Diode-Germanium Const. Current=12.1mA Temperature
Rising
Falling
Mean
30
1296
1300
1298
35
1278
1282
1280
40
1262
1264
1264
45
1240
1244
1242
50
1220
1224
1222
55
1206
1210
1208
60
1188
1192
1190
65
1172
1176
1174
70
1156
1160
1158
75
1136
1140
1138
80
1116
1120
1118
Conclusion Diode is used as a temperature sensor to measure the unknown temperature by keeping voltage constant (or current) for calibration and temperature measures.
Bibliography 1. S. Sankararaman “Enjoy Physics through Projects— A Play with Diodes”. Sastra vedi publications 2010. 2. Ittiavirah Kurian “Electronis & Practicals” 3. V. K Mehta “Principles of Electronics” S chand & company ltd. 1999 4. www.encyclopedia.com 5. www.wikipedia.com
