It is common for IVRs to ask callers to provide a zip or postal code. Functions that use zip/postal code input include, for example, store locators, pay-by-phone, and service coverage/activation.
"Postal code" is a generic term that applies to postal delivery codes. Postal codes can be numeric or alphanumeric, with structures that vary considerably from country to country, but are standard within a country. "Zip code" refers to the 5 and 5+4 digit postal codes used in the US.
When they are part of a country's postal delivery system, it is reasonable to assume that callers will know the permissible patterns in their postal codes (e.g., five digits in the US – most callers know their personal five-digit zip code but fewer know their 5+4 zip code; six alternating letters and digits in Canada like M4B1C2). In general, an alphanumeric postal code can convey a fairly precise location, whereas US five-digit zip codes are less precise.
It takes more work to write these grammars than to write simple five-digit of six-character alphanumeric grammars, but it's necessary to achieve decent recognition accuracy. Functions requiring zip/postal codes as input are so ubiquitous, however, that your development platform probably has one built in, or you could purchase one from a vendor.
It's common in US IVRs to hear prompts like, “Please say or enter your five-digit zip code” – but in the US, everyone knows that the basic zip code has five digits, virtually everyone knows their own zip code, and very few people know their 5+4 zip by heart. For these reasons, initial prompts like “What's your zip?” or “What's the billing zip?” will be more concise and conversational. If a caller doesn't respond correctly to the quick prompt, then you can always play the longer, more formal prompt on the retry (see How to phrase reprompts for a given situation).