Lecture5

第五讲 载流子产生与复合（续）9月12，2001内容：1.热平衡之外的G&R率2.表面产生与复合阅读作业del Alamo Ch. 3，§§3.4 ,3.6主要问题●当载流子浓度被扰动而偏离热平衡时的值时，对产生和复合之间的平衡发生了什么影响？●对每个G&R机制是如何打乱的？●决定G&R率平衡的主要因素是什么？●如何能表征表面G&R？⒈ 平衡之外的G&R率●在热平衡时：●在热平衡之外（载流子浓度被扰动而偏离热平衡时的值）：如果,G R 载流子浓度随时间变化。

定义净复合率U 是十分有用的：U R G=−反映内部G&R 机制的平衡：如果0R G U >，净复合占优势如果0R G U <，净产生占优势如果几个机制同时作用，定义：i i iU R G =−而iU U =在热平衡之外的不同机制对G&R 率会发生什么影响？a ）能带到能带光学G&R●光产生率没有变化，因为键合数目没有变化：00rad rad rad G g r n p ==●如果电子和空穴浓度发生变化时，光复合率受到影响：rad rad R r np=●定义净复合率：()00rad rad rad rad U R G r np n p =−=− －如果00np n p >，0rad U >，净复合占优势－如果00np n p <，0rad U <，净产生占优势●注意：我们假定rad g 和rad r 与平衡时无变化b ） 俄歇G&R●包括热电子 ：eeh eeh G g n= 2eeh eeh R r n p=如果eeh g 和eeh r 间关系和TE 时无差别：()00eeh eeh eeh eeh U R G r n np n p =−=−●同样，包括热电子：()00ehh ehh U r p np n p =−●总的 俄歇 ：()()00Auger eeh ehh U r n r p np n p =+−c ） 与陷阱有关的热G&R在平衡之外，如果产生复合率常数不受影响：复合：捕获一个电子＋一个空穴净复合率＝净电子捕获率＝净空穴捕获率tr ec ee hc heU r r r r =−=−从这，推导出t n ，并最终得到tr U ：()()00tr ho i o inp n p U n n p n ττ−=+++d ） 所有过程组合起来□ 特殊情况：低水平掺杂定义过剩载流子浓度：'0n n n =+ '0p p p=+LLI ：平衡的少数载流子浓度占主导但对多数载流子浓度扰动可以忽略－对n 型：－对p型：在LLI中：U的所以表达式仿效下面形式：τ为过程i的载流子寿命，每个G&R过程的一个特征常数：i在LLI 情况下，净复合率作为材料和温度的一个常数，线性的取决于过剩载流子浓度。

5.1. Public goods5.1. Public goods - IntroductionIn the perfectly competitive market, property rights are assumed to be perfectly defined and enforced. This implies goods and services are excludable and rivalrous in consumption.Excludable Non-excludableRivalrous Non-rivalrousClub goods Common resources Public goodsIn reality, many goods and services are associated with property rights problems:Private goodse.g. ice-cream, clothing e.g. cable TV, club membershipe.g. fish in the ocean, the environment e.g. basic research, national defenceDefinitions: non-excludable: once produced, no one can be prevented from using the good; and non-rivalrous: one person’s use of the good does not diminish other people’s use.5.1. Public goods - Market failurePrivate goods and club goods do not present market failure – they have prices attached to them. Public goods and common resources present market failure – externalities arise because something of value has no price attached:• If a person were to provide a public good, for e.g. national defence, others would be better off and yet they are not charged for this benefit;• If a person uses a common resources, for e.g. fish in the ocean, others would be worse off and yet they are not compensated for this loss.Due to these externalities, private decisions about production and consumption can lead to inefficient outcomes (market failure).Government intervention (public solutions) can potentially correct inefficiency and raise economic well-being.5.1.1. Public goodsDue to these two features, people have an incentive to be free riders:The existence of free riders lead to the under-provision of public goods in the market (the free rider problem ).The market fails to provide the efficient outcome because those who gain a benefit fromconsuming the public good do not compensate the supplier for the production costs. Hence, the supplier has no incentive to provide the good.The government can remedy this problem by providing or subsidising the public good and paying for it with tax revenue, to make everyone better off. This is a public solution.Some examples: fireworks displays, lighthouses, national defence, basic research (knowledge), free-to-air TV and radio.Definition: public goods are goods that are non-excludable and non-rivalrous.Definition: free rider is a person who receives the benefit of a good but avoids paying for it.National defence - one of the most expensive public goods.• Solution: People may disagree on the appropriate levels, but most will agree that some government spending on defence is necessary.Basic research (knowledge) – general knowledge is a public good; profit seeking firms have incentive to free ride on the knowledge created by others.• Solution: Government subsidises the basic research carried out by universities and other research organisations (this is a corrective subsidy on the positive externality generated). Fighting poverty – everyone prefers living in a society without poverty, but fighting poverty is not a ‘good’ that private actions will adequately provide.• Solution: Many government programs are aimed at helping the poor, for e.g. unemployment benefits, old-age pensions, disability support, funded by tax revenue.Before providing a public good, government conducts a cost-benefit analysis to determine whether it is efficient to do so.Definition: cost-benefit analysis is a study that compares the costs and benefitsto society of providing a public good.Free-to-air TV and radio - non-excludable and non-rivalrous, yet provided by private firms as for-profit business. For e.g. Freeview.How is revenue generated, when consumers enjoy for free?• Solution: broadcasters sells a complementary, private good i.e. advertising. Sells airtime to advertisers.Advertisers are willing to pay more if their ads are shown during a program that has many viewers. This gives broadcasters incentive to show programs that viewers want to watch. Hence, viewer demand drives what is shown.Other examples of the private provision of public goods: search engines e.g. Google and Bing; and video sharing sites e.g. YouTube and Vimeo. These are funded by the revenue from the ads displayed on the webpages.5.1.2. Common resourcesThe tragedy of the commons refers to the overgrazing of communal land surrounding medieval English villages.Each family in the village has the right to graze sheep on the commons. When one family ’s flock grazes on the common land, it reduces the quality of the land available for other families. Because people neglect this negative externality when deciding how many sheep to own, the result is an excessive number of sheep. Overgrazing eventually damages the land ’s ability to replenish itself, destroying the common resource for all families in the village.Some examples: clean air and climate change, oil deposits, congested non-toll roads, fish, whales and other wildlifeSolutions to the common resource problem can be private and/or public. Definition: common resources are goods that are non-excludable but rivalrous.Definition: the tragedy of the commons is a parable that illustrates why common resources get used more than is desirable from the standpoint of society as a whole.Clean air and climate change – greenhouse gasses emitted in one country spread around the world contributing to climate change in every country. When a government in one country regulates emissions, it considers only its own environment, not the effects on other countries. • Solution: the Coase Theorem suggests that nations can enter into a treaty (e.g. the Kyoto Protocol) which commits them to reduce their own emissions. The treaty behaves like contract, internalising the externality.Oil deposits – a large oil field lies under many properties with different owners. Any of the owners can extract the oil, but when one owner extracts oil, less is available for the others. Because each owner who drills a well imposes a negative externality on the other owners, the benefit to society of drilling a well is less than the benefit to the owner who drills it. If owners of the properties decide individually how many oil wells to drill, they will drill too many.• Solution: some type of joint action or agreement among the owners is necessary to solve the problem and ensure that oil is extracted at lowest cost.Overgrazing on the commons - the community can prevent the tragedy in a number of ways. • Solution: regulate the number of sheep in each family ’s flock or divide up the land among the families.Congested roads - yield a negative externality. When one person drives on the road, it becomes more crowded, and other people must drive more slowly.• Solution: Government levies a toll or a congestion charge. A toll is a corrective tax on the externality of congestion. Sometimes congestion is a problem only at rush hour. Government can charge higher tolls at rush hour as an incentive for drivers to alter their schedules.Many species of animals (fish, whale, other wildlife) – are common resources.Fish, for instance, have commercial value, and anyone can go to the ocean and catch whatever is available. Each person has little incentive to maintain the species for the next year. Just as excessive grazing can destroy the commons, excessive fishing can destroy marine populations. • Solution: ??Two problems prevent successful Government regulation of fish stocks:(1) many countries have access to the oceans, so any solution would require internationalcooperation among countries that hold different values;(2) because the oceans are so vast, enforcing any agreement is difficult.5.2. Government intervention - IntroductionGovernments intervene in markets to correct market failures, such as inequality, externalities and public goods. Objective: to restore efficiency and increase economic well-being of society. Government can intervene: • Directly – by controlling prices in the markets• Indirectly – by taxing and/or subsiding demand and supplySome policy tools used bygovernment:• Price controls• Taxes• Subsidies5.2.1. Price controlsInequality and fighting poverty are market failures.Governments can directly control prices in different markets by using price ceilings and price floors to ensure all members of society enjoy a certain standard of living.Definition: price ceiling is a legal maximum on the price at which a good can be sold. Definition: price floor is a legal minimum on the price at which a good can be sold.5.2.1. Price controls: price ceilingA binding price ceiling is set below the equilibrium price.Price ceilings result in shortages of the good, as the market cannot achieve equilibrium.To manage the shortage, somemechanism for rationing the good will naturally develop, for e.g. queuing. In the case of rent control , landlords may be discouraged from maintaining their buildings.A price ceiling is only binding if set belowthe equilibrium price. If set above , it is non-binding as it does not prevent the market from achieving equilibrium.SupplyDemandPrice ceiling $3 $2100 75 125Price QuantityQuantity supplied Quantity demandedShortage5.2.1. Price controls: price floorA binding price floor is set above the equilibrium price.Price floors result in surpluses of the good. Some sellers are able to sell their goods at the higher price, but others will not be able to.Some method for rationing will naturally develop, for e.g. appealing to the personal biases of the buyers. In the case of minimum wage , the surplus is unemployment.Rationing may lead to discriminatory hiring practices in the labour market.A price floor is only binding if set above theequilibrium price. If set below , it is non-binding as it does not prevent the market fromachieving equilibrium. SupplyDemandPrice floor$3$4 100 75 125 Price Quantity Quantity suppliedQuantity demanded SurplusDefinition: tax incidence is the study of who bears the burden of taxation, the degree to which buyers and sellers will be worse off due to the tax.5.2.2. TaxesGovernment taxes firms and households in different markets.Taxes fulfill two functions:(1) Provide government with the resources required for intervention, for e.g. government uses taxrevenue to provide or subsidise public goods;(2) Corrective measure to internalise externalities, for e.g. government can tax activities that havenegative externalities an amount equaling its external cost.Definition: tax is a payment to government, from buyers or sellers, for each unit of good that is bought or sold.The government requires buyers to pay a tax of $0.50 on each unit purchased.This shifts demand to the left (demand falls) by the amount of the tax.The tax creates a wedge between the price buyers effectively pay ($3.30), and the price sellers receive ($2.80).Although the tax is levied on buyers, the burden of the tax falls on both buyers and sellers. The price buyers pay is $0.30 higher than before, the price sellers receive is $0.20 lower than before.Moreover, the quantity traded falls (100 to 90).SupplyDemand 1 $3 $2.8010090 Price QuantityEquilibrium without tax Demand 2$3.30 Equilibrium with taxTax $0.50The government requires sellers to pay a tax of $0.50 on each unit sold.This shifts supply to the left (supply falls) by the amount of the tax. Otherwise, the effects are identical to tax incidence on buyers.How taxes affect market outcomes:Taxes discourage market activity:• When a good is taxed, the quantity traded falls;• Buyers pay more for the good and sellers receive less.Buyers and sellers share the tax burden. It does not matter who the tax is levied on. The effects on the market and the tax incidence are identical.Supply 1Demand$3 $2.8010090 PriceQuantityEquilibrium without tax$3.30 Equilibrium with taxTax $0.50Supply 25.2.2. Taxes: elasticity and tax incidenceSupply 1DemandPrice without tax PriceQuantityEquilibrium without taxEquilibrium with taxTaxSupply 2Price buyers payPrice sellers receiveTax incidence on buyersTax incidence on sellersSupply 1DemandPrice without tax PriceQuantityEquilibrium without taxEquilibrium with taxTaxSupply 2Price buyers pay Price sellers receiveTax incidence on buyersTax incidence on sellersBecause supply is elastic , the price sellers receive does not fall much, so sellers bear only a small burden. In contrast, the price buyers pay risessubstantially, so buyers bear most of the tax burden.Because demand is elastic , the price buyers pay does not rise much, so buyers bear only a small burden. In contrast, the price sellers receive falls substantially, so sellers bear most of the tax burden.5.2.3. SubsidiesGovernment sometimes subsidises firms and households in different markets.Definition: subsidy is a payment from government, to buyers or sellers, for each unitof good that is bought or sold.Definition: subsidy incidence is the study of who receives the benefit of the subsidy,the degree to which buyers and sellers will be better off due to the subsidy.Subsidies fulfill two functions:(1) It can be regarded as negative taxes, for e.g. government subsidises the provision of publicgoods;(2) Corrective measure to internalise externalities, for e.g. government can subsidise activitiesthat have positive externalities an amount equaling its external benefit.5.2.3. Subsidies: subsidy incidence on sellersThe government pays sellers a subsidy of $1.00 for each unit sold.This shifts supply to the right (supply increases) by the amount of the subsidy.Like a tax, the subsidy creates a wedge between the price buyers pay ($2.40), and the price sellers receive ($3.40).In this case the subsidy is paid to sellers, yet the benefits areenjoyed by both buyers and sellers. The price buyers pay is lower than before and the price sellers receive is higher. Moreover, the quantity traded rises as a result of the subsidy.The market outcomes are identical if the subsidy is paid to buyers.How subsidies affect market outcomes:Subsidies encourage market activity:• When a good is subsidised, the quantity traded rises;• Buyers pay less for the good and sellers receive more (the government makes up the difference).Buyers and sellers share the benefit. It does not matter whoreceives the subsidy. The effects on the market and the subsidy incidence are identical.Supply 2Demand$3 $2.40120100 PriceQuantity $3.40 Equilibrium with subsidySubsidy $1.00Supply 1Equilibrium without subsidyThe demand of first home buyers for housing tends to be relatively elastic. The supply of housing tends to be relatively inelastic.The subsidy creates a wedge between the price paid by buyers and the price received by sellers.The price buyers pay does not fall much, so buyers gain a small benefit. In contrast, the price sellers receive rises substantially, indicating that sellers gain most of the benefit.Price QuantityPrice buyers payDemand1SupplyPrice sellers receivePrice without subsidy Subsidy ($7000)Sellers’ shareBuyers’ shareUnder this scheme, to assist first time home buyers,the government pays buyers a subsidy of $7000 when they purchased their first home.Using the tools of demand, supply and elasticity, we can determine who gets the benefits from this scheme.Demand2 5.2.3. Subsidies: application - who benefits from the First Home Owner Grant scheme?。