Description

I would like to share and discuss about Engineering Subjects, Technical Seminars, Softwares Explantion and General Knowledge Discussions in this Blog.

Thursday, 3 September 2020

Theory and analysis of P-N Junction Diode

Open Circuited P-N Junction, 
Biased P-N Junction, , 
P-N Junction Diode, 
Current Components in PN Junction Diode, 
Diode Equation, 
V-I Characteristics, 
Temperature Dependence on V-I Characteristics, 
Diode Resistance, 
Diode Capacitance, 
Energy Band Diagram of PN Junction Diode  

Theory of P-N Junction Diode

PN Junction diode in Equilibrium with no applied Voltage (can be treated as Open Circuited PN Junction)

In a piece of sc, if one half is doped by p type impurity and the other half is doped by n type impurity, a PN junction is formed. The plane dividing the two halves or zones is called PN junction. As shown in the fig the n type material has high concentration of free electrons, while p type material has high concentration of holes. Therefore at the junction there is a tendency of free electrons to diffuse over to the P side and the holes to the N side. This process is called diffusion. As the free electrons move across the junction from N type to P type, the donor atoms become positively charged. Hence a positive charge is built on the N-side of the junction. The free electrons that cross the junction uncover the negative acceptor ions by filing the holes. Therefore a negative charge is developed on the p –side of the junction. This net negative charge on the p side prevents further diffusion of electrons into the p side. Similarly the net positive charge on the N side repels the hole crossing from p side to N side. Thus a barrier sis set up near the junction which prevents the further movement of charge carriers i.e. electrons and holes. As a consequence of induced electric field across the depletion layer, an electrostatic potential difference is established between P and N regions, which are called the potential barrier, junction barrier, diffusion potential or contact potential, Vo. The magnitude of the contact potential Vo varies with doping levels and temperature. Vo is 0.3V for Ge and 0.72 V for Si.

No Applied Bias (V = 0 V)

At the instant the two materials are “joined” the electrons and the holes in the region of the junction will combine, resulting in a lack of free carriers in the region near the junction, as shown in Fig.   1.5a   . Note in Fig.   1.5a    that the only particles displayed in this region are the positive and the negative ions remaining once the free carriers have been absorbed.

This region of uncovered positive and negative ions is called the depletion region due to the “depletion” of free carriers in the region.

Figure 1.5a: No bias Semi Conductor Diode

Figure 1.5b: No bias Semi Conductor Diode without ions

Figure 1.5c Symbol of PN Junction Diode

Figure 1.5d: Physical Representation of PN Junction Diode

The electrostatic field across the junction caused by the positively charged N-Type region tends to drive the holes away from the junction and negatively charged p type regions tend to drive the electrons away from the junction. The majority holes diffusing out of the P region leave behind negatively charged acceptor atoms bound to the lattice, thus exposing a negatives pace charge in a previously neutral region. Similarly electrons diffusing from the N region expose positively ionized donor atoms and a double space charge builds up at the junction as shown in the fig. 1.7a

 

Figure 1.7a: Diffusion of holes and electrons in P-N Diode

It is noticed that the space charge layers are of opposite sign to the majority carriers diffusing into them, which tends to reduce the diffusion rate. Thus the double space of the layer causes an electric field to be set up across the junction directed from N to P regions, which is in such a direction to inhibit the diffusion of majority electrons and holes as illustrated in fig 1.7b. The shape of the charge density, ρ, depends upon how diode id doped. Thus the junction region is depleted of mobile charge carriers. Hence it is called depletion layer, space region, and transition region. The depletion region is of the order of 0.5µm thick. There are no mobile carriers in this narrow depletion region. Hence no current flows across the junction and the system is in equilibrium. To the left of this depletion layer, the carrier concentration is p= NA and to its right it is n= ND.

Figure 1.7b: Diffusion of holes and electrons in P-N Diode

Barrier voltage

Positive charge present at n-side and negative charge present at p-side of p-n junction acts as barrier between p-type and n-type semiconductor. Thus, a barrier is build near the junction which prevents the further movement of electrons and holes.

Figure 1.8: Indicates barrier potential and depletion width

The negative charge formed at the p-side of the p-n junction is called negative barrier voltage while the positive charge formed at the n-side of the p-n junction is called positive barrier voltage. The total charge formed at the p-n junction is called barrier voltage, barrier potential or junction barrier as shown in Figure 1.8.

The size of the barrier voltage at the p-n junction is depends on, the amount of doping, junction temperature and type of material used. The barrier voltage for silicon diode is 0.7 volts and for germanium is 0.3 volts.

This electric field created by the diffusion process has created a “built-in potential difference” across the junction with an open-circuit (zero bias) potential of

 

Eo is the zero bias junction voltage, VT the thermal voltage of 26mV at room temperature, ND and NA are the impurity concentrations and ni is the intrinsic concentration.

Typically at room temperature the voltage across the depletion layer for silicon is about 0.6 – 0.7 volts and for germanium is about 0.3 – 0.35 volts. This potential barrier will always exist even if the device is not connected to any external power source, as seen in diodes.

 Depletion Width:

Let us consider the width of the depletion region in the junction as shown in Figure 1.8 figure. The region contains space charge due to the fact that, donors on the N-Side and acceptors on the P-Side have lost their accompanying electrons and holes. Hence electric field is established which turns causes a difference in potential is built up across the junction. Hence space charge finally described as an alloy junction, the depletion width W is proportional to (VO )1/2

Biased P-N Junction


 Forward-Bias Condition (VD> 0 V):

forward-bias  or “on” condition is established by applying the positive potential to the p -type material and the negative potential to the  n -type material as shown in  Fig. 1.9. The application of a forward-bias potential VD will “pressure” electrons in the n -type material and holes in the p -type material to recombine with the ions near the boundary and reduce the width of the depletion region as shown in Fig. 1.9a   . The resulting minority-carrier flow

Figure 1.9: Forward-biased P-N junction: (a) internal distribution of charge under forward-bias conditions; (b) forward-bias polarity and direction of resulting current.

of electrons from the p -type material to the n -type material (and of holes from the n –type material to the p -type material) has not changed in magnitude (since the conduction level is controlled primarily by the limited number of impurities in the material), but the reduction in the width of the depletion region has resulted in a heavy majority flow across the junction. An electron of the n-type material now “sees” a reduced barrier at the junction due to the reduced depletion region and a strong attraction for the positive potential applied to the p-type material. As the applied bias increases in magnitude, the depletion region will continue to decrease in width until a flood of electrons can pass through the junction, resulting in an exponential rise in current as shown in the forward-bias region of the characteristics of Fig. 1.16 Note that the vertical scale of Fig. 1.16 is measured in milli amperes (although some semiconductor diodes have a vertical scale measured in amperes), and the horizontal scale in the forward-bias region has a maximum of 1 V. Typically, therefore, the voltage across a forward-biased diode will be less than 1 V. Note also how quickly the current rises beyond the knee of the curve.

Figure 1.10: Forward biased P-N Junction with flow of charge carriers with resistor.

                          Figure 1.11: Circuit connection of Forward biased PN Diode

Reverse-Bias Condition (VD < 0 V):

If an external potential of V volts is applied across the pn junction such that the positive terminal is connected to the n -type material and the negative terminal is connected to the p -type material as shown in Fig.   1.12   , the number of uncovered positive ions in the depletion region of the n-type material will increase due to the large number of free electrons drawn to the positive potential of the applied voltage. For similar reasons, the number of uncovered negative ions will increase in the p-type material. The net effect, therefore, is a widening of the depletion region.

Figure 1.12:  Reverse-biased P-N Junction: (a) internal distribution of charge under reverse-bias conditions; (b) reverse-bias polarity and direction of reverse saturation current.

Figure 1.13: Reverse-biased P-N Junction with resistor

Figure: 1.14 Circuit Connection of Reverse biased PN Diode

This widening of the depletion region will establish too great a barrier for the majority carriers to overcome, effectively reducing the majority carrier flow to zero, as shown in Fig. 1.12a   .

 The number of minority carriers, however, entering the depletion region will not change, resulting in minority-carrier flow vectors of the same magnitude indicated with no applied voltage.


The current that exists under reverse-bias conditions is called the reverse saturation current and is represented by Is

The reverse saturation current is seldom more than a few microamperes and typically in µA and nA, except for high-power devices. The term saturation comes from the fact that it reaches its maximum level quickly and does not change significantly with increases in the reverse-bias potential, as shown on the diode characteristics of Fig. 1.15 for VD<0V.  The reverse-biased conditions are depicted in Fig.1.13b for the diode symbol and PN Junction. Note, in particular, that the direction of IS is against the arrow of the symbol. Note also that the negative side of the applied voltage is connected to the p -type material and the positive side to the n -type material, the difference in underlined letters for each region revealing a reverse-bias condition.

 Sometimes this avalanche effect has practical applications in voltage stabilizing circuits where a series limiting resistor is used with the diode to limit this reverse breakdown current to a preset maximum value thereby producing a fixed voltage output across the diode. These types of diodes are commonly known as Zener Diodes 

 This increase in level is due to a wide range of factors that include

Leakage currents, Generation of carriers in the depletion region and Temperature Sensitivity whereas a 10°C increase in current will result in doubling of the actual reverse current of a diode

Current Components in PN junction Diode :

Drift current

The flow of charge carriers, which is due to the applied voltage or electric field is called drift current. In a semiconductor, there are two types of charge carriers, they are electrons and holes. When the voltage is applied to a semiconductor, the free electrons move towards the positive terminal of a battery and holes move towards the negative terminal of a battery.

Electrons are the negatively charged particles and holes are the positively charged particles. As we already discussed that like charges repel each other and unlike charges attract each other. Hence, the electrons (negatively charged particle) are attracted towards the positive terminal of a battery and holes (positively charged particle) are attracted towards the negative terminal.

In a semiconductor, the electrons always try to move in a straight line towards the positive terminal of the battery. But, due to continuous collision with the atoms they change the direction of flow. Each time the electron strikes an atom it bounces back in a random direction. The applied voltage does not stop the collision and random motion of electrons, but it causes the electrons to drift towards the positive terminal.

The average velocity that an electron or hole achieved due to the applied voltage or electric field is called drift velocity. 

 The drift velocity of electrons is given by

                              Vn = µnE

 The drift velocity of holes is given by

                                Vp = µpE

 Where vn = drift velocity of electrons

             vp = drift velocity of holes
             µn = mobility of electrons
             µp = mobility of holes   
             E = applied electric field                       

 The drift current density due to free electrons is given by

                                                    Jn= enE

and the drift current density due to holes is given by

                                                    Jp = epE

   Where Jn = drift current density due to electrons
               Jp = drift current density due to holes
               e = charge of an electron = 1.602 × 10-19 Coulombs (C).
               n = number of electrons
               p = number of holes

Then the total drift current density is 
   J = Jn + Jp

                                = enE + epE
                                   J = e (nµn + pµp) E

 Diffusion current:

The process by which, charge carriers (electrons or holes) in a semiconductor moves from a region of higher concentration to a region of lower concentration is called diffusion.  

The region in which more number of electrons is present is called higher concentration region and the region in which less number of electrons is present is called lower concentration region. Current produced due to motion of charge carriers from a region of higher concentration to a region of lower concentration is called diffusion current. Diffusion process occurs in a semiconductor that is non-uniformly doped.

Consider an n-type semiconductor that is non-uniformly doped as shown in below figure. Due to the non-uniform doping, more number of electrons is present at left side whereas lesser number of electrons is present at right side of the semiconductor material. The number of electrons present at left side of semiconductor material is more. So, these electrons will experience a repulsive force from each other.

The electrons present at left side of the semiconductor material will moves to right side, to reach the uniform concentration of electrons. Thus, the semiconductor material achieves equal concentration of electrons. Electrons that move from left side to right side will constitute current. This current is called diffusion current. In p-type semiconductor, the diffusion process occurs in the similar manner.

Both drift and diffusion current occurs in semiconductor devices. Diffusion current occurs without an external voltage or electric field applied. Diffusion current does not occur in a conductor. The direction of diffusion current is same or opposite to that of the drift current.

Concentration gradient

The diffusion current density is directly proportional to the concentration gradient. Concentration gradient is the difference in concentration of electrons or holes in

 a given area. If the concentration gradient is high, then the diffusion current density is also high. Similarly, if the concentration gradient is low, then the diffusion current density is also low.

The concentration gradient for n-type semiconductor is given by

The concentration gradient for p-type semiconductor is given by

 

Where

Jn =diffusion current density due to electrons
Jp = diffusion current density due to holes

Diffusion current density

The diffusion current density due to electrons is given by

Where Dn is the diffusion coefficient of electrons

The diffusion current density due to holes is given by

Where Dp is the diffusion coefficient of holes

The total current density due to electrons is the sum of drift and diffusion currents.

Jn = Drift current + Diffusion current

The total current density due to holes is the sum of drift and diffusion currents.

                                            Jp = Drift current + Diffusion current

The total current density due to electrons and holes is given by

J = Jn + Jp

The following figure shows a P-N Junction with a forward bias by an external voltage V as shown in Figure 1.15a. Due to the applied voltage, there exists a potential gradient in P and N materials.

Figure: 1.15a PN Diode by an external voltage V.

Now, the holes from P-region and the electrons from N-region drift towards the junction. The holes drifted from P-region towards the junction enter the N-region where they represent minority carriers. Similarly, the electrons drifted from N-region towards the junction enter the P-region where they represent minority carriers. The minority carriers diffuse away from the junction exponentially with distance as shown following Figure: 1.15b.

Figure: 1.15b Current components in forward-biased unsymmetrical junction.

Their concentration reduces steadily because of recombination with electrons and holes respectively. We know that diffusion current of minority carriers is proportional to the concentration gradient and hence this must also vary exponentially with distance.

Current Components:

Ipn(x) = hole current in N material.

Ipn(0) = hole current at junction (x=0)

Inp(x) = electron current in P material.

Inp(0) = electron current at junction (x=0)

(The first letter refers to the type of the carrier and the second to the type of material)

At junction (x=0), the electrons crossing from right to left constitute a current in the same direction as hole crossing from left to right.

Thus the total current I at junction is given by

I = Ipn(0) + Inp(0)

The majority (electron) current Inn is given by Inn(x) = I - Ipn(x)

The majority (hole) current Ipp is given by Ipp(x) = I – Inp(x) 

Quantitative Theory of PN Diode currents

By using Quantitative theory to derive the expression for the total current as a function of the applied voltage. When a P-N diode is forward biased, then the holes are injected from P-Side into the N-Material. As shown in following figure the several components of hole concentration in N-side of a forward biased diode. It is obvius from the figure the hole concentration decreases exponentially with distance.

Figure: 1.15c Graph between Concentration and Distance

i) The hole concentration in N material is given by

iii) Using Boltzmann relationship of Kinetic theory of gases, it can be established that

This is known as Law of Junction. Here

V = applied voltage, and

VT= Volt equivalent of temperature = KT/q = T/ 11,600

Where k is Boltzmann Constant.

 

Total Diode Current

The total diode current I at x = 0 is given by

I = Ipn(0) + Inp(0),

Ipn(0)  = current caused by holes entering N – region

Inp(0) = current caused by electrons entering P – region

 

Diode Equation :

In solid-state physics that the general characteristics of a semiconductor diode can be defined by the following equation, referred to as Shockley’s equation, for the forward- and reverse-bias regions for exact demonstration.

IS is the reverse saturation current

VD is the applied forward-bias voltage across the diode

ŋ is an ideality factor, which is a function of the operating conditions and physical construction; it has a range between 1 and 2 depending on a wide variety of factors ( n  =1 will be assumed throughout this text unless otherwise noted).

The voltage VT is called the thermal voltage and is determined by

Where k  is Boltzmann’s constant= 1.38 x  10-23 J/K

T K is the absolute temperature in kelvins = 273 + the temperature in oC

q is the magnitude of electronic charge = 1.6 X10-19c

  Problem 1   At a temperature of 27°C (common temperature for components in an enclosed operating system), determine the thermal voltage VT

Solution:

= 25.875mV =  26Mv

The thermal voltage will become an important parameter in the analysis to follow in this chapter and a number of those to follow.   

 V-I Characteristics:

https://youtu.be/wqIcQW7Rzvk



Initially, Eq. (1.2) with all its defined quantities may appear somewhat complex. However, it will not be used extensively in the analysis to follow. It is simply important at this point

to understand the source of the diode characteristics and which factors affect its shape.  A plot of Eq. (1.2) with  Is= 10 pA is provided in  Fig.   1.15    as the dashed line. If we expand Eq. (1.2) into the following form, the contributing component for each region of Fig.   1.15 can be described with increased clarity:

For positive values of VD the first term of the above equation will grow very quickly and totally overpower the effect of the second term. The result is the following equation, which only has positive values and takes on the exponential format x appearing in Fig 1.16:

Figure: 1.16a Silicon semiconductor Diode Characteristics 

Figure: 1.16b Silicon semiconductor Diode Characteristics with exponential representation

Figure: 1.16c Diode Characteristics in Forward Bias and Reverse Bias

Figure: 1.16d Comparison of Ge, Si, and GaAs commercial diodes.

Simply plots the actual response of commercially available units. The total reverse current is shown and not simply the reverse saturation current. It is immediately obvious that the point of vertical rise in the characteristics is different for each material, although the general shape of each characteristic is quite similar. Germanium is closest to the vertical axis and GaAs is the most distant. As noted on the curves, the center of the knee (hence the K is the notation VK) of the curve is about 0.3 V for Ge, 0.7 V for Si, and 1.2 V for GaAs as shown in Figure 1.16d

Temperature Dependence on V-I Characteristics:

Temperature can have a marked effect on the characteristics of a semiconductor diode, as demonstrated by the characteristics of a silicon diode shown in Fig. 1.17. An increase from room temperature (20°C) to 100°C (the boiling point of water) results in a drop of 80(2.5 mV) = 200 mV, or 0.2 V, which is significant on a graph scaled in tenths of volts. A decrease in temperature has the reverse effect, as also shown in the figure: In the reverse-bias region the reverse current of a silicon diode doubles for every 10°C rise in temperature. 

 

Figure: 1.17 Variation in Si diode characteristics with temperature change.

It is not uncommon for a germanium diode with an Io in the order of 1 or 2 A at 25°C to have a leakage current of 100 A - 0.1 mA at a temperature of 100°C. Typical values of Io for silicon are much lower than that of germanium for similar power and current levels. The result is that even at high temperatures the levels of Io for silicon diodes do not reach the same high levels obtained. For germanium—a very important reason that silicon devices enjoy a significantly higher level of development and utilization in design. Fundamentally, the open-circuit equivalent in the reverse bias region is better realized at any temperature with silicon than with germanium. The increasing levels of I with temperature account for the lower levels of threshold voltage, as shown in Fig. 1.11. Simply increase the level of Io in and not rise in diode current. Of course, the level of TK also will be increase, but the increasing level of Io will overpower the smaller percent change in TK. As the temperature increases the forward characteristics are actually becoming more “ideal,”

Problem :

  Using the curves of Fig 1.16d:

   a.   Determine the voltage across each diode at a current of 1 mA. 

   b.   Repeat for a current of 4 mA.

   c.   Repeat for a current of 30 mA.

   d.   Determine the average value of the diode voltage for the range of currents listed above.

 

 

Diode resistance:

DC or Static Resistance

The application of a dc voltage to a circuit containing a semiconductor diode will result in an operating point on the characteristic curve that will not change with time. The resistance of the diode at the operating point can be found simply by finding the corresponding levels of VD and ID as shown in Fig. 1.18 and applying the following Equation: 

The dc resistance levels at the knee and below will be greater than the resistance levels obtained for the vertical rise section of the characteristics. The resistance levels in the reverse-bias region will naturally be quite high. Since ohmmeters typically employ a relatively constant-current source, the resistance determined will be at a preset current level (typically, a few milliamperes). In general, therefore, the higher the current through a diode, the lower is the dc resistance level.

Typically, the dc resistance of a diode in the active (most utilized) will range from about 10 Ω to 80Ω

Figure 1.18a Determining the dc resistance of a diode at a particular operating point.

Problem 2   Determine the dc resistance levels for the diode of following figure. at

   a. ID= 2 mA (low level)

   b. I D=20 mA (high level)

   c. VD=10 V (reverse-biased)   


a.      


Clearly supporting some of the earlier comments regarding the dc resistance levels of a diode.      AC or Dynamic Resistance

The dc resistance of a diode is independent of the shape of the characteristic in the region surrounding the point of interest.

If a sinusoidal rather than a dc input is applied, the situation will change completely. The varying input will move the instantaneous operating point up and down a region of the characteristics and thus defines a specific change in current and voltage as shown in Fig.1.18b with no applied varying signal, the point of operation would be the Q –point appearing on Fig. 1.18b, determined by the applied dc levels. The designation Q-point is derived from the word quiescent, which means “still or unvarying.” 

Figure 1.18b Defining the Dynamic or ac resistance.

A straight line drawn tangent to the curve through the Q -point as shown in Fig. 1.18c    will define a particular change in voltage and current that can be used to determine the ac or dynamic resistance for this region of the diode characteristics. An effort should be made to keep the change in voltage and current as small as possible and equidistant to either side of the Q -point. In equation form.

where Δ signifies a finite change in the quantity

Figure 1.18c Determining the ac resistance at a Q – point.

Diode Equivalent Circuits (Add on Course)

An equivalent circuit is a combination of elements properly chosen to best represent the actual terminal characteristics of a device or system in a particular operating region. 

 In other words, once the equivalent circuit is defined, the device symbol can be removed from a schematic and the equivalent circuit inserted in its place without severely affecting the actual behavior of the system. The result is often a network that can be solved using traditional circuit analysis techniques. 


Diode capacitance:

Transition and Diffusion Capacitance

Every electronic or electrical device is frequency sensitive.

That is, the terminal characteristics of any device will change with frequency. Even the resistance of a basic resistor, as of any construction, will be sensitive to the applied frequency. At low to mid-frequencies most resistors can be considered fixed in value. However, as we approach high frequencies, stray capacitive and inductive effects start to play a role and will affect the total impedance level of the element.

For the diode it is the stray capacitance levels that have the greatest effect. At low frequencies and relatively small levels of capacitance the reactance of a capacitor, determined by XC = 1/2πfc is usually so high it can be considered infinite in magnitude, represented by an open circuit, and ignored. At high frequencies, however, the level of XC can drop to the point where it will introduce a low-reactance “shorting” path. If this shorting path is across the diode, it can essentially keep the diode from affecting the response of the network.

In the pn semiconductor diode, there are two capacitive effects to be considered. Both types of capacitance are present in the forward- and reverse-bias regions, but one so outweighs the other in each region that we consider the effects of only one in each region.  Recall that the basic equation for the capacitance of a parallel-plate capacitor is defined by C = €A/d where € is the permittivity of the dielectric (insulator) between the plates of area A separated by a distance d. 

Figure 1.19 Transition and diffusion capacitance versus applied bias for a silicon diode.

Where τ is the minority carrier lifetime the time is world take for a minority carrier such as a hole to recombine with an electron in the n -type material.   However, increased levels of current result in a reduced level of associated resistance (to be demonstrated shortly), and the resulting time constant (τ = RC), which is very important in high-speed applications, does not become excessive. In general, therefore,

The transition capacitance is the predominant capacitive effect in the reverse-bias region whereas the diffusion capacitance is the predominant capacitive effect in the forward-bias region. 

Energy Band Diagram of PN Junction Diode:

A p-n junction consists of two semiconductor regions with opposite doping type as shown in Figure 4.2.1. The region on the left is p-type with an acceptor density Na, while the region on the right is n-type with a donor density Nd. The dopants are assumed to be shallow, so that the electron (Hole) density in the n-type (p-type) region is approximately equal to the donor (Acceptor) density.

Figure 1.20: P-N Junction diode with density representation


Cross-section of a P-N Junction

 

 

We will assume, unless stated otherwise, that the doped regions are uniformly doped and that the transition between the two regions is abrupt. We will refer to this structure as an abrupt p-n junction. Frequently we will deal with p-n junctions in which one side is distinctly higher-doped than the other. We will find that in such a case only the low-doped region needs to be considered, since it primarily determines the device characteristics. We will refer to such a structure as a one-sided abrupt p-n junction.

The junction is biased with a voltage Va as shown in Figure 1.21 (a). We will call the junction forward-biased if a positive voltage is applied to the p-doped region and reversed-biased if a negative voltage is applied to the p-doped region. The contact to the p-type region is also called the anode, while the contact to the n-type region is called the cathode, in reference to the anions or positive carriers and cations or negative carriers in each of these regions.

Flatband diagram

Figure 1.21 Energy band diagram of a p-n junction (a) before and (b) after merging the n-type and p-type regions

Note that this does not automatically align the Fermi energies, EF,n and EF,p. Also, note that this flatband diagram is not an equilibrium diagram since both electrons and holes can lower their energy by crossing the junction. A motion of electrons and holes is therefore expected before thermal equilibrium is obtained. The diagram shown in Figure 1.21 (b) is called a flatband diagram. This name refers to the horizontal band edges. It also implies that there is no field and no net charge in the semiconductor.

Thermal Equilibrium

To reach thermal equilibrium, electrons/holes close to the metallurgical junction diffuse across the junction into the p-type/n-type region where hardly any electrons/holes are present. This process leaves the ionized donors (acceptors) behind, creating a region around the junction, which is depleted of mobile carriers. We call this region the depletion region, extending from x = -xp to x = xn. The charge due to the ionized donors and acceptors causes an electric field, which in turn causes a drift of carriers in the opposite direction. The diffusion of carriers continues until the drift current balances the diffusion current, thereby reaching thermal equilibrium as indicated by a constant Fermi energy. 

Figure 1.22a Energy band diagram of a p-n junction in thermal equilibrium

Figure 1.22 b Energy Band Structure

While in thermal equilibrium no external voltage is applied between the n-type and p-type material, there is an internal potential, fi, which is caused by the work function difference between the n-type and p-type semiconductors. This potential equals the built-in potential, which will be further discussed in the next section.

The built-in potential

The built-in potential in a semiconductor equals the potential across the depletion region in thermal equilibrium. Since thermal equilibrium implies that the Fermi energy is constant throughout the p-n diode, the built-in potential equals the difference between the Fermi energies, EFn and EFp, divided by the electronic charge. It also equals the sum of the bulk potentials of each region, fn and fp, since the bulk potential quantifies the distance between the Fermi energy and the intrinsic energy. This yields the following expression for the built-in potential.

Forward and reverse bias

We now consider a p-n diode with an applied bias voltage, Va. A forward bias corresponds to applying a positive voltage to the anode (the p-type region) relative to the cathode (the n-type region). A reverse bias corresponds to a negative voltage applied to the cathode. Both bias modes are illustrated with Figure 1.23. The applied voltage is proportional to the difference between the Fermi energy in the n-type and p-type quasi-neutral regions.

As a negative voltage is applied, the potential across the semiconductor increases and so does the depletion layer width. As a positive voltage is applied, the potential across the semiconductor decreases and with it the depletion layer width. The total potential across the semiconductor equals the built-in potential minus the applied voltage.

Figure 1.23 Energy band diagram of a p-n junction under reverse and forward bias












 



 







 



2 comments: