01 Semiconductor PN Junction Theory Application Student Copy

Chapter 1

Semiconductor PN Junction

Theory

and

Applications

Version 1.0

Dr. Lim Soo King

This is a copyright document. No any part of the document should be copied or distributed without prior approval from the writer. Dr. Lim Soo King May 12, 2009.

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Chapter 1

Semiconductor PN Junction Theory and Applications

_____________________________________________

1.0 Introduction Semiconductor pn junction is a two-terminal device. It is the most fundamental device element that forms the basis of many electronic devices such as pn diodes, optoelectronic devices like light-emitting diode and photodetector, field effect transistors and bipolar transistor. PN junction conducts high current in one direction and conduct very small amount of current in the reversed direction. Thus, pn junction has the property of rectification.

PN junction is formed in a single crystal of semiconductor by making one end of the crystal p-type by doping it with acceptor atom and making the other end n-type by doping with donor atoms. The region where p-type and n-type meet is the junction.

1.1 PN Junction at Equilibrium The equilibrium state is the state where the pn junction is left without any external stimulant such as electrical potential connected to it. This is also the state of zero bias voltage condition.

When two semiconductor material type, p-type and n-type are brought to contact, majority carrier of each type would diffuse across the junction. This shall mean that the majority carrier - hole from p-type diffuses to n-type material and the majority carrier of n-type diffuses to p-type material. The diffusion would stop after an electric field is built up sufficiently high to oppose diffusion. As the majority carrier such as hole diffuses across the junction, it combines with electron in the n-type side, which creates a net positive charge. Likewise, the majority carrier electron from n-type material diffuses across the junction recombines with hole in p-type side creates net negative charge. The net charge at each side creates an electric field in the direction, which would oppose further diffusion. The electric field created would drift the minority carrier in the opposite direction across the junction. Thus when equilibrium attained, the drift carriers and diffused carriers should be balanced in termed of

1 Semiconductor PN Junction Theory and Applications

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magnitude and in opposite direction. Mathematically, current density J due to various carrier types can be written as shown in equation (1.1) and (1.2). Jp(drift) + Jp(diff.) = 0 (1.1) Jn(drift) + Jn(diff.) = 0 (1.2) As the result of this process, a depletion region meaning a region that lack of carrier of certain thickness is created at both side of the junction. At time the depletion region is also termed as space charge region. Figure 1.1 to Fig. 1.3 illustrates the flow process of carriers in p-type and n-type materials and how equilibrium is attained when they come in contact.

Figure 1.1: Majority carrier diffusion in pn junction

Figure 1.2: A pn junction showing depletion region, space charge layer and electric field


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Figure 1.3: The carrier current at equilibrium cross a pn junction

1.2 Conduction of PN Junction From the study of above Section 1.1, one would know that the conduction of pn junction involves four carrier types, which are majority diffusion hole and electron and minority drift hole and electron. Hence there are four current components, which are derived from the four mentioned carrier types as illustrated in Fig. 1.3.

Conduction in pn junction physical involves in conduction band and

valence band. Electron flows in conduction band, whereas the hole flows in valence band.

At zero bias voltage equilibrium condition, the minority hole and electron can drift easily under the influence of built-in electric field E. The diffusion majority carriers have to overcome the potential barrier VB of the junction created as the result of depletion region. This shall mean that majority carrier should at least acquire energy of qVB electron volt before it can overcome the barrier and diffuse into either p or n region. Figure 1.4 illustrates the energy


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band diagram showing the location of the carrier at zero bias voltage equilibrium condition.

Figure 1.4: The energy band diagram of a pn junction showing the location of carriers

under zero voltage bias. 1.2.1 Forward Bias PN Junction A pn junction can be forward biased to lower the voltage across the junction. If a positive forward voltage VF is applied to the p-side of the pn junction relative to the n-side, the effective voltage across the junction is (VB – VF) not VB. Thus, the energy required by the majority carrier to overcome the potential barrier is lesser than earlier zero voltage bias case. As the result more majority carrier will be able to diffuse across the junction. Figure 1.5 shows the condition of the carrier under forward bias voltage.

Figure 1.5: The energy band diagram of a pn junction showing the location of carriers under forward bias voltage


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1.2.2 Reverse Bias PN Junction Figure 1.6 shows that the barrier potential increases under reverse bias voltage – VF. The bias voltage is effectively subtracted from the potential barrier. Consequently, the voltage across the junction is (VB + VF). As the result, lesser chance for majority carrier to diffuse across the junction and more easily for the minority carrier to drift across the junction would be happened.

Figure 1.6: The energy band diagram of a pn junction showing the location of carriers under

reverse bias voltage.

1.3 Characteristics of Diode The characteristic of diode is shown in Fig. 1.7. It consists of two parts namely the forward biased condition part and reverse biased condition part. The current is very small when the forward voltage is below the barrier potential. The current increases rapidly when the forward voltage exceeds the barrier potential VB. The forward-voltage VF dropped across the diode is approximately equal to the barrier potential. More details explanation of the forward voltage will discussed in the diode model section. For the case of silicon diode, the barrier potential is 0.7V and for the case of germanium type, it is 0.4V. Barrier potential is also named as turn-on potential or barrier height. Barrier potential follows equation (1.3).

=

2i

DAB n

NNln

q

kTV (1.3)


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ni is the intrinsic concentration, and NA and ND are doping concentration of p-type and n-type of diode.

Figure 1.7: Characteristics of the diode In reverse biased mode, the current flowed in the diode is extremely small. However, upon further applying the reverse biased voltage until the point VBR where breakdown occurs. The current would increase rapidly. Normally diode breakdowns at about negative 25.0V and avalanche breakdown occurs beyond this voltage point.

From the characteristic curve, an ideal diode equation can be obtained from equation (1.4).

IF = [ ]1eI kT/qV

S − (1.4) IS is the reversed saturation current which is the leakage current of the pn junction. This is also the current come from the minority carriers of both junctions. At room temperature T is equal to 300K. Boltzmann constant k is equal to 1.3806x10-23J/K and the electronic charge q is equal to 1.602x10-19C.

q/kT is also called thermal voltage VT. At room temperature, the thermal voltage VT is equal to 25.8mV.


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At forward bias voltage region, for a forward voltage V of a few thermal voltage value say 5, the term TV/Ve is much greater than 1. Thus, the forward current IF is approximated equal to TV/V

SF eII = , which is shown as exponential curve.

At reverse bias voltage region before breakdown, the bias voltage V has a

negative value. Reverse bias voltage of a few thermal voltage value say 3, the term TV/Ve− is much less than 1. Thus, the reverse bias current IF is approximated equal to IF = -IS, which is basically the reverse saturation current. In the graph is shown as a constant horizontal line with a small magnitude.

At breakdown, the current through the diode increases sharply. There are

two types of breakdown, which are zener effect and avalanche breakdown. If the breakdown voltage VBR is less the 4EG/q, which is 4.48V, zener effect would occur. If the breakdown voltage VBR is greater than 6EG/q, which is 6.72V, avalanche breakdown would occur. EG is the energy band-gap of the semiconductor. For silicon, it is 1.12eV.

For zener effect to occur, it requires a very high electric field. Typical electric field for silicon and gallium arsenide is about 106V/cm or higher. To achieve such a high electric field, the doping concentration of both p and n regions must be greater than 1017cm-3.

(a) (b)

Figure 1.8: Zener effect shown by a heavily doped diode When the heavily doped diode is reverse-biased, the energy bands become crossed at the relatively reverse low voltage, which is shown in Fig. 1.8. The n-


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region conduction band appears opposite the p-region valence band. The crossing of band aligns the large number of empty states, which are holes in the n-region conduction band with filled with electrons valence band in p-region. If the barrier separation between the two bands is narrow, tunneling of electrons can occur. Tunneling of electron constitutes a reverse current. For lightly doped diode, which has doping concentration less than 1015cm-3, electron tunneling is negligible and the breakdown mechanism involves the impact ionization of host atoms by the energy of the carriers. Normally lattice-scattering event can result in the creation of electron-hole pair EHP if the carrier being scattered has sufficient high energy. If the reverse voltage is sufficient high, the kinetic energy of the electron enters the n-region from p-region would cause ionizing collision with the lattice as shown in Fig. 1.9. A single such event results in creation of an EHP pair. The created EHP would also have the chance to impact and create second EHP pair. The process multiple and would go on. This process is termed as avalanche process or breakdown. The electron-

hole multiplication factor M is M = [ ]nBR )V/V(1

1

−, whereas n is a value between

4 and 6.

Figure 1.9: Electron-hole pairs created by impact ionization The equation governing the breakdown voltage VBR due to avalanche

breakdown shall be B

2CritoS

BR qN2

EKV

ε= , which equal to 21.6V if critical electric

field ECrit of 1.0x105V/cm and bulk doping concentration VB of 1.5x1015cm-3 are used. KS is the dielectric constant, which is 11.7 for silicon and εo is permittivity in free space, which is 8.854x10-14F/cm.


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1.4 Model of Diode Presented here are three models of diode, which is ideal model, piecewise model, real model. Depending on the circumstance, the selection of right model can be applied. For an example, ideal model can be used for the analysis of high voltage circuit

(a) I-V characteristic of ideal diode where V < 0, IF = 0 and IF > 0,V = 0

(b) I-V characteristic of piecewise linear model of diode IF <, V <Vturn-on and IF> 0,V >Vturn-on Figure 1.10: Current-voltage I-V characteristics of an ideal diode

The ideal diode is modeled as an element with zero forward voltage, zero forward resistance, zero reverse current, infinite reverse resistance and no breakdown voltage as shown in Fig. 1.10(a) or as piecewise linear model with non-zero forward voltage, zero forward resistance, zero reverse current, infinite reverse resistance, and no breakdown voltage as shown in Fig. 1.10(b). The


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non-zero forward voltage of the diode depends on the material type used. For silicon type, it is about 0.7V, whereas it is about 0.4V for germanium type.

The real diode has a finite forward resistance RF and reverse-biased resistance RB, which are shown in Fig. 1.8. Thus, the forward voltage VF for the diode beyond turn-on shall be VF = VB + IFRF (1.5)

1.5 Load Line Analysis of Diode The applied load normally has an impact on the point or region of operation. In performing the static analysis, a load line is drawn on the characteristic curve of the diode that represents the applied load. Consider a diode circuit shown in Fig. 1.11.

Figure 1.11: A series diode circuit

Based on ohm’s law, the input voltage Vin is Vin = VB + IFR. If the current IF is equals to zero ampere then the barrier potential is VB = Vin. Likewise, if VB is equal to zero volt, then forward current is IF = Vin/R. From the results, the load line of the circuit is drawn and shown in Fig. 1.12.

The point of intersection is called quiescent or Q-point, which is the static-point defined for a dc network. The Q-point can also be determined iteratively by solving the transcendental equation ( )R1eIVV TB V/V

SBin −+= .


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Figure 1.12: dc load line of a series diode circuit

If the input voltage Vin of the circuit shown in Fig. 1.12 is replaced by an ac voltage Vi = Vpsin ωt riding on dc voltage Vm, then the Q-point will dynamically move along the forward current (IFQ, VBQ) point. The ac resistance rD of the diode is the reciprocal of the differentiation of equation IF =

[ ]1eI kT/qVS − at Q-point, which is equal to

rD = VT/IFQ (1.5)

1.6 Temperature Dependence of Diode Diode equation shown in equation (1.4), which is IF = [ ]1eI kT/qV

S − has two temperature dependent terms. One is the exponential term and one is in reverse

saturation current term IS in which it is IS =

+

n

pon

p

nop

L

nqD

L

pqDA . Dp and Dn are

the diffusion coefficient of hole and electron. Lp and Ln are diffusion length of hole and electron. pno and npo are the minority hole concentration in n-type material and minority electron concentration in p-type material. A is the cross sectional area of the diode.

A silicon diode at temperature T = 300K has doping concentration NA = ND = 1.2x1016cm-3, ni = 1.5 x1010cm-3, Dn = 25cm2s-1, Dp = 10cm2s-1, KS = 11.7, Lp = 2.2x10-3cm and Ln = 3.5x10-3cm, and cross section area = 1x10-2cm2. The minority hole in n-region pno is 2.25x1020/1.2x1016 = 1.875x104cm-3. The


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minority electron in npo p-region is 2.25x1020/1.2x1016 = 1.875x104cm-3.The

reverse saturation current Is is equal to

+

n

0pn

p

0np

L

nqD

L

pqDA =

+ −−

−−3

4

3

4219

10x5.3

10x875.1x25

10x2.2

10x875.1x1010x1x10x602.1 = 3.51x10-13A.

The reserve saturation current is dependent on the intrinsic concentration ni

of the semiconductor whereby this parameter is strongly dependent on temperature. The intrinsic concentration follows equation ni = 3.87x1016T3/2exp(-7.02x103/T), which is dependent on density state of the semiconductor, temperature, and energy band-gap. The value of reverse saturation current IS approximately doubles for every 50C increases in temperature. The exponential term has a smaller value as temperature increases. However, this decrease is not as significant as the increase of IS current. Thus, the overall effect shall be; as temperature increases, for a given current, less bias voltage is required. For silicon diode, the change is approximately 2.0mV/0C. The temperature dependent characteristic graph of the diode is shown in Fig. 1.13. As temperature increases the forward voltage of the diode decrease, this shall that the diode has negative temperature coefficient. Likewise, other diode such as zener diode, it has positive temperature coefficient. This is simply because as temperature increase, the forward voltage VF of the zener diode increases.

Figure 1.13: Temperature dependent characteristic of a diode


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1.7 Application of Diode There are a number of diode types. Out of them some are shown in Fig. 1.14, which are rectifier diode, zener diode, light emitter diode, and photo diode. Physically, the terminal with a bar is cathode, whereas the other terminal is anode.

Rectifier diode Zener diode LED Photo diode

Figure 1.14: The symbols of various types of diode There are a few important applications for pn junction or diode, which depend on how the diode is biased. Figure 1.15 shows different quadrants of the I-V characteristic of diode used for six diode types, which are rectifying diode, light-emitting diode, laser diode, zener diode, photodetector, and the solar cell.

Rectifying diode operates in quadrant one and three as shown in Fig. 1.15(a). Light-emitting diode and laser-diode operate in quadrant one as shown in Fig. 1.15(b). Zener diode and photodetector operate in quadrant three shown in Fig. 1.15(c). Lastly, solar cell operates in quadrant four as shown in Fig. 1.15(d).

(a) (b)


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(c) (d)

Figure 1.15: The operating quadrants of important diode types

1.7.1 Rectifying Diode A fundamental application of the rectifying diode is to make use of its non-linear current-voltage I-V characteristic curve utilizing it in the rectifier circuit as shown in Fig. 1.16. Rectifying diode or rectifier is used to convert an ac voltage into dc voltage. Rectification can be divided into two groups namely the half-wave and full-wave rectification. During the positive cycle of the ac Vin = Vpsin ωt, output voltage Vout is equal to 00 180t0P )7.0tsinV(

≤ω≤−ω and during the

negative cycle, output voltage Vout is equal to zero.

(a) (b)

Figure 1.16: A half wave rectifier circuit and its output results One can also use the dc load line curve shown in Fig. 1.12 to obtain the Q-point and subsequently obtaining the result shown in Fig. 1.16. The average output

voltage is equal to Vavg = ∫ ω−2/T

0

p tdtsin)7.0V(T

1 =π− 7.0Vp , which approximately

1/3 of the peak voltage.

Since half of the input cycle, the diode is in reverse bias mode, therefore, it is necessary to know the peak inverse voltage PIV of the diode. If the peak voltage Vp of the circuit is large than the peak inverse voltage of the diode, the


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diode will eventually be damaged by high voltage. For a reliable half-wave rectifier circuit design, the maximum input voltage should be less than the peak inverse voltage PIV of diode i.e. PIV ≥ Vp.

If a capacitance of capacitor with value C is connected parallel with the resistance R as shown in Fig. 1.17, the capacitor would act as a filter. Owing to charging and discharging of capacitor, it would produce a Vpp ripple voltage riding on a dc voltage level Vdc as shown in Fig. 1.17(b).

(a) (b)

Figure 1.17: The circuit and output result of a half wave rectifier with filter capacitor For a small ripple voltage Vpp as compared with dc voltage level Vdc, this condition is called light loading. The load current in resistor R shall be considered constant. For small ripple voltage, the charging and discharging can be considered linear. The change in ripple voltage ∆Vpp follows equation (1.7).

C

tIV F

PP

∆=∆ (1.7)

If the charging time or discharging time ∆t is equal to period T of the ac voltage then equation (1.7) becomes equation (1.8) after substituting Vdc = IFR.

RC

V

C

IV dcF

PP ff== (1.8)

From the result shown in Fig. 1.17, the dc voltage Vdc is equal to equation (1.9). Vdc = Vp – 0.7 – Vpp/2 (1.9) Substituting equation (1.8) into (1.9), it yields equation (1.10) for dc voltage Vdc.


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Vdc =

RC2

11

7.0VP

f+

− (1.10)

The ratio of Vpp/Vdc = RC

1

f is defined ripple factor for half wave rectification.

A full-wave rectification circuit and its corresponding output are shown

Fig. 1.18. The voltage at the secondary coil is n

tsinVV p

sec

ω= , where n is the coli

ratio. Since it is a centre tapped type rectifier, the maximum voltage at the

resistance R is 7.0n2

V7.0

2

V psec −=− .

Figure 1.18: A full wave rectifier circuit and its output If a capacitance C of value C farad is connected across resistor of R ohm, The

change of ripple voltage is C

tIV F

PP

∆=∆ . If the charging time or discharging time

∆t is equal to period T/2 of ac input then ripple voltage is RC2

VV dc

PP f= after

substituting Vdc = IFR. The dc voltage Vdc = Vsec/2– 0.7 – Vpp/2. Thus, the dc

voltage Vdc is equal to Vdc =

RC4

11

7.02/Vsec

f+

−. The average dc voltage before filtering

shall be Vavg = Vavg = ∫ ω−2/T

0

sec tdtsin)7.02/V(2T

1 =π

− )7.02/V(2 sec . The ripple factor

is equal to RC2

1

f for full-wave rectifier circuit.


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During the positive input cycle, the maximum voltage at the cathode terminal of diode D1 and diode D2 is Vsec/2-0.7V. The anode of diode D2 is receiving a maximum voltage – Vsec/2. Thus, the maximum reverse bias voltage across diode D2 is Vsec/2-0.7 –(-Vsec/2) = Vsec -0.7V. Based on the analysis, the peak inverse voltage of the diode used for the circuit should be at least (Vsec-0.7) volt.

A full- wave bridge rectifier circuit is shown in Fig. 1.19. The peak voltage

of the secondary coil is Vsec = Vp/n. The maximum voltage at node D shall be Vsec – 1.4V, which is Vp/n-1.4V.

Figure 1.19: A full-wave bridge rectifier circuit During the positive cycle of the signal, the maximum voltage at node B is. The minimum voltage at node A is zero. Therefore, the reverse bias across diode D1 is Vsec. Thus, the peak inverse voltage PIV of diode is Vsec. 1.7.2 Zener Diode Zener diode is designed to utilize the breakdown voltage VBR of the diode. At breakdown, the reverse current increases rapidly with a small increase of reverse voltage. This makes it useful as the reverse bias of voltage regulator and voltage reference because of its ability to maintain a nearly constant voltage over a wide range of reverse current. It operates in quadrant three of the I-V characteristic curve, which shall mean operate in reverse bias voltage mode i.e. negative part of characteristic shown in Fig. 1.7.


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Figure 1.20 shows the simple voltage regulator designed using zener diode. In order for a zener diode to be conducting, the voltage at node A should be at least equal to the breakdown voltage of the zener diode VZ, which is VA≥

inS

VRR

R ⋅+

. Once the VA is greater than VZ, the voltage at node shall then be

maintained at voltage VZ.

Figure 1.20: A simple voltage regulator designed using zener diode From Kirchhoff’s current law, current IS is IS = IL + IZ and Kirchhoff’s voltage law, -Vin + ISRS + VZ = 0. Thus, the resistance RS is equal to

RS = LZ

Zin

II

VV

+−

(1.11)

IZ is the zener current flows in the zener diode in breakdown region and IL is the load current. Vin is the power supply voltage. Zener diode also has a maximum power rating PZM which defined as maximum allowable current flows into the zener diode IZM multiply by VZ.

1.7.3 Light-Emitting Diode and Laser Diode Light-emitting diode LED and laser-diode utilize the principle of recombination of majority carrier in pn junction to produce light, which is also termed as injection electroluminescence. It is basically converting current into light. Forward biasing the pn junction would inject the majority carrier across the junction whereby it will recombine with the majority carrier at the other side of the junction to produce visible light. Indirect semiconductor such as silicon and germanium produce heat and dissipate in the lattice because there is change in momentum. Recombination of electron-hole pair in direct semiconductor such


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as gallium arsenide or gallium indium arsenide phosphide is very efficient and produces photon, which has an energy equal in magnitude to the transition energy. By proper mixing gallium indium arsenide phosphide compound or alloy semiconductor, LED that produces visible light range from red to violet can be achieved. Figure 1.21 illustrates the structure of light-emitting diode LED diode.

Figure 1.21: Structure of LED

Light-emitting diode LED integrated into an optical cavity is laser diode. The working principle is similar to an LED that it is essentially forward biased pn junction in which recombining carrier produces light. In the laser diode, the excited electrons are stimulated to recombine simultaneously and produce an intense beam of photon of the same wavelength. Some of these photons are then reflected back in the optical cavity through the device to generate more electron-hole pair, which in turn recombines to produce more light. Figure 1.22 illustrates the structure of laser diode.

Figure 1.22: Structure of laser diode

1.7.4 Photodetector and Solar Cell Photodetector and solar cell convert optical signals into current. Photodetector is also called photo diode operates in third quadrant and solar cell is using the fourth quadrant of the current-voltage I-V characteristic curve of the diode. When pn junction is illuminated, electron-hole pairs EHP are optically generated. The minority carriers generated are swept across the depletion region


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by drifting provided they are within the diffusion length of the depletion region. Depending on the amount of illumination received by the pn junction, the amount of reverse saturation current can be increased substantially as shown in Fig. 1.23. The method of creating minority carrier is also known as optical injection. The carriers are called "excess" carrier because they are extra to those generated thermally.

Figure 1.23: Typical I-V characteristic of pn junction under dark and light condition

If the pn junction is forward biased, the diffusion would increase and drift current is negligible. If the pn junction is reverse biased, the diffusion current would be negligible and the drift current would increase drastically.

The typical structure of a photodetector is shown in Fig. 1.24. It consists of a pn junction separated by a wide depletion region. The depletion region is wide so that a large electric field E can be exerted across it. The electric field E then sweeps the excess holes and electrons across it to contribute as photocurrent.

Figure 1.24: Structure of photodetector


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A typical solar cell is shown in Fig. 1.25.

Figure 1.25: Structure of solar cell

Power is generated from solar cell since it operates in forth quadrant of the current-voltage I-V characteristic curve of the diode. The negative generated current, which comes from minority carrier and forward bias of the pn junction given rise to negative power, which shall mean power is generated. Usually the contact area of electrode should large and at the same time the exposed area for the incident photon should very much larger than the area of electrode. The electrode is designed having comb-like structure. Individual solar cell is not capable of delivering sufficient power, so it is commonly connected in the form of large arrays.

Figure 1.26 shows the characteristic curve of a solar cell. The power generated is the product of Imax and Vmax.

Figure 1.26: Characteristic curve of a solar cell


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All solar cells have a figure of merit associated with them, which is used to indicate how good the device is. The figure of merit is the fill factor or power efficiency η, which is defined as

η = ocsc

maxmax

ocsc

max

VI

VI

VI

P= (1.12)

where Isc is the short circuit current, Voc is the open-circuit voltage. Imax and Vmax are maximum current and voltage respectively.

Solar efficiency ηs is defined as

solar

maxs P

P=η (1.13)

where Psolar is the amount of solar power reaching the cell. Ideally, ηs would be equal to one indicating that all incident solar radiation is being converted to electrical power. However, the known solar efficiency so far is less than 30% utilizing gallium arsenide.

1.8 Diode in Circuit Designs Diode is also widely used in the circuit design. Some usages of diode in the circuit design are discussed here. Examples are DTL logic, clamper, voltage multiplier and etc.

1.8.1 Diode-Transistor Logic Design Diode is used in the diode-transistor logic DTL digital logic gate design like OR gate and AND gate. Figure 1.27(a) is an OR gate. Therefore, it follows logical function Vout = VA + VB + VC (1.14) Fig. 1.27(b) shows an AND gate that follows logical function Vout = VA • VB • VC (1.15)


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(a) (b)

Figure 1.27: Logic gate (a) OR gate and (b) AND gate

1.8.2 Voltage Multiplier Design of voltage multiplier - voltage doubler - utilizing diode such as the half-wave doubler circuit is shown in Fig. 1.28.

(a) Positive cycle charge via diode D1 (b) Negative cycle charge via diode D2

Figure 1.28: Voltage doubler circuit During the positive cycle of the ac voltage, capacitor C1 is charged to voltage VP – 0.7V via diode D1, whilst during the negative cycle, capacitor C1 holds its charge and at the same time charge capacitor C2 via diode D2. From Kirchhoff’s voltage law, during positive cycle -Vin + VC1 + 0.7 = 0. This implies VC1 = Vp – 0.7V since RC constant is small. During the negative cycle, -Vin - Vp + 0.7 + 0.7 + VC2 = 0. This implies that VC2 = 2Vp – 1.4V since RC constant is small. If ideal diode model is used, then voltage across capacitor C2 is VC2 = 2Vp.

Voltage tripler and quadrupler circuit can be designed with extension of the half wave doubler circuit shown in Fig. 1.28. 1.8.3 Clipper or Limiter Circuits Clipper circuit is used to clip or cut-off unwanted voltage. There are four clipper configurations, which are negative series clipper, positive series clipper, negative shunt clipper, and positive shunt clipper. Figure 1.29 shows the mentioned configurations.


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In the analysis of clipper circuit, one may use ideal diode model shown in Fig. 1.10(a), where the diode is in forward bias, it is assumed to have zero forward voltage. When it is in reverse bias, it is assumed to be an open circuit. The piecewise linear model of the diode shown in Fig. 1.10(b) can also be used depending on the significance of the forward bias voltage to the overall results.

Negative series clipper clips the negative portion of the ac voltage, while the positive series clipper clips the positive portion of the ac voltage. If the amplitude of the ac voltage is Vp, then the maximum voltage of the clipper shall be (Vp – 0.7) for negative series clipper circuit and minimum voltage is – (Vp- 0.7) for positive series clipper circuit.

(a) Negative series clipper

(b) Positive series clipper

(c) Negative shunt clipper

(d) Positive shunt clipper

Figure 1.29: Type of clipper configurations From Kirchhoff’s voltage law, the equation for the load voltage VL for negative series clipper is ( ) 2/Tt

0tPL 7.0tsinVV=

=−ω= ; Tt

2/TtL 0V=

== (1.16)

The equation for load voltage VL for positive series clipper is ( ) Tt

2/TtPL 7.0tsinVV=

=+ω−= ; 2/Tt

0tL 0V=

== (1.17)

Figure 1.30 shows the operation of a negative shunt clipper.

Figure 1.30: The operation of a negative shunt clipper


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During the positive cycle of the ac signal, diode D1 is in reverse bias mode. Thus, by voltage divider law, the voltage across the load RL is equal to

inSL

L VRR

R⋅

+= tsinV

RR

RP

SL

L ω⋅+

.

During the negative cycle of the ac signal, diode D1 is in forward bias

mode. Thus, the voltage drops across the load resistor RL shall be the forward bias voltage of the diode, which is - 0.7V. This can be explained using KVL. –V in +0.7V +IFRS = 0. Thus voltage across RL is -0.7V.

The operation of a positive shunt clipper can be explained like the

operation of negative shunt clipper but in the reverse manner. A positive and a negative biased clipper circuits are shown in Fig. 1.31.

The bias voltage VB is used to shift the clipped voltage a voltage level VB either above or below the reference zero level. For a positive bias VB, the clipped signal is shifted VB positive. For a negative bias – VB, the clipped signal is shifted VB voltage level below the zero reference level.

(a) Positive bias clipper

(b) Negative bias clipper

Figure 1.31: (a) The positive-biased clipper and (b) the negative-biased clipper


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For positive bias clipper circuit, during the positive cycle of the ac signal, the diode is in forward bias. Thus, the voltage across the load RL is clipped to 0.7 V + VB.

During the negative cycle of the ac signal, diode D1 is in reverse bias

mode. Thus, the voltage across the load RL is equal to inSL

L VRR

R⋅

+− .

For negative bias clipper circuit, during the positive cycle of the ac signal,

diode D1 is in reverse bias mode. Thus, the voltage across the load RL shall be

inSL

L VRR

R⋅

+= tsinV

RR

RP

SL

L ω⋅+

.

During the negative cycle of the ac signal, diode is in reverse bias mode.

Thus, the voltage drops across the load resistor shall be forward bias voltage of the diode, which is – (0.7 V + VB).

1.8.4 Clamper A clamper is a circuit designed to shift ac waveform either above or below a given reference voltage, which is usually the zero reference. A negative clamper circuit is shown in Fig. 1.32.

Figure 1.32: A negative clamper circuit

During positive cycle of the ac signal, the diode is in forward bias mode and the capacitor will charge very quickly to its amplitude Vp due short time constant. During negative cycle of the ac signal, the diode is in reverse bias. Owing to large discharging time, the capacitor is able to maintain its charge. Thus, from Kirchhoff’s voltage law, the maximum voltage across the load RL shall be approximately equal to – 2Vp. If the input ac voltage is Vin = Vp sinωt, by KVL,


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during the positive cycle, Vpsinωt = VC + VL. Knowing that during the positive cycle VC is approximately equal to Vp, the voltage across the load L shall be VL = -Vp(sinωt + 1) (1.18) A positive bias clamper circuit is shown in Fig. 1.33. The bias voltage VB is used to shift the negative clamped signal to a voltage level VB above the zero reference level.

Figure 1.33: A positive clamper circuit During the positive cycle of the input voltage Vin = Vpsinωt, the maximum voltage across the capacitance VC is VC = Vp - 0.7 - VB ≅ Vp - VB. By Kirchhoff’s voltage law, during the positive cycle, Vpsin ωt = VC + VL = Vp - VB + VL. Thus, the load voltage VL is VL = Vpsin ωt – (Vp – VB) (1.19) If one changes the bias voltage VB to a negative value, the output negative clamped signal would shift a voltage level VB below the zero reference level. The equation of the voltage across the load VL is VL = Vpsin ωt – (Vp + VB) (1.20) 1.8.5 Peak Detector The diode and operational amplifier can be configured as a peak voltage detector such as the one shown in Fig. 1.34. If the input voltage Vin has a variable magnitude, its peak voltage would be stored in capacitor C and subsequently, it can be measured.


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Figure 1.34: A peak voltage detector

The input voltage Vin would produce a high-level voltage at the output. This would cause forward bias of the diode and begins to charge the capacitor C. As soon as the voltage of the capacitor C reaches the voltage of the input voltage V in. It causes the output of comparator to swing low. This prevents to the capacitor to discharge because the diode is in reversed bias mode and the input current of the operational amplifier is negligible. For next instant, if the Vin is less than previous instant, the Vout would hold the highest voltage vlue of the previous instant. 1.8.5.1 Positive Signal Detector The diode and operational amplifier are configured as current buffer for a positive signal detector as shown in Fig. 1.35.

Figure 1.35: A positive signal detector


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The current source is used to keep the diode current constant irrespective of the value of input voltage. Thus, the voltage drop across diode shall remain constant. The diode that has highest input voltage will conduct and the output voltage is approximately equal to the input voltage.

1.9 Voltage Regulation An example of 5V voltage supply utilizing 7805 voltage regulator is shown in Fig. 1.36. This circuit is also a power supplies circuit that supplies 5V. Regulator combines with capacitor input filter can produce dc voltage with reduce ripple voltage from input power.

Figure 1.36: A 5.0V power supply circuit

As the line dc input change, which should be within a certain limit, there is no change at the output is called line regulation. Line regulation can also be defined as the percentage change in the output voltage for a given change in the line input voltage. Thus, mathematically line regulation can be express as

Line regulation = ( )

in

outout

V

%100V/V

∆∆

(1.21)

When the output voltage remains constant within a certain limit for a change of output load is called load regulation. Load regulation also is defined as the percentage change of output voltage for a given change in load current. Thus,

Load Regulation = current load of change given

voltageoutputof% (1.22)

In terms of voltage, it can be expressed as percentage change in output voltage from no-load NL to full-load FL conditions.


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Load regulation = ( )V V

VNL FL

FL

− 100% (1.23)

01 Semiconductor PN Junction Theory Application Student Copy

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