Electronics

Drift Current Density

To understand drift, assume an electric field is applied to a semiconductor. The field produces a force that acts on free electrons and holes, which then experience a net drift velocity and net movement. Consider an n-type semiconductor with a large number of free electrons. An electric field E applied in one direction produces a force on the electrons in the opposite direction, because of the electrons' negative charge. The electrons acquire a drift velocity v_>dn (in cm/s) which can be written as

v_dn = − µ_nE

where µ_n is a constant called the electron mobility and has units of cm²/V–s. For low-doped silicon, the value of µ_n is typically 1350 cm²/V–s. The mobility can be thought of as a parameter indicating how well an electron can move in a semiconductor. The negative sign in the equation above indicates that the electron drift velocity is opposite to that of the applied electric field. The electron drift produces a drift current density J_n (A/cm²) given by

J_n = − e n v_dn = − e n (− µ_n E) = +e n µ_n E

where n is the electron concentration (#/cm³) and e, in this context, is the magnitude of the electronic charge. The conventional drift current is in the opposite direction from the flow of negative charge, which means that the drift current in an n-type semiconductor is in the same direction as the applied electric field.

Next consider a p-type semiconductor with a large number of holes. An electric field E applied in one direction produces a force on the holes in the same direction, because of the positive charge on the holes. The holes acquire a drift velocity v_dp (in cm/s), which can be written as

v_dp = + µ_p E

where µ_p is a constant called the hole mobility, and again has units of cm²/V–s. For low-doped silicon, the value of µ_p is typically 480 cm2/V–s, which is less than half the value of the electron mobility. The positive sign in the equation above indicates that the hole drift velocity is in the same direction as the applied electric field. The hole drift produces a drift current density J_p (A/cm²) given by

J_p = + e p v_dp = +e p (+µ_p E) = + e p µ_p E

where p is the hole concentration (#/cm3) and e is again the magnitude of the electronic charge. The conventional drift current is in the same direction as the flow of positive charge, which means that the drift current in a p-type material is also in the same direction as the applied electric field.

Since a semiconductor contains both electrons and holes, the total drift current density is the sum of the electron and hole components. The total drift current density is then written as

J = e n µ_n E + epµ_p E = σ E = (1 / p) E

where

σ = e n µ_n + e p µ_p

and where σ is the conductivity of the semiconductor in (ohm–cm)⁻¹ and where ρ = 1/σ is the resistivity of the semiconductor in (ohm–cm). The conductivity is related to the concentration of electrons and holes. If the electric field is the result of applying a voltage to the semiconductor, then foregoing equation becomes a linear relationship between current and voltage and is one form of Ohm's law.

From the equation above, we see that the conductivity can be changed from strongly n-type, n >> p, by donor impurity doping to strongly p-type, p >> n, by acceptor impurity doping. Being able to control the conductivity of a semiconductor by selective doping is what enables us to fabricate the variety of electronic devices that are available.

Two factors need to be mentioned concerning drift velocity and mobility. The foregoing equations seem to imply that the carrier drift velocities are linear functions of the applied electric field. This is true for relatively small electric fields. As the electric field increases, the carrier drift velocities will reach a maximum value of approximately 107 cm/s. Any further increase in electric field will not produce an increase in drift velocity. This phenomenon is called drift velocity saturation.

The mobility values are actually functions of donor and/or acceptor impurity concentrations. As the impurity concentration increases, the mobility values will decrease. This effect then means that the conductivity is not a linear function of impurity doping.

These two factors are important in the design of semiconductor devices, but will not be considered in detail in this page.

Diffusion Current Density

In the diffusion process, particles flow from a region of high concentration to a region of lower concentration. This is a statistical phenomenon related to kinetic theory. To explain, the electrons and holes in a semiconductor are in continuous motion, with an average speed determined by the temperature, and with the directions randomized by interactions with the lattice atoms. Statistically, we can assume that, at any particular instant, approximately half of the particles in the high-concentration region are moving away from that region toward the lower-concentration region. We can also assume that, at the same time, approximately half of the particles in the lower-concentration region are moving toward the high-concentration region. However, by definition, there are fewer particles in the lower-concentration region than there are in the high-concentration region. Therefore, the net result is a flow of particles away from the high-concentration region and toward the lower-concentration region. This is the basic diffusion process.

For example, consider an electron concentration that varies as a function of distance x. The diffusion of electrons from a high-concentration region to a low-concentration region produces a flow of electrons in the negative x direction. Since electrons are negatively charged, the conventional current direction is in the positive x direction.

The diffusion current density due to the diffusion of electrons can be written as (for one dimension)

J_n = e D_n(dn/dx)

where e, in this context, is the magnitude of the electronic charge, dn/dx is the gradient of the electron concentration, and D_n is the electron diffusion coefficient.

[T]he hole concentration is [understood to be] a function of distance. The diffusion of holes from a high-concentration region to a low-concentration region produces a flow of holes in the negative x direction. (Conventional current is in the direction of the flow of positive charge.)

The diffusion current density due to the diffusion of holes can be written as (for one dimension)

J_p = − e D_p (dp/dx)

where e is still the magnitude of the electronic charge, dp/dx is the gradient of the hole concentration, and D_p is the hole diffusion coefficient. Note the change in sign between the two diffusion current equations. This change in sign is due to the difference in sign of the electronic charge between the negatively charged electron and the positively charged hole.

The mobility values in the drift current equations and the diffusion coefficient values in the diffusion current equations are not independent quantities. They are related by the Einstein relation, which is

D_n / µ_n = D_p / µ_p = k T / e ~ 0.026 V (approximately)

at room temperature.

The total current density is the sum of the drift and diffusion components. Fortunately, in most cases only one component dominates the current at any one time in a given region of a semiconductor.

Excess Carriers

Up to this point, we have assumed that the semiconductor is in thermal equilibrium. In the discussion of drift and diffusion currents, we implicitly assumed that equilibrium was not significantly disturbed. Yet, when a voltage is applied to, or a current exists in, a semiconductor device, the semiconductor is really not in equilibrium. In this section, we will discuss the behavior of nonequilibrium electron and hole concentrations.

Valence electrons may acquire sufficient energy to break the covalent bond and become free electrons if they interact with high-energy photons incident on the semiconductor. When this occurs, both an electron and a hole are produced, thus generating an electron–hole pair. These additional electrons and holes are called excess electrons and excess holes.

When these excess electrons and holes are created, the concentrations of free electrons and holes increase above their thermal equilibrium values. This may be represented by

n = n_o + δ_n

and

p = p_o + δ_p

where n_o and p_o are the thermal equilibrium concentrations of electrons and holes, and δ_n and δ_p are the excess electron and hole concentrations.

If the semiconductor is in a steady-state condition, the creation of excess electrons and holes will not cause the carrier concentration to increase indefinitely, because a free electron may recombine with a hole, in a process called electron–hole recombination. Both the free electron and the hole disappear causing the excess concentration to reach a steady-state value. The mean time over which an excess electron and hole exist before recombination is called the excess carrier lifetime.

Excess carriers are involved in the current mechanisms of, for example, solar cells and photodiodes.

The Equilibrium pn Junction

The interface at x = 0 is called the metallurgical junction. A large density gradient in both the hole and electron concentrations occurs across this junction. Initially, then, there is a diffusion of holes from the p-region into the n-region, and a diffusion of electrons from the n-region into the p-region. The flow of holes from the p-region uncovers negatively charged acceptor ions, and the flow of electrons from the n-region uncovers positively charged donor ions. This action creates a charge separation, which sets up an electric field oriented in the direction from the positive charge to the negative charge.

If no voltage is applied to the pn junction, the diffusion of holes and electrons must eventually cease. The direction of the induced electric field will cause the resulting force to repel the diffusion of holes from the p-region and the diffusion of electrons from the n-region. Thermal equilibrium occurs when the force produced by the electric field and the force produced by the density gradient exactly balance.

The positively charged region and the negatively charged region comprise the space-charge region, or depletion region, of the pn junction, in which there are essentially no mobile electrons or holes. Because of the electric field in the space-charge region, there is a potential difference across that region. This potential difference is called the built-in potential barrier, or built-in voltage, and is given by

V_bi = (k T / e) ln (N_a N_d / n_i²) = V_T ln (N_a N_d / n_i²)

where V_T ≡ kT /e, k = Boltzmann's constant, T = absolute temperature, e = the magnitude of the electronic charge, and N_a and N_d are the net acceptor and donor concentrations in the p- and n-regions, respectively. The parameter V_T is called the thermal voltage and is approximately V_T = 0.026 V at room temperature, T = 300 K.

The potential difference, or built-in potential barrier, across the space-charge region cannot be measured by a voltmeter because new potential barriers form between the probes of the voltmeter and the semiconductor, canceling the effects of V_bi. In essence, V_bi maintains equilibrium, so no current is produced by this voltage. However, the magnitude of V_bi becomes important when we apply a forward-bias voltage, as discussed later on.

Reverse-Biased pn Junction

Assume a positive voltage is applied to the n-region of a pn junction. The applied voltage V_R induces an applied electric field, E_A, in the semiconductor. The direction of this applied field is the same as that of the E-field in the space-charge region. The magnitude of the electric field in the space-charge region increases above the thermal equilibrium value. This increased electric field holds back the holes in the p-region and the electrons in the n-region, so there is essentially no current across the pn junction. By definition, this applied voltage polarity is called reverse bias.

When the electric field in the space-charge region increases, the number of positive and negative charges must increase. If the doping concentrations are not changed, the increase in the fixed charge can only occur if the width W of the space-charge region increases. Therefore, with an increasing reverse-bias voltage V_R, space-charge width W also increases.

Because of the additional positive and negative charges induced in the space-charge region with an increase in reverse-bias voltage, a capacitance is associated with the pn junction when a reverse-bias voltage is applied. This junction capacitance, or depletion layer capacitance, can be written in the form

C_j = C_j0 ( 1 + V_R / V_bi ) ^{- 1/2}

where C_jo is the junction capacitance at zero applied voltage. The junction capacitance will affect the switching characteristics of the pn junction. The voltage across a capacitance cannot change instantaneously, so changes in voltages in circuits containing pn junctions will not occur instantaneously.

The capacitance–voltage characteristics can make the pn junction useful for electrically tunable resonant circuits. Junctions fabricated specifically for this purpose are called varactor diodes. Varactor diodes can be used in electrically tunable oscillators, such as a Hartley oscillator.

As implied in the previous section, the magnitude of the electric field in the space-charge region increases as the reverse-bias voltage increases, and the maximum electric field occurs at the metallurgical junction. However, neither the electric field in the space-charge region nor the applied reverse-bias voltage can increase indefinitely because at some point, breakdown will occur and a large reverse bias current will be generated. This concept will be described further on.

Forward-Biased pn Junction

We have seen that the n-region contains many more free electrons than the p-region; similarly, the p-region contains many more holes than the n-region. With zero applied voltage, the built-in potential barrier prevents these majority carriers from diffusing across the space-charge region; thus, the barrier maintains equilibrium between the carrier distributions on either side of the pn junction.

If a positive voltage v_D is applied to the p-region, the potential barrier decreases. The electric fields in the space-charge region are very large compared to those in the remainder of the p- and n-regions, so essentially all of the applied voltage exists across the pn junction region. The applied electric field, E_A, induced by the applied voltage is in the opposite direction from that of the thermal equilibrium space-charge E-field. However, the net electric field is always from the n- to the p-region. The net result is that the electric field in the space-charge region is lower than the equilibrium value. This upsets the delicate balance between diffusion and the E-field force. Majority carrier electrons from the n-region diffuse into the p-region, and majority carrier holes from the p-region diffuse into the n-region. The process continues as long as the voltage v_D is applied, thus creating a current in the pn junction. This process would be analogous to lowering a dam wall slightly. A slight drop in the wall height can send a large amount of water (current) over the barrier.

This applied voltage polarity (i.e., bias) is known as forward bias. The forward-bias voltage v_D must always be less than the built-in potential barrier V_bi.

As the majority carriers cross into the opposite regions, they become minority carriers in those regions, causing the minority carrier concentrations to increase. . These excess minority carriers diffuse into the neutral n- and p-regions, where they recombine with majority carriers, thus establishing a steady-state condition.

Ideal Current–Voltage Relationship

an applied voltage results in a gradient in the minority carrier concentrations, which in turn causes diffusion currents. The theoretical relationship between the voltage and the current in the pn junction is given by

The parameter I_S is the reverse-bias saturation current. For silicon pn junctions, typical values of I_S are in the range of 10⁻¹⁸ to 10⁻¹² A. The actual value depends on the doping concentrations and is also proportional to the cross-sectional area of the junction. The parameter V_T is the thermal voltage, and is approximately V_T = 0.026 V at room temperature. The parameter n is usually called the emission coefficient or ideality factor, and its value is in the range 1 ≤ n ≤ 2.

The emission coefficient n takes into account any recombination of electrons and holes in the space-charge region. At very low current levels, recombination may be a significant factor and the value of n may be close to 2. At higher current levels, recombination is less a factor, and the value of n will be 1. Unless otherwise stated, we will assume the emission coefficient is n = 1.

This pn junction, with nonlinear rectifying current characteristics, is called a pn junction diode.

pn Junction Diode

For a forward-bias voltage, the current is an exponential function of voltage. With only a small change in the forward-bias voltage, the corresponding forward-bias current increases by orders of magnitude. For a forward-bias voltage v_D > +0.1 V, the (−1) term in the equation above can be neglected. In the reverse-bias direction, the current is almost zero.

The diode can be thought of and used as a voltage controlled switch that is off for a reverse-bias voltage and on for a forward-bias voltage. In the forward-bias or on state, a relatively large current is produced by a fairly small applied voltage; in the reverse-bias, or off state, only a very small current is created.

When a diode is reverse-biased by at least 0.1 V, the diode current is i_D = −I_S. The current is in the reverse direction and is a constant, hence the name reverse-bias saturation current. Real diodes, however, exhibit reverse-bias currents that are considerably larger than I_S. This additional current is called a generation current and is due to electrons and holes being generated within the space-charge region. Whereas a typical value of I_S may be 10⁻¹⁴ A, a typical value of reverse-bias current may be 10⁻⁹ A or 1 nA. Even though this current is much larger than I_S, it is still small and negligible in most cases.

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The Digital Revolution is Also Analog

The digital revolution is constructed on top of an analog reality. This fact simply won't go away. Somewhere, somehow, you have to get into and out of the digital system and connect to the real world.

Unfortunately, the predominance and glamor of digital has done harm to analog. Too few analog designers are being educated, creating a void. This leaves decisions affecting analog performance to engineers with a primarily digital background.

In integrated circuits, the relentless pressure toward faster digital speed has resulted in ever-decreasing supply voltages, which are anathema to high-performance analog design.

In a 350 nm process operating at 3.3 V, there's still enough headroom for a high-performance analog design, though 5 V would be better. At 180 nm (1.8 V), the job becomes elaborate and time-consuming, and performance starts to suffer. At 120 nm (1.2 V), analog design becomes very difficult, even with reduced performance. At 90 nm, analog design is all but impossible.

There are "mixed signal" processes that purportedly allow digital and analog circuitry on the same chip. A 180 nm process, for example, will have some devices that can work with a higher supply voltage (e.g. 3 V). Such additions are welcome, if marginal. However, the design models are often inadequate and oriented toward digital design.

Mealy and Moore Machines*

FPGAs for Maximum Power Point Tracking

Consider solar power. Solar farms rely on maximum power point tracking (MPPT) to wring the most energy from photovoltaic panels. Traditionally, this is handled by a microcontroller, but an FPGA can do it faster and more efficiently. Using parallel processing, an FPGA-based controller samples panel voltage and current thousands of times per second and adjusts the power converter in real time. When a cloud passes overhead, the FPGA reacts in microseconds to tweak the operating point, ensuring no watt is wasted.

One FPGA can even manage dozens of panels at once, coordinating an entire array for peak output. The payoff is tangible: advanced FPGA-based MPPT can boost a solar installation's energy harvest by 5–30%. Even a 5% gain on a 100 MW solar farm means an extra 5 MW of clean power delivered without adding a single new panel.

Using FPGAs to Manage Turbines

Wind turbines present a different challenge but offer similar benefits. Turbine controllers constantly adjust blade pitch and yaw to capture optimal wind energy and avoid damage in high winds. FPGAs can run these control loops with minimal latency, reading sensors and sending out blade adjustments faster than traditional setups. They can detect a sudden gust and feather the blades in milliseconds, then quickly restore optimal angles to keep energy flowing.

FPGAs also help smooth out the turbine's output. Using high-speed DSP blocks, they convert the generator's wild AC into a steady, grid-synchronized output in real time. The net result is that each turbine operates closer to peak efficiency and delivers more consistent power, even under gusty conditions.

Controlling Smart Grids

Modern electric grids are becoming digital smart grids, instrumented with thousands of smart meters, sensors, and phasor measurement units that stream data every second. Traditional centralized systems struggle to keep up with this torrent of real-time information.

FPGAs, by contrast, thrive on parallel, high-speed tasks. They can calculate grid phasors, detect faults, and adjust controls in mere milliseconds, helping the grid respond instantly to changing conditions. For example, an FPGA-based controller can sense a voltage drop in one sector and immediately dispatch battery power or adjust a transformer to compensate.

In addition to these split-second reactions, FPGAs also enable proactive management. By running AI forecasting models on dedicated FPGA hardware, grid operators can predict near-future supply and demand shifts with high accuracy. That means the system can pre-charge storage or schedule backup power ahead of an evening peak. Smarter grids with FPGA muscle make sure renewable energy is used fully and efficiently, with minimal waste.

Energy Storage and Electric Vehicles

Because renewable generation and consumption don't often align in time, energy storage is crucial. Large battery farms exist, but there are also countless smaller batteries distributed throughout the grid—in homes, businesses, and electric vehicles—that we can leverage. FPGAs can coordinate these dispersed batteries into a virtual power plant.

An FPGA-based battery management system monitors the status of dozens of batteries in real-time, adjusting charging to prevent stress and extend battery life. At a higher level, FPGA controllers decide when batteries should charge or discharge to balance the grid. They might soak up excess solar at midday and feed it back during the evening peak.

Electric vehicles take this concept to another level. The revenue of the electric vehicles market is projected to reach $990B USD by 2029, which means an enormous number of collective batteries on wheels. With smart control, even a fraction of those EVs supplying power at peak times could cover a significant share of grid demand. Such rapid, decentralized decision-making is exactly what FPGAs excel at.

Wrapping Up

To optimize our clean power systems, we must embrace advanced control technologies. Though not as celebrated as solar panels or wind turbines, FPGAs are crucial enablers behind the scenes. They ensure every ray of sunshine and every gust of wind is converted into usable electricity, that the grid handles fluctuations without waste, and that batteries deliver when needed.

The influence of FPGAs in clean energy is only set to grow. New low-power FPGA designs with AI capabilities will make grids even more autonomous and efficient. We can expect self-healing networks that isolate faults and reroute power in microseconds to prevent outages. Communities may run their own microgrids with FPGA controllers, optimizing local energy flow and even enabling peer-to-peer energy trading among neighbors.

In an era of urgent climate action, we can't afford to let any efficiency gain slip away—every percentage point counts. By integrating technologies like FPGAs into renewable energy and smart grids, we can accelerate progress toward a truly sustainable, low-carbon future. The clean energy revolution is only half the battle. The other half is making that clean energy smart, and that's a battle we can win with ingenuity and silicon.

HDLs' Levels of Description

These are, from more abstract to more detailed:

• System
• Architectural
• Behavioral
• Algorythmic
• Register Transfer Logic (RTL)
• Boolean Equations
• Structural
• Gates
• Switches
• Transistors
• Polygons
• Masks

Types of HDL Languages

There are two types of HDLs: loosely typed, and strongly typed.

A loosely typed language allows automatic type conversion, which lets you put the value 137 on an 8-bit bus. A strongly typed language would not permit you to do this because it would consider 137 to be an integer; an 8-bit bus is an array of 8 bits, and would not allow you to put an integer into an array.

Each type of language has its advantages; A loosely typed language will do what you mean most of the time. A strongly typed language will not allow you to make a mistake by combining the wrong types of objects. Strongly typed languages have conversion functions, so you could put the value 137 on an 8-bit bus by calling the integer to 8-bit array conversion function.

VHDL is considered to be a strongly-typed language, whereas Verilog is a weakly-typed one.