00:02 before we dive in deep to the physics of
00:04 semiconductors and semiconducting
00:08 now stop here and describe some of the
00:11 motivating that physics because it's a
00:14 lot easier to appreciate why you want to
00:16 know these things about the
00:17 carrier concentrations the density of
00:19 states the fermi energies and everything
00:22 else that comes into the physics
00:24 if you know a little bit about how
00:26 that's used in the design
00:28 of a device so i'll describe
00:31 three device categories starting with
00:36 junctions dominate semiconducting device
00:40 especially in integrated circuits where
00:43 dealing with transistors they're filled
00:46 if you don't have junctions then you're
00:48 not going to have non-linear
00:49 semiconductor devices
00:51 a pn junction is made from two types of
00:54 semiconductor materials
00:56 a p-type whole built material and n-type
00:59 or electron-doped material
01:01 the prototype we'll illustrate with here
01:05 ribbon of semiconductor all one material
01:09 silicon and it was formed by diffusing
01:13 donor dopants and acceptor dopings into
01:17 first the right side was masked off and
01:19 donor dopants were diffused in
01:21 and then the left side was masked off
01:23 and hole dopants were diffused into
01:26 it the result is this ribbon that's
01:29 half n type and half p type a battery is
01:34 with the positive terminal of the
01:35 battery connected to the p
01:37 type side and the negative terminal of
01:40 the battery connected to the end type
01:42 side but there's a switch between
01:44 the battery and the semiconductor we
01:47 will first talk about what
01:48 the carrier concentration across the
01:52 semiconductor looks like
01:53 when that switch is open and it is just
01:57 junction that was found sitting there
02:00 and we're going to look at how the
02:02 carrier concentration the number of
02:04 cubic centimeter varies going from the
02:08 where n is the electron concentration
02:11 is the hole concentration for now let's
02:15 open so we can answer the question of
02:18 how are the carriers distributed
02:20 throughout the semiconductor
02:22 when there is no bias on it no
02:25 current is able to pass through it that
02:28 condition is referred to as thermal
02:31 when current cannot pass through the
02:34 the left side is full of electrons and
02:36 the right side is full of holes and so
02:39 we can sketch that accordingly
02:41 in this first graph which is a carrier
02:45 versus position along the junction
02:48 let's look at how the carrier
02:49 concentration varies across where n
02:52 is the electrons per cubic centimeter
02:55 is the holes per cubic centimeter with
02:58 open electrons are a high population
03:02 over on the left side and low population
03:05 on the right you see these two types of
03:06 semiconductors are attached
03:09 which means that the electrons in the
03:12 will diffuse into the p-type because the
03:15 n-type being full of the electrons and
03:18 virtually any electrons will mean that
03:20 some of these electrons
03:22 will diffuse over because when you have
03:24 a dense population of one
03:26 particle type in one region and no
03:29 population in another region diffusion
03:33 the holes will do the same thing because
03:35 you have a lot of holes on the right and
03:38 not many holes on the left
03:40 and so holes will diffuse into the
03:43 now you might wonder why don't they
03:45 diffuse more than this
03:47 so the n-type region is donor doped
03:51 donor ions are positively charged
03:55 an n-type semiconductor all by itself is
03:58 electrostatically neutral there are as
04:00 many free electrons as there are
04:02 positive donor ions charge neutrality
04:06 will be maintained throughout this
04:11 so when the electrons move from the
04:14 charge neutral n-type side into the
04:17 charge neutral p-type side they
04:20 encounter not just a bunch of holes
04:23 should be attracting them they counter
04:27 of negative acceptor ions and so when
04:32 from the left side to the right side
04:35 the right p-type side becomes negatively
04:40 and when a hole moves from the right
04:42 p-type side into the left
04:44 n-type side the left n-type side becomes
04:47 positively charged for now we will
04:50 define the junction as the place where
04:52 the carrier concentrations have gone to
04:56 value deep inside their respective
05:00 we can look at the energy of this
05:01 situation we'll put that in the bottom
05:04 as you go across the junction from the
05:06 left side to the right side
05:08 the potential energy experienced by
05:10 electrons and holes is going to change
05:14 the electrons have their preferred
05:16 location where the potential energy
05:18 that's therefore lower and the holes
05:20 have their preferred location where
05:22 their potential energy
05:23 is therefore lower in semiconductor
05:26 physics we always plot the electron
05:30 energy not the whole energy so the
05:34 energy as you go across this junction
05:37 looks like this it's lower in the n-type
05:40 region and is higher in the p-type
05:44 for that same reason that i just
05:46 mentioned when an electron moves into
05:49 it encounters all of those negative
05:52 dopants and it finds itself being
05:56 back to the n-type and so there's a
05:59 energetically favorable region for
06:02 and conversely holes are energetically
06:05 favorable on the right
06:06 when the electron is on the right it's
06:08 energetically unfavorable
06:10 it is in a more negative electric field
06:13 meaning that the potential energy of the
06:16 which equals minus q times the
06:20 potential goes up just remember that
06:23 charge is in a region of
06:27 the same charge it goes up and so when
06:30 electron encounters acceptor dopants it
06:32 wants to go back home
06:35 so the potential energy of an electron
06:38 as it diffuses into the p-type region
06:40 and that's reflected in this graph
06:42 of the electrons energy as it goes
06:46 across the junction
06:47 it's lower on the n side and it's higher
06:50 on the p side and so the electrons
06:53 energy goes up as it diffuses into the
06:57 and that's reflected in the energy level
07:00 of the conduction electrons as the
07:04 up and amount delta e so the electrons
07:08 because there's a low population of
07:11 electrons over there and that's what
07:13 is going to where the population is low
07:15 but when they get there they find
07:17 themselves to be electrostatically
07:19 unwelcome and so they roll back downhill
07:23 so that's the conduction bandage all
07:27 have an energy that is higher than this
07:30 energy of called e sub c
07:33 then there's the valence band edge all
07:36 bound electrons that are stuck in atoms
07:39 have an energy that is below
07:41 this level the separation between the
07:45 conduction band edge and the valence
07:49 is the energy gap and it's the same
07:52 throughout because doping doesn't change
07:56 so e sub g like 1.12 electron volts or
08:01 is the same everywhere across the n and
08:07 took my electron tweezers and dragged an
08:10 electron from the left side
08:12 over to the right side i'll be dragging
08:16 a hill of height delta e
08:19 the built in energy which is
08:22 best referred to actually in voltage so
08:26 q 1.6 times 10 minus 19 coulombs
08:29 times the built-in potential p sub b
08:32 i will encounter this quantity built in
08:37 over the next many quite a few chapters
08:40 it's simply the difference in the
08:41 conduction band edge
08:42 on the p side minus the conduction band
08:46 n side fisa bi the built-in potential is
08:50 what you would actually
08:51 measure with the laboratory instrument
08:53 with contacts placed on either side of
08:56 junction to replace the battery with the
08:59 you would read visa bi so the electron
09:02 does have to climb a potential hill
09:04 to get from the n side to the p side and
09:08 that's a big deterrent
09:09 but you also have the diffusion force
09:12 pushing it over there
09:13 and so there's a trade-off between the
09:15 electrostatic repulsion
09:17 that it encounters when it gets there
09:20 and the fact that the concentration
09:23 attracting therefore the electrons over
09:28 i want to point out one more energy in
09:30 this diagram and that's this horizontal
09:32 dashed line labeled e sub f
09:36 f is for fermi doesn't show here so i'll
09:40 r m i is the fermi energy
09:43 it's an energy that's characteristic of
09:46 when there's no battery connected as in
09:50 case it's a horizontal line
09:53 when we close a switch and apply a
09:55 potential difference across
09:57 the junction the shape of that fermi
09:59 energy will change but for now it's just
10:03 the fermi energy is in the gap
10:06 and it's always closer to the conduction
10:09 band edge in an n-type semiconductor
10:12 and it's always closer to the valence
10:14 band edge in a p-type semiconductor
10:17 and so you can think of that as an
10:18 explanation also for why these
10:20 bands have to bend up because that
10:23 condition has to be met with the fermi
10:25 energy as a horizontal line
10:26 it has to be closer to the valence band
10:28 on the right and the conduction band on
10:32 so this is a one dimensional energy band
10:34 diagram following the
10:35 energy as you proceed in one dimension
10:37 from the left side to the right side
10:39 i do want to mention one thing about
10:44 so it's the same everywhere throughout
10:46 the junction provided the junction is
10:48 one base material so provided is
10:50 fabricated as i described
10:52 a piece of say silicon that's been
10:55 on the left and p-doped on the right
10:59 junctions are made from two different
11:01 base semiconductor materials
11:04 in which case they're called
11:05 heterojunctions and that's done
11:07 specifically to get a different band gap
11:10 on the left and the right so maybe
11:11 silicon on one side and some alloy on
11:15 so that's with the switch open no
11:18 current passes through the junction
11:20 and we're in a condition called thermal
11:24 so think of those as synonymous no
11:27 junction and thermal equilibrium when
11:29 you're in thermal equilibrium there's no
11:31 current passing through the fermi energy
11:33 is a horizontal line
11:36 it will be different when current is
11:37 allowed to flow we're not going to
11:39 address that until later
11:42 so let's go ahead and close the switch
11:45 when we close the switch now we've
11:49 potential on the right end on the p-type
11:53 and the negative potential on the left
11:55 end on the n-type side
11:57 so the n-type is filled with the
11:58 electrons but we've put
12:00 negative potential over here those
12:04 are chased to the right they feel
12:07 less of a problem with heading into the
12:11 because they really don't like it over
12:14 so they have less of a potential hill to
12:16 climb that built-in potential
12:19 is no longer the barrier it once was
12:22 the height of the potential hill has
12:26 it used to be q times built-in potential
12:28 but now we have to deduct the
12:30 voltage of this battery from the
12:34 to get the new voltage difference
12:37 between these two sides
12:38 it subtracts it to the opposite so now
12:41 there's a shorter hill
12:42 and less of a voltage drop across the
12:46 the electrons have a much easier time
12:51 this bias condition is referred to as
12:53 forward bias where you put the positive
12:57 side and the negative potential is in
13:00 n side and current goes through much
13:05 i drew the fermi energy is still
13:07 horizontal that's not
13:09 really right if you have a significant
13:11 amount of current going through the
13:13 it will change shape and that will be a
13:16 subject that we have to consider
13:18 later but we will consider it
13:22 so for now we're not going to focus on
13:24 what the fermi energy looks like
13:26 when we have current going through the
13:29 the battery has no ability to change
13:33 so it's the same if this is silicon
13:36 based material it's the same 1.12
13:38 electron volts all the way across
13:41 now if we vary the voltage starting at
13:44 zero for the origin
13:46 and increasing it as we go to the right
13:49 we can measure the current and generate
13:51 in the current voltage characteristic
13:54 we can flip the battery around put the
13:56 positive terminal on the left and the
13:58 negative terminal of the battery on the
14:01 b to the left of the origin have
14:05 so those two conditions are referred to
14:06 as forward biased when you have the
14:08 positive terminal on the p-type or
14:10 reverse biased when you have the
14:11 positive terminal on the end type
14:13 and if you measure current versus
14:15 voltage you get this exponential
14:17 behavior described by the shockley diode
14:22 in the shockley diode model you have qv
14:25 q the charge of the electron 1.69 minus
14:29 v is applied voltage k is boltzmann's
14:33 t is temperature in kelvin
14:36 i zero is the reverse bias current
14:40 when the voltage becomes negative so if
14:42 you flip the battery around and you have
14:44 a large negative voltage
14:45 this term very quickly becomes
14:50 and you just have i equals minus i zero
14:52 for large negative voltages
14:54 and it levels off so that's why i sub 0
14:57 is called the reverse bias current
14:59 and then there's the ideality factor eta
15:02 oftentimes eta is just left at 1 meaning
15:06 but in a real pn junction you have a
15:09 phenomenon at the junction going on
15:12 electron hole recombination
15:15 which alters the behavior of the diode
15:18 and this ideality factor is meant to
15:21 that empirically for a lot of integrated
15:24 circuit devices we can go ahead and take
15:28 one especially since we're focused
15:30 primarily on the field effect
15:32 in integrated circuits rather than the
15:36 real data indicates a much stronger
15:39 dependence on voltage for a
15:41 germanium-based diode than a
15:43 silicon-based diode
15:45 a germanium based out will pass a lot
15:46 more current as well
15:48 they both follow the shockley diode
15:52 but the reverse bias current for a
15:54 germanium diode is much larger a tenth
15:57 compared to a tenth of a nano amp
15:59 perhaps for a silicon
16:01 based diode and the consequence of a
16:04 bias current is that you also have a
16:07 larger forward biased current
16:09 because of the just the structure of the
16:13 so two salient points to remember about
16:17 pn junction devices is one
16:20 that there is a built-in potential fisa
16:23 it's a consequence actually of the
16:25 doping level and it's going to keep
16:27 coming back to us so we'll have to get
16:29 comfortable with the idea that when you
16:32 and an n-type semiconductor together
16:34 there's a potential hill
16:36 that carriers need to climb to cross
16:38 over to the other side
16:40 the second sailing point is that the
16:43 band gap is a constant
16:45 throughout the junction fabricated from
16:48 piece of semiconductor and it does not
16:52 doping or with bias voltage
16:56 now i'll speak briefly about two other
16:58 device categories the field effect
17:01 and the opto electronic devices those
17:04 are the three device types we'll cover
17:07 the field effect is the really
17:09 fundamental basis of
17:10 the transistors that are used in
17:12 integrated circuits
17:14 imagine a p-type semiconductor and
17:18 they have an electrode that faces it and
17:21 there's an air gap between them
17:23 the electrode is held at a voltage v
17:26 the p-type semiconductor is grounded the
17:30 positive so as i turn up that voltage
17:33 start at zero and then turn it up higher
17:36 i have this capacitor formed from it
17:40 positive charge on this electrode plate
17:44 that chases the holes out of the p-type
17:48 as i slowly raise this voltage holes
17:51 begin to exit the p-type
17:52 but also as i slowly raise this voltage
17:56 from ground into the p-type and they're
18:00 strongly attracted to that electrode
18:02 they just can't get to it because of the
18:05 so what they do is they form a layer at
18:08 the top of the semiconductor slab
18:11 and so you have this layer of electrons
18:14 in what is otherwise a p-type
18:17 so you have this top region of this
18:20 b-type semiconductor that has been
18:22 into an n-type and it's called the
18:25 channel the voltage on that electrode
18:29 where the n-type channel begins to
18:32 itself is called the threshold voltage
18:35 and once you exceed that voltage we say
18:38 that the semiconductor is in
18:39 inversion because now there is a layer
18:42 on the top of the semiconductor that has
18:45 other type this is the essence of
18:49 the electric field effect the
18:52 transistors that we're going to focus on
18:55 field effect transistors operate on the
18:57 principle of this effect
18:59 this sort of capacitor and pn junctions
19:02 are integrated together into a single
19:04 device called a field effect transistor
19:07 and we're going to be studying that in
19:09 quite a bit of detail
19:11 the device type that dominates the
19:13 design of integrated circuits is in fact
19:15 the mosfet the metal oxide semiconductor
19:19 field effect transistor
19:21 this field effect capacitor is the
19:23 beginning the building block for all of
19:26 when we finish pn junctions we will do
19:30 unit on optoelectronics leds and
19:33 led lasers light emitting diodes are
19:38 junction when you forward bias the pn
19:41 junction by putting the positive
19:43 external voltage on the
19:45 p side and the negative external
19:48 potential on the n side
19:49 the bands become less bent the
19:52 conduction band edge moves up in the end
19:54 type and there's less of a potential
19:56 hill for electrons to climb to get over
19:58 to the peace side so they do and they go
20:01 over to the peace side
20:03 when they're over there they find a hole
20:06 except an electron vacancy so an
20:09 electron sees a vacancy down there in
20:11 the valence band where the energy is
20:13 lower so that's preferable so it goes
20:15 there and in the process of going down
20:18 to the vacancy it emits a photon
20:22 annihilation produces a photon and you
20:26 say what's the chances of that because
20:30 also diffuse over into the n-type side
20:33 and you might not have sufficient
20:35 electrons and holes in the same
20:36 region to get a lot of light and that
20:38 would actually be very true
20:40 leds depend on a fact that was going to
20:43 become important for us soon
20:45 that electrons are much more mobile than
20:49 move but electrons move more readily and
20:53 so the p-type side can fill up with the
20:55 electrons more easily than the n-type
20:58 what you end up having then is in this
21:00 region near the junction on the p-type
21:03 a high population of both the electrons
21:06 and they recombine in that small region
21:09 creating a very bright light so that's a
21:13 overview to how an led works we will go
21:17 much more detail later when we have
21:20 finished up with pn
21:22 junctions and we'll look at the physics
21:24 of how that photon is generated
21:27 and how that affects the design
21:30 of an led as well as we'll look at what
21:34 issues are in making efficient
21:37 light emitting diodes so those are the
21:41 types the pn junction the field effect
21:44 and the optoelectronic devices the three
21:47 categories that we're going to spend
21:50 this semester next we'll start talking
21:52 about the physics of semiconductors
21:54 what the carrier concentrations are why
21:58 what they are how they can be controlled
22:01 doping can affect the carrier
22:03 concentration and what that does
22:05 to the performance of the semiconductor
22:07 that's all coming up next
