ECSE 330 Introduction to Electronics Silicon
ECSE 330 Introduction to Electronics Lecture 02: Operational Amplifiers Roni Khazaka
Silicon • Silicon – Atomic number 14 – Atomic weight: 28.09au 28 09au
electron
• The material is the most purified substance man has ever attempted to produce. • It has 4 valence electrons and if properly grown in crystal-form it takes on a face-body cubic crystal pattern.
R. Khazaka
proton neutron
ECSE330 Introduction to Electronics
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1
Silicon Semiconductor. •
Intrinsic silicon has a regular crystal lattice of atoms – held together by covalent bonds – each atom has four valence electrons
5´1022 atoms/cm3
Silicon
Rubber
Copper
(semi-conductor) R. Khazaka
ECSE330 Introduction to Electronics
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Intrinsic Silicon
• At low temperatures, all covalent bonds are intact (T → 0K), there are no free electrons R. Khazaka
ECSE330 Introduction to Electronics
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2
Intrinsic Silicon Electron Hole pair
• •
As temperature rises, some electrons break free, leaving holes in lattice with positive charge. These are called Electron-hole pairs. The electrons move in the conductionband and holes move in the valence-band
R. Khazaka
ECSE330 Introduction to Electronics
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Intrinsic Silicon • The number of holes ‘p’ and the number of electrons ‘n’ increases equally with temperature. • At room-temperature (T>273K), n = p = 1.5´1010 carriers/cm3. n =n= p n 2 = np i
R. Khazaka
i
ECSE330 Introduction to Electronics
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3
Electron Hole Recombination • Electrons in conduction band and holes in valence band may interact with each other. A free electron and a free hole interact and annihilate each other.
Before R. Khazaka
After ECSE330 Introduction to Electronics
7
Semiconductor Doping • Phosphorous-doping – This atom has 5 valence electrons electrons. • This creates a “N-type” semiconductor. It is also called a DONOR atom. • At room temperature, there is an excess of FREEelectrons. • If the doping is significant and T=273K, then:n = ND and p = ni2/ND
R. Khazaka
Extra electron
Extra FREE electron
ECSE330 Introduction to Electronics
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N-Type Silicon • In n-type silicon: – electrons are majority carriers and holes are minority carriers Majority carrier phosphorous
Minority Mi it carrier
R. Khazaka
ECSE330 Introduction to Electronics
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Semi Conductor Doping • Boron-doping – This atom has 3 valence electrons. electrons • This creates a “P-type” semiconductor. It is also called a ACCEPTOR. • At room temperature, there is an excess of FREE-holes. • If the doping is significant and T=273K, then: p = NA and n = ni2/NA
R. Khazaka
Extra hole
Extra FREE hole
ECSE330 Introduction to Electronics
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5
P-Type Silicon • In p-type silicon: – holes are majority j y carriers and electrons are minorityy carriers Minority carrier
boron Majority M j it carrier
R. Khazaka
ECSE330 Introduction to Electronics
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The PN Junction • When a p-type material is brought into contact with an ntype material, the interface changes and creates a “builtin” voltage. in voltage
R. Khazaka
ECSE330 Introduction to Electronics
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6
Diffusion of holes and electrons
• The FREE electrons from the ntype material diffuse to the right
•
The FREE holes from the p-type material diffuse to the left
• Diffusion is part of the thermodyna mic law of MAXIMUM ENTROPY
•
Just like the wayy pperfume diffuses across a room over time
R. Khazaka
ECSE330 Introduction to Electronics
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Diffusion and Drift
Diffusion Electrons
Diffusion Holes
• As the carriers diffuse across the junction, they recombine with the majority carriers on the opposite side, this creates local charge sites and a depletion region. R. Khazaka
ECSE330 Introduction to Electronics
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Diffusion and Drift
Drift Electrons
Drift Holes
• When the rate of Diffusion equals the rate of Drift a steady-state condition is obtained and no more macroscopic changes occur. R. Khazaka
ECSE330 Introduction to Electronics
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The pn Junction Equations Diffusion current I Diff = qA⎛⎜ Dn dp − D p dn ⎞⎟ ⎝
dx
dx ⎠
I Drift = qA( pμ p + nμ n )E Drift current When the external current I = 0 I Diff = I Drift This produces a built in voltage of: built-in ⎛N N ⎞ Vbi = VT ln⎜⎜ A 2 D ⎟⎟ ⎝ ni ⎠ kT where VT = q R. Khazaka
ECSE330 Introduction to Electronics
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The pn Junction Reverse Biase • When a reverse-bias voltage is applied to junction, depletion-region widens to accommodate the higher reverse reverse-bias. bias. • As the majority carriers are depleted from the junction, the diffusion current decreases, and the drift current increases until the junction voltage equals the applied reverse-bias. This stops the current.
Note: explanation neglects saturation current IS R. Khazaka
ECSE330 Introduction to Electronics
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The pn Junction Forward Bias • Forward-bias voltage injects majority carrier electrons into n-type, majority carrier holes into pp-type type material Dominant current is the diffusion current. • Diffusion of carriers across the junction, and the subsequent recombination completes the circuit. • The process “takes-off” after 0.7V and collapses the built-in voltage to almost zero.
(
)
I = I S e v / nVT − 1 R. Khazaka
ECSE330 Introduction to Electronics
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PN Junction Operational Summary • Reverse bias operation dominated by: – drift current – minority carriers in majority type material (e.g. holes in n-type material) – magnitude of current flow limited by ability to reduce diffusion effects and onset of breakdown
• Forward bias operation dominated by: – diff diffusion i currentt effects ff t – majority carriers in majority type material (e.g. holes in p-type material) – magnitude of current flow limited by how many carriers one can shove into the device before it melts R. Khazaka
ECSE330 Introduction to Electronics
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PN Junction Physics Summary • • • • • •
Lattice structure of intrinsic silicon Electrons and holes in conduction and valence bands Recombination Doping: n-type and p-type silicon Charge carrier motion: diffusion and drift Open-circuit p-n junction: diffusion, drift, d l i region, depletion i built-in b il i voltage l • Reverse-bias, reverse-breakdown and forward bias operation of pn junction
R. Khazaka
ECSE330 Introduction to Electronics
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10
Diode Symbol and Terminal Characteristics
v anode (p)
cathode (n)
i Exponential model:
R. Khazaka
⎛ nVVv ⎞ T ⎜ i = I S e − 1⎟ ⎜ ⎟ ⎝ ⎠
ECSE330 Introduction to Electronics
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Characteristic Equation
Y = (e(x) - 1)
R. Khazaka
ECSE330 Introduction to Electronics
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11
Exponential Model Definitions ⎛ nVv ⎞ i = I S ⎜ e T − 1⎟ ⎜ ⎟ ⎝ ⎠ • IS: reverse saturation t ti
• VT: Thermal Voltage
current – proportional to cross-sectional area of current flow – discrete Si devices: IS ~ 10-9-10-13 A – IC Si devices: IS ≤ 10-15 A
• n: fitting parameter – – –
normally between 1 and 2 for Si discrete Si devices: n ~ 2 IC Si devices: n ~ 1
R. Khazaka
–
from device physics:
VT = – – – –
k ⋅T q
k: Boltzmann constant (1.38x1023 J/K) T: Temperature (Kelvin) q: electron charge (1.6x10-19 C) At room temperature, VT ~ 25 mV
ECSE330 Introduction to Electronics
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Forward Bias ⎛ ⎞ As V increases, exp⎜⎜ v ⎟⎟ >> 1 ⎝ n ⋅ VT ⎠
i ≅ ISe
v nV T
When diode is fully conducting, V remains constant at ~ 0.7V 0 7V for silicon diodes
• The voltage at which the diode starts to conduct appreciably is called the cut-in voltage; value is ~ .5V for silicon diodes R. Khazaka
ECSE330 Introduction to Electronics
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12
Silicon • Silicon – Atomic number 14 – Atomic weight: 28.09au 28 09au
electron
• The material is the most purified substance man has ever attempted to produce. • It has 4 valence electrons and if properly grown in crystal-form it takes on a face-body cubic crystal pattern.
R. Khazaka
proton neutron
ECSE330 Introduction to Electronics
2
1
Silicon Semiconductor. •
Intrinsic silicon has a regular crystal lattice of atoms – held together by covalent bonds – each atom has four valence electrons
5´1022 atoms/cm3
Silicon
Rubber
Copper
(semi-conductor) R. Khazaka
ECSE330 Introduction to Electronics
3
Intrinsic Silicon
• At low temperatures, all covalent bonds are intact (T → 0K), there are no free electrons R. Khazaka
ECSE330 Introduction to Electronics
4
2
Intrinsic Silicon Electron Hole pair
• •
As temperature rises, some electrons break free, leaving holes in lattice with positive charge. These are called Electron-hole pairs. The electrons move in the conductionband and holes move in the valence-band
R. Khazaka
ECSE330 Introduction to Electronics
5
Intrinsic Silicon • The number of holes ‘p’ and the number of electrons ‘n’ increases equally with temperature. • At room-temperature (T>273K), n = p = 1.5´1010 carriers/cm3. n =n= p n 2 = np i
R. Khazaka
i
ECSE330 Introduction to Electronics
6
3
Electron Hole Recombination • Electrons in conduction band and holes in valence band may interact with each other. A free electron and a free hole interact and annihilate each other.
Before R. Khazaka
After ECSE330 Introduction to Electronics
7
Semiconductor Doping • Phosphorous-doping – This atom has 5 valence electrons electrons. • This creates a “N-type” semiconductor. It is also called a DONOR atom. • At room temperature, there is an excess of FREEelectrons. • If the doping is significant and T=273K, then:n = ND and p = ni2/ND
R. Khazaka
Extra electron
Extra FREE electron
ECSE330 Introduction to Electronics
8
4
N-Type Silicon • In n-type silicon: – electrons are majority carriers and holes are minority carriers Majority carrier phosphorous
Minority Mi it carrier
R. Khazaka
ECSE330 Introduction to Electronics
9
Semi Conductor Doping • Boron-doping – This atom has 3 valence electrons. electrons • This creates a “P-type” semiconductor. It is also called a ACCEPTOR. • At room temperature, there is an excess of FREE-holes. • If the doping is significant and T=273K, then: p = NA and n = ni2/NA
R. Khazaka
Extra hole
Extra FREE hole
ECSE330 Introduction to Electronics
10
5
P-Type Silicon • In p-type silicon: – holes are majority j y carriers and electrons are minorityy carriers Minority carrier
boron Majority M j it carrier
R. Khazaka
ECSE330 Introduction to Electronics
11
The PN Junction • When a p-type material is brought into contact with an ntype material, the interface changes and creates a “builtin” voltage. in voltage
R. Khazaka
ECSE330 Introduction to Electronics
12
6
Diffusion of holes and electrons
• The FREE electrons from the ntype material diffuse to the right
•
The FREE holes from the p-type material diffuse to the left
• Diffusion is part of the thermodyna mic law of MAXIMUM ENTROPY
•
Just like the wayy pperfume diffuses across a room over time
R. Khazaka
ECSE330 Introduction to Electronics
13
Diffusion and Drift
Diffusion Electrons
Diffusion Holes
• As the carriers diffuse across the junction, they recombine with the majority carriers on the opposite side, this creates local charge sites and a depletion region. R. Khazaka
ECSE330 Introduction to Electronics
14
7
Diffusion and Drift
Drift Electrons
Drift Holes
• When the rate of Diffusion equals the rate of Drift a steady-state condition is obtained and no more macroscopic changes occur. R. Khazaka
ECSE330 Introduction to Electronics
15
The pn Junction Equations Diffusion current I Diff = qA⎛⎜ Dn dp − D p dn ⎞⎟ ⎝
dx
dx ⎠
I Drift = qA( pμ p + nμ n )E Drift current When the external current I = 0 I Diff = I Drift This produces a built in voltage of: built-in ⎛N N ⎞ Vbi = VT ln⎜⎜ A 2 D ⎟⎟ ⎝ ni ⎠ kT where VT = q R. Khazaka
ECSE330 Introduction to Electronics
16
8
The pn Junction Reverse Biase • When a reverse-bias voltage is applied to junction, depletion-region widens to accommodate the higher reverse reverse-bias. bias. • As the majority carriers are depleted from the junction, the diffusion current decreases, and the drift current increases until the junction voltage equals the applied reverse-bias. This stops the current.
Note: explanation neglects saturation current IS R. Khazaka
ECSE330 Introduction to Electronics
17
The pn Junction Forward Bias • Forward-bias voltage injects majority carrier electrons into n-type, majority carrier holes into pp-type type material Dominant current is the diffusion current. • Diffusion of carriers across the junction, and the subsequent recombination completes the circuit. • The process “takes-off” after 0.7V and collapses the built-in voltage to almost zero.
(
)
I = I S e v / nVT − 1 R. Khazaka
ECSE330 Introduction to Electronics
18
9
PN Junction Operational Summary • Reverse bias operation dominated by: – drift current – minority carriers in majority type material (e.g. holes in n-type material) – magnitude of current flow limited by ability to reduce diffusion effects and onset of breakdown
• Forward bias operation dominated by: – diff diffusion i currentt effects ff t – majority carriers in majority type material (e.g. holes in p-type material) – magnitude of current flow limited by how many carriers one can shove into the device before it melts R. Khazaka
ECSE330 Introduction to Electronics
19
PN Junction Physics Summary • • • • • •
Lattice structure of intrinsic silicon Electrons and holes in conduction and valence bands Recombination Doping: n-type and p-type silicon Charge carrier motion: diffusion and drift Open-circuit p-n junction: diffusion, drift, d l i region, depletion i built-in b il i voltage l • Reverse-bias, reverse-breakdown and forward bias operation of pn junction
R. Khazaka
ECSE330 Introduction to Electronics
20
10
Diode Symbol and Terminal Characteristics
v anode (p)
cathode (n)
i Exponential model:
R. Khazaka
⎛ nVVv ⎞ T ⎜ i = I S e − 1⎟ ⎜ ⎟ ⎝ ⎠
ECSE330 Introduction to Electronics
21
Characteristic Equation
Y = (e(x) - 1)
R. Khazaka
ECSE330 Introduction to Electronics
22
11
Exponential Model Definitions ⎛ nVv ⎞ i = I S ⎜ e T − 1⎟ ⎜ ⎟ ⎝ ⎠ • IS: reverse saturation t ti
• VT: Thermal Voltage
current – proportional to cross-sectional area of current flow – discrete Si devices: IS ~ 10-9-10-13 A – IC Si devices: IS ≤ 10-15 A
• n: fitting parameter – – –
normally between 1 and 2 for Si discrete Si devices: n ~ 2 IC Si devices: n ~ 1
R. Khazaka
–
from device physics:
VT = – – – –
k ⋅T q
k: Boltzmann constant (1.38x1023 J/K) T: Temperature (Kelvin) q: electron charge (1.6x10-19 C) At room temperature, VT ~ 25 mV
ECSE330 Introduction to Electronics
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Forward Bias ⎛ ⎞ As V increases, exp⎜⎜ v ⎟⎟ >> 1 ⎝ n ⋅ VT ⎠
i ≅ ISe
v nV T
When diode is fully conducting, V remains constant at ~ 0.7V 0 7V for silicon diodes
• The voltage at which the diode starts to conduct appreciably is called the cut-in voltage; value is ~ .5V for silicon diodes R. Khazaka
ECSE330 Introduction to Electronics
24
12
