Understanding Solid State Devices Made Easy

Understanding Solid State Devices Made Easy
Shreepad Karmalkar Professor Electrical Engineering Department Indian Institute of Technology Madras

Learning outcomes At the end of this six hour session, you should be able to

Learning outcomes At the end of this six hour session, you should be able to state why study solid state devices.

Learning outcomes At the end of this six hour session, you should be able to state why study solid state devices. sketch the current-voltage characteristics of a p-n junction, Bipolar Junction Transistor (BJT) and a Metal Oxide Semiconductor Field Effect Transistor (MOSFET).

Learning outcomes At the end of this six hour session, you should be able to state why study solid state devices. sketch the current-voltage characteristics of a p-n junction, Bipolar Junction Transistor (BJT) and a Metal Oxide Semiconductor Field Effect Transistor (MOSFET). describe the evolution of solid state devices, namely – diodes and transistors.

Learning outcomes At the end of this six hour session, you should be able to state why study solid state devices. sketch the current-voltage characteristics of a p-n junction, Bipolar Junction Transistor (BJT) and a Metal Oxide Semiconductor Field Effect Transistor (MOSFET). describe the evolution of solid state devices, namely – diodes and transistors. state the steps involved in analyzing a solid state device to obtain an equation for its current-voltage characteristics.

Learning outcomes At the end of this six hour session, you should be able to state why study solid state devices. sketch the current-voltage characteristics of a p-n junction, Bipolar Junction Transistor (BJT) and a Metal Oxide Semiconductor Field Effect Transistor (MOSFET). describe the evolution of solid state devices, namely – diodes and transistors. state the steps involved in analyzing a solid state device to obtain an equation for its current-voltage characteristics. state how mobile charges are generated and transported in semiconductors.

Learning outcomes At the end of this six hour session, you should be able to state why study solid state devices. sketch the current-voltage characteristics of a p-n junction, Bipolar Junction Transistor (BJT) and a Metal Oxide Semiconductor Field Effect Transistor (MOSFET). describe the evolution of solid state devices, namely – diodes and transistors. state the steps involved in analyzing a solid state device to obtain an equation for its current-voltage characteristics. state how mobile charges are generated and transported in semiconductors. distinguish between a BJT and a MOSFET.

Learning outcomes At the end of this six hour session, you should be able to explain the rectifying operation of a p-n junction and amplifying operation of a transistor - bipolar and MOS - without using equations or energy band diagrams.

Learning outcomes At the end of this six hour session, you should be able to explain the rectifying operation of a p-n junction and amplifying operation of a transistor - bipolar and MOS - without using equations or energy band diagrams. explain the features and utility of the energy band diagram of a semiconductor.

Learning outcomes At the end of this six hour session, you should be able to explain the rectifying operation of a p-n junction and amplifying operation of a transistor - bipolar and MOS - without using equations or energy band diagrams. explain the features and utility of the energy band diagram of a semiconductor. write and explain the equations based on drift-diffusion carrier transport, that are employed to model a solid state device.

Learning outcomes At the end of this six hour session, you should be able to explain the rectifying operation of a p-n junction and amplifying operation of a transistor - bipolar and MOS - without using equations or energy band diagrams. explain the features and utility of the energy band diagram of a semiconductor. write and explain the equations based on drift-diffusion carrier transport, that are employed to model a solid state device. state some standard approximations employed to simplify the solution of the above equations.

Learning outcomes At the end of this six hour session, you should be able to explain the rectifying operation of a p-n junction and amplifying operation of a transistor - bipolar and MOS - without using equations or energy band diagrams. explain the features and utility of the energy band diagram of a semiconductor. write and explain the equations based on drift-diffusion carrier transport, that are employed to model a solid state device. state some standard approximations employed to simplify the solution of the above equations. state how to check and remember a device model equation, and what precautions should be taken while making calculations with it.

Diode Transistor Small-signal Power Microwave Generic Symbol Rectifier
LED

Why study solid state devices

Solid state devices enhance Performance Reliability Cost effectiveness of Energy systems Information systems

Solid state devices enhance Performance Reliability Cost effectiveness of Energy systems Information systems (generate, distribute, regulate as large an energy as possible)

Solid state devices enhance Performance Reliability Cost effectiveness of Energy systems Information systems (store, process, communicate information expending as small an energy as possible) (generate, distribute, regulate as large an energy as possible)

Hand Held Calculator Mechanical Electronic

Microsensor Clusters Wrist-worn environmental monitor (has acceleration, humidity, temperature, and pressure sensors) Smart Pen for signature verification (has acceleration, force and tilt sensors)

Current-voltage characteristics of a p-n junction

(nA) I (mA) V (V) - BV -IBV I P N V

(nA) I (mA) V (V) - BV -IBV I P N V I (mA) V (V) - BV

(nA) I (mA) V (V) - BV -IBV I P N V I (nA) V (V) - BV -IBV I (mA) V (V) - BV

Current-voltage characteristics of a BJT

P+ N P C B

VCE IB P+ N P C E B Common-Emitter

VCE IB P+ N P C E B Common-Emitter 250 200 150 100 50 |IC | (A) |VCE | (V) 5 4 3 2 1 |IB| (A) Output characteristics

VCE IB P+ N P C E B Common-Emitter 250 200 150 100 50 |IC | (A) |VCE | (V) 5 4 3 2 1 |IB| (A) |IB | (A) 42 VBE (V) |VCE | (V) 1 2 Input characteristics Output characteristics

Current-voltage characteristics of a MOSFET
D G S B p n

Common-Source ID D G S B p n VDS VBS VGS

Common-Source ID D G S B p n VDS VBS VGS Output characteristics

Common-Source ID D G S B p n VDS VBS VGS MOSFET does not have input characteristics since IG = 0. Output characteristics

Evolution of solid state diodes and transistors

Evolution of solid state diodes and transistors
Year Device Discoverer (D) / Inventor (I) 1874 Point-contact diode Braun (D) 1925 Semiconductor Triode Lilienfield (I) 1934 O’Hiel (I) 1940 P-N Junction Ohl (D) 1948 Bipolar Junction Transistor Shockley, Bardeen, Brattain (D) 1952 Junction Field Effect Transistor Shockley (I) 1958 Integrated Circuit Kilby, Noyce (I) 1960 Metal Oxide Semiconductor Field Effect Transistor Kahng, Atalla 1966 Metal Semiconductor Field Effect Transistor Mead (I)

Analyzing a solid state device for its I-V equation

Step 1: Partition the device into space-charge and neutral regions.

Step 1: Partition the device into space-charge and neutral regions. Step 2: Analyze each region separately to obtain the distributions of the carriers (n, p) and potential ().

Step 1: Partition the device into space-charge and neutral regions. Step 2: Analyze each region separately to obtain the distributions of the carriers (n, p) and potential (). Step 3: Combine the information regarding n, p and  obtained in different regions, ensuring continuity of these parameters across boundaries separating the regions, to obtain the complete picture regarding the terminal current as function of the voltage applied between the device terminals.

Generation of mobile charges in semiconductors

Nearest neighbors 5.43 Ao The silicon crystal is obtained by repeating this unit cube in 3-D

Nearest neighbors Nearest neighbor distance 5.43 Ao The silicon crystal is obtained by repeating this unit cube in 3-D 2-D representation of the 3-D crystal

Intrinsic silicon at 0 K There are no mobile charges or carriers

A crystal under equilibrium (animation) T = 0 K Still T > 0 K Agitated

Intrinsic silicon at 300 K Carriers contributed by silicon ionization or thermal generation which yields electron-hole pairs (EHPs).

Intrinsic silicon at 300 K Carriers contributed by silicon ionization or thermal generation which yields electron-hole pairs (EHPs). EHP generation rate = EHP recombination rate, resulting in a steady carrier concentration.

Intrinsic silicon at 300 K Carriers contributed by silicon ionization or thermal generation which yields electron-hole pairs (EHPs). EHP generation rate = EHP recombination rate, resulting in a steady carrier concentration. The hole is like a bubble in a liquid

Phosphorus doped silicon at 0 K There are no mobile charges or carriers. P +

Phosphorus doped silicon at 300 K Carriers contributed by : impurity ionization which yields carriers of one polarity only + P + P + P + P

Phosphorus doped silicon at 300 K Carriers contributed by : impurity ionization which yields carriers of one polarity only 2) silicon ionization or thermal generation which yields electron- hole pairs or EHPs. P +

Phosphorus doped silicon at 300 K Carriers contributed by : impurity ionization which yields carriers of one polarity only 2) silicon ionization or thermal generation which yields electron- hole pairs or EHPs. EHP generation rate = EHP recombination rate, resulting in a steady carrier concentration. P +

Boron doped silicon at 0 K There are no mobile charges or carriers. B -

Boron doped silicon at 300 K Carriers contributed by: impurity ionization which yields carriers of one polarity only B - B - B - B -

Boron doped silicon at 300 K Carriers contributed by: impurity ionization which yields carriers of one polarity only 2) silicon ionization or thermal generation which yields electron- hole pairs or EHPs. B - B - B - B -

Boron doped silicon at 300 K Carriers contributed by: impurity ionization which yields carriers of one polarity only 2) silicon ionization or thermal generation which yields electron- hole pairs or EHPs. B - B - B - B - EHP generation rate = EHP recombination rate, resulting in a steady carrier concentration.

Boron doped silicon at 300 K Carriers contributed by: impurity ionization which yields carriers of one polarity only 2) silicon ionization or thermal generation which yields electron- hole pairs or EHPs. B - I B - G I R G B - B - I I R EHP generation rate = EHP recombination rate, resulting in a steady carrier concentration.

Snapshot of generation, recombination and impurity ionization processes at different locations in a semiconductor

In an extrinsic semiconductor Majority carrier concentration Ionized impurity concentration EHP concentration = +

In an extrinsic semiconductor Majority carrier concentration Ionized impurity concentration EHP concentration = + Under equilibrium, recombination rate = generate rate leading to 2 Minority carrier concentration Majority carrier concentration Intrinsic carrier concentration =

Transport of mobile charges in semiconductors

V Drift current E = - h+ e-

V Drift current E = - h+ e- Diffusion current Light p, n h+ e-

V Drift current E = - h+ e- Diffusion current Light p, n h+ e- These carrier currents are the consequences of a directed carrier motion (due to potential or concentration gradients) superimposed over random thermal carrier motion.

Equilibrium picture (n-type semiconductor)

Equilibrium picture (n-type semiconductor) Snapshot of generation, recombination and impurity ionization at any instant G R I

Equilibrium picture (n-type semiconductor) Snapshot of generation, recombination and impurity ionization at any instant Random thermal motion of electrons and holes (G/R not shown) G R I

Analogy Illustrating Directed Motion Superimposed over Random Motion

Hovering insects Box of sweets

Hovering insects Box of sweets Movement of the box

Carrier motion Insect motion Hovering insects Force on carriers due to electric field Longing of insects for sweets Box of sweets Movement of the box

Equilibrium picture (n-type semiconductor) n-type semiconductor A   B R  G  h+ e-

Equilibrium picture (n-type semiconductor) RMS velocity or thermal velocity, vth n-type semiconductor A   B R  G  h+ e-

Equilibrium picture (n-type semiconductor) RMS velocity or thermal velocity, vth Mean free path between collisions (length AB), lc n-type semiconductor A   B R  G  h+ e-

Equilibrium picture (n-type semiconductor) RMS velocity or thermal velocity, vth Mean free path between collisions (length AB), lc Mean free time between collisions (time AB), c = lc / vth n-type semiconductor A   B R  G  h+ e-

Equilibrium picture (n-type semiconductor) RMS velocity or thermal velocity, vth Mean free path between collisions (length AB), lc Mean free time between collisions (time AB), c = lc / vth Minority carrier lifetime (time GR),  minority (> c but <<  majority ) n-type semiconductor A   B R  G  h+ e-

V Drift current E = - h+ e-

V Drift current E = - h+ e- An electron subjected to an electric field achieves a constant acceleration in vacuum, but

V Drift current E = - h+ e- An electron subjected to an electric field achieves a constant acceleration in vacuum, but a constant average velocity in semiconductors, because it has to move through other electrons and holes in random motion which act like a viscous medium.

V Drift current E = - h+ e- An electron subjected to an electric field achieves a constant acceleration in vacuum, but a constant average velocity in semiconductors because it has to move through other electrons and holes in random motion which act like a viscous medium. The drift current density is given by for electrons and for holes.

Diffusion current Light p, n h+ e-

Diffusion current Light p, n h+ e- Electrons and holes in random thermal motion diffuse from regions of higher concentration to lower concentration much like gas molecules.

Diffusion current Light p, n h+ e- Electrons and holes in random thermal motion diffuse from regions of higher concentration to lower concentration much like gas molecules. The diffusion current density is proportional to the concentration gradient and can be written as for electrons and for holes.

Learning outcomes

Learning outcomes At the end of this six hour session, you should be able to explain the rectifying operation of a p-n junction and amplifying operation of a transistor - bipolar and MOS - without using equations or energy band diagrams.

Learning outcomes At the end of this six hour session, you should be able to explain the rectifying operation of a p-n junction and amplifying operation of a transistor - bipolar and MOS - without using equations or energy band diagrams. explain the features and utility of the energy band diagram of a semiconductor.

Learning outcomes At the end of this six hour session, you should be able to explain the rectifying operation of a p-n junction and amplifying operation of a transistor - bipolar and MOS - without using equations or energy band diagrams. explain the features and utility of the energy band diagram of a semiconductor. write and explain the equations based on drift-diffusion carrier transport, that are employed to model a solid state device.

Learning outcomes At the end of this six hour session, you should be able to explain the rectifying operation of a p-n junction and amplifying operation of a transistor - bipolar and MOS - without using equations or energy band diagrams. explain the features and utility of the energy band diagram of a semiconductor. write and explain the equations based on drift-diffusion carrier transport, that are employed to model a solid state device. state some standard approximations employed to simplify the solution of the above equations.

Learning outcomes At the end of this six hour session, you should be able to explain the rectifying operation of a p-n junction and amplifying operation of a transistor - bipolar and MOS - without using equations or energy band diagrams. explain the features and utility of the energy band diagram of a semiconductor. write and explain the equations based on drift-diffusion carrier transport, that are employed to model a solid state device. state some standard approximations employed to simplify the solution of the above equations. state how to check and remember a device model equation, and what precautions should be taken while making calculations with it.

Dr. R.S. Rao, Professor, ECE, MITS, Madanapalle.
In the first session, you told no energy is required for electron to fall into a hole. My point is, energy is not required but energy gets released during recombination. Kindly throw some light on this aspect.

Intrinsic silicon at 300 K Carriers contributed by silicon ionization or thermal generation which yields electron-hole pairs (EHPs). EHP generation rate = EHP recombination rate, resulting in a steady carrier concentration. The hole is like a bubble in a liquid

My video lectures on internet
Solid State Devices (NPTEL video lecture) transcripts available at Semiconductor Device Modeling (NPTEL video lectures) Introduction to Research

Rectifying operation of a p-n junction
(nA) I (mA) V (V) - BV -IBV

Equilibrium, V = 0 (nA) I (mA) V (V) - BV -IBV

Equilibrium, V = 0 I (mA) V (V) P+ N

Equilibrium, V = 0 I (mA) V (V) P+ N When P region is brought into contact with N region, holes diffuse from P to N and electrons from N to P, setting up a positively charged region on the N-side, a negatively charged region on the P-side, and a built-in voltage.

Equilibrium, V = 0 I (mA) V (V) P+ N When P region is brought into contact with N region, holes diffuse from P to N and electrons from N to P, setting up a positively charged region on the N-side, a negatively charged region on the P-side, and a built-in voltage. Equilibrium is reached when the field due to the space-charge sets up a drift tendency which exactly counter balances the diffusion.

Forward bias, V > 0 I (mA) V (V) P+ N

Forward bias, V > 0 I (mA) V (V) P+ N Applied voltage opposes the built-in voltage, reducing the field in the space-charge region.

Forward bias, V > 0 I (mA) V (V) P+ N h+ e- Applied voltage opposes the built-in voltage, reducing the field in the space-charge region. Consequently, drift tendency reduces and diffusion dominates, causing injection of holes from P to N and electrons from N to P.

Forward bias, V > 0 I (mA) V (V) P+ N h+ e- Applied voltage opposes the built-in voltage, reducing the field in the space-charge region. Consequently, drift tendency reduces and diffusion dominates, causing injection of holes from P to N and electrons from N to P. P region can readily supply holes and N regions electrons, so a large current is obtained for any applied voltage.

Reverse bias, - BV < V < 0 (nA) I (mA) V (V) P+ N h+ e-

Reverse bias, - BV < V < 0 (nA) I (mA) V (V) P+ N h+ e- Applied voltage aids the built-in voltage, increasing the field in the space-charge region.

Reverse bias, - BV < V < 0 (nA) I (mA) V (V) P+ N h+ e- Applied voltage aids the built-in voltage, increasing the field in the space-charge region. Consequently, drift tendency dominates over diffusion causing extraction of holes from N to P and electrons from P to N.

Reverse bias, - BV < V < 0 (nA) I (mA) V (V) P+ N h+ e- Applied voltage aids the built-in voltage, increasing the field in the space-charge region. Consequently, drift tendency dominates over diffusion causing extraction of holes from N to P and electrons from P to N. Electrons are minority carriers in P and holes are so in N, leading to a small current for any applied voltage.

Breakdown, V < - BV (nA) I (mA) V (V) - BV -IBV P+ N h+ e-

Breakdown, V < - BV (nA) I (mA) V (V) - BV -IBV P+ N h+ e- In the space-charge region, the electric field exceeds a critical value Ecrit.

Breakdown, V < - BV (nA) I (mA) V (V) - BV -IBV P+ N h+ e- In the space-charge region, the electric field exceeds a critical value Ecrit. In heavily doped junctions, the space- charge region is thin enough to allow a tunneling current of electrons across the space-charge region from P to N.

Breakdown, V < - BV (nA) I (mA) V (V) - BV -IBV P+ N h+ e- In the space-charge region, the electric field exceeds a critical value Ecrit. In moderately doped junctions, carriers drifting in the space- charge region acquire high enough kinetic energy to break Si- Si bonds and generate EHPs which in turn generate more EHPs leading to an avalanche.

Amplifying operation of a transistor

The arrows within the device indicate the direction of carrier flow while those outside indicate conventional current.

The arrows within the device indicate the direction of carrier flow while those outside indicate conventional current. Almost the entire current through a forward biased junction can be transferred to a nearby zero biased or shorted junction located less than a diffusion length away from the former junction.

The arrows within the device indicate the direction of carrier flow while those outside indicate conventional current. Only the hole flow in the device is shown. The transferred current IC can be passed through a load resistor to tap amplified power.

The arrows within the device indicate the direction of carrier flow while those outside indicate conventional current. Only the hole flow in the device is shown. The transferred current IC can be passed through a load resistor to tap amplified power. However, the voltage drop across the resistor forward biases the C-B junction causing injection of holes from C to B, killing the current IC and hence the tapped power.

The arrows within the device indicate the direction of carrier flow while those outside indicate conventional current. Only the hole flow in the device is shown. The transferred current can be restored to its maximum value by compensating the voltage drop across R with a power supply Vc.

The arrows within the device indicate the direction of carrier flow while those outside indicate conventional current. Only the hole flow in the device is shown. The price paid is a temperature sensitive collector current I0 uncontrollable by VEB , base-width modulation which reduces amplification, and collector-base breakdown if Vc is high.

VCE IB P+ N P C E B Common-Emitter

VCE IB P+ N P C E B Common-Emitter 250 200 150 100 50 |IC | (A) |VCE | (V) 5 4 3 2 1 |IB| (A) Output characteristics

Metal Oxide Semiconductor Field Effect Transistor
Step by step development

Step by step development N+ Poly silicon P-bulk / substrate _ _ N+ Poly silicon depletes P-bulk as in a P-N junction

Step by step development N+ Poly silicon P-bulk / substrate Oxide _ _ The depletion region shrinks on introducing the thin oxide between N+ and P regions

Step by step development N+ Poly silicon P-bulk / substrate Small VGB _ _ The depletion region expands on the application of a small VGB

Step by step development N+ Poly silicon P-bulk / substrate Large VGB _ _ _ _ The depletion region saturates and inversion layer appears on the application of a large VGB

Step by step development N+ Poly silicon P-bulk / substrate Large VGB N+ _ _ _ _ Connect source and drain terminals to pass current through the inversion layer which is controlled by the gate.

Step by step development N+ Poly silicon P-bulk / substrate Large VGB N+ _ _ _ _ In practice, the source and drain terminals are embedded in the substrate

Step by step development Large VGB N+ Poly silicon _ _ Small VDB N+ _ _ N+ ID P-bulk / substrate ID increases linearly with VDB for small VDB

Step by step development N+ Poly silicon P-bulk / substrate Large VGB N+ Large VDB ID _ Inversion layer shrinks and depletion layer expands from source to drain, causing ID to saturate with VDB, for large VDB.

Step by step development N+ Poly silicon P-bulk / substrate Large VGB N+ Large VDB ID _ For a given VDB, ID increases with VGB

Common-Source ID D G S B p n VDS VBS VGS Output characteristics

Features and utility of energy band diagrams

0 c i v

0 Energy of an electron outside the semiconductor but touching its surface c i v

0 Energy of an electron outside the semiconductor but touching its surface c i v Potential energy of a conduction electron Potential energy of a hole

0 Energy of an electron outside the semiconductor but touching its surface Electron moved out of the semiconductor c i v Potential energy of a conduction electron Potential energy of a hole

0 Energy of an electron outside the semiconductor but touching its surface c i v Potential energy of a conduction electron Generation of EHP Recombination of EHP Potential energy of a hole

0 Energy of an electron outside the semiconductor but touching its surface Electron in random thermal motion under equilibrium c i v Potential energy of a conduction electron Potential energy of a hole Hole in random thermal motion under equilibrium

0 Energy of an electron outside the semiconductor but touching its surface Kinetic energy of a conduction electron c i v Potential energy of a conduction electron Potential energy of a hole Kinetic energy of a hole

0 Energy of an electron outside the semiconductor but touching its surface c f i v Potential energy of a conduction electron d Potential energy of a hole N-type semiconductor

0 Energy of an electron outside the semiconductor but touching its surface c i f v Potential energy of a conduction electron a Potential energy of a hole P-type semiconductor

0 Energy of an electron outside the semiconductor but touching its surface c i f v Potential energy of a conduction electron d a Potential energy of a hole Compensated P-type semiconductor

0 Energy of an electron outside the semiconductor but touching its surface c f i v Potential energy of a conduction electron d a Potential energy of a hole Compensated N-type semiconductor

When P-Si and N-Si are brought into contact, electrons move from the N-Si region where their concentration is higher to the P-Si region where their concentration is lower. P-Si N-Si Homo-junction

When P-Si and N-Si are brought into contact, electrons move from the N-Si region where their concentration is higher to the P-Si region where their concentration is lower. P-Si N-Si Homo-junction P-Si Metal Hetero-junction

When P-Si and N-Si are brought into contact, electrons move from the N-Si region where their concentration is higher to the P-Si region where their concentration is lower. P-Si N-Si Homo-junction When P-Si and Metal are brought into contact, we cannot determine the direction of electron transfer without the help of energy band diagram. P-Si Metal Hetero-junction

When P-Si and N-Si are brought into contact, electrons move from the N-Si region where their concentration is higher to the P-Si region where their concentration is lower. P-Si N-Si Homo-junction When P-Si and Metal are brought into contact, we cannot determine the direction of electron transfer without the help of energy band diagram. It can happen that electrons may move from the P-Si to the Metal, i.e. from a region of lower concentration to a region of higher concentration !!! P-Si Metal Hetero-junction

Equations based on drift-diffusion transport for device analysis

Flow Creation Continuity Jn Jp E

Transport equations Flow Creation Continuity Jn Jp E

Transport equations Flow Creation Continuity Jn Jp E Electrostatic equations

Current density equations Continuity equations Flow Creation Continuity Jn Jp E Electrostatic equations Gauss’ law

Simplifying approximations for solving equations

Flow Creation Continuity Jn Jp E

Flow Creation Continuity Jn Jp E Equilibrium: Jn = 0, Jp = 0, G = 0, n = 0, p = 0

Flow Creation Continuity Jn Jp E Equilibrium: Jn = 0, Jp = 0, G = 0, n = 0, p = 0 Steady state: tn = 0, tp = 0

Flow Creation Continuity Jn Jp E Equilibrium: Jn = 0, Jp = 0, G = 0, n = 0, p = 0 Steady state: tn = 0, tp = 0 Charge neutrality:  = 0 or n = p

Flow Creation Continuity Jn Jp E Equilibrium: Jn = 0, Jp = 0, G = 0, n = 0, p = 0 Steady state: tn = 0, tp = 0 Charge neutrality:  = 0 or n = p Diffusion approximation: e.g.

Flow Creation Continuity Jn Jp E Depletion approximation:   - qNa on p-side,   qNd on n-side

Flow Creation Continuity Jn Jp E Depletion approximation:   - qNa on p-side,   qNd on n-side Gradual channel approximation: xE >> yE

Flow Creation Continuity Jn Jp E Depletion approximation:   - qNa on p-side,   qNd on n-side Gradual channel approximation: xE >> yE Charge sheet approximation: mobile carriers are concentrated into a sheet

Checking and remembering model equations

P N V (nA) (mA) V (V) T = 300 K Example: Ideal diode model

We can confirm whether a model equation is correct or not by checking if the units of the RHS of the eqn. match with those of the LHS I P N V (nA) (mA) V (V) T = 300 K Example: Ideal diode model

We can confirm whether a model equation is correct or not by checking if the units of the RHS of the eqn. match with those of the LHS the current I predicted for limiting values of voltages V such as V = 0, +  and -  should be physical I P N V (nA) (mA) V (V) T = 300 K Example: Ideal diode model

Precautions while making calculations using model equations

Example: Calculate the current I in a small-signal silicon diode with the following parameters for V = 0.26 V and T = 300 K using the ideal diode model:

Example: Calculate the current I in a small-signal silicon diode with the following parameters for V = 0.26 V and T = 300 K using the ideal diode model: A = 1 mm2 P+ region: Na = 1017 cm-3, Dn = 18 cm2 / s, n = 100 ns N region: Nd = 1015 cm-3, Dp = 13 cm2 / s, p = 1 s ni = 1.5 x1010 cm-3

While putting the value of any physical parameter in the equation, always include the units as well.

While putting the value of any physical parameter in the equation, always include the units as well. Collect the powers of 10 together and evaluate them separately from the multiplying constants.

While putting the value of any physical parameter in the equation, always include the units as well. Collect the powers of 10 together and evaluate them separately from the multiplying constants. Be aware of the order of magnitudes of the physical parameters, voltages and expected current.

Thank you

Understanding Solid State Devices Made Easy

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