Financial Information by Geographic Area - Financial Information by Geographic Area (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
Property, plant and equipment, net	354,771	362,067	276,818
North America
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenue from Contract with Customer, Excluding Assessed Tax	405,426	399,993	372,247
Property, plant and equipment, net	246,413	250,895	133,682
Asia
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenue from Contract with Customer, Excluding Assessed Tax	631,904	546,866	515,833
Property, plant and equipment, net	63,242	66,872	68,823
Europe, Middle East, and Africa
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenue from Contract with Customer, Excluding Assessed Tax	161,861	169,099	149,305
South America
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenue from Contract with Customer, Excluding Assessed Tax	640	312	311
Europe
Revenues from External Customers and Long-Lived Assets [Line Items]
Property, plant and equipment, net	$ 45,116	$ 44,300	$ 74,313