Download Medical Instrumentation Application Lecture #1

Introduction to Semiconductor
Lecture #2
‫ נקודות זיקוי‬3.5- 334011 ‫חשמלי‬-‫יסודות תכן ביו‬
Syllabus:
1. General introduction
2. Introduction to semiconductor
3. PN Junction
4. Diode
5. MOS capacitor
6. MOSFET Transistor
7. Circuits - Small signal analysis
8. Circuits – MOSFET amplifier
9. Circuits - MOSFET advanced
10.Differential amplifier
11.Negative feedback
12.Digital circuits
Material in
electronics
Conductors
𝐼
=1 𝑅
𝑉
• Linear Device (ohm's
law) (V>0  I>0)
• Resistors (R)
Semiconductors
𝑑𝐼
=1 𝑅
𝑑𝑉
• Non Linear Device
(I>0 only for V>Vth)
• Diode, transistors,
switches, amplifiers…
Insulator
𝑑𝑉
𝐼=𝐶
𝑑𝑡
• I=0 for any voltage
• Capacitor – charges
accumulation
Conductors
Material in electronics
material that easily conducts electrical current, have low resistance
The best conductors are copper, silver, gold, aluminum
 no energy is needed to get free electrons
Insulators
 material does not conduct electric current, have high resistance
 no free electrons
 most commonly use (SiO2 – silicon dioxide)
Semiconductors
 material between conductors and insulators in its ability to conduct electric
current
 most commonly use semiconductor ; silicon(Si), germanium(Ge), and
carbon(C).
 need a small amount of energy to get free electrons (Temperature, voltage)
Atom structure of conductors
• The atomic structure of good conductors usually includes only one
electron in their outer shell:
• It is called a valence electron
(‫(אלקטרון ערכיות‬.
• It is easily striped from the atom,
producing current flow.
• Insulator: The atoms are tightly bound to one another so electrons
are difficult to strip away for current flow.
Atom structure of semiconductors
• The main characteristic of a semiconductor
element is that it has four electrons in its
outer or valence orbit.
• Silicon: +14 Atomic number, electrons per
shell (2,8,4)
sharing of valence
electron produce the
covalent bond
• Covalent bonding – holding atoms together by
sharing valence electrons
• The center atom shares an electrons with each
of four surrounding atoms, creating a covalent
bond with each.
Intrinsic Semiconductors
Combining the atoms in unique
arrangement that is a repeated
we get a new structure called
“crystal lattice”
The result of the bonding:
1. The atoms link together with one another sharing their outer
electrons (covalent bands) forming a solid substrate.
2. The atoms are all electrically stable, because their valence shells are
complete. Since the outer valence electrons of each atom are tightly
bound together with one another, the electrons are difficult to
dislodge for current flow
3. The complete valence shells cause the silicon to act as an insulatorintrinsic (pure) silicon is a very poor conductor
Conductance in Semiconductors
How can we make a pure (intrinsic) semiconductor to be conduct?
Conduction
level
Covalent level
Conductance in Semiconductors
How can we make a pure (intrinsic) semiconductor to be conduct?
Temp (K) Temp (°C) Germanium Silicon
300
26
400
126
500
226
600
326
Thermal energy or light (photon energy) produce free electrons in
intrinsic semiconductor
Applying electrical field cause a
flow of electrons current
Extrinsic Semiconductors - Doping
How can we make a pure (intrinsic) semiconductor to be conduct?
Doping:
To make the semiconductor conduct electricity, other atoms called
impurities with 5 or 3 valence electrons must be added.
• Adding arsenic (doping with 5 valence electrons) will allow four of the
arsenic valence electrons to bond with the neighboring silicon atoms.
• The one electron left over for each arsenic atom becomes available to
conduct current flow, because it is not attached to any atom
As doping
atom
n-type Semiconductors – Doping
• If we use lots of arsenic atoms for doping, there will be lots of extra
electrons so the resistance of the material will be low and current will flow
freely.
• Doping atom that gives up an electron -call a donor atom
• Current carries in n-type are electrons – majority carries
• No. of conduction electrons can be controlled by the no. of impurity
atoms. By controlling the doping amount, virtually any resistance can be
achieved.
p-type Semiconductors – Doping
• You can also dope a semiconductor material with an atom such as boron
that has only 3 valence electrons.
• The 3 electrons in the outer orbit do form covalent bonds with its
neighboring semiconductor atoms as before. But one electron is missing
from the bond.
• This place where a fourth electron should be is referred to as a hole.
• The hole assumes a positive charge so it can attract electrons from some
other source.
• Holes become a type of current carrier with positive charge like the
electron to support current flow.
B doping
atom
When a valance electron moves left to fill a hole
while leaving another hole behind; the hole has
effectively moved from right to left
p-type Semiconductors – Doping
Holes as charge carriers
p-type Semiconductors – Doping
• If we use lots of Boron atoms for doping, there will be lots of extra holes
(missing electrons) so the resistance of the material will be low and
current will flow freely.
• Doping atom that take an electron -call a acceptor atom
• Current carries in p-type are hole – majority carries
• No. of holes can be controlled by the no. of impurity atoms. By controlling
the doping amount, virtually any resistance can be achieved.
Current Flow in Extrinsic Semiconductors
• The voltage source has a
positive terminal that attracts
the free electrons in the
semiconductor and pulls them
away from their atoms leaving
the atoms charged positively.
• Current (electrons) flows from
the negative terminal to the
positive terminal.
• Electrons from the negative supply
terminal are attracted to the positive
holes and fill them.
• Current (electrons) flows from the
negative terminal to the positive
terminal.
• Inside the semiconductor current
flow is actually by the movement of
the holes from positive to negative
Summary
• In its pure state, semiconductor material is an excellent
insulator.
• The commonly used semiconductor material is silicon.
• Semiconductor material has a crystal lattice structure.
• Semiconductor materials can be doped with other atoms
(doping) to add or subtract electrons.
• An N-type semiconductor material has extra free electrons
with negative charges (doping atoms are donor atoms with
positive charge, they lose their electron) .
• A P-type semiconductor material has a shortage of electrons
with vacancies called holes positive charges (doping atoms
are acceptor atoms with negative charge, they accept
electrons).
• By controlling the doping of silicon the semiconductor
material can be made as conductive as desired.
Energy Band of Semiconductors
The electrons in free atoms can be found only in certain discrete
energy states (quantum mechanic). These sharp energy states are
associated with the orbits or shells of electrons in an atom
Energy Band of Semiconductors
When atoms come together to form a compound, their atom orbital energies mix to
form molecular orbital energies. As more atoms begin to mix and more molecular
orbitals are formed, it is expected that many of these energy levels will start to be
very close to, or even completely degenerate, in energy. These energy levels are then
said to form bands of energy.
Energy Band of Semiconductors
e: free electrons
h: holes
e: tightly bound electrons
Valence Band: The band of energy where all of the valence electrons reside
and are involved in the highest energy molecular orbital. Electrons are tightly
bound and holes are free to move throughout the crystal lattice.
Conduction Band: where electrons freely move throughout the crystal lattice
and are directly involved in the conductivity of semiconductors
Energy gap: Is the minimum energy required to break a covalent bond and
generate free electron-hole pairs
Energy Band of Semiconductors
−∆𝐸𝐶𝐹
𝑛 ∝ 𝑒𝑥𝑝
𝐾𝑇
−∆𝐸𝐹𝑉
𝑝 ∝ 𝑒𝑥𝑝
𝐾𝑇
∆𝐸𝑔𝐶𝐹 = 𝐸𝐶 − 𝐸𝐹
∆𝐸𝑔𝐹𝑉 = 𝐸𝐹 − 𝐸𝑉
K is Boltzmann constant, T is temperature
KT=26meV is the thermal energy in room temperature
Fermi level: the chemical potential of electrons in steady state, and its value
represents the concentration of free electrons (n) and holes (p) in the
semiconductor
Energy Band of intrinsic Semiconductors
At room temperature, sufficient thermal energy exists to break some of the
covalent bonds, resulting in a production of electron-hole pairs (thermal
generation). These electrons are free and can conduct when electrical field is
applied.
In this process , the number of electrons and holes are equal: 𝒏 = 𝒑 ≡ 𝒏𝒊
The Fermi level is equal to the intrinsic level
𝑬𝑭 = 𝑬𝒊 = 𝑬𝒈 𝟐
ni is called the intrinsic carrier density (1/cm^3)
Energy Band of intrinsic Semiconductors
Some numbers @ Room Temperature (RT): T=300K
Energy gap
Eg
Density of intrinsic carrier ni
Density of atoms
units
eV
Germanium Silicon
0.72
1.1
Maybe the number of ni seem large, however, to put it into context, we
should compare it to the density of atoms and we will find that only 1 atom
from 5xE12 atoms contribute to the conductivity in room temperature.
Mass action law:
𝒏 ∙ 𝒑 = 𝒏𝒊 𝟐
−∆𝐸𝐶𝐹
𝑛 ∝ 𝑒𝑥𝑝
𝐾𝑇
−∆𝐸𝐹𝑉
𝑝 ∝ 𝑒𝑥𝑝
𝐾𝑇
−∆𝐸𝐶𝐹 − ∆𝐸𝐹𝑉
𝑛 ∙ 𝑝 ∝ 𝑒𝑥𝑝
𝐾𝑇
−∆𝐸𝑔
𝑛 ∙ 𝑝 ∝ 𝑒𝑥𝑝
𝐾𝑇
Energy Band of extrinsic Semiconductors
n-type: Doping the semiconductor with atoms having 5 valence electrons.
e: free electrons by doping
e: free electrons by thermal
h: holes by thermal
Donors (dopant atoms)
Donors change the Fermi level
toward the conduction level
∆𝑬𝒈𝑪𝑭 < 𝑬𝒈 𝟐
• Donors level: is the energy level of dopant atoms and it is approximated to
be equal to the conductance level ED≈EC. Every dopant atom donates one
free electron to the semiconductor and therefor their charge is positive.
• Doping process generates only free electrons without any holes. All the
holes in the n-type are those generated by thermal process.
• Free electrons has two sources: (1) Donors and (2) thermal process.
Generally the contribution of doping process is much larger than thermal
process.
Energy Band of extrinsic Semiconductors
How to calculate the concentration of free electrons and holes in n-type?
1. We assume that the concentration of free electrons produced by doping
is much larger than electrons produced by thermal energy
𝒏𝒏 ≈ 𝑵𝑫
ND is the concentration of donors
nn is the concentration of total free electrons in n-type
2. Holes in n-type (pn) generates only by thermal process
3. Mass action law is also correct in extrinsic semiconductor
𝒏𝒊 𝟐
 𝒑𝒏 = 𝑵
𝑫
𝒏𝒏 ∙ 𝒑𝒏 = 𝒏𝒊 𝟐
Given an n-type silicon semiconductor @ T=300K, Dopant concentration (ND)
is 1E+17/cm^3, Find the concentration of holes (pn) and electrons (nn)?
nn=ND=1E+17/cm^3, ni (@T=300K)=1.5E+10/cm^3
 pn=(1.5E+10)^2/(1E+17)=2.25+E3/cm^3
 n-type: electrons are majority and holes are minority
Energy Band of extrinsic Semiconductors
p-type: Doping the semiconductor with atoms having 3 valence electrons.
h: holes by doping
h: holes by thermal
e: free electrons by thermal
Acceptors (dopant atoms)
Acceptors change the Fermi level
toward the valence level
∆𝑬𝒈𝑭𝑽 < 𝑬𝒈 𝟐
• Acceptor level: is the energy level of dopant atoms and it is approximated
to be equal to the valence level EA≈EV. Every dopant atom accept one
electron and produce one hole and therefor their charge is negative.
• Doping process generates only holes. All the free electrons in the p-type
are those generated by thermal process.
• Hole has two sources: (1) Acceptors and (2) thermal process. Generally
the contribution of doping process is much larger than thermal process.
Energy Band of extrinsic Semiconductors
How to calculate the concentration of free electrons and holes in p-type?
1. We assume that the concentration of holes produced by doping is much
larger than holes produced by thermal energy
𝒑 𝒑 ≈ 𝑵𝑨
NA is the concentration of acceptors
pp is the concentration of total holes in p-type
2. Free electrons in p-type (np) generates only by thermal process
3. Mass action law is also correct in extrinsic semiconductor
𝒏𝒊 𝟐
 𝒏𝒑 = 𝑵
𝑨
 p-type: holes are majority and electrons are minority
𝒏𝒑 ∙ 𝒑𝒑 = 𝒏𝒊 𝟐
Energy Band of electronic material
Eg~9eV
Eg~1.1eV
Eg<26meV
Conduction band
is empty
Conduction band Conduction band
is fully filled
is partially filled
Carrier Transport in semiconductors
How can current flow in semiconductors?
First condition: having free electrons or holes in the semiconductor
Can the thermal energy give a force to electrons/holes to move? Yes,
Kinetic energy = Thermal energy
𝟏
𝒎
𝟐 𝒆𝒇𝒇
∙ 𝒗𝒕𝒉 𝟐 =
𝑲𝑻
𝟐
meff: effective mass of electrons/holes
vth : average thermal velocity
In silicon, for electrons:
𝑚𝑒𝑓𝑓 = 2.37 × 10−31 𝑘𝑔
𝐾 = 1.38 ×
2
𝑚 ∙𝑘𝑔
10−23 𝑠𝑒𝑐 2∙𝑘
,
𝑇 = 300𝑘

𝑣𝑡ℎ = 1 × 107 𝑐𝑚/𝑠𝑒𝑐
Electrons/holes are moving rapidly in all directions. Their thermal
motion is random because electrons/holes impact with atoms of the
semiconductor (scattering. As a results the net current is zero.
Carrier Transport in semiconductors
Having free electrons or holes in semiconductors with thermal energy is
not enough to get a flow of electrons. We need an external force to give a
direction to the motion of electrons/holes
1. Drift
2. Diffusion
Carrier Transport: Drift
When a small electric field (E) is applied to the semiconductor sample, each
electron will experience a force –qE from the field and will be accelerated along
the field (in the opposite direction to the field) during the time between collisions.
Therefore, an additional velocity component will be superimposed upon the
thermal motion of electrons. This additional component is called the drift velocity.
The combined displacement of an electron due to the random thermal motion and
the drift component is illustrated in Fig. Note that there is a net displacement of the
electron in the direction opposite to the applied field.
E=0
Random thermal motion:
net flow is zero
E
Combined motion due to random thermal
motion and an applied electric field.
Carrier Transport: Drift
lc : mean free path- average distance
between collisions
τc: mean free time- average time between
collisions
lc
The force (F) that is applied on electron with effective mass (mneff) when electrical
field (E) is applied:
𝑭 = −𝒒 ∙ 𝑬 = 𝒎𝒏𝒆𝒇𝒇 ∙
𝒗𝒏
𝝉𝒄
q is the charge of electron (1.6 × 10-19 coulombs)
vn is the electron drift velocity of electron
𝒗𝒏 = −
𝒒∙𝝉𝒄
𝒎𝒏𝒆𝒇𝒇
∙𝑬

The electron drift velocity is proportional to the applied
electric field. That depends on the mean free time and
the effective mass
Carrier Transport: Drift
We define new parameter “ electron mobility” with units cm2/(V⋅sec) that
describes how strongly the motion of an electron is influenced by an applied
electric field
𝝁𝒏 ≡
𝒒∙𝝉𝒄
𝒎𝒏𝒆𝒇𝒇
𝒗𝒏 = −𝝁𝒏 ∙ 𝑬
𝝁𝒑 ≡
𝒒∙𝝉𝒄
𝒎𝒑𝒆𝒇𝒇
𝒗𝒑 = 𝝁𝒑 ∙ 𝑬
Similar expression can be written for holes in the valence band. vp is the hole drift
velocity and μp is the hole mobility. The negative sign is removed because holes drift
in the same direction as the electric field.
The mobility of electrons for intrinsic silicon is [1350 cm2/(V⋅sec)] larger than the
mobility of holes [480 cm2/(V⋅sec)] (why?)
The mobility depends on concentration of dopant atoms, why?
The mobility depends on temperature, why?
Carrier Transport: Drift
The mobility is related directly to the mean free time between collisions, which in turn is
determined by two dominant scattering mechanisms:
1. Lattice scattering results from thermal vibrations of the lattice atoms. Since lattice vibration
increases with increasing temperature, lattice scattering becomes dominant at high
temperatures;  mobility decreases with increasing temperature
2. Impurity scattering results when a charge carrier travels past a positive/negative dopant
(donor or acceptor). The charge of dopants affect the charge of electrons/holes. At higher
temperatures, the carriers move faster (they gain energy); they remain near the dopant for a
shorter time  mobility decreases with increasing temperature
 Therefore, there is a tradeoff between mobility and temperature.
Drift Current
Calculate the drift current in semiconductor:
The total drift current is equal:
𝑰 = 𝑰𝒏 + 𝑰𝒑
Electron drift current with charge (-q):
V : voltage applied on the sample [V]
A: surface area [cm2 ]
L: length [cm]
n: electrons concentration [cm-3]
p: holes concentration [cm-3]
q: electron charge [coulomb]
vn : electron drift velocity [cm/sec]
vp: hole electron velocity [cm/sec]
E: electrical field [V/cm]
μn: electron mobility [cm2/(V⋅sec)]
μp: hole mobility [cm2/(V⋅sec)]
Hole drift current with charge (+q):
𝑰𝒏 = −𝑨 ∙ 𝒒 ∙ 𝒏 ∙ 𝒗𝒏
𝑰𝒑 = 𝑨 ∙ 𝒒 ∙ 𝒑 ∙ 𝒗𝒑
𝒗𝒏 = −𝝁𝒏 ∙ 𝑬
𝒗𝒑 = 𝝁𝒑 ∙ 𝑬
 𝑰𝒏 = 𝑨 ∙ 𝒒 ∙ 𝒏 ∙ 𝝁𝒏 ∙ 𝑬
 𝑰 𝒑 = 𝑨 ∙ 𝒒 ∙ 𝒑 ∙ 𝝁𝒑 ∙ 𝑬
Drift Current
The total drift current is equal:
 𝑰 = 𝑨 ∙ 𝒒 ∙ (𝒏 ∙ 𝝁𝒏 + 𝒑 ∙ 𝝁𝒑 ) ∙ 𝑬
We define the current density as :
𝑰
 𝑱 = = 𝒒 ∙ (𝒏 ∙ 𝝁𝒏 + 𝒑 ∙ 𝝁𝒑 ) ∙ 𝑬
𝑨
By ohm’s law, we have defined resistivity ρ [Ω∙cm]:
𝝆=
𝑬
𝑱
⇒
𝝆=
𝟏
𝒒∙(𝒏∙𝝁𝒏 +𝒑∙𝝁𝒑 )
And conductivity σ [1/ Ω∙cm]:
𝝈≡
𝟏
𝝆
The electrical field E=V/L

𝑰=
𝑨
𝑳∙𝝆
∙𝑽
𝑰=𝑽 𝑹
Resistor
𝑳
 𝑹=𝑨∙𝝆
= 𝒒 ∙ (𝒏 ∙ 𝝁𝒏 + 𝒑 ∙ 𝝁𝒑 )
Diffusion Current
Calculate the diffusion current in semiconductor:
Diffusion current results from the random thermal motion of carriers in from a
region of high concentration to a region of low concentration.
Diffusion is a result of thermal motion:
⇒ 𝒗 = 𝒗𝒕𝒉 =
𝑳𝒄
𝝉𝒄
The current density at x = 0 due to carriers that originate at x = -Lc and move from left
to right equals:
𝑱𝟏(𝒍𝒆𝒇𝒕→𝒓𝒊𝒈𝒉𝒕) = 𝒒 ∙ 𝒗𝒕𝒉 ∙ 𝒏(𝒙 = −𝑳𝒄 ) 𝟐
where the factor 1/2 is due to the fact that electrons have equal probability to move
left or right
Lc is the free mean path due to thermal motion
vth average thermal velocity
Diffusion Current
The flux at x = 0 due to carriers that originate
at x = Lc and move from right to left, equals:
𝑱𝟐(𝒓𝒊𝒈𝒉𝒕→𝒍𝒆𝒇𝒕) = 𝒒 ∙ 𝒗𝒕𝒉 ∙ 𝒏(𝒙 = +𝑳𝒄 ) 𝟐
The total flux of carriers moving from left to right at x = 0 equals to carriers moving
from right to left is subtracted from the flux due to carriers moving from left to right
𝑱=
𝒒∙𝒗𝒕𝒉
𝟐
∙ 𝒏 𝒙 = +𝑳𝒄 − 𝒏(𝒙 = −𝑳𝒄 )
⇒ 𝑱 = 𝒒 ∙ 𝒗𝒕𝒉 ∙ 𝑳𝒄 ∙
𝒏 𝒙=+𝑳𝒄 −𝒏(𝒙=−𝑳𝒄 )
𝟐∙𝑳𝒄
Diffusion Current
For Lc  0:
𝒏 𝒙 −𝒏 𝒙+𝑳𝒄
𝑳𝒄
≈
𝒅𝒏
𝒅𝒙
Diffusion current density is equal to:
𝑱 = 𝒒 ∙ 𝑫𝒏 ∙
𝒅𝒏
𝒅𝒙
𝟐
Dn is the diffusion coefficient for electrons [cm2/sec]: 𝑫𝒏 = 𝒗𝒕𝒉 ∙ 𝑳𝒄 = 𝑳𝒄 𝝉𝒄
Einstein Relation between mobility and diffusion:
𝑫𝒏 = 𝒗𝒕𝒉 ∙ 𝑳𝒄 = 𝒗𝒕𝒉 ∙ 𝒗𝒕𝒉 ∙ 𝝉𝒄 = 𝒗𝒕𝒉 𝟐 ∙ 𝝉𝒄
𝟏
𝒎𝒆𝒇𝒇
𝟐
𝝁𝒏 ≡
∙ 𝒗𝒕𝒉 𝟐 =
𝒒∙𝝉𝒄
𝒎𝒏𝒆𝒇𝒇
𝑲𝑻
𝟐
𝑲𝑻
 𝒗𝒕𝒉 𝟐 = 𝒎
𝒏𝒆𝒇𝒇
 𝝉𝒄 =
𝝁𝒏 ∙𝒎𝒏𝒆𝒇𝒇
𝒒

𝑫𝒏 = 𝝁𝒏 ∙
𝑲𝑻
𝒒
Current Density Equations
When an electric field is present in addition to a concentration gradient, both
drift current and diffusion current will flow. The total current density at any
point is the sum of the drift and diffusion components:
𝒅𝒏
Current density for electrons: 𝑱𝒏 = 𝒒 ∙ 𝝁𝒏 ∙ 𝒏 ∙ 𝑬 + 𝒒 ∙ 𝑫𝒏 ∙ 𝒅𝒙
Current density for holes:
𝑱𝒑 = 𝒒 ∙ 𝝁𝒑 ∙ 𝒑 ∙ 𝑬 − 𝒒 ∙ 𝑫𝒑 ∙
Total Current density for electrons and holes:
𝒅𝒑
𝒅𝒙
𝑱 = 𝑱𝒏 + 𝑱𝒑