MPhil in micro- and nanotechnology enterprise course of the University of Cambridge

Moiré fringes arise when two overlapping periodic structures contribute closely spaced reciprocal lattice vectors to the transmission electron microscopy image. Their relative phase varies slowly across the image, producing a coarse modulation with a period much larger than either atomic spacing. The structures may have different lattice spacings, a small relative rotation, or both. The modulation is an interference or beat phenomenon; its spacing is not itself a new atomic-plane spacing. Its orientation is perpendicular to the difference vector of the two contributing projected reciprocal-lattice vectors.

Let the relevant projected reciprocal lattice vectors have magnitudes $g_1=1/d_1$ and $g_2=1/d_2$, with angle $\theta$ between them. Subtracting their phases gives the slow spatial modulation $2\pi ({\mathbf{g}}_1-{\mathbf{g}}_2)\cdot \mathbf{r}$. The moiré fringe spacing formula is thereforeFor parallel planes, $\theta =0$ and $D=d_1{d}_2/|d_1-d_2|$. For equal spacings, $D=d/[2|\sin (\theta /2)|]\simeq d/|\theta |$ at a small angle measured in radians. The apparent divergence as both mismatch and rotation vanish means that there is no finite beat period; it does not predict an infinite number of visible fringes.

For each spacing pair, the largest geometrical period occurs with parallel projected reciprocal vectors. The closest pair is $d_{\mathrm{Cu}}=0.208\mathrm{nm}$ and $d_{\mathrm{substrate}}=0.212\mathrm{nm}$, givingHowever, the crystal is only $10\mathrm{nm}$ across. It contains at most $10/11.024\simeq 0.91$ of this period, so the largest formal period cannot appear as a repeated fringe train inside one crystal. It can instead give a broad variation of contrast. A period of order the particle diameter is the largest directly sampled scale, and even that is poorly constrained by one particle.

The distinction matters if “see” means a complete repeat. Of the exactly parallel spacing pairs, the largest other period is approximately $2.09\mathrm{nm}$ from the $0.208$ and $0.231\mathrm{nm}$ pair. If relative rotation is continuously variable, the closest pair can instead be rotated slightly to shorten its period below $10\mathrm{nm}$, so $2.09\mathrm{nm}$ is not a universal maximum visible period for arbitrary orientations.

A coarse fringe in a high-resolution transmission electron microscopy image need not directly identify the lattice spacing of a new phase. Check whether overlapping crystals, a particle and its substrate, or differently oriented domains can produce the corresponding moiré fringe. Compare the underlying reciprocal-space peaks and their difference, use the particle boundary to constrain how many periods are actually sampled, and examine neighbouring or differently oriented regions. For the closest pair here, fitting a periodicity from less than one complete period is particularly unreliable. Distinguishing lattice contrast from a beat envelope prevents misidentifying a phase or over-interpreting local strain.

With suitable atomic force microscopy feedback gains, the trace follows the accessible surface while maintaining the chosen oscillation-amplitude setpoint. The measured trench is narrower than the accessible opening because the finite tip encounters an edge before its apex reaches that edge's true lateral position. For an ideal tip flank angle $\alpha =15^{\circ }$ relative to the tip axis and height change $h=1.3\mu \mathrm{m}$, the geometrical setback is $h\tan \alpha \simeq 0.35\mu \mathrm{m}$ per side.

The conventional tapered tip cannot recover the underside of the overhang, even when feedback is perfect: the first contact with the upper edge or shank limits access. This geometrical envelope must be distinguished from errors caused by feedback dynamics. The stated tip height is sufficient for the vertical range; it does not remove the lateral-access problem.

With gains too low for the scan speed, the vertical response lags the surface. On entering the depression during the left-to-right trace, the tip descends too slowly and the recorded edge rounds or extends into the trench. On climbing out, the tip can approach or contact the rising feature before the controller lifts it sufficiently, again distorting the edge. Thus the error depends on scan direction and can differ between trace and retrace. Slower scanning can reduce this bandwidth limitation, but it does not correct the geometrical inability to probe an overhang.

Excessive feedback gain can make the closed loop underdamped or unstable. Edge transitions then produce overshoot, ringing or oscillatory streaks in the recorded height. The apparent structure is a controller response rather than a real series of surface ridges. The exact amplitude and frequency depend on the actuator, cantilever, loop delay and controller settings; without those data one can sketch the qualitative ringing but cannot predict a unique quantitative trace.

In tapping-mode atomic force microscopy, the cantilever is driven near a resonance and its oscillation amplitude is monitored. Tip-surface interaction changes that amplitude. A controller compares it with a chosen setpoint and moves the vertical piezoelectric actuator to reduce the error. The recorded actuator displacement supplies the topography channel. A smaller amplitude during approach commonly triggers withdrawal and an increased amplitude during separation triggers approach, with the actual feedback sign set by the instrument's operating convention. Correct tracking requires enough response bandwidth without destabilizing the loop.

A conventional tapping tip tapers toward its apex, so its shank contacts an overhanging feature before its apex can probe underneath it. Critical-dimension atomic force microscopy instead uses a calibrated flared or laterally extended tip, with a relatively narrow neck and side-sensitive control. The lateral extension can contact a reentrant sidewall while the neck clears the upper edge. The measured profile still includes the tip's finite shape and must be interpreted with a tip calibration; changing the tip does not automatically eliminate all convolution errors.^[ref]

Lateral oscillation or dithering is added to the vertical oscillation. It provides a tip-sidewall interaction signal that can drive lateral feedback while the vertical channel maintains height control. This is how a suitable flared tip can track steep or reentrant walls. Treating the additional signal as merely a larger vertical tapping amplitude would not supply the required sidewall sensing.^[ref]

An attached particle changes the effective tip shape, potentially creating a second contact apex. The image can then show duplicated or broadened copies of surface features, shifted edge positions and altered apparent roughness: a double-tip artefact or more general AFM tip-convolution artefact. Detachment can produce a sudden line-to-line change in that image kernel, so a region may abruptly recover a sharper profile. A change that follows the probe state or scan history should not be interpreted as a real reconstruction of the semiconductor surface.

For a positive photoresist, let $D_r$ be the largest dose retaining the nominal film and $D_c$ the clearing dose. With the conventional photoresist contrast definition,For a sinusoidal aerial image, the bright-to-dark dose ratio is $(1+C)/(1-C)$, where $C$ is the Michelson contrast. A dose window that clears bright regions while retaining dark regions requiresThis assumes a fully modulated input pattern and that the plotted modulation transfer function gives the aerial-image contrast. It is a dose-window criterion, not a statement that the resist creates optical information absent from the image.^[ref]

The two thresholds are approximatelyReading their intersections with the supplied curve gives, to graphical accuracy,for the lower- and higher-contrast resists respectively. These are the results independent of the dimensional frequency convention. Their minimum full periods are $P=1/\nu$, and equal line/space widths are half those periods:An ArF excimer laser uses $\lambda \simeq 193\mathrm{nm}$. A numerical length requires specifying what the caption's “Rayleigh limit” means. Taking it literally as the reciprocal of the Rayleigh criterion point separation givesIf instead the graph uses the common incoherent-cutoff normalization ${\nu }_0=2\mathrm{NA}/\lambda$, the widths are $302\mathrm{nm}$ and $201\mathrm{nm}$, with periods twice those values. The caption does not explicitly provide an equation for ${\nu }_0$ or define whether “feature size” means period or half-pitch, so these conventions must not be silently mixed. The higher-contrast resist resolves the higher normalized frequency in either convention.

An on-axis point illuminator increases spatial coherence. It is not a point object, and it does not remove diffraction. For an ideal aberration-free pupil, coherent imaging is linear in field amplitude and has cutoffFor a real amplitude grating $U(x)=a[1+m\cos (2\pi \nu x)]$, with $0\le m\le 1$ and all three field orders inside this pupil, the intensity contrast is $C=2m/(1+m^2)$. Flat coherent field transfer preserves this contrast; weak input modulation does not itself meet a high resist contrast threshold. Assume a sufficiently high-contrast amplitude mask: for example, $m=1$ gives $C=1$, exceeding both resist thresholds. Under this assumption, both resists have the same limiting equal-line/space widthThis is an approach to the cutoff from below; finite dose latitude, aberrations and a real binary mask can make usable resolution worse. A general coherent intensity image cannot be obtained by applying an incoherent intensity MTF unchanged: $I=|h\ast U{|}^2$, rather than $I=|h{|}^2\ast |U{|}^2$.^[ref]

With ${\nu }_0=2\mathrm{NA}/\lambda$, this coherent cutoff is $0.5{\nu }_0$: the low-contrast resist improves from roughly $302$ to $241\mathrm{nm}$, while the high-contrast resist worsens from roughly $201$ to $241\mathrm{nm}$. Coherence improves contrast within its passband but reduces the ultimate bandwidth relative to incoherent illumination.

With the literal Rayleigh-spacing normalization ${\nu }_0=1/R_R$, the same physical cutoff is instead $0.61{\nu }_0$, not $0.5{\nu }_0$. The corresponding widths from the preceding part would improve from roughly $368$ and $245\mathrm{nm}$ toward $241\mathrm{nm}$. The cutoff in physical units is unambiguous under the stated ideal on-axis model; the claimed direction and size of a change inferred from the plotted normalized axis depend on its definition. Off-axis illumination, partial coherence and arbitrary phase objects require a fuller imaging model.

Depth of focus is the axial tolerance over which the projected pattern remains acceptable. Wafer topography, resist thickness, wafer tilt and focus-setting errors can move part of the film outside that range, reducing contrast and changing printed linewidth. Increasing numerical aperture can improve lateral resolution while reducing this axial process window.

Using the supplied coefficient in the conventional expression,This is the range assigned to DOF by that convention. Whether an instrument reports a full allowable interval or a one-sided defocus tolerance must be stated separately; an additional factor of two cannot be inferred from the numerical coefficient alone.

A simple chemical vapor deposition model separates transport through a gas boundary layer, with coefficient $h_m$, from surface reaction, with coefficient $k_s$:For $k_s\gg h_m$, growth is mass-transfer-limited deposition. A typical cold-wall, flowing reactor heats the substrate strongly while keeping most chamber walls cooler. A shaped inlet, controlled flow and tilted or rotating susceptor help control boundary-layer thickness and precursor depletion. The essential design problem is delivering a similar flux everywhere; heating a surface still further gives little benefit once delivery limits growth.

For $k_s\ll h_m$, growth is reaction-limited deposition. A hot-wall, low-pressure batch tube can hold many wafers in a nearly uniform-temperature zone. Faster gas transport makes surface concentrations more uniform, while slow chemistry reduces consumption before precursors reach downstream surfaces. Temperature uniformity is particularly important because surface rates can depend strongly on temperature.

These are illustrative architectures, not a rule that wall type alone determines the regime. Temperature, pressure, flow and precursor chemistry jointly set $k_s/h_m$.

At fixed reactant partial pressures and temperature, their ideal-gas bulk concentrations $C_i=p_i/(RT)$ remain approximately fixed. Lowering total pressure means removing diluent rather than automatically lowering the reactant concentration.

In the continuum molecular-diffusion regime, gas diffusivities scale approximately as $D\propto 1/P_{\mathrm{total}}$. Delivery through a comparable boundary layer is therefore faster, increasing $h_m$ relative to $k_s$. The system tends toward reaction-limited operation, where concentration differences between substrate locations are smaller. This commonly improves thickness uniformity and access to recessed surfaces.

The qualification is important: changing pressure can also change flow velocity and the boundary layer, gas-phase chemistry and precursor depletion. In narrow structures at low pressure, Knudsen transport limits the simple $1/P$ improvement. Improved transport does not correct a large substrate-temperature gradient in a strongly temperature-sensitive reaction-limited process.

In evaporative deposition, atoms travel mainly along straight trajectories from a compact source. For an ideal cosine-emitting source below a parallel wafer, a point at lateral radius $r$ and source separation $H$ receives approximatelyConsequently $F(r)/F(0)=[1+(r/H{)}^2{]}^{-2}$. Increasing $H$ makes arrival angles and distances more similar across a fixed wafer, improving uniformity. But the central flux falls as $H^{-2}$ for a fixed source output, so the deposition rate decreases and less evaporated material is collected.

Rotation averages azimuthal variations, and source shaping or multiple sources can help, but simple rotation does not remove a radial flux gradient. Raising source output can partly compensate at the cost of source heating, consumption and possible material limitations. The trade-off follows from geometry rather than an intrinsic prohibition on simultaneously optimizing a more elaborate system.

Zero step coverage means that a sidewall or hidden surface receives essentially no film even though a horizontal reference surface is coated. Deposition shadowing occurs when an upper edge intercepts trajectories that would otherwise reach a lower region. A directional high-vacuum evaporant flux can therefore coat a feature top while leaving vertical or reentrant walls uncoated.

Sputtering generally releases material from an extended target with a broad angular distribution; gas collisions can further redistribute arrival directions. More oblique trajectories can reach sidewalls, so the extreme zero-coverage behavior of an ideal collimated evaporant beam is reduced.

The absolute claim that these effects never occur in sputtering is too strong. Low-pressure directional sputtering and high-aspect-ratio or reentrant features can still exhibit shadowing and poor coverage. Broader incidence improves access; it does not make a physical deposition process universally conformal.

The oxygen atom has $1s^{2}2s^{2}2p^4$. Each oxygen contributes six valence electrons, so the molecular diagram contains twelve. Taking the internuclear direction as $z$, the relevant ordering for oxygen isThe valence occupation isThe final two electrons occupy the degenerate antibonding orbitals singly with parallel spin, following Hund's rules. Thus oxygen has two unpaired electrons and is paramagnetic. The $1s$ core orbitals are deliberately omitted from the valence-only molecular orbital diagram.

For oxygen, eight valence electrons occupy bonding orbitals and four occupy antibonding orbitals. Its bond order isThe additional electron in superoxide enters a ${\pi }_g^{\ast }(2p)$ antibonding orbital, givingReduced bond order weakens and lengthens the bond, consistent with the longer bond in superoxide. The diagram explains the direction of the change; it does not predict the two numerical bond lengths without a quantitative electronic-structure calculation.

The stabilizing outer groups should be compatible with the solvent, while the thiol-derived sulfur anchors the ligand shell to the gold nanoparticle.

These choices concern colloidal stability, not merely whether a free ligand dissolves. Coverage, chain packing and particle separation also matter. In the aqueous cases, high electrolyte concentrations can screen electrostatic repulsion, so ionization alone does not guarantee stability at every acid or base concentration.

The expected order from most to least acidic isHI is stronger than HCl because the H–I bond is weaker and the larger iodide ion accommodates negative charge well. In water both strong acids are substantially leveled to hydronium; their intrinsic ordering should not be mistaken for a large difference in the acidity of equal-concentration fully dissociated aqueous solutions.

Removing the marked proton alpha to the nitro group in (3) gives a resonance-stabilized nitronate, with charge distributed onto oxygen. It is far more favorable than forming the unactivated carbon anions in (1) or (2).

The marked aromatic C–H in (1) is more acidic than the alkane C–H in (2). The resulting aryl carbon lone pair has greater s character than an alkyl carbanion's, and chlorine also exerts an inductive effect. The aryl anion's lone pair is not simply delocalized through the aromatic pi system in the same way as a phenoxide ion. The specified proton positions are essential: this is not an ordering of arbitrary hydrogens on the molecules.

The left-hand open quinoid dianion is pink/purple; the right-hand closed lactone is colorless. In the colored form, a longer conjugated electronic system extends through the quinoid framework. The resulting lower-energy electronic transitions can absorb visible light, producing the observed complementary color.

The closed lactone contains a tetrahedral central carbon that interrupts conjugation between the aromatic fragments. Its remaining electronic transitions are mainly at higher energy, so the molecule does not strongly absorb visible wavelengths. It still absorbs ultraviolet light: colorless does not mean absence of electronic transitions.

The explanation concerns the two drawn forms of phenolphthalein. It does not assert that a single colored form remains dominant at arbitrarily high pH; additional equilibria can alter the spectrum outside the usual indicator range.

A reference electrode should provide a stable, reproducible potential from a well-defined reversible equilibrium, with fixed relevant activities. It should pass negligible measuring current, resist contamination and drift, and avoid changing the sulfate sample through incompatible ions or reactions.

Silver is suitable when coupled to a sparingly soluble silver salt and a controlled filling electrolyte; a silver sulfate reference electrode avoids introducing chloride into a sulfate system. Mercury is also electrochemically suitable in a mercury/mercurous-sulfate reference system, although its toxicity and handling requirements make silver attractive where practical.

Sodium is unsuitable because it reacts with water rather than maintaining a quiet metal/ion reference equilibrium. Calcium and strontium are likewise too reactive in water. Magnesium is not a dependable reference simply because it sometimes reacts slowly: corrosion, oxide/hydroxide films and mixed potentials make its open-circuit potential dependent on surface history and solution conditions. A relatively inert-looking surface is not equivalent to a reproducible reversible electrode.

Even a suitable reference is not just an arbitrary piece of metal immersed in the sample. The metal, equilibrium salt, controlled electrolyte and liquid junction together define the reference system.

Use a silver wire or strip in contact with excess solid silver sulfate, immersed in a sulfate filling solution of known, stable activity. A porous frit connects the filling solution ionically to the sample while limiting bulk mixing. The reference housing should maintain the salt/electrolyte composition rather than letting the sample directly determine it.

Connect the unknown working electrode to the positive input and the silver reference to the negative input of a high-input-impedance voltmeter. The frit or sulfate-compatible salt bridge completes the ionic circuit. At negligible measuring current,A stable, small junction contribution is desirable. The reference electrode should not carry the counterelectrode current in a driven experiment: a separate counterelectrode is used when current is passed.

The equilibrium written in the reduction direction isWith pure-solid activities set to one, the Nernst equation givesMaintaining sulfate activity fixes the reference potential; protonation to bisulfate in strongly acidic filling solutions must be included in specifying that activity.

Calibrate against, or use a reliable tabulated potential relative to, the standard hydrogen electrode for the same filling solution and temperature. With the voltmeter sign specified above and a corrected or negligible junction potential,There is no universal numerical offset for every silver reference: silver/silver-chloride, silver/silver-sulfate and different sulfate filling solutions define different potentials.

At fixed discharge current, delivered voltage can be represented aswhere $Q$ is discharged charge and the terms denote distinct physical losses. A typical trace has an initial drop from open circuit, an approximately flat useful region and a final decline toward cutoff. Its exact shape depends on the cell chemistry and current; not every battery has an equally flat plateau.

Four distinguishable contributions are:

Terminology sometimes groups solid-state transport or phase-change effects differently. The important distinction is the mechanism, not counting the same diffusion loss under two names. A falling equilibrium voltage as composition changes is also not, by itself, polarization.

The hydrogen fuel cell is the more likely high-power choice at low temperature, for otherwise comparable electrodes, oxidant supply and device design. Similar equilibrium oxidation potentials imply similar thermodynamic voltage opportunities; they do not imply similar current densities.

Hydrogen oxidation on an appropriate catalyst is relatively facile. Ammonia oxidation requires multiple bond-breaking and nitrogen-coupling steps; adsorbed intermediates can occupy catalytic sites and inhibit continued reaction. A larger anodic activation overpotential and slower turnover reduce the useful current and operating voltage of a low-temperature ammonia cell.

Since areal power is $P/A=jV(j)$, a cell retaining substantial voltage at a larger current density can deliver more power even when its equilibrium voltage is similar. Ammonia's favorable storage characteristics are a separate system-level consideration; a comparison of power cannot be made by counting the electrons per fuel molecule alone. This is a kinetic expectation, not a universal numerical ranking independent of catalysts, temperature and transport.

An incident SEM probe undergoes elastic deflections by atomic potentials and inelastic interactions that excite or ionize the specimen. Repeated scattering generates an interaction volume wider and deeper than the incident probe. The measured resolution depends both on where a signal is generated and on whether it can escape.

Transmitted electrons from a sufficiently thin specimen can instead support scanning transmission electron microscopy. The values above are orders of magnitude, not intrinsic constants of the signal: beam energy, atomic number, specimen thickness, probe size and detector geometry all matter. The spatial origin explains why a fine topographic SEM image does not guarantee equally fine X-ray mapping.

Prepare a dilute dispersion of separated nanoparticles on an electron-transparent support, for example a thin carbon film on an electron-microscopy grid. A sparse deposited aliquot can be dried and the grid mounted over an open transmission aperture in the holder. The beam path must not be blocked by a bulk substrate.

Dilution and a thin, clean support reduce overlap, multiple scattering and background. Remove excess soluble residue where compatible with the particle surface chemistry, and ensure the support and mounting provide adequate electrical conduction. The desired object is an isolated, vacuum-compatible particle layer, rather than a thick dried droplet or an opaque slab.

Use a sufficiently high SEM acceleration voltage to transmit through the particle/support combination and provide useful diffracted intensity; operation near the high-voltage end of the SEM range is a reasonable starting point. The supplied wavelength is used directly for the camera-length calculation, rather than assigning a precise voltage from an approximate wavelength relation.

Choose the smallest beam current consistent with usable counting statistics, because the stated source-size contribution obeysHigher gun brightness permits more current at the same small probe. A relatively short working distance can give a larger convergence semiangle and reduce this term. In the specified fixed lens-to-detector geometry, shortening working distance also increases the specimen-to-detector camera length, reducing the detector's collection angles.

The objective aperture should be optimized, not made arbitrarily large: increasing $\alpha$ reduces the source-size and diffraction contributions, but spherical/chromatic aberrations and angular broadening eventually worsen the probe or diffraction selectivity. A suitable aperture balances those effects while keeping the chosen diffraction rings within the annulus. Adjust specimen height to meet that angular condition, focus and align at the operating voltage, and control drift and contamination.

Low convergence favors angular discrimination of diffraction, whereas high convergence can favor probe size. The optimum therefore depends on whether spatial detail or sharply selected Bragg diffraction contrast is the limiting requirement.

For a face-centered cubic lattice, allowed reflections have indices all odd or all even. The first two are $\{111\}$ and $\{200\}$, withFor first-order Bragg diffraction, $2d\sin \theta =\lambda$. The detector intercepts the beam at the full scattering angle $2\theta$, givingThe inner detector radius supplies the minimum length for each ring:Thus both rings reach the annulus when $L\gtrsim 90.2\mathrm{mm}$. At this minimum the 200 ring is at roughly $3.12\mathrm{mm}$, well inside the $10\mathrm{mm}$ outer radius. Both remain within the detector for approximatelyEquality at the inner edge gives vanishing acceptance for an ideal infinitely narrow ring, so practical operation requires a small margin. The calculation concerns ring positions; individual nanoparticle orientation and the finite probe convergence also affect observed diffraction contrast. Using the Bragg angle instead of the full scattering angle would introduce an erroneous factor of about two.

Molecular beam epitaxy is a suitable research-scale choice. Independently controlled elemental beams and shutters allow abrupt composition changes, controlled silicon donor incorporation and thin spacer layers. Growth can proceed sequentially from the GaAs substrate through the undoped GaAs, undoped AlGaAs spacer, doped AlGaAs supply layer and highly doped GaAs cap.

A clean crystalline surface and controlled substrate temperature support epitaxial interfaces; separating the donor layer from the channel is modulation doping. Metalorganic vapor-phase epitaxy can also grow such structures, but MBE's controllable research-scale layer sequence is a strong match to the stated task. Merely depositing the right total elemental amounts would not guarantee the required crystallinity and interface abruptness.

A suitable sequence isFirst pattern the source/drain resist, then deposit and lift off the corresponding metal. Anneal these contacts to produce the low-resistance source/drain interfaces. Remove the exposed cap layer before gate lithography, leaving the cap beneath the contact metal; this uses the contact pads as an etch mask, with suitable protection where required. Finally define and deposit the gate onto exposed AlGaAs and lift off.

The key dependencies are that source/drain metal lands on the n+ cap, the gate lands on AlGaAs after cap removal, and the contact anneal precedes formation of the sensitive Schottky gate. A gate-recess variant can put gate lithography before the local cap etch if that resist is deliberately used as its mask, but it must additionally specify how unwanted conducting cap elsewhere is removed or isolated. The sequence above directly matches the cap remaining only beneath the source/drain contacts in the diagram.

Choose process B, the citric-acid/peroxide wet etch. Its GaAs-to-AlGaAs etch selectivity is $200/1=200$, giving strong protection of the underlying barrier and a controllable removal rate for the thin cap.

For comparison, A has selectivity one and therefore no useful etch stop. It is also extremely fast: a nominal $20\mathrm{nm}$ GaAs layer would be removed in only $0.048\mathrm{s}$. C has selectivity $1000/20=50$, useful but inferior to B, and clears the same cap in about $1.2\mathrm{s}$. D has selectivity four, clears the cap in about $0.060\mathrm{s}$ and additionally risks plasma-induced surface damage or altered interface properties.

B clears the nominal cap in about $6\mathrm{s}$. Its slower underlying etch permits a more forgiving endpoint or modest overetch, although actual rates must be checked for the relevant composition and conditions. Wet-etch lateral undercut and contact-metal compatibility still matter; selectivity alone does not make every mask geometry acceptable.

Higher donor concentration moves the semiconductor Fermi level toward the conduction band, reducing the semiconductor work function ${\Phi }_s=\chi +(E_c-E_F)$ when these quantities are expressed as energies. Equilibration with the metal aligns electrochemical potentials and creates band bending.

For an ideal n-type Schottky interface the barrier energy ${\Phi }_{Bn}={\Phi }_m-\chi$ is not automatically reduced merely by raising doping. The decisive change is the narrower depletion region:Large $N_D$ allows electrons to tunnel through the thin barrier, reducing the contact resistance and promoting an approximately Ohmic contact. Contact annealing can further modify the local interface and doping. This allows low-resistance source/drain injection while preserving a more rectifying gate contact; real interface-state pinning can modify the ideal work-function picture.

Use equal-width rectangular contact windows in a row with several different edge-to-edge spacings. For positive-resist lift-off, the future metal pads correspond to clear windows in an otherwise chrome-covered mask: exposure removes resist there, and the unexposed background retains resist beneath unwanted metal.

For ordinary ohmic transmission line contact measurement, a conducting strip or isolated mesa of width $W$ connects adjacent pads. Measure several spacings $d$ so thatThe intercept separates two contact contributions from the sheet-resistance slope. Large enough pad length relative to the transfer length is needed for the simplest contact-resistivity extraction.

Prepare separate arrays on the appropriate surfaces: annealed source/drain metal on the n+ cap, and gate metal on cap-removed AlGaAs. A Schottky gate is nonlinear, so its interface cannot be assigned an ohmic zero-bias contact resistivity merely by fitting the same straight line. Use bias-dependent current–voltage or differential-contact analysis, accounting for the two rectifying contacts.

Starting from the clean wafer, dehydrate it and use an appropriate adhesion treatment if required. Spin coat the positive resist to obtain a uniform film, then soft bake to remove solvent and stabilize handling. Align the mask and expose the clear pad windows. Develop away the exposed resist, rinse and dry, leaving openings at future metal locations.

Inspect the openings and clear residual resist gently if needed. Perform a compatible surface preparation immediately before metallization so that an unintended oxide or contaminant film does not dominate the contact. Deposit metal with a resist profile and film thickness that leave an accessible discontinuity at the resist edge; an undercut or suitable lift-off stack helps prevent continuous sidewall coating.

Dissolve the sacrificial resist and lift off metal above it, leaving the pads on the exposed semiconductor. Rinse, dry and inspect for residues or bridges. For source/drain test contacts, apply the intended contact anneal; for gate test contacts, preserve the intended Schottky interface. An aggressive final resist hard bake or a fully conformal bridging metal film can defeat lift-off, so these are not automatic extra steps.