While Li Si 李斯 was the politician, Han Fei 韓非 was the theoretician of legism at the court of the King of Qin 秦 during the late Warring States period 戰國時代. His ideas are collected in the book Hanfeizi 韓非子 (sometimes abbreviated as Hanzi 韓子). Han Fei was a disciple of Xunzi 荀子, and the most important element of Confucianism in his thinking was the relationship between ruler and minister. If anyone behaved wrong, he had to correct his attitudes (zhengming 正名) according to his right position in the social structure. In the legist state, everyone had to act to the welfare of the state. Only a strong state could exist in a world of warfare where each state fought against each other. The center of the state was the ruler who had to keep care that none of his ministers had ambitions to overthrow him. He was the state itself (or the dao 道 of the state, like a Daoist would say), pivot and kernel of a state structure that worked by itself once established. Daoist thinking can be seen in such a state where the ruler rules by doing nothing (wuwei 無為). Practically, the ruler had to initiate behaviour standards ("laws", fa 法), controlling methods (shu 術) and controlling strength (shi 勢).
Han Fei was a native of the state of Han 韓 before he went to Qin to present his writings to the future emperor. The emperor was pleased with his ideas and employed him as an ambassador. When he came back Hann, he was arrested and charged having secret relations to his home state. He was forced to drink poison. The role of Li Si during this plot is less than clear.
See an example the book of Han Fei, chapter 7, where he discribes the two handles of the ruler to have control over his ministers.

７．二柄
明主之所導制其臣者，二柄而已矣。二柄者，刑、德也。何謂刑德？曰：殺戮之 謂刑，慶賞之謂德。為人臣者畏誅罰而利慶賞，故人主自用其刑德，則群臣畏其威而歸其利矣。
故世之姦臣則不然，所惡則能得之其主而罪之，所愛則能得之其主而賞之。今人主非使賞罰之威利出於己也，聽其臣而行其賞罰，則一國之人皆畏其臣而易其君，歸其臣而去其君矣，此人主失刑德之患也。
夫虎之所以能服狗者、爪牙也，使虎釋其爪牙而使狗用之，則虎反服於狗矣。人主者、以刑德制臣者也，今君人者、釋其刑德而使臣用之，則君反制於臣矣。故田常上請爵祿而行之群臣，下大斗斛而I於百姓，此簡公失德而田常用之也，故簡公見弒。子罕謂宋君曰：『 夫 慶賞賜予者，民之所喜也，君自行之；殺戮刑罰者，民之所惡也，臣請當之。』 於是宋君失刑而子罕用之，故宋君見劫。田常徒用德而簡公弒，子罕徒用刑而宋君 劫。故今世為人臣者兼刑德而用之，則是世主之危甚於簡公、宋君也。
故劫殺擁 蔽之主，非失刑德而使臣用之而不危亡者，則未嘗有也。
The two handles
The item by which the enlightened ruler leads and controls his ministers, are simply the two handles. The two handles are punishment and favour. What means punishment and reward? Execution means punishment, and favour means reward. Somebody who acts as a minister, fears being penalized, and wants to profit rewards. If the ruler therefore makes use of punishment and favour himself, the ministers fear his authority and make all to gain profit (for themselves and therewith for their ruler). Because of this the evil ministers in this world are not like this: what they don't like can be obtained their ruler to punish them, and what they like can be obtained their ruler to reward them. If the ruler of men does now not use the authority and profit of reward and punishment his own base, does not listen to (the proposals) of his ministers and act using reward and punishment, the people of this country will fear the ministers and will change out the ruler, they will follow the ministers and fire the ruler. Such a case would be the disaster that results having lost the handles of punishment and favour.
The things by means of which the tiger is able to make the dog serve him, are his claws and his teeth. If he could give up his claws and teeth and give them to the dog that to use them, then the tiger had to serve the dog. The ruler of men uses punishment and favour to control his ministers. If the the ruler would now give up his punishment and favour and give them to the ministers to use them, the ruler would be controled by his ministers. Therefore, Tian Chang (a minister in the state of Qi) suggested to introduce ranks and emolument to grant them to the ministers and to give a great bushel of grain to every people. Following this advice, duke Jian the Simple lost his handle of favour, that could now be used by Tian Chang, that later killed duke Jian. Zihan (a minister in the state of Song) once said to the ruler of Song: "Rewards and offerings are something that all people like and should therefore be given by yourself. Executions and punishments are something that people don't like and therefore I beg you to make me responsible for this." Following this advice, the ruler of Song had lost his handle of punishment and had handed it over to Zihan, that later kicked him off the throne. Tian Chang made only use of the handle of favour, but duke Jian was killed. Zihan made only use of the handle of punishment, but the ruler of Song was demised. If somebody acts as a minister in this time and makes use of both punishment and favour, his ruler is even more endangered than duke Jian and the ruler of Song.
For these reasons, every ruler being plundered, killed and hindered had to suffer these dangers and his ruin because he had lost the handles of punishment and favour to his ministers.