The fabrication procedure of a p-n junction defines the belongingss of the device. The assignment discusses the disconnected junction theory, the ensuing depletion bed and its electrical capacity Cdep. The end of the assignment is to mensurate Cdep per unit country of the device. A circuit has been employed in which the rectifying tube is rearward biased and a Wayne Kerr Bridge is used to mensurate Cdep. A graph is plotted between 1/Cdep2 and the contrary electromotive force Vr. The device and the depletion bed parametric quantities can be determined from the graph. The disconnected junction theory shows that in a contrary prejudice manner, the rectifying tube acts like a parallel-plate capacitance. The factors on which Cdep depends are critically analysed in the assignment. The belongings of fluctuation in the electrical capacity with the rearward electromotive force makes the device utile for many applications.

Introduction

p-n junction

A p-n junction is formed when a semiconducting material bed in a p-type substrate is converted into n-type by adding givers, or, transition of an n-type semiconducting material bed into p-type by adding acceptors would besides organize a p-n junction [ 1 ] shown in Fig. 1 ( Appendix 1 ) .

Depletion or infinite charge part

The formation of a p-n junction causes the bulk bearers ( negatrons in the n-side and holes in the p-side ) to migrate across the junction. After diffusion they will unite with the bulk bearers on both sides, negatrons with holes in the p-side and holes with negatrons in the n-side, and disappear. Therefore, a infinite charge part or depletion part will be where the stuffs join [ 3 ] . It therefore consists of the fixed positive and negative charges shown in a rectangular signifier [ 4 ] in Fig. 2-a ( Appendix 1 ) .

Dopant densenesss

The net or the remunerated dopant densenesss in the P and n sides are by and large taken as NA and ND severally. In the p-type bed, for illustration, if there are important concentrations of acceptor and giver, so NA will be the former subtraction the ulterior [ 1 ] .

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Depletion bed belongingss [ 4 ]

Abrupt or step junction

An disconnected nonreversible p+-n ( or n+-p ) junction is obtained when NA & gt ; & gt ; ND ( or frailty versa ) [ 2 ] where p+ and n+ represent the to a great extent doped sides of the junction [ 1 ] .

Energy set diagram at equilibrium

Fig. 3 ( Appendix 1 ) illustrates a p-n junction set diagram at equilibrium. EC and EV of P and n sides bend towards the equilibrium value of EF near the junction. The far ends of the two sides remain impersonal. In the depletion bed, the concentrations of hole and negatron are really little. Figure shows that in the center, EF is neither close to EC nor EV [ 1 ] . Therefore, it is by and large assumed that a depletion bed is depleted of both negatrons and holes [ 1,3 ] .

Electric field

The electric field is merely present in the depletion bed due to the ionized giver atoms in the part shown in Fig. 1-a, B ( Appendix 1 ) . The electric field is uninterrupted in the depletion part [ 4 ] and is given by

( 1 )

( Beginning: [ 4 ] )

( 2 )

( Beginning: [ 4 ] )

where WDp and WDn are the drawn-out distances of NA and ND severally. The electric field is therefore maximal at x = 0 and zero at the boundaries [ 4 ] . Equating ( 1 ) and ( 2 ) gives

( 3 )

( Beginning: [ 4 ] )

The equation ( 3 ) shows that the net charge on either sides of the junction, positive in the n-side and negative in the p-side, is equal [ 4 ] . It besides reveals that the depletion bed chiefly penetrates into the igniter doping side while its breadth can be neglected in the to a great extent doped stuff [ 1,4 ] .

Junction potency

Fig. 3 ( Appendix 1 ) indicates that EC and EV are non level. Thus a possible difference is present at the junction of the two dissimilar stuffs, called the constitutional possible [ 1 ] Vbi ( =I?bi or I¦bi ) given by

( 4 )

( Beginning: [ 1 ] )

where Ni is the electron-hole braces denseness, K is the Boltzmann ‘s changeless = 1.38 A- 10-23 J/K [ 4 ] and T is the temperature. The electromotive force distribution [ 2 ] is shown in Fig. 2-c ( Appendix 1 ) . It has a uninterrupted value in the depletion part but nothing for x = 0. It is besides changeless for ten a‰¤ -WDp & A ; x a‰? WDn [ 4 ] . As

( 5 )

( Beginning: [ 4 ] )

so by incorporating ( 1 ) and ( 2 ) and using the above mentioned boundary conditions, we get

0 a‰¤ x a‰¤ -WDp ( 6 )

( Beginning: [ 1 ] )

WDn a‰¤ x a‰¤ 0 ( 7 )

( Beginning: [ 1 ] )

The constitutional possible gives the country of the depletion part shown in Fig. 2-b ( Appendix 1 ) .

Depletion bed breadth

The entire breadth of the depletion bed [ 1 ] Wdep will be

( 8 )

( Beginning: [ 1 ] )

As electromotive force is uninterrupted in the depletion bed, so comparing ( 6 ) and ( 7 ) at x = 0 [ 1 ] gives

( 9 )

( Beginning: [ 1 ] )

where N is the igniter dopant denseness [ 1 ] .

Depletion bed electrical capacity

A electrical capacity is present in the depletion bed in the signifier of a parallel-plate capacitance, because of the opposite mark fixed charges which are separated by a part of high-resistance [ 4 ] , called the depletion-layer electrical capacity given by

( 10 )

( Beginning: [ 1 ] )

where A is the country, Wdep is the depletion bed breadth and Cdep is the depletion bed electrical capacity. Fig. 4 ( Appendix 1 ) shows that a p-n junction can be assumed as the two music directors separated by an dielectric [ 1 ] .

Reverse biasing a p-n junction

Fig. 5-a ( Appendix 1 ) shows a p-n junction under contrary prejudice where Vr is the rearward electromotive force [ 1 ] . When a rectifying tube is rearward biased, negatrons in the n-side and holes in the p-side move off from the junction [ 5 ] . The minority bearers, holes in the n-side and negatrons in the p-side, move in the opposite way due to which a little current flows in the junction. As a consequence, the electromotive force bead at the far ends will be really little and, therefore, all the contrary electromotive force will look across the junction. It is apparent from the Fig. 5-b, hundred ( Appendix 1 ) that there is an addition in the junction possible barrier from qVbi to q ( Vbi + Vr ) [ 1 ] .

Depletion bed breadth under contrary prejudice

By replacing Vbi with Vbi + Vr [ 1 ] in the equation ( 9 ) gives

( 11 )

( Beginning: [ 1 ] )

Depletion bed electrical capacity under contrary prejudice

Fig. 6 ( Appendix 1 ) shows the depletion bed electrical capacity Cdep ( =Cd ) in the tantamount circuit [ 3 ] of a contrary biased rectifying tube, where rd is the junction opposition under contrary prejudice electromotive force Vr ( =Vs ) . From the equation ( 10 ) , the depletion bed electrical capacity per unit country of the junction [ 4 ] is

( 12 )

( Beginning: [ 1,6 ] )

From equations ( 11 ) and ( 12 ) , we get

( 13 )

( Beginning: [ 1 ] )

which suggests a proportionality between Vr and 1/Cdep2 shown in Fig. 1 ( Appendix 3 ) . N can be determined from the incline of the line. The constitutional potency can be found from the intercept of the line with the horizontal axis [ 1,2 ] .

Experiment

To mensurate the depletion bed electrical capacity as a map of the contrary electromotive force and, therefore, to look into the cogency of an disconnected junction theory for a big Si p+-n rectifying tube [ 6 ] .

Circuit diagram

Fig. 7 ( Appendix 1 ) shows the circuit connected in the research lab to mensurate the depletion bed electrical capacity.

Apparatus

DC power supply, 100kI© opposition ( offers high electric resistance to the span ) , digital voltmeter, 1AµF capacitance ( blocks dc come ining the span ) , Wayne Kerr Bridge ( digitally measures the values ) , big Si p+-n ( NA & gt ; & gt ; ND ) rectifying tube [ 6 ] .

Procedure

Connect the circuit shown in Fig. 7 ( Appendix 1 ) . Note the contrary prejudice electromotive force on DVM and the measured-depletion bed electrical capacity Cmeas on Wayne Kerr Bridge by changing the electromotive force from -30V to -2V, in stairss of 2V, and from -2V to 0V in stairss of 0.5V. Repeat the process to find the circuit electrical capacity Ccir. In this instance, the rectifying tube will be removed from the circuit. Calculate the depletion bed electrical capacity Cdep per unit country [ 6 ] as

( 14 )

( Beginning: [ 6 ] )

Precautions

The power supply should be set at its minimal value before the circuit is switched on. The electromotive force should non transcend -30V for the given rectifying tube [ 6 ] .

Observations

By taking the rectifying tube from the circuit, the circuit electrical capacity remains changeless for assorted values of the applied electromotive force = 80.02 pF. It is because the electrical capacity of a capacitance depends on

The dielectric thickness between the home bases of a capacitance

The dielectric type

The surface country of the home bases of a capacitance

[ 7 ] so none of these parametric quantities changed with the applied scope of the electromotive force.

Table 1 ( Appendix 2 ) shows the diode C-V informations [ 1 ] .

Fig. 1 ( Appendix 3 ) shows a graph between Vr and 1/Cdep2. The graph shows that the rectifying tube in a contrary prejudice Acts of the Apostless like a capacitance whose electrical capacity varies reciprocally with the square root of the applied electromotive force [ 3,5 ] . So the experimental consequences are in conformity with the disconnected junction theory.

Fig. 1 ( Appendix 3 ) . The constitutional potency of the junction can be determined by the intercept of the line with the horizontal axis [ 1 ] . In this instance, we will generalize the line towards the negative x-axis which gives Vbi = -1.0 V. Equation ( 9 ) shows that an addition in Vbi additions Wdep which in bend will diminish Cdep and frailty versa.

The equation of the consecutive line of Fig. 1 ( Appendix 3 ) is

( 15 )

so the incline of the line = 0.175 A- 1010 m4F-2V-1.

The incline of the line of Fig. 1 ( Appendix 3 ) can besides be determined by distinguishing the equation ( 13 ) with regard to the contrary electromotive force [ 2 ] as

Slope = ( 16 )

( Beginning: [ 2 ] )

since NA & gt ; & gt ; ND therefore N = ND.

Neodymium can be determined from the equation ( 16 ) by seting the value of the incline in it and it comes ND = 6.723 A- 1019 m-3. It is obvious from the equation ( 4 ) that Vbi increases with an addition in ND or NA [ 1 ] . This in bend will diminish Cdep by increasing Wdep, as mentioned above, and frailty versa.

Wdep is calculated by the equation ( 11 ) for assorted values of Vr and tabulated in Table 2 ( Appendix 2 ) . Fig. 2 ( Appendix 3 ) indicates that the depletion bed breadth additions with an addition in the contrary electromotive force. It is because the electric field proportionately increases with Vr [ 5 ] . Thus, an addition in the breadth of the depletion bed is required so that the dissipation of big electromotive force bead can take topographic point across it [ 1 ] .

Fig. 3 ( Appendix 3 ) shows a graph between Vr and 1/Cdep2. In this instance, Cdep is calculated from the equation ( 12 ) and the information is tabulated in Table 3 ( Appendix 2 ) . The graph shows a direct relation between Vr and 1/Cdep2 which indicates the cogency of the equation ( 12 ) for our informations.

Decision

The depletion bed electrical capacity is one of the belongingss of the depletion bed that makes the device really utile to run under contrary prejudice. The assignment focused on the measuring of Cdep and the factors on which it depends. There exists a direct relation between Wdep and Vr that makes the best usage of the device as a variable capacitance. Proportionality between Vr and 1/Cdep2 enables the disconnected junction to be used as Varactor rectifying tube to modulate the frequences in the communicating webs. Furthermore, the experimental consequences show that the depletion bed electrical capacity gives the information about the doping concentration and the constitutional potency of the device. This gives rise to the fact that the device can be designed harmonizing to the demand of electrical capacity under contrary prejudice.

Appendixs

Appendix 1

Figures

Fig. 1 Fabrication of a p-n junction by spreading an n-type dross into a p-type stuff.

( Beginning: [ 1 ] )

Fig. 2 At thermic equilibrium. ( a ) Space charge part. ( B ) Electric field in the depletion part. ( hundred ) Built-in potency of an disconnected junction.

( Beginning: [ 2 ] )

Fig. 3 Energy set diagram at equilibrium.

( Beginning: [ 1 ] )

Fig. 4 A parallel home base capacitance theoretical account.

( Beginning: [ 1 ] )

( a )

( B )

( degree Celsius )

Fig. 5 ( a ) A p-n junction under contrary prejudice ( B ) Energy set diagram at equilibrium Vr = 0 ( degree Celsius ) Reverse biased energy set diagram.

( Beginning: [ 1 ] )

Fig. 6 Equivalent circuit of a rectifying tube under contrary prejudice.

( Beginning: [ 3 ] )

Fig. 7 Circuit diagram.

( Beginning: [ 6 ] )

Appendix 3

Graph

Fig. 1

Fig. 2

Fig. 3

x

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