Semiconductor DevicesA brief review Dr. K. Fobelets
Purpose of the course • Study bipolar devices in more detail • Diodes and BJTs • Closer to reality: recombination • What causes the delays in these devices when switching?
The most frequently used sentence in this course will be: Excess minority carrier concentration
Structure • 1. Lectures : 10 hrs • Basic principles based on Q&A session • Recombination and how does it impact the characteristics • LONG pn diode – correct and approximated solutions • LONG BJT • Switching of pn diodes and BJTs • 2. Classes: solving past exam papers
Review • Electrons and holes • Minority and majority carriers • Energy band diagram
Thermal energy: kT Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Extrinsic Si Extrinsic Si Si Extrinsic Si Si Si B Obtained by doping As B As ND NA Free charged carriers in Si Covalent bond Movement: kT Intrinsic Si Si Si Si Si Si Si Si p-type n-type
Si Si Si + Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si In semiconductors two types of free charged carriers exist: electrons and holes. Q1: What are holes? • Spherical voids in a semiconductor • A positively charged Si atom that has lost its electron • A positively charged particle that is the result of quantum mechanics
C The two charged particles describe together the conduction in semiconductors. Electron e- with charge q=-e and mass mn = m0 m*n Hole h+ with charge q=+e and mass mp = m0 m*p
Intrinsic silicon (Si) has a small number of both free electrons and holes such that ni=pi. In order to increase the free carrier concentration, the semiconductor can be doped. With donors ND more electrons are created, with acceptors NA more holes are generated. Q2: When intrinsic Si is doped with donor atoms, which of the following statements is correct? • n = p = ni = pi • n > ni & p < ni • n > p > ni • p > n > ni n: electron concentration p: hole concentration ni: intrinsic electron concentration pi: intrinsic hole concentration
By heart B n > ni & p < ni in an n-type semiconductor. n-type semiconductor n = ND p = ni2/ND p-type semiconductor n = ni2/NA p = NA
The concept of majority carrier and minority carrier is important in semiconductor devices. Majority carrier is the carrier type in a doped semiconductor with the highest concentration. Minority carrier is the carrier type with the lowest concentration. Q3: True or False? The holes are the majority carriers in a p-type semiconductor (doped with acceptor atoms NA).
TRUE p-type semiconductor > n p p p p-type semiconductor p-type semiconductor hole concentration electron concentration n-type semiconductor > n p n n n-type semiconductor n-type semiconductor electron concentration hole concentration MAJORITY CARRIERS MINORITY CARRIERS
Drift and diffusion • Two types of carrier movement • As a result of an electric field → DRIFT • As a result of a carrier gradient → DIFFUSION
The purpose of semiconducting devices is to generate a current/voltage in response to an applied voltage/current. Two different types of current can exist in a semiconductor: drift and diffusion current. The expression of the total current that can flow in a semiconductor is given by the drift-diffusion equation: Q4: Which statement is true? (1) (2) • Term (1) is drift current and (2) diffusion current • Term (2) is drift current and (1) diffusion current • Only term (1) can exist in a semiconductor • Only term (2) can exist in a semiconductor
A Drift current is proportional to the carrier concentration and the electric field Diffusion current is proportional to the carrier gradient. E(x) Jndrift Jpdrift n(x) Jndiff p(x) Jpdiff
Motion of free charged carriers in a semiconductor. Q5: If a p-type semiconductor at room temperature is conducting carriers due to drift, which of the following motion paths would be followed by the holes? E - E - + + a) c) (b) (d) - + - + E E
B When carriers move in a semiconductor they are scattered along the way. This means that they will be accelerated by the electric field (in this case) and then interact with atoms, impurities, other carriers that makes them lose some of their kinetic energy = scattering. Therefore the carriers will travel with an average velocity in amplitude and direction.
p+ p Q6: Solve diffusion processes n • Draw arrows indicating the direction of diffusion of carriers. • Identify the type of carriers that is diffusing.
Solution p+ n p Holes Electrons
p+ n p Q7: Why is there no net current while diffusion is happening? • Because hole diffusion and electron diffusion cancel each other. • Because an internal electric field is built up across each junction causing drift of holes/electrons that cancel the diffusion of .holes/electrons. • Because holes and electrons diffuse automatically back to where they came from.
E E - + - + p+ n p Holes Holes diffusion drift Electrons Electrons 2. Because an internal electric field is built up across each junction causing drift of holes/electrons that cancel the diffusion of .holes/electrons.
Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si As Si Si Si Si Si + - : arsenic atom ionised : boron atom ionised As B Depletion ND n-Si NA p-Si Si Si Si B - + As B Capacitive effect Capacitive effect - + Si B As + - - + E E
Q8: True - False Ec EF Ev The position of the Fermi level EF determines the type of the semiconductor.
Q9: Multiple choice Ec EF Ev • This is the energy band diagram of an n-type semiconductor. • This is the energy band diagram of a p-type semiconductor. • This is the energy band diagram of an intrinsic semiconductor.
Ec Bottom of conduction band EF EG Bandgap. No energy levels in this energy region. Intrinsic “level”. Is the position of the Fermi level EF when the semiconductor is intrinsic. Ei Ev Top of valence band Position of Fermi level is determined by the doping type and density For n-type Si:
Devices • A combination of n and p type semiconductors plus ohmic contacts to apply the external voltages/currents makes devices • When combining a-similar materials diffusion will occur and as a result an internal electric field will be built up to an amount that opposes diffusion current.
Energy band diagram e.g. p-Si – n-Si p-Si – n-Si – p-Si It is possible to start from the knowledge on workfunctions,f and the energy reference: the vacuum level, Evac. The workfunction is dependent on the doping concentration!
e×fn-Si e×fp-Si Evac Evac p-Si n-Si EF EF
e×fp-Si e×fn-Si Evac Evac p-Si n-Si EF EF
e×fp-Si e×fn-Si Depleted region on both sides Evac Evac p-Si n-Si Ec Ec EF EF Ev Ev
Diffusion and drift can occur at the same time. A charge packet E Both also always occur across junctions
p n E p n A look at the short pn-diode PN diode I p n V
p n E p n Short PN diode DIFFUSION I p n V
p n E p n Short PN diode DIFFUSION I p n V
p n E Minority carrier concentration p n distance Short PN diode DIFFUSION I How do we find the current? p n V Linear variation of minority carrier concentration Apply diffusion current formula to the minority carrier variation
p n E p n Short PN diode I p n V Only few carriers can contribute to the current
Contents of course this year • Long pn diode • Introducing the concept of recombination of carriers. • Switching of the pn diode, where does the delay come from? • Bipolar junction transistor • Internal functioning • Switching delays
p n p n Long Ln Lp Minority carrier diffusion length But what happens in a long pn diode? Short
Excess holes, in an n-type semiconductor will recombine with the large amount of available electrons. Loss of both carrier type, but felt most in excess minority carriers. Remember: the amount of majority carriers is much larger than the excess. In long semiconductors recombination of the minority carriers will occur whilst diffusing
Diffusing minority carriers (e.g. holes) recombine with majority carriers (electrons) within a diffusion length Lp Excess holes, in an n-type semiconductor will recombine with the large amount of available electrons. Loss of both carrier type, but felt most in excess minority carriers. Remember: the amount of majority carriers is much larger than the excess. In long semiconductors recombination of the minority carriers will occur whilst diffusing Injection of carriers x Lp
Generation-recombination • Generation of carriers and recombination is continuously happening at the same time such that the equilibrium carrier concentrations are maintained. R=G Charge neutral
Recombination - generation • In case there is an excess carrier concentration then the recombination rate R of the excess, will be larger than its generation rate, G: R>G When there is a shortage, then G > R
Recombination - generation • Simple model: Recombination/generation rate is proportional to excess carrier concentration. • Thus no net recombination/generation takes place if the carrier density equals the thermal equilibrium value. Recombination of e- in p-type semiconductor Recombination of h+ in n-type semiconductor
Diffusion, drift and recombination of carriers What is the consequence of this recombination on the characteristics of the pn diode with neutral regions larger than the diffusion lengths of the minority carriers?
In the pn diode the carrier gradient determines the current thus we have to find the function p(x) of the minority carrier concentration. • Note, reasoning done for p(x). For n(x) analogous approach.
A Rate of hole variation Variation of hole concentration in Dx x A/s Recombination rate + = Mathematical description of diffusion and recombination Jp(x) Jp (x+Dx) x x+Dx x
with Mathematical description of diffusion and recombination = bulk defined + excess concentration Jp : total current = drift + diffusion Neglect drift current (no electric field applied)
with Mathematical description of diffusion and recombination = bulk defined+ excess concentration