SEMICONDUCTOR DEVICES Umesh Tyagi DEVIC… · SEMICONDUCTOR DEVICES Umesh Tyagi CAREER PHYSICS...

SEMICONDUCTOR DEVICES Umesh Tyagi

CAREER PHYSICS CLASSES, NAND NIKUNJ, GHAZIABADPH.

9811156956/9868141642 email- [email protected]

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P-N JUNCTION: - When a P-type crystal is joined with a N-type crystal in such a manner that crystal structure remains continuous then this structure is called as P-N Junction. Formation of P-N junction: - Diffusion method is used to form a P-N Junction. In this method a trivalent element (like Boron, Aluminum) is coated on a slice of N-type semiconductor called wafer or a pentavalent element (like phosphorus, Arsenic) is coated on P-type semiconductor. When this semiconductor is heated at a high temperature (about 500°C) the impurity is diffused inside the semiconductor. Diffusion is more at surface and decreases as the depth increases. The depth up to which the diffusion takes place, a junction is formed which is called P-N Junction. On the one side of this junction there is P-type semiconductor and on the other side there is N-type semiconductor. What happens at the time of formation of P-N Junction (formation of depletion region and potential barrier): As soon as a junction is formed the holes from p-region diffuse towards n- region and electron from n- region diffuse towards p-region due to the high concentration of holes and electron into two different regions. In the vicinity of junction the Electrons and holes recombine with each other and vanish. Due to which there is an excess of immobile +ve ions in n-region and –ve ions in p-region. Thus an electric field and hence a potential difference called potential barrier is developed across the junction which stops the further diffusion of holes and electrons. And it appears as if some fictitious battery is connected across the junction with its negative pole connected to p-type and positive pole to N type. The region, free form charge-carriers on both side of junction is called depletion region or space charge region. The thickness of the depletion region is of the order of 10-6 meter while the potential barrier is about 0.7 volt. Therefore

Biasing of p-n junction: - (I) Forward Bias: - When p-region of a p-n junction is joined to the (+) ve pole of a battery and n-region to -ve pole then the junction is said to be forward biased. Action of p-n junction: - When the p-n junction is made forward bias the (+) ve pole of the battery repels the holes towards n-region and the (-) ve pole repels the electron towards p-region. Due to which the electrons and holes enter the depletion region and the thickness of depletion

15

6107

10

7.0

VmeldElectricFi

P-Type N-Type

Immobile - ve ions Immobile +ve ions Depletion region

Holes

majority carrier

Electrons

majority

carrier

Potential Barrier




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region decreases. If the external potential is greater than the potential barrier then near the junction electrons recombine with holes. For each electron-hole combination that takes place near the junction, a covalent bond breaks in p-region near the positive pole of battery. Due to which electrons and holes are produced in pair, the electron is captured by the (+) ve terminal, while the hole moves towards the junction. At the same time an electrons enters the n-region from the –ve terminal of the battery, thus a forward current flows in the circuit due to the flow of electrons and hole. During the forward bias the applied D.C. voltage opposes the potential barrier due to which the thickness of the depletion layer decreases. Thus p-n junction offers low resistance in forward bias. (II) Reverse Bias: - When p-region of a p-n junction is joined to the (-) ve pole of a battery and n-region to +ve pole then the junction is said to be reversed biased Action of p-n junction: - when p-n junction is reversed biased, the –ve pole of the battery attracts the holes present in P-region, while the +ve pole of the battery attracts the electrons present in the n-region. Thus the electrons and holes get away from the junction and the thickness of depletion region increases. But a very small current flows through the junction due to the recombination of minority carriers. This current is called as reverse current. If the reverse bias voltage is made very high, all the covalent bonds near the junction break and a large number of electron-hole pairs are created due to which reverse current increases abruptly. This phenomenon is called avalanche breakdown and the reverse voltage at which this phenomenon occurs is called as reverse break down voltage or zener voltage which depends upon the density of impurity atoms. Due to the over heating at this voltage, the p-n junction may be damaged. During the reverse bias the applied D.C. voltage aids the potential barrier due to which the thickness of the depletion layer increases and hence it offers the high resistance in reverse bias. Symbol of P-N junction diode:- Characteristics of P-N junction: -There are two types of characteristics- (I) Forward bias Characteristics- First of all makes the connection according to the circuit shown in following figure. By changing the forward voltage (Vf) with the help of potential divider note down the corresponding forward current (If) and plot the graph between forward voltage and forward current. The graphs so obtained are called as Characteristic in Forward Bias of p-n junction.

0.2 0.4 0.6 0.8 1.0 FORWARD VOLTAGE Vf

Knee Voltage

Fo

rwar

d C

urr

ent

I f

P N

I

F

f

P

N

V

f

+

-

+ -




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From the graph it is clear that initially the current increases very slowly and the curve is non- linear. It is because the external applied voltage is used up in overcoming the potential barrier. However, once the external voltage exceeds the potential barrier voltage, the p-n junction behaves like an ordinary conductor. Therefore, the current rises very sharply with increase in external voltage called knee voltage. The curve is almost linear (II) Reverse Characteristic Curve: - Make the connection according to the circuit shown in the following figure. Change the reverse voltage and note the corresponding reverse current. The graph plotted between reverse voltages (Vr) and reverse current (Ir) is called Characteristic in Reverse Bias. Practically in reverse bias there is no current if the applied voltage is low but a very small current flows due to minority carriers. This current is called reverse current. On increasing the reverse voltage to a very high value, the current increases abruptly, which is clear from graph. It is due to the fact that at very high voltage, a large number of holes & electrons are liberated due to the breakage of a large number of covalent bonds near the junction and the corresponding voltage is called as Zener voltage. DYNAMIC RESISTANCE: - The ratio of the small change in voltage to the small change in the current is called as dynamic or a.c. resistance of the junction diode. It is represented by Vd.

The region of the characteristic curve where dynamic resistance is almost independent of the applied voltage is called the linear region of junction diode. Junction diode as Rectifier: - An electronic device, which converts a.c. power in to D.C. power, is called rectifier. Half – wave Rectifier: - A rectifier, which rectifies only one half of each a.c. input supply cycle is called half wave rectifier. Principle: - It is based on the principle that the diode offers low resistance when it is forward bias and high resistance when it is reversed bias i.e. current can flow through the diode when it is forward biased. Arrangement:- The p-region of the junction diode is joined to the one terminal of the secondary coil of a step down transformer and the load resistance is joined between n-region and the IInd terminal of the secondary coil.

Zener

Voltage

REVERSE VOLTAGE

Rev

erse Cu

rrent I

r (

I

VVd

Ir

P N

Vr

- + -

+




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Working:- Let during the first half cycle of the input a.c. upper end i.e. point S1 of secondary is at +ve potential and the lower end i.e. point S2 is at –ve potential. Thus the diode is forward bias. During first half cycle and current flows through diode in loadresistance from C to D.

During the next half cycle the upper end becomes –ve and lower end becomes +ve and thus the diode gets reverse biased and no current fows through it. In the next half cycle diode gets forward biased and current flows through it from C to D and this process repeated again and again. The current obtain in output is discontinuous and pulsating d.c. due to which there is a huge loss of energy. Full-wave Rectifier:- A rectifier which rectifies both halves of the a.c. input is called a full wave rectifier. Principle:- It is based on the principle that the diode offers low resistance when it is forward bias and offers high resistance when it is reverse biased.

Arrangement:- The a.c. supply is fed across the primary coil P of a step down transformer. Two two ends of the secondary coil S of the transformer are connected to the p- regions of the junction diodes D1 and D2 . A load resistance R is connected beteen the n-regions of the two diodes and the central tapping (C) of the secondary coil. The out put d.c. is obtained across the load reistance. Working:-Suppose that during first half of the input, the upper end A of the secondary is at + ve pot. and lower end B is at (–) ve pot. So the diode D1 gets forward bias and D2 gets reverse

A.C.

Input

Voltag

e

D.C.

0utput

Voltage

A.C.

Input

Voltage

D.C.

0utput

Voltage

RL

E F




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Regulated Output Voltage

Input Voltage (Vi)

Ou

tpu

t V

olt

age

(VO)

VZ

VZ

bias hence current flows through D1 in load resistance from E to F. During the next half cycle A becomes –ve and B becomes +ve and hence D1 gets reverse bias and D2 gets forward bias. Thus the current flows through D2 from E to F in load resistance. Hence the full wave rectifier, rectifies the both halves of a.c. The output d.c. is continuous but pulsating. To reduce the fluctuations, filter circits are used in output circits. Electrolytic condenser and zener diodes are use to reduce the fluctuations of d.c. Different types of junction diode :- (I) Zener diode:- A specially designed diode in which P and N region are heavily dopped due to which the depelation layer junctioin width is small and the junction field & potential barrier are high and which can operate continuously, with out being damaged in the region of reverse breakdown voltage, is called zener diode. After the break down a large change in current can be produced by almost insufficient change in reverse bis voltage ie for widely different currents, the voltage across the zener diode remains constant so a zener diode can be used as a d.c. voltage regulator. Zener Diode as a Voltage Regulator- To use a zener diode as a dc voltage regulator, it is joined in reverse bias to irregulated dc input voltage through a resistance R (called dropping resistance) and the regulated output voltage is obtained across load resistance RL. If I is the current from the supply, IZ the current through zener diode and IL the current through the load resistance, then

I= IZ + IL If RZ is the resistance of zener diode, then

VO = VZ = IZRZ =ILRL Applying Kirchhoff’s law to the mesh containing R, we get

IR+ VZ = Vi VZ = Vi – IR

i. When Vi < VZ, almost no current flows through the zener diode i.e. IZ =0 and VO = Vi

ii. When VI =VZ, the junction diode operates in the breakdown region and out put voltage VO = VZ = (Vi – IR) becomes constant.

iii. Vi > VZ, then the voltage across zener diode remains constant (= VZ) but the current rises abruptly as the resistance of the zener diode reduces to almost zero. Due to which there is an increase in voltage drop across R. Since RL is connected in parallel so the voltage across RL remains the same as that of zener break down voltage. Hence the output voltage remains constant.

Question-What is a photo diode? Explain its working principle. Also give some uses. Photo diode: - A junction diode made from light sensitive semiconductors is called a photo diode.

SYMBOL OF

ZENER

DIODE

P N IRREGULATE

D. C. VOLTAGE

(Vi) REGULATED

VOLTAGE (VO)

R

RL

IL

I

IZ

VL




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A photo diode is always made reversed bias. When no light falls on it, a small reverse current flows through the junction. This current is due to the thermally generated electron-hole pairs and is called as dark current. When the photodiode is illuminated with light photons of energy hν>Eg then additional electron-hole pairs are created in the depletion layer due to which the reverse current increases and becomes maximum. This current is called as reverse saturation current. It is found that the reverse saturation current increases with the increase in the intensity of light. A photodiode can turn its current ON and OFF in nanoseconds. So it can be used as a fastest photo detector. Uses:

1. In detection of optical signals. 2. In demodulation of optical signals 3. In light-operated switches 4. In speed reading of computer punched cards. 5. In electronic counters.

Light Emitting Diode (LED): - A light emitting diode is simply a forward biased p-n junction made of gallium arsenide or indium phosphide and emits spontaneous light radiation. When a LED is made forward bias then the energy released due to the recombination of electrons and holes, falls in visible region or infrared region of EM spectrum. Hence light is emitted by a LED. Advantages over conventional incandescent lamps:

1. Low operational voltage and less power consumption. 2. Fast action and no warm up time required. 3. Long life and ruggedness. 4. Light emitted is nearly monochromatic.

Uses: 1. Infrared LED’s are used in burglar alarm systems. 2. In optical communication system. 3. LED’s are used in numeric displays (in watches and calculators). 4. In optical mouses for the computers. 5. In remote controls.

LIGHT

P

N

RL

LIGHT

RL

Reverse bias

Volts

mA

µA

I1

I2

I3

I4

I4 > I3 > I2 > I1

LIGHT

R




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Solar cell: - It is a junction diode which converts solar energy into electrical energy and is based on photovoltaic effect (generation of voltage due to bombardment of photons).It consists of a p-n junction made of Si or gallium-arsenide. A very thin layer of p-type semiconductor is grown over a n-type semiconductor by using diffusion method. (So that the energy falling on the diode not greatly absorbed before reaching to junction) Working:- When light falls on the top of the solar cell, it gets absorbed. The absorbed energy knocks out electrons and creates the holes, which flow across the junction in opposite direction and collected at the two sides of the junction giving rise to a p.d. between the top and bottom electrodes. When an external load is connected across metal electrodes a photo current flows. Thus, a current is generated without mechanical input energy. Transistor: - A transistor is a semiconductor device used to amplify and switch electronic signals and electrical

power. It is composed of semiconductor material with at least three terminals for connection to an

external circuit. A voltage or current applied to one pair of the transistor's terminals changes the

current through another pair of terminals. Because the controlled (output) power can be higher than

the controlling (input) power, a transistor can amplify a signal.

The three terminals of a transistor are

Emitter- It is a segment on one side of moderate size, heavily doped and a supplier of large number

of majority careers.

Base- It is the central segment of very thin size and lightly doped. It controls the flow of majority

charge carriers from emitter to collector.

Collector- It is the segment of larger size and moderately doped. It collects the majority carriers

supplied by emitter.

Types of transistors- These are of two types: - (I) N-P-N Transistor: - When a p-type

semiconductor is sandwiched between two layers of n-type semiconductor is known as NPN transistor.

(II) P-N-P Transistor: - A junction transistor in which a thin layer of N-type semiconductor is sandwiched between two layers of P-type semiconductors is known as PNP transistor.

http://en.wikipedia.org/wiki/Semiconductor_device

http://en.wikipedia.org/wiki/Electronic_amplifier

http://en.wikipedia.org/wiki/Switch

http://en.wikipedia.org/wiki/Electronics

http://en.wikipedia.org/wiki/Electrical_power

http://en.wikipedia.org/wiki/Electrical_power

http://en.wikipedia.org/wiki/Semiconductor

http://en.wikipedia.org/wiki/Electric_current

http://en.wikipedia.org/wiki/Electric_power

http://en.wikipedia.org/wiki/Gain




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Biasing of Transistor- When a transistor is used in a circuit, emitter-base junction is always made forward bias while the base- collector junction is reverse bias. When the transistor is biased in such a manner, it is said to be in active state. Action of Transistor - (a) Action of n-p-n Transistor: - The emitter base junction is made forward bias by using a battery VEE while the collector base junction is made reversed bias by using the VCC. The –ve

pole of battery VEE repels the electrons in emitter region (as majority carrier in n-region) towards base. Since the base is very thin and lightly doped, hence about 95% electrons cross over the base region and entered the collection region where they are attracted by the +ve pole of the battery VCC. As soon as an electron enters the +ve pole of the battery VCC, at the same time an electron enters the emitter region from the –ve pole of the battery VEE and this process is carried out continuously. About 5% electrons recombined with holes in base region. For each recombination a covalent bond breaks which creates the hole and electron in pair. Electron enters +ve pole of VEE through B and hence base current IB flows which is very small. If IE, IC and IB are the emitter, collector and base current then (According to Kirchhoff’s 1st law)

IE = IB + IC It may note that in n-p-n transistor current flows due to the flow of electrons in and outside of transistor. Action of P-N-P transistors:- Characteristics of n-p-n transistor in Common Emitter configuration: - Common Emitter characteristics of a transistor are the graph plotted between the voltage and the current when emitter is earthed, base is used as input terminal and the collector as output terminal.

Emitter Collector

C E

B

VEE VCC

IE IB IC

P N P

Legends: - Hole-

Electron-

Holes

Electrons

Emitter Collector

C

N P N

E

B

VEE VCC

IE IB IC




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N-P-N Transistor: -The base emitter circuit is made forward biased by using a battery VBB while the emitter, collector circuit is made reversed bias by using battery VCC. To draw the characteristic the circuit arrangement is shown in the above figure in which a n-p-n transistor is used. A transistor has two types of characteristics. D. C. Input characteristics: - Keeping VCE at constant voltage, charge VBE (Base emitter voltage) and note down the corresponding values of base current. Now for some other value of VCE , find out the change in base current for the corresponding change in VBE. Now plot the graph between VBE and IB at different constant value of VCE. The graphs so obtained are called as input characteristics. A.C.I input resistance:- The ratio of the change in the emitter base voltage (Δ VBE) to the change in base current (Δ IB) at the constant VCE is called as a.c. input resistance. It is denoted by Rin.

(2) Output characteristics:- The graphs plotted between emitter collector voltage and the collector current (IC) at different constant values of base current (IB). Following result may be drawn from the output characteristic curves- (I) The collector current changes rapidly in beginning but soon it becomes saturated. (II) The saturation current increases on increasing the base current. (III) In audio frequency amplifiers the linear part of the output characteristics is used in order to obtain undistorted output. Output resistance :-The radio of the change in emitter collector voltage to the change in

collector current at the constant base current. It is denoted by Rout.

Transfer characteristics:-The graph plotted between collector current (IC) and the base current (IB) at different constant values of collector voltages (VCE).

Ic

C mA

IB

n-p-n

µA B

E

VCC

VBB +

+

VBE VCE

_ _

CEVB

BEin

I

VR

BIC

CE

outI

VR




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Current gain :- The ratio of change in collector current to the change in base current at constant collector – emitter voltage is called as current gain. It is also called as current transfer ratio. It

is denoted by: - TRANSISTOR AS AN AMPLIFIER:- An amplifier is a device which is used for increasing the amplitude of variation of alternating voltage or current or power. A transistor can be used as an amplifier. There are three configurations- 1. Common base amplifier 2. Common emitter amplifier 3. Common Collector Amplifier

Common Emitter Amplifier: - Amplifier is a device which produces enlarged version of the input signal. It is used for increasing the amplitude of variation of alternating voltage or current or power. Amplifier Circuit Using an N-P-N Transistor in CE Configuration: - The emitter is common to both the input and output circuit. The emitter-base circuit is forward biased by the battery VBB while the collector-emitter circuit is reverse biased by the battery VCC. Thus the input resistance is low and the output resistance is high. The weak input voltage signal is applied across emitter-base circuit and amplified output voltage is obtained across collector-emitter circuit. If RL is the load resistance then ICRL will be voltage drop across it. Hence, the voltage across emitter-collector (VCE) is given as-

I B (

mA

)

(VBE)

(VCE) = 2v (VCE) =3v

INPUT CHARACTERISTICS

I C (

m A

)

(VCE)

IB = 250

IB = 200

IB = 150

IB = 100

IB = 50

0UTPUT CHARACTERISTICS

IB (mA)

I C (

mA

)

(VCE) = 3V

TRANSFER

CHARACTERISTICS

CEVB

C

I

I

VCE

VBB

VCC




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VCE =VCC – IC RL ---------------------(2)

The variation in input signal voltage causes the variation in emitter-current which produce the variation in collector current and hence in collector voltage. These variations in collector voltage appear as amplified output-voltage. The input signal and output signal are in opposite phase. Phase relation between input and output signals: - The input signal and the output signal are in opposite phase, which can be explained as below- When an a. c. signal is fed to the input circuit, the forward bias increases during positive half cycle of the input. This results in increase in IC and consequent decrease in VCE, thus during positive half cycle of the input, the collector becomes less positive and hence negative half cycle is obtained. During negative half cycle of the input, forward bias decreases, therefore, the value of IE and IC also decreases and VCE would increase making the collector more positive and hence positive half cycle is obtained. Thus, in common emitter amplifier, thus there is 180 out of phase amplification. Current Gain: - It is defined as the ratio of the change in collector current to the change in base

current at constant emitter base voltage. It is denoted β. Voltage Gain: - It is defined the ratio of the change in the output voltage to the change in input voltage. It is denoted by AV.

Since β > α so the voltages gain in common emitter amplifier is very large as compared to that in common base amplifier. A.C. Power Gain:-It is defined as the ratio of change in output power to change in the input power. It is denoted by AP i.e.-

β> α so the power gain in common emitter amplifier is very large as compared to that in common base amplifier. Trans conductance:- It is defined as the ratio of the change in the collector current (ΔIC ) to the change in emitter base voltage (ΔVBE) at constant collector voltage. It is denoted by gm i.e.

B

C

I

I

gain resistance

powerinput in Change

poweroutput in Change

2

2

2

P

iB

Oc

P

i

O

P

P

A

RI

RIA

P

PA

A

Gain ResistanceA

A

A

V

V

V

ac

inB

outC

inB

outC

in

out

RI

RI

RI

RI

V

V




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in

acm

BE

B

B

Cm

VBE

cm

Rg

V

I

I

Ig

V

Ig

CE

1

Transistor as an oscillator ( NOT IN CBSE FROM 2015)- A transistor oscillator is a device used to produce undamped oscillations of desired frequency The figure (1) shows the block diagram of a transistor oscillator. Its essential components are: (i) Tank Circuit: A tank circuit consisting of an inductor L and a variable capacitor C in

parallel. The frequency of oscillations

is given by:1

2 LC

By changing the value of C or L (or both) oscillations of desired frequency can be obtained.

(ii) Transistor Amplifier: The oscillations produced in the tank circuit are applied to the input of the transistor amplifier due to which an amplified output of these oscillations is obtained.

(iii) Feedback Circuit: It is a circuit which receives output of the transistor and supplies correct amount of energy to LC circuit to meet the loses (due to resistance)

The circuit diagram of an oscillator using NPN transistor in common emitter is shown in the figure (2). The tank circuit is connected in the input circuit i.e. emitter base circuit. A impedance coil L1 called feedback (or trikler) coil is connected in the output circuit i.e. in the emitter collector circuit which is reversed biased. Coil L and L1 are inductively coupled. Working: - When the switch K is closed, collector current starts increasing through the coil L1. This increasing collector current induces an emf in inductor L (as L1 and L are inductively coupled). Due to which the forward biasing and hence the collector current increases. Due to the increase in collector current the magnetic flux linked with L1 & L increases; thus the voltage induced in L also increases and hence forward bias is further increased which increases IC and IE. This process continues until the induced emf across the inductor L attains a saturation value. The upper plate of the capacitor gets +ve charge during this process. When induced emf attains saturation value the induced emf becomes zero. Now the capacitor discharges through L; as a result emitter current decreases and hence collector current also decreases. The decreasing collector current will induce an emf in inductor L in the reverse direction, which decrease the emitter current and hence collector current. This process continues till the collector current reduces to zero. Now the mutual induction stops playing its role. At this stage the lower plate of the capacitor C will get + ve charge and discharges through L. Thus the emitter current and hence the collector current again start to increasing i.e. the process gets repeated and the collector current oscillates between a maximum and zero value.




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TRANSISTOR AS A SWITCH ( NOT IN CBSE FROM 2015) A transistor can be used as a switch; the following fig (1) shows the circuit diagram of a base biased n-p-n transistor in CE configuration states Here RB is a resistor in the input circuit and Rc in the output circuit. Applying Kirchhoff’s rule to the input and output circuits separately, we get VBB = IBRB + VBE = Vi -----------------------------(1) VCE=VCC—ICRC = Vo ------------------------------(2) The voltage VBB has been regarded as the dc input voltage Vi and VCE as the dc output voltage V0. Fig. 2 shows typical output voltage (V0) — input voltage (Vi) characteristic, called the transfer characteristic of the base biased transistor. It has three well-defined regions as follows

1. Cutoff region: When Vi increases from zero to a low value (less than 0.6 V in case of a Si transistor), the forward bias of the emitter-base junction is insufficient to start a forward current i.e. IB = 0 and hence Ic = 0. The transistor is said to be in the cutoff region. From equation (1), the output voltage Vo = Vcc. 2. Active region: When Vi increases slightly above 0.6 V. a current Ic flows in the output circuit and the transistor said to be in the active state. 3. Saturation region: When Vi becomes very high, a large collector current Ic flows which produces such a large potential drop across load resistance Rc that the emitter-collector junction also gets forward biased and output voltage V0 decreases to almost zero. Now the transistor is said to be in the saturation state because it cannot pass any more collector current Ic. Switching action of a transistor: A transistor can be used as a switch if it is operated in its cutoff and saturation states only. A switch circuit is designed in such a manner that the transistor does not remain in the active state. As long as the input voltage is low and unable to forward-bias the transistor, the output voltage V0 (at Vcc) is high. If Vi is high enough to drive the transistor into saturation, then V0 is low, nearly zero. Thus when the transistor is not conducting (in cutoff region), it is said to be switched off and when it is driven into saturation, it is said to be switched on.




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Zener diode (In short):

These are specially designed junction diodes which can operate in the reverse breakdown voltage region without being damaged.

An important application of Zener diode is that it can be used as voltage regulator. The regulating action takes place because of the fact that in reverse breakdown region, a very small change in voltage produces large change in current. This causes a sufficient increase in voltage drop across the resistance to lower voltage back to normal. Similarly, when the voltage across the diode tends to decrease, the current through diode goes down out of proportion so that voltage drop across the resistor is much less and it raises voltage back to normal.

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SEMICONDUCTOR DEVICES Umesh Tyagi DEVIC… · SEMICONDUCTOR DEVICES Umesh Tyagi CAREER PHYSICS...

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