This paper presents a novel approach to generating behavior trees for robots using lightweight large language models (LLMs) with a maximum of 7 billion parameters. The study demonstrates that it is possible to achieve satisfying results with compact LLMs when fine-tuned on a specific dataset. The key contributions of this research include the creation of a fine-tuning dataset based on existing behavior trees using GPT-3.5 and a comprehensive comparison of multiple LLMs (namely llama2, llama-chat, and code-llama) across nine distinct tasks. To be thorough, we evaluated the generated behavior trees using static syntactical analysis, a validation system, a simulated environment, and a real robot. Furthermore, this work opens the possibility of deploying such solutions directly on the robot, enhancing its practical applicability. Findings from this study demonstrate the potential of LLMs with a limited number of parameters in generating effective and efficient robot behaviors.