which is the function of the reverse biased voltage V

Varacter Diodes

The reverse biased pn junctions exhibit a charge storage effect that is modelled with the depletion layer or the transition capacitance C

which is the function of the reverse biased voltage V

. This dependence can be used in a number of applications, such as automatic tuning of the radio receivers.

Special diodes are therefore fabricated to be used as a voltage variable capacitors known as varactors.

r_r C_T

Transition Capacitance

The equivalent circuit given above is used to model the

reverse-biased diode. The resistance r

is the incremental

resistance with the subscript ‘r’ specifying the reverse

biased. The element C

called the depletion, transition,

barrier, or space-charge capacitance, represents the change

in charge stored in the depletion region with respect to a

change in the junction voltage. The increase in the level of

reverse bias causes the width of the depletion region W to

increase. An increase in W is accompanied by additional

uncovered charges in the space-charge region. Because

positive charges exist on one side of the junction and

negative charges on the other, C

is analogous to a parallel-

plate capacitor.

Schottky Barrier Diodes

The junction formed by metal and extrinsic semiconductor (moderately doped n-type semiconductor material) can be either rectifying or ohmic. Because of the differences in the carrier concentrations in the two materials, a potential barrier exists.

Ohmic contacts, used to make connections to semiconductor devices, exist when care is exerted to eliminate the effect of the barrier. Such is the case of the junction between aluminium and heavily doped silicon used in IC fabrication. When lightly doped silicon is used, the aluminium-silicon junction is rectifying and the devices so formed are called Schottky barrier or simply Schottky diodes. The I-V charcteristic of the silicon and schottky diode is shown in the figure below.

In SBD current is carried by majority carriers (electrons). Thus the SBD does not show the minority-carrier charge-storage effects found in forward-biased pn junctions. As a result, the SBD can be switched from ON to OFF and vice versa much faster than is possible with the pn-junction diodes. The forward voltage drop of a conducting SBD is lower than that of the pn-junction diode, 0.3 to 0.5 V compared to the 0.6 to 0.8 V in the pn-junction diodes.

The figure above displays the comparison of the volt-ampere characteristics of a Schottky barrier diode and a silicon junction diode. They have almost similar shapes. However, two major differences between the two characteristics are also observed:

1) The cut-in voltage V_γ is lower

2) The reverse saturation current is higher in the case of Schottky diode.

Both features result from the high electron concentration in the metal.

A principal use of Schottky barrier diodes in IC is that it switches faster than the junction diodes. It is the majority carrier device since there are no minority carriers in the metal.

Tunnel diode

Tunnel diode definition

A Tunnel diode is a heavily doped p-n junction diode in which the electric current decreases as the voltage increases.

In tunnel diode, electric current is caused by “Tunneling”. The tunnel diode is used as a very fast switching device in

computers. It is also used in high-frequency oscillators and amplifiers.

Symbol of tunnel diode

The circuit symbol of tunnel diode is shown in the below figure.

In tunnel diode, the p-type semiconductor act as an anode and the n-type semiconductor act as a cathode.

We know that a anode is a positively charged electrode

which attracts electrons whereas cathode is a negatively

charged electrode which emits electrons. In tunnel diode, n-

type semiconductor emits or produces electrons so it is

referred to as the cathode. On the other hand, p-type

semiconductor attracts electrons emitted from the n-type

semiconductor so p-type semiconductor is referred to as the

anode.

The operation of tunnel diode depends on the quantum

mechanics principle known as “Tunnelling”. In electronics,

tunnelling means a direct flow of electrons across the small

depletion region from n-side conduction band into the p-

side valence band.

The germanium material is commonly used to make the tunnel diodes. They are also made from other types of materials such as gallium arsenide, gallium antimonide, and silicon.

Width of the depletion region in tunnel diode

The depletion region is a region in a p-n junction diode where mobile charge carriers (free electrons and holes) are absent. Depletion region acts like a barrier that opposes the flow of electrons from the n-type semiconductor and holes from the p-type semiconductor.

The width of a depletion region depends on the number of

impurities added. Impurities are the atoms introduced into

the p-type and n-type semiconductor to increase electrical

conductivity.

If a small number of impurities are added to the p-n junction

diode (p-type and n-type semiconductor), a wide depletion

region is formed. On the other hand, if large number of

impurities are added to the p-n junction diode, a narrow

depletion region is formed.

In tunnel diode, the p-type and n-type semiconductor is heavily doped which means a large number of impurities are introduced into the p-type and n-type semiconductor.

This heavy doping process produces an extremely narrow depletion region. The concentration of impurities in tunnel diode is 1000 times greater than the normal p-n junction diode.

In normal p-n junction diode, the depletion width is large as compared to the tunnel diode. This wide depletion layer or depletion region in normal diode opposes the flow of current. Hence, depletion layer acts as a barrier. To overcome this barrier, we need to apply sufficient voltage.

When sufficient voltage is applied, electric current starts

flowing through the normal p-n junction diode.

Unlike the normal p-n junction diode, the width of a depletion layer in tunnel diode is extremely narrow. So applying a small voltage is enough to produce electric current in tunnel diode.

Tunnel diodes are capable of remaining stable for a long duration of time than the ordinary p-n junction diodes. They are also capable of high-speed operations.

Concept of tunneling

The depletion region or depletion layer in a p-n junction diode is made up of positive ions and negative ions. Because of these positive and negative ions, there exists a built-in-potential or electric field in the depletion region. This electric field in the depletion region exerts electric force in a direction opposite to that of the external electric field (voltage).

Another thing we need to remember is that the valence band and conduction band energy levels in the n-type semiconductor are slightly lower than the valence band and conduction band energy levels in the p-type semiconductor. This difference in energy levels is due to the differences in the energy levels of the dopant atoms (donor or acceptor atoms) used to form the n-type and p-type semiconductor.

Electric current in ordinary p-n junction diode

When a forward bias voltage is applied to the ordinary p-n junction diode, the width of depletion region decreases and at the same time the barrier height also decreases. However, the electrons in the n-type semiconductor cannot penetrate through the depletion layer because the built-in voltage of depletion layer opposes the flow of electrons.

If the applied voltage is greater than the built-in voltage of

depletion layer, the electrons from n-side overcomes the

opposing force from depletion layer and then enters into p-

side. In simple words, the electrons can pass over the barrier

(depletion layer) if the energy of the electrons is greater

than the barrier height or barrier potential.

Therefore, an ordinary p-n junction diode produces electric current only if the applied voltage is greater than the built- in voltage of the depletion region.

Electric current in tunnel diode

In tunnel diode, the valence band and conduction band

energy levels in the n-type semiconductor are lower than

the valence band and conduction band energy levels in the

p-type semiconductor. Unlike the ordinary p-n junction

diode, the difference in energy levels is very high in tunnel

diode. Because of this high difference in energy levels, the

conduction band of the n-type material overlaps with the

valence band of the p-type material.

Quantum mechanics says that the electrons will directly penetrate through the depletion layer or barrier if the depletion width is very small.

The depletion layer of tunnel diode is very small. It is in nanometers.

So the electrons can directly tunnel across the small depletion region from n-side conduction band into the p-side valence band.

In ordinary diodes, current is produced when the applied voltage is greater than the built-in voltage of the depletion region. But in tunnel diodes, a small voltage which is less than the built-in voltage of depletion region is enough to produce electric current.

In tunnel diodes, the electrons need not overcome the opposing force from the depletion layer to produce electric current. The electrons can directly tunnel from the conduction band of n-region into the valence band of p-region. Thus, electric current is produced in tunnel diode.

How tunnel diode works?

Step 1: Unbiased tunnel diode

When no voltage is applied to the tunnel diode, it is

said to be an unbiased tunnel diode. In tunnel

diode, the conduction band of the n-type material

overlaps with the valence band of the p-type

material because of the heavy doping.

Because of this overlapping, the conduction band electrons at n-side and valence band holes at p-side are nearly at the same energy level. So when the temperature increases, some electrons tunnel from the conduction band of n-region to the valence band of p-region. In a similar way, holes tunnel from the valence band of p-region to the conduction band of n-region.

However, the net current flow will be zero because an equal number of charge carriers (free electrons and holes) flow in opposite directions.

Step 2: Small voltage applied to the tunnel diode

When a small voltage is applied to the tunnel diode which is less than the built-in voltage of the depletion layer, no forward current flows through the junction.

However, a small number of electrons in the conduction band of the n-region will tunnel to the empty states of the valence band in p-region. This will create a small forward bias tunnel current. Thus, tunnel current starts flowing with a small application of voltage.

Step 3: Applied voltage is slightly increased

When the voltage applied to the tunnel diode

is slightly increased, a large number of free

electrons at n-side and holes at p-side are

generated. Because of the increase in voltage,

the overlapping of the conduction band and

valence band is increased.

In simple words, the energy level of an n-side conduction band becomes exactly equal to the energy level of a p-side valence band. As a result, maximum tunnel current flows.

Step 4: Applied voltage is further increased

If the applied voltage is further increased, a

slight misalign of the conduction band and

valence band takes place.

Since the conduction band of the n-type material and the valence band of the p-type material sill overlap. The electrons tunnel from the conduction band of n-region to the valence band of p-region and cause a small current flow. Thus, the tunnelling current starts decreasing.

Step 5: Applied voltage is largely increased

If the applied voltage is largely increased, the tunnelling

current drops to zero. At this point, the conduction band

and valence band no longer overlap and the tunnel diode

operates in the same manner as a normal p-n junction

diode.

If this applied voltage is greater than the built-in potential of the depletion layer, the regular forward current starts flowing through the tunnel diode.

The portion of the curve in which current decreases as the voltage increases is the negative resistance region of the tunnel diode. The negative resistance region is the most important and most widely used characteristic of the tunnel diode.

A tunnel diode operating in the negative resistance

region can be used as an amplifier or an oscillator.

Advantages of tunnel diodes



Long life



High-speed operation



Low noise



Low power consumption

Disadvantages of tunnel diodes



Tunnel diodes cannot be fabricated in large numbers



Being a two terminal device, the input and output are not

isolated from one another.

Applications of tunnel diodes



Tunnel diodes are used as logic memory storage devices.



Tunnel diodes are used in relaxation oscillator circuits.



Tunnel diode is used as an ultra high-speed switch.



Tunnel diodes are used in FM receivers.

Bipolar Junction Transistor

The bipolar junction transistor (BJT) is a three- element device formed from two junctions which share the common semiconductor layer. There are two types of BJTs: pnp and npn. The three elements of the BJT are referred to as the emitter, base, and the collector. This is depicted in the figure below.

The arrow on the emitter lead specifies the direction

of the current when the emitter-base junction is

forward-biased.

BJT modes of operation

Cutoff EBJ is Reverse Biased CBJ is Reverse Biased Active EBJ is Forward Biased CBJ is Reverse Biased Reverse Active EBJ is Reverse Biased CBJ is Forward Biased Saturation EBJ is Forward Biased CBJ is Forward Biased

Operation of The npn Transistor in the Active Mode

Operation of npn BJT in Active Mode

The forward bias on the emitter-base junction will cause the current to flow across this junction. Current consists of two components: electrons injected from the emitter into the base, and holes injected from the base into the emitter. It is highly desirable to have the first component (electrons from emitter to base) at a much higher level than the second component (holes from the base to emitter). This can be accomplished by fabricating the device with a heavily doped emitter and a lightly doped base. The current that flows across the emitter-base junction will constitute the emitter current i_E.

The Electrons injected from emitter into the base will be minority carriers in the p- type base region. Because the Base is usually very thin, in the steady state the electron concentration will be highest at the emitter side and lowest at the collector side.

Some of the electrons that are diffusing through the base region will combine with holes which are the majority carriers in the base. However, since the base is actually very thin, the proportion of electrons lost due to recombination will be quite small.

The electron concentration will be highest [denoted by n

(0)] at the emitter side and lowest (zero) at the collector side. As in the case of any forward-biased pn junction, the concentration n

(0) will be proportional to e

𝑛

0 = 𝑛

𝑒

Where 𝑛_𝑝0 is the thermal equilibrium value of the minority-carrier (electrons) concentration in the based region, 𝑣_𝐵𝐸 is the forward biased base-emitter voltage, and 𝑉_𝑇 is the thermal voltage, which is equal to 25 mV at room temperature.

This electron diffusion current I_n is directly proportional to the slope of the straight-line concentration profile, Where A_E is the cross- sectional area of the base–emitter junction, q is the magnitude of the electron charge, Dn is the electron diffusivity in the base, and W is the effective width of the base.

𝐼_𝑛 = 𝐴_𝐸𝑞𝐷_𝑛 ^{𝑑𝑛𝑝(𝑥)}

𝑑𝑥 = 𝐴_𝐸𝑞𝐷_𝑛 − ^𝑛𝑝(0)

𝑊

The tapered minority carrier concentration profile causes the electrons injected into the base to diffuse through the base region toward the collector.

Some of the electrons that are diffusing through the base region will combine with holes, which are the majority carriers in base region. However, since the base is usually very thin the proportion of the electrons lost due to recombination process will be quite small. Nevertheless, the recombination in the base region causes the excess minority carrier concentration profile to deviate from a straight line and take the slightly concave shape indicated by the broken line in the figure above.

The Collector Current

Most of the diffusing electrons from emitter will reach the boundary of the collector-base depletion region. Since the collector is more positive than the base, these electrons will be swept across the CBJ depletion region into the collector.

They will get collected to constitute the collector current i_C.

T BE

V V S C

I e i 

B

C

i

i  

E

C i

i   1





 1

 

 



 

  1

B C

E i i

i  

Where

β = common-emitter current gain α = common-base current gain

BJT as an Amplifier and a Switch

The figure given below show the basic structure of the most commonly used BJT amplifier, the grounded-emitter or common- emitter (CE) circuit. The total input voltage v_I (bias+signal) is applied between the base and emitter (v_BE = v_I). The total output voltage v_O (bias+signal) is taken between collector and ground (v_O

= v_CE). The resistor RC has two functions, first to establish a desired dc bias voltage at the collector, and to convert the collector signal current i_C to an output voltage v_CE or v_O.

V

R

v

= v

+

-

+

-

v

= v

i

(a)

The transfer characteristics of the circuit in (a) is given in (b) above.

The amplifier is biased at the point Q, and a small signal v_I is superimposed on the bias voltage v_BE. The resulting output signal v_O, appears superimposed on the dc collector voltage V_CE. The amplitude of v_O is larger than that of v_I by voltage gain A_v.

C C

CC CE

O v V R i

v   

T BE

V v S

C

I e

i 

T I

V v S e

 I

Thus we obtain

T I

V v S

C CC

O V R I e

v  

We observe that the exponential term in this equation gives rise to the steep slope of the YZ segment of the transfer curve. Active mode operation ends when the collector voltage (v_O or v_CE) falls by 0.4 V or so below that of the base (v_I or v_BE). At this point, the CBJ turns on, and the transistor enters the saturation region. This is indicated by the point Z on the transfer curve. A further increase in v_BE causes v_CE to decrease only slightly. In saturation region v_CE = V_CEsat, which falls in the narrow range of 0.1 V to 0.2 V. The collector current will also remain nearly constant at the value I_Csat.

Amplifier Gain

To operated the BJT as a linear amplifier, it must be biased at the point in the active region. The figure given above shows such point, labeled Q (for quiesent point) and characterized by a dc base-emitter voltage V_BE and a dc collector-emitter voiltage V_CE. Then,

C C

CC

CE V R I

V  

Small signal Amplifier gain Av can be found out by

differentiating the expression in v

given above and

evaluating the derivative at point Q for v

= V

.

BE I

I

V v v

O

v

d

A  dv

C V

V S T

R e

V I

T

1 BE





T C C

V R

 I



T RC

V

 V



Where V

is the dc voltage drop across R

CE CC

RC V V

V  

Observe that the CE amplifier is inverting, that is, the output is 180⁰ out of phase relative to the input signal. It follows that to maximize the voltage gain we should use as large a volatge drop across R_C as possible. Thus for a given value of V_CC, to increase V_RC we have to operate at lower V_CE. The lowest V_CE is V_CEsat. Hence,

T

CEsat CC

v

V

V

A V 





T CC

v V

A _max   V

BJT Small-Signal Operation and Models

vb e

v_BE +

V_BE

V_CC

i

R_C

v_CE

+ -

-

i

i

An expanded view of the common-emitter characteristics

in the saturation region

As can be seen from the figure the incremental β is lower in the saturation region than in the active region. A possible operating point in the saturation region is that labelled X. It is characterised by a base current I

, a collector current Icsat and a collector -emitter voltage V

. Note that I

< β

I

. Since the value of Icsat is established by the circuit designer, a saturation transistor is said to be operating at a forced β given by

B Csat forced

I

 I

 _Thus,

F forced 

 

The ratio of β

to β

is known as the overdrive factor.

The greater the overdrive factor, the deeper the transistor is driven into saturation and the lower the V

becomes.

The collector to emitter resistance R

is given below.

Typically R

ranges between a few ohms to a few tens of ohms.

Csat C

B

B

I i I

i C

CE CEsat

i

R v _{ }



  _,

T be T

be T

BE T

be BE

T BE

V v C V

v V

V S

V v V

S V

v S

C

I e I e I e e I e

i    

 ) (

If v

<< V

, we approximate this equation as

c C

T be C

C T

be C

C

I i

V v I I

V I v

i  ( 1  )    

T C m

be m

c

V g I

v g

i







Where g

is called the

transconductance of the BJT and is

directly proportional to the

collector current I

.

The Emitter Current and the Input Resistance at the Emitter

be T

E be

T c C

e E C

e E

E

V v v I

V i I

i I I

i I

i













 



If we denote the small-signal resistance between base and the emitter, looking into the emitter by r_e, it can be defined as

E T e

be

e

I

V i

r  v 

m m

e

g g

r   1

 

Hence,

e b e

e

e e

b be

r r

i r r i

r i

r i

v

) 1 (

) (















 





m b be

be m

b

b B

B

be T

C C

C B

r g

i r v

g v i

i I

i

V v I I

i i





































 1

Where r_π is the small signal resistance between the base the emitter looking into the base. Thus r_π is directly proportional to the bias current I_C. Substituting from the g_m as given earlier,

B T T C

I r V

I V r













The Hybrid-π Model

This model represents the BJT as a voltage-controlled current source and explicitly includes the input resistance looking into the base, r_π. In the figure on the right g_mv_be can be replaced by βi_b. This can be directly derived from the equations above

The T Model

Although the hybrid-π model can be used to carry out the small-signal analysis of all the transistor circuits, there are situations in which an alternative model is much more convenient. This Model is called The T Model as shown below.

 



 

r v r

i v

r v r

i v

r r g

v v r g

i v

be e

be b

e be e

be b

e m e

be be

m e

be b

 





 

















) 1 (

1 ) 1

( )

1 (

) 1

(

In the terms of emitter current

e e

e m

e e m

be

m v g i r g r i i

g ^{ ( )  ( ) } 

Metal Oxide Semiconductor Field Effect Transistor (MOSFET)

The transistor is fabricated on a p-type substrate, which is

single-crystal silicon wafer that provides physical support

for the device. Two heavily doped n-type regions, indicated

in the figure below as n+ source and the n+ drain regions,

are created in the substrate. A thin layer of silicon dioxide

(SiO

) of the thickness typically between 2-50 nm serves as

an excellent electrical insulator, is grown on the surface of

the substrate covering the area between the source and the

drain regions. Metal is deposited on top of the oxide layer

to form the gate electrode of the device.

Physical structure of the enhancement-type NMOS transistor (a) Perspective View (b) Cross-section

Another name for the MOSFET is the insulated-gate FET or IGFET.

This name also arise from the physical structure of the device, emphasizing the fact that the gate electrode is electrically insulated from the device body (by the oxide layer). It is this insulation that causes the current in the gate terminal to be extremely small (of the order of 10^-15 A).

The enhancement-type NMOS transistor with a positive voltage applied to the gate is shown in the figure above. An n-channel is induced at the top of the substrate beneath the gate. The value of the v_GS at which a sufficient number of mobile electrons accumulate in the channel region to form a conducting channel is called the threshold voltage and is denoted by V_t which is positive for n-channel FET. The value of V_t is controlled during device fabrication and typically lies in the range 0.5 V to 1.0 V.

The gate and the channel region of the MOSFET form a parallel plate capacitor, with the oxide layer acting as the capacitor dielectric. The positive gate voltage causes positive charge to accumulate on the top plate of the capacitor. The corresponding negative charge on the bottom plate is formed by electrons in the induced channel. An Electrical field thus develops in the vertical direction. It is this field that controls the amount of charge in the channel, and thus determines the channel conductivity and, in turn, the current that will flow through the channel when the voltage v_DS is applied.

Applying a small v_DS

An NMOS transistor with v_GS > V_t and with a small v_DS applied. The device acts as a resistance whose value is determined by v_GS. Specifically, the channel conductance is proportional to v_GS – V_t and thus i_D is proportional to (v_GS – V_t) and v_DS. Current is carried by free electrons travelling from the source to drain. By convention, the direction of the current flow is opposite to that of the flow of negative charge. Thus the current flows from the drain to source in the channel. The magnitude of i_D depends upon the density of the electrons in the channel, which in turn depends upon the magnitude of v_GS. Specifically, for v_GS = V_t, the channel is just induced and the current conducted is still negligibly small.

As v

exceeds V

, more electrons are attracted into the channel. We may visualize the increase in charge carriers in the channel as the increase in the channel depth. The result is a channel of increased conductance or, equivalently, reduced resistance.

Figure given below shows a sketch of i

versus v

for

various values of v

. We observe that the MOSFET is

operating as a linear resistance whose value is controlled

by v

. The resistance is infinite for v

≤ V

and its value

decreases v

exceeds V

.

The i_D–v_DS characteristics of the MOSFET in this figure when the voltage applied between drain and source, v_DS, is kept small. The device operates as a linear resistor whose value is controlled by v_GS. For the MOSFET to conduct a channel has to be induced. Then, increasing the v_GS above the threshold voltage V_t enhances the channel, hence the name of this type of MOSFET is enhancement- type MOSFET. Finally, we note that the current that leaves the source terminal (i_S) is equal to the current that enters the drain terminal (i_D) and the gate current i_G = 0.

t GS

DSsat v V

v  

Obviously for every value of v_GS ≥ V_t, there is a corresponding value of v_DSsat. The device operates in the saturation region if v_DS ≥ v_DSsat. The region of i_D-v_DS characteristics obtained for v_DS < v_DSsat is called the triode region.

The i_D-v_DS Characteristics

The characteristics given in the following figure indicate that there are three distinct regions of operation: the cutoff region, the triode region, and the saturation region. The saturation region is used if the FET is to operate as an amplifier. For operation as a switch, the cutoff and triode regions are utilized. The device is cut off when v_GS < V_t. To operate the MOSFET in the triode region we must first induce a channel,

v_GS ≥ V_t (induced channel)

And then keep v_DS small enough so that the channel remains continuous. This is achieved by ensuring that the gate-to-drain voltage is

v_GD > V_t (continuous channel)

This condition can be stated explicitly in terms of v_DS by writing v_GD = v_GS + v_SD = v_GS – v_DS

Thus,

v_GS - v_DS > V_t Which can be rearranged to yield

v_GD < v_GS – V_t (continuous channel)

In words, the n-channel enhancement-type MOSFET operates in the triode region when v_GS is greater than V_t, and the drain voltage is lower than the gate voltage by at least V_t volts.

(a) An n-channel enhancement-type MOSFET with v_GS and v_DS applied and with the normal directions of current flow indicated.

(b) The i_D–v_DS characteristics for a device with k’n (W/L) = 1.0 mA/V².

In the triode region the i_D-v_DS characteristics can be described by the relationship

 

   



2 ) 1

(

n

D

v V v v

L k W i

DS t

GS n

D

v V v

L k W

i 

(  )

This linear relationship represents the operation of the MOS transistor as a linear resistance whose value is controlled by v_GS. Specifically, for v_GS set to a value V_GS, r_DS is given by

Where 𝑘_𝑛^′ is the process transconductance parameter (is equal to 𝜇_𝑛𝐶_𝑜𝑥), its value is determined by the fabrication technology. If v_DS is sufficiently small, we get

1

'

( )



 

  

 



GS GS

DS D

DS

DS

V V

L k W

V v

small v

i r v

The boundary between the triode and saturation regions is characterised by

t GS

DS v V

v  

Substituting in the first equation above we get

2

' ( )

2 1

t GS

n

D v V

L k W

i  

MOSFET as an Amplifier and as a Switch

When the MOSFET is used as a switch, it is operated at the extreme points of the transfer curve. Specifically the device is turned OFF by keeping 𝑣_𝐼 < 𝑉_𝑡 resulting in operation somewhere on the segment XA with 𝑣_𝑂 = 𝑉_𝐷𝐷. The switch is turned ON by applying a voltage close to 𝑉_𝐷𝐷, resulting in operation close to point C with 𝑣₀ very small (at C, 𝑣₀ = 𝑉_𝑂𝐶).