Semiconductor devices sze solution manual

From the Fig. Therefore, the As content will be lost when the temperature is increased. Thus the composition of liquid GaAs always becomes gallium rich. We divide the wafer into four symmetrical parts for convenient dicing, and discard the perimeter parts of the wafer.

Usually the quality of the perimeter parts is the worst due to the edge effects. For close-packing arrange, there are 3 pie shaped sections in the equilateral triangle. The molecular weight is The x value is about 0. The time required to grow 0. For the field oxide with an original thickness 0. Another method is to use boron doped P-glass which will reflow at temperatures less than Moderately low temperatures are usually used for polysilicon deposition, and silane decomposition occurs at lower temperatures than that for chloride reactions.

In addition, silane is used for better coverage over amorphous materials such SiO 2. There are two reasons. One is to minimize the thermal budget of the wafer, reducing dopant diffusion and material degradation.

In addition, fewer gas phase reactions occur at lower temperatures, resulting in smoother and better adhering films. Another reason is that the polysilicon will have small grains. The finer grains are easier to mask and etch to give smooth and uniform edges. For TiSi2 : Advantage: low resistivity It can reduce native-oxide layers TiSi2 on the gate electrode is more resistant to high-field- induced hot-electron degradation.

Disadvantage: bridging effect occurs. With reference to Fig. The available exposure energy in an hour is 0. We can also develop new resists that provide lower k1 and higher k2 for better resolution and depth of focus. Therefore, a shaped beam can save time and increase throughput compared to a Gaussian beam. We can then use them to do alignment with e-beam radiation and obtain the signal from these marks for wafer alignment.

X-ray lithography is a proximity printing lithography. Its accuracy requirement is very high, therefore alignment is difficult. With a projection printing system is much more difficult to produce defect-free masks than it is with a reduction step-and-repeat system. The main reason is that X-rays cannot be focused by an optical lens. When it is through the reticle.

So we can not build a step-and-scan X-ray lithography system. As shown in the figure, the profile for each case is a segment of a circle with origin at the initial mask-film edge. As overetching proceeds the radius of curvature increases so that the profile tends to a vertical line. Using the data in Prob. If we protect the IC chip areas e. A three—step process is required for polysilicon gate etching.

Step 1 is a nonselective etch process that is used to remove any native oxide on the polysilicon surface. Step 2 is a high polysilicon etch rate process which etches polysilicon with an anisotropic etch profile.

Step 3 is a highly selective polysilicon to oxide process which usually has a low polysilicon etch rate. Traditional RIE generates low-density plasma cm-3 with high ion energy. Advantages of ECR and ICP are low etch damage, low microloading, low aspect-ratio dependent etching effect, and simple chemistry. The corrosion reaction requires the presence of moisture to proceed.

Therefore, the first line of defense in controlling corrosion is controlling humidity. Low humidity is essential,. Second is to remove as much chlorine as possible from the wafers before the wafers are exposed to air. Thus, Al-Cl bonds are replaced by Al-F bonds. Whereas Al- Cl bonds will react with ambient moisture and start the corrosion process , Al-F bonds are very stable and do not react.

Furthermore, fluorine will not catalyze any corrosion reactions. The process is called the ramping of a diffusion furnace. For low-concentration drive-in diffusion, the diffusion is given by Gaussian distribution. Intrinsic diffusion is for dopant concentration lower than the intrinsic carrier concentration ni at the diffusion temperature. Extrinsic diffusion is for dopant concentration higher than ni.

The total implanted dose is integrated from Eq. The projected range is nm see Fig. Therefore the neutralbasewidth is To improve a, we can makethe basewidth narrower.

In the figure, we can see when WlLo. In Problem 3, 1. Therefore, the collectorcurrentis directly proportionalto the minority carrier chargestoredin the base.

The mobility of an averageimpurity concentrationof e. The averagebaseresistivity pu is given by. Therefore" Rux to1 po. At low 1, , because of generation-recombination current, Fo Bo is not a constant.

At high I B, vEBincreases with l, , this in turn causes a reduction of lzr. The reduction of Vu, causes a wideningof the neutralbaseregion,thereforepo decreases. The following chart shows Bo as function of I B. Comparing the equations with Eq. In the collectorregion,. O FromProblem20, we have. The impurity concenhationof the nl region is t0racm For a breakdown voltage reverseblock vottageof V, we can choosea width suchthat punch-through occurs, i.

In the nl -p2 - n2 trarsistor,the basedrive currentrequiredto maintaincurrent conduction is. Thus, the condition for hrm-on of the thyristor is t s. From Pr o b5. I Performing Taylor'sexpansion on the 2nd termin Eq. JO'tTy The bandgap in degenerately dopedSi is aroundleV dueto bandgapnarrowingeffect. High manufacturing cost. C x3. T'e-qQBt1 tkr. The built-in potentialis. The saturation cunent densityis I t. Therefore, From Eq. The threshold voltageis Vr : Vni- Vo: 0.

The pinch-offvoltage is l. The pinch-offvoltage is r l r ' q NUr d l ' 28" l. By neglectingthe. LT The total voltage at breakdown across the diodeis. A" I 0-te x x x 5. However,at T" : K , 87Yo, i. For sameenergybut a width of 8 meV, we usethe samewell thicknessof 6. The resonant-tunneling currentis relatedto the integrated flux of electronswhoseenergyis in the rangewherethe transmission coefficientis large.

Therefore, the currentis proportionalto the width A,En,andsufficientlythin baniersarerequiredto achievea high currentdensity. For l": 0. Take the solution which is the only g fuo, practical givesl"s Therefore the laserwith To: 50 oC is worse for high-temperature operation.

Maximumpoweroutput: 1. The acceptor concentration for p : 0. We assume the volumeis a sphere, so the radiusof the sphere r is the average distance between two boron atoms. The segregation coefficient of boronin siliconis 0.

It is smallerthanunity, so the solubility of B in Si undersolid phaseis smallerthanthat of the melt. Therefore, the excess B atomswill be thrown-off into the melt, then the concentration of B in the melt will be increased. The tailend of the crystal is the last to solidify. Therefore,the concentration of B in the tail-end of grown crystalwill be higherthan that of seed-end. The reason is that the solubility in the melt is proportional to the temperature, and the temperature is higher in the centerpart than at the perimeter.

Therefore, the solubility is higher in the centerpart,causinga higher impurity concentration there. The segregation coefficientof Ga in Si is 8 x FromEq. We havefrom Eq. For the conventionally-doped silicon,the resistivity variesfrom C -cm to f -cm. The corresponding dopingconcentration variesfrom 2. From the Fig. Therefore, the As content will be lost when the temperatureis increased.

Thus the composition of liquid GaAsalwaysbecomes gallium rich. We divide the wafer into four symmetrical parts for convenient dicing, and discardthe perimeterpartsof the wafer. Usually the quality of the perimeter partsis the worst dueto the edgeeffects. For close-packing affange, there are 3 pie shapedsections in the equilateral triangle. The molecular weightis Therefore the anival rate is. The time required to grow 0. After a window is openedin the oxide for a second oxidation,the rate constants are B: 0.

If the initial oxide thicknessis 20 nm : 0. For the field oxide with an original thickness 0. Set : 3t, e1: ,area: 41 BST thickness : t, a Let :3t" e TazOs thickness : t, e2: 3. Thereforefor Tt : K. Another methodis to use boron doped P-glass which will reflow at temperatures lessthan Moderatelylow temperatures are usually used for polysilicon deposition,and silane decompositionoccurs at lower temperaturesthan that for chloride reactions.

In addition, silane is used for better coverageover amorphous materials suchSiO-,. There are two reasons. One is to minimize the thermal budget of the wafer, reducingdopant diffusion and material degradation. In addition, fewer gas phasereactionsoccur at lower temperatures, resulting in smootherand better adheringfilrns. Anotherreason is that the polysiliconwill havesmall grains.

The finer grains are easierto mask and etch to give smooth and uniform edges. However,for temperatures lessthan "C the deposition rateis too low. Therefore, the resistance of the metalline is 5x O. For TiSiz: Advantage: lowresistivity lt can reducenative-oxide layers TiSiu on the gate electrodeis more resistantto high-fieldinducedhot-electron degradation.

Disadvantage: bridging effectoccurs. LargerSi consumption during formationof TiSiu Lessthermalstabilifv F o rC o S b : Advantage: lowresistivity High temperature stability No bridgingeffect A selective chemicaletchexits Low shearforces Disadvantage: not a goodcandidate for polycides. Ratio: o4 ,r; Thetotal resistance is. The limiting current1 is given by the maximum allowed current density times cross-sectional areaofthe thinnerconductorsections:. With reference to Fig. We can also developnew resiststhat provide lower h and higher k2 for better resolutionand depthof focus.

This raisesthe. A shapedbeam system enablesthe size and shapeof the beam to be varied, thereby minimizing the number of flashesrequired for exposing a given area to be patterned. Therefore,a shapedbeamcan savetime and increase throughputcomparedto a Gaussian beam. We can makealignmentmarkson wafersusing e-beam and etchthe exposed marks. We can then usethem to do alignmentwith e-beam radiationand obtainthe signal from thesemarks for wafer alignment. X-ray lithographyis a proximity printing lithography.

X-ray lithographyusing synchrotron radiationhasa high exposure flux so X-ray has better throughput than e-beam. With a 1:l projectionprinting systemis much more difficult to producedefect-freemasksthan it is with a 5:l reductionstep-and-repeat system. The main reasonis that X-rays cannot be focusedby an optical lens. When it is through the reticle. So we can not build a step-and-scan X-ray lithography system.

As shown in the figure, the profile for eachcaseis a segment of a circle with origin at the initial mask-film edge. From Eqs. The Fresnel transmission coefficient from Eq. We assume a conventional p-n junction laser and a stripe DH laser have the same active area. It is impractical. Take the solution which is the only practical one, i.

The threshold current in Fig. The photons with 1. However, since the cells are in series, the top cell wiI1 block the current generated by the bottom cell once the current is larger than the top cell's dark saturation current va1ue.

We can assume that absorption and hence photogeneration occurs over the entire i layer. The earth is hotter. The efficiencies are The segregation coefficient of boron in silicon is 0.

It is smaller than unity, so the solubility of B in Si under solid phase is smaller than that of the melt. Therefore, the excess B atoms will be thrown-off into the melt, then the concentration of B in the melt will be increased.

The tail-end of the crystal is the last to solidify. Therefore, the concentration of B in the tail-end of grown c1ystal will be higher than that of seed-end. The reason is that the solubility in the melt is prop01tional to the temperature, and the temperature is higher in the center prut than at the perimeter. Therefore, the solubility is higher in the center prui, causing a higher impmity concentration there.

The segregation coefficient of Ga in Si is 8 x 1o-3 FromEq. We have from Eq. The corresponding doping concentration varies from 2. From the Fig. Therefore, the As content will be lost when the temperature is increased. Thus the composition of liquid GaAs always becomes gallium rich. We divide the wafer into four symmetrical patts for convenient dicing, and discard the perimeter parts of the wafer.

Usually the quality of the perimeter patts is the worst due to the edge effects. Where f. For close-packing arrange, there are 3 pie shaped sections in the equilateral triangle. The molecular weight is The x value is about 0.

The time required to grow 0. For the field oxide with an original thickness 0. A1 A2 8. Moderately low temperatures are usually used for polysilicon deposition, and silane decomposition occurs at lower temperatures than that for chloride reactions. In addition, silane is used for better coverage over amorphous materials such SiO2. There are two reasons.

One is to minimize the thermal budget of the wafer, reducing dopant diffusion and material degradation. In addition, fewer gas phase reactions occur at lower temperatures, resulting in smoother and better adhering films.

Another reason is that the polysilicon will have small grains. The finer grains are easier to mask and etch to give smooth and uniform edges. For TiSi2: Advantage: low resistivity It can reduce native-oxide layers TiSi2 on the gate electrode is more resistant to high-field-induced hot-electron degradation. Disadvantage: bridging effect occurs. With reference to Fig. The available exposure energy in an hour is 0. We can also develop new resists that provide lower k1 and higher k2 for better resolution and depth of focus.

This raises the concern of damage to stepper lens, lower exposure speed and reduced throughput. Therefore, a shaped beam can save time and increase throughput compared to a Gaussian beam. We can then use them to do alignment with e-beam radiation and obtain the signal from these marks for wafer alignment. X-ray lithography is a proximity printing lithography.

Its accuracy requirement is very high, therefore alignment is difficult. With a projection printing system is much more difficult to produce defect-free masks than it is with a reduction step-and-repeat system. The main reason is that X-rays cannot be focused by an optical lens. When it is through the reticle. As shown in the figure, the profile for each case is a segment of a circle with origin at the initial mask-film edge.

As overetching proceeds the radius of curvature increases so that the profile tends to a vertical line. Using the data in Prob. If we protect the IC chip areas e.