Financial Information by Geographic Area - Revenue by Major Foreign Customers (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenue from Contract with Customer, Excluding Assessed Tax	$ 1,199,831	$ 1,116,270	$ 1,037,696
China | Customer concentration risk | Revenue benchmark
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenue from Contract with Customer, Excluding Assessed Tax	157,876	113,570
South Korea | Customer concentration risk | Revenue benchmark
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenue from Contract with Customer, Excluding Assessed Tax	143,737	127,972	135,844
Taiwan | Customer concentration risk | Revenue benchmark
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenue from Contract with Customer, Excluding Assessed Tax	$ 138,852	$ 133,059	$ 125,895