Unlike routine tasks where consistency is prized, in creativity and innovation the goal is to create a diverse set of ideas. This paper delves into the burgeoning interest in employing Artificial Intelligence (AI) to enhance the productivity and quality of the idea generation process. While previous studies have found that the average quality of AI ideas is quite high, prior research also has pointed to the inability of AI-based brainstorming to create sufficient dispersion of ideas, which limits novelty and the quality of the overall best idea. Our research investigates methods to increase the dispersion in AI-generated ideas. Using GPT-4, we explore the effect of different prompting methods on Cosine Similarity, the number of unique ideas, and the speed with which the idea space gets exhausted. We do this in the domain of developing a new product development for college students, priced under $50. In this context, we find that (1) pools of ideas generated by GPT-4 with various plausible prompts are less diverse than ideas generated by groups of human subjects (2) the diversity of AI generated ideas can be substantially improved using prompt engineering (3) Chain-of-Thought (CoT) prompting leads to the highest diversity of ideas of all prompts we evaluated and was able to come close to what is achieved by groups of human subjects. It also was capable of generating the highest number of unique ideas of any prompt we studied.