A Silicon Or Germanium Crystal Biology Essay


This paper, I investigate about the electrical chanracteristics, parameters, features, application and technology. A p-n-p bipolar junction transistor consists of a silicon or germanium crystal in which a thin n type layer is sandwiched between two layers of p-type called emitter and collector. In n-p-n BJT, thin p-type base layer is sandwiched between n-type emitter and collector layers. The first deals with the physical behavior of a semiconductor triode called bipolar junction transistors. This junction transistor is referred to as a bipolar junction transistor because in this device conduction takes place by motion of charge carriers of both the polarities namely electrons and holes.

A junction transistor of PNP type consists of a silicon crystal in which a thin layer of n-type silicon is sandwiched between two layers of p-type silicon. On the other hand, a junction transistor of NPN type consists of a semiconductor crystal in which a thin layer of p-type semiconductor is sandwiched between two layers on n-type semiconductor. The entire crystal is hermetically sealed against moisture inside a metal or plastic case. The thick horizontal line represents the base while the two inclined lines represent the emitter and the collector. (Jimmie J. Cathey) The emitter may be distinguished from the collector by an arrowhead placed on the inclined line representing the emitter. The direction of the arrowhead represents the director of the emitter current with the forward bias on the emitter. Thus in a p-n-p transistor emitter current is constituted by the flow of holes from emitter into the base region so that the direction of conventional electric current corresponding to this carrier flow is also from emitter into the base into the emitter. According in the symbol for n-p-n transistor, an arrowhead is placed on the emitter electrode pointing away from the base. Sometimes letters, E, B and C are added to designated emitter, base and collector respectively. Sometimes the entire symbol is enclosed in a circle.

Electrical Characteristics:

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A BJT is said to operate in active region when emitter junction JE is forward biased and the collector junction is reverse biased (Le Croissette). Convention regarding currents: all currents in a transistor are assumed positive when these currents flow into the transistor.

The emitter region doping is kept much heavier than the base region doping. Hence the emitter current is essentially that one contributed by holes crossing JE from emitter into the base in p-n-p (n-p-n) transistor.

Emitter current: the emitter current in p-n-p transistor consists of two parts are holder current IDE constituted by hole crossing JE from emitter to base and electron current JnE constituted by electrons crossing JE from base into emitter (Middlebrook). Current IpF > InE.

Recombination in Base Region: In p-n-p transistor in base region some of the holes recombine with majority carrier electrons. Hence the collector current is slightly less than the emitter current.

Conventions for Polarities of Voltages and currents:

In p-n-p and n-p-n transistors, all the currents namely the emitter current IE, base current IB and collector current IC are assumed positive when these currents flow into the transistor. Further in common base configuration, the emitter and the collector voltages are referred to the base (Hambley). Thus VEB is the voltage of the emitter with respect to the base while VCB is the voltage of the collector with respect to the base. Finally VCE is the collector-emitter voltage. A dot on the arrow head indicates the assumed positive polarity.

Consider the transistor with no external biasing voltages. In this condition all transistor currents must be zero. To ensure that no free charge carriers cross each junction, the potential barriers at the junctions adjust themselves to a value equal to the contact difference of potential Vo, typically a few tenths of a volt (Ebers). Let us assume, for the sake of simplicity that the junctions are completely symmetrical that is the emitter and the collector regions have identical physical dimensions and doping concentrations. Then the barrier heights at the emitter junction JE and the collection junction JC are identical. In this diagram, the narrow depletion regions at the junctions have been neglected.

Under open-circuit condition, the minority carrier concentration in each section of the transistor is constant and is equal to the thermal equilibrium value. Thus n-type base has minority carrier concentration of pno wile p-type emitter and collector regions have minority carrier electron concentration of npo (Hambley). A p-n-p transistor may be considered as a p-n diode followed by n-p diode. Hence the theory developed for junction diode may be used to explain the physical behavior of the transistor.

Current components in a Transistor:

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The various current components which flow across the forward biased emitter junction and reverse biased collector junction in a p-n-p transistor. The emitter current ED consists of two parts are hole current IpE constituted by holes crossing JE from emitter to base and electron current InE constituted by electrons crossing JE from base into emitter. The ratio IpE/InE is proportional to the ratio of the conductivity of the p-material of the emitter region to the conductivity of the n-material to the ratio of the conductivity of the p-material of the emitter region to the conductivity of the n-material of the base region. In commercial transistors, the doping of the emitter region is made much heavier than that of the base (L). Hence in a p-n-p transistor, the electron current component InE is negligibly small in comparison with the hole current component IpE. Accordingly in a commercial p-n-p transistor, the emitter current consists almost entirely of holes. This is a desirable feature since the current InE does not contribute carriers which ultimately reach the collector.

We assume that the injection of electrons into the base region is a low level injection. Hence the minority carrier current IpE is a hole diffusion current into the base (Gray P.E). Its magnitude is proportional to the slope of hole concentration pn at JE and is given by

IpE = -q DpA (dpn/dx)

Where Dp is the diffusion constant for holes, A is the cross sectional area and q is the magnitude of the charge of an electron. Similarly InE is the electron diffusion current into the emitter and is given by

InE = +qDp A(dnp/dx)

Where Dn is the diffusion constant for electrons. Thus InE is proportional the slope of electron concentration np at JE. The total emitter current crossing the emitter junction is the sum of IpE and InE and is thus given by IE = IpE + InE. All these currents IpE, InE and IE are positive in a p-n-p transistor.

The holes on crossing the emitter junction diffuse through the base region. In this journey through the base, some of these holes combine with the majority carrier electrons in the n-type base. This reduces the number of holes which ultimately reach the collector. In order to reduce the number of holes so lost through recombination with electrons, the width of coming from emitter region and traversing the base region (Bird). The difference (IpE - IpC) is the recombination current which leaves the base. In fact, electrons enter the base region through the base lead to replenish those electrons which have been lost by recombination with the holes injected into the base across JE.

The holes on reaching the collector junction cross this junction readily and enter the p-region of the collecto (Ebers)r. If the width of the base region is very small in comparison with the diffusion length Lp, then almost all the holes injected into the base reach the collector junction and get collected by the p-region forming the collector.

Consider the situation when emitter is open-circuited while the collector junction is reversed biased. Then IE = 0 and IpC = 0. Under this condition, the base and the collector together act as a reverse biased diode and the collector current IC equals the reverse saturation current ICO. This reverse saturation current ICO consists of two components namely InCO and IpCO. The component InCO is caused by electrons moving across JC from p-region to n-region while the component IpCO is caused by holes moving across JC from n-region to p-region (Giuseppe Massobrio). Thus we may write,

-ICO = InCO + IpCO

The minus sign has been chosen deliberately so that IC and ICO may have the same assigned direction of flow. Under open circuited condition, IE = 0 and hence no holes are injected across JE into the base. No holes, therefore, reach JC from the emitter (Jimmie J. Cathey). Accordingly IpCO results only from the holes generated thermally within the base. We now come back to the general case in which emitter is forward biased. Under this condition, IE ≠ 0 and collector current IC is given by

IC = ICO - IpC

= ICO - α IE

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Where α≡ fraction of the total emitter current IE which represents holes which have travelled from the emitter across the base to the collector. In a p-n-p transistor IE is positive while both IC and ICO are negative, signifying that the current in the collector lead flows in a direction opposite to that indicated by the arrow of IC (Gray P.E). In an n-p-n transistor, the direction of these currents are reversed and ICO is positive.

InCO gives the electron current crossing JC caused by electrons diffusing from the collector into the base. Hence InCO forms a conventional current from the base into the collector. The magnitude of InCO is proportional to the slope of np distribution at JC. Total diffusion hole current crossing JC from the base is given by

IpCt = IpC + IpCO

The magnitude s of IpCt is proportional to the slope of pn distribution at JC.

Large signal current gain α:

The quantity α has already been defined above and permits us to define α in an alternative manner. α may be defined as the ratio of the negative of the collector current increment from cut-off condition (IC = ICO) to the emitter-current increment from cut-off (IE = 0) (Hambley). Thus we may write,

α ≡ - (IC - ICO) / (IE - 0)

α is accordingly called the large signal current gain of a common base transistor. Now IC and IE have opposite signs in both p-n-p and n-p-n transistors. Hence α is always positive and typically α lies in the range 0.90 to 0.995. Further α is not constant but varies with the emitter current IE, collector voltage VCB and the temperature.

A Generalized Expression for collector current:

The collector current is valid only for operation in the active region that is with the emitter forward biased and collector reverse biased. Thus for operation in the active region, the collector current IC is almost independent of the collector voltage and depends only on the emitter current IE (Gray P.E). We now proceed to obtain a generalized expression for Ic which is valid not only when the collector junction Jc is substantially reverse biased but also for any voltage across Jc. In usch a general case, we are required to replace Ico by the current in a p-n diode constituted by the base and collector regions. In such a case, we may put Ico ( 1 - ε VC/VT) instead of Ico, where Vc represent the voltage drop across the collector junction Jc from the p-side to the n-side and Vt is volt equivalent of temperature (J.M). Then the generalized expression corresponding for Ic for any values of Vc and Ie becomes,

Ic = - αIE + Ico [1-ε VC/VT]

Now if Vc is negative and large in magnitude as compared with VT the physical interpretation that the p-n diode current Ico (1- ε VC/VT) is supplemented by a fraction α of the current IE coming from the emitter region.

Analysis of Currents in a Transistor

The analysis taken up here follows that given for the current components in a junction diode. The net current crossing a junction equals the sum of the electron current Inp in the p side and the hole current Ipn on the n-side evaluated at the junction (x=0). In a p-n-p transistor, electrons gent injected from the base region across Jf into the p-region which is long in comparison with the diffusion length of electrons Ln. this condition is exactly the same as existing in a p-n diode (w). Accordingly the expression for Inp obtained in the case of a p-n diode is valid here also. We may thus write the following expression for Inp (0) on replacing V by VE and npo by nEo subscript E signifying the emitter region

Inp(0) = AqDnnEo / IE (ε VE/VT - 1)

We have changed Ln to LE since the diffusion length of minority carrier electrons now pertains to the emitter region. The new symbols now being used have the meanings given below

nEo (nco ) is the thermal equilibrium electron concentration in the p type material of the emitter per metre3

Le(Lb) (Lc) is the diffusion length of minority carriers in the emitter (base) (collector), metre

Vc (vc) is the voltage drop across emitter (collector) junction taken positive for forward bias that is with the p-side positive with respect to the n-side.

Hole current in the n-type Base region:

The magnitude of Ipn in the base region of a p-n-p transistor is not the same as that in the n-region of p-n diode because in the transistor the hole current exists in a base region of small width whereas in a p-n diode, the n-region is large in comparision with Lp (Sah). The hole concentration in the n-type base region in accordance with equation is given by

Pn -pno = K1 ε -x/LB + K1 ε -x/LB

Where K1 and K2 are constants to be determined by boundary conditions. At each junction, the situation is exactly the same as for the diode junction and the boundary condition is given by equation. Thus we have

Pn = { pno ε VE/VT at x = 0 , pno ε VC/VT at x = W

Using these boundary conditions the exact solution may be obtained. In all transistors, however, the base width W is kept small compared with diffusion length LB and hence we may simplify the solution making use of this inequality (Phillips). Now since 0≤x≤W, we may safely assume that x/LB <<1. Then the exponential in equation may be expanded into a power series. Retaining only the first two terms in the series yields,

Pn - pno = k3 + k4x

Where k3 and k4 are constants, yet to be determined. As per this approximation, pn is a linear function of distance x in the base.

Ipn = -AqDpK4 = constant

Thus the minority carrier current is a constant throughout the base region. This is to be expected since we have assumed that base width W>>LB . assuming this inquality (W<< LB), little recombination takes place within the base and the hole current entering the base at the emitter junction reaches the collector junction Jc with no attenuation (Neudeck). On substituting the boundary conditions , we may readily solve for K4 and arrive at the following expression for IpE (0),

IpE (0) = AqDppno / W [ (ε VL/VT - 1) - (ε VC/VT- 1)

Emitter Efficiency and Transport Factor:

The emitter efficiency or injection efficiency denoted by γ is defined as,

Emitter efficiency, γ = current of injected carriers at JE / Total emitter current

In p-n-p transistor, we have

γ = IpE (0) / IpE (0) + InE (0)

= IpE (0) / I E

Thus emitter efficiency signifies the fraction of the total emitter current which is effective in producing any collector current. In order to maximize the emitter efficiency and make it approach unity as closely as possible, it is necessary to make emitter conductivity much larger than the base conductivity (Middlebrook). Typically the emitter efficiency equal about 1 / 1.00017 at low frequencies and 1 / 1.0067 at high frequencies.


A p-n-p transistor with voltage sources biasing the emitter-base junction in the forward direction and the collector-base junction in the reverse direction. The dashed curve pertains to the open circuit transistor while the solid curve refers to the transistor biased. Almost the complete biases VEB is available across the emitter junction. Hence the emitter junction barrier gets reduced by |VEB| as indicated. On the other hand, the reverse bias of magnitude |VCB| at the collector junction increases the collector-base junction potential barrier from its original value Vo to new value Vo + |VCB|. Lowering of the emitter-base potential barrier results in injection of minority carrier holes into the n-type base region and minority carrier electrons into the p-type emitter region (Bird). Across the base region, the potential remains constant except for an extremely small ohmic voltage drop. The excess holes so injected into the base region diffuse across the n-type base and reach the collector junction. At the collector JC, the holes come across a large positive electronic field (ε = - dV/dx >>0) and are therefore, accelerated across the junction. Stated otherwise, the holes which ultimately manage to reach JC fall down the potential barrier at JC and get collected by the collector. A negative potential of magnitude |VCB| is available at the collector junction. Hence from the law of junction, (pn = pnoεV/VT) pn gets reduced to zero at the collector. Similarly the reverse collector junction bias reduces the electron density np in the collector region to zero at JC.

Collector reverse saturation current:

On substituting values of coefficients a12, a21 and a22, we get the values of collecter reverse saturation current Ico.

Base width modulation:

For transistor operating in the active region, JE is given a forward bias while Jc is given a reverse bias (Ebers). The magnitude of the reverse bias at the collector junction Jc increases, the width of the collector junction depletion layer increases. Since the doping of the base region is ordinarily substantially smaller than that in the collector. Accordingly as the magnitude of the collector junction reverse bias increases, the effective base width W decreases. This phenomenon is called the Early Effect and the variation of the base width with variation of collector reverse bias is called base width modulation (Giuseppe Massobrio). Decrease of the base width with increase of magnitude of reverse collector junction voltage produces the following three effects:

The probability of recombination within the base region gets reduced. Hence as β and α get increased. The minority carrier concentration gradient in the base region gets increased. Hence injected hole current density in p-n-p transistor at JE gets increased.

For extremely large reverse collector voltages, the effective base width W may to zero causing a voltage breakdown of the transistor. This phenomenon is known as the punch through (Gray P.E).

Dynamic Emitter Resistance:

The dynamic emitter resistance of a transistor symbolized by re' is defined as the reciprocal of the slope of the emitter current-emitter voltage characterisitic. Thus re' is given by

re' ≡ dVE / dIE

This rc' is the same as the dynamic resistance of a semiconductor diode with forward bias VE. re' is given by

re' = nVr / IE

For germanium, η = 1 while for silicon η = 2 for small forward current and η ≈ reduce 1 for large currents. Thus re' varies inversely as the emitter current IE. At room temperature that is T = 300 K, η = 1, re' = 26/IE where re' is in ohms and IE is in milli amperes. Thus for emitter current of 26 mA, re' = 1 ohms. In any case, re' remains small (Hambley).

Transistor as an amplifier:

A load resistance RL connected in series with the collector supply voltage Vcc. Then a small increment ΔVi in the input voltage between emitter and base result in a relatively large change ΔIE in the emitter current. Let this change ΔIE result in a change ΔIc in the current through the resistor RL. This ratio of ΔIc to ΔIE is denoted by the symbol α'. Then the change in the output voltage across the load resistor RL is given by

ΔVo = - RL ΔIc = -α' RL ΔIE

This change ΔVo is much large than the input voltage ΔVi so that the voltage amplification, Av = Δvo / ΔVi is much greater than unity. Thus the transistor works as voltage amplifier. Let the dynamic resistance of the emitter junction be re'. Then,

Δvi = re' ΔIE


Transport Factor β:

β = injected carrier current reaching Jc / injected carrier current at JE

= I pc (0) / I pE (0)

Evidently then, α = I pc (0) / IE

= I pc (0) / I pE (0) * I pc (0) / IE

= βγ

Expression for Transistor α, β and γ

Ic = ( a21 / a11) IE + (a22 - (a21a12/a11) (ε VC/VT- 1)

Hence by comparison, we may write

α ≡ - ( a21 / a11)

Ico ≡ (a21a12/a11) - a22

On substituting the values of constants a11 and a21, we get

α = 1 / 1+ (DnnEo W / LE Dp pno)

But base region conductivity is given by

σB = q [Nn µn + Pn µp]

Emitter region conductivity is given by

σE = q [Np µn + Pp µp]


Dp / µp = Dn / µn = VT

Finally Nn Pn = NpPp = Ni2

By combining the equation, we get

α = 1 / 1+ W σB /LEσE

However, if the base width is appreciable, the expressions for γ, β and α are obtained using general expressions for currents (Jimmie J. Cathey)

γ = I pE (0) / (I pE (0) + I nE (0))

the general analysis for various currents in a p-n-p transistor has not been taken up here. However, if we use those general expressions valid even when W / LB is not much smaller than unity, then for operation in the active region we get

β = I PC (0) / IPE (0) = sech (W / LB)

γ = 1 / 1+ (W σB /LEσE)

= 1 - (W σB /LEσE)

At high values of emitter current IE, σB gets increased because of the additional charges injected into the base and this increased σB reduces γ. This is referred to as the conductivity modulation (L). Similarly at very low values of IE, recombination of charge carriers in the transition region at the emitter junction causes a recombination current which is a large fraction of the total emitter current. Hence value of γ gets reduced. Silicon has many recombination centers in the emitter junction transition layer so that γ as well as α tend to zero as IE tends to zero. Germanium on the other hand, may be made relatively free of recombination centres so that even at IE = 0, the transistor still have α≈0.9 (Le Croissette)

Parameter α':

This parameter has already been introduced above and is formally defined as the ratio of the change in the collector current to the change in the emitter current at constant collector to base voltage. It is called the negative of the small signal short circuit current gain, thus

α' = - α

BJT applications

Bipolar junction transistors stay behind significant devices for ultra-high-speed discrete logic circuits such as emitter coupled logic (ECL), power-switching applications and in microwave power amplifiers. BJTs are commonly used in electrical circuits where current desires to be controlled (Middlebrook). Some of the districts are switching elements to control DC power to a load, amplifiers for analog signals, 3D bipolar simulation, NPN device, AC frequency response, emitter-coupled logic element simulation, 3-phase AC motors.


BJT are generally of p-n-p type. In this case, two small pallets of indium are attached to opposite sides of a thin wafer of n-type germanium and the entire assembly is heated for a short time at 500 C. this causes the indium to dissolve the germanium below it forming a saturation solution. On cooling the assembly this saturated solution recrystallizes with adequate indium content so as to change the impurity from n-type to p-type. These two p-regions on either side of the n-type wafer form the emitter and the collector regions of the complete transistor (Neudeck). The collector is made larger than the emitter. Accordingly as viewed from the emitter, the collector subtends a large angle. The result of this geometrical arrangement is that very little emitter current follows a diffusion path taking the carriers direct to the base terminal rather than the collector.

Each such grown crystal is then cut into small thin wafers by means of diamond cutting wheels of slicing and dicing machine. Typically the size of such a wafer is 5mm X 5 mm X 0.05 mm thick. Each such wafer may then be used to form a semiconductor transistor. When made into a p-n-p transistor, this wafer acts as the base of n-type. After cutting, each wafer is ground, polished and then etched. The cleaning agent called the etch removes all contaminants and also surface irregularities caused by cutting process. The small pellets of indium are placed on each side of the slice. One pellet is larger about 3 times than the other. The larger one is finally used as collector while the smaller pellet is used as the emitter. The assembly consisting of n-type wafer and two pellets is than heated to about 500 C in an atmosphere of hydrogen. At such a high temperature, the indium pellets melt.

Germanium on the otherhand, does not melt since its melting point is above 500 C. the molten indium dissolves some of the germanium from the slice or wafer and forms a saturated solution. On cooling molten germanium with indium content recrystallizes to form a crystal of p-type germanium at the solid-liquid interface. On further cooling, the rest of the indium pellet solidifies as an alloy containing a little germanium (Phillips).

Leads for the emitter and collector are soldered to the pellets making non-rectifying contact. Further non-rectifying base contact is usually made be welding a strip or loop of gold plated wire to the base plate. The whole assembly is then etched to remove surface contamination. It is then covered with moisture proof grease mounted in a suitable mechanical structure and is hermetically sealed in a small glass envelope with leads passing through the glass foot. Care is taken during the sealing process to avoid overheating the transistor. Opaque paint is usually coated on the outside of glass bulb to exclude incident light.