Provide a comprehensive explanation of idempotency in the context of designing a payment processing API. Your explanation should cover:

1. Definition of Idempotency: What idempotency means in the context of API calls, particularly for operations like 'create payment'.
2. Problem Statement: Detail the specific problem of duplicate 'create payment' requests due to client network issues and retries, and why it's critical to prevent multiple charges.
3. Idempotency Key Strategy: Describe a robust strategy for implementing idempotency using a client-generated idempotency key (e.g., a UUID).
   • Client-Side Behavior: How the client should generate and send the key with the request.
   • Server-Side Logic: Step-by-step logic the API server should follow upon receiving a request with an idempotency key:
     • Checking for existing keys and their associated results.
     • Handling concurrent requests with the same key.
     • Storing the key and the outcome of the operation (success or failure) once processed.
     • Returning the previously stored result for duplicate requests without re-processing.
4. Benefits: Explain how this strategy effectively ensures the customer is only charged once, even with multiple identical requests.
5. Considerations: Briefly mention other important considerations for implementation (e.g., key expiration, scope of idempotency).