NOVELTY - Manufacturing graphene, comprises providing a copper substrate including a first copper layer in contact with a second copper layer, and growing a graphene monolayer via chemical vapor deposition on the second copper layer, where the first copper layer has a first copper percentage by weight and the second copper layer has a second copper percentage by weight. The second copper percentage is greater than the first copper percentage.    USE - The method is useful for manufacturing graphene used in a graphene-copper composite (all claimed), which is useful in high speed integrated circuits, flexible displays, solar cells, hand-held devices, multiprocessor systems, microprocessor-based or programmable consumer electronics, minicomputers, mainframe computers, comparable computing devices.    ADVANTAGE - The method is capable of simply and economically manufacturing the graphene with improved quality and purity and desired thickness.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for:    (1) a graphene-copper composite, comprising the first copper layer, the second copper layer having a first surface in contact with the first copper layer, the graphene monolayer in contact with a second surface of the second copper layer; and    (2) a system for manufacturing a copper substrate for growing graphene, comprising a deposition chamber, a sample stage configured to hold a copper substrate in the deposition chamber, a copper deposition source, a cleaning agent source configured to direct cleaning agent to the copper substrate held by the sample stage, a sensor configured to determine a thickness of a layer deposited by the copper deposition source, a heater configured to heat the copper substrate held by the sample stage to an annealing temperature of 750-1000 degrees C, a gas source configured to provide a thermal annealing gas to the copper substrate held by the sample stage, and a microprocessor coupled to the deposition chamber, where the sample stage, the copper deposition source, the cleaning agent source, the sensor, the heater and the microprocessor are programmable to employ the sample stage to hold the first copper layer in the deposition chamber, employ the cleaning agent source to direct cleaning agent to the first copper layer, employ the copper deposition source and the sensor to deposit a second copper layer on the first copper layer, and employ the heater and the gas source to thermally anneal the first copper layer at the copper substrate, where the second copper layer is thinner compared to the first copper layer.