The pn junction: 3 Depletion width variation with voltage For an abrupt junction, the depletion width W for zero external applied voltage is: 2 ( +ε NNV ) W = DAbi NeN DA
Applying an external voltage V: Vbi → Vbi-V (V positive for forward bias, negative for reverse bias)
2 ( )( +−ε NNVV ) W =⇒ bi DA Forward bias: NeN DA
e(V -V) - bi p-type + - + n-type
W Reverse bias:
p-type - - - e(Vbi+V) - - + - + + + n-type + + Depletion capacitance
As the depletion region consists of equal but opposite space charges which are physically separated, its behaviour is like a capacitor
For a parallel plate capacitor, A Q=CV ε ε A C = 0 r d d
For a depletion region, both the total charge C and the effective separation d (related to W) are a function of the voltage. Hence C will not be constant as V is varied.
Generally, we are interested in the response of a pn junction to a small a.c. voltage applied in addition to a static d.c. voltage. Hence, the differential capacitance is usually derived:
dQ dQ dx dQ C = Where a small change in the external voltage = d . dV dV changes the depletion charge by dQ dV dV dxd Start by considering the n-type side of an abrupt junction. If V varies by dV then xd (the width of the depletion region on the n-type side) varies by dxd, where: dx dx = d dV. d dV From lecture 2, we know:
2 ( bi −ε )NVV A xd = ()+ NNeN DAD
dx 1 2εN d −=⇒ A dV 2 ()()biDAD −+ VVNNeN
Now, we need to relate the change in the depletion region width to the change in the charge contained in the depletion region dQ:
Space charge is N e, therefore the extra charge in NDe NDe D additional length dxd is:
x dx 2 d d dQ = (NDe)dxd /m dQ eN εN2 =⇒ D A dV 2 ()()biDAD −+ VVNNeN dQ ε NNe C ==⇒ DA Per unit area dV ()()biDA −+ VVNN2 Conclusions: pn junctions
We have covered the following topics:
1. Schematic band diagrams (a) n and p type materials (b) pn junction in equilibrium (c) pn junction under forward and reverse bias
2. Derivation of I=I0(exp(eV/kT)-1)
3. Depletion region electrostatics, variation with bias
4. Mechanisms responsible for reverse breakdown
5. Depletion capacitance Transistors
Short for transfer resistor
An electronic device where, by varying the voltage between two terminals, the current flowing into (or out of) a third terminal can be altered
Current The output can be converted into a voltage by (output) Control passing it through a suitable resistor (V=IR) Voltage (input) Amplification is obtained if the output voltage is greater than the input voltage
2 main transistor types
1. Junction (or bipolar) transistor 2. Field effect transistor (FET) The junction transistor
Formed by an additional layer to a pn junction
Two possibilities: n-p-n p-n-p
Behaviour is similar for both – just the actions of the electrons and holes are reversed. In the following we’ll just consider the n-p-n junction transistor.
Physical construction
n+ p n EMITTER BASE COLLECTOR cb EF No external voltage vb
The base region is generally very thin (<1µm) The doping level in the emitter (n+) is generally much higher than in the base (p) or collector (n) Normal operation In this mode the base-emitter junction is forward biased, the base collector is reverse biased.
n+ p n Ensures a common ground point EMITTER BASE COLLECTOR
electrons Forward biasing the emitter- base junction reduces the potential step holes This leads to a large number of electrons flowing from the emitter into the base
Holes also flow from the base to emitter but less important as base doping is lower The emitter-base electron current is given by the pn junction IV equation: ⎛ eV ⎞ ⎜ BE ⎟ 0 ⎝ kT ⎠ Where I 0=constant E ≈ EeII E
In a single pn junction all of the electrons that flow into the p-type material eventually recombine with a hole.
However, in a junction transistor the base width is much smaller than the decay length for electrons Still, a small fraction (1-α), where α~1, of the electrons recombine with a hole The remaining fraction, α, reach the base-collector junction and ‘fall down’ the large potential step, flowing out through the collector contact
Electrons lost in base Electron density Electrons reaching collector
BE BC Distance The collector current is therefore given by:
⎛ eV ⎞ ⎜ BE ⎟ 0 ⎝ kT ⎠ C α=α= EE eIII
⎛ eV ⎞ ⎜ BE ⎟ 0 ⎝ kT ⎠ 00 =⇒ CC eII C α= E )ttancons(IIwhere
Hence by varying the base-emitter voltage (VBE) the collector current can be varied
IC
VBE Current gain
Defined as
IOUTPUT IC β== FE )hor( IINPUT IB
There are 2 contributions to IB
a) A small current must flow into the base to replenish holes in the base which are destroyed when they recombine with electrons flowing in from the emitter a) IB =(1-α)IE
b) Holes from the base can flow into the emitter across the forward biased base-emitter junction. This contribution can be made very small by keeping the base doping level (and hence the number of free holes) low
Neglecting contribution from b):
IC=αIE, IB=(1-α)IE I α C ==β IB 1 α− As α~1, β>>1 (typically β~100) Dependence of IC on VCE When electrons reach the base-collector junction they will ‘fall down’ the potential step into the collector
This process does not depend on the height of the potential step
Apart from the initial strong variation as the potential step is formed there is very little dependence of IC on VCE
IC VBE (c)
VBE (b)
VBE (a)
VBE (c) > VBE (b) > VBE (a)
VCE
Initial strong dependence Very little dependence of IC on VCE as base-collector step in this region formed In addition to varying the height of the base-collector step, VCE also affects the case-collector depletion width
b b cb e e
c
c As VCE increases the base-collector depletion region extends further into the base
The effective base width is therefore reduced and the probability of an electron recombining with a hole also deceases (α increases and hence β also increases)
Therefore IC increases slightly with increasing VCE This is known as the Early Effect IC with
without
VCE EARLY VOLTAGE
To find the Early voltage, draw a tangent at a particular VCE, intercept with the x axis gives the value
It can be calculated from
Q AxeN V = base = bA Cbase−collector C The Field Effect Transistor Many types of FET – we’ll consider the junction FET (JFET) briefly. GATE p+
SOURCE DRAIN
n-type channel In operation, current flows from drain to source (electrons from source to drain) The gate is reverse biased with respect to the channel, producing a depletion region in the channel
G G
S D S D IDS IDS Current in the channel can only flow in the non-depleted region Increasing the gate reverse bias voltage increases the width of the depletion region and hence decreases the effective channel width
The resistance of the channel increases, reducing IDS Therefore varying the gate voltage alters the source-drain current Comparison of Junction Transistors and FETs
1. A junction transistor uses both electrons and holes – it is a bipolar device A FET uses only one type of carrier, it is therefore a unipolar device 2. A junction transistor uses changes in the height of a potential step to control current A FET uses changes in the effective channel width
Can be thought of like water flow: Junction FET
Water flowing over ground Water flowing through a pipe
A bump controls the flow A tap controls the flow Comparison of Junction Transistors and FETs
3. Input resistances VIN/IIN
Junction transistor Base current = IC/β ~0.1mA for IC=10mA, β=100
FET gate current is the reverse leakage current of a pn junction, ~10-9A
5 Hence for similar VGS and VBE values RIN (FET) ~ 10 RIN (JT)
i.e. FETs have much larger input resistances than bipolar transistors
4. FETs are generally easier to mass produce and integrate in large numbers
The metal-oxide-semiconductor FET (MOSFET) forms the basis of the majority of modern integrated circuits Conclusions
You should now understand the basics of the physical construction and operation of junction and field effect transistors
Junction transistor
a) IC vs VBE relationship b) IC vs IB relationship c) IC vs VCE relationship
FET Depletion region operation
Comparisons of junction and field effect transistors