prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: How is the vacuum processing system configured in terms of the arrangement of the vacuum processing apparatus?

Read the following text and answer briefly.

Context 1: PROBLEM TO BE SOLVED: To provide a vacuum processor which can suppress the rise of manufacture cost while coping with the enlargement of diameter of a sample, and besides is excellent in maintainability  SOLUTION: This vacuum processor comprises an air loader 1 which is equipped with a plurality of juxtaposed cassette stands 2a and 2b and a carrier 13 for carrying a wafer 20 from or to the cassette stands, a vacuum loader 7 which is equipped with etching treatment chambers 11 and 11b for processing the wafer and a vacuum carriage chamber 16 connected to them through gate valves 15a and 15b, and a lock device 6 consisting of a load lock chamber 6b and an unload lock chamber 6b equipped with gate valves 12a, 12b, 12c, and 12d for connecting the said carrier 13 with the vacuum carriage chamber 16  For the etching treatment chambers, two are provided only on the opposite side of the vacuum carriage chamber symmetrically about the axis line A passing the center, and besides the arrangement positions of the two etching treatment chambers are at an acute angle on the opposite side of the vacuum carriage chamber 
エッチング，ＣＶＤ（化学的気相成長），スパッタリング，アッシング，リンサ（水洗）等の枚葉処理をするのに好適な真空処理装置とそれを用いて半導体デバイスを製造する半導体製造ラインに関するものである。 Those etching, CVD (chemical vapor deposition), sputtering, ashing, to rinser (water washing) suitable vacuum processing apparatus for single wafer processing, such as a semiconductor manufacturing line for manufacturing a semiconductor device using the same  
【従来の技術】試料を処理する真空処理装置は、大別すると、カセットブロックと真空処理ブロックから構成されており、カセットブロックは、半導体製造ラインのベイ通路に面して長手方向に伸びるフロントを有し、試料用のカセットや試料のオリエンテーションを合わせるアライメントユニットと、大気ロボットがある。 BACKGROUND OF THE INVENTION Vacuum processing apparatus for processing a sample, the roughly is constituted by a cassette block and a vacuum processing block, the cassette block, a front extending in the longitudinal direction facing the bay aisle of a semiconductor manufacturing line a, an alignment unit for aligning the cassette and sample orientation for sample, there is an atmospheric robot  真空処理ブロックには、ロード側ロードロック室，アンロード側ロードロック室，真空処理室，後真空処理室，真空ポンプ及び真空ロボット等が設けられている。 The vacuum processing block, the load-side load lock chamber, the unload side load lock chamber, the vacuum processing chamber, a rear vacuum processing chamber, a vacuum pump and a vacuum robot and the like 
【０００３】これらの真空処理装置では、カセットブロックのカセットから取り出された試料が、大気ロボットにより真空処理ブロックのロードロック室まで搬送される。  In these vacuum processing apparatus, a sample taken from the cassette in the cassette block is transported to the load lock chamber in the vacuum processing block by the atmospheric robot  ロードロック室から真空ロボットによりさらに処理室に搬送され、電極構造体上にセットされた試料は、プラズマエッチング等の処理がなされる。 Is conveyed from the load lock chamber to the further processing chamber by the vacuum robot, the sample is set on an electrode structure, processing such as plasma etching is performed  その後、必要に応じて後真空処理室に搬送，処理される。 Thereafter, the conveyance to the rear vacuum processing chamber as necessary and processed  処理済みの試料は、真空ロボット及び大気ロボットによりカセットブロックのカセットに搬送される。 Processed sample is conveyed to the cassette of the cassette block by the vacuum robot and the atmospheric robot 
【０００４】試料をプラズマエッチング処理する真空処理装置の例としては、例えば特公昭61−8153号公報，特開昭63−133532号公報，特公平6−30369号公報，特開平  Examples of the sample vacuum processing apparatus for plasma etching treatment, for example Japanese Patent Publication 61-8153, JP-Sho 63-133532 and JP Kokoku 6-30369, JP-A No 
6−314729号公報，特開平6−314730号公報，米国特許第 6-314729, JP-A No  6-314730, JP-U S  Patent No 
5,314,509号明細書および5,784,799号明細書に記載されたようなものがある。 There are such as described in Pat and 5,784,799 Pat 5,314,509 
509号明細書に記載された装置は、真空処理ブロックの中央付近に真空ロボット、その周囲に３個の処理室が同心状に配置され、真空ロボットとカセットブロックの間に、ロード側ロードロック室，アンロード側ロードロック室が設けられている。 Device described in 509 Pat are vacuum robot in the vicinity of the center of the vacuum processing block, three process chambers around it are arranged concentrically, between the vacuum robot and the cassette block, the load-side load-lock chamber , unload side load lock chamber is provided  これらの装置では、大気ロボットや真空ロボットの搬送アームの回転角度が大きく従って装置全体の必要床面積が大きいという問題がある。 In these devices, there is a problem that needs floor space for the entire rotation angle is large therefore device of the transfer arm of the atmospheric robot and the vacuum robot is large 
【０００６】一方、真空処理装置の真空処理ブロック内の処理室や真空ポンプその他各種の配管機器については、定期，不定期に点検修理等のメンテナンスを行うことが必要である。  On the other hand, the processing chamber and the vacuum pump and other various piping components of the vacuum processing block of the vacuum processing apparatus, periodically, it is necessary to perform maintenance such as inspection and repair irregularly  そのため、一般に、真空処理ブロックの周囲には、扉が設けられており、この扉を開けることにより、ロードロック室，アンロードロック室，処理室，真空ロボット及び各種の配管機器の点検修理ができるようになっている。 Therefore, in general, around the vacuum processing block, the door is provided by opening the door, load lock chambers, unload lock chambers, processing chambers, the servicing of the vacuum robot and various piping devices It has become way 
キャリアポッドが必要となるために、約３５０mm程度と大きくなり、複数のキャリアポッドを収納するカセットブロックの幅も大きくなる。 For carrier pod required, large as about 350 mm, the greater width of the cassette block for housing a plurality of carrier pods  この幅に合わせて真空処理ブロックの幅を決定すると、真空処理装置全体が大きなスペースを必要とすることになる。 When determining the width of the vacuum processing block in accordance with the this width, the entire vacuum processing apparatus requires a large space  一例として、４個のキャリアポッドを収納するカセットブロックについて考えると、試料の直径ｄが８インチから１２インチになった場合、カセットの幅は少なくとも約４０cm以上大きくならざるを得ない。 As an example, considering the cassette block for accommodating four carriers pods, if the diameter d of the sample was a 12-inch 8 inch wide cassette inevitably increases at least about 40cm or more 
【０００８】一方、試料に各種の処理を行いながら大量の処理を行うために、一般の半導体製造ラインでは、同じ処理を行う複数の真空処理装置を同じベイに集め、各ベイ間の搬送を自動またはマニュアルで行っている。 On the other hand, in order to perform a lot of processing while performing various processes in the sample, in a general semiconductor manufacturing lines, gathering a plurality of vacuum processing apparatus for performing the same processing in the same bay, automatic conveyance between the bays or it is carried out manually  このような半導体製造ラインは、高いクリーン度を必要とするため、半導体製造ライン全体が大きなクリーンルーム内に設置される。 Such a semiconductor manufacturing line, requires a high degree of cleanliness, the whole semiconductor manufacturing line is placed in a large clean room  試料の大口径化に伴う真空処理装置の大型化は、クリーンルーム占有面積の大型化を伴うが、これはもともと建設コストの高いクリーンルームの建設コストを一層増加させることになる。 Size of the vacuum processing apparatus due to the large diameter of the sample is accompanied by a large clean room area occupied, which will be further increased construction costs of the high construction cost clean room originally  もし、同じ面積のクリーンルームに占有面積の大きな真空処理装置を設置するとすれば、真空処理装置の全体の台数を減らすか、あるいは各真空処理装置間の間隔を狭くせざるを得ない。 If, if the clean room of the same area to install a large vacuum processing apparatus of the occupied area, reduce the overall number of the vacuum processing apparatus, or interval narrower forced between the vacuum processing apparatus  同じ面積のクリーンルームにおける真空処理装置の設置台数減少は、必然的に半導体の製造ラインの生産性の低下ひいては半導体の製造コストの上昇を伴う。 Installed base reduction in the vacuum processing apparatus in a clean room having the same area is accompanied inevitably rise of the semiconductor decrease and thus the semiconductor manufacturing cost of productivity of the production line  他方、各真空処理装置間の間隔を狭くすることは、点検修理のためのメンテナンススペースが不足し、真空処理装置のメンテナンス性を著しく阻害する。 On the other hand, to reduce the distance between each of the vacuum processing apparatus, the maintenance space for inspection and repair is insufficient to significantly inhibit the maintenance of the vacuum processing apparatus 
【０００９】本発明の目的は、試料の大口径化に対応しつつ、製造コストの上昇を抑えることのできる真空処理装置を提供することにある。 An object of the present invention, while corresponding to the large diameter of the sample, is to provide a vacuum processing apparatus capable of suppressing an increase in manufacturing cost 
【００１０】本発明の他の目的は、試料の大口径化に対応しつつ、メンテナンス性に優れた真空処理装置を提供することにある。 Another object of the present invention, while corresponding to the large diameter of the sample is to provide a vacuum processing apparatus having excellent maintainability 
【００１１】本発明の他の目的は、試料の大口径化に対応しつつ、真空処理装置の必要設置台数を確保して製造コストの上昇を抑え、かつ、メンテナンス性も損なわない半導体製造ラインを提供することにある。 Another object of the present invention, while corresponding to the large diameter of the sample, to ensure the necessary number of installed vacuum processing apparatus suppressing an increase in manufacturing cost, and a semiconductor manufacturing line is not impaired maintainability It is to provide 
【課題を解決するための手段】本発明は、並設した複数のカセット台およびカセット台から、あるいはカセット台へウエハを搬送するための搬送装置を備えた大気ローダと、ウエハを処理するための真空処理室およびこれにゲート弁を介して連接された真空搬送室を備えた真空ローダと、前記搬送装置と前記真空搬送室とを連接するためのゲート弁を備えたロードロック室およびアンロードロック室からなるロック装置とを含んで構成される真空処理装置において、ウエハを処理するための真空処理室は、有磁場ＵＨＦ帯電磁波放射放電方式リアクタ（以下、ＵＨＦ−ＥＣＲリアクタという。）によって形成される真空処理室であり、該真空処理室には、分解可能な側壁インナーユニットおよびアンテナが設けられ、該真空処理室は、真空搬 The present invention SUMMARY OF THE INVENTION from a plurality of cassette tables and cassette stand juxtaposed, or the atmosphere loader having a conveying device for conveying the wafer to the cassette table, for processing a wafer the load lock chamber and the unload lock having a gate valve for connecting the vacuum loader vacuum processing chamber and having a vacuum transfer chamber which is connected via a gate valve to the said vacuum transfer chamber and the conveying device in the vacuum processing apparatus configured to include a lock device comprising a chamber, a vacuum processing chamber for processing a wafer it is formed by a magnetic field UHF band electromagnetic wave radiation discharge type reactor (hereinafter  referred UHF-ECR reactor) that a vacuum processing chamber, the vacuum processing chamber, degradable sidewall inner unit and an antenna are provided, the vacuum processing chamber, a vacuum transportable 室およびロック装置の中央を通る軸線に対して対称にして、かつ真空搬送室を中心にしてロック装置の反対側のみに２つ設けられ、かつ真空搬送室に対して前記２つの真空処理室の配置位置は鋭角をなしている真空処理装置を提供する。 And symmetrically with respect to the axis passing through the center of the chamber and the locking device, and the opposite side only two provided for to lock device around the vacuum transfer chamber, and the two vacuum processing chamber to the vacuum transfer chamber position is to provide a vacuum processing apparatus which forms an acute angle 
ＣＲリアクタによって形成される真空処理室であり、該真空処理室は、真空搬送室およびロック装置の中央を通る軸線に対して対称にして、かつ真空搬送室を中心にしてロック装置の反対側のみに２つ設けられ、かつ真空搬送室に対して前記２つの真空処理室の配置位置は鋭角をなしており、ＵＨＦ−ＥＣＲのアンテナは、前記軸線に対して平行で、かつ前記真空搬送室とは反対側に開放される真空処理装置を提供する。 A vacuum processing chamber formed by a CR reactor, vacuum processing chamber, and symmetrically with respect to the axis passing through the center of the vacuum transfer chamber and the locking device, and the opposite side of the locking device around the vacuum transfer chamber only two provided, and positions of the two vacuum processing chamber to the vacuum transfer chamber is an acute angle, the UHF-ECR antennas, and parallel, and the vacuum transfer chamber with respect to said axis to provides a vacuum processing apparatus is opened to the opposite side 
かつ真空搬送室を中心にしてロック装置の反対側のみに２つ設けられ、かつ真空搬送室に対して前記２つの真空処理室の配置位置は鋭角をなしており、大気ローダ，真空ローダおよびロック装置はＴ字配置とされた真空処理方法を提供する。 And around the vacuum transfer chamber opposite only two provided a locking device, and positions of the two vacuum processing chamber to the vacuum transfer chamber is an acute angle, atmospheric loader, vacuum loader and locking apparatus to provide a vacuum processing method which is a T-arrangement 
【００１５】本発明は、並設した複数のカセット台およびカセット台から、あるいはカセット台へウエハを搬送するための搬送装置を備えた大気ローダと、ウエハを処理するための真空処理室およびこれにゲート弁を介して連接された真空搬送室を備えた真空ローダと、前記搬送装置と前記真空搬送室とを連接するためのゲート弁を備えたロードロック室およびアンロードロック室からなるロック装置とを含んで構成される真空処理装置が平行に複数台並設された真空処理システムにおいて、ウエハを処理するための真空処理室は、ＵＨＦ−ＥＣＲリアクタによって形成される真空処理室であり、該真空処理室は、真空搬送室およびロック装置の中央を通る軸線に対して対称にして、かつ真空搬送室を中心にしてロック装置の反対側のみに２ The present invention, a plurality of cassette tables and cassette stand juxtaposed, or the atmosphere loader having a conveying device for conveying the wafer to the cassette base, the vacuum processing chamber for processing the wafer and to a vacuum loader having a vacuum transfer chamber which is connected via a gate valve, the locking consisting of the conveying device and the load lock chamber and the unload lock chamber with gate valves for connecting the said vacuum transfer chamber apparatus and in the vacuum processing system vacuum processing apparatus is constituted with a plurality Tainami set in parallel include vacuum processing chamber for processing a wafer is vacuum processing chamber formed by the UHF-ECR reactor, vacuum processing chamber, and symmetrically with respect to the axis passing through the center of the vacuum transfer chamber and the locking device, and 2 only on the opposite side of the locking device around the vacuum transfer chamber 設けられ、かつ真空搬送室に対して前記２つの真空処理室の配置位置は鋭角をなしており、並設された複数の真空処理装置のすべての真空処理室に一直線上に配列される真空処理システムを提供する。 Provided, and positions of the two vacuum processing chamber to the vacuum transfer chamber is an acute angle, a vacuum process that is arranged in alignment with all of the vacuum processing chamber of a plurality of vacuum processing apparatus are arranged in parallel to provide a system 
【発明の実施の形態】以下、本発明にかかる一実施例を図面に基づいて説明する。 BEST MODE FOR CARRYING OUT THE INVENTION Hereinafter, will be explained based on an embodiment according to the present invention with reference to the accompanying drawings 
１０Ｂ，１０Ｃで示す。 10B, shown by 10C 
【００１８】図１に示す真空処理システムを説明する前に、図２から図４に基づいて真空処理装置を説明する。  Before describing the vacuum processing system shown in FIG  1, illustrating a vacuum processing apparatus on the basis of FIGS  2-4 
５ｂを介して連接された真空搬送室１６を備えた真空ローダ７と、前記搬送装置と前記真空搬送室とを連接するためのゲート弁を備えたロードロック室６ａおよびアンロードロック室６ｂからなるロック装置６とを含んで構成される。 5b a vacuum loader 7 having a vacuum transfer chamber 16 which is connected via consist load lock chamber 6a and the unload lock chamber 6b has a gate valve for connecting and said vacuum transfer chamber and the conveying device configured to include a locking device 6 
平行形に配置され、その位置および姿勢を変えることなく、装置への導入／払出しが可能な位置、すなわち、カセット１ａないし１ｃを略水平の平面上で常に一定の位置に固定される。 Arranged parallel type, without changing its position and orientation, the introduction / dispensing of the locations of the device, i e , always fixed to a constant position to free the cassette 1a 1c on a substantially horizontal plane  カセット台２ａおよび２ｂは、平行に隣合わせて配置してある。 Cassette tables 2a and 2b, are arranged side by side in parallel  カセット台２ｃは、最右端に配置してある。 Cassette table 2c is, are arranged on the top right edge  カセット１ａおよび１ｂは、処理を行うための末処理ウエハを収納したり、処理済みのウエハを回収するためのもので、複数枚（通常２５枚）の被処理基板であるウエハ２０が収納可能となっている。 Cassettes 1a and 1b, or storing the processed wafers end for processing, for recovering the processed wafer, the wafer 20 is a substrate to be processed in a plurality (25 pieces Normal) can be stored going on  カセット１ｃは、この場合、プラズマを用いたドライクリーニング（以下、「プラズマクリーニング」という。）を行うためのダミーウエハを収納したり、プラズマクリーニング後のダミーウエハを回収するためのもので、複数枚（通常２５枚）のダミーウエハ３０が収納可能となっている。 Cassette 1c in this case, dry cleaning using plasma (hereinafter, "plasma cleaning" hereinafter ) Or housing a dummy wafer for performing, for recovering the dummy wafers after plasma cleaning, a plurality (usually dummy wafer 30 of 25 sheets) has become can be stored 
とカセット１ａ，１ｂとの間でウエハ２０を、そしてロードロック室６ａおよびアンロードロック室６ｂとカセット１ｃとの間でダミーウエハ３０を授受可能に動作する。 A cassette 1a, the wafer 20 with the 1b, and operates to allow exchanging dummy wafer 30 between the load lock chamber 6a and the unload lock chamber 6b and the cassette 1c 
ａ，１５ｂを介して真空処理室であるエッチング処理室１１ａ，１１ｂが設けてある。 a, etching chamber is a vacuum processing chamber through a 15b 11a, 11b are provided  以下、エッチング処理室を例に取って説明する。 Hereinafter will be described taking the etching chamber as an example  真空搬送室１６内には、ロードロック室６ａ，アンロード室６ｂおよびエッチング処理室１１ａ，１１ｂとの間でウエハ２０またはダミーウエハ３０を授受可能に動作する搬送装置１４が設けてある。 The vacuum transfer chamber 16, load lock chambers 6a, unload chamber 6b and etching chambers 11a, conveying device 14 is provided that operates to allow transferring the wafer 20 or dummy wafer 30 between 11b  真空搬送室１６は、独立に真空排気可能な真空排気装置１７を装備している。 Vacuum transfer chamber 16 is equipped with a vacuum evacuable vacuum evacuation device 17 independently 
【００２２】ＵＨＦ−ＥＣＲリアクタのエッチング処理室１１ａ，１１ｂは、この場合、同一の構成で対称配置とされてエッチング処理が行われるようになっている。 The UHF-ECR reactor etching chambers 11a, 11b is in this case are symmetrically arranged in the same configuration so that the etching process is performed 
エッチング処理室１１ａを例に説明する。 The etching chamber 11a will be described as an example  エッチング処理室１１ａは、ウエハ２０を配置するための試料台を有し、試料台８ａの上部に放電部７ａを形成するように放電室が設けてある。 Etching chamber 11a has a sample stage for placing the wafer 20, the discharge chamber so as to form a discharge portion 7a at the top of the sample table 8a is provided  エッチング処理室１１ａは、放電部７ａへの処理ガス供給のためのガス導入装置１０ａを有するとともに、エッチング処理室１１ａ内を所定圧力に減圧排気する真空排気装置９ａを有し、放電部７ａの処理ガスをプラズマ化するための、この場合、ＵＨＦ波と磁場の発生手段を有している。 The etching chambers 11a, which has a gas introduction device 10a for processing the gas supply to the discharge portion 7a, having a vacuum exhaust device 9a for evacuating the etching chamber 11a to a predetermined pressure, the process of the discharge portion 7a for plasma gas, in this case, it has a generating means of the UHF wave and magnetic field 
９は、センサ１８からの計測値を所定値と比較して、エッチング処理室内のクリーニング時期を判断する。 9, the measured value from the sensor 18 is compared with a predetermined value to determine the cleaning time of the etching chamber  また、制御装置１９は、真空搬送装置１３および１４を制御して、ダミーウエハ３０をカセット１ｃおよびエッチング処理室１１ａないし１１ｂの間で搬送制御する。 The control device 19 controls the vacuum transfer apparatus 13 and 14, to the dummy wafer 30 to the cassette 1c and the etching process chamber 11a carrying controlled between 11b 
いずれかの方法によりウエハ処理またはプラズマクリーニングを実行する。 It executes the wafer processing or plasma cleaning by any method 
によって、カセット１ａ内のウエハ２０を下から順にエッチング処理室１１ａ，１１ｂに搬入し、それぞれのウエハ２０をエッチング処理する。 Accordingly, the wafer 20 to an etching treatment chamber in order from the bottom 11a of the cassette 1a, and carried into 11b, and each of the wafer 20 is etched  処理されたそれぞれのウエハ２０は、真空搬送装置１４および搬送装置１３によって、カセット１ａ内の元の位置に収納する。 Each wafer 20 processed by vacuum transfer apparatus 14 and the carrier 13 is housed in its original position in the cassette 1a  この場合、運転開始から終了に至る間、カセットの位置および姿勢を変えることなく未処理のウエハを取り出し、そして処理済みのウエハを未処理のウエハが収納されていた元の位置に戻して収納する。 In this case, while leading to completion of the start of the operation, it takes out an unprocessed wafer without changing the position and posture of the cassettes, and the processed wafer unprocessed wafer is accommodated back into position which is housed   このようにすることで、生産ラインの自動化への対応が容易で、且つ、ゴミの発生によるウエハの汚染を低減でき、高い生産効率と高い製品歩留まりを実現できる。 In this way, it is easy to respond to automation of production lines, and can reduce the contamination of the wafer due to the generation of dust can achieve high production efficiency and high product yield 
の処理が全て終り次のカセットの内のウエハ処理に移る前でも良い。 Of the process is good, even before moving on to the wafer processing of all end next cassette 
【００２７】プラズマクリーニングの実施にあたっては、次の順序で行われる。 The practice of plasma cleaning is performed in the following order  この場合、カセット１ｃに収納されたダミーウエハ３０（この
Context 2: South Dakota v  Wayfair, Inc  - Harvard Law Review
Fourth Circuit Invalidates Maryland Statute Regulating Price Gouging in the Sale of Generic Drugs 
South Dakota Supreme Court Holds Unconstitutional State Law Requiring Internet Retailers Without In-State Physical Presence to Remit Sales Tax 
Judicial junk, the Court has long thought, is easier to scrap when the erroneous precedent cannot be fixed by Congress, as in constitutional cases 1× 1  See Burnet v  Coronado Oil & Gas Co , 285 U S  393, 405–10 (1932) (Brandeis, J , dissenting); Lee Epstein, William M  Landes & Adam Liptak, The Decision to Depart (or Not) from Constitutional Precedent: An Empirical Study of the Roberts Court, 90 N Y U  L  Rev  1115, 1116 (2015) (“[Justice Brandeis’s] dissenting opinion       now has the status of black letter law ”)  On the flip side, whenever a bad precedent can be corrected by Congress, stare decisis applies with “special force ”2× 2  See Patterson v  McLean Credit Union, 491 U S  164, 172–73 (1989)  The Court, following Justice Brandeis, usually articulates the rule as distinguishing between “constitutional” and “statutory” precedents  See, e g , id  But the distinction is occasionally said to be between “constitutional” and “nonconstitutional cases ” See, e g , Glidden Co  v  Zdanok, 370 U S  530, 543 (1962) (plurality opinion)  Nomenclature aside, the Court has — until now — adhered to Justice Brandeis’s key insight that the important factor is whether or not the mistake may be legislatively corrected  Last Term, in South Dakota v  Wayfair, Inc ,3× 3  138 S  Ct  2080 (2018)  the Court tinkered with this thinking in overruling an outdated dormant commerce clause precedent  Dormant commerce clause decisions technically produce constitutional holdings, but Congress may override them at will 4× 4  See Prudential Ins  Co  v  Benjamin, 328 U S  408, 421–27 (1946)  Under the usual logic of stare decisis, it should take special force to dislodge such precedents  But Wayfair applied the weakened stare decisis of constitutional cases, asserting that the Court must “address a false constitutional premise         whether or not Congress can or will act ”5× 5  Wayfair, 138 S  Ct  at 2096–97 
Emerging from Wayfair is an odd and ominous development in stare decisis doctrine  Odd, because it turns on a formal classification instead of on Congress’s practical ability to fix the problem  Ominous, because the Court’s logic leads far past the dormant commerce clause  Wayfair grants only feeble stare decisis to precedents that set a “constitutional default rule,”6× 6  Id  at 2096 (“While       Congress has the authority to change the physical presence rule, Congress cannot change the constitutional default rule ”)  meaning constitutional decisions that allow for legislative adjustment or override  This new stare decisis analysis makes other precedents setting constitutional default rules more vulnerable — including, perhaps, mainstays of criminal procedure like Miranda v  Arizona7× 7  384 U S  436 (1966)  and Mapp v  Ohio 8× 8  367 U S  643 (1961) 
Since its 1967 decision in National Bellas Hess, Inc  v  Department of Revenue,9× 9  386 U S  753 (1967)  the Court has held that, under the “dormant” or “negative” implication of the Commerce Clause,10× 10  The dormant or negative commerce clause is a judicial derivation from the Commerce Clause “prohibiting States from discriminating against or imposing excessive burdens on interstate commerce without congressional approval,” which “strikes at one of the chief evils that led to the adoption of the Constitution, namely, state tariffs and other laws that burdened interstate commerce ” Comptroller of the Treasury of Md  v  Wynne, 135 S  Ct  1787, 1794 (2015)  states may not compel remote sellers with no physical presence in the state to collect and remit sales taxes 11× 11  See Bellas Hess, 386 U S  at 759–60  In Quill Corp  v  North Dakota,12× 12  504 U S  298 (1992)  the Court refused to overrule the “bright-line, physical-presence requirement” of Bellas Hess, leaning heavily on stare decisis 13× 13  Id  at 317–18  Three Justices joined a concurrence explaining that their decision rested solely “on the basis of stare decisis ” Id  at 320 (Scalia, J , concurring in part and concurring in the judgment)  So the physical presence test remained the law of the land while the internet conquered the earth  Justice Kennedy had joined the Quill majority and Justice Scalia’s concurring opinion emphasizing stare decisis, but by 2015 he had second thoughts  Writing separately in Direct Marketing Ass’n v  Brohl,14× 14  135 S  Ct  1124 (2015)  Justice Kennedy acknowledged that “[t]he Internet has caused far-reaching systemic and structural changes in the economy” and therefore “Quill now harms States to a degree far greater than could have been anticipated earlier ”15× 15  Id  at 1135 (Kennedy, J , concurring)  He concluded with the wish that “[t]he legal system should find an appropriate case for this Court to reexamine Quill and Bellas Hess ”16× 16  Id 
Seldom has a concurring opinion signed by a lone Justice prompted a state to officially declare an emergency  Yet in 2016, in response to Justice Kennedy’s overture, the South Dakota legislature passed a law, S B  106, “to provide for the collection of sales taxes from certain remote sellers       and to declare an emergency ”17× 17  2016 S D  Sess  Laws ch  70 pmbl  217 (codified at S D  Codified Laws § 10-64 (2017))  It required every remote seller to collect and remit sales tax if the seller’s business in South Dakota comprised either a “gross revenue” greater than $100,000 or at least 200 “separate transactions” within one calendar year 18× 18  Id  § 1  Significantly, the law did not apply retroactively 19× 19  Id  § 5  The “emergency” declaration was necessary to give the law immediate effect, for the purpose of “permitting the most expeditious possible review of the constitutionality of this law” by the U S  Supreme Court 20× 20  Id  § 8(8)  As Justice Alito put it, the “South Dakota law [was] obviously a test case ”21× 21  Transcript of Oral Argument at 27, Wayfair, 138 S  Ct  2080 (No  17-494), https://www supremecourt gov/oral_arguments/argument_transcripts/2017/17-494_7lho pdf [https://perma cc/8HYH-VU8N] 
Expeditiously, a group of remote sellers challenged the law  After being sued by South Dakota for refusing to register for the newly required sales tax license, Wayfair, Inc , Overstock com, Inc , and Newegg, Inc  moved for summary judgment in South Dakota circuit court on the grounds that S B  106 was unconstitutional under Quill and Bellas Hess — a point South Dakota conceded, indicating that it was seeking review by the U S  Supreme Court to overturn Quill 22× 22  State v  Wayfair Inc , 2017 SD 56, ¶¶ 9–11, 901 N W 2d 754, 759–60  Accordingly, the South Dakota circuit court granted the motion for summary judgment and South Dakota appealed to the state’s highest court 23× 23  Id  ¶ 12, 901 N W 2d at 760  The South Dakota Supreme Court unanimously affirmed, recognizing that South Dakota’s “arguments on the merits” may be “persuasive” but “Quill remains the controlling precedent ”24× 24  Id  ¶ 18, 901 N W 2d at 761  See generally Recent Case, State v  Wayfair Inc , 2017 SD 56, 901 N W 2d 754 (S D  2017), 131 Harv  L  Rev  2089 (2018) 
The U S  Supreme Court vacated and remanded 25× 25  Wayfair, 138 S  Ct  at 2100  Writing for the Court one last time, Justice Kennedy26× 26  Justices Thomas, Ginsburg, Alito, and Gorsuch joined Justice Kennedy’s opinion  pilloried Quill’s physical presence rule as “arbitrary, formalistic,” “anachronistic,” and “unfair and unjust” to both states and brick-and-mortar retailers 27× 27  Wayfair, 138 S  Ct  at 2092, 2095  After all, the rationale of Quill was that remote sellers lacked a sufficiently “substantial nexus” with the state to justify imposing a duty of tax collection 28× 28  Quill Corp  v  North Dakota, 504 U S  298, 311 (1992) (quoting Complete Auto Transit, Inc  v  Brady, 430 U S  274, 279 (1977))  This was wrong even in the mail-order catalog days of 1967 and 1992, but “the Internet revolution has made [Quill’s] earlier error all the more egregious and harmful ”29× 29  Wayfair, 138 S  Ct  at 2097; see also id  at 2092  The rule deprived the states of billions of dollars, since they could not force remote sellers to collect the tax and consumers hardly ever paid it on their own 30× 30  Id  at 2088 (“[C]onsumer compliance rates are notoriously low ”)  Quill “serve[d] as a judicially created tax shelter” for remote retailers who do a great deal of business online 31× 31  Id  at 2094 
Satisfied that Bellas Hess and Quill were wrongly decided, the Court then jumped the hurdle of stare decisis  The Quill Court had feared upsetting reliance interests 32× 32  Quill, 504 U S  at 317 (“Bellas Hess       has engendered substantial reliance and has become part of the basic framework of a sizable industry ”)  Wayfair shrugged off this concern, noting that “stare decisis accommodates only ‘legitimate reliance interest[s]’”; by contrast, reliance on the physical presence rule was largely due to consumers evading their use-tax obligations 33× 33  Wayfair, 138 S  Ct  at 2098 (alteration in original) (quoting United States v  Ross, 456 U S  798, 824 (1982))  Quill had also appealed to Congress’s ultimate authority over interstate commerce as a reason to abide by a precedent, even if wrongly decided 34× 34  See Quill, 504 U S  at 318–19; id  at 320 (Scalia, J , concurring in part and concurring in the judgment) (“Congress       can change the rule of Bellas Hess by simply saying so ”)  But Wayfair denied that Congress’s ability to change the law was a proper consideration:
While it can be conceded that Congress has the authority to change the physical presence rule, Congress cannot change the constitutional default rule  It is inconsistent with the Court’s proper role to ask Congress to address a false constitutional premise of this Court’s own creation  Courts have acted as the front line of review in this limited sphere; and hence it is important that their principles be accurate and logical, whether or not Congress can or will act in response 35× 35  Wayfair, 138 S  Ct  at 2096–97 
Having dispensed with the physical presence rule, the Court remanded the case to the South Dakota courts to determine in the first instance “whether some other principle in the Court’s Commerce Clause doctrine might invalidate the Act ”36× 36  Id  at 2099  But the Court listed “several features [of South Dakota law] that appear[ed] designed to prevent discrimination against or undue burdens upon interstate commerce ” Id 
Justices Thomas and Gorsuch each filed concurring opinions  Justice Thomas wistfully likened himself to Justice White — who voted for Bellas Hess but against Quill a quarter-century later — and confessed that he “should have joined [Justice White’s dissenting] opinion ”37× 37  Id  at 2100 (Thomas, J , concurring)  Justice Thomas added that the “Court’s entire negative Commerce Clause jurisprudence” is wrong and should be abandoned 38× 38  Id  Justice Gorsuch also wrote separately to express skepticism of the Court’s dormant commerce clause jurisprudence, raising “questions for another day” of whether the doctrine “can be squared with the text of the Commerce Clause, justified by stare decisis, or defended as misbranded products of federalism or antidiscrimination imperatives flowing from Article IV’s Privileges and Immunities Clause ”39× 39  Id  at 2100–01 (Gorsuch, J , concurring) 
Chief Justice Roberts dissented 40× 40  Justices Breyer, Sotomayor, and Kagan joined the Chief Justice’s dissent  Surprisingly, the dissenting Justices “agree[d] that Bellas Hess was wrongly decided, for many of the reasons given by the Court ”41× 41  Wayfair, 138 S  Ct  at 2101 (Roberts, C J , dissenting)  The dispute between the majority and the dissent turned entirely on the principles and application of stare decisis  Chief Justice Roberts argued that whether or how to reverse Quill should be left to Congress, which “has the flexibility to address these questions in a wide variety of ways” and “can focus directly on current policy concerns rather than past legal mistakes ”42× 42  Id  at 2104  He also pointed to the “baffling” burdens of compliance with the idiosyncratic tax codes of “[o]ver 10,000 jurisdictions,” particularly for small businesses, and doubted that new “software” — the majority’s proposed solution to this mess43× 43  Id  at 2098 (majority opinion) (“Eventually, software that is available at a reasonable cost may make it easier for small businesses to cope with these problems ”)  — would soon solve the problem 44× 44  Id  at 2103–04 (Roberts, C J , dissenting)  In Bellas Hess, the Court reasoned that the dormant commerce clause protects interstate business from being “entangle[d]       in a virtual welter of complicated obligations to local jurisdictions ” Nat’l Bellas Hess, Inc  v  Dep’t of Revenue, 386 U S  753, 759–60 (1967)  The dissent replied that the Court “vastly underestimate[d] the skill of contemporary man and his machines ” Id  at 766 (Fortas, J , dissenting)  The dispute in Wayfair over whether software is up to the task effectively reprised the old debate from Bellas Hess, only this time couched as part of the stare decisis inquiry’s concern for reliance interests rather than as a matter of dormant commerce clause doctrine  While Wayfair acknowledged that “[c]omplex state tax systems could have the effect of discriminating against interstate commerce,” 138 S  Ct  at 2099, the Court remarked that “[t]he physical presence rule is a poor proxy” for an inquiry into any actual burdens imposed on interstate commerce, id  at 2093 
Chief Justice Roberts emphasized that a “heightened form of stare decisis”45× 45  Wayfair, 138 S  Ct  at 2102 (Roberts, C J , dissenting)  applies when “Congress       can, if it wishes, override this Court’s decisions with contrary legislation ”46× 46  Id  at 2101 (first citing Michigan v  Bay Mills Indian Cmty , 134 S  Ct  2024, 2036 (2014) (tribal sovereign immunity); then citing Kimble v  Marvel Entm’t, LLC, 135 S  Ct  2401, 2409 (2015) (statutory interpretation); and then citing Halliburton Co  v  Erica P  John Fund, Inc , 134 S  Ct  2398, 2411 (2014) (judicially created doctrine implementing a judicially created cause of action))  In Quill, the Chief Justice noted, the Court had taken to heart that “Congress may be better qualified” and “has the ultimate power to resolve” the question47× 47  Id  at 2102 (quoting Quill Corp  v  North Dakota, 504 U S  279, 318 (1992))  while Justice Scalia had “recogniz[ed] that stare decisis has ‘special force’ in the dormant Commerce Clause context due to Congress’s ‘final say over regulation of interstate commerce ’”48× 48  Id  (quoting Quill, 504 U S  at 320 (Scalia, J , concurring in part and concurring in the judgment))  Moreover, “[i]f stare decisis applied with special force in Quill, it should be an even greater impediment” afterward since Quill effectively “tossed [the ball] into Congress’s court ”49× 49  Id  (alteration in original) (quoting Kimble, 135 S  Ct  at 2409); cf  Bay Mills, 134 S  Ct  at 2039 n 12 (“When we inform Congress that it has primary responsibility over a sphere of law, and invite Congress to consider a specific issue within that sphere, we cannot deem irrelevant how Congress responds ”)  Because the Court invited Congress to act and then “suddenly chang[ed] the ground rules, the Court may have waylaid Congress’s consideration of the issue ”50× 50  Wayfair, 138 S  Ct  at 2102–03 (Roberts, C J , dissenting) 
In Wayfair, the Court applied the flimsier form of stare decisis to a precedent that could have been overruled by Congress  It did so in the context of a dormant commerce clause case, but Wayfair’s logic extends to all constitutional default rules — that is, constitutional decisions that Congress remains free to change  Not only does Wayfair deviate from the Court’s decades-old stare decisis analysis, it also imperils other precedents that set constitutional default rules 
The Court’s reasoning in Wayfair departs from its prior stare decisis analysis  In 1932, Justice Brandeis posited that stare decisis must bend “in cases involving the Federal Constitution, where correction through legislative action is practically impossible ”51× 51  Burnet v  Coronado Oil & Gas Co , 285 U
Context 3: \section{Introduction}

Despite the rise of graphene and other 2D materials, semiconducting single-walled carbon nanotubes (SWNT) are still regarded as strong candidates for the next generation of high-performance ultrascaled transistors~\cite{Cao_IBM_2015,IBM_2017,3D_CNT_FET} as well as for opto-electronic devices~\cite{Review_Avouris,CNT_photonics} such as chip-scale electronic-photonic platforms~\cite{Pernice_2016} or low-threshold near-infrared tunable micro-lasers~\cite{Graf_2017}  
Engineering a quantum dot (QD) along a (suspended) semiconducting SWNT foreshadows promising opportunities in the field of quantum information processing and sensing through recently proposed schemes such as detection and manipulation of single spins via coupling to vibrational motion~\cite{Palyi_2012}, optomechanical cooling~\cite{Wilson_Rae_2012} as well as all optical manipulation of electron spins~\cite{Galland_all_optical_2008}  Furthermore, the quasi one-dimensional geometry of SWNTs allows for defining tunable p-n junctions induced by electrostatic doping through local gates~\cite{Buchs_JAP,tunable_pn_2011}  Combining a well-defined QD within such a p-n junction structure could constitute a crucial building-block for the realization of highly desirable electrically driven, on-demand single photon emitters operating at telecom wavelength, based $e g $ on a turnstile device architecture~\cite{turnstile_1994,turnstile_1999} 
In practice, QDs in carbon nanotubes have been reported predominantly for two different confinement structures: i) Engineered tunneling barriers at metal-nanotube contacts~\cite{Pablo04nat} and/or by gate electrodes, used \emph{e g } to manipulate single electron spins~\cite{Laird:2015}, ii) Unintentional localization potentials stemming from environmental disorder~\cite{Hofmann_2016}, allowing for single-photon emission mediated by localization of band-edge excitons to QD states~\cite{CNT_photonics,Hoegele_2008,Walden_Newman_2012,Hofmann_2013,Pernice_2016_2}  Both types of structures are usually operated at cryogenic temperature due to small energy scales ranging from a few to few tens of millielectronvolts 
\\
\indent Another technique for achieving confinement in SWNTs makes use of artificial defects such as covalently bound oxygen or aryl functionalization groups on the side walls of semiconducting SWNTs, inducing deep exciton trap states allowing for single-photon emission at room temperature~\cite{Htoon_2015,tunable_QD_defects}  Also, carrier confinement between defect pairs acting as strong scattering centers has been reported for mechanically induced defects~\cite{Postma_SET} as well as for ion-induced defects with reported level spacings up to 200 meV in metallic SWNTs~\cite{Buchs_PRL}  The latter technique, combined with recent progress in controlling defects structure and localization~\cite{Robertson_2012,Yoon_2016,Laser_writing_2017} offers a high potential for engineering a broad set of SWNT-based quantum devices operating at room temperature  
\\
\indent Here, we demonstrate confinement of electrons and holes in sub-10 nm QD structures defined by ion-induced defect pairs along the axis of semiconducting SWNTs  Using low temperature scanning tunneling microscopy and spectroscopy (STM/STS), bound states with level spacings of the order of 100 meV and larger are resolved in energy and space  By solving the one-dimensional Schr\"odinger equation over a piecewise constant potential model, the effects of asymmetric defect scattering strength as well as the influence of the Au(111) substrate such as terrace edges on the bound states structure are remarkably well reproduced  By means of ab-initio calculations based on density functional theory and Green's functions, we find that single (SV) and double vacancies (DV) as well as chemisorbed nitrogen ad-atoms are good candidates to produce QDs with the experimentally observed features  These simulations also allow to study the scattering profile as a function of energy for different defect combinations 

\section{Experimental section}

The experiments have been performed in a commercial (Omicron) low temperature STM setup operating at $\sim5$~K in ultra high vacuum  Topography images have been recorded in constant current mode with a grounded sample, using mechanically cut Pt/Ir tips  Differential conductance $dI/dV$ spectra, proportional in first approximation to the local density of states (LDOS)~\cite{Tersoff85} have been recorded using a lock-in amplifier technique  The LDOS spatial evolution along a nanotube axis is obtained by $dI/dV(x,V)$ maps built by a series of equidistant $dI/dV$ spectra  Spatial extent mismatches between topography images and consecutive $dI/dV(x,V)$ maps have been systematically corrected~\cite{Buchs_Ar}, and the metallic nature of the tip has been systematically checked on the gold substrate to prevent any tip artefacts before recording STM or/and STS data sets  
\\
\indent Nanotube samples were made of extremely pure high-pressure CO conversion (HiPCo) SWNTs~\cite{Smalley01} with a diameter distribution centered around 1 nm, FWHM $\sim$ 0 3 nm~\cite{Buchs_conf}  The measured intrinsic defect density was below one defect every 200 nm  SWNTs were deposited on atomically flat Au(111) surfaces from a 1,2-dichloroethane suspension, followed by an in-situ annealing process~\cite{Buchs_APL_07,Buchs_Ar} 
\\
\indent Local defects in SWNTs have been created in-situ by exposure to: (i) Medium energy $\sim$ 200 eV argon ions (Ar$^{+}$) produced by an ion gun \cite{Buchs_Ar,Buchs_PRL}, (ii) Low energy (few eV's) nitrogen ions (N$^{+}$) produced by a 2 45 GHz ECR plasma source~\cite{Buchs_APL_07,Buchs_NJP_07}  In both cases, the exposure parameters have been calibrated to reach an average defect separation along the SWNTs of about 10 nm~\cite{Buchs_Ar,Buchs_APL_07} 

\section{Results and discussion}
\subsection{Experimental LDOS patterns}
\begin{figure}
  \includegraphics[width=8cm]{Figure_1 pdf}
  \caption{\label{exp_data_1} (a)-(b) 3D topography images (processed with WSXM~\cite{WSXM}) of SWNT I with Ar$^{+}$ ions-induced defects, with sample-tip bias voltage ($V_\mathrm{S}$) 1 V and tunneling current $I_\mathrm{S}$ 0 1 nA  (c) Corresponding $dI/dV(x,V)$ map recorded along the horizontal dashed lines in (b), with $V_\mathrm{S}=1$ V, $I_\mathrm{S}=0 2$ nA  Spatial resolution $\sim$ 0 3 nm  (d) 3D topography image of SWNT II with N$^{+}$ ions-induced defects, with $V_\mathrm{S}=1$ V, $I_\mathrm{S}=128$ pA  (e) Corresponding $dI/dV(x,V)$ map recorded along the horizontal dashed lines in (d), with $V_\mathrm{S}=1 5$ V, $I_\mathrm{S}=0 3$ nA  Spatial resolution $\sim$ 0 2 nm }
\end{figure}
In Fig ~\ref{exp_data_1} (a) and (b), we show 3D STM images of the same semiconducting SWNT (referred as SWNT I in the following) with Ar$^{+}$ ions-induced defect sites labeled $d1-d5$   Panel (d) shows a 3D STM image of a second semiconducting SWNT (referred as SWNT II) with N$^{+}$ ions-induced defect sites labeled $d6-d7$  In both cases, defect sites typically appear as hillock-like protrusions with an apparent height ranging from 0 5~{\AA} to 4~{\AA} and an apparent lateral extension varying between 5~{\AA} and 30~{\AA}~\cite{Buchs_NJP_07,Buchs_Ar,Thesis_Buchs}  
\\
\indent The resulting $dI/dV(x,V)$ maps recorded along the horizontal dashed line drawn in the STM images (b) and (d) are displayed in panels (c) and (e) in Fig ~\ref{exp_data_1}, respectively  Defect signatures in the LDOS in both cases are characterized by deep in-gap states at the defects positions  This is consistent with the expected defect structures, $i e $ mainly SVs, DVs and combinations thereof for collisions with Ar$^{+}$ ions~\cite{Buchs_Ar} and bridgelike N ad-atom for collisions with N$^{+}$ ions~\cite{Thesis_Buchs,Nitrogen_prb_07}  Note that gap states at energy levels $\sim$~0 2 eV and $\sim$~0 05 eV in panels (c) and (e), respectively, are shifted to the right from $d3$ by about 1 nm and to the right from $d6$ by about 2 nm  This indicates the presence of intrinsic or ion-induced defects on the lateral or bottom side wall of the SWNTs~\cite{Kra01prb}, not visible in the topographic images  These defects are labelled $d3'$ and $d6'$, respectively   
\\
\begin{figure}
  \includegraphics[width=12cm]{Figure_2 pdf}
  \caption{\label{exp_data_Ar} (a)-(b) QD I detailed $dI/dV(x,V)$ maps in conduction and valence bands  Lower subpanels contain QD states linecut profiles and stationary wave-like fits in left and right QD parts  Right subpanels contain experimental energy dispersion relation data sets $k_\mathrm{n}(E_\mathrm{n})$ and tight-binding calculations  (c)-(d) Resulting LDOS calculated from a one-dimensional piecewise constant potential model featuring potential barriers and a potential step (gray area), with position of the potential step: 5 09 nm from the right barrier's center, potential step heigth: $U_\mathrm{C}=V_\mathrm{L}-V_\mathrm{R}=60$ meV, barrier heights: $V_\mathrm{d3'}=1$ eV, $V_\mathrm{d4}=0 85$ eV, barrier widths: $a_\mathrm{d3'}=a_\mathrm{d4}=3 4$ nm   Valence band: $V_\mathrm{d3'}=-0 4$ eV, $a_\mathrm{d3'}=a_\mathrm{d4}=2 5$ nm, $V_\mathrm{d4}=-0 4$ eV  $E_\mathrm{g}$ stands for bandgap energy }
\end{figure}
\begin{figure}
  \includegraphics[width=12cm]{Figure_3 pdf}
  \caption{\label{exp_data_N} (a) QD II detailed $dI/dV(x,V)$ map  Lower subpanels contain QD states linecut profiles and stationary wave-like fits in the left and right QD parts  Right subpanel contains experimental energy dispersion relation data sets $k_\mathrm{n}(E_\mathrm{n})$ and tight-binding calculations  (b) Resulting LDOS calculated from a one-dimensional piecewise constant potential model featuring potential barriers and a potential step (gray area) with position of the potential step: 4 7 nm from the right barrier's center, potential step heigth: $U_\mathrm{C}=V_\mathrm{L}-V_\mathrm{R}=60$ meV, barrier heights: $V_\mathrm{d6'}=0 6$ eV, $V_\mathrm{d7}=0 6$ eV, barrier widths: $a_\mathrm{d6'}=1 5$ nm, $a_\mathrm{d7}=2 6$ nm }
\end{figure}
\indent Remarkably, the $dI/dV(x,V)$ maps in Fig



ground_truth: Multiple vacuum processing apparatuses are arranged in parallel.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What did Justice Kennedy argue about Quill in Direct Marketing Ass'n v. Brohl?

Read the following text and answer briefly.

Context 2: S  393, 406–07 (1932) (Brandeis, J , dissenting)  The Court has long since adopted his argument,52× 52  See, e g , Smith v  Allwright, 321 U S  649, 665 (1944)  as well as its corollary — that stare decisis commands “special force in the area of statutory interpretation” where “Congress remains free to alter what [the Court has] done ”53× 53  Patterson v  McLean Credit Union, 491 U S  164, 172–73 (1989)  For normative evaluations of heightened stare decisis for statutory precedents, see generally Einer Elhauge, Statutory Default Rules: How to Interpret Unclear Legislation 211–23 (2008); and William N  Eskridge, Jr , Overruling Statutory Precedents, 76 Geo  L J  1361, 1364–1409 (1988)  Justice Brandeis’s logic demands that dormant commerce clause cases, where Congress is free to act, be granted the weightier stare decisis 54× 54  Scholars have noted the curious fact that Justice Brandeis included many dormant commerce clause cases as examples of overruled constitutional precedents  See, e g , Earl M  Maltz, Commentary, Some Thoughts on the Death of Stare Decisis in Constitutional Law, 1980 Wis  L  Rev  467, 468–469, 469 n 11  One explanation for this is that Justice Brandeis sought the authority of Chief Justice Taney’s dictum that the Court’s “opinion upon the construction of the Constitution is always open to discussion” — which referred to the dormant commerce clause  See Burnet, 285 U S  at 408 n 3 (Brandeis, J , dissenting) (quoting The Passenger Cases, 48 U S  (7 How ) 283, 470 (1849) (Taney, C J , dissenting))  In Chief Justice Taney’s time, it was thought that Congress could not override the Court’s dormant commerce clause decisions, see Cooley v  Bd  of Wardens, 53 U S  (12 How ) 299, 321 (1852), so the context of Chief Justice Taney’s dictum does not conflict with Justice Brandeis’s theory of stare decisis  The Court applied this reasoning in Quill, as Chief Justice Roberts underscored 55× 55  Wayfair, 138 S  Ct  at 2102 (Roberts, C J , dissenting) 
Yet the Wayfair majority refused to consider Congress’s authority to legislate as a relevant factor for stare decisis 56× 56  Even Justice Kennedy’s earlier opinion in Direct Marketing contemplated judicially overruling Quill, conspicuously neglecting a possible legislative solution  See supra p  278  The Court even insisted that to do so “is inconsistent with the Court’s proper role,” since Quill embodied “a false constitutional premise of th[e] Court’s own creation ”57× 57  Wayfair, 138 S  Ct  at 2096 (emphasis added)  This refusal breaks from the practical Brandeisian wisdom that has guided the Court’s treatment of precedent for the better part of a century  The point is not that stare decisis should have ultimately propped up Bellas Hess yet again, as Wayfair’s dissenting Justices maintained  After all, a realistic approach that is alert to each branch’s institutional capacities might have led to the conclusion that Congress was actually ill-equipped to overrule Quill  In this vein, the Court could have sensibly pointed out that Congress is unlikely to stick its neck out with a tax hike (or a look-alike) from which only the states would benefit 58× 58  For two practical arguments to this effect, see Brian Galle, Essay, Kill Quill, Keep the Dormant Commerce Clause: History’s Lessons on Congressional Control of State Taxation, 70 Stan  L  Rev  Online 158, 160–62 (2018), https://review law stanford edu/wp-content/uploads/sites/3/2018/03/70-Stan -L -Rev -Online-158-Galle pdf [https://perma cc/22YP-P4V5]; Edward A  Zelinsky, The Political Process Argument for Overruling Quill, 82 Brook  L  Rev  1177, 1191–92 (2017)  Indeed, South Dakota advanced such practical arguments in its brief 59× 59  See Petitioner’s Brief at 54, Wayfair, 138 S  Ct  2080 (No  17-494) (“Congress has little incentive to act here because it would be (or appear to be) authorizing new or greater tax collections from its constituents, while receiving none of the revenue in return ”)  More generally, the Court might have discussed the limits of the states’ influence in the federal system as a reason not to wait for congressional intervention, a topic it has debated on other occasions 60× 60  See Richard H  Pildes, Institutional Formalism and Realism in Constitutional and Public Law, 2013 Sup  Ct  Rev  1, 30–32; see also Galle, supra note 58, at 159 (“Congress is not a trustworthy guardian of state fiscal power, making continuing judicial involvement a more appealing prospect ”)  Or it could have argued that new facts on the ground — namely, the blast of e-commerce that hit like a comet after Quill — overpowered stare decisis of any force, special or plain 61× 61  Two recent studies of stare decisis highlighted the physical presence rule as exemplifying a precedent that may reasonably be overruled due to changed facts  See Bryan A  Garner et al , The Law of Judicial Precedent 364–65 (2016); Randy J  Kozel, Settled Versus Right: A Theory of Precedent 112–13 (2017)  It should be noted that the authors of The Law of Judicial Precedent classify the physical presence rule as a constitutional precedent for stare decisis purposes, thus anticipating the Court’s misstep in Wayfair  Garner et al , supra, at 354–65  Because even statutory precedents may sometimes be overruled,62× 62  See Patterson v  McLean Credit Union, 491 U S  164, 173–74 (1989) (discussing justifications for overruling statutory precedents)  Contra Lawrence C  Marshall, “Let Congress Do It”: The Case for an Absolute Rule of Statutory Stare Decisis, 88 Mich  L  Rev  177 (1989)  the Court could have killed Quill without first planting its constitutional kiss of death 63× 63  Cf  Thomas R  Lee, Stare Decisis in Historical Perspective: From the Founding Era to the Rehnquist Court, 52 Vand  L  Rev  647, 704 (1999) (“Justice Brandeis’       memorable prose has since become a mandatory part of the burial rite for any constitutional precedent ”) 
The Court resisted such arguments  Instead, Wayfair reasoned that Congress’s total ability to correct an erroneous decision counts for nothing when the Court gets the Constitution wrong  That such a theory sprouts from a case like Wayfair, which repudiated a “formalistic distinction,”64× 64  Wayfair, 138 S  Ct  at 2092  is ironic  Wayfair’s stare decisis analysis resorts to the formalism of making constitutional a “magic” word65× 65  See Transcript of Oral Argument, supra note 21, at 12  rather than asking whether Congress can step in 
Moreover, the Court’s new thinking on stare decisis threatens other constitutional default rules  Wayfair now stands for the proposition that a “constitutional default rule” — a term the Court apparently lifted from South Dakota’s reply brief on the merits66× 66  Reply Brief at 22, Wayfair, 138 S  Ct  2080 (No  17-494) (“Congress is polarized, which makes it critical       to get the constitutional default rule right ”)  — gets only weakened stare decisis  To appreciate why this holding matters, it is worth exploring the concept and scope of constitutional default rules  Contract theory describes default rules as legal rules that the parties may “contract around ”67× 67  See, e g , Ian Ayres & Robert Gertner, Filling Gaps in Incomplete Contracts: An Economic Theory of Default Rules, 99 Yale L J  87, 87 (1989)  Although “constitutional default rule” could be read broadly to include a variety of actors and contracting mechanisms,68× 68  See John Ferejohn & Barry Friedman, Toward a Political Theory of Constitutional Default Rules, 33 Fla  St  U  L  Rev  825, 826 (2006) (“When we speak of default rules in constitutional law, we typically are talking about specifications of ways the government can act (or modify its behavior) to get around a constitutional prohibition ”)  the Court’s use of the term for purposes of stare decisis may be narrowly defined as judicial precedents of constitutional law that “are ultimately subject to congressional control ”69× 69  Gillian E  Metzger, Congress, Article IV, and Interstate Relations, 120 Harv  L  Rev  1468, 1525 (2007) (describing judicially enforceable “constitutional default rules imposing obligations on the states in the name of union [that] are ultimately subject to congressional control”)  The dormant commerce clause is a paradigmatic constitutional default rule because what the Court does today Congress may undo tomorrow  Justice Scalia declared this fact “[t]he clearest sign that the negative Commerce Clause is a judicial fraud,” for “[h]ow could congressional consent lift a constitutional prohibition?”70× 70  Comptroller of the Treasury of Md  v  Wynne, 135 S  Ct  1787, 1808 (2015) (Scalia, J , dissenting)  But that’s what a constitutional default rule is  The Court has allowed Congress to overturn its dormant commerce clause cases since 1891 71× 71  See In re Rahrer, 140 U S  545, 560–62 (1891) 
Dormant commerce clause cases are not the only constitutional default rules  Professor Laurence Tribe’s treatise identifies two others 72× 72  1 Laurence H  Tribe, American Constitutional Law § 6-35 (3d ed  2000)  And in a groundbreaking article, Professor Henry Monaghan revealed “a substructure of substantive, procedural, and remedial rules” forming “a constitutional common law subject to amendment, modification, or even reversal by Congress ”73× 73  Henry P  Monaghan, The Supreme Court, 1974 Term — Foreword: Constitutional Common Law, 89 Harv  L  Rev  1, 2–3 (1975); see also Susan R  Klein, Identifying and (Re)Formulating Prophylactic Rules, Safe Harbors, and Incidental Rights in Constitutional Criminal Procedure, 99 Mich  L  Rev  1030 (2001) (further developing Monaghan’s theory in criminal procedure context)  What follows is a list of six lines of cases beyond the dormant commerce clause that may be fairly described as constitutional default rules  The first two are drawn from Tribe’s treatise while the next four are found in Monaghan’s article:
(1) State Taxation of Federal Instrumentalities: States may not tax instrumentalities of the federal government74× 74  McCulloch v  Maryland, 17 U S  (4 Wheat ) 316, 436 (1819)  — unless Congress consents 75× 75  See, e g , Helvering v  Gerhardt, 304 U S  405, 411 n 1 (1938) (“Congress may curtail an immunity which might otherwise be implied or enlarge it beyond the point where, Congress being silent, the Court would set its limits ” (citations omitted))  One court has described such judicial decisions as setting a “constitutional default rule ” United States v  Delaware, 958 F 2d 555, 560 n 9 (3d Cir  1992) (“[W]e must decide the constitutional default rule for this type of tax, fully aware that Congress could decide at any time to reverse our decision statutorily ”)  (2) Article I, Section 10 Cases: Article I, Section 10 provides that certain prohibitions on the states may be waived by Congress 76× 76  See U S  Const  art  I, § 10, cls  2–3  The Court has taken note of this when considering whether to overrule, for instance, an Import-Export Clause precedent 77× 77  See Hooven & Allison Co  v  Evatt, 324 U S  652, 668 (1945) (“In view of the fact that the Constitution gives Congress authority to consent to state taxation of imports and hence to lay down its own test for determining when the immunity ends, we see no convincing practical reason for abandoning the test which has been applied for more than a century        ”), overruled on other grounds by Limbach v  Hooven & Allison Co , 466 U S  353 (1984)  In Michelin Tire Corp  v  Wages, 423 U S  276 (1976), the Court left open the question whether “Congress may authorize, under the Import-Export Clause, an exaction that it could not directly impose under the Tax Clause ” Id  at 301 n 13  Metzger, however, argues that the Import-Export Clause is free of other clauses’ limits on congressional power  See Metzger, supra note 69, at 1500 & n 120  (3) Bivens Cases: In Bivens v  Six Unknown Named Agents of Federal Bureau of Narcotics,78× 78  403 U S  388 (1971)  the Court held that a violation of the Fourth Amendment gives rise to a right to sue for damages 79× 79  Id  at 397  But the Court has also held that “[s]uch a cause of action may be defeated       when       Congress has provided an alternative remedy which it explicitly declared to be a substitute for recovery directly under the Constitution and viewed as equally effective ”80× 80  Carlson v  Green, 446 U S  14, 18–19 (1980)  (4) Miranda Cases: The Miranda Court famously “encourage[d]” Congress and the states to explore alternative “procedures which are at least as effective in apprising accused persons of their right of silence and in assuring a continuous opportunity to exercise it ”81× 81  Miranda v  Arizona, 384 U S  436, 467 (1966)  In Dickerson v  United States, 530 U S  428 (2000), the Court struck down a congressional attempt to effectively abolish Miranda, holding that “Miranda announced a constitutional rule that Congress may not supersede legislatively ” Id  at 444  But Dickerson also stood by Miranda’s “invitation for legislative action” to replace Miranda with an adequate substitute  Id  at 440; see also Michael C  Dorf & Barry Friedman, Shared Constitutional Interpretation, 2000 Sup  Ct  Rev  61 (discussing legislative alternatives to Miranda)  (5) The Police Lineup Case: In United States v  Wade,82× 82  388 U S  218 (1967)  the Court created an exclusionary rule for evidence obtained from a police lineup in violation of the Sixth Amendment right to counsel but acknowledged that it could be replaced by “[l]egislative or other regulations       which eliminate the risks of abuse ”83× 83  Id  at 239  (6) The Exclusionary Rule Cases: Mapp v  Ohio made the Fourth Amendment “exclusionary rule” binding on the states,84× 84  367 U S  643, 655 (1961)  yet Congress is thought to have the power to replace it 85× 85  See Bivens v  Six Unknown Named Agents of Fed  Bureau of Narcotics, 403 U S  388, 422–24 (1971) (Burger, C J , dissenting) (inviting Congress to replace the Fourth Amendment exclusionary rule); Harold J  Krent, How to Move Beyond the Exclusionary Rule: Structuring Judicial Response to Legislative Reform Efforts, 26 Pepp  L  Rev  855, 864–71 (1999) 
All of the above are arguably constitutional default rules set by the Court that remain, to one degree or another, open to congressional revision  The list could be longer or shorter, depending on which default rules the Court will view as constitutional86× 86  A shorter list could be produced by whittling away at the constitutional status of the cases identified by Monaghan  While the Court has held that Miranda is a constitutional decision, Dickerson, 530 U S  at 444, some of the other cases may be viewed as nonconstitutional  See, e g , Collins v  Virginia, 138 S  Ct  1663, 1675–80 (2018) (Thomas, J , concurring) (arguing that Mapp is “nonconstitutional,” id  at 1678 n 5); Richard H  Fallon, Jr  et al , Hart and Wechsler’s The Federal Courts and the Federal System 775–77 (7th ed  2015) (discussing whether Bivens is constitutionally required)  Conversely, a longer list might include any constitutional right that can be waived by a party  See, e g , Daniel A  Farber, Another View of the Quagmire: Unconstitutional Conditions and Contract Theory, 33 Fla  St  U  L  Rev  913, 918 (2006) (describing the Eleventh Amendment as “just a contractual default rule that the states are free to barter away”)  Such a list might also include various constitutionally inspired judicial presumptions  See, e g , Jack Goldsmith & John F  Manning, The President’s Completion Power, 115 Yale L J  2280, 2299 (2006) (describing the Chevron presumption of delegated interpretive power to administrative agencies as “a constitutionally inspired default rule”); Nicholas Quinn Rosenkranz, Federal Rules of Statutory Interpretation, 115 Harv  L  Rev  2085, 2097–98 (2002) (describing clear statement rules as “constitutional default rules” reversible by Congress)  Many other decisions could likely be characterized as constitutional default rules; the list above is only an initial stab  and on how it will answer open questions about congressional authority over certain constitutional provisions 87× 87  See, e g , Thomas v  Wash  Gas Light Co , 448 U S  261, 272 n 18 (1980) (plurality opinion) (leaving unresolved whether Congress may limit constitutional full faith and credit obligations); White v  Mass  Council of Constr  Emp’rs, Inc , 460 U S  204, 215 n 1 (1983) (Blackmun, J , concurring in part and dissenting in part) (leaving unresolved “whether Congress may authorize       what otherwise would be a violation” of the Privileges and Immunities Clause); 1 Tribe, supra note 72, § 6-35, at 1243–44 (arguing that Congress cannot override judicial constructions of the Privileges and Immunities Clause); Metzger, supra note 69, at 1486–89 (arguing the opposite)  But the takeaway is clear: weaker stare decisis for constitutional default rules  Pre-Wayfair, one would have thought that stare decisis applies with special force to such precedents, given congressional power to set them straight  Not anymore  Why? Because it is improper to “ask Congress to address a false constitutional premise of th[e] Court’s own creation ”88× 88  Wayfair, 138 S  Ct  at 2096  The Latin for Wayfair’s doctrine is not stare decisis, which should reflect a realistic, working relationship between the legislative and judicial branches  It is mea culpa 
In its zeal to update the Constitution for “the Cyber Age,”89× 89  Id  at 2097  the Court deleted Congress from stare decisis doctrine in constitutional cases  The Court had better options  It could have left Quill on Congress’s doorstep, as the dissent argued  Or it could have justified overruling Quill notwithstanding the special force of stare decisis  Instead, the Court reasoned that it doesn’t matter whether Congress is willing and able to do the job: a constitutional mess calls for a judicial clean-up crew  For constitutional default rules — a category of decisions embracing the dormant commerce clause and sweeping far beyond — Wayfair’s new theory of stare decisis makes the Court’s precedents less sticky and Congress less relevant 
Context 3: ~\ref{exp_data_1} exhibit several broad discrete states in the conduction bands of SWNT I, II (white dashed boxes in panel (c) and (e), respectively) and in the valence band of SWNT I (white dashed box in panel (c)), characterized by a modulation of the $dI/dV$ signals in the spatial direction between pairs of consecutive defect sites $d3'-d4$ and $d6'-d7$  Enlarged plots of these boxed regions are displayed in Fig ~\ref{exp_data_Ar}(a)-(b) and Fig ~\ref{exp_data_N}(a) for SWNTs I and II, respectively  In the conduction bands, cross-sectional curves recorded along the black horizontal dashed lines labelled m1--m3 in Fig ~\ref{exp_data_Ar}(a) and m1--m4 in Fig ~\ref{exp_data_N}(a) are plotted below the LDOS panels  These clearly reveal one to three and respectively one to four spatially equidistant maxima  The number of maxima increases for increasing $\left|V_\mathrm{bias}\right|$ and the measured level spacings between consecutive discrete states is of the order of 100 meV and larger for both cases  This indicates that defect sites $d3'-d4$ and $d6'-d7$, respectively separated by 12 1 nm and 11 2 nm, act as strong scattering centers able to confine carriers in semiconducting SWNTs~\cite{Buchs_PRL,Bercioux_prb_2011}  Such intrananotube QD structures will be referred as QD I (in SWNT I) and QD II (in SWNT II) in the following  We estimated the level spacings in the conduction band of QD I to 98 meV (m1-m2) and 116 meV (m2-m3)  For QD II, we measured 122 meV (m1-m2), 185 meV (m2-m3) and 210 meV (m3-m4) 
\\
\indent In the valence band of SWNT I, discrete states with level spacings of the order of 80-90 meV, with one clear maximum at the level m-1, can also be distinguished between defect sites $d3'-d4$ in Fig ~\ref{exp_data_Ar}(b)  The discretization of the states indicates that this QD structure also confines holes  Discrete states starting from m-2 and lower show less well defined structures compared to the conduction band states  In the case of SWNT II, no clear discrete states are observed in the valence band (see supplementary information)  These observations are most probably the result of an energy dependent scattering strength of the defects, respectively $d3'$-$d4$ and $d6'$-$d7$, leading here to a weaker confinement in the valence band  Such energy dependence is well known for metallic SWNTs~\cite{Chico96,vac_2007,mayrhofer:2011,Bockrath_Science01} and is corroborated by our ab-initio calculations  Note that mixing effects with defect states and substrate-induced effects~\cite{substrate_effects} cannot be ruled out 
\\
\indent Another remarkable feature in the LDOS is the strong spatial asymmetry of the lowest energy states m1 and m-1 in QD I and m1 in QD II  In QD I, m1 is shifted to the right side of the dot while m-1 is shifted to the left side  Higher states m2 and m3 show more symmetry in terms of position of the maxima relative to the center of the QD  In QD II, m1 is shifted to the right side of the QD  We attribute the observed lowest energy states asymmetry (for electrons as well as for holes) in part to their strong sensitivity to weak potential modulations within the QD structure (as we will show in section \ref{1D})  For QD I, this assertion is supported by the observation of a 0 25 nm high Au(111) terrace edge located around the center of the QD, leading to a supported-suspended interface (see white dashed lines in Fig ~\ref{exp_data_1}(b) and more topographic details in Fig ~S2(a)-(d) in supplementary information)  Such configurations have been reported to induce a rigid shift in the SWNT bands~\cite{Clair_2011}, for instance here a down-shift in the right side of QD I corresponding to the "suspended" portion between two terraces  In QD II, we attribute the spatial shift of m1 to a potential modulation induced by a layer of disordered impurities, most probably residua from the 1,2-dichloroethane suspension, lying between the gold substrate and the SWNT (see Fig ~\ref{exp_data_1}(d) and Fig ~S2(e)-(h) in supplementary information)  
\\
\indent Also, the LDOS in QD I and II (Fig ~\ref{exp_data_Ar}(a) and Fig ~\ref{exp_data_N}(a), respectively) reveals asymmetric patterns with curved stripes oriented from top left to bottom right for QD I and from bottom left to top right for QD II  These are characteristic signatures for defect pairs with different scattering strengths~\cite{Bercioux_prb_2011,Buchs_PRL}  For instance here, the left defect in QD I ($d3'$) has a larger scattering strength than the right one ($d4$), while the right defect in QD II ($d7$) has a larger scattering strength than the left one ($d6'$)  
\\
\indent The exact atomic structure of the defects could in principle be determined from a comparison of $dI/dV$ spectra with simulated first-principle LDOS signatures of expected defect types  In reality, this is hampered by the large number of possible geometries to simulate, including complex multiple defect structures~\cite{Buchs_Ar}, together with the large unit cells of the semiconducting chiral SWNTs studied here 
\\
\subsection{1D piecewise constant potential model}
\label{1D}
To better understand the physical origins of the non-trivial signatures of the quantized states, we model the experimental $dI/dV$ maps by solving the time independent one-dimensional Schr\"odinger equation over a piecewise constant potential model of QD I and QD II  The scattering centers are approximated by semi-transparent rectangular tunneling barriers leading to a square confinement potential~\cite{Laird:2015}  This is supported by previous results on defect-induced confinement in metallic SWNTs using the same experimental conditions~\cite{Buchs_PRL} and is consistent with ab-initio simulations presented later in this work  The potential modulation within the QD is approximated by a potential step  The resulting potential geometries are illustrated with gray shaded areas in Fig ~\ref{exp_data_Ar} (c) and (d) and Fig ~\ref{exp_data_N}(b)  Dispersion relations $E(k)$ can be extracted experimentally from the quantized states wavefunctions by measuring the energy and corresponding momenta in the left and right sides of the QDs  The wavevectors $k$ are determined using stationary wave-like fitting functions~\cite{Buchs_PRL} displayed with dashed red curves in Figs ~\ref{exp_data_Ar}(a)-(b) and ~\ref{exp_data_N}(a))  From this procedure, the potential step height and position can be estimated (see supplementary information)  The experimental data sets $E(k)$ are plotted in the right panels of Figs ~\ref{exp_data_Ar}(a) and \ref{exp_data_N}(a) together with dispersion relations from a third-nearest neighbor tight-binding calculation closely approximating ab-initio results~\cite{Reich_TB_2002}  These chirality-dependent tight-binding dispersion relations, calculated within an extended Brillouin zone resulting from the defect-induced breaking of the translation invariance~\cite{Bercioux_prb_2011}, are used in the Hamiltonian of our one-dimensional model  Taking into account the measured chiral angle, diameter distribution~\cite{Buchs_conf} and measured bandgaps, we find the best match with chiralities $(7,6)$ for QD I and $(11,1)$ for QD II (see supplementary information)  
\\
\indent Once chiralities together with potential step heights and positions are optimized, one can fit the height and width of the rectangular tunneling barriers in order to reproduce the experimental level spacings and general LDOS patterns  On a qualitative ground, a symmetric double barrier system results in the formation of spatially symmetric discrete bound states  Increasing both barrier heights simultaneously shifts the bound state energy levels and level spacings up  This leads to sharper bound states as the confinement in the QD is made stronger thus increasing the lifetime of the confined electrons  Increasing the barrier thickness with constant inner edge separation does not affect much the level spacings but further sharpens the bound states  Any asymmetry introduced by a change in the width or height of one single barrier leads to broader bound states  The presence of a potential step modifies the LDOS in lifting the levels of the bound states, with a more pronounced effect on the lower states  In QD I and II, the center of each barrier is aligned with the center of the gap states ($d3'$-$d4$ for QD I and $d6'$-$d7$ in QD II) and the width ratio is kept proportional to the ratio of the spatial extent of the gap states  Thus, by increasing the width of the barriers, we decrease the length of the QD leading to higher level spacings, and vice versa  The experimental level spacings can then be approximated by tuning both barrier widths in the same ratio and the heights individually, knowing that the scattering strength of $d3'$ ($d7$) is larger than $d4$ ($d6'$) according to the observed asymmetry in the LDOS described above \footnote{The transmission probability through a rectangular tunneling barrier is given by $T=\left( 1+\frac{V^{2}\sinh^{2}\left( a \cdot \sqrt{2m^{*}(V-E)}/\hbar \right)}{4E(V-E)} \right)^{-1}$, where $V$ and $a$ are respectively the barrier height and width  For the argument in the $\sinh$ sufficiently small such that $\sinh(x)\simeq x$, it can be shown that $a$ and $V$ can be coupled such that the transmission probability becomes a function of the area under the barrier $A=a\cdot V$, with $T=\left( 1+ \frac{m^{*}A^{2}}{2\hbar^{2}E} \right)^{-1}$  In our case, this condition is not satisfied and thus the barrier geometries are tuned empirically to fit the experimental level spacings }  
\\
\indent For QD I, we find a good match in the conduction band for the barrier heights $V_\mathrm{d3'}=1$ eV and $V_\mathrm{d4}=0 85$ eV, widths $a_\mathrm{d3'}=a_\mathrm{d4}=$ 3 4 nm,  and potential step $V_\mathrm{L}-V_\mathrm{R}=60$ meV  With these parameters, the spatial profile of the obtained quantized states (see lower subpanels in Fig ~\ref{exp_data_Ar}(a) and (c)) reproduces the experimental modulation features remarkably well  Also, the simulated LDOS displays a pattern with curved stripes oriented from top left to bottom right, as observed experimentally, due to a left barrier with a larger scattering strength  In the valence band, although modes m-2 and lower do not show a well defined structure in the spatial direction, thinner barriers with dimensions $a_\mathrm{d3'/d4}=2 5$ nm, $V_\mathrm{d3'/d4}=-0 4$ eV, leading to a slightly longer QD length (9 6 nm compared to 8 7 nm in the conduction band) can reproduce the measured level spacings very well  
\\
\indent For QD II, we observed that the measured energy levels are overestimated by a factor $\alpha\sim1



ground_truth: Quill harmed states more than anticipated due to the Internet.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What experimental techniques were used to study the quantum dot structures in this research?

Read the following text and answer briefly.

Context 3: 29$, presumably due to a voltage division effect induced by the impurity layer mentioned above (see details in supplementary information)  We find a good agreement with the experimental LDOS with the parameters: $V_{d3'}=V_{d4}\simeq$ 0 47 eV, $a_\mathrm{d6'}=1 5$ nm, $a_\mathrm{d7}=2 6$ nm and $U_\mathrm{C}=V_\mathrm{L}-V_\mathrm{R}\simeq 47$ meV  Note that in Fig ~\ref{exp_data_N}(b) the barrier and potential heights are multiplied by $\alpha$ to allow a direct comparison with the experimental LDOS  The simulated LDOS shows a pattern with curved stripes oriented from bottom left to top right, as observed experimentally, due to a right barrier exhibiting a larger scattering strength  Also, the spatial profile of the obtained bound states (see lower subpanels in Fig ~\ref{exp_data_N}(a) and (b)) reproduces the experimental features quite well  Note also that one can distinguish an isolated state in the experimental LDOS at an energy level between m1 and m2, about in the middle of the QD  This state that prevented an accurate fit of the state m2 in the right QD part is attributed to a spatial feature visible in the STM topography image in Fig ~\ref{exp_data_Ar}(d) (see also supplementary information, Fig S2(f)), probably a physisorbed impurity which does not affect the LDOS significantly 
\\
\subsection{Ab-initio calculations}
\begin{figure}
  \includegraphics[width=16cm]{Figure_4 pdf}
  \caption{\label{num_data} (a)-(c) LDOS ab-initio simulations of a semiconducting $(16,0)$ SWNT with combinations of vacancies defects separated by 11 1 nm  Subpanels display QD state linecut profiles  (d) Tight-binding (black curve) and ab-initio dispersion relations (green circles) for a pristine $(16,0)$ SWNT with $E_\mathrm{n}(k_\mathrm{n})$ data sets extracted from (a)-(c)  (e)-(g) LDOS ab-initio simulations of a semiconducting $(17,0)$ SWNT with combinations of N ad-atoms and vacancies defects separated by 10 7 nm  (h) Tight-binding (black curve) and ab-initio dispersion relations (green circles) for a pristine $(17,0)$ SWNT with $E_\mathrm{n}(k_\mathrm{n})$ data sets extracted from (e)-(g) }
\end{figure}
In order to elucidate the physical nature of the electron/hole confining scattering centers, we performed ab-initio simulations based on a combination of density functional theory~\cite{pbe,paw,vasp_paw,VASP2}, maximally localized Wannier orbitals~\cite{transportwannier90} and Green's functions (see supplementary information)  Without loss of generality, we have simulated short unit cell semiconducting zigzag SWNTs with different combinations of the most probable defect structures  Results for vacancy defects likely being induced by 200 eV Ar$^{+}$ ions, separated by about 11 nm in a $(16,0)$ SWNT are shown in Fig ~\ref{num_data}(a)-(c) with DV-DV, DV-SV and SV-SV pairs, respectively  The LDOS displays midgap states at the defect positions as expected as well as defect states in the valence band~\cite{Buchs_Ar}  Most importantly, clear quantized states with a number of maxima increasing with energy are observed between the defects in the conduction band, emphasizing the ability of SVs and DVs to confine carriers  For the asymmetric configuration DV-SV, one can distinguish faint curved stripe patterns oriented from top left to bottom right, indicating a larger scattering strength for DVs compared to SVs  This is consistent with observations in transport experiments~\cite{Gomez05nm}  On the other hand, the patterns in the valence band strongly depend on the defect types  Discrete states can be distinguished for the DV-DV case, with m-2 being mixed with defect states  For the DV-SV case, clear curved stripe patterns oriented from bottom left to top right indicate again a stronger scattering strength for DV  Also, broader states are observed, indicating that the scattering strength of DVs and SVs is weaker in the valence band compared to the conduction band 
\\
\indent More insight on the energy dependent scattering strength for each defect pair configuration can be obtained by extracting the wavevector $k_\mathrm{n}(E_\mathrm{n})$ for each resonant state  This data set is plotted in Fig ~\ref{num_data}(d) for the conduction and valence bands together with the $(16,0)$ dispersion relations calculated from the third-nearest neighbor TB model and from the ab-initio calculation for the pristine nanotube  A first observation is the excellent agreement between TB and ab-initio results, further validating the method used in Figs ~\ref{exp_data_Ar}(a)-(b) and ~\ref{exp_data_N}(a)  The vertical dashed lines indicate the limiting $k_\mathrm{n,\infty}=\frac{\pi \cdot n}{L}$ values corresponding to the closed system (infinite hard walls potential) with $L=11 1$ nm being the defect-defect distance  In the conduction band, we find that $k_\mathrm{n}(E_\mathrm{n})=\frac{\pi \cdot n}{L_\mathrm{eff}(n)} < k_\mathrm{n,\infty}$, indicating that the effective lengths $L_\mathrm{eff}(n)$ of the QD are larger than $L$ ($i e $ the resonant states wavefunctions are characterized by penetrating evanescent modes inside the defect scattering potential), as expected for an open system  The shortest $L_\mathrm{eff}(n)$ are obtained for the DV-DV configuration with 12 1 nm (m1), 13 1 nm (m2) and 12 9 nm (m3), which we attribute to wider scattering potential profiles for DVs compared to SVs  In the valence band, we find that $k_\mathrm{n}(E_\mathrm{n})=\frac{\pi \cdot n}{L_\mathrm{eff}(n)} > k_\mathrm{n,\infty}$, with $L_\mathrm{eff}(n)$ values between 7 9 nm (DV-DV, m-1) and 9 66 nm (DV-SV, m-2)  We attribute this pronounced QD shortening to wider scattering potential profiles of both DVs and SVs in the valence band, probably due to mixing with wide spread defect states in the valence band 
\\
\indent Ab-initio calculations for different defect pairs combinations containing at least one N ad-atom, $i e $ N-DV, N-SV and N-N, are presented in Fig ~\ref{num_data}(e)-(h) for a $(17,0)$ SWNT, along with details on the defects geometries  Remarkably, clear QD states are generated for all three configurations, underlining the potential of N ad-atoms to confine carriers in semiconducting SWNTs and thus to generate intrananotube QDs  
\\
\indent In order to demonstrate the scattering strengths of the different defects, we calculated the energy dependent conductance in addition to the LDOS for the different combinations of the QD defining scattering defects on the $(16,0)$ and $(17,0)$ SWNTs, see supplementary information  Generally we can observe strong conductance modulation of the order of 30-40\% with regard to the pristine CNT for all three tested defects (double vacancies DV, single vacancies SV and chemisorbed C-N) with the DVs having the largest scattering strength in the CB and VB   
\\
\indent Note that the choice of the zigzag SWNT chiralities in the two different ab-initio scenarios is motivated by the different effective masses of both chiralities ($m^{*}_{(17,0)}>m^{*}_{(16,0)}$) which is typical for chirality families $(3n-1,0)$ and $(3n-2,0)$~\cite{ZZ_families}  Taking advantage of recent reports on SWNT chirality control~\cite{chirality_control_EMPA,chirality_control_chinese,chirality_chemistry}, this property could be used in practice to design QDs with different level spacings for the same QD length  From an application point of view, however, QDs generated by DVs will have far superior stability at room temperature due to their high migration barrier above 5 eV ($\sim$~1 eV for single vacancy)~\cite{Kra06vm}  This value drops down by at least 2 eV for N ad-atoms depending on their chemisorption configuration~\cite{Nitrogen_prb_07,Yma05nitr} 
\\
\indent Our ab-initio simulations do not take into account any substrate effect  In the experimental case, the carriers can decay through the substrate, thus limiting their lifetime  This leads to state broadening, measured between about 60 meV up to 120 meV in QD I and II, while the quantized states widths in ab-initio simulations vary between about 5 meV and 45 meV  This suggests that a better contrast of the experimental quantized states, especially in the valence band, could be achieved by lowering the nanotubes-substrate interaction through $e g $ the insertion of atomically thin insulating NaCl films~\cite{Ruffieux_Nature_2016}  This would allow to gain more insight on the electronic structure of the QDs as well as in the associated scattering physics at the confining defects~\cite{Buchs_PRL}  

\section{Conclusions and outlook}
In summary, using low-temperature STM/STS measurements supported by an analytical model and ab-initio simulations, we have demonstrated that intrananotube quantum dots with confined electron and hole states characterized by energy level spacings well above thermal broadening at room temperature can be generated in semiconducting SWNTs by structural defects such as vacancies and di-vacancies, as well as nitrogen ad-atoms  These results, combined with recent progresses in type and spatial control in the formation of defects~\cite{Robertson_2012,Yoon_2016,Laser_writing_2017} as well as chirality control~\cite{tunable_QD_defects}, hold a high potential for applications in the design of SWNT based quantum devices  These include $e g $ electrically driven single-photon emitters operating at room temperature and telecom wavelength  In this context, the observation of quantum confinement effects in the emitted light of cut, sub-10 nm, semiconducting SWNTs~\cite{Dai_2008} shall be seen as an additional motivation for investigating the optical properties of our "QD with leads" building-blocks  These would include $e g $ studying optical transitions selection rules for different types and configurations of defect pairs~\cite{sel_rules_2006} associated with experimental studies such as photoluminescence~\cite{Lefebvre06} combined to $g^{(2)}$ correlation measurements~\cite{Hofmann_2013} in suspended SWNT devices as well as photocurrent imaging~\cite{Buchs_Nat_comm} and spectroscopy~\cite{Gabor_2009} 

\section*{Acknowledgements}
The authors thank Ethan Minot, Lee Aspitarte, Jhon Gonzalez, Andres Ayuela, Omjoti Dutta and Arkady Krasheninnikov for fruitful discussions 
The work of DB is supported by Spanish Ministerio de Econom\'ia y Competitividad (MINECO) through the project  FIS2014-55987-P and by the (LTC) QuantumChemPhys  LM acknowledges support from the BMBF-project WireControl (FKZ16ES0294) and computing time for the supercomputers JUROPA and JURECA at the J\"ulich Supercomputer Centre (JSC) 


\clearpage

\section*{References}






ground_truth: Low temperature scanning tunneling microscopy and spectroscopy (STM/STS).