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A distributed energy resource is a localized source or store of electrical energy connected near the consuming part of an electric power system, commonly through electric power distribution. Examples include a nearby electrical generator, an array of solar cells, and an electric battery with its power-conversion equipment. Energy storage can either absorb or deliver power; calling it a resource does not make it a net source of energy over a complete charge-discharge cycle.^[ref]

For an original boundary calculation, a site consumes $50\mathrm{kW}$, its solar cells supply $30\mathrm{kW}$ at the stated output boundary, and an electric battery supplies $10\mathrm{kW}$. Neglecting site losses, the imported power isIf the same electric battery instead charges at $10\mathrm{kW}$, its signed supply is $-10\mathrm{kW}$ and import becomes $30\mathrm{kW}$. If solar output rises to $70\mathrm{kW}$ while storage is idle, the algebra gives $-20\mathrm{kW}$ import: an export, provided the connection and controls permit that operating point.

The location matters physically. Local generation can reduce upstream electric current when it offsets downstream consumption, but sufficiently large export can reverse the electric current. In a simplified resistive two-terminal branch, $V_s-V_r=RI$ for signed electric current from supply to site; negative $I$ makes the receiving-site electric potential difference higher. This is an illustrative direct current relation, not a complete alternating current feeder calculation.

A group of distributed energy resources becomes a microgrid only with an appropriate boundary and coordinated operation. Installed generating capacity alone does not establish that disconnected operation can regulate the local supply. A useful test records import or export together with each resource's signed power, so an apparent reduction in imported energy is not confused with a change in the consuming electrical loads.

Electricity generation converts another form of energy into electrical energy supplied to an electrical load or electric power system. A rotating electrical generator uses electromagnetic induction; a solar cell instead converts incident radiation through the photovoltaic effect. Neither process creates energy. The relevant input and output boundaries determine which losses enter a quoted conversion fraction.

For an original ideal rotating-coil model, let $N$ turns of area $A$ rotate at constant angular velocity $\omega$ in a uniform magnetic field $B$. With the coil normal initially aligned with that field, the linked magnetic flux and induced electromotive force areFor $N=100$, $A=0.01{\mathrm{m}}^2$, $B=0.5\mathrm{T}$ and $\omega =100\mathrm{rad}{\mathrm{s}}^{-1}$, the peak is $50\mathrm{V}$ and the sinusoidal root mean square value is $50/\sqrt{2}\approx 35.36\mathrm{V}$. Doubling the speed doubles both the amplitude and frequency in this model. The DOE exposition develops the rotating-conductor waveform and distinguishes peak from effective values.^[ref]

An open-circuit induced electric potential difference does not specify deliverable power. On connecting a load, the resulting electric current produces an opposing electromagnetic torque; sustained electrical output requires corresponding mechanical input and provision for losses. For a stipulated steady shaft input of $2.0\mathrm{kW}$ and combined losses of $0.2\mathrm{kW}$, output is $1.8\mathrm{kW}$ and the shaft-to-electrical conversion fraction is $0.9$. This fraction excludes any earlier conversion from fuel or another primary supply into shaft power.

A proposed demonstration couples a small electrical generator to a controllable drive, measures rotational speed and open-circuit waveform, then applies several known electrical loads while recording shaft torque, electric current and terminal electric potential difference. The additional mechanical effort under load tests the electromechanical conversion power balance; an open-circuit waveform alone cannot test that balance.

Hans-Joachim Queisser and William Shockley calculated an ideal efficiency limit for a single-junction solar cell using detailed balance. The cell must emit as well as absorb photons, and radiative recombination therefore limits the electrical work extracted from illumination even when other losses are removed. Their 1961 analysis varies the band gap and allows a specified fraction of nonradiative recombination. The familiar limit belongs to stated assumptions about the illumination, cell temperature and device; it is not one universal numerical efficiency for every photovoltaic design.^[ref]

A physicist who coauthored Detailed Balance Limit of Efficiency of p-n Junction Solar Cells by William Shockley and Hans-Joachim Queisser.

Hans J. Queisser coauthored Detailed Balance Limit of Efficiency of p-n Junction Solar Cells by William Shockley and Hans J. Queisser. The analysis balances photon absorption and radiative emission to constrain the efficiency of an idealized single-junction solar cell. The result is an upper limit under stated optical and recombination assumptions, so a comparison with a real solar cell must identify which assumptions apply.^[ref]

A semiconductor researcher whose work with Jerry M. Woodall improved gallium arsenide solar cells using a heterojunction. A surface layer reduced surface recombination while transmitting much of the useful incident light. Comparing the spectral response before and after removing that layer exposed how surface losses suppress charge collection, connecting device efficiency with a measurable microscopic loss mechanism.^[ref]

A researcher in semiconductor devices whose joint work with H. J. Hovel demonstrated heterojunction solar cells made from gallium arsenide and an aluminum-containing alloy. The additional layer admits useful light while reducing surface recombination and electrical resistance. Their 1972 experiment illustrates why an efficient solar cell depends on controlling what happens to generated carriers at a surface, as well as on absorbing incident light.^[ref]

Keep the illumination and cell temperature approximately constant. Connect an ammeter and an adjustable resistor as a series circuit across the solar cell; connect a high-resistance voltmeter across its terminals. Vary the electrical resistance and record pairs of electric potential difference $V$ and delivered electric current $I$. This measures the illuminated current-voltage characteristic.

A load close to a short circuit estimates $I_{\mathrm{sc}}$ at $V\simeq 0$. With the load disconnected, an open circuit measurement using a high-resistance voltmeter estimates $V_{\mathrm{oc}}$ at $I\simeq 0$. Neither endpoint delivers useful power: $P=VI$ vanishes there. The intermediate readings locate the maximum of $VI$ and determine the solar-cell fill factor. Holding illumination fixed matters because the photogenerated electric current changes with light intensity; holding temperature fixed matters because the diode saturation current and junction response change with it.

This experiment distinguishes producing an electric potential difference from delivering energy to a load. To determine conversion efficiency as well, measure the incident power on the illuminated area, rather than equating it to a lamp's electrical rating.

A metal-halide perovskite is a crystalline material in which a halide-based framework adopts the perovskite structure or a related arrangement. In the common $AB{X}_3$ description, $B$ is a metal cation, $X$ a halide and $A$ a larger charge-balancing cation, which can be inorganic or molecular.

Connectivity and distortion of the metal–halide framework influence electronic structure and optical absorption. This makes the family important in solar cells and light-emitting devices. The structural name alone does not specify one composition, stability or band gap; substitutions, dimensionality and defects can change those properties.

The Shockley-Queisser limit is the detailed-balance efficiency bound for an ideal single-junction solar cell with radiative recombination under specified illumination and optical conditions. Below-gap photons are not absorbed and excess energy of above-gap photons is thermalized; radiative emission further limits the output voltage. The often quoted unconcentrated terrestrial maximum is roughly one third, not an illumination-independent universal percentage.

A multi-junction solar cell places a high-gap junction before lower-gap junctions, dividing the spectrum so photons generate carriers in a better-matched absorber. This reduces transmission and thermalization losses and can exceed the single-junction bound without violating its assumptions: there is now more than one junction. In a two-terminal series stack, all junctions carry the same current, so the lowest photocurrent limits the whole device. Current matching uses bandgap choice, absorber thickness, optical management and sometimes lateral area to make the generated currents comparable for the intended spectrum. Independently contacted junctions need not share the same current.^[ref]

Donor doping supplies conduction electrons to n-type semiconductor; acceptor doping supplies holes to p-type semiconductor. In the nondegenerate, fully ionized limit, majority densities are approximately $n_n=N_D$ and $p_p=N_A$, while minority densities follow $np=n_i^2$. On contact, majority carriers diffuse across the junction, exposing positive donor ions on the n side and negative acceptor ions on the p side. The depletion-region electric field points from n to p and opposes further diffusion. At thermal equilibrium the Fermi level is uniform and drift balances diffusion, with no net current.

For an abrupt junction with uniform doping and permittivity ${\epsilon }_s$, charge neutrality gives $N_D{x}_n=N_A{x}_p$. Poisson's equation then givesPositive applied $V$ means forward bias: it lowers the barrier and narrows the depletion region. Most depletion width lies in the more lightly doped side. The formula assumes the depletion approximation and fails once its operating assumptions break down.

forward bias increases minority densities at the depletion edges by the factor $e^{qV/k_{B}T}$. In the neutral material, the steady diffusion–recombination equation gives exponentially decaying excess minorities, with lengths $L_n=\sqrt{D_n{\tau }_n}$ and $L_p=\sqrt{D_p{\tau }_p}$. Taking the carrier gradients at the junction yieldsThis ideal diode law assumes low injection, nondegenerate statistics, negligible depletion-region recombination and series resistance, and sufficiently long neutral regions. Its exponential comes from the bias-dependent injection barrier; there is no universal abrupt “turn-on” voltage. reverse bias suppresses injection, giving an approximate $-I_S$ current until additional leakage or breakdown matters.^[ref]

Rectification uses the asymmetric current-voltage characteristic; controlled reverse breakdown enables voltage references, with current limiting. Bias-dependent depletion capacitance enables varactors. photodiodes and solar cells collect optically generated carriers through the junction field and diffusion toward it; efficient light-emitting diodes use radiative electron–hole recombination, preferably in a direct-gap material. Series resistance, high injection, trap-assisted recombination, heating and finite carrier storage explain departures from the ideal steady-state law.

A p-n junction brings p-type and n-type regions into contact. Majority-carrier diffusion initially leaves exposed ionized acceptors and donors, producing a depletion region and a built-in potential. At thermal equilibrium the electrochemical potential is constant: drift and diffusion currents cancel. The internal barrier is not a freely extractable battery voltage.

For a nondegenerate abrupt homojunction,Here $V>0$ denotes forward bias and the depletion approximation is assumed. forward bias lowers the barrier and injects minority carriers; reverse bias widens the depleted region and suppresses ordinary majority injection. In the ideal diffusion regime,Recombination can change the ideality factor; series resistance, high-level injection, leakage and breakdown limit this simple Shockley diode equation. The original junction theory explicitly treats both electron and hole currents, which is essential to carrier injection and transistor action.^[ref]

As a rectifying diode, the junction conducts strongly in one bias direction and weakly in the other before breakdown. This permits power rectification, signal detection and electronic switching. Stored minority charge affects turn-off time, so a static exponential current-voltage relation alone does not specify switching speed. A junction capacitance $C_j\simeq {ϵ}_{s}A/W$ varies with reverse bias and can be used in a voltage-controlled capacitor; heavily doped or high-field junctions can instead exploit controlled tunnelling or avalanche breakdown.

In a photodiode, absorbed photons generate electron-hole pairs and the depleted-region field assists collection. reverse bias widens the collecting region and can improve speed, but adds dark-current noise and breakdown constraints. In a solar cell, the same carrier generation supplies current against an external voltage. An ideal illuminated characteristic is $I=I_s(e^{qV/(k_{B}T)}-1)-I_{\mathrm{ph}}$: at open circuit the forward diode current balances photocurrent, while useful power is taken at an intermediate operating point. Neither short circuit nor open circuit delivers power to a load.

A forward-biased light-emitting diode injects electrons and holes that can recombine radiatively. Efficient emission favors suitable direct-gap materials and carrier confinement; the characteristic photon energy is near the semiconductor band gap. nonradiative recombination, escape losses, series resistance and heating limit efficiency. Two coupled junctions also form a bipolar junction transistor: an emitter injects minority carriers through a thin base, and a reverse-biased collector collects them. Useful current gain depends on efficient injection and limited base recombination, not simply on joining any three arbitrary regions.

These functions are experimentally distinguished by measuring dark and illuminated current-voltage curves, bias-dependent capacitance, transient switching or optical emission, with controlled temperature and current limits. The common mechanism is bias-controlled carrier injection or collection at a depletion barrier; the device geometry and operating mode determine which function is useful.

A p-n junction joins p-type and n-type semiconductors. Initial carrier diffusion exposes ionized acceptors and donors, creating a depletion region and an internal electric field. At equilibrium the Fermi level is uniform and drift balances diffusion, so the built-in potential produces no net terminal current. For nondegenerate abrupt doping, its magnitude is $V_{\mathrm{bi}}=(k_{B}T/e)\ln (N_A{N}_D/n_i^2)$.

Forward bias lowers the barrier and injects minority carriers across the junction. In the ideal low-injection diffusion model, the Shockley diode equation is $I=I_s[e^{eV/(k_{B}T)}-1]$. Reverse bias broadens the depletion region and leaves a small leakage current until breakdown mechanisms become important.

The asymmetric current-voltage curve enables rectification. Illumination produces electron-hole pairs that the junction field can separate, giving a photodiode or solar cell. Forward injection and radiative recombination in a suitable direct-gap material give a light-emitting diode. Measuring dark and illuminated current-voltage curves distinguishes electrical injection from photogenerated current; an ideal junction need not have zero reverse leakage or identical behavior in every material.

A solar cell uses the photovoltaic effect to turn photon energy into electrical work. In a semiconductor, above-gap photon absorption generates an electron in the conduction band and an electron hole in the valence band. A p-n junction, together with selective electrical contacts, collects the two carrier species at opposite terminals. Carrier diffusion and the built-in electric field help separate them before electron-hole recombination. Illumination maintains different quasi-Fermi levels for electrons and electron holes; their splitting, divided by $e$, sets the available terminal voltage in an ideal device. The equilibrium built-in potential alone cannot continuously deliver work.

For an ideal junction, the illuminated output current density isHere $J_{\mathrm{sc}}$ is the photogenerated short-circuit current density and $J_0$ the diode saturation current. The useful operating point maximizes $VJ$, rather than either current or voltage separately. With solar-cell fill factor $\mathrm{FF}=P_{\max }/(V_{\mathrm{oc}}{I}_{\mathrm{sc}})$,Series resistance, shunts, incomplete photon absorption and nonradiative recombination reduce the attainable efficiency.

The Shockley-Queisser limit removes these avoidable losses but retains the following physical constraints. There is one semiconductor junction with one band gap; each absorbed above-gap photon yields at most one collected electron-hole pair; carriers thermalize to the cell temperature; and the inverse optical process produces unavoidable radiative recombination. If ${\Phi }_{\odot }(E)$ is the incident photon flux per unit energy, ideal photon absorption givesThe same ability to absorb light requires the junction to emit it. At a forward voltage $V$, the emitted photon population has a chemical potential $eV$; in the ordinary nondegenerate limit the resulting recombination current is the exponential diode term above. Maximizing $VJ$ with this radiative $J_0$, and then choosing $E_g$, gives the limiting efficiency.

A small band gap collects many photons but gives a low voltage and large thermalization losses. A large band gap permits a larger voltage but transmits too much of the incident spectrum. Below-gap photons are lost to transmission, excess photon energy above the gap becomes heat, and radiative emission and its associated entropy loss keep $e{V}_{\mathrm{oc}}$ below $E_g$. The optimum single-junction conversion is roughly thirty percent under ordinary unconcentrated sunlight; the precise ceiling depends on spectrum, cell temperature and optical geometry. The original detailed-balance calculation gave about $30\%$ at $E_g\simeq 1.1\mathrm{eV}$ under its specified assumptions.^[ref] Multiple junctions and optical concentration change the assumptions and consequently change the bound.

The Shockley-Queisser limit is the radiative conversion-efficiency bound for an ideal single-junction solar cell, with one collected electron-electron hole pair per absorbed above-gap photon, carrier thermalization, and radiative recombination required by the reverse optical process. Photons below the band gap are not absorbed, while excess photon energy above it is thermalized. Maximizing the electrical power over the operating electric potential difference and then the band gap gives a ceiling of roughly thirty percent for ordinary unconcentrated sunlight; its precise value depends on the incident spectrum, cell temperature and emission geometry. The original calculation by William Shockley and Hans-Joachim Queisser obtained approximately $30\%$ at $1.1\mathrm{eV}$ for a $6000\mathrm{K}$ blackbody source and a cell at $300\mathrm{K}$.^[ref]

A solar cell converts incident light into electrical power through the photovoltaic effect. A semiconductor p-n junction separates and collects photogenerated electrons and electron holes. An ideal illuminated junction has output current densityHere $J_{\mathrm{sc}}$ is the short-circuit current density, $J_0$ is the diode saturation current, and $V_{\mathrm{oc}}$ is the open-circuit electric potential difference. The conversion efficiency is the largest delivered $VJ$ divided by the incident power per unit area; the short-circuit and open-circuit operating points themselves deliver zero power.

Vladimir Bulović's organic-optoelectronics course connects molecular excited states with practical light-emitting and photovoltaic devices. Its treatment follows excitons from their creation through diffusion and energy transfer, then asks whether that excitation produces light or collected electric charge. This distinction explains why efficient absorption alone does not guarantee an efficient solar cell or organic light-emitting diode. Comparing molecular energy levels, interfaces and transport makes device behavior understandable from the processes that compete inside the material.^[ref]

MIT lists the instructor of Organic Optoelectronics lecture notes by Vladimir Bulović as Vladimir Bulovic.