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The contact dimensions are readily accessible to UV photolithography followed by directional evaporation and lift-off. A possible sequence is:

A real device must also have appropriate ohmic contact metallurgy. gold alone on arbitrary GaAs is not automatically an ohmic contact: surface preparation, heavy contact-layer doping and, where required, a suitable alloyed contact stack are needed. The schematic gold label specifies the visible electrode, not all such process details. Order the mesa etch and contact steps so that the etchant and any anneal do not damage an already formed contact.

Grow the semiconductor stack epitaxially by molecular beam epitaxy or metalorganic vapor-phase epitaxy on a suitable crystalline GaAs substrate. Sequential changes of source flux or precursor supply set the GaAs/AlGaAs compositions, while dopant supply sets the n-type and p-type regions. Growth time and calibrated rate control the thicknesses of the InGaAs quantum well and the alternating reflector layers.

epitaxy preserves a common crystal orientation and clean, abrupt semiconductor interfaces. These are important both for carrier confinement in the quantum well and for low-loss optical reflection. For a DBR centered at free-space wavelength ${\lambda }_0$, the approximate quarter-wave condition is $n_j{d}_j={\lambda }_0/4$ in each layer. Ordinary deposition of a polycrystalline coating would not provide the required active semiconductor heterostructure.

The conspicuous approximately vertical streaks are focused ion beam milling curtaining: different sputtering rates beneath the rough, compositionally varying cap and interfaces leave stripes of different foil thickness. The uneven lower foil edge, contrast gradient and locally thinned regions are also consistent with nonuniform milling; redeposition can add material to other regions.

A dark gap or pull-out may have been enlarged or created during milling, so its original dimensions cannot be inferred securely from this one image. ion implantation and an amorphized surface layer are additional possible focused ion beam milling effects, but they are not independently demonstrated by these intensity variations. A lower-energy final polish, improved protective cap and examination of another lamella could test the preparation contribution.

The thin scanning transmission electron microscopy foil restricts scattering to a much smaller projected specimen volume than bulk SEM at $30\mathrm{kV}$. It reveals the nanoscale shape and continuity of the gold/NiP interface, the narrow low-density opening and the fine heterogeneous region underneath the gold, which the larger SEM interaction volume and surface-sensitive collection obscure.

The enlarged view resolves structure on the tens-of-nanometres scale: local interface roughness, small bright and dark domains and the relationship of the gold layer to the damaged or porous-looking NiP${}_y$ region. This helps distinguish an interface-associated defect from merely a change between nominal alloy layers. It still does not identify a crystalline phase or quantify composition without diffraction or spectroscopic analysis. Since the SEM surface and focused ion beam milling lamella need not cut precisely the same volume, correlations should allow for section position.

In high-angle annular dark-field imaging scanning transmission electron microscopy, electrons scattered to large angles give predominantly incoherent mass–thickness and atomic-number contrast. For comparable thickness, gold is much brighter than nickel–phosphorus because its atomic number is much larger. carbon in the protective cap scatters weakly, whereas its tungsten component scatters strongly. The cap is not a homogeneous low-atomic-number reference.

The gold layer follows a curved, locally distorted interface. The dark central opening in the overview is consistent with a crack, void or locally missing/thinned foil: little material along the beam path gives little high-angle scattering. The granular and columnar variations beneath the gold indicate nanoscale heterogeneity in the affected NiP${}_y$ region. Differences in thickness, density, porosity and composition can all contribute; diffraction/channeling effects are reduced in high-angle annular dark-field imaging but not eliminated in every geometry.

A black region is therefore evidence of low projected scattering mass, not by itself the identity of a chemical phase. In particular, a single high-angle annular dark-field imaging image does not distinguish a pre-existing void from material lost during specimen preparation.

Atomic-number contrast can explain why the gold-rich regions are bright and why the phosphorus-rich NiP${}_y$ layer should be somewhat darker than the other nickel–phosphorus layers. However, the calculated alloy yields differ only modestly: the NiP${}_y$ and NiP${}_z$ yields differ by about $5.5\%$ relative to NiP${}_z$. Composition-only backscattering does not explain all of the strong local edge and defect contrast.

An Everhart–Thornley detector normally collects secondary electrons, not a pure backscattered-electron signal. Secondary-electron escape and collection depend strongly on local slope and edge geometry. Differential polishing, relief at interfaces, a crack or cavity, surface oxidation and local charging can therefore alter brightness without the corresponding change in bulk atomic number. backscattered electrons can also generate secondary electrons elsewhere. Crystallographic channeling and orientation can contribute additional contrast. The observed dark and bright areas should therefore be correlated with topography and composition rather than assigned a phase from intensity alone.

Use the supplied polynomial as an effective-atomic-number approximation for the alloys. Interpreting each quoted phosphorus number as an atomic fraction $x_P=N_P/(N_P+N_{\mathrm{Ni}})$,The gold reference yield is $\eta (79)=0.486996$. Substitution gives:

The ordering is gold brightest, then copper, NiP${}_z$, NiP${}_x$ and NiP${}_y$. The phosphorus-rich layer has the lowest effective atomic number.

There is a wording ambiguity in “atomic fraction of P relative to Ni.” If those numbers instead mean $r=N_P/N_{\mathrm{Ni}}$, first convert $x_P=r/(1+r)$, giving $\bar{Z}=(28+15r)/(1+r)$. The three alloy contrasts then become $0.4243$, $0.4361$, $0.4129$, respectively. The qualitative ordering is unchanged. Both calculations explicitly use $\eta (\bar{Z})$; this simple alloy approximation is not a full electron-transport simulation.

The main characteristic peaks identify nickel and phosphorus: the spectrum has a strong Ni $K\alpha$ peak near $7.48\mathrm{keV}$, the Ni $L$ region near $0.85\mathrm{keV}$ and P $K\alpha$ near $2.01\mathrm{keV}$. Weaker associated lines, including Ni $K\beta$ near $8.26\mathrm{keV}$, can accompany them. The continuous background is bremsstrahlung from decelerated electrons.

Small carbon and oxygen signals at low energy can arise from contamination, surface oxide or preparation materials; a copper contribution can arise from the adjacent substrate within the finite interaction volume. The Cu $L$ region lies close to Ni $L$, so overlap is particularly troublesome at low energy. A weak Cu $K\alpha$ contribution near $8.04\mathrm{keV}$ is better separated, though still close to Ni $K\beta$. At $30\mathrm{kV}$ the beam can excite these K lines.

Peak height is not an atomic fraction: ionization cross-sections, fluorescence yields, absorption, detector response, background and line overlap require correction. The large nickel peak therefore supports the nickel-rich assignment but does not directly give the nickel-to-phosphorus atomic ratio.

Treat the film as a parallel-plate capacitor, initially compensated and then isolated electrically. Its capacitance and temperature-induced electric polarization charge areThe corresponding ideal open-circuit signal, with the electrode polarity defined consistently with this charge convention, isArea cancels because both charge and capacitance are proportional to it. Substitution givesThe voltage magnitude is approximately $0.99\mathrm{V}$; interchanging the voltmeter leads reverses its sign. This is an ideal capacitive result, before leakage, mobile-charge screening or loading by the measurement circuit reduces the signal.

A pyroelectric material has a spontaneous electric polarization that changes with temperature. electrodes collect the resulting change in compensating charge. For a uniform element,Consequently temperature variation in time, rather than a steady temperature difference alone, drives a pyroelectric generator. A cyclic thermal input and a suitable electrical circuit are needed for repeated energy extraction.

The primary pyroelectric effect is the change of electric polarization at fixed strain. The secondary pyroelectric effect arises because thermal expansion strains a piezoelectric crystal and thereby changes its electric polarization. In component notation its contribution iswith piezoelectric coefficients $e_{ij}$ and thermal-expansion coefficients ${\alpha }_j$. Choosing orientation, mechanical constraint and substrate expansion so that the secondary contribution reinforces the primary one can increase the response; the signs can instead oppose one another.

An array of slender nanowires can expand more freely than a film clamped to a substrate and can exchange heat rapidly because of its high surface-to-volume ratio. Reduced clamping can recover a secondary response suppressed in the film. Faster thermal cycling can also increase electric current through $dT/dt$. This is a geometrical opportunity rather than a universal increase of the intrinsic coefficient: screening, leakage, orientation and the actual thermal excursion must be compared. ZnO nanowire generators provide an experimental realization of pyroelectric energy conversion.^[ref]

Use electron lenses and a digitally scanned, blanked electron beam; no physical mask is required for direct writing. Electromagnetic lenses focus the charged-particle beam, deflectors place it, and the pattern generator controls position and dose. Electrostatic elements can also form part of electron optics, but these are not refractive glass lenses.

The extreme ultraviolet mask mentioned in the problem is the object being manufactured by this maskless write process, rather than a mask placed in the electron path.

Use multilayer reflective optics and a reflective patterned mask. Near the usual extreme ultraviolet wavelength of 13.5 nm, ordinary lenses and thick transmissive masks absorb too strongly. Multilayer mirrors focus and project the image, while an absorber pattern on a multilayer-coated mask defines the exposed regions.

The optical path operates in vacuum to avoid absorption by air. The key distinction is reflective mask projection, rather than a transparent chromium-on-glass mask or a scanned electron probe.

A transmissive mask is placed in contact with the resist, or a small distance above it for proximity printing. Chromium-patterned glass or quartz is a typical mask. Illumination is normally collimated ultraviolet light, with refractive illumination optics used to prepare the beam.

There is no projection objective imaging a reduced mask pattern onto the resist: the mask shadows the resist approximately one-to-one. The finite gap in proximity printing introduces diffraction and limits edge sharpness; contact printing reduces that gap at the cost of mask wear and contamination risk.

At fixed spectrum and temperature, photocurrent is approximately proportional to irradiance, so the magnitude of short-circuit current increases nearly linearly. In the ideal model,so open-circuit voltage rises only logarithmically with irradiance. More incident optical power generally raises the maximum electrical power, within the device's thermal and resistive limits.

Increasing temperature strongly increases the dark saturation electric current. In silicon this normally reduces open-circuit voltage and maximum power, despite a small increase in short-circuit current associated with the temperature dependence of absorption and band gap. The thermal-voltage factor alone is insufficient to predict the sign; the temperature dependence of $I_0$ matters.

maximum power point tracking adjusts the load seen by the cell as irradiance and temperature change. A controlled DC–DC converter can transform the external load so that operation stays near the changing maximum of $-VI$, instead of at the generally suboptimal intersection with a fixed load. It matches operating conditions and cannot generate additional energy beyond the photovoltaic output.

Absorbed photons with energy at least the band gap generate electron–hole pairs. The built-in field of the p-n junction separates carriers generated in or reaching the depletion region; minority carriers generated nearby can diffuse into that collection region. Selective contacts carry electrons and holes into an external circuit before they recombine.

Define positive electric current into the positive-voltage terminal. In the ideal illuminated-diode model,The dark curve has $I_{\mathrm{ph}}=0$; illumination shifts it downward. At short circuit $I\simeq -I_{\mathrm{ph}}$; at open circuit $I=0$ and $V=V_{\mathrm{oc}}$. Between them the illuminated cell lies in quadrant IV and supplies power $P_{\mathrm{out}}=-VI>0$. The maximum power point maximizes the area of the rectangle with sides $V$ and $-I$:It is neither the open-circuit point nor the short-circuit point, both of which supply zero power.

Increase the electrochemically accessible area and reduce transport resistance rather than merely forcing more electric current through the same thick electrode. A thinner, porous composite distributed over a larger area, a conductive-carbon network, good electrolyte wetting and short ionic paths reduce local current density and electric polarization. Adequate battery separator conductivity and low-resistance collectors also help. Parallel cells can distribute total electric current while retaining the total active-material inventory.

The objective is to preserve usable capacity at a higher rate by avoiding premature voltage cutoff and inaccessible active material. It does not create more charge: a fixed inventory with $175.2\mathrm{Ah}$ delivers a greater electric current for a proportionally shorter time. Maintaining the original two-year duration at greater electric current requires proportionally more capacity.

If the voltage were held at $4.57\mathrm{V}$ for the entire ideal discharge, thenand the electrical power would beThese are constant-voltage estimates, not a determination of the actual energy from the fresh-cell open-circuit voltage. Under load the voltage depends on state of discharge, electric polarization and internal resistance. The physical result is $E=I{\int }_0^{t_f}{V}_{\mathrm{load}}(t)dt$, and $P(t)=I{V}_{\mathrm{load}}(t)$. The supplied single open-circuit value does not specify that voltage curve; practical delivered energy will generally be lower than the simple estimate.

This is a primary cell and should not be treated as rechargeable. Discharge converts the fluorinated-carbon electrode into carbon and lithium fluoride. It does not simply insert lithium into a host that can be reversibly deintercalated. Reversing electric current does not cleanly reconstruct the original distributed C–F bonding and electrode microstructure.

Insulating LiF, loss of the original reaction interfaces and unwanted electrolyte reactions obstruct reversibility. Replating lithium can also produce an irregular metallic deposit and internal shorting. A thermodynamically possible formal reverse reaction is therefore not evidence of a practical rechargeable cell.

For the $x=1$ reaction there is one mole of transferred electrons per mole of reaction. Treating the supplied fresh-cell open-circuit voltage as the standard equilibrium cell potential givesA fresh-cell voltage alone would not normally establish standard conditions or equilibrium. The result above is the formal standard-free-energy estimate under the interpretation required to use the given datum; a metastable open-circuit voltage should not be mistaken for an independently measured standard thermodynamic potential.

The reaction consumes one mole of CF for each mole of electrons. Using $M_{\mathrm{CF}}=12.01+19.00=31.01\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$,This is active CF alone for the same single-cell-equivalent assumption, not the full positive-electrode or pack mass. Conductive additive, binder, electrolyte, battery separator, collectors and casing add mass, and incomplete utilization increases the required CF.